Untitled

Abstract

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.

Modeling Kinetics of Subcellular Disposition of Chemicals

“…(2255) The use of physiological models, currently hampered by the need for more-detailed experimental data,(2256) is expected to expand. The SBSP principles can be applied to physiologic models to the same extent as the compartmental models.…”

Physiologically Based Pharmacokinetic Modeling: Methodology, Applications, and Limitations with a Focus on Its Role in Pediatric Drug Development

“…For example, if the drug is not lipid soluble, the details of the adipose tissues of the body are not particularly important; or if only the absorption of the drug is of interest, then a model that includes only those body tissues or organs involved in the absorption process may be sufficient. The complexity of the models and the amount of incorporated information increase with the increasing number of represented tissues/organs; however, due to the fact that the main features of drug distribution can often be described with models that have surprisingly few details, a common strategy in structuring PBPK models, called “lumping,” is implemented [15, 16]. Tissues that share similar physiological, physicochemical, and biochemical properties are grouped as one compartment, while tissues with distinct properties—such as the liver, where metabolism occurs, or target tissues—are separated from the lumped compartments.…”

“…Four types of mathematical descriptions of the tissues within PBPK models have been used [4, 15]: (i) algebraic descriptions, which are used when the processes are assumed to equilibrate instantly and can be considered static (e.g., alveolar and inhaled air concentrations), (ii) linear ordinary differential, which are the most commonly used descriptions in describing dynamic pharmacokinetic processes, (iii) nonlinear differential, which are used to represent non-linear processes within a particular tissue (e.g., concentration-dependent clearance and/or binding), and (iv) partial differential, which are used with the dispersion tissue model. Figure 2 shows examples of different differential equations that can be used in a PBPK model.…”

“…Diagrams and equations for a perfusion rate-limited, one-compartment model (a) and a permeability rate-limited, two-compartment model with the permeability at the vascular membrane (b) of noneliminating organs, adapted from Nestorov et al [15]. Q = blood flow; C = concentration; V = volume; Kp = tissue : plasma distribution coefficient; PS = permeability surface area coefficient; subscripts T , ART, VEN, V, and EV indicate tissue, arterial, venous, vascular compartment, and extravascular compartment, respectively.…”

A physiologically oriented mathematical model for the description of in vivo drug release and absorption

“…The introduction of the GICS has allowed to effectively transform the very detailed pharmacokinetic model proposed by [14], (consisting in 21 compartments and 38 ordinary differential equations with roughly one hundred parameters), into a simple and effective model (7 compartments and 7 ordinary differential equations, with about twenty parameters). This effort saw several researchers spending lot of work, with limited and ineffective results (see, for example (see, for example, [15]). The GICS is assumed to be a well-stirred environment characterized by its own constant volume (V GICS ) and time dependent drug concentration (C GICS ).…”