Hemodynamic Principles Used to Construct Computer Model

This model demonstrates the effects of changes in vascular resistance on blood flow and pressure within a branching vascular network.  The three vascular branches are R1, R2, and R3, with R2 (branch A) and R3 (branch B) in-parallel with each other and in-series with R1.  As a coronary circulation model, R1 represents the left main coronary artery (LC), R2 the left anterior descending artery (LAD), and R3 the circumflex artery (CX). 

The arterial pressure (PA) is the perfusion pressure (venous pressure is assumed to equal zero).  Therefore, the basic equation relating flow to arterial pressure and total resistance (RT) in this model is:  

The total resistance is determined by the equations for series and parallel resistances as follows:  

             

Furthermore, both R2 and R3 are each composed of two series resistances; large vessel (R2L or R3L; LAD or CX) and small vessel resistances (R2S or R3S; microcirculation supplied by the large vessels).  Therefore, R2 = R2L + R2S, and R3 = R3L + R3S.

The user can change R1 or the individual components of R2 and R3.  The pressure drop across R1 (DPR1) equals the product of flow and R1; therefore, the pressure distal to R1 equals the arterial pressure minus the pressure drop across R1 (PA – DPR1).  This is the pressure perfusing the R2 and R3 branches.  There are also pressure drops across R2L and R3L, which are determined by the flow in each branch times the resistance.   The pressure distal to these sites represents the pressure perfusing the distal microcirculatory beds (R2S and R3S).  Laminar flow conditions are assumed in all the calculations incorporated into this model.

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