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Multi Compartment Models

Applied BioMath Assess contains several one-compartment models and several multi-compartment models. Within each compartment the reactants are assumed to be well mixed, or more specifically, that the activity of the reactants can be related to the amount of the reactants divided by the compartment volume. The two exceptions to this are membrane-membrane binding and membrane-membrane trans binding reactions, which are described in detail in Binding Reactions.

The following diagram shows the connectivity between compartments.

Compartment volumes

Compartment Definition
Central In a one-compartment model, the central compartment is the only compartment and it typically represents the steady state volume of distribution of the drug. The default value is 5 L. In a four-compartment model, the central compartment represents the acellular component of the peripheral blood and can be compared to plasma or serum PK measurements. For a typical adult male (70 kg, S = 1.9 m2), and adult female (60 kg, S = 1.6m2) this is 3.0 and 2.3 L respectively. (Pearson 1995) The default value in most multi-compartment models is 2.5 L.
Peripheral Represents the non-blood fluids that the drug can distribute to. This compartment is less well defined than the central compartment and, in reality, represents a collection of individual compartments with different volumes and exchange rates with the plasma. As such, it is typically approximated as either (1) the same volume as the central compartment, (2) a function of the intercompartmental distribution parameters such that at steady state the drug concentration is the same concentration in central and peripheral compartments, (3) an approximate physiologic volume computed from the sum of all of the interstitial fluid volumes for the major organs. The default value is (3) with the specific volumes from the Shah and Betts Physiologically Based Pharmacokinetic Model which is 13 L. (Shah and Betts 2012). The default volume of the tox and the disease compartments (0.1 L each) are subtracted from this value to give 12.8 as the default value.
Disease This represents the interstitial fluids of the diseased tissue. In general, this would also include the lymph. This may be whole organs or specific involved regions of an organ. In the case of a whole organ, the default value for the volume should be the volume of the interstitial fluid of the relevant organ from Shah and Betts 2012. In the case of involved tissues, this may either be the proportional fraction of the tissue that is involved: Vinvolved,isf = Vorgan,isfVinvolved,total / Vorgan, total Or by a tissue specific calculation: Vinvolved,isf = Vorgan,total(1-fcellular-fblood-fsolid) The most common of the second kind is tumors where we typically assume fcellular=0.8, fblood=0, and fsolid=0. The default value is 0.1 L which corresponds to a 0.5L solid tissue with 80% cellularity.
Tox This represents the compartment where the tox pharmacology happens (assuming it is different from the disease compartment). The volume of this compartment is computed in the same way as the disease compartment. The default value is 0.1 L which corresponds to a 0.5L solid tissue with 80% cellularity.

Steady state volume of distribution

In multicompartment models, the steady state volume of distribution can be computed using the individual compartment volumes and the partition coefficients.

\[ V_{ss} = V_c + \Sigma_i P_i V_i \]

Soluble protein trafficking

All soluble proteins are able to traffic between compartments. This allows soluble proteins that are transported to a tissue in the form of drug protein complexes to unbind and equilibrate between compartments. The rate of distribution is determined by \(T_{dist}\) and \(P_{dist}\), and the partition coefficients are determined by the initial steady state concentrations.