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