Pharmacy Calculations
the osmolarity of blood and other body fluids is between:
300 to 310 mOsmol/L
osmotic pressure - water will move
across a semipermeable membrane to equalize the concentrations of dissolved particles on either side
Total Body Weight (TBW)
actual body weight - what the patient actually weighs
adjust isotonicity of solutions by
adding a tonicity agent - an agent added to increase the osmotic pressure of a solution
hypotonic solution
have fewer dissolved particles than body fluids - can result in lysing of red blood cells
hypertonic solution
have more dissolved particles than body fluids - results in red blood cell shrinkage
calculation of doses by body surface area (BSA)
because body surface area (BSA) has a stronger relationship to renal clearance and to metabolic capacity than does body weight, BSA is preferred for calculating doses of drugs with narrower margins of safety
infusion rates
how quickly fluid is pumped into body - infusion administered in two ways: drip sets, infusion pumps
drip sets
drip sets deliver from 10 drops/mL to 60 drops/mL - flow rate is expressed in drops per minute
MDRD Equation
eGFR (mL/min/1.73 m^2) = 186 x (Scr)^-1.154 x (Age)^-0.203 x (0.742 if female) x (1.212 if African-American) - the equation does not require weight or height - MDRD calculates the GFR for the surface area of the 5'9", 70 kilogram average person (1.73 m^2) - eGFR is a NORMALIZED value
isotonic solution
equivalent to 0.9% sodium chloride (normal saline) is considered isotonic
percent error
error in your measurement % error = [sensitivity of balance * 100%] / quantity desired % error = ([actual weight - theoretical weight] / theoretical weight) * 100%
milliequivalents: as H+ has a single charge,
every ion with a single charge is considered equivalent - 1 equivalent of Na+ replaces 1 equivalent of H+ - 1 Equivalent of Cl- can combine with 1 equivalent of H+
the van't Hoff factor (i) : substances that dissociate into 3 ions
ex: CaCl2, magnesium gluconate i factor: 2.6
the van't Hoff factor (i) : substances that dissociate into 4 ions
ex: aluminum chloride, ferric chloride i factor: 3.4
the van't Hoff factor (i) : nonelectrolyte and slightly dissociated substances
ex: dextrose, weak electrolytes: i factor: 1.0
the van't Hoff factor (i) : substances that dissociate into 2 ions
ex: sodium chloride, KCl i factor: 1.8
linearity or linear accuracy
for a digital balance: the minimum reproducible readable value
readability
for digital balances: the smallest weight increment that can be read (0.001 g)
sensitivity
for torsion balances: the smallest weight that gives a one subdivision deflection on the pointer
creatine
found in skeletal muscle - the metabolism of creatine to creatinine is constant throughout the day
the van't Hoff factor (i) : substances that dissociate into 5 ions
i factor: 4.2
titration
in certain patient populations, initial drug doses should be low and the dose increased at specific intervals until the desired response is obtained - additionally, certain medications require they be slowly tapered when discontinuing the medication - pharmacists must be able to correct calculate the amount of drug the patient will use during these titrations
if creatinine is built up in blood
indicates kidneys are not functioning properly - or a lot of muscle --> body builders -> create extra creatinine
IV admixtures
involves the transfer of one or more additives into a large volume parenteral - additives may be drugs, electrolytes, trace minerals, etc.
SI: basic units
length: meter volume: liter weight: gram
millosmoles: for nonelectrolytes
like dextrose 1 mmol = 1 mOsmol
MWQ for a digital balance
linear accuracy / % error
Denver XE 100 analytical balances
linearity: 0.2 mg capacity: 100 g
ScoutPro 202 compounding balance
linearity: 10 mg capacity: 200 g
ScoutPro 123 compounding balance
linearity: 3 mg capacity: 120 g
to convert a weight to an amount in milliequivalents: mEq =
mEq = (mg x valence) / MW
density
mass / unit volume SI units = g/mL
to convert milliequivalents into a weight, rearrange the equation: mg =
mg = (mEq x MW) / valence
SI: mc
micro 0.000,001 10^-6
MDRD Equation (Modification of Diet in Renal Disease)
most hospitals now provide the estimated glomerular filtration rate (eGFR) based on the MDRD equation in their standard Basic Metabolic Panel print-out: eGFR = _____ mL/min/1.73 m^2 1.73 m^2 = avg body surface area of a person
calculate osmolarity
multiply the mmol/L of each component by its van't Hoff factor - total osmolarity is the sum of each components' individual osmolarities: mOsmol/L = (sum) i*C => [sum] i * mmol/L - i = van't Hoff factor of each component - C = mM concentration (millimoles/L)
SI: n
nano 0.000,000,001 10^-9
dosage forms that should be isotonic
nasal, ophthalmic, or injectable solutions
functional unit of the kidneys
nephrons - responsible for the filtration, secretion, and reabsorption of drugs
v/v
percent volume in volume - solutions of liquids in liquids = mL/ 100 mL soln
w/v
percent weight in volume - solutions or suspensions of solids in liquids = g/ 100 mL soln
w/w
percent weight in weight - mixtures of solids or semisolids = g/ 100 g mixture
SI: p
pico 0.000,000,000,001 10^-12
specific gravity
ratio of the weight of a substance to the weight of a standard substance when both substances are at the same temperature -> the standard substance for liquids is water - no units and is constant for a particular substance
glomeruli
receive all of the blood from the renal artery (1200 mL/min or ~20% of cardiac output) - glomerulus filters ~10% of the plasma water
dosage regimen
schedule of dosing
avoirdupois system
used in the US to measure weights in ounces and pounds
ratio strength
used to denote the concentration of very dilute solutions - customary for the first number of the ratio to be 1
english system
used to measure lengths in feet and inches
to calculate the amount of tonicity agent to add:
utilize the E value method
1:750 means
solid in a liquid: 1 g drug in 750 mL soln liquid in a liquid: 1 mL drug in 750 mL soln solid in a solid: 1 g drug in 750 g mixture
electrolytes
substances that do dissociate in solution, and therefore, carry an electrical charge - examples: sodium chloride, magnesium sulfate, sodium citrate, (salts)
nonelectrolytes
substances that do not dissociate in solution - examples: dextrose, urea, glucose
dosage forms: rectal
suppositories, solutions, ointments, creams
dosage forms: oral
tablets, capsules, suspensions, solution, drops, syrups
Individualized GFR (iGFR)
to use it for dosing drugs, need to individualize it to using the patient's BSA iGFR = eGFR x (patient BSA in m^2 / 1.73 m^2) units = mL/min
two types of balances used in preparation of pharmaceutical dosage forms:
torsion digital
1 Equivalent
weight of a substance that can combine with or replace one gram atomic weight of hydrogen (one mole)
1 milliEquivalent
weight of a substance that can combine with or replace one milligram atomic weight of hydrogen (one millimole)
isotonic
when the concentrations of dissolved particles in a solution are at the same concentration as those in the blood
iso-osmotic
when the concentrations of dissolved particles on either side of a membrane are equal
'Units' refer to
units of activity measured in a bioassay - compared to a reference standard ex: activity of insulin is assayed by determining how a new batch of insulin compares to a standard in its ability to lower blood sugar in a rabbit
divided dose
a daily dose subdivided
parenteral products
- Large volume parenterals (LVP) = contain > 100 mLs - Small volume parenterals (SVP) = vials or ampules; contain < or equal to 100 mLs
activity of products (and their dose) can be expressed as
- Units or International Units (IU) - Micrograms per millgram (mcg/mg) - some other expression - there is no relationship between the unit of potency of one drug and the unit of potency of another drug (IU Nystatin does not equal IU penG) - need to be able to convert units of potency
calculation of doses: dose of a drug needed by a patient can be determined in a variety of ways
- age - body weight (actual, lean) or even adjusted - surface area - kidney function - degree of liver dysfunction
direct proportions
- as one value doubles an associated value doubles - can use either ratios or related terms in direct proportions
creatinine
- common way to assess kidney function = creatinine clearance - creatinine = metabolite of creatine - creatinine does not bind to proteins; freely filtered by kidneys (does undergo some secretion - so it slightly overestimates GFR)
related terms
- define the relationship between two amounts - simple related terms have numerical values and units - can be used to construct conversion factors, proportions and dimension analysis strings
Cockcroft-Gault equation: which "weight" to use
- if patient's actual weight < IBW, use actual body weight - if patient's actual weight is > IBW but < 1.25xIBW, use ideal body weight (IBW) - if patient's actual weight is > 1.25xIBW, use adjusted body weight (AdjBW)
milliosmoles
- osmotic pressure is proportional to the total number of particles in solution - measured in units of millosmoles (mOsmol)
osmotic pressure
- phenomenon created by particles in solution which are prevented from diffusing throughout a solution by a semipermeable membrane
concentration vs density
- solutions of drugs or other ingredients in water will have a density AND a concentration - both have units of g/mL - distinguish density from concentration by LABELING substance appropriately in your calculation density: g soln / mL soln concentration: g drug or substance / mL soln
adjusted body weight (AdjBW)
- some patients are overweight or obese - the physiologic alterations that accompany an increase in body fat can alter the pharmacokinetics of some drugs - requires that we use an adjusted body weight when calculating a dose of a drug or when estimating renal function
ratios
- the relative magnitude of two like numbers - when doing story problems 'like numbers' are numbers with the same units
the van't Hoff factor (i)
- theoretically - complete dissociation - however, (ex: NaCl) - partial dissociation: NaCl -> only 80% dissociates
milliequivalents
- used commonly in US to express the concentration of electrolytes in solution - related to the total number of ionic charges in solution and considers the valence (charge of each ion)
once a drug is in the body, there are two main ways it is removed
- via the liver by metabolism or excretion into the bile - via the kidneys (urine) - when one of these organs does not function appropriately, the rate of drug removal greatly changes - we adjust the doses or frequency of administration of drugs to prevent toxic levels in our patients
aliquots
- way to measure quantities of ingredients that are less than your MWQ or MMV - to do this, we dilute the drug to a quantity that can be measured with the analytical equipment - we can then take an "aliquot" of this dilution to get the weight or volume that contains the desired amount of drug
milliosmoles vs. milliequivalents:
- when calculating milliosmoles: you count all of the species of a chemical substance - when calculating milliequivalents, you count either the positive or the negative charges --> milliequiVALENCE: think of valence as charge!
AdjBW =
0.4 (actual BW - LBW) + LBW
density of water
1 g / 1 mL
steps in a liquid in liquid aliquot problem
1. determine your MMV 2. select a multiple of the amount that will equal or exceed the MMV 3. select an aliquot volume 4. calculate the amount of diluent to add 5. divide the total amount of dilution by your multiplication factor
steps in a solid in solid aliquot problem
1. determine your MWQ 2. select a multiple of the amount that will equal or exceed the MWQ 3. select an aliquot weight 4. calculate the amount of diluent to add 5. divide the total amount of dilution by your multiplication factor
steps for using E value
1. using E value, calculate the amount of sodium chloride equivalent to the drug 2. calculate the weight of sodium chloride necessary to make the solution isotonic 3. calculate the amount of sodium chloride that needs to be added - either a weight of solid NaCl or a volume of 0.9% NaCl
IBW (female)
45.5 kg + [ 2.3 * (# inches over 5 ft) ]
the % error used in prescription compounding is usually
5% - can use lower cutoff if weighing accuracy is critical
IBW (male)
50 kg + [ 2.3 * (# inches over 5 ft) ]
specific gravity (equation)
= weight of substance / weight of equal volume of water because 1 mL of water = 1 g = # grams of substance / # mL of substance
common anions in the blood include
Cl- SO4 2- (sulfate) HCO3 - (bicarbonate) CO3 2- (carbonate) C2H3O2 - (citrate) HPO4 2- (phosphate)
Cockcroft-Gault equation (females)
CrCl (females) = [ (140 - age) * body weight * 0.85 ] / (72 * Scr) (females have 15% less muscle mass)
Cockcroft-Gault equation (males)
CrCl (males) = [ (140 - age) * body weight ] / (72 * Scr) CrCl (creatinine clearance) = mL/min age = year body weight = kg Scr (serum creatinine) = mg/dL -> note that some clinicians will round Scr up to 1 mg/dL
Ideal Body Weight (IBW)
IBW (males) = 50 kg + [ 2.3 * (# inches over 5 ft) ] IBW (females) = 45.5 kg + [ 2.3 * (# inches over 5 ft) ]
common cations in the blood include
Na+ K+ Ca2+ Mg2+
BSA =
SQUARE ROOT [ (height * weight) / 3600 ] units BSA: m^2 height = cm weight = kg
related terms should be given
a number, a unit, and a substance
parenteral administration
administration by injection, infusion, or implantation
overfill
although a vial or a bag of IV fluid may be labeled to contain a certain volume, the actual volume is larger due to overfill **for the purpose of doing infusion calculations in this course, ignore overfill amounts and assume no fluids are removed from the bag
dose of a drug
amount of drug administered or taken by a patient
single dose
amount taken at any one time
total dose
amount taken during the course of therapy
daily dose
amount taken in a day
functions of electrolytes
are numerous - maintain acid/base balance - maintain body water volume
intravenous route
can administer drugs as a bolus or an infusion
SI: c
centi 0.01 10^-2
dosage forms: topical/transdermal
creams, ointments, lotions, patches
SI: d
deci 0.1 10^-1
osmolarity
describes the number of milliosmoles in 1 liter of solution (mOsmol/L) - osmolarity is calculated and cannot be directly measured
tonicity agents include
dextrose, glycerin, mannitol, potassium chloride, and sodium chloride
GFR
glomerular filtration rate = 120 mL/min
milliequivalents: if an ion has a +2 or -2 charge
it is considered the equivalent of 2 hydrogen ions - 1 equivalent of Ca2+ replaces 2 equivalents of H+ - 1 equivalent of SO4 2- can combine with 2 equivalents of H+
SI: k
kilo 1000 10^3
calculation of doses by age and weight
labeling of many drugs provides a dose or dosage range for adults, a second dose or dosage range for children, and a third for elderly patients or patients with reduced kidney function - in addition to age, doses are described on a per unit weight basis
calculating E value
large tables of E values have been published E = [ (MW of NaCl / i for NaCl) * (i for substance/MW of substance) ] i = van't Hoff factor MW of NaCl / i for NaCl = 58.5 / 1.8 = 32.5
SI: m
milli 0.001 10^-3
osmolality:
milliosmoles of solute per kilogram of solution
MMV
minimum measurable volume MMV = total capacity * 0.2
MWQ
minimum weighable quantity - the smallest weight that can be accurately weighed on the balance
millimoles
mmol/L - electrolyte solutions can be expressed in a number of way including: millimoles per liter (mmol/L)
valence
number of usable outer electrons - to calculate the valence, simply divide a chemical compound into its positive or negative components, and then count the number of either positive or negative charges - NOT BOTH positive and negative
Adjusted Body Weight (AdjBW)
obese AdjBW = 0.4(Actual BW - IBW) + IBW
mmol =
one thousandth of a mole 1 mole / 1000 mmol
ppb
parts per billion - parts of a drug to 1,000,000,000 parts of the solution 15 ppb of lead in drinking water: 15 parts of lead to every 1,000,000,000 parts of water
ppm
parts per million - parts of a drug to 1,000,000 parts of the solution 3.5 ppm of fluoride in drinking water: 3.5 parts of fluoride to every 1,000,000 parts of water
percentage strenth
percent (%) means parts per 100 or in 100 - denominator: always the total amount of solution or mixture (not the amount of diluent)
units of potency
potencies of some medications (antibiotics, vitamins, biologics, etc.) derived from nature are expressed in terms of units
molecules in solution may
remain intact or may dissociate into ions that carry an electrical charge
MWQ for a torsion balance
sensitivity / % error
class A torsion balance
sensitivity: 5-6 mg capacity: 120 g
infusion pumps
set infusion rate in mL/hour or mL/min typical rates: 42 to 150 mL/hr
IV infusion
solution slowly and continuously infused into a vein
dosage forms: nasal
solutions, sprays, ointments
dosage forms: parenteral
solutions, suspensions
dosage forms: opthalmic
solutions, suspensions, ointments
dose measurement
some dosage forms are individual units (ie. tablets) while some need a device to measure (ie. solutions)
ideal body weight
some drugs partition mainly into lean tissues (muscles) such that lean body mass will be a better predictor of drug concentration than total body weight -> this means an obese patient could receive more drug than required to produce therapeutic levels in the lean tissues if the dose were based on actual body weight - lean body mass (ideal body weight) usually estimated from an equation
IV Push or Bolus
the drug is injected from a syringe directly into a vein or IV port over < or equal to 5 minutes - rapid, small volume
osmotic pressure: water moves to the side containing
the greater concentration of dissolved particles until the concentrations are equal - ANY dissolved solute will contribute to the osmotic pressure: sodium, chloride, proteins, glucose
capacity
the maximum weight, including containers and tares, that can be placed on the balance
E value
the number of grams of sodium chloride that would produce the same tonicity effect as 1 gram of the drug -> the tonicity agent is added as a solid so you calculate the weight needed
millosmoles: for electrolytes
the total number of particles in solution depends on the degree of dissociation assuming complete dissociation: - 1 mmol NaCl represents 2 mOsmol of total particles (Na+ and Cl-) - 1 mmol sodium citrate represents 4 mOsmol of total particles (3 Na+ and 1 citrate) - complete dissociation does not actually happen for most compounds
tonicity agent other than NaCl
there may be instances when the tonicity agent you will use is not sodium chloride. these calculations are done with the same 3 initial steps with the addition of a 4th step: - convert the grams of sodium chloride to grams of other tonicity agent using the E value as a conversion factor
if E value for a drug was 0.15
this means that 0.15 g of sodium chloride would produce the same tonicity effect as 1 gram of drug = 0.15 g NaCl / 1 g drug
apothecaries' system
traditional system of measure for pharmacists