Generic solving of physiologically-based kinetic models in support of next generation risk assessment due to chemicals

Increasing the confidence in using in vitro and in silico model-based data to aid the chemical risk assessment process is one, if not the most, important challenge currently facing regulatory authorities. A particularly crucial concern is to fully take advantage of scientifically valid Physiologically-Based Kinetic (PBK) models. Nevertheless, risk assessors remain still unwilling in employing PBK models within their daily work. Indeed, PBK models are not often included in current official guidance documents. In addition, most users have limited experience in using modelling in general. So, the complexity of PBK models, together with a lack to evaluation methods of their performances, certainly contributes to their under-use in practical risk assessment. This paper proposes an innovative and unified modelling framework, in both the writing of PBK equations as matrix ordinary differential equations (ODE), and in its exact solving simply expressed with matrix products. This generic PBK solution allows to consider as many as 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 compartmentalisation to be considered, as well as all appropriate inter-connections between compartments and with the external medium. We first introduce our PBK modelling framework, with all 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 in terms of species, compounds and model complexity. ![Figure][1] ### Competing Interest Statement The authors have declared no competing interest. [1]: pending:yes