Biophysics

Physical and physiological acoustics: Acoustic impedance

Acoustic impedance (z) of a plane acoustic wave passing through some medium is defined as the ratio of effective acoustic pressure to the effective acoustic velocity z= Pef/vef = pc z=pV p=denisty v=acoustic velocity of material Zair = 440 pa.s.m-1 unit is pa.s.m-1 *Acoustic impedence is greater in more dense materials

Electricity in medicine: Coulomb´s law, permittivity

Chapter 6 Electricity in medicine: 1. Coulomb's law, permittivity Coulomb's Law gives the magnitude of the electrostatic force F between two charges q1 and q2 that are seperated by a distance r. * The attractive or repulsive force F acting between 2 charges qo and q is directly proportional to their product and inversely proportional to the distance between them. -the electrostatic force can be attractive or repulsive in nature -it is dependent on -charge q → The greater the charge, the greater the electrostatic force -radius r → electrostatic force decreases as distance between the two charges increases -permittivity constant є → the greater the permittivity constant, the smaller the electrostatic force. permittivity constant є - a measure of a material's ability to transmit an electrical field -a higher permittivity value is associated with a material's ability to store the same amount of charge but with a smaller electrical field. This leads to increased capacitance. Value in a vacuum: -Permittivity values in insulators are higher than Eo. -This is the result of dielectric polarization which occurs in insulators and leads to a decreased force between the charges as compared to a vacuum. -Therefore, relative permittivity can be defined. This is the ratio of the permittivity of a given material to that of a vacuum. -The high permittivity of water enables good solubility of salts in water. Water molecules decrease the attractive forces between negatively and positively charged ions in solution. This hydration of ions is accompanied by a decrease in free enthalpy (thermodynamically favorable). -Various ions are hydrated to various extents: ~Positively charged ions have higher hydration numbers bc their positive charge induces a greater polarization effect in the electron shells of water molecules than does a negative charge. ~Smaller ions also possess higher hydration numbers than larger ions of the same size. For ex: K+ has a greater radius in crystalline structure than does Na+. However, in water solution, the effective radius of Na+ is greater than that of K+ due to its smaller size. This means that Na+ is hydrated to a greater extent and its effective radius increases. *This quality is important when considering the permeability of ions in cell membranes and the resulting membrane potential. Since Na+ is hydrated to a greater extent, it has more difficulty transversing the phospholipid bilayer of the cell membrane. This explains why cell membranes are more permeable to K+ than Na+.

Question from Protocol #6 Blood Pressure What are the mechanics of taking blood pressure? What noise do you hear during systole/diastole? Fluid dynamics?

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Optics in medicine: General classification of electromagnetic waves;

1. General classification of electromagnetic waves -Electromagnetic waves are trasverse waves because the electric and magnetic field vectors oscillate perpendicular to the direction of propagation. -The electrical and magnetic field vectors are in phase and oriented perpendicular to one another. The magnitudes of the fields are relatd by E=cB -Electromagnetic waves can vary in wavelength and frequency but they all travel at the speed of c = 3 x 108 m/s in a vacuum. c = fλ The speed of light in a vacuum stems from Where -The electromagnetic spectrum refers to the full range of frequency and wavelength of electromagnetic waves. Radiowaves 109 m - 1mm Infrared 1mm - 700nm Visible light 360nm-760nm Ultraviolet light 400 - 10 nm X-ray 10nm - 10-2 Gamma ray less than 10-2 -Light of well defined wavelengths is produced by electrons undergoing transitions between energy levels -Light of a continuous range is produced by the random accelerations of electrons in hot bodies. Intensity of Light: instantaneous power incident on a unit area (Watts/m2) Given by the Poynting vector S which is defined as the product of E and B Since E and B flunctuate with time, the average intensity can be defined The electrical and magnetic field components carry the same amount of energy. An electromagnetic wave transports momentum and exerts radiation pressure Radiation pressure = F/A Units are N/m2 or J/m3

Physical and physiological acoustics: Physical properties of acoustic waves

1. Physical properties of acoustic waves -Sound is a mechanical disturbance propagated through a deformable medium and can be transmitted through solids, liquids, and gases but not through a vacuum. -Sound waves are produced by a vibration source of suitable frequency and are transmitted through media by the oscillation of its particles -They are longitudinal in nature meaning that the media particles oscillate around their equilibrium positions in the direction of wave motion. *In the solid phase, oscillation in the transverse direction can also occur *Sound waves propagate through different media with different velocities. In gas, velocity of sound = *Velocity of sound is also dependent on temperature. -This stems from the fact that density =m/v and mass = moles x Molar mass and # of moles is directly proportional to temperature. Thus c is directly proportional to density which is directly proportional to T In liquid, the velocity sound = ***The velocity of sound in air is 344 m/s*** In water and soft tissues velocity of sound is 1400 -1600m/s, and in glass it is 6000 m/s. Thus the speed of sound is fastest in solids. -The wavelength of an accoustic wave λ = c/f c= λf Acoustic amplitude (a) - the amplitude of oscillation of media particles which varies between a max value and 0 a=amaxsin(2πft) Acoustic Velocity - the velocity of the vibrating motion of media particles -Also varies between a maximum value and 0 thus effective accoustic velocity was defined. Effective acoustic velocity Acoustic pressure - due to oscillations of media particles producing periodic changes in the density of the media. These produce periodic changes in the acoustic pressure. Acoustic pressure is in phase with acoustic velocity. Effective accoustic pressure *The effective accoustic pressure is related to the effective accoustic velocity, density of the medium, and velocity of sound by Acoustic impedance (z) of a plane acoustic wave passing through some medium is defined as the ratio of effective acoustic pressure to the effective acoustic velocity z= Pef/vef = pc z=pV p=denisty v=acoustic velocity of material Zair = 440 pa.s.m-1 unit is pa.s.m-1 *Acoustic impedence is greater in more dense materials

Use of X-rays in medicine: Production of X-rays, energy spectra

1. Production of X-rays, energy spectra X-rays - electromagnetic waves produced by high-energy electrons that were stopped upon striking some target. The wavelength of X-rays is very short → 5 - 120 pm which corresponds to a high photon energy of .01 - .02 MeV -Due to their high energy, x-rays have a great penetrating ability. X-ray production: The source of x-rays is an evacuated x-ray tube containing a heated cathode and cooled anode. A high voltage exists between them. -electrons escaping from the heated cathode are accelerated by an accelerating voltage U (unit is the volt) and have energy E =eU X-rays are of 2 types: * At high accelerating voltages, both types of x-rays and their respective spectra are produced in an x-ray tube and superimposition of the two spectra occurs 1) Bremsstrahlung - results in a continuous spectrum. Bremsstrahlung x-rays are produced by electromagnetic interaction of the accelerated e- with the fields of atomic nuclei -They are created when the kinetic energy of the accelerated electrons is transformed into the energy of EM waves in the field of atomic nuclei -The highest possible photon energy = eU =hfmax c=fλ then λ = c/f -the maximum energy and frequency therefore correspond to the shortest wavelength -Because the interaction with the fields of atomic nuclei occurs at various distances from the nucleus, the photon energies will vary as will their corresponding wavelengths and a continuous spectrum will be created. -The peak of the spectrum is shifted to the left (shorter wavelengths, higher energy) with an increased accelerating voltage -The emitted power of Bremstrahlung is proportional to the accelerating voltage, intensity of the e- current, and atomic # Z of the anode target P=kV2IZ *from this relationship, power can be increased with a higher accelerating voltage, intensity of electron current, and atomic # of anode Efficiency: Only 1% of the energy transported by e- to the anode is transformed into electromagnetic waves, 99% is converted into thermal energy. Therefore, a method of cooling the anode is needed and the anode must have a high melting point. The efficiency n of a x-ray tube is given by N= kVZ 2) Characteristic x-rays produce a line spectrum. -Characteristic x-rays are emitted from the electron shells of anode atoms by ionization due to the energy of the incoming accelerated electron beam. -If the energy of the accelerated electrons is higher than the binding energy of the electrons in the inner electron shells, ionization of these electrons will occur. -The subsequent de-exitation results in emission of photons -A line spectrum is formed since electron transitions have well defined energies associated with them -Higher atomic #s of the target anode will shift the line spectra to the left (shorter wavelengths, higher energies) X-rays have several effects: -Primary effects are excitation and ionization of target nuclei -Other effects occur as well and they are the result of primary effects of x-rays: Luminescence: Ionizing effect: the electrical conductivity of some materials is increased (due to free flowing electrons that were ionized and now free to roam) Photographic effect: darkening of a photographic plate Chemical effect: production of hydrogen peroxide in water Biological effect: structural and functional changes in cells

Radioactivity and ionising radiation: Radioactive decay

1. Radioactive decay Radioactive atoms are those with unstable nuclei (radionuclides) which will spontaneously decay by emitting a particle or a quantum of electromagnetic radiation. -Their decay may lead to the formation of a stable or unstable daughter nuclei. There are two basic types of radionuclides: Natural: occur in nature Light natural radionuclides: atomic # less than 75 amu, do not form decay series, resulting nuclei are stable Heay natural radionuclides: form decay series in which parent nuclei give rise to daughter nuclei Artificial: are produced artificially in atomic reactors or accelerators Decay Rate: Number of nuclei at time t: Where N is the number of nuclei at time t, e is euler's # for natural logarithms λ is the disintegration or decay constant: it represents the relative rate of decay - unit is s-1 *The # of radioactive nuclei decreases exponentially with time *The value of the ln N decreases linearly with time Activity: the # of nuclei that decay in 1s A = λN -activity can be used to estimate the decay rate -activity decreases exponentially with time -unit of activity is the Becquerel (Bq) -a radioactive sample will have an activity of 1 Bq if the number of nuclei that decay in 1s is 1.

Thermodynamics: Thermodynamic system, state quantities

1. Thermodynamic system -A thermodynamic system is one that is governed by conservation of energy and that is separated from its surrounding by real or imaginary boundaries. -Heat (Q) or matter (# of moles n) may penetrate the boundaries. Work (W) can be performed by or on the system. There are 3 types of thermodynamic systems: (i) Isolated: the system cannot exchange energy or matter with its surroundings Q = 0 , W = 0 , ∑n = 0 (energy remains constant whenever any chemical or physical processes occur) (ii) Closed: the system can exchange energy but not matter Q ≠ 0 , W = 0 , ∑ n = 0 (iii) Open: the system can exchange both energy and matter (ex: an alive system) Q ≠ 0 , W ≠ 0 , ∑n ≠ 0 There are two types of systems parameters: (i) Global (extensive): describe the system as a whole and possess additive properties; total value of a global parameter for the whole system is the sum of the values of its individual parts (mass, total charge, total number of particles, etc) (ii) Local (intensive): depend on time and spatial coordinates (temperature, pressure, chemical potential, etc) Thermodynamic forces: gradients of temperature, concentration, or charge that cause the flow of heat, substance, or electric charge (thermodynamic flows) 2. State Functions The state of a system is described by its state functions. State functions: properties of a thermodynamic system whose magnitude depends only on the initial and final states of a system and not on the path of change The state variables are • number of moles (n) • Pressure P • Temperature T • Volume V related by the state equations pV=nRT The state functions are • enthalpy (H) • entropy (S) • free energy (G) • internal energy (E or U) related by the state equation ∆G = ∆H -T∆S *All physical and chemical processes that occur in a system are related to changes of variables and functions of state and are not dependent on the path of change. -During the course of evolution, an isolated reaches an equilibrium state. An equilibrium state is the most thermodynamically probable arrangement of the system. All states tend toward equilibrium. -The rate at which a system returns to equilibrium after deviating from it is called the relaxation time. -The deviation I from equilibrium state at time t is given by reversible process: proceeds in only one direction irreversible process: proceeds in both the forward and backward direction and is dependent on thermodynamic forces (gradients)

Structure of Matter: Binding energy in atomic nucleus

10. Binding energy in atomic nucleus Mass Defect (∆m): the difference between the calculated and actual mass of a nucleus ~The mass of a nucleus is always less than the combined mass of it's protons and neutrons ~The difference is due to matter that has been converted to binding energy which holds the nucleons together. *binding energy peaks at iron which is the most stable atom. In general, intermediate sized nuclei are the most stable. *The greater the defect, the greater the binding energy

Radioactivity and ionising radiation: Principles of detection of ionising radiation

11. Principles of detection of ionizing radiation -Detection of various forms of radiation is based on interaction of the radiation with the sensitive part of the detector. Detectors covert radiation energy into other forms of energy that can be registered by other devices. -After a detector absorbs radiation, it generates electrical pulses. The pulses produced by the detector are amplified, formed in shape, measured, and individually registered or their mean count rate is calculated by other parts of the radiation measurement device. The pulses are registered by the counter. Detection efficiency: the ratio of the number of particles registered by the detector to those that pass through the detector. -Multiple types of detectors are available and their function is based on the various interaction radiation may have: ionization, excitation, chemical, thermal, or photographic. ***The three types of detectors used for ionizing radiation are the ionization chamber, the geiger-muller counter, and the scintillation counter

Thermodynamics: Measurement of temperature; Calorimetric measurements

10. Measurement of temperature Temperature is a measure of the average kinetic energy of molecules in a substance. The SI unit of temperature is Kelvin. -The lower limit of temperature on the Kelvin scale is 0 and is called absolute zero -Kelvin temperature is related to the Celsius scale by Tk = Tc +273 The relationship between the Celsius and Fahrenheit scale is Tf = (9/5)Tc +32 The Fahrenheit scale has a different zero point. Water freezes at 32 F. Various methods exist for measuring temperature. All of these are based on changes in the thermometric properties of matter. (expansion, changes in electrical resistance, emmision of radiation, voltage changes) 1. Liquid thermometers -used in the laboratory setting. The thermometric property that is exploited here is volumetric expansion. When a liquid at Vi is heated by a temperature T, its volume increases by ∆V. Thus the column of mercury expands in proportion to the temperature increase. Formula for volumetric expansion is ∆V = βVi∆T where β is the coefficient of volumetric expansion 2. Medical thermometers - it is a mercury thermometer used to measure body temperature. The scale is from 35-42ºC. 3. Calorimetric thermometer- used for the measurement of small temp differences 4. Thermocouple -Measures the voltage difference induced by changes in temperature. Consists of thin wires of two diff metals welded together. One of the junctions (the hot junction") is placed into thermal contact with the object. The other junction is kept at constant temp. A thermocouple generates a voltage difference that is measured by a voltmeter. 5. Electrical resistance thermometer -based on the fact that the electrical resistance of a metal wire changes with temperature. A platinum wire is placed in contact with the object to be measured and electrical resistance is measured as a function of temperature increase 6. Thermistor- based on the fact that the electrical resistance of a semiconductor decreases with increased temp. i.e. the density of free e- increases. Resistance is measured as a function of temperature. Produces very reliable results. 7. Thermography -method of measuring the intensity of emitted radiation due to a temp source -the intensity of radiation emmitted increases with increasing temp -produces a thermogram which displays the various infrared intensities in color -used in medicine, to detect malignant cancers, since cancer tissue is associated with increased metabolic activity and elevated temp. 8. Bimetallic strip - two metals with different expansion coefficients are welded together, when temp is increased, the strip bends toward the side with the lower expansion coefficient -it is used to control temp in devices that need to maintain a constant temp (thermostats)

Use of X-rays in medicine: Principle of computed tomography, Roentgen methods, Principle of Computed Tomography

10. Principle of computed tomography -Computed tomography is the most advanced x-ray imaging technique and has a high resolving power and produces a higher contrast -produces an image of a single layer (crossection) of the body -The body cross-section to be examined is divided into small pixels of size less than 1 mm -A narrow x-ray beam is passes through the body and it's intensity is measured by a photomultiplier. -The value of attenuation coefficients of each individual pixel is calculated. -This allows for the calculation of the emerging intensity I and subsequent image production by a computer. -produces a detailed image with good contrast, results are stored electronically, radiation load for patient is the same as traditional x-ray

Optics in medicine: Refractometry, Polarimetry

10. Refractometry & Polarimetry Refraction - the bending of light rays at the boundary of two media. -This occurs because the speed of light in media is less than that in a vacuum. Dispersion: separation of white light into its spectral components of different wavelengths due to various velocities of the spectral components and resulting refractive indices. -Although the speed of light for all wavelengths in a vacuum is the same, light of different wavelengths travels through a medium of refractive index n, with different velocities. Refractometry: -Used to determine the refractive index of a substance in order to assess its composition or purity. * Refraction is applied in spectroscopy to identify different molecules according to how they refract light. -Using a prism spectroscope, the dispersion of light according to wavelength is studied. -A diverging beam of white light is emitted from a source and the rays are collimated and made parallel. The rays are dispersed through a prism and passed through an objective lens which forms the corresponding spectrum on an indicator (photographic plate or photomultiplier). * Also used in determining the refraction of the eye. This gives the degree to which the eye differs from normal which will determine whether or not the patient needs glasses and, if so, how strong they should be. Polarimetry -Unpolarized light - a beam of natural light in which the electrical field vectors of the waves are oriented randomly in space. -Linearly polarized light - light in which the electrical field vectors are all oriented in the same direction (parallel to eachother) The magnetic field vectors are also aligned. -Polarization is the process of separating linearly polarized light from a beam of natural (white) light. It can be carried out in 3 ways: Reflection & Refraction -when light is incident on the boundary between two media at Brewster's angle of incidence, the reflected and refracted angles are perpendicular to each other and their sum = 90º. At this angle of incidence, the reflected and refracted rays are linearly polarized. Birefringence - polarization of natural light using an anisotropic substance Isotropic materials - properties do not depend on direction. (arrangement of atoms is random) Ex: liquids and amorphous substances such as glass Anisotropic materials - properties depend on direction. There is an ordered arrangement of atoms which only transmits electrical fields in a certain direction and absorbs all other incident light. Results in linearly polarized light. (sunglasses) -absorb ordinary rays -transmit extraordinary rays bc their electrical field is aligned with the polarization axis -If two polarizing materials are placed in sequence, the amount of light transmitted through them varies from a minimum to maximum value depending on how they are oriented in respect to one another. • If the polarization axes are aligned (parallel), all light passing through the first passes through the second as well • If the polarization axes are perpendicular, no light is able to pass through Law of Malus - gives the intensity of light transmitted by a polarizer Where Io gives the intensity at α = 0 (when the polarization axes are parallel and the same amount of light is transmitted through the second polarizer as is transmitted through the first) -Optically active substances rotate the plane of polarized light. • The angle of rotation is directly proportional to the concentration of the optically active substance. • This property is exploited in polarimetry which is used to determine the concentration of optically active compounds. In polarimetry, a beam of light is emitted from a source, passed through a filter, polarizer, cuvette, analyzer, and finally the intensity of its transmitted light is evaluated. ~when the cuvette is filled with water, max intensity of light is observed between the polarizer and analyzer ~when the cuvette is filled with an optically active substance, the analyzer must be rotated by an angle corresponding to the new angle of plane polarized light in order for max amount of intensity to be observed The angle of rotation of plane polarized light by an optical substance is given by

Radioactivity and ionising radiation: Selective and integral detection of gamma radiation

10. Selective and integral detection of * radiation Because the amplitude spectrum produced by scintillators possess continuous character due to the presence of compton scattering, using an amplitude discriminator, two modes of detection can be performed: Integral detection: all pulses with amplitudes greater than a set level are counted, The total # of pulses is proportional to the area under the curve of number of pulses plotted as a function of energy. Selective detection- at photopeak, only pulses with amplitude between the lower level and upper discriminatoion level are registered; -advantage is good spatial resolution of head and decreased detection of cosmic rays and scattered radiation. Energy resolving power (R) of a scintillation head is defined by the width of the photopeak measured at half its height expressed as a function the mean energy in percent

Biophysics of vision

11. Biophysics of vision -The eye functions in detecting light energy and transmitting information about intensity, color, and shape to the brain -sensitive to wavelengths of 400 - 750nm -The transparent cornea at the front of the eye bends and focuses incoming light. The rays travel through the pupil whose diameter is controlled by the muscular iris. The iris responds to the intensity of light by adjusting the size of the pupil. -The light continues on to the lens which focuses the image on the retina. The shape of the lens is controlled by the ciliary muscle. -Changing the shape of the lens allows the eye to vary its focal length and focus on objects at various distances (accommodation). -The retina contains photoreceptors called cones and rods. Cones - sense high intensity illumination and color (located in the fovea centralis and some in the periphery) Rods - detect low intensity illumination and are important in night vision (located in the periphery of the retina) *we have much more rods than cones -Rods and cones transduce light energy into nerve impulses. This process contains a photochemical step which functions in adaptation of the eye to the current light intensity. -the cones contain three types of pigments each of which absorbs light of a certain band of wavelength. -The rods contain a red pigment called visual purple or rhodopsin that is bleached by light. It is a conjugated protein bonded to the pigment retinene. Rhodopsin is stable until exposed to light. Light causes it to disscociate into protein and retinene. Under dark conditions, it is reformed with the help of vitamin A. * Only about 10% of light intensity stimulates the photoreceptors and some wavelengths stimulate the retina more than others. Photopic vision - maximum sensitivity in daylight is 550 nm (yellowish green) Scotopic vision - maximum sensitivity in the dark is shifted toward shorter wavelengths of 505 nm. -The image formed on the retina is inverted and reduced in size. -The information obtained by the photoreceptors is transmitted to the brain via the optic nerves. Far point -the furthest distance at which the human eye can focus is infinity Near point -the closest distance that the human eye can comfortably focus on is 25cm. The distance of the near point increases with age (presbyopia or old-sightedness) Photopic vision is the scientific term for human colour vision under normal lighting conditions during the day. In the range above 3.4 cd/m2 human eye uses three types of cones to sense light in three respective bands of colour. The pigments of the cones have maximum absorption values at wavelengths of about 445 nm (blue), 535 nm (green), . 575 nm (red).Their sensitivity ranges overlap to provide continuous (but not linear) vision throughout the visual spectrum. The maximum efficacy is 683 lumens/W at a wavelength of 550 nm (yellow).

Molecular biophysics: Dispersion systems and their classification

11. Dispersion systems and their classification -A Dispersion system has at least 2 phases: dispersive portion & dispersive medium dispersive portion- dispersed in the medium, not continuous dispersive medium- continuous -A dispersion system can be classified by various parameters: A. Size of the particles → reciprocal value of particle diameter (m-1) is called the dispersion degree -very fine particles possess a high dispersion degree Several types: Monodispersed system: dispersed particles are of the same size Polydispersed system: dispersed particles are of various sizes Based on specific size: Analytical dispersion: dispersed portion particles are up to 1nm in diameter Colloidal dispersion: 1- 1000 nm Coarse dispersion: 1 μm and greater

Structure of Matter: Potential barrier of atomic nucleus

11. Potential barrier of atomic nucleus ~At short distances, strong interactions are stronger than electromagnetic interactions. ~A charged nucleus of Ze forms as electromagnetic force field around it with potential U(r) that is a function of the r = distance from nucleus. ~This creates a potential barrier around the nucleus due to the electromagnetic interaction for positively charged particles (protons,dueterons,alpha-particles) that enter the nucleus. Positively charged particles must overcome the potential barrier to enter the atom.

Thermodynamics: Specific heat, latent heat

11. Specific heat Specific heat: the amount of heat energy needed to raise the temperature of 1 kg of a substance by 1 ºC or 1 K. (unit J.kg-1.K-1) ~The specific heat of a substance varies with temperature. Ex: liquid water has a higher specific heat than ice. ~Specific heat is a property of the given substance. -The quantity of heat ∆Q required to change the temperature ∆T of a substance is proportional to the object's mass and the specific heat of a substance. ∆Q = mc∆T *Where m is the mass of the object and c is the specific heat 12. Latent heat L is the latent heat (units J/Kg): the amount of heat required to change the phase of 1kg of a particular substance heat of fusion: latent heat for a phase change between solid and liquid heat of vaporization: latent heat for a phase change between liquid and gas Phase Change Temperature remains constant when a substance undergoes a phase change. -The amount of heat gained or lost by a system undergoing a phase change or -The amount of heat required to change the phase of a particular substance is given by ∆Q =mL *Water has a relatively high latent heat of fusion and evaporation. This means that a great amount of heat energy must be supplied to change the phase of water. -For water, the specific latent heat of fusion at melting temperature 0ºC is 334kJ/kg and the specific latent heat of evaporation at boiling temperature 100ºC is 2.26 MJ/kg.

Electricity in medicine: Use of electricity in diagnostics

11. Use of electricity for diagnostic purposes The major application of electricity in diagnostic medicine is the electrocardiogram. -The electrocardiogram records heart action potentials produced by changes in polarity of cardiac cells. -To record an ECG, electrodes are placed on different parts of the body. Each of these leads monitors distinct areas of the heart. Using combinations of these electrodes, different tracings of the heart's electrical activity can be made and recorded on paper or in a computer. Diagnoses- abnormal heart rates: bradycardia = slower rate, bachycardia= faster rate, amythmia= irregular rate; myocardium damage as a result of myocardial infarction Other applications include the electroencephalogram which records brain activity by detecting electrical potential across regions of the brain. Diagnoses: epilepsy, sleep patterns, brain death.

Radioactivity and ionising radiation: Detectors of ionising radiation

12. Detectors of ionizing radiation The three types of detectors for ionizing radiation are the ionization chamber, the Geiger-muller counter, and the Scintillation counter

Optics in medicine: Eye defects

12. Eye defects Emmetropia - The condition of the normal eye when parallel rays converge exactly on the retina and vision is perfect. -There is no need for the aid of glasses or contact lenses to help with focusing on objects in the distance. -Ametropia - any deviation from normal resulting from the eye's inadequate refractive ability. Includes nearsightedness, farsightedness, and astigmatism. Farsightedness (hyperopia) occurs when light entering the eye focuses behind the retina, instead of directly on it. -This is caused by an eye that is shorter than the normal eye. -Farsighted people have trouble seeing up close, but may have difficulty seeing far away as well. -Corrected with a converging lens. Nearsightedness (myopia) occurs when light entering the eye focuses in front of the retina instead of directly on it. This is caused by an eye that is longer than the normal eye. -Nearsighted people typically see well up close, but have difficulty seeing far away. -Corrected with a diverging lens. Presbyopia - is caused by an age-related process. These age-related changes occur within the proteins of the lens making the lens harder and less elastic with age. Age-related changes also take place in the muscle fibres surrounding the lens. With less elasticity, the eye has difficulty focusing on near objects. (Focal length increases with age) -Corrected with converging lens

Electricity in medicine: Use of electricity in therapy

12. Use of electricity in therapy Electrotherapy is based on the three different effects of electric current. The effects are dependent on the type of electrical current used. Electrolytic: -A direct current has strong electrolytic effects (bc the organisms fluid has many electrolytes, alkaline compounds deposit on cathode, acidic compounds deposit on anode). It results in the changed stimulation of nerves. Higher direct current densities can result in tissue damage. -A weak electrolytic effect can be produced by low frequency alternating current Stimulatory: -Low frequency alternating current has a strong stimulatory effect (if this current passes through the heart it can disrupt the heart's electrical activity and have lethal effects). -Direct current can only produce stimulatory results at sudden changes of intensity. Thermal -A high frequency alternating current has a strong thermal effect. -It is applied safely for heating tissues during diathermy. *Electrotherapy is applied in physciatry, balneology, rehabilitation.

Molecular biophysics: Properties of colloid particles

13. Properties of colloid particles -Particle size is 1- 1000 nm -There are 2 types of colloidal solutions: (lyophobic and lyophillic) according to their behavior with respect to the solvent. -There are two types of colloidal particles: Macromolecules: molecular polymers of smaller molecular components bound by chemical bounds (ex: proteins, carbohydrates, etc) Micelles: clusters of particles without any chemical bonds. Properties: • Colloidal particles move in solution as individual particles. • Movement is zigzagged -Brown motion due to repeated collisions with molecules of solvent • Velocity of sedimentation due to gravity = • Permeability or impermeablility across membranes (used to separate colloidal particle from the analytical portion of the solution or the dispersing medium itself) • Tyndal phenomenon: scattering of light rays that hit colloidal particles in a solution. The intesity of scattered light depends on the particle's size. For monodispersed systems, (particles are of the same size) the intensity of scattered light can be used to estimate the conc. of the particles. • On the surface of colloidal particles lays a double layer of charged particles

Radioactivity and ionising radiation: Scintillation detector

13. Scintillation detector -The scintillation detector is used for detection of gamma radiation -It consists of 3 parts 1) Scintillator- converts radiation to luminescence (crystals of sodium iodide NaI are frequently used as the scintillator) 2) Photomultiplier - detects scintillations 3) electronic parts fore registration of the signals -Atoms of the scintillator are excited upon absorption of gamma radiation -Photons of visible or ultraviolet light are then emitted during deexitation of the electrons in the atoms -The resulting luminescent photons impact the photocathode of the photomultiplier and cause emission of electrons via the photoelectric effect. - The photomultiplier consists of 8-14 dynodes which are electrodes with subsequently increasing voltage. The 1st dynode has the lowest voltage. It ejects electrons which then are accelerated to the next dynode and cause ejection of electrons there -Thus many electrons are formed due to the impact of the first. This leads to great amplification (105 - 107) -The avalanche of electrons come to final dynode and creates a pulse of voltage -The pulses are amplified and measured. Detection efficiency = 30 - 50% for gamma radiation Scintillation head - the scintillator and photomltiplier (and preamplifier) are located within the same container to prevent light from entering from the outside

Radioactivity and ionising radiation: Geiger-Muller tube

14. Geiger-Muller Counter -Used for the detection of beta radiation -The Muller tube consists of metallic cylinder which represents the cathode and an axially mounted tungsten wire which represents the anode. -The tube is filled with an inert but ionizable gas (mostly argon and some other polyatomic gas) -A high voltage is set up between the electrodes -When radiation enters the tube, the gaseous atoms are ionized. -Due to the high voltage difference between the electrodes, the newly formed ions are accelerated to high kinetic energies and may cause more ionization in other gaseous atoms -Thus an electron avalanche is created from only one ion pair. -This produces a pulse in the electrical current within the tube that can be registered by the counter part of the measuring device. When count rate is plotted as a function of voltage, a plateau is formed at higher voltages. At these points, the count rate is independent of the applied voltage Detection efficiency = ratio of number of registered particles/ photons passing through detector

Optics in medicine: Optical properties of colloids

14. Optical properties of colloids -Colloidal particles are macromolecules or micelles that move in solution as individual particles. -Scattering of light that passes through a solution containing colloidal particles is called the Tyndal phenomenon. -Since intensity of scattered light depends on particle size, measurement of the intensity of scattered light can be applied for the estimation of concentration in monodispersed colloidal system. -Some solutions may non exhibit the Tyndal effect because the solute particles are too small to scatter light.

Structure of Matter: Physical principles of mass spectroscopy

14. Physical principles of mass spectrometry ~Mass spectrometry can be used to determine the isotopic composition of a given sample. ~This method is based on the fact that the trajectory of charged particles moving in a magnetic field is dependent on their mass Method (1) sample is ionized-(e- removed) to become positive ions of charge q (2) the ions are accelerated by a potential difference V to E=qV (a beam of ions is formed) (3) The ion beam is seperated into several beams depending on each ion's specific charge m/q. The path/deflection of an ion in a magnetic field depends on its mass to charge ratio. (4) Each beam is detected and its intensity is measured → intensity provides information about the relative amount of each isotope present in the sample (% composition) E=qV = 1/2mv2

Molecular biophysics: Dialysis, Principle of electrophoresis, electrokinetic potential

14. Principle of electrophoresis -Electrophoresis is a technique used to separate and sometimes purify macromolecules - especially proteins and nucleic acids - that differ in size, charge or conformation. -It is one of the most widely-used techniques in biochemistry and molecular biology. -When a charged molecule is placed in an electric field, it migrates toward either the positive (anode) or negative (cathode) pole according to its mass: charge ratio. -The migration velocity is proportional to the strength of the electrical field & the charge of the molecule, and inversely proportional to its mass. In contrast to proteins, which can have either a net positive or net negative charge, nucleic acids have a consistent negative charge imparted by their phosphate backbone, and migrate toward the anode. 15. Electrokinetic potential Electrokinetic potential is the potential across the interface of all solids and liquids. Specifically, the potential across the diffuse layer of ions surrounding a charged colloidal particle, which is responsible for colloidal stability.

Radioactivity and ionising radiation: Accelerators of particles

15. Accelerators of particles -Instrument that yields charged particles with high kinetic energy -These high energy particles are then used for bombardment of target nuclei in order to induce nuclear reactions or high energy bremsstrahlung -Accelerators are typically used to accelerate positively charged particles. + charged particles such as alpha particles, protons, and deuterons are good sources of ionizing radiation however they do not have sufficient energies. Thus using a potential differences to accelerate the particles increases their kinetic energy and allows them to be used for practical purposes -In medicine, they are used in the production of short lived radio nucleotides (betatron) or the production of High Energy Bremsstrahlung to destroy malignant tumors -There are two types of acceleratorss -Linear or Circular A) Linear accelerators: -Particles are accelerated when passing through the the straight or high frequency accelerating tube Electrostatic: power source for the voltage difference is the Van de Graaf generator High frequency linear accelerator => power source is the klystron generator -20-40 kV accelerator. -Ions pass through gaps between metal cylinders of alternating polarity (the charge on the first cylinder must be opposite of ion) - There is stepwise increase in the lengths of the cylinders since velocity of accelerated ions in each cylinder is higher than the previous one. -the target atoms are located at the end of the last cylinder -acceleration process takes place in a vacuum. b) Circular Accelerators: Cyclotron: used to accelerate heavy particles (protons, deuterons, alpha particles) -consiste of 2 parts or Duants connected to high freq alternating voltage which creates an alternating electrical field in the space between the duants -The source of the particles is located between the two duants -The particles are attracted to the oppositely charged daunt and simultaneously accelerated upon entering the magnetic field. -The magnetic field causes the particle to move in a circular motion -The polarity of the duants changes repeatedly so that the particle is attracted to one duant and then to the other. -the radius of the particles path increases as does its velocity and energy (inc. Volt & Elec) Particles leave as a continuous flux *Used in medicine in the production of short lived radio nucleotides for diagnostic purposes. c) Accelerators of Negatively charged particles: Betatron- device for the acceleration of e- -The accelertion takes place in an evacuated glass ring -The ring is situated at the poles of an electromagnet and pulsed jets of e- are delivered into the ring -A periodically changing magnetic induction results in variable magnetic flux which produces electromotoric force proportional to the variation of magnetic flux. -The EMF accelerates e- during the 1st period when magnetic induction increases -Therefore the Betatron=pulse accelerater. The accelerated e- move w/ relativistic velocity E= expressed in eV, r=radius and Bm teslas -The accelerated electrons then hit the target to produce high energy Bremsstrahlung *** Because neutrons do not have a charge they cannot be accelerated ***

Structure of Matter: Physical principles of nuclear magnetic resonance, Magnetic resonance-Relaxation, MR spectroscopy, Magnetic resonance-Image Formation, Force interactions

15. Physical principles of nuclear magnetic resonance *The magnetic properties of nuclei provide the basis for NMR -Nucleons possess their own half-integer value of angular momentum. -Magentic moment of proton is 2.8nm and neutron is 1.9nm (dependent on the mass of the particle) -the magentic moments of nuclei with non-zero values of spin (and thus magnetic moments) can be utilized to provide information about the amount of particular nucleus within a given sample. -The magnetic moments of such nuclei are oriented randomly under normal conditions and can align with an external magnetic field when one is present ~The potential energy of a nucleus/proton in the presence of an external magnetic field B =μB where μ is the magnetic moment of the proton ~Protons can exist in two possible energy states within a magnetic field → +-μB depending on their spin number of +-1/2 In the higher energy state, the magnetic moments are oriented antiparallel to the field In the lower energy state, the magnetic moments are aligned with the field ~If protons are exposed to electromagnetic radiation with energy that equals the difference between these two energy states, resonance exchange of energy occurs between the nuclei and incident wave. E = hf = 2μB w= angular frequency B= magnetic induction ~Resonance exchange of energy is called nuclear magnetic resonance ~This resonance exchange of energy occurs at Lamors frequency which is f=w/2π from w=2πf -If a proton is in a lower energy state with energy -μB, a photon is absorbed and transition into a higher energy state with energy +μB occurs. -If a proton is in a higher energy state with energy μB, then a photon is emitted and transition into lower energy state -μB occurs MRI (Magnetic Resonance Imaging) -diagnostic application of NMR -free protons in the hydrogen nuclei of water are utilized since almost all biological tissues contain water. -The patient is placed into an external magnetic field which aligns the magnetic moments of hydrogen nuclei, pulses of radio waves are passed through the patient causing deflection of the magnetic moments. The magnetic moments then return to their lower energy aligned states with simultaneous emission of a photon by the nucleui. The strength, frequency, and time it takes for the nuclei to return to their pre-excited state produces a signal. The signal is analyzed by a computer and an image is produced in which the differences in tissue composition can be visualized. -MRI produces 3 images in one: a distribution of proton density, and relaxation times T1 and T2. -The frequency at which resonance exchange of energy occurs is dependent on the atom's environment. Thus a compound can contain many nuclei that resonate at different frequencies producing a complex spectrum. *magnetic moment is influenced by the shielding action of a nuclei's own electrons as well as the electrons of other atoms in its vicinity.

Optics in medicine: Principle of laser

15. Principle of laser LASER: Light amplification by stimulated emission of radiation -A laser is a device that produces a very narrow, intense, monochromatic, coherent light beam Principles behind laser function: -Electrons can only exist in defined energy states and transition from a higher to lower energy state is accompanied by the release of a quantum of radiation with frequency -If an electron spontaneously falls to a lower energy state due to interaction with an electromagnetic field, the atom will emit a noncoherent electromagnetic wave. (called induced transitions) -induced radiation is of the same frequency, polarization, and direction of the radiation that induced the emission The Boltzmann law describes the distribution of energy levels under normal conditions *The number of atoms in the excited state is dependent on temperature. *At normal conditions, only a small portion of atoms are in the excited state. How a laser works: -Lasers are able to produce intense coherent light by a process called inversion. ~During inversion, there are more atoms in the excited state than the ground state. -This is accomplished by exciting atoms into a higher energy level and allowing them to fall into a metastable state for a relatively long period of time (for 10-3 s). Thus many atoms enter and collect in this semi-excited state producing inversion. (occurs in the ruby crystal of a ruby laser) -When light with energy equal to the difference between the metastable and ground state passes through the crystal, all atoms simultaneously transit into the ground state emitting in a pulse of intense coherent light. Its wavelength is equal to the wavelength of the incident radiation. -The intensity of the pulse is inversely proportional to its duration I = F/A P = E/t (unit is Watts) *Lasers are used in medicine in the destruction of small sized tissues, in coagulation of tissues, and healing of ulcers.

Radioactivity and ionising radiation: Ionisation chamber

16. Ionization chambers This is basically a capacitor (seperates and stores charge with a potential difference between the parallel plates) with 2 electrodes filled with air. -Ion pairs (electrons and positively charged ions) are formed in the chamber though interaction with ionizing radiation and are then attracted to the electrodes. -Therefore, an electric current flows through the chamber and can be registered when exposed to radiation -The higher the operating voltage, the higher the accelerating force, the greater the intensity of the electrical current flowing through the chamber -The produced ions can disappear at the electrodes, chamber walls or by recombination. -Ions with charge e move in electric field due to force F=eE where E is intensity of electric field. ** Ionisation chambers are used as pocket personal dosimeters for evaluation of exposure to radiation.

Optics in medicine: Optical and electron microscopy

16. Optical microscope -An optical microscope makes use of of the refractive properties of lenses to bend light and magnify an image. -In a compound microscope, 2 lenses are used to provide greater magnification of the object. -The first lens is the objective and the second is the eyepiece. -The function of the objective is to put an image of the object at a point closer to the eyepiece that the focal point of the eyepiece. -The eyepiece then acts as a simple magnifier. -Fo = 5mm -Fe = 15 mm -Optical tube length (∆) is the distance between the focal points of the objective and eyepiece. -The distance between the lenses is • If the object is placed just beyond the focal point of the objective, a real, inverted, and enlarged image is formed. • This image acts as a real object for the eyepiece • The final image produced is virtual, inverted, and enlarged. The magnification of the objective is (neg bc the image is inverted The numerical aperature A is Where є is the half of the aperature angle at which the objective lens is seen from the object on the optical axis And n is the refractive index between the object and the objective. The total magnification of the objective and eyepiece is e is the shortest distance between 2 points that can be resolved The resolving power of a microscope is 1/e Resolving power is dependent on • wavelength of light (the shorter the wavelength, the greater the resolving power of the microscope) • numerical aperature (numerical aperature can be increased by using an immersion objective instead of a dry objective. n=1 for air vs. n=1.5 for oil) *The resolving power limits the magnification of the microscope. 17. Principles of electron microscopy -Electron microscopes use beams of electrons instead of light to form images. -Their ability to produce greater magnification is a result of a much higher resolving power as compared to light microscopes. -The greater resolution and magnification is due to the wavelength of an electron being much smaller than that of a photon. Transmission electron microscopy (TEM) involves a high voltage electron beam emitted by a cathode, usually a tungsten filament and focused by electrostatic and electromagnetic lenses. The electron beam that has been transmitted through a specimen that is in part transparent to electrons carries information about the inner structure of the specimen in the electron beam that reaches the imaging system of the microscope. The spatial variation in this information (the "image") is then magnified by a series of electromagnetic lenses until it is recorded by hitting a fluorescent screen, photographic plate, or light sensitive sensor. The image detected may be displayed in real time on a monitor or computer. the Scanning Electron Microscope (SEM) produces images by detecting low energy secondary electrons which are emitted from the surface of the specimen due to excitation by the primary electron beam. In the SEM, the electron beam is rastered across the sample, with detectors building up an image by mapping the detected signals with beam position. -The SEM has a large depth of focus.

Molecular biophysics: Transport phenomena

16. Transport phenomena Transport phenomena are related to the motion of molecules and interaction between molecules causing the net movement of physical quantities. • viscosity is the transport of momentum • conduction of heat is the transport of energy • diffusion is the transport of molecules. -In order for transport of any of these things can occur, an appropriate gradient must exist. Ex: concentration, temperature, or velocity gradient

Radioactivity and ionising radiation: Methods of personal dosimetry

17. Methods of personal dosimetry Personal dosimeters are used to determine the amount of ionizing radiation that people who work with radionuclides Their function is based on 3 different interactions of radiation with matter (1) Film-Dosimetry (effect on photographic emulsion) a photographic emulsion that is sensitive to ionizing radiation is exposed to ionizing radiation and after its development the dose is measured by the amount of blackening on the film. -not accurate below 5 μC/kg (2) Thermoluminesence Dosimetry (based on the excitation effect of radiation)- The electrons of lithium flouride crystals are excited to higher energy levels upon exposure to radiation. They remain in the excited state until temp is increased (100 ºC) and then deexitation occurs with emission of visible light. The intensity of the light is measured by a photomultiplier and it is proportional to the dose absorbed by the crystal. -good for 3mnths, work good at room temp and humidity (3) Pocket Dosimetry - (based on the ionizing effect of radiation)- utilizes a small ionization chamber filled with air and charge. The ionization effect creates ion pairs and electrical charge decreases thus measuring the dose disadvantage: sensitive to humidity

Radioactivity and ionising radiation: Units of exposition and absorbed dose of irradiation, Gamma camera, Positron emission tomography, Single photon emission tomography

18. Units of exposure and of absorbed dose of radiation The basic quantity which describes a radiation source is emission -Emission is the number of particles ( quanta) emitted by the source in one unit of time, s-1 Emission = # of quanta divided by second -If the source is radionuclide, its emission is related to its activity (A). -Activity: the # of nuclei that decay in 1s A = λN -activity can be used to estimate the decay rate -activity decreases exponentially with time -unit of activity is the Becquerel (Bq) -a radioactive sample will have an activity of 1 Bq if the number of nuclei that decay in 1s is 1. est s-1imated decays divided by one second unit is Bq which is becqurel Bq used to be known as curie( ci) where 1 ci = 3.7 x 1010 bq.. -Based on the decay curve, it is easy to estimate the activity of the pharmaceutical preparation at the time of its application to the patient. -Because activity decreases exponentially with time, a larger volume of the radionuclide preparation must be administered to ensure the proper dose . Mass , M of radionuclide = 2.073 x 10-15 A ( Mbq) Tf M= mass expressed in micrograms A =nucleon # Mbq= activity expressed in mbq, and Tf = half life in days. Exposure: is a characteristic of x-ray and gamma radiation and it is based on ionization effects and estimates the ionizing power of radiation in the air. Exposure X = ratio of electric charge, ∆Q, of ions created by complete absorption of particles ( electrons and positrons) formed by interaction of X- of Y- rays in vol of air with mass ∆m. Unit of exposure is Coulombs/kg The formerly applied unit was the roentgen Exposure Rate dX/dt is the change in exposure over change in time. Its unit is A/kg and dimension is m2s-2A Absorbed dose D = ratio of mean energy of ionizing radiation (∆E) absorbed to its mass. Unit is gy ( grey) 1gy = J/kg -1. -formally applied unit was the rad Dose rate = mean increase of dose, (∆D), in time interval (t) dD/dt = ∆D/∆t unit is W.Kg -1. Dose equivalent H is applied for the evaluation of the radiation effect on living organisms H = DQN SI units, Transformation of Units Factor Prefix Symbol 1018 exa E 1015 peta P 1012 tera T 109 giga G 106 mega M 103 kilo k 10-1 deci d 10-2 centi c 10-3 milli m 10-6 micro µ 10-9 nano n 10-12 pico p 10-15 femto f 10-18 atto a Frequency hertz: Hz = 1/s Force Ionizing radiation is produced by unstable atoms. Unstable atoms differ from stable atoms because they have an excess of energy or mass or both. Unstable atoms are said to be radioactive. In order to reach stability, these atoms give off, or emit, the excess energy or mass. These emissions are called radiation. Types of ionizing radiation. Alpha particles (He2+ nucleus) Beta particles (B-) Gamma rays (photons) Neutrons (uncharged nucleon)

Molecular biophysics: Viscosity and its measurement

18. Viscosity and its measurement -Viscosity is a measure of the internal friction of a fluid between adjacent layers of liquid molecules as they slide past each other. -The ideal fluid has 0 viscosity. ~Fluids that have small values of viscosity move more readily and behave more like ideal fluids. -In a cylindrical tube of radius r, a velocity gradient exists with the velocity vectors oriented in a parabolic fashion. Tangent tension (σ): the force of internal friction F results in tangent tension. It is proportional to the vector of the velocity gradient. Unit is the Pascal (N/m2) σ = F/A σ = n ∆v ∆r Dynamic viscosity: the proportionality coefficient n (unit is Pa.s) Kinetic viscosity: the dynamic velocity / density (unit is m2.s-1) Newtonian liquids: have a tangent tension proportional to the velocity gradient ex: single component liquids and analytical solutiosn Non-Newtonian liquids: have a tangent tension that is not proportional to the velocity gradient ex: colloidal particles, suspensions, and emulsions Factors that influence viscosity: • Temperature → Since the motion of particles depends on temp so does viscosity. ~In liquids, viscosity decreases with increasing temp ~In gases, viscosity increases with increasing temp • Concentration of suspended particles (c) → The greater the conc. of suspended particles, the greater the viscosity. i.e. higher hematocrit raises the viscosity of blood *The highest Velocity Vmax is in the center of the tube. ~Velocity decreases with increasing distance from the center of the tube until it reaches 0 at the walls of the tube. Viscosity Measurement: -Use the equation for flow rate Q Ostwald viscosimeter: Body viscosimeter: applies Stoke's law -The internal friction force F for a sphere of the radius r moving in a medium of viscosity n at velocity v is given by: Stokes law: F= 6πnrv

Molecular biophysics: Diffusion, 1st law of Fick

19. Diffusion -In spite of the random motion of molecules, diffusion is the net movement of dissolved particles down their concentration gradient from a region of higher concentration to a region of lower concentration. -it functions against the vector of concentration gradient ∆c/∆x where ∆c = c1-c2 -density of diffusion flux -is proportional to the concentration gradient n/At = -D(∆c/∆x) ← Fick's Law n = # of moles A = area through which diffusion takes place t = time taken unit for diffusion is (mol.m-2.s-1) D = diffusion coefficient (m2 s-1) *D is negative because the direction of flux is opposite to the direction of the concentration gradient. where T=temp, n=viscosity, r=radius, k=boltzmann constant -The mean squared displacement is proportional to time and the diffusion coefficient by xrms2 = 2Dt *This equation can be used to calculate the time required for a diffusing particle to move a certain distance D = diffusion coefficient (m2 s-1) -The value of D is dependent on the nature of the diffusing particle and the choice of solvent or medium. -It is also dependent on temperature (the relationship is directly proportional) D = kT/6πnr Where k is the Boltzmann constant *Therefore, an increase in temperature accelerates diffusion Importance of Diffusion: -It is the primary mechanism for absorption and distribution of substances between cells and with the organism's environment → absorption in small intestine, respiration in lungs, excretion in the kidney. 20. 1st law of Fick -Describes the relationship between the density of diffusion flux and the concentration gradient → they are directly proportional. n/At = -D(∆c/∆x) n = # of moles A = area through which diffusion takes place t = time taken unit for diffusion is (mol.m-2.s-1) D = diffusion coefficient (m2 s-1) *D is negative because the direction of flux is opposite to the direction of concentration gradient. ***Both surface tension and adsorption are phase border phenomena that result from the forces between molecules***

Use of X-rays in medicine: Control of the energy and intensity of X-rays

2. Control of the energy and intensity of X-rays -The penetrating ability of Bremsdtrahlung can be controlled by the accelerating voltage of in the x-ray tube, the higher the voltage the higher the x ray energy and the greater it's penetrating ability E =qV -The intensity can be controlled by changing the intensity of the anode current. This can be done by varying the degree of heating of the cathode filament. It is a useful technique when is desired to change the intensity of without varying the energy of radiation. P=kV2IZ

Radioactivity and ionising radiation: alpha, beta and gamma radiation

2. Energy spectra of * and * radiation α decay: Decay of heavy radionuclides results in emission of an α particle. α particle: composed of 2 protons + 2 neutrons. It is the nucleus of a Helium atom. -has a charge of +2 - α particle are absorbed by material very easily adn do not penetrate shielding material very far. -emission of an α particle results in a daughter nucleus with an atomic # of 2 less than the parent and an atomic mass of 4 less than the parent nucleus. The daughter nucleus is to the left of the parent on the perdiodic table. The parent nucleus changes according to the scheme : -if the energy of the α particle emitted is lower than the transmutation energy, then the daughter nucleus that is formed is in the excited state and can fall to the ground state by emission of gamma radiation β decay : is known as an isbaric transmutation of the nucleus since nucleon number is conserved. There are 3 types of β decay: 1. β- Decay: Emisson of Electron and its antineutrino: A neutron decays into a a proton and β- Mass number is conserved and atomic number increases by 1 (new proton) * the electrons produced possess a continuous energy spectrum 2. β+ Decay: Emission of positron: A proton decays into a positron and an neutron Mass # is conserved and atomic # decreases by 1 (a proton has decayed) * the positron energy spectrum is continuous 3. Electron Capture: occurs when unstable radionuclides capture an electron from the inner K shell. The electron combines with a proton to form a neutron. -The mass number is once again concerved but atomic number decreases by 1 *characteristic electromagnetic radiation is emitted *Excited nuclei are formed in all three types of B decay and immediate transition into the ground state occurs with simultaneous emission of gamma radiation 3. Energy spectrum of * radiation Gamma decay- This radiation is represented by gamma rays or high energy photons emitted by the nuclei of radioactive elements. -Since gamma rays do not carry charge or mass, both the mass number and atomic number is conserved in the nucleus. -The cobalt gun is used as a source of radiation used in radiotherapy. Uses radioactive cobalt -60 -The known intensity of y-radiation decreases slowly with time since the half-life of this radionuclide is about 5 years. -It can used in therapy of malignant tumors by using ionising radiation.

Electricity in medicine: Intensity of electric field, Electric current, voltage, resistance, impedance and their measurement, units

2. Intensity, voltage, resistance, impedance and their units INTENSITY: The intensity of an electrical field is given by The electrical field strength is defined as the electrostatic force felt by a positive test charge qo divided by its charge. Units are Newtons/coulomb which equals volts/meter Intensity can also refer to the amount of energy transmitted via acoustic or electromagnetic radiation. Intensity is the measure of average energy flux. For example in the case of sound, intensity = power/area Intensity is a vector quantity and has units watts/m2 VOLTAGE (V): Since work must be done to move a charge in an electrical field, voltage is the amount of work that must be performed to move a positive test charge q0 through an electric field from point a to point b. The voltage or potential difference is the difference in electric potential between two points. -The work depends only on the electric potential at the two points and is independent of the path taken by the charge. Unit is the Volt. 1V = 1J/1C *voltage is a parameter of electricity which causes current to flow when circuit is compeleted. * V is a scalar quantity whose sign is dependent on the sign of the charge *0 electric potential is defined at an infinite distance away from the source. RESISTANCE (R): opposition to the flow of charge in a direct current (electrical current). *Resistance does not effect the flow of charge, it just results in a potenial drop. R=U/I The SI unit of resistance is the ohm. Resistance of a conductor is dependent on its: Length (L)- directly proportional -the longer the resistor, the greater the resistance (e- have to travel longer through the resistor-greater potential drop) Crosssectional area (A) -inversely proportional -the greater the crossectional area, the greater the resistance (an increase in the amount of conduction paths for the e-) Resistivity (ρ)- directly proportional - the greater the materials resistivity, the greater the resistance. Resistivity is value that characterizes a material's intrinsic resistance to current flow SI unit is ohm x meter Temperature - most conductors have higher resistance at higher temperatures (due to more oscillations in the atoms of the conductor causing a resistance to e- flow) *conductors have low values of resistance while resistors have high values of resistance IMPEDANCE (Z): opposition to the the flow of charge in an alternating current Z=U/I -it is based on three components Resistance (R) Inductive reactance (L) Reactive capacitance (Rc) In tissues, inductive reactance can be neglected 3. Donnan´s equilibrium in a cell membrane -Donnan's equilibrium is the behavior of diffusable ions near a semipermeable membrane failing to distribute themselves evenly across the membrane due to the presence of another charged nondiffusable particle. This results in an uneven charge distribution across the membrane and the formation of an electrical potential between the two solutions (Donnan's potential). In the absence of a nondiffusable ion: If a solution of KCl is added to one side (side 1) of a semipermeable membrane and water is added to the other side (side 2), KCl will dissociate and the two ions will move down their concent to side 2. The ions will continue to diffuse back and forth until equilibrium is acheived and there are equal concentraions of K+ and Cl- on either side of the membrane. At equilibrium, equal numbers of K+ and Cl- ions will diffuse back and forth across the membrane to maintain equal concentrations on either side and electrical neutrality. In the presence of a nondiffusable ion: If an impermeable anionic protein is added to side 1, there are equal concentrations of K+ on either side and no Cl- ions in side 1. In the beginning, some Cl- ions will diffuse down their concencentration gradient to side 1. This gives side 1 a net negative charge and establishes an electrical gradient for Cl- ions which restricts more Cl- ions from entering side 1. This electrical gradient also attracts K+ ions from side 2 to side 1. K+ ions will then move back to side 1 as a result of a K+ concentration gradient. At equilibrium, the product of the concentrations of the diffusable ions on either side is equal. However, there is a slight excess of cations on side 2 along with a sight excess of anions on side 1 producing an electrical potential between the two sides.

Physical and physiological acoustics: Sound intensity and loudness, units

2. Sound intensity and loudness, units Sound intensity, I - The amount of energy passing through an area of 1m2 perpendicular to the direction of wave propagation within 1s (Intensity =P/A) Units W/m2 I = vef Pef = P2ef / ρc *Intensity of sound is directly proportional to the effective accoustic pressure squared. Intensity Level L (units are the bell or decibel) In decibels... L = 10 log I/Io In bells... L = log I/Io * If intensity increases by 100, intensity level is 20 dB Loudness -Is a physiological quantity that describes the perception of sound. -Intensity of sound of frequency 16Hz to 16kHz that comes to the ear results in hearing and the perception of sound is described by its physiological quantity loudness. - Sound perception is subjective and the ear is sensitive to various frequencies to various extents, therefore loudness is NOT proportional to intensity -The dependence of loudness on the intensity of the stimulus is described by Weber-Ferchner's Law : the change in loudness (∆L is proportional to the relative change in the stimulus -Units of Loudness are the phones (ph) speech is 40-60 phones

Optics in medicine: Planck´s law, Stefan-Boltzmann and Wien laws

2. Stefan-Boltzmann and Wein laws At temperatures above 0 K, matter emits electromagnetic radiation. The amount of energy radiated depends on the temperature of the emitter. Wein's Displacement Law Wein's displacement law states that the wavelength of maximum emission is inversely proportional to temperature. -the greater the temperature of the emitter the smaller the wavelength of emitted radiation. We get Weinís Law by: taking the first derivative of Planckís Law setting it equal to zero solving for wavelength λmax= a/T where a = Wein's constant = 2.90 x 10-3 mK Stefan-Boltzmann law: The Stefan- Boltzmann law states that the total energy being emitted per unit area per second is proportional to the 4th power of the absolute temperature. P =power in watts, A is in m2, T in degrees Kelvin, Stefan-Boltzmann constant (s) = 5.67 10-8 W/m2K4. 3. Lens equation Converging lens- are thicker at the center than at the rim. -cause parallel rays to be focuses at the focal point Diverging lens- are thicker at the rim than the center. -cause parallel rays to diverge from a virtual focal point Thin lens equation -relates the object distance, image distance and focal length of the lens. 1/f = 1/a + 1/b where a= object distance, b = image distance, f= focal distance Sign convention: -image distance is + and real behind the lens since rays of light actually converge there -focal length (f= r/2) is + for a converging lens and - for a diverging lens *converging lenses can produce all types of images depending on the object distance, but a diverging lens can only create a virtual, reduced, and erect image. Magnification -the ratio of the image height to the object height M = -b/a Power of a Lens (D) P = 1/f -Unit is the diopter -P has the same sign as f, so if f is +, P is + and vice versa Therefore, a converging lens has a + power while a diverging lens has a - power If several lenses are placed in series, the total optical power for the system is Followup info: Lens suffer from Chromatic aberration - different colors have different focal points Sherical aberration - a monochromatic beam cannot be brought to the focal point *Least distance of distinct vision - the closest point that a person can comfortable bring an object to their eye is 25 cm for a normal eye (children can bring it closer, the elderly must hold it further).

Structure of Matter: Wave properties of particles, quantum properties of waves;

2. Wave properties of particles ~Elementary particles possess (as do their systems: atoms, molecules) both corpuscular and wave properties (corpuscular-wave dualism) wave property ← diffraction and interference experiments show that light is represented by waves corpuscular property ← photoelectric effect demonstrates that light is a flux of energy in the form of photons. ~Wave theory of matter: Motion of a particle with mass m, momentum p, and energy E is related to the wavelength of de Broglie's wave by λ = h/p And to the frequency by f = E/h ~The equation for wavelength suggests that wavelengths of elementary particles are very short (shorter than visible light). This is why the resolving power of an electron microscope is better than that of an optical microscope. *The energy E of photon (J) is related to the frequency f of the wave and to its wavelength lamda (λ) by E=hf = hc/ λ where h = 6.63 x 10-34 J.s = 4.13x10-15 eV = Planks constant c=velocity of light ~The corpuscular-wave dualism has its consequences: The Heisenberg Uncertainty Principle: it is impossible to determine with perfect accuracy the position and momentum of a particle simultaneously. If the position vector r is being measured, its momentum will change and vice versa. 3. Quantum properties of waves Energy emitted from electromagnetic radiation comes in discrete bundles called quanta. The energy value of a quantum is E=hf = hc/ λ This suggests a particulate nature of electromagnetic radiation where each light particle (photon) carries an energy that is proportional to its frequency. High frequency (short wavelength) → high energy Low frequency (long wavelenth) → low energy ~The corpuscular-wave dualism has its consequences: The Heisenberg Uncertainty Principle: it is impossible to determine with perfect accuracy the position and momentum of a particle simultaneously. If the position vector r is being measured, its momentum will change and vice versa.

Molecular biophysics: Surface tension, adsorption

21. Surface tension -Surface tension is a property of the surface of liquids in which the surface behaves like an outstretched rubber sheet -The cohesive forces (attractive in nature) between liquid molecules are responsible for surface tension. -cohesive forces at the surface are directed toward the center of a liquid and cause the liquid to have a minimum surface area. (this is why droplets of liquid obtain a spherical shape → min surface area) -Below the surface of a liquid, the cohesive forces act on a molecule from all directions and are equilibriated. -However, at the surface of a liquid, the cohesive forces are unbalanced causing a net force pulling the molecules back toward the liquid. -Surface tension is a force acting perpendicularily to the surface of the liquid and its unit is N/m and dimension is kg/s2 Surface tension is dependent on: Temperature → surface tension decreases with increasing temperature Nature of dissolved particles → some particles can decrease surface tension (surface-active particles) *surface tension is NOT dependent on the surface area of a liquid 22. Adsorption -Adsorption is a process that occurs when a gas or liquid solute accumulates on the surface of a solid or a liquid (adsorbent), forming a molecular or atomic film. -Like surface tension, it is the result of surface energy. -Surface-active molecules decrease surface tension and thus facilitate adsorption -At the surface of a liquid, atoms are not wholly surrounded by other atoms of the same type and bonding forces are not equilibriated. Thus the molecules will bind to whatever is available including molecules or atoms of the adjacent phase. This is due to molecules having an attractive force to unlike molecules → van der waals force or interaction. Van der waals forces are created between atoms/molecules with regions of positive and negative charge. -When the molecules of a liquid are attracted to those of a solid it is know as adhesion and it is the phenomenom seen in water sticking to the sides of its container. -Against the tendency of adsorption, is the need to equilibriate the concentration within the liquid. Thus diffusion of solute takes place until an adsorption equilibrium is reached along the boundary of the liquid. -This equilibrium state is described by Gibb's adsorption equation which describes the surface concentration of a substance (mol/m2)

Molecular biophysics: Colligative properties of solutions

23. Colligative properties of solutions Colligative properties of solutions are those that depend only on the number of solute particles and not on the identity of those particles *They are independent of size, form, chemical behaviour, or type: molecules/ions -There are 4 Vapor-pressure lowering (1st Law of Raoult) -if a substance is dissolved in a solvent, the partial pressure of the solvent above the solution will be lower with respect to pure solvent Boiling-point elevation (2nd Law of Raoult) -A liquid boils when its vapor pressure equals atmospheric pressure. If the vapor pressure of a solvent has been decreased by addition of solute particles, more energy is required to reach the boiling point Freezing-point depression (3rd Law of Raoult) -The freezing point of a solution is lower than that of pure solvent because the solute particles interfere with crystalline structure formation Osmotic pressure -Osmotic pressure is the pressure exerted by a column of water that counterbalances osmosis across a semi-permeable membrane → the flow of water molecules from a region of low solute concentration to a region of high solute concentration. -It is dependent on the number of particles present in solution that can't diffuse across the semi-permeable membrane

Molecular biophysics: Osmotic pressure

24. Osmotic pressure -Osmotic pressure is a colligative property meaning that it is dependent only on the number of particles present and not on the nature of those particles. -Osmotic pressure is the pressure exerted by a column of water that counterbalances osmosis across a semi-permeable membrane → the flow of water molecules from a region of low solute concentration to a region of high solute concentration. Thus osmotic pressure opposes the influx of water into a compartment with high solute concentration. Influx of water ceases when the hydrostatic pressure of the inflowing water molecules equals the osmotic pressure of the solution. *Only solute molecules that can't cross the semi-permeable membrane contribute to osmotic pressure. *Vant Hoff Laws quantitatively describe osmotic pressure. a) At constant pressure, osmotic pressure is directly proportional to the molar concentration of a solution Posm = kCm *Where units of Cm are mol/m3 b) Osmotic pressure is directly proportional to temperature Posm = CmRT *where R is the universal gas constant c) At a given osmotic pressure, the same volumes of different solutions (at same temp) contain the same amount of dissolved particles. *analytical solutions have higher osmotic pressures than colloidal solutions bc the latter particles are large and there are less of them in solution. (osmotic pressure is directly proportional to the # of solute particles) *Also dissociated ion solutions have twice higher osmotic pressures as compared to nondissociated solutions of the same concentration. Osmosis Hypotonic solution: one of low solute concentration Hypertonic solution: one of high solute concentration Isotonic solutions: those that have equal solute concentrations -Water will move from a hypotonic to hypertonic solution -A cell will expand and lyse if placed into a hypotonic solution -A cell will shrivel up if placed into a hypertonic solution Biological importance Osmotic pressure is crucial in the proper transport and distribution of nutrients, gases, and wastes throughout the body. -At the arteriole end of a capillary bed, hydrostatic pressure (ρgh) due to the pumping action of the heart exceeds osmotic pressure of the surrounding fluid, thus blood flows out of the vessels into the ECF. -At the venule end of a capillary bed, hydrostatic pressure of blood has dropped while osmotic pressure stays the same thus forcing blood back into the vessels. -The organ responsible for maintaining osmotic balance in the body is the kidney.

Molecular biophysics: Blood pressure measurement, Starling´s hypothesis

25. Blood pressure measurement -Blood pressure is the force per unit area that blood exerts on the walls of blood vessels. -Blood pressure is measured by a sphygmomanometer. (units mmHg) -It is expressed as systolic/diastolic pressure which corresponds to the pressure at ventricular systole over the pressure at ventricular diastole. -Normal blood pressure is 120/70 Method: Auscultation: -The sphygmomanometer is wrapped around the upper arm and a stethoscope is placed on the brachial artery to aid the examiner in the hearing of sound due to blood flow. -The blood pressure cuff is inflated to a pressure above the predicted systolic pressure and the pressure is slowly released. -Above systolic pressure, no sound can be heard bc no blood flows through the brachial artery (the artery has been occluded) -Systolic pressure is recorded as the pressure at which the examiner begins to hear the tapping noises associated with blood flow in phase with heart beat. -This noise slightly increases in loudness and then tapers off as blood flow through the artery becomes steady. -Diastolic pressure is recorded as the pressure at which the tapping sound disappears. Palpation: -A sphygnomanometer is used in the same way but instead of using a stethoscope, the examiner uses two fingers to palpate the first heart beat. -Systolic pressure is recorded as the pressure at which the examiner can palpate the first heart beat (pulse) -not a very reliable method of blood pressure measurement -cannot be used to determine diastolic pressure *blood pressure gradually drops as blood flows from arteries to capillaries due to increased friction between the vessel walls and blood as well as the increase in cross-sectional area of the capillary network (increased peripheral resistance)

Physical and physiological acoustics: Field of hearing

3. Field of hearing The field of hearing is a region of sound intensities and frequencies that induces the effect of hearing. -The field of hearing can be visualized by a graph of frequency (hz) vs. intensity (dB). -Curve of lowest intensity level represents the threshold of hearing. → corresponds to a loudness of 0 phones -The threshold of pain (130Db) represents the upper boundary of hearing and is virtually independent of frequency. -Each curve in between represesnts an intensity level of the same loudness and the frequencies at which it occurs. Between 2 curves can be plotted iso-loudness lines. Speech = 40-60Ph street=60-90 Ph jet=120-130 Ph *Sound of frequency 16 Hz to 16,000 Hz can be perceived by the human ear

Molecular biophysics: State equation of ideal gas

3. State equation of an ideal gas There are 4 assumptions of an ideal gas (i) consists of large number of identical molecules moving with random velocities (ii) all kinetic energy is in the form of translational energy (iii) molecules do not interact expect during brief elastic collisions with their container and themselves (iv) average distance between molecules is greater than their diameter *Ideal gas law: the pressure and volume of an ideal gas is directly proportional to the # of moles (n), and the temperature of the gas P V = n R T Gas constant R= 8.31 J/ mol-1 K-1 Avogadro's number (N): the number of atoms/molecles in one mole N = -If we denote N (total # of atoms/molecules) instead, (N = n x Na ) and we use Boltzmann's constant k = R/Na, then pV =NkT *The state equation of an ideal gas holds for real gases at low pressure and high temperature. In this case, interaction between molecules is minimal and can be ignored. Boyles Law: For isothermal processes -The volume of a gas is inversely proportional to its pressure PV=constant P1V1 = P2V2 *as pressure increases, volume decreases and vice versa Charles Law: For isobaric processes -The volume of a gas is directly proportional to its temperature V/T= constant V1/T1 =V2/T2 *as temperature increases, volume increases and vice versa *pressure and temperature are related in the same way

Use of X-rays in medicine: X-ray apparatus

3. X-ray apparatus An x-ray machine is a machine used to produce x-rays via x-ray tubes. -X-ray machines generating a beam of x-rays from a source (x-ray tube). -The beam is projected through the body. Some of the X-rays will pass through the body and others will be attenuated in the tissues. The transmitted x-rays then fall onto a photocathode which contains luminescent screen or onto a photographic film. Semiconductor plates or image intensifiers. -Images taken with such devices are known as x-ray photographs or radiographs.

Optics in medicine: Extinction, Lambert-Beer law

4. Extinction, Lambert-Beer law EXTINCTION (absorbance): the absorption of a portion of light's energy as it passes through a material. The resulting intensity is given by *Where d is the thickness of the medium and α is the coefficient of absorption -The absorption coefficient is a function of wavelength. Therefore, absorption is a selective process and materials absorb only a distinct wavelength or set of wavelengths. * α is 10-3 m-1 in air, 1m-1 in glass, 106 m-1 in metal. Therefore, intensity decreases to 1/e or 1/2.7 = 36% of its initial value when passed through 103 m of air, 1m of glass, or 10-6 m of metal. -When light is passed through a solution, its absorption coefficient is proportional to its concentration. -where є is the molar extinction coefficient. Its value depends on the type of molecules present in solution, the solvent, and the wavelength of incident light. -The Lambert-Beer Law states that the extinction (absorbance) of a solution is directly proportional to its concentration. ~Also, there is a logarithmic dependence of the intensity of light passing through a solution and the concentration of the sample. * The Lambert-Beer law is used for determining concentration of a substance by measuring the extinction E.

Thermodynamics: First law of thermodynamics; Second law of thermodynamics

4. First law of Thermodynamics -The change in internal energy of a system is equal to the heat added to a system minus the work done by the system. -This relationship stems from conservation of energy ∆U = Q - W W+ when the system performs work W- when work is done on the system by its surroundings Q+ when heat enters the system Q- when heat flows out of the system 5. Second law of Thermodynamics -Entropy of the universe is always increasing. Entropy: a measure of the disorder of a system (JK-1) -Entropy is also known as the thermodynamic function that describes the degradation of energy For reversible isothermal processes: -The entropy of the system and its surroundings does not change ∆ S = 0 For irreversible processes: -The entropy of the system + surroundings (the universe) increases ∆S > 0 • Each spontaneous irreversible adiabatic process leads to an increase in the entropy of the universe. • Spontaneous irreversible processes tend toward equilibrium. At equilibrium, entropy is at it's maximum and disorder is at its greatest → this is the most probable arrangement of the system Entropy of various phases: Entropy of gas > liquid > solid • since molecules in a gas are in state of chaotic motion there is a greater degree of disorder than in liquids and finally solids in which motion is restricted to the vibrational energy of bonds. • Thus, a phase change from a solid to liquid and liquid to gas are accompanied by increasese in entropy Clausias statement: heat will flow spontaneously from a substance at a higher temperature to a substance with a lower temperature and will not flow in reverse. The Carnot Principle: an alternate explanation of the 2nd law -No irreversible engine working between 2 reservoirs at constant temperature can be more efficient than a reversible engine operating between the same temperatures

Radioactivity and ionising radiation: Radioactive equilibrium

4. Radioactive equilibrium In a series of radioactive decay, an equilibrium will be reached at which time identical #s of parent + daughter nuclei decay per unit time. Rate of change of number of parent nuclei is Rate of change of daughter nuclei is -If T1 (half life of parent) << T2 (half life of daughter), then the activity of the parent decreases due to its short half-life and and the activity of the daughter increases initially and then decreases due to its own decay rate *no equilibrium -If T1>T2, then the activity of the parent decreases according to its decay rate. -and since the half life of the daughter is short, the # of daughter nuclei increases up to a maximum and then their activity decreases proportionally to the parent *transitional equilibrium -If T1>>T2, (the half life of the parent is so long that it does not decay during measurement) then the activity of the daughter will rise until it reaches that of the parent. Thus the # of nuclei formed will equal the number that is decaying -At this point the parent and daughter nuclei are in a state of permanent radioactive equilibrium. -Thus the ratio of the number of parent and daughter nuclei equals the ratio of their half lives.

Electricity in medicine: Rest membrane potential

4. Resting membrane potential (Donnan's Potential) -Every neuron has a seperation of positive and negative electrical charge across its cell membrane.. -The electrical potential difference is about 60 - 70mV at rest and is known as the resting membrane potential. -The negative resting membrane potential is a result of the membrane being significantly more permeable to K+ ions than Na+ ions. Thus K+ diffuses down its electrochemical gradient into the cell to join anionic proteins. Na+ remains outside of the cell. Since , by convention, the potential outside the cell is arbitrarily defined as zero, and given the relative excess of negative charges inside the membrane; the potential difference across the membrane is expressed as a negative value. *The potential difference across the membrane can be measured with two glass microelectrodes

Molecular biophysics: Kinetic theory of gases, Equipartition theorem, Bernoulli equation, equation of continuity

4. Theorem of the equipartition of energy -According to Maxwell's theorem of the equipartition of energy, each degree of freedom has an average energy of (1/2)kT. -When heat energy is supplied to a molecular system, it is fuels vibrational and rotational motion -The number of degrees of freedom, i, depends on the number of atoms in a molecule. -i=3 for single atom gas -i=5 for molecules composed of two atoms -i=6 for molecules composed of 3 or more atoms. Kinetic Theory of Gases- The total energy Uk of translational motion of 1 mole of a single atom is given by K = Uk = (3/2)RT *Temperature is related to kinetic energy ~The spectra of a molecular system contains lines corresponding to excited vibration and rotation states of molecules. Small energy differences correspond to changes between states thus these lines can be observed in the infrared region.

Physical and physiological acoustics: Weber-Fechner´s law in acoustics

4. Weber-Fechner´s law in acoustics -The dependence of loudness on the intensity of the stimulus is described by Weber-Ferchner's Law : the change in loudness (∆L is proportional to the relative change in the stimulus Loudness -Is a physiological quantity that describes the perception of sound. -Intensity of sound of frequency 16Hz to 16kHz that comes to the ear results in hearing and the perception of sound is described by its physiological quantity loudness. - Sound perception is subjective and the ear is sensitive to various frequencies to various extents, therefore loudness is NOT proportional to intensity -Units of Loudness are the phones (ph)

Radioactivity and ionising radiation: Physical, biological and effective half-life

5. Physical, biological and effective half-life -unit of half life is time (days, secs, hrs, years, whatever is appropriate) Physical Half-life: (Tf) The time it takes for ½ of the radioactive nuclei in a sample at zero time to decay Biological Half-life: (Tb) The time required for half the quantity of a drug or other substance deposited into a living organism to be metabolized or eliminated by normal biological processes. Effective Half-life: The time required for the radioactivity of material administered or deposited into an organism to be reduced to half its initial value by a combination of biological elimination processes and radioactive decay. The relative disappearance rate λef is the sum of the excretion rate and the decay rate.

Optics in medicine: Scattering of light

5. Scattering of light Light may be scattered in two ways: Rayleigh Scattering -occurs when light passes through a dilute gas and interacts with its molecules. ~In order for interaction to occur, the molecules must have a size much smaller than the wavelength of incident light. -the interaction occurs as the electric field of the incident electromagnetic wave induces an oscillating magnetic moment that emits an electromagnetic wave of the same frequency and wavelength → elastic scattering ~light is scattered into all directions but its intensity is very low ~The ratio of the intensity of scattered light to incident light is -k is a constant, M is the molar mass, λ is the wavelength of incident light -this relationship suggests a very strong dependence of scattering intensity on incident wavelength. Violet light (short wavelength) scatters much more intensely than does red light (long wavelength). -Red light which has a wavelength 2 x that of blue light scatters 16 x less intensely than blue light. -If the concentration is known, the molar mass can be calculated from this equation Raman Scattering -Raman scattering occurs when light interacts with molecules and the resulting spectrum has added spectral lines corresponding to short and long wavelengths of scattered light. -Two types of energy changes can occur in the scattering molecules upon interaction with light ~the vibrational and rotational energy of the molecules can increase (the photons transfer some of their energy) → the scattered photon has a lower energy ~the vibrational and rotational energy of the molecules can decrease → the scattered photon has a higher energy *the probability of Raman scattering is very low and the intensity of the spectral lines is very weak (cannot be detected by the naked eye) → can use laser to increase intensity, photomultipliers to detect radiation.

Physical and physiological acoustics: Ultrasound generators

5. Ultrasound generators -Ultrasound waves have frequencies greater than 20 kHz -these are beyond the frequency that humans can detect. -Ultrasound waves can be produced by mechanical, magnetic, or piezoelectric generators. -Piezoelectric generators are important in medicine. mechanical waves are generated by suitable materials vibrating due to a high-frequency alternating electrical field in a liquid medium (oil) -Piezoelectric generators are capable of producing intensities of 10 W/m2. -The velocity of an ultrasound wave is the same as normal sound but ultrasound has a much higher frequency and thus shorter wavelength. λ = v/f ex: determine the wavelength at 1MHz. =1500/(106) is 1.5nm

Use of X-rays in medicine: X-ray absorption

5. X-ray absorption Attenuation = absorption The intensity of a monchromatic x-ray beam propagating in some medium decreases according to Two processes cause the attenuation of X-rays: 1) Photoelectric effect ñ photon transfers its whole energy to an electron, therby ionising the atom. After leaving the atom, the electron induces ionization and excitation until its excess energy is lost -Therefore, x-rays do not cause ionization and excitation directly but rather through the high energy electrons that are released as a result of their collisions with atoms -This process occurs during Characteristic x-ray emission nad is accompanied by a line spectrum -Attenuation in bone due to the photoelectric effect is higher in bone than in soft tissue because the effective atomic number of bone is higher -tissues that attenuate x-rays well appear white on a radiograph while those that do not are black -Bone is seen as the unexposed region on the x-ray film (white). 2) Compton scattering -During compton scattering a photon transfers only a fraction of its energy to an electron causing a scattering effect. -The scattered photon moves in a changed direction with a lower energy hf. (longer wavelength) This type of interaction does not depend on the atomic number of the absorber and the probability of its occurence depends on incident photon energy. -compton scattering plays an important role in x-ray contrast *The total linear mass attenuation coefficient is equal to the sum of the attenuation coefficients for the photoelectric effect and compton scattering

Radioactivity and ionising radiation: Absorption of gamma radiation

6. Absorption of * radiation -Gamma radiation is high energy electromagnectic radiation that is highly penetrating. -Only dense materials such as lead are capable of absorbing such high energy radiation. -The attenuation coefficient for gamma radiation is the sum of the three attenuation coefficients for the photoeffect, compton scattering, and formation of electron-positron pairs. The photoelectric effect: a photon will transfer all of its energy to an electron in the shell of an atom with which it is interacting. A part of this energy will contribute to the ionization energy required to completely remove an electron from an atom. The remainder of the energy will be converted to the kinetic energy of the electron as it leaves the atom. Probability of absorption due to the photoelectric effect: -Thus the photoelectric effect is most probable at low energies and in heavy absorbers. -This type of absorption is most probable in tissues with high Z - for ex: bone Compton scattering- occurs at high photon energies -In this type of interaction, the photon interacts with a free electron in the absorber. -Part of the photon's energy is transferred to the electron and the electron and photon move away from each other in a scattered direction. The resulting photon has a lower energy. - The energy of the resulting photon is dependent on the scattering angle -The highest decrease is expected for backscattering where the angle is 180 degrees. -This process may be repeated several times until the photon donates the last bit of its energy via the photoelectric effect. Formation of electron-positron pairs: probability of this type of absorption is proportional to the energy of the photon. -also more probable in absorbers with higher atomic numbers -At high energies, the photon will disappear and its energy will be converted to the rest mass of the electron-positron pair and their kinetic energy. Half-thickness: the thickness of the absorber which reduces the intensity of incident radiation by 50% Half-layer: the mass per unit area of absorber (kg/m2) with density p that reduces the intensity of incident radiation by 50%

Thermodynamics: Definitions of thermodynamic functions (U, H, S, F, G)

6. Definitions of Thermodynamic Functions. (U,H,S,F,G) Internal Energy (U) (joules): -The change in internal energy of a system is equal to the heat added to a system minus the work done by the system. -This relationship stems from conservation of energy ∆U = Q - W W+ when the system performs work W- when work is done on the system by its surroundings Q+ when heat enters the system Q- when heat flows out of the system Enthalpy (H) (j.mol-1) H = U + p∆V -This state function expresses heat changes at constant pressure (of isobaric processes) -The change in enthalpy is equal to the heat absorbed or given off by a system at constant pressure. Exothermic reaction: (∆H -) heat is given off by the system Endothermic reaction: (∆H+) heat is added to the system *For spontaneous exothermic chemical processes occuring at constant pressure, heat is given off, the enthalpy of the system decreases and the system reaches equilibrium. Entropy (S) (j.k-1) Entropy: a measure of the disorder of a system (JK-1) -Entropy is also known as the thermodynamic function that describes the degradation of energy For reversible isothermal processes: -The entropy of the system and its surroundings does not change ∆ S = 0 For irreversible processes: -The entropy of the system + surroundings (the universe) increases ∆S > 0 • Each spontaneous irreversible adiabatic process leads to an increase in the entropy of the universe. • Spontaneous irreversible processes tend toward equilibrium. At equilibrium, entropy is at it's maximum and disorder is at its greatest → this is the most probable arrangement of the system Entropy of various phases: Entropy of gas > liquid > solid • since molecules in a gas are in state of chaotic motion there is a greater degree of disorder than in liquids and finally solids in which motion is restricted to the vibrational energy of bonds. • Thus, a phase change from a solid to liquid and liquid to gas are accompanied by increasese in entropy Free Energy (F) (Joules): -also known as the Helmholtz function, it is defined by: F = U - TS -the unit of free energy is Joule -its decrease equals max work done in an isothermal reversible process Interpretation: -The total energy is composed of the free (available) E that can be used for work done at isothermal ireversible process and of the [TS] portion of energy which is not useful. F=U-TS lower=more work *A spontaneous irreversible process occuring at constant temperature is accompanied by a decrease in free energy which reaches a minimum at equilibrium Free Enthalpy (G) (Joules) Represents the maximum amount of energy released by a process occuring at constant temperature and pressure that is available to perform useful work. G = H - TS *the unit of free enthalpy is Joule -A spontaneous process occuring at constant temperature and pressure is accompanied by a decrease in free enthalpy which reaches a minimum at equilibrium -∆G = negative for sponateous processes

Optics in medicine: Dispersion of light

6. Dispersion of light Dispersion: separation of white light into its spectral components of different wavelengths due to various velocities of the spectral components and resulting refractive indices. -Although the speed of light for all wavelengths in a vacuum is the same, light of different wavelengths travels through a medium of refractive index n, with different velocities. -The speed of light through a medium is a function of its wavelength and the refractive index of a medium is therefore a function of the wavelength of incident light. -The effect is seen when white light is incident at an angle upon a glass surface where the two sides are nonparallel (prism). - The nonparallel surfaces act to increase the angular separation between wavelengths. -Thus each color has its own angle of deviation. ~Red has the longest wavelength, smallest refractive index and thus it is bent at an angle much smaller than that violet light which has a short wavelength and large refractive index.

Physical and physiological acoustics: Audiometry

7. Audiometry -The testing of hearing is most often carried out by establishing the threshold of hearing, the softest sound which can be perceived in a controlled environment. -It is typical to do this testing with pure tones by providing calibrated tones to a person via earphones, allowing the person to increase the level until it can just be heard. -Various strategies are used, but pure tone audiometry with tones starting at about 125 Hz and increasing by octaves, half-octaves, or third-octaves to about 8000 Hz is typical. -Hearing tests of right and left ears are generally done independently. The results of such tests are summarized in audiograms. L= 10log I / Io (db)

Emission, ionization and excitation

6. Emission Spectrum of the hydrogen atom ~Electrons within an atom can be excited to higher energy levels when heat or other forms of energy are applied. The excited state is not stable and short-lived. Thus the electron returns rapidly to its initial state simultaneously emitting energy in the form of a photon. ~The energy of the released photon equals the energy difference between the excited and initial states of the electron ~Since there are discrete values of electron energies only certain energies (frequencies, wavelengths) may be emitted by the atom. ~The different electrons within the atom will be excited to different energy levels and each will emit a photon characteristic of the energy transition it undergoes. ~Thus a line spectrum is produced with each line corresponding to a specific electron transition. ~Each element produces a unique emission spectrum that can serve as its fingerprint. ~The set of spectral lines observed during transitions from all higher levels into a certain energy level corresponding to the given n is called a series. The atomic emission spectra of hydrogen is composed of several series Lyman Series: lines corresponding to e- transition from higher energy levels into the ground state (n = 1) I-observed in the ultraviolet region of light (high energy emission) Balmer series: lines corresponding to e- transitions from higher energy levels into n = 2 -observed in the region of visible light Paschen series: lines corresponding to e- transitions from higher energy levels into n = 3 (Paschen's series) and to higher values of n -observed in the region of infrared light (low energy emission) *The greatest energy emitted is in the Lyman series and corresponds to an electron falling from n = to n = 1 7. Ionization and Excitation Electrons with minimum E are in the ground state Excitation: Electrons within an atom can be excited to higher energy levels when heat or other forms of energy are applied (i.e. absorption of a photon). ~The energy absorbed MUST equal the energy difference between the excited and initial states of the electron ~The excited state that is formed is not stable and short-lived. ~Thus the electron rapidly transits to a lower energy simultaneously emitting energy in the form of a photon (energy corresponds to energy difference between final and initial states). -of lower energy Luminescence- energy transitions from higher to lower states are accompanied by the emission of radiation in the form of photons. 2 types: Flourescence - spontaneous deexcitation releasing a photon (occurs at 10-5 - 10-7s) The electron can transition into a metastable state from which transition into the ground state is not allowed (δl ≠ +-1), a metastable state. Phosphorescence - an electron remains in the metastable state and emits radiation at a later time Ionisation: occurs when an e- absorbs energy hf greater than its binding energy (the work that must be done/energy that must be supplied to completely remove an e- from an atom). ~the energy absorbed must overcome the electrostatic forces holding the proton to the electron The remainder of energy is converted to kinetic energy of the e- and the e- is able to escape the atom. Photoeffect E + Eb = 0 Eb=-E E= Eb + Ek Photoeffect hf= Eb + ½mv2 where hf is the energy absorbed ~Binding energy (ionization potential) varies. *Lowest values are for valence electrons *Heavy atoms have much higher binding energies (Z2 x higher than in the H atom) • a positively charged ion is formed by ionization • an ionized atom is not stable. i.e. electron loss increases the energy of the system • the atom tends to return to it's ground state with simultaneous emission of fluorescent radiation

Physical and physiological acoustics: Physical principles or diagnostic use of ultrasound

6. Physical principles and diagnostic use of ultrasound At the boundary of tissues of different acoustic impedances z, the reflection and refraction of sound waves is observed according to the equation Due to energy loss, sound waves are weakened in each medium to certain extents The absorption of ultrasound in gas is much higher than in liquid -Ultrasound is used in medical imaging to visualize muscles, tendons, and many internal organs -A piezoelectric generated is used to generate ultrasound waves that are directed into the area to be examined - a water-based gel is placed between the patient's skin and the probe to increase the efficiency of sound transmission -The sound waves are partially reflected from layers between different tissues. Specifically, sound is reflected anywhere there are density changes in the body -The time taken for echoes to return back to the transducer along with some other parameters are used to create the image . -An ultrasound produces a reflection signature which reveals details about the inner structure of the medium . -The effects of ultrasound are mechanical - cavitations thermal - increase the temp within regions ultrasound is absorbed electrochemical - decomposition of some high molecular weight compounds and polymerization biological - structural changes, changes in the permeability of cell membranes and conductivity of nerves, alteration of pH, analgesic effects, etc. -The biological effects of ultrasound depend on intensity The intensity of ultrasound for diagnostic purposes must not exceed 1.5 W/m2, or irreversible morphological changes may occur. -Can use ultrasound for pre-natal screening, internal medicine, gynecology. frequencies >20khz

Use of X-rays in medicine: X-ray contrast;

6. X-ray contrast -The intensity of an x-ray beam passing through a patient decreases due to attenuation by the photoelectric effect and compton scattering. -The degree of attenuation varies for different tissues. -The contrast Cr of traditional x-ray image (shadow image) resulting from different x ray absorption coefficients in various tissues (of various density and effect atomic number) is defined by where I2,I1 are different x ray intensities -The contrast of the resulting photographic plate is evaluated by brightness *Since the linear attenuation coef. of bone or soft tissue decreases with increasing incident photon energy, the contrast between bone and soft tissue decreases with increasing accelerating voltage installed in the x ray tube. -In oder to differentiate between tissues with similar absorbing properties, contrast materials are added. Positive contrast: strong absorbers Negative contrast: weaker absorbers The following conclusions can be drawn according to the above equation: A: the contrast is negative: more absorbing material will lower x-ray beam intensity on the photographic film B: contrast doesn't depend on the thickness of the irradiated object C: for empty spaces the contrast is positive

Radioactivity and ionising radiation: Absorption of alpha and gamma radiation

7. Absorption of * and * radiation Alpha particles- Due to their relatively large mass and electric charge, the ionization losses of energy are high and several 1000s of ion pairs may be formed during the absorption of one alpha particle. -Energy losses due to ionization and excitation are approx 50/50. -The range of penetration is very small. i.e. with an energy of 10 MeV, penetration is about 10cm in air and several µm in soft tissue or water. → therefore apha particles can have a negative biological effect when passing through tissue bc all energy is concentrated into several micrometers of tissue. Beta- -Ionization and excitation represents the highest energy losses of electrons during their passage through an absorber. -Their specific linear ionization is lower than alpha because of the lower mass to charge ratio. -In addition to ionization and excitation, Bremsstrahlung can also be produced. -But the energy losses due to bremsstrahlng are relatively low and more important at high energies -Bremsstrahlung is high energy quanta of electromagnetic radiation that is produced when accelerated electrons are stopped in the electrical field of an atomic nucleus. -The intensity of Bremsstrahlung is proportional to the atomic number of the absorber and the electron's energy. -Bremsstrahlung radiation produces a continuous energy spectrum The intensity of a beta beam decreases according to:

Thermodynamics: Chemical potential

7. Chemical potential (µi) is the measure of the affinity of a given substance -This formula indicates that at a constant temperature and pressure, a partial change in the free enthalpy corresponds to a partial change in the # of moles. i.e. a change in composition is related to a change in energy -Which reactions will take place in system and their rate depend on their chemical potential and on the amount of substance. Chemical reaction change composition of system, therefore state changes as well; ? states ? ?Energy, and each trngle E can be expressed as product of extensive and inextensive factor unit is (J.MOL-1) delta G= partial change enthalpy delta n= partial change in no of moles 8. Calorimetry -Method for measurement of thermal energy. -Calorimeters used to measure heat. Dewar's vessel is commonly used -it is a mixing vessel Water value k = the amount of water in (kg) which requires the same amount of heat to increase its temp by 1 deg celcius as that consumed by the device The equation for the calorimeter is: Q = (M+K)c∆T Where K = water value (kg) Q=Heat supplied (J) M= mass of heated water Generally Q = mc∆T C = specific heat capactity T = temperature change m = mass of substance Specific heat is the amount of energy required to raise the temperature of 1kg of substance by 1 degree C. Constant-volume calorimetry -The apparatus consists of strong steel container in which the reactants are placed. The bomb is placed into an insulating container filled with a known amount of water and is fitted with a timer and thermometer. The initial temperature is measured and the reaction is ignited. Heat given off during the reaction is absorbed by the bomb and water and the temperature of the apparatus rises. -Since no heat enters or leaves the system, the process is adiabatic, and ∆Q = 0. Thus it is possible to determine the heat of the reaction. * Calorimetry can also be used for energy requirements of an organism as well as the evaluation of energy content in nutrients.

Molecular biophysics: Law of Laplace

7. Law of LaPlace Describes the relationship between the pressure difference (∆P) across the surface of a closed circular membrane and its wall tension T (N/m). ∆P = T (1/R1+1/R2) Where R1 and R2 are the main radii of the membrane curvature at a given point. • The greater the pressure change, the greater the tension in the wall of the membrane • Smaller radii are able to withstand relatively high blood pressures (i.e. capillaries) -For a cylindrical form of the membrane, one of the radii is infinitely large and thus: ∆Pcylinder = T/R -For a sphere where R1=R2=R and thus ∆P = 2T/R The Law of LaPlace is of great importance in physiology → it allows us to calculate the tension in the walls of vessels of a given radii undergoing certain changes in pressure.

Electricity in medicine: Measurement of el. conductivity in solutions

7. Measurement of electrical conductivity in solutions Both intracellular and extracellular fluids contain a sufficient amount of ions which makes them good conductors of electric charge. The property of a solution to conduct electrical current is described by the Specific Conductivity K which is inversely proportional to ρ (resistivity) Molar Conductivity: used to relate the dependence of specific conductivity on ion concentration *Molar conductivity is dependent on temperature. It increases slightly. In dilute solutions, where ions move around independently, the molar conductivity is additive Conductometry *If only one type of electrolyte is present in solution, then electrical conductivity is directly proportional to the concentration of the electrolyte. Therefore, concentration can be estimated by measuring specific conductivity (k) Measurement of specific conductivity is carried out by using a conducting vessel with two platinum electrodes. The vessel contains the solution and is located in the Wheatstone bridge circuit whose resistance is unknown. Before, specific conductivity can be calculated, l and q must be determined. The ratio of l/q can be determined experimentally by first filling the vessel with a standard solution of known specific conductivity. The ratio l/q is called the capacity C of the reacting vessel. With this information, the vessel is then filled with the solution and the resistance is measured. Specific conductivity is calculated and the concentration of the solution is estimated since specific conductivity and concentration are proportional

Optics in medicine: Refraction and its use in spectroscopy

7. Refraction of light and its use in spectroscopy Reflection -the rebounding of light rays at the boundary of a medium. Governed by the law of reflection which states that the angle of incidence is equal to angle of reflection Refraction - the bending of light rays at the boundary of two media. -This occurs because the speed of light in media is less than that in a vacuum. -A ray will bend toward the normal when it enters a medium in which its wave velocity is slower. -The refractive index n is defined as the ratio of the speed of light in a vacuum c to the speed of light in a particular medium v. . Snells Law: predicts the bending of light rays as they pass from one media to another. ~If the refractive index of the second medium is greater than that of the first, the light rays will bend toward the normal ~If it is smaller, the light rays will bend away from the normal (angle of refraction will be greater than the angle of incidence) *The frequency of the wave does NOT change as light passes from one medium to another. *only its wavelength and speed change *wavelength of light is reduced when traveling through a medium Total Internal Reflection -When light passes from a medium with a higher index of refraction to one with a lower index of refraction, it bends away from the normal. -If the angle of incidence is increased to the critical angle, the refracted ray will be at an angle of 90º to the normal and will emerge parallel to the surface of the boundary. -Total Internal Reflection occurs when the angle of incidence is greater than the critical angle and the light ray is reflected back into the original material. * Application of total internal refraction is endoscopy and optic fibers. * Refraction is applied in spectroscopy to identify different molecules according to how they refract light. -Using a prism spectroscope, the dispersion of light according to wavelength is studied. -A diverging beam of white light is emitted from a source and the rays are collimated and made parallel. The rays are dispersed through a prism and passed through an objective lens which forms the corresponding spectrum on an indicator (photographic plate or photomultiplier).

Use of X-rays in medicine: Use of X-rays for diagnostic purposes

7. Use of X-rays for diagnostic purposes -X-rays can be used for diagnostic purposes due to the fact that different tissues in the body absorb x-rays to various extents -X-rays emitted by the x-ray tube pass through a certain body part and are then viewed on a screen do to the luminescent properties of x-rays (summation image) or on photographic film due to the photographic properties of x-rays. -the image produced is a summation image -depth can only be assessed by moving the patient -Electronic image transfer can be used to increase the brightness. This is acheived by acceleration of the e- produced by the photoelectric effect as they pass through the body Because x-rays are damaging, least dose is desirable. Scintigraphy: technique used to lower the dose of radiation for patients during examination This technique utilizes a photographic film that contains a photographic emulsion on both sides which increases the sensitivity The density of blackening is equal to The difference between the densities of two neighboring areas is called the radiographic contrast *photographic plates provide better resolution than due luminescent screens Radiography : X-rays are highly penetrating, and x-ray machines are used in radiology to take pictures of bones and teeth. They can also be used to diagnose fractured bones. Imaging of the digestive tract can be done with the help of barium sulphate as a contrast medium.

Electricity in medicine: Action potentials of heart muscle and their detection

9. Action potentials of heart muscle and their detection -The heart contracts due to electrical stimulation controlled by the SA node (pacemaker of the heart) in the right atrium which causes a path of depolarization to the AV nodes and the rest of the conducting cells of the heart. SA node causes atrial contraction AV causes ventricular contraction Repolarization occurs and the cycle repeats. -The shape of the action potential in cardiac conducting cells is a wide plateau and the duration of the action potential is much longer relative to that of neurons. An electrocardiogram is used to detect the action potential of the heart. • P wave corresponds to atrial depolarization • QRS corresponds to ventricular depolarization • T wave- ventricular repolarization

Electricity in medicine: Action potential and its detection

8. Action potential and its detection - Action potentials are generated by neurons after being excited by a stimulus of sufficient magnitude. -A neuron at rest has a membrane potential of -70 mV due to the unequal distribution of ions across the neuronal membrane. Thus the inside of the cell is negative (anionic proteins & higher K+) and the outside is positive (higher Na+). -If a neuron is sufficiently stimulated, some Na+ channels open and sodium enters the cell down its electrochemical gradient. This causes the membrane potential to rise slowly. Once it reaches a threshold potential of -60 - -50 mV, an action potential is generated and all voltage gated Na+ channels open. Na+ rushes into the cell and depolarizes the membrane to a positive value. -An action potential is an all or none response. This means that whenever a threshold potential is triggered, an action potential of consitent size and duration is produced irrespective of the strength of the stimulus. -K+ channels then open and K+ rushes out of the cell down its electrochemical gradient causing repolarization of the membrane to a negative value. → hyperpolarization -During an action potential it is impossible to invoke another → absolute refractory period -Immediately following an action potential it is difficult to initiate a response from the neuron (need stronger stimuli) → relative refractory period. *The refractory period is important in the one way conduction of the action potential along the length of the neuronal axon. -Mylenated axons propagate action potentials much faster than unmyelinated axons through saltatory conduction. In this method, regions of the axon are surrounded by an insulating myelin sheath and the neuronal membrane is only permeable to ions at the Nodes of Ranvier. Thus the action potential jumps from one node to the next. Detection of Action Potentials: An axon can be stimulated using two electrodes and some external source of voltage. One electrode is placed inside the axon and the other on its surface. • If the external electrode is positive, hyperpolarization of the membrane occurs (membrane potential decreases) • If the internal electrode is positive, depolarization occurs (membrane potential increases) -Rheobase -magnitude of current just sufficient to excite a given nerve or muscle. -Chronaxie -duration of reponse time interval if the current of twice the rheobase is applied. *resting membrane potential and the shape of the action potential varies for different types of excitable cells (cardiac, neuronal, muscle) Q

Molecular biophysics: Gibbs´s phase rule, phase chart of water; Liquid crystals

8. Gibbs´s phase rule Gibb's Law: The degree of freedom of a heterogeneous system is uniquely determined by the # of phases that coexist together and by the # of independent portions that created the system. -Relates # of components, phases and degrees of freedom of a dispersion system p + d = c +2 p-phase, c-chemical component, d-# degrees of freedom of system -A Dispersion system has at least 2 phases: dispersive portion & dispersive medium dispersive portion- dispersed in the medium, not continuous dispersive medium- continuous Heterogeneous- a boundary exists between the dispersive portion and the dispersive medium (water & oil) -if the refractive index of the two phases or portions is not the same, heterogenity in light transmission can be observed. Homogeneous- 2 portions existing in a single phase. The dispersion portion is dispersed in the medium in the form of particles so small that they cannot be observed (sugar in water). Such systems are also opticaly homogeneous. -Single phase systems can be made of more than one component, thus the law of Gibb's related the number of components, phases, and degrees of freedom *The # of degrees of freedom of a heterogenous system is the # of independent variables defining the equilibrium state (pressure, temp, concentration) and which can be individually changed without change of # of phases. i.e. when 2 phases are in equilibrium (gas & liquid) the system has 1 deg of freedom (either Pressure or Temp); however, with 3 phases (sol/liq/gas) there are 0 degrees of freedom -The latter is the case at the triple point

Optics in medicine: Interference and light reflection

8. Interference of light -Evidence for the wave character of light is provided by the interference and diffraction of light. -Interference is caused by the interaction of light waves which leads to the addition of their amplitudes. -Interference can be observed in two ways: • When light passes through a thin layer of medium with refractive index n between two parallel planes and the refractive and reflected waves interact with one another. • During diffraction in which light deviates from its original path when passing through a narrow slit. -Interference can only observed with coherent waves -light waves whose phase difference does not change with time. In relation to each other, they differ in wavelength, frequency, and phase shift. -Interference can be constructive or destructive in nature: -Constructive interference (maximum) - occurs if the path difference is an integer multiple of wavelength -regions where two light waves interfere constructively appear as bright spots (max light intensity) on the screen -Destructive inteference (minimum) - appears if the path difference is an odd number of half wavelength -regions where two light waves interfere destructively appear as dark areas on the screen (min light intensity) The path difference and phase difference of interfering light waves are related by: Phase difference: Wavelength of a light wave changes in a medium with refractive index n according to New phase speed is: The phase difference between a wave traveling path d1 in a medium with refractive index n1 and a wave traveling path d2 with a refractive index of n2 equals: The phase difference is also equal to the difference between optical paths multiplied by Where according to the Fermet principle, the optical path is equal to the product of refractive index and geometrical path *When light passes through a thin layer of medium with a refractive index of n between two parallel planes, the interference of refracted and reflected waves takes place. Difference in optical paths is given by (when n of air =1) Where d is the thickness of the layer, α is the angle of incidence, λ is the wavelength of applied light. When light encounters a medium of higher refractive index, the reflected wave undergoes a phase shift equal to π and λ/2 (path change that corresponds to π) must be added to the right side of the equation. -The interference of the reflected and refracted wave will increase in intensity if -and will decrease if -when white light passes through a thin layer, maxima and minima on the screen appear for each wavelength individually (soap bubbles)

Structure of Matter: Structure of electron shells in atoms

8. Structure of electron shells in atoms Electron configuration is the pattern by which electrons fill an atom. Electron filling is governed by two principles: 1. The arrangement is at minimal energy 2. No two electrons within the atom occupy the same quantum state -electrons fill shells and subshells in order of increasing energy and each subshell is filled completely before the next subshell begins filling -in the case of heavy atoms, higher shells can fill prior to lower ones if the total energy associated with the shell is lower in the higher shell. -highest # of electrons in a shell is 2n2 Closed shell/subshell: one that is completely occupied by electrons s (2 e-), p (6 e-), d (10e-), f (14 e-) -Total orbital and spin angular moment =0 and distribution of the electrons' eff charge is symmetrical. Hund's Rule: within a given subshell, orbitals are filled so that there are a maximum number of half-filled orbitals with parallel spins. -electrons prefer empty orbitals due to the repulsion of neg. charges that occurs in filled orbitals -filled orbitals contain 2 e- with opposite spin 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6, 5s2, 4d10, 5p6, 6s2, 4f14, 5d10, 6p6, 7s2, 6d10

Use of X-rays in medicine: X-ray therapy

8. X-ray therapy -The use of x-rays in therapy is based on the principle that certain types of cells are more susceptible to x-ray damage than others (i.e. young and actively dividing cells such as are present in cancerous growths) -Used in destruction of malignant tumours. Process: -Low energy photons must be filtered out from the x-ray beam because they cause damage to superficial tissues. (can use Zn, Cu, Al filters) -This results in a more homogeneous x-ray beam that can be targeted to a particular tissue. -The more narrow the the energy range of photons, the greater the quality of the beam. -Quality is assessed by the HVL (half value layer) which reduces initial intensity by 50%. The quality factor is : HVL1/HVL2 and should be about 1.5. HVL1 absorbs x-rays with longer wavelength and HVL2 absorbs higher wavelength Absorbed dose of radiation or exposure: the energy absorbed per unit mass. =E/m (unit is Grey Gy) I Gy = J/kg There are several types Air dose Surface dose Depth dose -To avoid superficial damage, high energy photons are positioned sufficiently distant from the patient; -In the treatment of superficial lesions, deep tissue damage is avoided by using low energy photons near to the skin. -Physicians and technicians must be protected by shielding. The radiation hazard has to be checked by film dosemeters. (1mGy/week is max) -Gamma ray therapy has become increasingly more common and often replaces x-ray therapy. It utilizes high energy photons emitted by radioisotopes

Structure of Matter: Atomic nucleus

9. Atomic nucleus The atomic nucleus is formed by nucleons: protons and neutrons ~It can be described by: Atomic # = Z, Mass # = A, Neutron # = N = A - Z ~The total electrical charge Z of a nucleus is 1.6 x 10-19 C ~Most of the atom's mass is found in the nucleus (nucleon mass is 2 x 103 times greater than electron mass) ~The mass of atoms is expressed in atomic mass units (AMU) 1 AMU = 1/12 the mass of a C-12 atom. 1 A.M.U.=1.66x10-27 kg = energy equivalent 931MeV Isotopes- nuclei of the same element with same proton #, different neutron # (same Z, diff A) Isobars- nuclei with equal # nucleons, # different protons (same A, diff Z) Isomers- same # of protons and neutrons but different energies of nuclei -not stable, e- fall to lower energy levels → emit radiation Radius of proton = 1.23x10-15 m Radius of heavy atoms can be calculated Ra= (1.23x10-15) x A1/3 *atomic radii decrease from left to right on the periodic table and increase down a group Nuclear forces hold an atom together via the strong interaction ~Range is 10-15 m ~Strength is not dependent on nucleon charge ~The strong interaction is the strongest force at this distance Energy e- =0.51 MeV Energy p =938MeV Energy n =939MeV Radius r =1.23x10-15 m

Use of X-rays in medicine: Depth dose

9. Depth dose This is one of the various types of dose (exposure). Depth dose is the amount of radiation absorbed at a certain depth below the surface. -Since intensity of radiation from a point source of radiation decreases proportionally to the squared distance from the source, the depth dose (Dd) observed at a depth d is related to the surface dose (Ds) as: where FS = distance between the focus of the X ray tube and the body surface The implication of this relationship is that objects closer to the source are more exposed to x-rays than objects further away. -Geometrical considerations play an important role in x-ray therapy -To avoid superficial damage, high energy photons must be positioned sufficiently distant from the patient; -In the treatment of superficial lesions, deep tissue damage is avoided by using low energy (low accelerating voltage) photons near to the skin. -Physicians and technicians must be protected by shielding. The radiation hazard has to be checked by film dose meters.

phase chart of water; Liquid crystals

9. Phase chart of water -It is a plot of temperature vs. pressure in which there are well defined areas corresponding to the solid, liquid, and gas phase. -The 3 phases are separated by lines of sublimation, fusion, and evaporation. These lines represent the equilibria that exists between the two phase area they dissect. Critical point -a gas cannot undergo phase change into a liquid beyond this temp and pressure Triple point - at this temp and pressure, all three phases exist in equilibrium

Thermodynamics: Thermoregulation in organisms

9. Thermoregulation in homiothermic organisms -Temperature effects the rate of chemical processes in the body as proper enzymatic action is dependent on an optimal temperature of 37 ºC. -In order to maintain a constant temperature and proper functioning of organs, heat production as a result of chemical processes and muscle activity must be offset by heat loss to the surroundings. -A constant body temperature is maintained by 4 different types of thermal losses. Radiation: Each body of a certain temperature emits energy in the form of electromagnetic waves. Radiation in the infrared region of the spectrum is given off at temperatures corresponding to the surroundings. -According to the Stephan-Boltzmann Law, the energy irradiated by a black body is proprtional to the 4th power of temperature. -Thus the net quantity of heat lost by the organism is equal to the difference between the 4th powers of the temperature of the body and its surroundings -The quantity of heat that irradiates is dependent on blood flow to the skin and is decreased by clothes and other insulating materials. -contributes to 40 -60 % of total thermal losses Flow of heat: Blood distributes heat to various parts of the body. To increase heat loss, blood flow to the skin is increased. To decrease heat loss, skin is diverted from the surfaces of the body by constriction of skin capillaries Conduction of heat: Through direct contact with objects at temperatures different from that of the body. *flow of heat and conduction are collectively responsible for 15-30% of losses. Evaporation: Method of heat loss during perspiration and respiration The organism secretes a water and salt mixture through sweat glands in the skin. The water droplets saturate the air in the skin's immediate vicinity (relative humidity at this point is 100% and movement of air carries the saturated air away from the body producing a cooling effect -Dew point- temperature at which the partial pressure of the vapor equals the equilibrium vapor pressure -100%) -production of sweat increases during physical exercise, higher body temperatures (fever), and elevated environmental temperatures This process contributes to 20 - 25% of total thermal losses ~Below 19ºC, thermal losses are minimal ~29-31ºC, production of heat and thermal losses are at equilibrium ~Above 31ºC, thermal losses are not sufficient to regulate body temperature and evaporation takes over * Thermal comfort of an organism is dependent on temperature of the air, relative humidity, and movement of air.

Molecular biophysics: Phase states of matter

Phase states of matter -Matter can exist in a various phases (its phase is mainly dependent on temperature and pressure) Gas - atoms or molecules move around rapidly and are far apart from each other. Only very weak intermolecular forces exist between the particles. Gases are easily compressible. Liquid -atoms or molecules are held together closely, liquids have definite volumes and are not easily compressible, can move and take the shape of their container Solid -attractive forces between atoms are strong, particles can only vibrate around a fixed position. The kinetic energy of solids is in the form of vibrational energy Plasma *gases and liquids are in a state of continuous irregular (thermal motion) while the thermal motion of solids is limited to vibration and rotation of the bonds between atoms

Structure of Matter: Quantum numbers

Quantum numbers The state (position and energy) of an electron can be described by a wave function composed of dimensionless parameters which equal the degrees of freedom. ~The degrees of freedom of an electron = 4 ~Thus, atomic theory states that the any electron in an atom can be completely described by 4 quantum numbers. With the exception of the last quantum number ms (spin), the numbers determine the geometry and symmetry of the electron cloud. ~The electron cloud is a space around the nucleus in which the probability of finding an electron is high. Pauli Exclusion Principle: no two electrons in a given atom can possess the same set of four quantum numbers. (i.e. each electron in a given atom has a unique set of quantum numbers and exist in the same quantum state) 1. Principle Quantum Number (n) n = any positive integer 1, 2, 3, ... n describes the electron's total energy and shell in which it can be found ~n = 1, 2, 3, 4, 5, 6, 7 corresponds to shell K, L, M, N, O, P, Q The greater the value of n, the higher the energy level and radius of the electron's orbit Maximum # of e- in energy level (shell) n = 2n2 *The difference in energy between two adjacent shells decreases with distance from the nucleus (1/n12 - 1/n22) n= total energy electron M= 9.11x10 -31 E0= 8.854x10 -12 FM-1 e= 1.6x10 -19 coloumbs 2. Orbital Quantum Number (L) For any given n, L is a number from 0 → n-1 It is determined by the angular momentum L where the magnitude of L = Describes the subshell of the electron Subshells s, p, d, f correspond to l values of 0, 1, 2, 3 Determines the shape of the orbital (s is spherical, p is bilobed, etc) The max # of e- that can exist within a subshell = 4l + 2 3. Magnetic Quantum Number (ml) Possible values are -l to +l ~For any value of l, there will be 2l +1 possibilities of ml ex: l=0, s subshell, 1 possibility of ml → 1 orbital ex: l=1, p subshell, 3 possibilities of ml → 3 orbitals (oriented in the x, y, and z axes) ~For any value of n, there are n2 orbitals Specifies the particular orbital within the subshell where an electron can be found Determines the spatial orientation of the orbital It also estimates the direction of vector L in an external magnetic field 4. Spin Quantum Number (ms) +-1/2 Describes the spin of the electron due to it's internal angular momentum (S) In the presence of an external magneticc field, electrons orient themselves in one of two possible orientations corresponding to +-1/2 Two electrons within the same orbital must have opposite values of spin (paired e-) ~Parallel e- are electrons in different orbitals that possess the same value of ms * Electron transitions may be probable or improbable (allowed vs. forbidden) ~allowed: transitions in which l changes by +-1 ~forbidden: transitions in which l changes by more than +-1 *During electron transitions n can vary arbitrarily