Patterns of mixing in tissues and organs

These two ideal models display different behaviors in response to a step change in inlet concentration of a tracer. In principle, then, one can determine 

In practice, the volume of distribution in the organ can be found using labeled inert compounds, which are allowed to reach equihbrium within the tissue  

Under what conditions do the two models give similar outlet concentrations In model I (well stirred), a mass balance over the plasma compartment (i.e., compartment 1) gives  

Defining a time constant for flow through the organ, t, and a dimensionless time based on this time constant, T  

For model II (plug flow), the concentration changes slowly throughout the tissue region. Since flow-limited behavior is assumed, a similar concentration gradient is slowly present within the peripheral compartment (compartment 2). Selecting a control volume. Ax, which includes the comparable regions of compartments 1 and 2, a mass balance on the control volume yields  

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