Compact Modeling of Reaction-Diffusion-Advection Mechanisms for the Virtual Prototyping of Lab-on-Chip

The topic of this paper is the development of compact models reaction-advection-diffusion phenomenon compatible with a SPICE simulation environment. From a mathematical perspective, biological systems that involve such phenomena are described by partial differential equations, which are not naturally handeled by SPICE. Our approach consists of discretizing these equations according to the finite-difference method and converting the resulting set of ordinary differential equations into an assembly of elementary equivalent electronic circuits written in Verilog-A. The main interest of this approach is the capability of coupling such models with third- party SPICE models of electronic circuits, sensors and transducers as well as biochemical models that can also be written in SPICE. The tool is validated both on simple problems for which analytical solutions are known and by comparison with a finite element simulator of reference: COMSOL Multiphysics.