Modeling Of Mass Transport Processes In Biologi... Online

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 how solutes cross the lipid bilayer via passive diffusion or protein channels (Kedem-Katchalsky equations). 4. Dimensionless Numbers (The "Reality Check") To understand which process dominates, engineers use: Péclet Number ( ): Ratio of convection to diffusion ( , flow dominates (like in large arteries). , diffusion dominates (like in the brain parenchyma).

𝜕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).

: 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 :

The core of these models is the , which ensures mass conservation:

(Diffusion Coefficient): In tissues, we use an Effective Diffusivity ( Deffcap D sub e f f end-sub

Predicting how a drug spreads through a solid tumor. High interstitial fluid pressure in tumors often opposes inward convection, making diffusion the primary (and often slow) delivery method.