Biomedical engineering approach of pharmacokinetic problems: computer-aided design in pharmacokinetics and bioprocessing

Abstract

In complex or nonlinear processes the identifiability of classical models fails because of too many parameters. To reduce this number and to keep a description which is significant to the user in pharmacokinetics or bioprocessing a modular representation model is built up. To define all parameters and internal variables of those models, the authors have chosen an electrical equivalent representation. This electrical representation leads to linear and nonlinear associative modules, and this strategy allows them to realise a computer-aided design well suited to biological processes. On the one hand, it allows optimal therapeutic drug control after defining optimal criteria. On the other hand, it may be used for biomedicine, ecology and bioprocessing problems. The CAD system is conceived like a ‘Lego’ game and it can be used with minimal or no knowledge of programming and computer science. Its main goals are to formulate, resolve and simulate quickly any linear or nonlinear hypothesis of biological processes, and give time for innovation in biological research. Pharmacokinetic models are founded on the hypothesis of transmembrane drug transfer and modelled by differential equations. These differential equations allow the description of drug kinetics or in vivo drug behaviour by a compartment model. This compartment model, which is a representative or descriptive model, tries to give a concrete physiological picture of transmembrane drug transfers. In the usual pharmacokinetic studies, the compartment model is a satisfactory approach to the treatment of simple linear diffusion and elimination processes. In these cases, the canonical form (diagonal form Σ aie-λit) deduced from those models includes a number of parameters approaching the number of parameters of the representative model. Then, for a set of experimental data, when the canonical form is identified, it is possible to reconstruct the original compartment model with few structural hypotheses. For more complex or nonlinear processes, the compartment model fails because of its large number of parameters with regard to the number of identified parameters in the diagonal form. To treat these processes, the paper presents a modular model which is a representative model. In such a model, the number of parameters approach the number of canonical form parameters. On the other hand, this modular network allows a simple extension to nonlinear functions included in the linear network. The definition of this model leads to a computer-aided-design tool, suitable for any linear or nonlinear pharmacokinetic problem. To define all components of the modular model it is necessary to unify all pharmacokinetic parameters; so the authors have established an analogy table between classical pharmacokinetic and electrical parameters. This equivalence table suggests an electrical representation with physiological meaning similar to the physiological compartment concept. In this electrical model, the physiological parameters, such as elimination clearance, volume of distribution and transfer clearance between several diffusion areas, are the constitutive parameters of the model. Then, this analogy allows the inclusion of major limiting parameters like arterial or hepatic blood flow in the model.