This model simulates the time-dependent flow, volume and presssure of a compliant, resistive vessel. A user-defined function defines an input flow driver. The input flow can vary with time based on the selected function prescribed as an input variable, F_in. An application of this model would be to calculate the volume-time and flow-time characteristics of a large vessel exposed to an oscillatory input flow (such as the human aorta). The resistance (R), compliance (C), resting volume (V_rest), and external pressure (P_ext), are prescribed in addition to the input flow function. Ohm's Law and the definitions of flow and compliance are used to determine the input pressure (P_in), output flow (F_out) and vessel volume (V). The governing equations are presented below in Equations.

There are three basic equations which are used in this model. The first is the definition of compliance given by:

where the variables and parameters are defined as in the model description. It must be noted that in this case P_ext is equal to the outlet pressure of the vessel but for a vessel in tissue this may not neccessarily be the case. Rearranging this expression we can solve for P_in.

The output flow is given by rearranging the fluid analog to Ohm's Law and then the rate of change of vessel volume as a function of time is calculated as the difference between the flowrate into the vessel and that going out. These expressions are given by:

and

Ohm GS. Die galvanische Kette. mathematisch bearbeitet, 1827

Resistive Element, Compliant Element, Single Vessel and Ventricle Driven Two Vessel Loop