Axially distributed models of blood-tissue exchange

1 Axially distributed models of blood-tissue exchange 

Spatially distributed systems and reaction-diffusion modeling 

By multiplying Equation (8.46) by Vb and Equation (8.47) by Visf and summing the resulting equations, we can show that the system governed by these equations conserves mass  

Since this model does not account for chemical transformation or diffusion in the axial direction, the rate of change of mass of solute at any location along the capillary is driven by advection alone. If the blood velocity were zero, then the total mass density at any location z would remain constant. 

Equations (8.46) and (8.47) describe the Sangren-Sheppard model. While the equations are straightforward and can be thought of as the minimal model that captures the important biophysical phenomena of solute exchange along a capillary, this model represents nearly the maximal level of complexity that can be effectively analyzed without invoking numerical approximations to simulate it.6 

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