Pharmacokinetic Software for Research and Education

Dose Amount

D

Fraction of dose absorbed

Used to correct dose amount for some oral dose calculations.

F

Exponential Summation

Expression for sum of 1^st order kinetic terms.

for n exponential terms

Y-Intercept

Coefficient of each exponential term. Note the sign of the absorption coefficient is negative.

Slope

Rate constant

Elimination rate constant

Half-life

C_initial

Initial concentration extrapolated to time zero for i.v. dose.

Tmax (obs)

Usually applies to oral doses only.

Cmax (calculated)

For biexponential oral data only.

where V is Vd (area).

Tmax (calculated)

For biexponential oral data only.

whereand are the apparent absorption and elimination rate constants, respectively.

Lag time

For biexponential oral data only.

whereand are the apparent absorption and elimination rate constants, respectively.

AUC(0-t) (obs area)

Trapezoid calculation of AUC using observed data points only (not extrapolated to infinity). Useful when final concentration values tend to exaggerate total AUC.

where n is the number of data points.

AUC (area)

Total AUC computed by combining AUC(0-t) with an extrapolated value.

where is the last concentration.

AUC (expo)

Total AUC computed using exponential terms.

% of AUC (expo)

Percent each exponential term contributes to the total AUC.

AUMC (area)

Calculation of total area under the first-moment curve (plot of Ct vs t) by combining trapezoid calculation of AUMC(_0-t) and extrapolated area.

+

AUMC (expo)

Total AUMC computed using exponential terms.

% of AUMC (expo)

Percent each exponential term contributes to the total AUMC.

MRT (area)

Mean Residence Time calculated using trapezoid area calculations extrapolated to infinity.

where both area terms use trapezoidal calculations

MRT (expo)

Mean Residence Time calculated using exponential terms.

Vc (initial central compartment)

Apparent volume of the central compartment for i.v. doses only.

Vd (obs area)

Apparent volume of distribution based on AUC_(0-t) trapezoid calculation and elimination rate. Use when total AUC (area) is exaggerated due to high terminal concentration values.

Vd (area)

Apparent volume of distribution based on trapezoid AUC (area) and elimination rate. Applies mainly to i.v., but also to oral if complete absorption (F=1) is assumed.

Vd (area) / kg

Apparent volume of distribution normalized by animal weight. Uses same equation as Vd (area).

Vd (expo)

Apparent volume of distribution calculated from exponential terms.

where is the elimination rate

Vss (area)

Apparent volume of distribution at steady state estimated graphically from trapezoidal total area measurements. Applies to iv dose.

Vss (expo)

Apparent volume of distribution at steady state estimated from exponential terms. Applies only after iv and assumes elimination from central compartment.

CL(sys) (obs area)

Systemic clearance based on AUC_(0-t) trapezoid calculation. Use when total AUC (area) is exaggerated due to high last concentration.

CL (area)

Systemic clearance based on trapezoid AUC (area). Applies mainly to i.v. data. Limited to oral data only if complete absorption (F=1) is assumed.

CL (area) / kg

Systemic clearance normalized by animal weight. Uses same equation as CL (area).

CL (expo)

Systemic clearance calculated using exponential terms.

Half-life based on Vd and CL

Alternate calculation of half-life using Vd (area) and CL (area). For i.v. data only.

k12

Microconstant calculated using exponentials. Applies to 2 compartment i.v. dose data only.

k21

Microconstant calculated using exponentials. Applies to 2 compartment i.v. dose data only.

k10

Microconstant calculated using exponentials. Applies to 2 compartment i.v. dose data only.

Dose Interval (tau)

Time span between dosing intervals. Distinguish from time after dose (t).

tau

Assume constant dose interval

C1(max)

Maximum concentration after first dose interval (tau). Equal to C_initial

C1(min)

Minimum concentration at end of first dose interval (tau).

C1(ave)

Average concentration during first dose interval (tau).

Css(min)

Minimum concentration during any dosing interval at steady state.

Css(min)

Minimum concentration during any dosing interval at steady state. Included on graph.

Css(max) - Css(min)

Difference between peak and trough concentration during steady state.

Css(ave)

Average concentration at steady state.

Css(ave) (area)

Average concentration at steady state calculated from trapezoidal AUC data for a single dose.

R based on Css(max)/C1(max)

Accumulation ratio based on maximum concentrations after first dose and at steady state.

R based on Css(min)/C1(min)

Accumulation ratio based on minimum concentrations after first dose and at steady state.

R based on Css(ave)/C1(ave)

Accumulation ratio based on average concentrations after first dose and at steady state.

To reach 95% Css(ave)

Time required to reach 95% of average steady state concentration. Assumes one-compartment characteristics apply.

where is the fraction of the steady state concentration.

To reach 99% Css(ave)

Time required to reach 95% of average steady state concentration. Assumes one-compartment characteristics apply.

where is the fraction of the steady state concentration.

Calculated loading dose

Loading dose required to produce an immediate steady state minimum concentration, Css(min).

Total time through Nth dose

Total time elapsed between first dose (t=0) and specified dose (N).

C(ave) during Nth dose

Average concentration during any dose interval (N). Becomes Css(ave) when steady state reached.

Fraction of Css(ave) after N doses

Fraction of the ultimate average steady state concentration reached after N doses.

where is the fraction of the steady state concentration

Css at t after ss dose

Steady state concentration at any time (t) during a dosing interval at steady state.

Conc. at any time and dose

Computes the concentration at any time during a dosing interval. Enter both time (t) and dose interval (N).

Dose Interval (tau)

Constant time span between dosing intervals. Distinguish from time after dose (t).

(tau)  Assumes equal dose intervals

Graphing Function

The graphing function is based on a mathematical generalization of the graphical superimposition principle. It involves the addition of a decay function (C_N) to the initial concentration (C₁)at repeated time points for a progressive series of doses (N). Assumes constant dose intervals during the postdistribution phase.

where

and

C1(max)

Observed maximum concentration taken from data set.

C1(min)

Minimum concentration at end of first dose interval (tau).

C1(ave)

Average concentration during first dose interval (tau).

Css(max)

Computed from a simplification of the graphing function to a steady state form as shown. The Css(max) is evaluated as the maximum concentration during the steady state dosing interval.

where

Css(min)

Computed using same steady state equation as Css(max) and evaluating the minimum concentration during a steady state dose interval.

Same as above.

Css(max) - Css(min)

Difference between peak and trough concentration during steady state.

Css(ave)

Average concentration at steady state.

Css(ave) (area)

Average concentration at steady state calculated from trapezoidal AUC data for a single dose.

R based on Css(min)/C1(min)

Accumulation factor based on elimination rate constant.

R based on Css(ave)/C1(ave)

Accumulation ratio based on average concentrations after first dose and at steady state.

Tmax (1^st dose, observed)

Observed time of largest concentration value from data set.

Tmax (1^st dose, calculated)

Calculation of time at which maximum concentration occurs after a single dose. Applies to 1-compartment characteristics, but calculated also to illustrate magnitude for 2-compartments.

whereis the absorption rate

and is the elimination rate.

Tmax(ss)

Calculation of time at which maximum concentration occurs after dosing during steady state. Applies to 1-compartment characteristics, but calculated also to illustrate magnitude for 2-compartments.

whereis the absorption rate

and is the elimination rate.