1ADME overview
2 equations
- 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.
- 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
2Absorption
10 equations
- 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
- 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
- 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.
- 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
- 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.
- 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.
- 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
- 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.
- 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.
- log P
- a measure of lipophilicity
- concentration in octanol
- the drug concentration in octanol
- concentration in water
- the drug concentration in water
3Distribution
12 equations
- Vd
- the volume of distribution
- plasma
- the liquid part of the blood
- Kp,uu
- the ratio of the unbound tissue concentration to the unbound plasma 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
- the ratio of the unbound tissue concentration to the unbound plasma concentration
- 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.
- Kp
- the total brain concentration, bound plus unbound, divided by the total concentration in plasma
- Kp,uu
- the same ratio as Kp, for unbound drug
- 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
- Fetal Kp,uu
- the unbound drug concentration in fetal plasma divided by that 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
- the milk concentration times the daily milk intake per kilogram of infant weight
- 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.
4Metabolism
7 equations
- 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
- allele value
- the activity value of the allele
- number of copies
- the number of gene copies of the allele
- activity score
- the sum of the values of the two alleles
- 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
- 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
- the clearance by the liver
- hepatic blood flow
- the volume of blood that passes through the liver per unit of time
- hepatic clearance
- the clearance by the liver
- unbound fraction x intrinsic clearance
- the product of the unbound fraction and intrinsic clearance
5Excretion
19 equations
- 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
- 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
- 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.
- 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
- 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
- the clearance of the kidneys
- AUC
- the area under the concentration-time curve over the interval
- 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.
- 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
- 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
- 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
- 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.
- 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
- 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
- CL
- clearance, the volume of plasma from which the body removes all of the drug per unit of time
- C
- the plasma concentration
- Vd
- the volume of distribution
- C
- the plasma concentration
- CL
- clearance
- Vd
- the volume of distribution
- C
- the plasma concentration
- k
- the elimination rate constant
- CL
- clearance
- Vd
- the volume of distribution
- t1/2
- half-life, the time for the plasma concentration to fall by half
- k
- the elimination rate constant
- 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.
6Pharmacokinetic models
37 equations
- k
- the elimination rate constant
- rate of elimination
- the amount removed per unit of time
- Vd
- the volume of distribution
- 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
- 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.
- Vd
- the volume of distribution
- C0
- the value of the fitted curve extended back to time zero
- 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.
- 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.
- 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.
- 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
- 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
- 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.
- CL
- clearance
- 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.
- 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
- 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.
- dose rate
- the dose divided by the interval between doses
- CL
- clearance
- C
- the plasma concentration
- C
- the average plasma concentration at steady state
- CL
- clearance
- Vd
- the volume of distribution
- target concentration
- a plasma concentration chosen to be effective and safe
- Vd
- the volume of distribution
- 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.
- target concentration
- a plasma concentration chosen to be effective and safe
- CL
- clearance
- 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.
- CL
- clearance
- Vmax
- the maximum rate
- Km
- the concentration that gives half of Vmax
- C
- the drug concentration
- CL
- clearance
- C1, C2
- the two concentrations of a pair of consecutive points
- t2 - t1
- the time between them
- AUC
- the area under the concentration-time curve
- 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
- Clast
- the last concentration
- lambda z
- the terminal rate constant
- CL/F
- the apparent clearance, the clearance divided by the bioavailability
- dose
- the oral dose
- 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(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.
- 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.
- 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.
- 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.
- 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.
- Vss
- the volume of distribution at steady state
- CL
- clearance
- MRT
- the mean residence time
7Prediction
18 equations
- CLint
- in vitro intrinsic clearance
- CLint
- in vitro intrinsic clearance
- k
- the steepness of the line of the natural logarithm of the amount left against time
- 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.
- 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.
- fu
- the fraction unbound
In human plasma in vitro, proteins bound about 87 percent, so fu was about 0.13.
- fu
- the fraction unbound
- unbound concentration
- the concentration of drug free in solution, not attached to proteins or membranes
- intrinsic clearance
- the removal by the enzymes alone, apart from any limit by blood flow or protein binding
- 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
- blood-to-plasma concentration ratio
- the ratio of the concentration in blood to the concentration in plasma
- fold error
- the predicted clearance divided by the observed clearance
This prediction was within twofold and 1.7 times too low.
- 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
- Vd
- the volume of distribution
- CLhuman/kg
- human clearance per kilogram
- CLmonkey/kg
- the monkey clearance per kilogram
- Kp
- the tissue-to-plasma partition coefficient, when both concentrations are constant
- 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
- 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.
- 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