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Basically the equation is:
Equation 7.7.1 Basic Convolution Equation
A general linear pharmacokinetic model with elimination via excretion into urine (ke), metabolism (km) or other processes (kother) is shown below.
Figure 7.7.1 General Multi Compartment Pharmacokinetic Model
Route of Administration | Input Function |
IV Bolus | |
IV Infusion - Continuous | |
IV Infusion^{1} | |
Oral^{2} |
^{1} This function includes additional flexibility. 'a' represents the time when the infusion is started and 'z' represents the time when the infusion is stopped. If a = 0 and z = ∞ this simplifies to k0/s.
^{2} The oral dose includes a bioavailability term, F. This is the fraction of the oral dose that is absorbed so F x Dose is the amount of drug which is absorbed into the central compartment.
Functions for more complex absorption processes could be developed.
Number of Compartments | Disposition Function |
One | |
Two^{1} | |
Three^{2} | |
Four^{3} |
^{1} where
α + β = kel + k12 + k21
and
α x β = kel x k21
^{2} where
α + β + γ = kel + k12 + k21 + k13 + k31
α x β + α x γ + β x γ = kel x k21 + kel x k31 + k13 x k21 + k12 x k31 + k21 x k31
and
α x β x γ = kel x k21 x k31
^{3} where
α + β + γ + δ = kel + k12 + k21 + k13 + k31 + k14 + k41
α x β + α x γ + α x δ + β x γ + β x δ + γ x δ = kel x (k21 + k31 + k41) + k12 x (k31 + k41) + k13 x (k21 + k41) + k14 x (k21 + k31) + k21 x k31 + k21 x k41 + k31 x k41
α x β x γ + α x β x δ + α x γ x δ + β x γ x δ = kel x k21 x k31 + kel x k31 x k41 + kel x k21 x k41 + k12 x k31 x k41 + k13 x k21 x k41 + k14 x k21 x k31 + k21 x k31 x k41
and
α x β x γ x δ = kel x k21 x k31 x k41
with help from de Biasi (de Biasi, J. 1989)
Sample Site | Function |
Drug in Central Compartment | 1 |
Drug in Peripheral Compartment^{1} | |
Drug in Urine | |
Metabolite in Central Compartment | |
Metabolite in Urine |
^{1} x refers to the 2nd, 3rd, or 4th, peripheral, compartment as shown in Figure 7.7.1.
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Copyright © 2001-2018 David W. A. Bourne (david@boomer.org)