Physiologically Based Pharmacokinetic Modelling - Building A PBPK Model

Building A PBPK Model

The model equations follow the principles of mass transport, fluid dynamics, and biochemistry in order to simulate the fate of a substance in the body. Connexions between compartment follow physiology (e.g., blood flow in exit of the gut goes to liver, etc.)

Drug distribution into a tissue can be rate-limited by either perfusion or permeability. Perfusion-rate-limited kinetics apply when the tissue membranes present no barrier to diffusion. Blood flow, assuming that the drug is transported mainly by blood, as is often the case, is then the limiting factor to distribution in the various cells of the body. That is usually true for small lipophilic drugs. Under perfusion limitation, the instantaneous rate of entry for the quantity of drug in a compartment is simply equal to (blood) volumetric flow rate through the organ times the incoming blood concentration. In that case; for a generic compartment i, the differential equation for the quantity Qi of substance is:

where Fi is blood flow (noted Q in the Figure above), Cart incoming blood concentration, Pi the tissue over blood partition coefficient and Vi the volume of compartment i.

A complete set of differential equations for the 7-compartment model shown above could therefore be: Gut:

Kidney:

Poorly-perfused tissues (muscle and skin):

Brain:

Heart and lung:

Pancreas:

Liver:

{dQ_L \over dt} = F_a C_{art} + F_g ({{Q_g} \over {P_g V_g}}) + F_{pn} ({{Q_{pn}} \over {P_{pn} V_{pn}}}) - (F_a + F_g + F_{pn}) ({{Q_l} \over {P_l V_l}})

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