R=−VmaxCKm+Ccap R equals negative the fraction with numerator cap V sub m a x end-sub cap C and denominator cap K sub m plus cap C end-fraction
Modeling Mass Transport in Biological Systems Biological mass transport involves the movement of molecules (oxygen, nutrients, drugs, waste) through cells, tissues, and organs. It is generally governed by three mechanisms: , convection , and binding/reaction . 1. Fundamental Equations Modeling of Mass Transport Processes in Biologi...
Movement driven by concentration gradients. : Net rate of production or consumption (e
𝜕C𝜕t+∇⋅N=Rthe fraction with numerator partial cap C and denominator partial t end-fraction plus nabla center dot bold cap N equals cap R : Concentration of the species. Nbold cap N : Mass flux (movement). waste) through cells
: Net rate of production or consumption (e.g., metabolic reaction). 2. The Mechanisms of Flux ( Nbold cap N
) because the path is obstructed by cells and extracellular matrix (ECM). Movement driven by fluid velocity ( ), like blood flow or interstitial fluid. Nconv=vCbold cap N sub c o n v end-sub equals bold v cap C 3. Key Applications Oxygen Delivery: Modeling how O2cap O sub 2 moves from capillaries into deep tissue. Since O2cap O sub 2 is consumed by mitochondria, is negative and usually follows Michaelis-Menten kinetics :
(Diffusion Coefficient): In tissues, we use an Effective Diffusivity ( Deffcap D sub e f f end-sub