Lumping of whole-body physiologically based pharmacokinetic models

Lumping is a common pragmatic approach aimed at the reduction of whole-body physiologically based pharmacokinetic (PBPK) model dimensionality and complexity. Incorrect lumping is equivalent to model misspecification with all the negative consequences to the subsequent model implementation. Proper lumping should guarantee that no useful information about the kinetics of the underlying processes is lost. To enforce this guarantee, formal standard lumping procedures and techniques need to be defined and implemented. This study examines the lumping process from a system theory point of view, which provides a formal basis for the derivation of principles and standard procedures of lumping. The lumping principle in PBPK modeling is defined as follows: Only tissues with identical model specification, and occupying identical positions in the system structure should be lumped together at each lumping iteration. In order to lump together parallel tissues, they should have similar or close time constants. In order to lump together serial tissues, they should equilibrate very rapidly with one another. The lumping procedure should include the following stages: (i) tissue specification conversion (when tissues with different model specifications are to be lumped together); (ii) classification of the tissues into classes with significantly different kinetics, according to the basic principle of lumping above; (iii) calculation of the parameters of the lumped compartments; (iv) simulation of the lumped system; (v) lumping of the experimental data; and (vi) verification of the lumped model. The use of the lumping principles and procedures to be adopted is illustrated with an example of a commonly implemented whole-body physiologically based pharmacokinetic model structure to characterize the pharmacokinetics of a homologous series of barbiturates in the rat.