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

Abstract

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 finitedifference 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 thirdparty 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.

Compact Empirical Model for Droplet Generation in a Lab-on-Chip Cytometry System

“…The concept of a compact model is widely used in the field of electronic and semiconductor microchip design [34] for two main reasons: lowering the computational workload and operation with measurable parameters. In droplet microfluidics, the need for compact models has not yet been explicitly recognized and only a few studies have used this term [35]- [38]. At the same time, nearly 1000 publications (see Figure 1) contain some approximate formulas for the calculation of droplet sizes or generation rates that may be interpreted as compact models for solving some subproblems of droplet microfluidic system design tasks.…”