Single
Dose Pharmacokinetics 
General
Disposition Parameters and Constants 
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

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


Slope


Rate constant


Elimination rate constant


Halflife


Descriptive
Curve Parameters 
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.

Curve Area
Calculations 
AUC(0t) (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(0t) 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.


Statistical
Moment Calculations 
AUMC (area)
Calculation of total area under the firstmoment curve (plot
of Ct vs t) by combining trapezoid calculation
of AUMC(_{0t)} 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.


Volume of
Distribution Calculations 
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_{(0t)} 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.


Systemic
Clearance Calculations 
CL(sys) (obs area)
Systemic clearance based on AUC_{(0t)} 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.


Halflife based on Vd and CL
Alternate calculation of halflife using Vd (area) and CL
(area). For i.v. data only.


Twocompartment
Open Model Microconstants 
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.


Multiple
Intravenous Dose Pharmacokinetics 
General 
Dose Interval (tau)
Time span between dosing intervals. Distinguish from time
after dose (t).

tau
Assume constant dose interval

First Dose
Concentration Calculations 
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).


Prediction
of Steady State Parameters 
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.


Accumulation
Factors 
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.


Time to
Reach Percent of Steady State 
To reach 95% Css(ave)
Time required to reach 95% of average steady state concentration.
Assumes onecompartment 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 onecompartment characteristics apply.

where is
the fraction of the steady state concentration.

Ad Hoc
Calculations 
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).


Multiple
Oral Dose Pharmacokinetics 
General
and Graphing Functions 
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 (C_{1})at repeated time points for a progressive
series of doses (N). Assumes constant dose intervals during
the postdistribution phase.

where
and

First Dose
Concentration Values 
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).


Prediction
of Steady State Parameters 
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.


Accumulation
Factors 
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.


Additional
Oral Dose Calculations 
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 1compartment characteristics,
but calculated also to illustrate magnitude for 2compartments.

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 1compartment characteristics,
but calculated also to illustrate magnitude for 2compartments.

whereis
the absorption rate
and is
the elimination rate.
