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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 Infusion - Continuous|
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|
α + β = kel + k12 + k21
α x β = kel x k21
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
α x β x γ = kel x k21 x k31
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
α x β x γ x δ = kel x k21 x k31 x k41
with help from de Biasi (de Biasi, J. 1989)
|Drug in Central Compartment||1|
|Drug in Peripheral Compartment1|
|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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