Generic Solving of Physiologically-based Kinetic Models in Support of Next Generation Risk Assessment Due to Chemicals

Abstract

Increasing confidence in using in vitro and in silico model-based data to aid the chemical risk assessment process is one of the most significant challenges faced by regulatory authorities. A crucial concern is taking full advantage of scientifically valid physiologically-based kinetic (PBK) models. Nevertheless, risk assessors remain unwilling to employ PBK models in their daily work. Indeed, PBK models are not often included in current official guidance documents. In addition, most users have limited experience with modeling in general. So, the complexity of PBK models and a lack of evaluation methods for their performance certainly contribute to their limited use in practical risk assessment. This paper proposes an innovative and unified modeling framework for writing PBK equations as matrix ordinary differential equations (ODE) and their solutions, expressed with matrix products. This generic PBK solution considers as many state variables as needed to quantify chemical absorption, distribution, metabolism, and excretion processes within living organisms when exposed to chemical substances. This generic PBK model makes possible any compartmentalization to be considered, as well as all appropriate interconnections between compartments and with the external medium. We first introduce our PBK modeling framework, with all the intermediate steps from the matrix ODE to the exact solution. Then we apply this framework to bioaccumulation testing before illustrating its concrete use through complementary case studies regarding species, compounds, and model complexity.