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Equations

105 equations from the lessons, grouped by module. Each has its symbols defined, and the lesson's example where it gives one.

1

ADME overview

2 equations
1.3 Metabolism
Oral bioavailability
F = Fa x Fg x Fh
F
the oral bioavailability, the fraction of the dose that reaches the systemic circulation unchanged
Fa
the fraction absorbed
Fg
the fraction of the absorbed drug that escapes metabolism in the gut wall
Fh
the fraction of the drug that passes through the liver unchanged

The gut wall then removes a little over 40 percent of the absorbed drug, and the liver removes a little over 40 percent of the rest, so F is only about 30 percent.

1.5 Paracetamol and pharmacokinetics
Bioavailability from the AUC
F = AUC (oral) / AUC (intravenous), for equal doses
F
the bioavailability
AUC (oral)
the area under the curve after an oral dose
AUC (intravenous)
the area under the curve after an equal intravenous dose
2

Absorption

10 equations
2.1 Dissolution and solubility
Noyes-Whitney equation
dM/dt = D x A x (Cs - C) / h
dM/dt
the dissolution rate, the mass of drug that dissolves in a unit of time
D
the diffusion coefficient, which tells how fast dissolved molecules move through the fluid
A
the surface area of the solid
Cs
the solubility
C
the drug concentration in the fluid
h
the thickness of the diffusion layer, a thin layer of still fluid around the particle
2.3 First-pass metabolism
Oral bioavailability
F = Fa x Fg x Fh
F
oral bioavailability, the fraction of the dose that reaches the systemic circulation unchanged
Fa
the fraction absorbed, the fraction of the dose that enters the gut wall
Fg
the fraction of this drug that escapes metabolism in the gut wall
Fh
the fraction of the drug that enters the liver and escapes removal there, mainly by metabolism
Fraction that escapes an organ
Fg = 1 - E and Fh = 1 - E
Fg
the fraction of the drug that escapes metabolism in the gut wall
Fh
the fraction of the drug that enters the liver and escapes removal there
E
the extraction ratio, the fraction of the drug that enters an organ and that the organ removes

The intravenous dose gave the extraction ratio of the liver, 0.44, so Fh was 0.56.

Fraction that passes both organs
fraction of the absorbed drug that passes both organs = Fg x Fh
Fg
the fraction of the drug that escapes metabolism in the gut wall
Fh
the fraction of the drug that enters the liver and escapes removal there
Bioavailability from the AUC
F = AUC (buccal) / AUC (intravenous), for equal doses
F
the bioavailability
AUC
the area under the plasma concentration-time curve

The buccal AUC was 74.5 percent of the intravenous AUC, so the buccal bioavailability was 74.5 percent.

2.4 Bioavailability
Bioavailability of an oral dose
F = Fa x Fg x Fh
F
bioavailability, the fraction of a dose that reaches the systemic circulation unchanged
Fa
the fraction absorbed, the fraction of the dose that crosses into the gut wall
Fg
the fraction of drug that enters the gut wall and escapes metabolism there
Fh
the fraction of drug that enters the liver and escapes metabolism there

For example, with an Fa of 0.9, an Fg of 0.8 and an Fh of 0.5, F is 0.36, or 36 percent.

Area under the curve
AUC = amount of drug that reaches the systemic circulation / clearance
AUC
the area under the curve of concentration against time
clearance
the volume of plasma from which the body removes all of the drug per unit of time
Absolute bioavailability
F = (AUC oral / dose oral) / (AUC intravenous / dose intravenous)
F
bioavailability, the fraction of a dose that reaches the systemic circulation unchanged
AUC
the area under the curve of concentration against time

Division of each AUC by its dose gives the correct value, 49 percent.

Relative bioavailability
relative bioavailability = (AUC test / dose test) / (AUC reference / dose reference)
AUC
the area under the curve of concentration against time
test
one product
reference
the other product, which the calculation uses as the reference

In one study, the relative bioavailability of an oral solution against the tablet was 105 percent.

2.5 Food effects
Log P
log P = log (concentration in octanol / concentration in water)
log P
a measure of lipophilicity
concentration in octanol
the drug concentration in octanol
concentration in water
the drug concentration in water
3

Distribution

12 equations
3.1 Volume of distribution
Volume of distribution
Vd = amount of drug in the body / plasma concentration, after distribution is complete
Vd
the volume of distribution
plasma
the liquid part of the blood
Kp,uu
Kp,uu = unbound tissue concentration / unbound plasma concentration
Kp,uu
the ratio of the unbound tissue concentration to the unbound plasma concentration
3.2 Protein and tissue binding
Fraction unbound
fu = unbound concentration / total concentration
fu
the fraction unbound
unbound concentration
the concentration of drug that is not bound to plasma proteins
total concentration
bound plus unbound
Kp,uu
Kp,uu = unbound tissue concentration / unbound plasma concentration
Kp,uu
the ratio of the unbound tissue concentration to the unbound plasma concentration
Liver clearance of a low-clearance drug
CLliver ~ fu x CLint
CLliver
the liver clearance
fu
the fraction unbound
CLint
the intrinsic clearance, which measures the activity of the liver enzymes on unbound drug

Suppose fu doubles for such a drug, and the dose rate, the dose given per unit time, and CLint stay the same. The clearance doubles, and the total concentration at steady state falls to half.

3.3 The blood-brain barrier
Kp
Kp = total brain concentration / total plasma concentration
Kp
the total brain concentration, bound plus unbound, divided by the total concentration in plasma
Kp,uu
Kp,uu = unbound brain concentration / unbound plasma concentration
Kp,uu
the same ratio as Kp, for unbound drug
Kp,uu at steady state
Kp,uu = clearance into the brain / clearance out of the brain
Kp,uu
the ratio of the unbound brain concentration to the unbound plasma concentration
clearance into the brain
the volume of plasma from which all unbound drug is removed per unit time
clearance out of the brain
the volume of brain fluid, the fluid between brain cells, from which all unbound drug is removed per unit time
3.4 Placenta and breast milk
Fetal Kp,uu
Fetal Kp,uu = unbound concentration in fetal plasma / unbound concentration in maternal plasma
Fetal Kp,uu
the unbound drug concentration in fetal plasma divided by that in maternal plasma
Milk-to-plasma ratio
milk-to-plasma ratio = concentration in milk / concentration in maternal plasma
milk-to-plasma ratio
the drug concentration in milk divided by that in maternal plasma

In the same women, 2 to 3 weeks after birth, the median milk-to-plasma ratio was 0.61.

Infant dose
infant dose = milk concentration x daily milk intake per kilogram of infant weight
infant dose
the milk concentration times the daily milk intake per kilogram of infant weight
Relative infant dose
relative infant dose = infant dose / (daily maternal dose per kilogram of maternal weight) x 100 percent
relative infant dose
the infant dose as a percentage of the daily maternal dose per kilogram of maternal weight

In the same study, the infant dose was 0.51 milligrams per kilogram per day, and the relative infant dose was 9.2 percent.

4

Metabolism

7 equations
4.4 Genes and metabolism
CYP2D6 activity score
activity score = value of allele 1 + value of allele 2
activity score
the sum of the values of the two alleles
value of an allele
0 for no function, 0.25 or 0.5 for decreased function, and 1 for normal function
Value of an allele with extra gene copies
value of the allele = allele value x number of copies
allele value
the activity value of the allele
number of copies
the number of gene copies of the allele
Activity score with a moderate inhibitor
adjusted activity score = activity score x 0.5
activity score
the sum of the values of the two alleles
4.5 Hepatic extraction
Hepatic clearance from blood
hepatic clearance = hepatic blood flow x extraction ratio
hepatic clearance
the clearance by the liver
hepatic blood flow
the volume of blood that passes through the liver per unit of time
extraction ratio
the fraction of the drug that enters the liver and that the liver removes in one pass of the blood
Extraction ratio in the well-stirred model
extraction ratio = (unbound fraction x intrinsic clearance) / (unbound fraction x intrinsic clearance + hepatic blood flow)
extraction ratio
the fraction of the drug that enters the liver and that the liver removes in one pass of the blood
unbound fraction
the concentration of drug that is not bound to proteins, divided by the total concentration in blood
intrinsic clearance
the rate of metabolism in the liver divided by the unbound drug concentration at the enzymes
hepatic blood flow
the volume of blood that passes through the liver per unit of time

Lidocaine is a high-extraction drug: in six healthy adults who received lidocaine by infusion into a vein, the extraction ratio was 0.86.

Hepatic clearance of a high-extraction drug
hepatic clearance approaches hepatic blood flow, and the extraction ratio approaches 1
hepatic clearance
the clearance by the liver
hepatic blood flow
the volume of blood that passes through the liver per unit of time
Hepatic clearance of a low-extraction drug
hepatic clearance approaches (unbound fraction x intrinsic clearance), and the extraction ratio is small
hepatic clearance
the clearance by the liver
unbound fraction x intrinsic clearance
the product of the unbound fraction and intrinsic clearance
5

Excretion

19 equations
5.1 Clearance
Rate of elimination
rate of elimination = clearance x plasma concentration
rate of elimination
the amount of drug that the body removes per unit of time
clearance
the volume of plasma from which the body removes all of the drug per unit of time
plasma concentration
the concentration of drug in plasma

With a clearance of 52 liters per hour, the body removes 52 milligrams per hour at a concentration of 1 milligram per liter.

Amount eliminated
amount eliminated = clearance x AUC
amount eliminated
the whole dose that the body eliminates
clearance
the volume of plasma from which the body removes all of the drug per unit of time
AUC
the area under the whole concentration-time curve, which measures the total exposure to the drug
Clearance after an intravenous dose
clearance = intravenous dose / AUC
clearance
the volume of plasma from which the body removes all of the drug per unit of time
intravenous dose
a dose that goes into a vein, so the whole dose enters the systemic circulation directly
AUC
the area under the whole concentration-time curve

The calculated AUC for a 400 milligram intravenous dose in these subjects is 400 divided by 52.2, about 7.7 milligram hours per liter.

Apparent oral clearance
clearance / F = oral dose / AUC
clearance / F
the apparent oral clearance
F
the oral bioavailability, the fraction of the dose that reaches the systemic circulation unchanged
AUC
the area under the whole concentration-time curve
Total clearance
total clearance = renal clearance + hepatic clearance + clearance by any other route
renal clearance
the clearance of the kidneys, which excrete unchanged drug into urine
hepatic clearance
the clearance of the liver, which removes drug by metabolism and by excretion into bile

The renal clearance was 26.5 liters per hour, and the nonrenal clearance was 25.8, which add to about the total.

Renal clearance from urine collection
renal clearance = amount of unchanged drug in the urine / AUC over the same interval
renal clearance
the clearance of the kidneys
AUC
the area under the concentration-time curve over the interval
Nonrenal clearance
nonrenal clearance = total clearance - renal clearance
nonrenal clearance
the total clearance minus the renal clearance

The renal clearance was 26.5 liters per hour, and the nonrenal clearance was 25.8, which add to about the total.

Dose for a target AUC
dose = clearance x target AUC
clearance
the volume of plasma from which the body removes all of the drug per unit of time
target AUC
the AUC on which the dosing decision depends
5.2 The kidney
Renal clearance from urine collection
renal clearance = amount of unchanged drug that enters the urine / AUC
renal clearance
the volume of plasma from which the kidneys remove all of the drug per unit of time
amount of unchanged drug that enters the urine
the amount over a time interval
AUC
the area under the plasma concentration-time curve for the same interval
Clearance of each renal process
clearance = rate of drug transfer / plasma concentration
clearance
the clearance of filtration, secretion or reabsorption
rate of drug transfer
the rate of drug transfer by the process
plasma concentration
the concentration of drug in plasma
Renal clearance
renal clearance = filtration clearance + secretion clearance - reabsorption clearance
filtration clearance
the clearance by filtration
secretion clearance
the clearance by secretion
reabsorption clearance
the clearance by reabsorption

Metformin, a drug for type 2 diabetes, shows filtration and secretion. Its renal clearance is about 510 milliliters per minute, about 4 times the creatinine clearance. Filtration accounts for about 120 milliliters per minute, and secretion by OCT2, MATE1 and MATE2-K for the other 390.

Filtration clearance
filtration clearance = fraction unbound in plasma x GFR
fraction unbound in plasma
the fraction of the drug that is not bound to plasma proteins
GFR
the glomerular filtration rate, the volume of plasma that passes from the glomeruli into Bowman's space per unit of time
5.4 Clearance, volume and half-life
Elimination rate constant
k = rate of elimination / amount of drug in the body
k
the elimination rate constant
rate of elimination
the amount of drug that the body removes per unit of time
amount
the amount of drug in the body
Clearance
CL = rate of elimination / C
CL
clearance, the volume of plasma from which the body removes all of the drug per unit of time
C
the plasma concentration
Volume of distribution
Vd = amount of drug in the body / C
Vd
the volume of distribution
C
the plasma concentration
Rate and amount from concentration
rate of elimination = CL x C; amount of drug in the body = Vd x C
CL
clearance
Vd
the volume of distribution
C
the plasma concentration
Elimination rate constant from clearance and volume
k = CL / Vd
k
the elimination rate constant
CL
clearance
Vd
the volume of distribution
Half-life from k
t1/2 = ln(2) / k = 0.693 / k
t1/2
half-life, the time for the plasma concentration to fall by half
k
the elimination rate constant
Half-life from volume and clearance
t1/2 = 0.693 x Vd / CL
t1/2
half-life
Vd
the volume of distribution
CL
clearance

For the group with obesity, 0.693 times 228 liters, divided by 1.92 liters per hour, gives 82 hours.

6

Pharmacokinetic models

37 equations
6.1 The one-compartment model
Elimination rate constant
k = rate of elimination / amount of drug in the body
k
the elimination rate constant
rate of elimination
the amount removed per unit of time
Volume of distribution
Vd = amount of drug in the body / plasma concentration
Vd
the volume of distribution
Plasma concentration after an intravenous bolus
C = C0 x e^(-k x t)
C
the plasma concentration at time t after the bolus
C0
the plasma concentration at time zero
e
the number e, about 2.718, the base of the natural logarithm
k
the elimination rate constant
t
time after the bolus
Initial concentration
C0 = dose / Vd
C0
the plasma concentration at time zero
Vd
the volume of distribution

The model gives the initial concentration as the dose, 2,000 milligrams, divided by the median volume of 58.3 liters. This is about 34 milligrams per liter.

Volume of distribution from the fitted curve
Vd = dose / C0
Vd
the volume of distribution
C0
the value of the fitted curve extended back to time zero
Half-life
t1/2 = 0.693 / k
t1/2
half-life, the time for the plasma concentration to fall by half
0.693
the natural logarithm of 2
k
the elimination rate constant

The half-life is then 0.693 divided by 0.35 per hour, about 2.0 hours.

Elimination rate constant from clearance and volume
k = CL / Vd
k
the elimination rate constant
CL
clearance
Vd
the volume of distribution

Their ratio, 20.3 liters per hour divided by 58.3 liters, is also about 0.35 per hour.

Elimination rate constant from two points
k = (ln C1 - ln C2) / (t2 - t1)
k
the elimination rate constant
C1, C2
the concentrations at two points on the line
t1, t2
the times of the two points

The natural logarithms of 22.5 and 3.9 differ by about 1.75. Divided by the 5 hours between these two times, this gives k of about 0.35 per hour.

6.2 Two compartments
Plasma concentration in a two-compartment model
C = A x e^(-alpha x t) + B x e^(-beta x t)
C
the plasma concentration at time t after the dose
A, B
the values of the two terms at time zero
e
the number 2.718, the base of the natural logarithm
alpha, beta
rate constants: the larger the constant, the faster its term falls; alpha is the larger
Terminal half-life
t1/2 = 0.693 / beta
t1/2
the terminal half-life, the half-life of the elimination phase
0.693
the natural logarithm of 2
beta
the rate constant of the slow term
Distribution half-life
t1/2 (distribution) = 0.693 / alpha
alpha
the rate constant of the fast term
0.693
the natural logarithm of 2

The mean distribution half-life was 0.35 hours, about 21 minutes.

Clearance
CL = rate of elimination / plasma concentration
CL
clearance
6.3 Repeated doses
Accumulation ratio
R = AUC over one interval at steady state / AUC over the first interval
R
the accumulation ratio
AUC
the area under the plasma concentration curve, the exposure to the drug over a period of time

R was the AUC over 12 hours on the last day, divided by the AUC over the first 12 hours.

Accumulation ratio in the simplest model
R = 1 / (1 - f)
R
the accumulation ratio
f
the fraction of a dose left at the end of one interval

When the interval equals the half-life, half of each dose is left when the next dose comes, so R is 2. With an interval of half the half-life, about 71 percent is left, and R is about 3.4. With an interval of two half-lives, 25 percent is left, and R is about 1.3.

Peak-to-trough ratio
peak-to-trough ratio = peak / trough
peak
the highest concentration in the interval
trough
the lowest concentration, just before the next dose

In the simplest model, at an interval equal to the half-life, the trough is half the peak.

6.4 Steady state and loading doses
Dose rate
dose rate = dose / dosing interval
dose rate
the dose divided by the interval between doses
Dose rate at steady state
dose rate = rate of elimination = CL x C
CL
clearance
C
the plasma concentration
Average concentration at steady state
C(average, steady state) = dose rate / CL
C
the average plasma concentration at steady state
CL
clearance
Volume of distribution
Vd = amount of drug in the body / plasma concentration
Vd
the volume of distribution
Amount of drug in the body at the target
amount = target concentration x Vd
target concentration
a plasma concentration chosen to be effective and safe
Vd
the volume of distribution
Loading dose into a vein
loading dose = target concentration x Vd
target concentration
a plasma concentration chosen to be effective and safe
Vd
the volume of distribution

For a target of 20 milligrams per liter, the loading dose is 20 times 0.97, about 19 milligrams per kilogram.

Maintenance dose rate
maintenance dose rate = target concentration x CL
target concentration
a plasma concentration chosen to be effective and safe
CL
clearance
6.5 Nonlinear pharmacokinetics
Michaelis-Menten equation
rate = Vmax x C / (Km + C)
rate
the rate of the process
C
the drug concentration
Vmax
the maximum rate
Km
the concentration that gives half of Vmax

With these values, the Michaelis-Menten equation gives a steady-state concentration of 10 milligrams per liter at 264 milligrams per day, and 20 at 323.

Clearance for saturable elimination
CL = Vmax / (Km + C)
CL
clearance
Vmax
the maximum rate
Km
the concentration that gives half of Vmax
C
the drug concentration
Clearance
CL = rate of elimination / plasma concentration
CL
clearance
6.6 Noncompartmental analysis and population PK
Area of one trapezoid
area = (C1 + C2) / 2 x (t2 - t1)
C1, C2
the two concentrations of a pair of consecutive points
t2 - t1
the time between them
AUC to the last sample
AUC(0 to last) = sum of the trapezoid areas
AUC
the area under the concentration-time curve
Terminal half-life
t1/2 = 0.693 / lambda z
t1/2
the terminal half-life, the time for the concentration to fall by half in the last phase
0.693
the natural logarithm of 2
lambda z
the terminal rate constant, minus the slope of the regression line of the natural logarithm of the concentration against time
AUC to infinity
AUC(0 to infinity) = AUC(0 to last) + Clast / lambda z
Clast
the last concentration
lambda z
the terminal rate constant
Apparent clearance of an oral dose
CL/F = dose / AUC(0 to infinity)
CL/F
the apparent clearance, the clearance divided by the bioavailability
dose
the oral dose
6.7 Noncompartmental analysis
Terminal half-life
t1/2 = 0.693 / lambda z
t1/2
the terminal half-life, the time for the concentration to fall by half in the terminal phase
lambda z
the rate constant of the terminal phase

Lambda z was 0.0815 per hour, and the terminal half-life was 8.5 hours.

AUC to infinity
AUC(0 to infinity) = AUC(0 to last) + Clast / lambda z
AUC(0 to last)
the AUC to the last sample
Clast
the last measured concentration
lambda z
the rate constant of the terminal phase

The area after the last sample was 15.3, so the log-down AUC to infinity was 102 milligram hours per liter.

Extrapolated percentage
extrapolated percentage = (Clast / lambda z) / AUC(0 to infinity) x 100
Clast / lambda z
the area after the last sample
AUC(0 to infinity)
the AUC to infinity

The extrapolated percentage was 15 percent, below the 20 percent maximum of the bioequivalence criterion.

Clearance
CL = dose / AUC(0 to infinity); CL/F = dose / AUC(0 to infinity) after an oral dose
CL
clearance after an injection into a vein
CL/F
the apparent clearance after an oral dose

CL over F was 3.13 liters per hour, and Vz over F was 38.5 liters.

Volume of distribution in the terminal phase
Vz = CL / lambda z
Vz
the volume of distribution in the terminal phase
CL
clearance
lambda z
the rate constant of the terminal phase

CL over F was 3.13 liters per hour, and Vz over F was 38.5 liters.

Mean residence time
MRT = AUMC / AUC
MRT
the mean residence time
AUMC
the area under the curve of time multiplied by concentration
AUC
the area under the concentration-time curve

The MRT was 12.9 hours.

Volume of distribution at steady state
Vss = CL x MRT
Vss
the volume of distribution at steady state
CL
clearance
MRT
the mean residence time
7

Prediction

18 equations
7.1 In vitro ADME assays
In vitro intrinsic clearance
CLint = rate of metabolism in the assay / drug concentration
CLint
in vitro intrinsic clearance
CLint from microsomes
CLint = k x mixture volume per milligram of microsomal protein
CLint
in vitro intrinsic clearance
k
the steepness of the line of the natural logarithm of the amount left against time
Apparent permeability
Papp = rate at which drug appears on the far side / (layer area x initial concentration)
Papp
the apparent permeability

In one Caco-2 study, the Papp of apixaban was 0.9 times 10 to the minus 6 centimeters per second.

Efflux ratio
efflux ratio = Papp (blood side to gut side) / Papp (gut side to blood side)
Papp
the apparent permeability

The efflux ratio was more than 10, in Caco-2 cells and in cells with added P-gp or BCRP, a second efflux transporter.

Fraction unbound
fu = unbound drug concentration in plasma / total concentration
fu
the fraction unbound

In human plasma in vitro, proteins bound about 87 percent, so fu was about 0.13.

Fraction unbound by equilibrium dialysis
fu = buffer concentration / plasma concentration
fu
the fraction unbound
7.2 From test tube to human
Unbound fraction
unbound fraction = unbound concentration / total concentration
unbound concentration
the concentration of drug free in solution, not attached to proteins or membranes
Intrinsic clearance
intrinsic clearance = rate of metabolism / unbound drug concentration at the enzymes
intrinsic clearance
the removal by the enzymes alone, apart from any limit by blood flow or protein binding
In vitro intrinsic clearance of total drug
in vitro intrinsic clearance = rate constant x incubation volume / amount of microsomal protein
rate constant
the rate of loss divided by the amount of drug that remains
incubation volume
the volume of the incubation
amount of microsomal protein
for hepatocytes, the number of cells replaces the amount of protein
Unbound fraction in blood
unbound fraction in blood = unbound fraction in plasma / blood-to-plasma concentration ratio
blood-to-plasma concentration ratio
the ratio of the concentration in blood to the concentration in plasma
Fold error
fold error = predicted clearance / observed clearance
fold error
the predicted clearance divided by the observed clearance

This prediction was within twofold and 1.7 times too low.

7.3 From animals to humans
Allometric power equation
Y = a x W^b
Y
the property, for example clearance
W
the body weight
a
the coefficient, the value of Y at 1 kilogram
b
the exponent, which sets how fast Y changes with body weight
Volume of distribution
Vd = amount of drug in the body / plasma concentration
Vd
the volume of distribution
Single-species scaling
CLhuman/kg = 0.407 x CLmonkey/kg
CLhuman/kg
human clearance per kilogram
CLmonkey/kg
the monkey clearance per kilogram
7.4 PBPK models
Tissue-to-plasma partition coefficient
Kp = total drug concentration in a tissue / total drug concentration in plasma
Kp
the tissue-to-plasma partition coefficient, when both concentrations are constant
Equation for each organ
rate of change of the drug amount = rate in - rate out
rate in
the rate at which arterial blood carries the drug into the organ
rate out
the rate at which venous blood carries the drug out of the organ
7.6 From molecule to dose
AUC of one dose
AUC = F x dose / CL
AUC
the area under the curve of plasma concentration against time
F
oral bioavailability, the fraction of an oral dose that reaches the systemic circulation unchanged
CL
clearance, the volume of plasma from which the body removes all of the drug per unit of time

For this dose, 0.87 times 100 milligrams, divided by 25 liters per hour, gives a daily AUC of about 3.5 milligram hours per liter.

Dose equation
dose = CL x target AUC / F
CL
clearance, the volume of plasma from which the body removes all of the drug per unit of time
target AUC
the target exposure, the area under the curve of plasma concentration against time
F
oral bioavailability, the fraction of an oral dose that reaches the systemic circulation unchanged