SEMMELWEIS UNIVERSITY Medical Biophysics I. Semifinal - Theory topics
Activity.
Defined as the rate of decaying atoms per unit sime (s) unit: Becquerel (Bq). 1Bq = 1 decay/sec
The dose rate.
Defined as the ratio of the dose and the time of irradiation
Kasha's rule.
The excited molecule first reaches the lowest vibrational level of S1 and photon emission occurs always from this state to any vibrational level of the ground (S0) state.
Kirchhoff's law.
States that a body which radiates more thermal energy is also absorbed thermal energy to a higher extent. The ratio between radiant emittance and absorption coefficient is constant within a narrow range of wavelength Mbody1/alphabody2 = Mbody2/alphabody2 = const
Teletherapy, geometric viewpoints.
Teletherapy: high gamma radiation induced (relative depth dose), from many different directions in order to create high dose on the cancer but split the dose between the healthy tissues (reduce damage) (isotope cs).
Types of radiation
according to energy transfer: Electromagnetic (light), mechanical (sound), particle (alpha) according to interaction with matter: ionizing (alpha), nonionizing (sound)
The fluorescence spectrometer.
A device which shines a light through a sample, measuring the excitation spectrum and the resulting emission spectrum.
Interaction of gamma radiation with matter II: Compton-scatter.
A gamma photon removes an electron from the outer shell: a "Compton electron", and a photon (of lower energy) is emitted. The initial energy of the gamma photon is thus divided between the work function (to remove the electron) and the energy of the photon.
Electronegativity
A measure of the strength with which an atom will hold on to its electrons and can ionize other atoms. $ Atoms of small size with a high atomic number are more electronegative (larger nucleus = more positive charges, yet small in size means electrons are closer to nucleus and that they don't produce much shielding for valence electrons, from the nucleus) Most electronegative atom is Fluorine. In a bond, atoms of higher electronegativity will pull electrons towards them, causing polarity in a molecule.
Multimodal imaging: PET/CT and SPECT/MRI.
A method which superimposes a functional imaging method (pet or spect) with structural imaging method (CT or MRI). The product is a high resolution image with identifiable anatomical structure and information about the function status.
Radiometric Quantities
Characterising the source: Radiant power (W=J/s) P = ΔE/Δt Radiant emittance and irradiance (W/ m2 ) M=ΔP/ΔA Einc=ΔP/ΔA inc Characterising the radiation: Radiant flux (W=J/s) IE= ΔE Δt Intensity JE = ΔIE/ΔA
Definition of radiopharmaceutical.
Chemical agent or drug having radioactivity (labeled with radioisotope for diagnostic and therapeutic purposes).
Role of collimators in radiation therapy, gamma-knife.
Collimator is essentially a led plate with holes, allowing passage to gamma photons which travel along the axis of the hole. The size of the hole is a compromise between spatial resolution and sensitivity (the smaller the hole, the better the resolution however less photons can be detected) ● Scintigraphy; collimator with only one hole ● Gamma camera and SPECT: collimator with thousands of holes Gamma-knife-radiation treatment can attack brain tumor. Method: machine which emits high intensity of focused gamma beam precisely
Parts and function of the gamma-camera.
Collimator: only allows gamma photons of a particular direction to enter (thus allowing special resolution) → Scintillation crystal → PMT → Amplifier → Computer and electronics. Gamma photons are detected as they exit the patients body, their spatial location and intensity provide information on the organ of interest.
a Wave interference.
Combination of at least 2 EM waves which encounter and result in: a. constructive interference: same phase (crest meet crest) or b. destructive interference: opposite phase (crest meet trough)
Planck's radiation law:
By studying the emission spectrum of black bodies, Planck introduced the concept that the energy emitted resulted from the vibration of atoms within the material. The vibrational energies have discrete values(quanta=1,2,3), never a value in between. If the oscillator changes from E1→ E2, the difference between those energy states will be emitted. E2 − E1 = h * f . h= planck's constant
Wave nature of light.
Diffraction, interference, polarization are phenomena which prove the wave nature of light.
The electron microscope.
Due to the small wavelength of the electron comparing to a photon the resolving power of electron based microscope allow us much higher resolution (abbe's formula and the de broglie relation )2 main types of electronic microscope : Transmitted electrons ( electron going through the sample and create the image on a screen) and Scanning EM (the scattered electrons create the image)the basic principles are: electron gun (tungsten filament which wired to an electric circuit, heats up and electrons shoot out due to their thermal thei thermal E), high voltage for the acceleration of the electrons(30kV-300kV), condenser electromagnetic lenses.
Thermoluminescent dosimetry.
Ionizing radiation excites an electron from the valence band to the impurity level of the dopant → this electron stays "trapped" in the dysprosium's activated energy level → heat applied to the crystal causes further excitation of the electrons into the conduction band from which they will relax → light is emitted. Number of photons is proportional to the dose. Application- personal dosimeter.
Dependance of irradiance on distance from the source
Irradiance is the incident radiation on a target. The dependence on distance from the source varies with the type of source. Assuming there is no attenuation: ● Point like source: irradiance is inversely proportional to the squared distancefrom the source. ● Cylindrical source: irradiance is inversely proportional to the distance from the source. ● Planar source: irradiance does not change with increasing distance from the source (as long as the distance is increased perpendicular to the plane and is not greater than the linear size of the source) If the distance from the source is not perpendicular: Ei=Einc,maxCosalpha
Quantum yield of luminescence.
Is a measure of the efficiency of photon emission through fluorescence, which is the loss of energy by a substance that has absorbed light via emission of a photon. Defined as the ratio of the number of photons emitted to the number of photons absorbed.
Interaction of gamma radiation with matter I: photoeffect.
Process in which gamma-photon removes an electron from the inner shell of an atom while being absorbed, the Ekin of the electron = incident of the photon energy (approximately). All the initial energy of the gamma photon is completely transferred to the electron.
Interaction of gamma radiation with matter III: pair production.
Process in which sufficiently high energy gamma photon (1.02Mev) is absorbed near the nucleus and an electron and a positron are created by that energy. [a short while after, they will collide by a process called annihilation and 2 gamma photons (of 0.511Mev) will be released at an angle of 180 from each other ]
Relative depth dose
Ratio of an absorbed dose in certain depth within the body to an absorbed dose at a reference point of the body central ray. The higher the ratio, the better (= More dose to a cancerous tissue in the depth vs lower dose to an healthy tissue.)
Shannon-Nyquist theorem.
States that for successful reconstruction of the signal, the frequency of the sampling should be at least twicehigher than the highest frequency signal component (overtone)
Matter waves.
The concept that matter can exhibit wavelike properties. Hypothesis by De-Broglie, who introducedthe wavelength for matter: wavelength = h/p = h/mv Where it equals the ratio of planck's constant and the momentum of the particle.Example: Davisson-Germer experiment which proved that electrons, which were scattered, formed diffraction patterns.
Energy levels of electrical conductors.
Conduction band and valence band with no forbidden band in between. (note, heating of a conductor results in lower conductivity)
Lyotropic liquid crystals.
Their order is affected by the concentration of their components (they change order depending on how many of them there are). Their components are amphiphilic molecules which form ordered structures in the presence of a solvent. Phospholipids, with their polar and nonpolar ends, form a membrane or micelles depending on their concentration.
Medical applications of thermal radiation.
Thermography is a test that uses an infrared camera to detect heat patterns and blood flow in body tissues. Digital infrared thermal imaging (DITI) is the type of thermography that's used to diagnose breast cancer. (note. thermotropic liquid crystals are used here)
Optical properties of crystalline materials.
They are anisotropic, which means that their physical properties are dependent on the direction of the measurement related to the orientation of the atoms in the crystal. Due to this, light will propagate with different velocities in different directions.
State equation of real gases.
Using van der Waal's equation which adds to the formula of ideal gas, some factors occurred in real life e.g.: particles have volume, there is interaction btw. the molecules, and thus there are less molecules and energy which collide on the walls of the container and form pressure. (constant a = correction for the intermolecular force, constant b = correction for the volume of particles).
Types of radioactive decay.
alpha, beta+, beta-, gamma, (electron capture)
Fluorescence.
is the emission of light by a substance that has absorbed light or other electromagnetic radiation. It's a form of luminescence. In most cases, the emitted light has a longer wavelength, and therefore lower energy, than the absorbed radiation. If the luminescence stops as the excitation stops (the relaxation step takes 10−8 seconds). (Application: fluorescent lamps lasers, page 133)
Dual nature of light.
light can behave in some cases as a wave (e.g. interference) and in other cases as a matter (e.g. photoelectric effect)its energy packed in quanta that depends on the frequency.
Concepts of magnification and angular magnification.
magnification is the ratio b/w image and object sizeangular magnification define as the ration b/w tan beta(angle of the image)e and tan alpha (the angle of the object)a.in case that the image is form on the near point [M(angle)=(nearpoin /focal length)+1] (near point=0.25meter) b. in case the image form at the infinity: M(angle)=nearpoint/focal length
Information obtained by isotope diagnostics.
● Function of an organ: metabolism (how quickly it absorbs and expels the tracker) ● Circulation in that organ (if the tracker is placed in the blood) ● Air circulation in that organ (if the tracker is inhaled)
The liquid state.
● Lacks the spatial order of a solid (short-range order). ● Isotropic; have no directional dependance (unlike crystals) ● Take the shape of the container ● Not compressible (generally)
Applications of lasers.
● Surgery (C02) ● photodynamic diagnosis and therapy, where fluorophores are inserted into the body, causing the tumor cells to florence, laser beams directed at that area will cause free radicals → killing tumor cells.
Kinetic gas theory.
5 main assumption which explain the behaviour of gas (ideal): 1) Particles are very small compared to the total volume 2) Constant random motion 3) Colliding of the particle one another is elastic 4) Particles exert pressure on walls when they are under higher psi/temp
Attenuation law
J=J0xe^-müx
Fluorescence microscopy
Uses a fluorescent dye that emits fluorescence when illuminated with ultraviolet radiation.
Interaction of beta positive radiation with matter.
*Radioactive particle in positive beta radiation is positron* When a positron interacts with matter it will collide with an electron by annihilation process which causes emittance of 2 gamma rays which emitted in 180 degrees to each other.
Emission spectrum of the absolute black body.
*The emission is in all wavelength spectrum. According to Wien's law, the maximum radiation is in wavelength that is inversely proportional to the temperature. wavelengthMax*T=constant. At low temp. black body appears black- most of the energy it radiates is infra-red. when it getting how it will start to glow at first in red color and than in yellow and finally white-blue - according to planck: radiation energy of a black body is emitted in discrete integer multiples. Quantum E = h*f - according to stephan boltzmann: Mblack(T) = sigmaT^4 describes the emittance of the black body as a proportion to temp. (fourth power proportionality)
Types of doped semiconductors.
1.p type (boron) (acceptor level) (holes) and n type (phosphorous) (donor level) (electrons)
Beta negative decay.
A process in which unstable nuclei convert a neutron into a proton (stay in the nucleus) electron and antineutrino (emitted). An unstable nucleus emits an electron and an antineutrino. A neutron in the nucleus becomes a protonthat remains in the product nucleus. Thus, negative beta decay results in a daughter nucleus, with a higher atomic number and the same mass number.
Laser: population inversion.
A process in which, by exerting energy on the system, the electrons are ''pumped'' from their ground state. Thus, most of the molecules are in their excited state and are staying in intermediate metastable state (until induced emission is formed) *require at least 3 energy levels.
Polarization of light.
A process which unpolarised light (light whose electric field vectors propagate in more than 1 plane, which contains the direction of propagation) become polarized light (light whose electric field vectors propagate only in 1 plane, which contains the direction of propagation) by an optical filter (polarizer)
Stokes-shift
A shift difference btw. the peak absorption (excitation) and the peak of emission wavelength, due to loss of energy in form of heat (vibration and rotation of the molecule)
Diffraction on an optical grating.
A structure with periodic optical properties. Its characteristic feature is the grating period (d) with a size on the order of the wavelength.
Polarization microscope.
A technique that makes birefringent details of a specimen visible. Examples of birefringent materials include: cell membranes, striated muscle and myelin sheath of neurons. The microscope is equipped with a polarizer which illuminates the specimen with linearly polarized light. On the other side of the specimen, another polarizer is used: "an analyzer", at 90 degrees from the polarizer. At this angle the view is dark. Light which was rotated by birefringent parts of the specimen passes, so that only these details are visible.
Laser: the optical resonator.
A tube with two mirrors on both sides. The mirrors reflect the light emitted by the laser material, and thus amplify it. One mirror will allow 1% of the light through, this is the beam which can be utilized. A condition for the resonator is that a wave that is reflected from its starting position, will return to that position in the same wavelength. L=length, m=integer. The double distance between the mirror must be an integer multiple of the wavelength.
Boltzmann distribution.
A universal organizing principle, in which energy levels in a thermally equilibrated system are populated by an exponential function. At higher temperatures, higher energy levels are more populated. P(h)/P(0)=e^(-mgh/kT)
Properties of the absorption spectrum.
Absorbance or transmittance as a function of wavelength. Varies depending on the atom or molecule, as it depends on their electronic structure, thus can be used to identify an element. Since absorption requires the excitation of an electron into the next energy level, it requires a photon of specific wavelength to make that transition: as a result some wavelengths will be absorbed completely, while others will be transmitted.
Energy levels of intrinsic semiconductors.
According to band theory, there is a valence band and a conduction band. In a semiconductor, the gap between them is large enough that electrons do not pass freely. However, the gap is not too large (Δε = 1eV ), therefore upon excitation, electrons can cross into the conduction band and electricity will be conducted.
Fourier-theorem for periodic and aperiodic signals.
According to this theorem, any signal can be decomposed as a sum of sinusoidal signals, and any signal can be constructed from sinusoidal components. This is useful in signal processing because if the frequency range of the measured signal is known, the signal processing system only has to transfer sinusoidal signals of this frequency range, and thus it can reconstruct the signal without distortion.
electromagnetic spectrum
All of the frequencies or wavelengths of electromagnetic radiation
Energy spectra of alpha, beta and gamma radiations.
Alpha spectrum: discrete (line) due to the fact that all the excess of energy goes to the alpha particle which releases from the unstable nucleus. Beta spectrum: continues, due to the fact that the emitted particles are the electron (or positron) and antineutrino (or neutrino) so the energy splits btw. them randomly. Gamma spectrum: discrete, due to the fact that gamma radiation is packed in quanta (different spectrum to different radionuclides)
Scintigraphy.
An examination for which a low quantity of radiopharmaceutical insert to the body, its aggregation in the target organ can provide us information about the investigated organ. The gamma energy is detected by a gamma camera and thanks to the collimator only the rays which are parallel to the detector are detected, and precise signal mapping can be formed.
Absolute black body.
An ideal, theoretical body which absorbs all the radiation incident on it and rememits it. A model can be created from a closed metal cavity with a hole drilled into it, so radiation energy cannot easily escape, thus it is absorbed completely. (Absorption coefficient of Stefan-Boltzman lawdescribes that the emittance of a black body is proportional to the fourth power of the temperature: Mblack(T)=sigmaT^4
Digitization of analog signals.
Analog signals need to be converted to digital signals so that they can be read and interpreted. ADC is the device which can make this conversion. It's done by performing many readings of voltage at different times, assigning values to them (i.e sample readings). The more sample readings, the more precisely it converts the original signal. The sample reading should take place at the same frequency as the signal, so that it doesn't miss anything.
Law of reflection.
Angle of incidence = angle of reflection Incident beam, reflected beam and optical axis are in the same plane.
Pressure of ideal gases.
Assuming no interactions between particles, and negligible particle volume: pV=NkT or pV=nRT. k= boltzmann constant n=moles N=number of particles R= gas constant
Resolving power of the atomic force microscope.
Atomic scale (sensitive to the van der waal's attraction) Resolution is in the order of fractions of a nanometer, which allows the study of strength and length of chemical bonds and the detail of molecular structure.
Processing of pulse signals.
Integral discrimination: selecting signals higher than a certain amplitude. Used when filtering out noise for example in scintillation counter. Differential discrimination: selecting signals within a defined range. For example, used when counting according to size distribution (coulter counter)
Potential energy of interatomic interactions.
Atoms within a molecule are organized in more or less fixed positions in which the molecule stores the least potential energy, thus is in its most stable. Sccording to this formula : E pot.=Eattraction+Erepulsion and this graph: (figure I.19 in textbook)
Luminescence spectra.
Atoms: line spectrum: due to Ephoton = E2 − E1 = h * f Molecules: because discrete energy levels are split into vibrational levels, electrons will lose some of the excitation energy while they relax to ground state. This means there will be a spectrum of wavelengths that can be emitted.
Half-life and average lifetime of an isotope.
Average life time: the time required for the number of undecayed nuclei to decrease to 1/e of the initial amount. 1/lamda= lifetime The amount of time it would take for a number of undecayed nuclei to decrease to 1⁄2 of their original amount. T=ln2/lamda
The Geiger-Müller counter.
Based on a gas ionization chamber. The difference is that the voltage is much higher that the one in the ionization chamber, thus every radiation will form avalanche of secondaries electrons which form maximum current (so it's insensitive to the energy of the radiation), but it is sensitive even to low energy radiation (due to high voltage) and counts the number of particles that interact with the device. Takes time for the system to reset itself (recombination of the iones) = dead time = 300 microsec.video *disadvantages: a. long dead time b. not sensitive to the energy of the radiation
Typical frequency and amplitude ranges of biological:
Biological signals include ECG, EEG, EMG, etc. ECG (ranges between 0.1 and 500 Hz, amplitude between 70 microV to 5mV) Intracellular voltage (0-10kHz, amplitude at 100mV)
Differential and integral forms of the decay law.
Integral: ΔN/Δt =− λN Differential: N(t) = N0e−λt N: number of undecayed nuclei, λ = decay constant 1/s
Interaction of beta negative radiation with matter.
Considered directly ionizing atoms by coulomb's force. Due to their minute mass, they are scattered on electrons, resulting in a zigzag path. Also: can cause breaking radiation (x-ray). Effective range: in air, a few meters in water: few cm (more penetration compared to an alpha particle due to its negligible mass and lower charge) Linear ion density: is lower than alpha particle (assume they have the same energy, beta particle will have to go through more distance to ionize the same no. of atoms)
The real gas.
Contrary to theoretical "ideal gas": Particles are not point-like, their volume is not negligible, consequently there is less volume available for motion. Interactions between particles arise and pressure becomes reduced. Additionally, behavior of real gases explains the possibility of condensation (transition from gas to solid)
The absorbed dose.
D = ΔE/Δm J/kg, gry. The amount of energy absorbed per mass. It is very difficult/impossible to measure due to the fact that even a lethal dose of 6gry corresponds to an unnoticeable temperature change.
Types of lasers.
Depending on wavelength; C02 (surgery), Krypton (ophthalmology), Ruby (dermatology).
Rules of image formation.
Depending on where the object is placed with respect to the focal point and double focal point, will determine the type of image that will be formed. ● Object is beyond 2F: image is real, inverted and diminished. ● Object is at the double focal point: image is real, inverted and the same size. ● object is between 2F and F: image is real, inverted and magnified. ● Object is at F: image is (virtual, upright and magnified at infinity) - Magnifying glass ● Object is closer than F: image is virtual, upright and magnified.
Stability of the atomic nucleus.
Depends on the ratio between protons and neutrons. Isotopes of an element have the same atomic number but differ in the amount of neutrons, so the mass number will be different. Isotopes can be stable or not stable. Unstable atoms will undergo radioactive decay, they will decay until they become stable.
The Stefan-Boltzmann law.
Describes that the emittance of a black body is proportional to the fourth power of the temperature:
The stochastic radiation effect.
Describes the radiation damage that can occur due to adsorbed dose. This method is valid for damage that can occur at low levels of absorption (there is no threshold), the probability of damage increases with the increasing dose.
Applications of the Boltzmann-distribution IV. electric conductivity of semiconductors.
Electric conductivity of semiconductors (a type of crystal) depends on the number of electrons which are able to transition from the valence band through the "gap" to the conduction band. This number increases with T (it is the opposite in conductors). Using the Boltzmann distribution, we are able to calculate the fractions of electrons that are able to cross the "gap"/"forbidden band" = Δε : (n/n0)=e^-(Δε/kT)
Electro- and thermo optical phenomena in liquid crystals.
Electro: nematic liquid crystal (characterized only by orientation order) When they have electric dipole moment, the orientation of the molecule can be controlled by electric field. The change in the orientation manipulates the optical transmission of the layer, which we can utilize to manufacture displays from that material. Thermo: choleric liquid crystal (twisted nematic) changes its orientation as dependence of temperature (change the inclinationof its helix shape), thus the colour of the layer will change with different temperature (by destructive interference of one wavelength the crystal will transmit its complementary color). One of those applications is the ''contact thermography'', which provides information about e.g. regional inflammation by the increased temp. in that region which means that the crystal will transmit different colors.
Wave nature of the electron. Davisson Germer experiment
Electrons behave like waves in certain situations like being diffracted. We can calculate the wavelength of electron the formula for de Broglie: wavelength=h/p, when p(momentum)= mass*velocity
Bohr's atomic model.
Electrons in an atom can only occupy certain distinct orbits around the nucleus. The electrons in their orbits won't radiate unless they will be excited and jump to an higher orbit. We can calculate the frequency of a radiated electron by calculating the difference of energy btw the 2 orbitals using this formula: hf=Em-Ei
FRET. (Fluorescence Resonance Energy transfer)
Energy transfers from donor molecules, without emission, to acceptor molecules when they form dipole dipole interactions. 3 main requirements: 1. they have to be in the right orientation 2. they have to be really close (efficiency of the FRET is proportional to the reciprocal of the distance btw. the donor and the acceptor by the sixth power!) 3. spectral overlap btw. donor and acceptor. application: protein-protein interactions investigation
Applications of the Boltzmann-distribution I. : Nernst equation.
Epot=q*U(charge*voltage) The distribution of charge particle at point A and B can be calculated by this formula: nA/nB=e^(-qU/kT)
Converting exposure in air to absorbed dose in tissue.
Every 1 C/kg exposure corresponds to 34 Gry absorbed dose in air. D= f* X (f34 J/C). If the mass attenuation coefficients are known: Dtissue/Dair=mu m tissue/mu m air
Huygens-Fresnel principle.
Every wave propagates so that each point of its primary wavefront serve as a source of secondary wavelets (of small amplitudes) that advance with the same speed and frequency as the primary wave.
FRAP .
Fluorescence Recovery after Photobleaching, is used to study the diffusion of molecules on the lipid membrane. The number of excitation and emission cycles is limited for fluorescent molecules, therefore they can be bleached. When the previously bleached area of the membrane "recovers", this is proof of the lateral diffusion.
Interpretation of momentum of light: optical tweezers.
Formula for photon momentum: ρ=h/λ Optical tweezers utilize the momentum of the laser beam to control little refractive microshpere structures which can be bound to a biological molecule and be controlled by moving the laser.
Feedback amplifiers.
Fraction of the Uout (output) is added to the Uin (input) If the signal has the same phase like the input→ positive feedback: higher amplification (advantage) lower transfer band (disadvantage) ex: ultrasound generator If the signal inverted and than added to the input→ negative feedback: less gain (disadvantage) higher transfer band (advantage) ex: all amplifiers
Structure of the atomic nucleus.
Function as the center of the atom and is composed of protons and neutrons. Protons have a positive charge and they both have approximately the same mass (1amu). The mass number of an atom is defined as the sum of the protons and the neutrons in the nucleus, while the atomic number is defined by the number of the protons only! *the volume of the nucleus is extremely small comparing to the volume of the whole atom
Parts and function of filter circuits
Function: remove unwanted frequencies from the signal. Parts: resistor and capacitor (dependent on frequency)
Principles of selecting the isotope for diagnostics according to radiation type and energy.
Gamma radioactive isotopes are used most frequently for diagnostics due to their long effective range, low absorbance in body tissue, and their high energy, which makes them easily detectable. The energy of the gamma radiation should be high enough that it is able to penetrate the body and be detected, however not too high, as it will be less effectively absorbed by the detector. In addition, low energy photos are more readily absorbed by the body, which is more damaging to the patient. That said, it should be absorbed to some extent (for contrast image). Activity needs to be high enough that sufficient photons can be detected.
The Beer-Lambert law.
In a dilute solution, if the solvent does not absorb in the applied wavelength- absorption coefficient is proportional to concentration of solute thus: (measuring concentration of solute by measuring the absorbance of light in a given wavelength)
Applications of the Boltzmann-distribution II.: equilibrium and rate of chemical reactions. (The Arrhenius plot).
In chemical reactions, atoms must transition from one energy state A in which its energy is εa to B state in which its energy is εb. In an equilibrium, the distribution between those states is calculated: nA/nB =e^-(εA-εB/kT). The ratio na /nb = K (equilibrium constant) The Arrhenius plot illustrates a logarithmic relationship between the K and the 1/T. The slope of the graph gives the energy distribution between the two states.
Weighting factors in dosimetry.
In dosimetry, we have two types of weighting factors: radiation (type of radiation)- different radiation cause biological damage in different severities. Tissue: (which tissue are exposed) different tissues have different sensitivity to radiation optional info : Depends on the priorities of the measurement as each measurement technique has pros and cons. Pocket chamber dosimeter:the same principle as the ionization chamber where the charge and voltage drop is proportional to the dose. Advantage is immediate readout. (not sure if they have energy level resolution..) Ionization chamber: Sensitive to the energy of the particle, and to the dose rate. However in Geiger-müller counter: simple and easily available, however it has a dead time so cannot be used for high counting rates. In addition, it can't distinguish between energies of nuclear particles. DLS: small and reusable (good for personal dosimeters). However, no particle energy resolution. Semiconductors detect: much higher sensitivity than the ionization chamber because the ionization energy required is 3-5 eV.
Principal light rays
In geometric optics, image formation is made by emerging of 3 principal light rays (parallel,focal and center). In case of converging lens it looks like this:
Cost-benefit principle in isotope diagnostics.
In terms of radiation exposure, if the risk of not having the examination is higher than that caused by the radiation exposure, the procedure can be done. In terms of the isotope, criteria such as energy and activity should be with the patient in mind. However, certain criteria (high energy ionizing radiation of a certain dose) need to be met in order to achieve a reliable image/result.
Applications of the Boltzmann-distributionIII.: barometric formula.
In thermal equilibrium, we can measure the decrease in atmospheric density vs altitude by this formula: (density of gas is concentration per volume, so we practically measured the distribution of concentration) rho(h)/rho(0) = e^-mgh/kT
Law of Refraction (Snell's Law)
Incident and refracted ray together with the normal line (=optical axis) are all located on the same plane. Snell's law: (sin alpha/sin beta) = c1/c2 = n21
Principles of brachytherapy.
Insertion of a sealed source of radiation into the patient's body near or in the site of a tumor. Radiation will harm the tumor cells with low damage to surrounding tissue. Used for the treatment of cervical, prostate, breast and skin cancers.
Measurement of the absorption spectrum.
Is a measurement of absorbance (log(J0/J)) vs wavelength of incident light. The absorption maxima (can be more than 1) related to the electron excitation energy (E2-E1) which is characteristic for the molecular structure. Electrons of the atom are quantized. Thus, to change their energy state, the incident light is required to be in a certain frequency (energy): E2-E1 = ε = hf = h(c/lamda) *we can use absorbance to find conc. of diluted solution (beer lambert law)
Dynamic light scattering.
Is a method for analyzing solutions from which the hydrostatic diameter of a particle can be measured. Light is directed through a sample → scattering of the light occurs (relative to the position of the particles in the solution) → the intensity of the light is detected on the other side → intensity changes when the particles in the solution diffuse (brownian motion) → the change will occur faster or slower if the molecules are smaller, or larger respectively. → Information about the intensity is used to calculate the diffusion coefficient. Next, Einstein-Stoke formula will allow us to calculate the r (size of the particle)
Alpha decay.
Is a type of radioactive decay in which an atomic nucleus emits an alpha particle (helium nucleus) and thereby transforms or 'decays' into a different atomic nucleus, with a mass number that is reduced by four and an atomic number that is reduced by two.
The function of the semiconductor diode.
It acts as a one way valve for electricity. It is composed of n-type and p-type semiconductors. These are made by doping a semiconductor to achieve either free electrons (n-type) or holes (p-type). The chemistry behind the diode requires for p-type doping to be a chemical with lower number of valence electrons than in the semiconductor. This will leave a vacancy which can be occupied by an electron (Al doping of Si). For n-type, an element with more valence electrons than the semiconductor is used (P doping of Si).
Principles of selecting the isotope for diagnostics according to half- life.
Its half-life should match the biological half-life (the time takes to the body to eliminate half of a concentration of a substance from the body) and also match the duration of measurement with the aim that all of them will be short as possible related formula: 1/Teff=1/Tphys+1/Tbiol
Interpretation of a typical isotope accumulation curve.
Lag time: time from introduction of isotope to uptake (characterises transport capacity) Ascending curve/slope: uptake of the isotope. T max: max activity, characterises the uptake and elimination ability of the organ (can be used to compare paired organs) Effective half-life/descending part of the curve: physician + biological decay. From known physical decay value, biological decay can be calculated. Area under the curve: mean isotope content of the organ
Lens combinations
Lenses are combined in a compound microscope to form a system of two lenses: objective and eye-piece lenses. Image magnification can be manipulated by adjusting the distances between the lens and specimen as well as the distance between the two lenses.
Image formation on a curved surface
Lenses are curved surfaces on which light rays refract. If light rays meet, an image will form. The angle of refraction depends on the index of refraction of the medium. A diagram of this should begin with drawing a normal ray which passes through the center of curvature, and travels perpendicular to the surface- no refraction! The incident angle of other incoming rays needs to be measured with respect to the normal.
Light scattering (Rayleigh and Mie).
Light scattering occurs when EM waves encounter particles in the air. The light waves will cause a dipole moment, making electrons in the atoms vibrate (forced oscillation), which will cause them to emit light. Rayleigh scattering depends on wavelength. (blue light is scattered more) When particles are spaced far enough apart (spacing is larger than the wavelength), there is no interference, thus the intensity of incident light = intensity of scattered light. We know that the dipole moment produced by the light is proportional to the angular frequency. ω = 2πf (angular frequency) Thus the higher the frequency the higher the scattering (blue light scatters much more → sky is blue) Mie scattering, on the other hand, is not wavelength dependent, thus all wavelengths scatter equally (producing white light) when the size of the particle is on the order of the wavelength, this type of scattering occurs closer to the earth's surface. (H2O in clouds)
Fermat's Principle
Light will choose the path which takes the least amount of time (i.e spend the least amount of time in the slower medium). Is the basis for the phenomenon of refraction and reflection.
Thermotropic liquid crystals.
Liquid crystal: substance which possesses properties of both liquid and crystalline solid. 2 types of order can be defined liquid crystal: a. Transitional order- the center mass point of the molecule form plane b. orientational order- the axes of the molecule alin almost parallel with one another thermotropic- the order of the structure depends of temperature Application: contact tomography: the changing colors of choloresteric film on the patient's body can indicate inflammation area (higher temp. than normal=different color than normal)
Wien's displacement law.
The black body radiation curve for different temp. peaks at a wavelength that is inversely proportional to the temp. ( high temp.=low wavelength) black body radiation v.s. wavelength curve:
The gas ionization chamber.
Measures radiation dose by measuring the charges produced in a mass of air b/w the charged plates of the capacitor. The charges move toward oppositely charged electrodes → potential difference is detected and represents a current pulse. The size of the current is proportional to the energy of the incident radiation. e.g. gas ionization chamber: GM-tube (but it does not provide information about the energy level of the particle due to the avalanche effect)
The effective dose.
Measures the absorbance dose but it is taking into account the sum of the types of radiation (and their weighting factors, because different radiations have different biological damage severity) and the type of the organ which is exposed to the radiation (and its weighting factor which describe the probability of stochastic damage, due to the fact that different organs have different sensitivity to radiation) *The sum of all the tissue weighting factors is 1. *If radiation affects more than one organ, the effective doses of the organs should be summed. unit: sievert Sv=1 J/Kg
The exposure.
Measures the positive charge produced in the air with a certain mass by ionization, its unit C/Kg.(can be measured by ionization chamber) Formula: X=Δq/Δm
Macrostate and microstate in thermodynamics.
Microstate: examination of the molecular state of the system and instant state (location of particles, velocity of particles, momentum) Macrostate: examine the system as a whole (temp. pressure) in thermal equilibrium the macrostates stay constant while the microstate always changes!
Models of the atom (Dalton, Thomson).
Models of the atom: Democritus: "Atomos" (uncuttable) atoms are the smallest article, and they have different shapes. Dalton: showed that matter was made of indivisible particles (atoms) which can not be broken down further. Thomson: discovered that atoms had electrons which were stuck throughout the positively charged substance (plum pudding) Rutherford: showed that all the positive charge was in the middle (nuclear model: atom has a nucleus) Bohr: the concept that electrons orbit around the nucleus (simplified concept used in chemistry for simplicity) Schrödinger: electrons don't move in concentric circles, rather orbitals can have different shapes which are not necessarily circular (quantum mechanical atoms). Rutherford and Chadwick: discovered protons and neutrons. (further quantum mechanical atoms)
Neutron radiation, proton radiation, the Bragg-peak
Neutron radiation occurs when an excited nucleus expels a neutron. Since neutrons do not carry charge, they do not ionize matter directly. Indirect ionization happens through collision and energy exchange between the neutron and the atom. Elastic scatter: neutron collides with another nucleus and transfers part of its kinetic energy to a proton, which is liberated and can ionize particles. Inelastic collision: as a result of the collision, the atomic nucleus will release excess energy in the form of a gamma photon or any particle. Neutron capture: nucleus absorbed the nucleus and an isotope is created (which then emits excess energy as a, b or gamma). Proton radiation acts very similarly to alpha particles. Large mass corresponds to shorter effective range. Bragg's peak: shows the relationship between penetration depth and amount of radiation deposited. For proton radiation, this peak occurs right before the proton stops.
Energy levels of electrical insulators.
Non-metals. In band theory, insulators are said to have a valence band and a conduction band, however the gap between them, the "forbidden band" where electrons cannot exist, is "too wide", Δε > 3 eV, meaning that electrons are not able to cross it to get to the conduction band. Therefore, it does not conduct electricity.
Phosphorescence.
Occurs during transition from a triplet state to a ground state, a slower luminescence than fluorescesce. Phosphorescence occurs by excitation of electrons from ground state → vibration and rotation to the lowest excitation state) --> intersystemic crossing into a triple excited state→ returning to ground state by luminescence.
Total internal reflection and its applications.
Occurs when light is propagated from a higher refractive index thoward a medium with lower refr.index and with a larger angle than the critical angle. The critical angle is calculated by this formula: (1/sinBetac)= (n2/n1). Application: endoscopy
Heisenberg's uncertainty principle.
One cannot know all the parameters describing a particle at a given time. For instance, when momentum is calculated, there is more uncertainty about its location and vice versa. This is due to the wave nature of particles. For example: when waves are compressed enough into one space, to gain information on it's exact location, it will not be possible to know the exact momentum of that wave. In the case of sound, the more we know about its location in space, the less accurately its frequency is determined.
Scintillation counter II.: the photomultiplier tube.
PMT is a tube with a photocathode (which converts scintillations from the crystal to electrons (photo effect). These electrons are multiplied on the dynodes before reaching the anode. The electrons are accelerated by a V through the tube, every collision with a dynode produces secondary electrons. The multiplication factor corresponds to the number of secondary electrons, usually 3-4, so for 10 dynodes = 3^10
Parts and working principle of PET.
Parts: positron radiating isotope ring detector (scintillator crystal, photomultiplier) PET is a functional imaging method, by providing information about the distribution of the positronradiative isotope. Emitted positrons interact with electrons and form annihilation, which will produce 2 gamma rays with an opposite direction, which will be detected by the ring detector.
Classification and comparison of signals.
Periodic (e.g. sinusoidal wave) // non periodic (e.g. a pulse) stochastic signal Electric (voice which amplified through megaphone ) // non electric (voice) Analog (e.g. audio) // digital (e.x signal which stored in code in electronic device) A quantity that is used to compare the magnitude of 2 signals in decibels: n=10*log(P2/P1) provides the energy difference. Practically we measure the voltage difference n=20*log(U2/U1)
Oscillations.
Phenomenon in which quantity varies as a function of time around an equilibrium value
Photon energy, the eV scale.
Photon energy is calculated as the product of planck's constant and the frequency. E = h * f or E = h * c/λ The energy is the formula is given in joules, but is often described using electron volt.Electron volt: the amount of kinetic energy in an electron that is accelerated in an electric field of one volt. 1eV = 1.6 * 10^−19 Joule
Beta positive decay.
Positron and an antineutrino are emitted. A proton in the nucleus becomes a neutron, which stays in the mother nucleus. Thus, the daughter nucleus will have an atomic number one less than the parent nucleus but the same mass number.
Parts and function of Tc-generator.
Practical machine which produces gamma radiation isotope from a ''parent'' isotope which has relatively long half-life. Parts: lead container, saline container, generator colomb, Tc(m)-elute container.
Primary and secondary bonds.
Primary bonds: include covalent (non metal-non metal), ionic (metal-non-metal) and metallic (metal-metal) bonds in which electrons are shared between atoms, in order to form a more stable electron configuration. Secondary bonds: are weaker because there is no electron sharing, rather bonding occurs due to instantaneous dipoles between two atoms. Van-der waals and hydrogen bonds are secondary bonds
The bound electron, quantum numbers.
Principal quantum no (n): 1, 2, 3, 4.. Angular momentum quantum no (l): n-1 Magnetic quantum no (m1): -l...+l Spin quantum no (ms): +1/2, -1/2
Scanning probe microscopy.
Principle: a method which can form an image of an atomic size object by detecting various interactions depending on the design probe. e.g.: AFM which measures the van der waal's force btw. the probe and the sample (the probe attracts to the sample until a certain distance, and after a certain value the force of repulsion takes place. The deflection of the cantilever is held constant by lifting or lowering the cantilever.) Composed of: a probe which is connected to cantilever and a laser beam that point on the probe and reflect into detector (measures the change in the position of the probe) 2 modes: contact, oscillating
Laser: induced emission.
Process by which the emission is stimulated by incoming photon → the incoming photon is amplified. Laserer materials are those for which there are 3 energy levels; and one of them should be of "long lifetime", meaning that the electrons will stay in that state for longer. Electrons are "pumped into this level" (population inversion), emission from this level spontaneously is unlikely, thus it is achieved by induced emission.
lens equation
Reciprocal of the image distance plus the reciprocal of the object distance, gives the reciprocal of the focal point, which equals the refractive power.
The Ideal gas.
Refers to non-realistic gas composed of molecules which follows the kinetic gas theory. The parameters characterising the state of the gas are connected by this formula : PV=NkT (temp. in kelvin)
Boltzmann's definition of entropy.
S = k * lnΩ where S = the entropy (the extensive quantity of heat) and where the number of microstates which belong to a particular macrostate are.
Maxwell-Boltzmann velocity distribution.
Upon increasing the temperature, the average of the absolute value of molecular speed increases. The width of the distribution increases due to an increase in the interactions between the molecules. (+ graph)
SPECT.
Single photon computed emission tomography: gamma radiopharmaceutical is injected into the body --> the detector gamma camera is rotated around the body axis → gamma photons are detected → multiple 2D images from multiple angles are acquired → Images are computed using tomography algorithm → 3D image is yielded.
The crystalline state (unit cell, crystal defects).
Solid which is arranged in a long range of periodic order and is composed of structural units which call the ''unit cell'', the latter making a bigger symmetrical structure called ''crystal lattice''. As in gases, we have a classification of ideal and real crystals. While ideal crystals have infinite periodic spatial sequences of identical structural elements, real crystals or microcrystalline keep their identical spatial sequence only in their microscopic scale and instead of being made of the same crystalline structure (same elements, same type of lattice) they appear in various sizes and orientations of building blocks. Crystal defects: a. point defects = occur on a single lattice point (types: empty space, doping, an extra atom btw. the lattice point) b. line defects = rows of atoms are arranged inconsistently c. surface defects = boundaries which separate the crystal into regions with different orientations. defects can cause fracture in the crystal.
Production of isotopes.
Some isotopes are unstable, therefore they emit radiation. Thus radiation can be harvested for medical usage. Isotopes are produced in nuclear reactors, bybombardment of a stable nucleus with high energy particles. However, Tc generators are also used, specifically, when a gamma radiation isotope of a short half life is required.
Types of waves.
Sound waves (longitudinal or transverse) - require a medium Electromagnetic waves (transverse waves) - do not require a medium Matter wave (matter can act as a wave; electrons can have wavelike interference)
The direct and indirect effects of ionizing radiations.
Tadiation ionizes a molecule such as DNA causing mutations. Indirect effect: radiation ionizes water molecules in the body, causing free radicals, which then damage molecules such as DNA.
The equivalent dose.
Takes into account that different types of radiation influence the biological tissue in different severity associated with a particular dose. Unit: Sievert=1 J/kg, Wr= radiation weighting factor (defines how many times greater the biological effect with a certain type of radiation comparing to a gamma radiation)
Scintillation counter I.: the scintillation crystal.
Thallium activated (doped) NaI crystal or NaI (Tl) are widely used as scintillator crystals. They are made by insulators which have intermediate energy states thanks to Tl doping. The material of the crystal absorbed the energy of the radiation (e.g. absorbed the kinetic energy of the primary electrons) in the form of excitation energy of the scintillation. The electrons return to their ground state by emission of fluorescence photons (blue in our case). *note: to be able to detect the scintillation, the scintillator has to be transparent to the emission wavelength .
Determination of the biological half-life of an organ.
The biological transport rate and its elimination from the target organ. Provides important information about the function of the organ. 1/Teff=1/Tphys+1/Tbiol
Energy levels of atoms and molecules: the Jablonski diagram
The diagram depicts the ground state which electrons strive to be on, and the excited states to which electrons can jump to if given the correct energy quanta. Excited electrons will undergo "internal conversion" in which they rotate and vibrate until they reach a semi-stable state S1 (following Kasha's rule), only from that state will they relax to the ground state. If they emit light during this relaxation it is called fluorescence. Intersystem crossing occurs when the electron jumps to the triple state. From the triple state to the ground state radiative relaxation is termed phosphorescence (slower process).
Interpretation of the color of light.
The different colours are the perception of our eyes for different frequency (different of EM radiations in the visible range) *complementary colour: object absorbs color and transmits other colour which the sum of them is the white light
Typical dose values and dose limits.
The dose limits: The lethal dose is 4-6Gy. ● Max limit for the body: 20mSv/year (10 micro sievert per hour) for the body. (for the skin and limbs the limit is 500mSv/year). Characteristic dose values: ● 2.4mSv/year from background radiation. ● X-ray image: 0.2-1 mSv. ● CT scan: 2-8 mSv.
Luminescence: excitation and relaxation.
The emission of excess energy, from excited electrons, in the form of light (cold emission, as opposed to thermal emission/incandescent emission). Many types of excitation: thermo, bio, photo electron. Process: Absorption of external energy → Excitation → Emission of energy in the form of light. Types of relaxation: Fluorescence: if the luminescence stops as the excitation stops (the relaxation step takes 10−8 seconds Phosphorescence: if the luminescence continues for much longer (minutes). Requires intersystem crossing into the triple state (from which there is a lower probability that the electron will relax).
Luminescence lifetime.
The inverse of the rates of all transitions (radiative + non-radiative). The lifetime: τUsed in distribution formula:
Interaction of alpha radiation with matter.
The linear ion density, which is the amount of ions produced over a certain length a , decreases after the particle has lost its energy. (The energy required for ionization is 34eV). The effective range is the distance covered by a particle until it's energy is lost. This value is longer in air (2-9 cm) than in liquid or soft tissue. (1-10mm). Things to consider: ● Mass (influences its velocity) ● Charge (influences its interaction with other particles, and its linear ion density). **In the case of beta particles, both mass and charge are much smaller, therefore it will have a higher effective range, but a much lower linear ion density (that said, a and b particles will produce the same number of ions, because b particles can travel further).
ALARA-principle AsLow AsReasonably Achievable
The principle state that we should aim to reduce the exposure to the minimal by: a. spending minimum time near the source b. the distance from the source should be maximalc. a person who is dealing with radioactive material should be c. wear a protective shield. d. the source must not cause any deterministic effect e. justification: cost/dose, radiation damage/radiation protection in inverse proportionality
The deterministic radiation effect.
The probability of radiation damage occurs above a certain threshold dose. Beyond the threshold, the probability dramatically increases. The severity of the damage above the threshold is proportional to the dose (e.g Cataracts- loss of transparency of the lens)
Gamma decay.
The product of an excited nucleus as it tried to achieve a stable state. The unstable nuclei that undergo gamma decay are the products either of other types of radioactivity (alpha and beta decay) or of some other nuclear process.
Magnification in the light microscope.
The product of the magnifications of the objective lense and the eyepiece lense: M=I/Ox(I'/O')=MoxMe
Franck-Hertz experiment.
The purpose of the experiment was to prove Bohr's atomic model, which states that electrons exist in quantized states within the atom. In the experiment, using a tube filled with Hg, an electron emitting cathode, a grid and an anode, it was proved that in order to interact with the Hg atoms, a specific discrete amount of energy had to be given to the electrons, by means of voltage. By measuring the current at the end of the tube, it was possible to measure how much of this energy was imparted on the atoms, and how much was left over, and thus the quanta of that particular atom.
Limit of resolution of the light microscope.
The smallest noticeable distance btw 2 points. Abbe's formula: omega = 0,61x(wavelength/nxsinomega) color which the sum of them is the white light
Semiconductor detectors in dosimetry.
Uses a diode connected in reverse bias which means there will be no current flowing through the circuit. An ionizing particle will cause an electron-hole pair in the depletion region, and thus current to flow. Current is evidence of the presence of radiation.
Thermal radiation.
Transfer of heat by using EM radiation → possible even in vacuum. Every matter above 0K radiates thermal radiation.
Turbidimetry and nephelometry.
Turbidimetry: Turbidimetry is involved with measuring the amount of transmitted light (and calculating the absorbed light) by particles in suspension to determine the concentration of the substance in question. Amount of absorbed light, and therefore, concentration is dependent on; a) number of particles, and 2) size of particles. Nephelometry: at low intensity of scattered light, measures the intensity of scattered light. (linearly proportional to concentration) Since the amount of scattered light is far greater than the transmitted light in a turbid suspension, nephelometry offers higher sensitivity than turbidimetry. • The amount of scattered light depends on the size and number of particles in suspension *how do we differentiate btw. light scattering and absorbance ?*
phase contrast microscope
Turns phase differences (to which the eye is not sensitive) and converts them into amplitude differences which translate to intensity differences I = A2 (which the eye is sensitive to). Useful for studying living cells, with no staining
Isotopes.
Two or more atoms which have the same atomic number but different atomic mass (same no. of proton and electrons and diff. no. of neutrons)
Notable transitions of luminescence: vibrational relaxation, intersystem crossing.
Vibrational relaxation: as kasha's rule states, an excited molecule will first reach the lowest vibrational level of s1, by vibration and rotation, losing energy in the form of heat (Ekin). Intersystem crossing: occurs in phosphorescence, a process in which electron transition occurs btw. the singlet and the triplet state (singlet and triplet state have different spin multiplicity [formula:2S+1]) *note: triplet has lower energy state than singlet
The photoelectric effect.
When a photon of energy E = h * f delivers enough energy to an electron, causing it to leave the atom. Experiments by Einstein proved this because not all types of light will result in the ejection of an electron, only lights of sufficient energy (UV for example). This proved the quantized nature of light =photon and thus the particle nature of light (and got him the nobel prize)
wave diffraction
When light passes through a slit which is near the size of the wavelength, it will spread around the slit. Ties us back to the Huygens-Fresnel principle, which explains diffraction. It results in a diffraction pattern.
Fundamentals of geometric optics
When light propagates through slits which are much larger than its wavelength, we can consider the wavefront as a line. This simplification allows us to calculate optical imaging with relative ease.
Physical foundations of the periodic table.
a. Numbered according to the numbers of protons b. Size: increases from right to left in the period and from up to down in the group c. In every group the number of valence electrons is the same d. Ionization energy: increases in the group from bottom to the top and in the period from left to right (oppositely to the atom size orientation) e. Electron configuration: s,p,d,f blocks (d=-1 f=-2)
Properties of laser light.
monochromatic coherent (due to induced emission→ constant phase difference) small divergence (the laser beam is nearly parallel) high intensity (because. 1. emitted from narrow beam and 2. can be further improved by focusing the beam) often polarized
Physical, chemical and biological phases of radiation effects.
physical: ionization chemical: free radicals biological: damage to DNA
Light sources based on thermal radiation.
sun, light bulb, heated metal (at first will glow in red and after further heating will change to yellow and blue = wien's law. Mblack(T)=sigmaT^4
refractive power
the degree to which lenses are able to converge or diverge light. formula: D=1/f (f=focal point)
