Incremental network analogue model of the coronary artery

Abstract

From Newton's equation and the continuity equation, an equivalent analogue circuit model can be derived for each small segment of the coronary arteries. Sapoznikov divided the coronary artery tree into 116 segments. By replacing each segment with its analogue circuit model, a final incremental network model was derived. The model was tested using typical physical parameters under normal conditions, as well as in the presence of coronary artery stenosis. In the case of stenosis, the arteriolar flow with and without autoregulation were compared. The model shows good agreement with the reported effects of stenoses and heart rate on coronary blood flow.

Sensitivity Analysis and Parameter Estimation of a Coronary Circulation Model for Triple-Vessel Disease

“…These ranges were arbitrarily defined by taking the mean values published by Maasrani et al [16], which were estimated from patient data, and multiplying it by 0.2 and 3.85 in order to create a range that is large enough to contain all patient-specific values used for this model until today in [15], [16], [23]. Parameters related to arteries and grafts (R, L and C) were defined similarly, taking the baseline values shown on Table II, which were estimated from angiographic measurements in [5], [6], and multiplying by the same factors. The observed outputs were the mean values of blood flows and pressures during six cardiac cycles.…”

“…In this model, each coronary artery is associated with an RLC circuit; the differential equations for these circuits can be found in [5]. Coronary arterioles and capillaries (LADc, RCAc, LCxc) and collateral vessels (col1, .…”

“…However, they can also be undeveloped, which would be represented by a very high value of the collateral resistance. Parameter values related to arteries and grafts are extracted from previous works by Pietrabissa et al [6], with adjustments according to the area reduction due to stenoses [5]; while parameters associated with small arteries will be identified from clinical data. Using the aortic (P ao ) and venous (P v ) pressure inputs, blood flows and pressures can be simulated across all arteries, capillaries, collaterals and grafts, including the total coronary flow (Q t ) as the sum of blood flows through all capillaries.…”

“…Considering Windkessel models of the coronary circulation, Wang et al [5] proposed a representation of the left coronary tree and its branches, while integrating the effect of stenoses on blood flow and the systolic flow drop that characterizes the coronary blood flow. Later, Pietrabissa et al [6] extended this approach with revascularisations through coronary bypass grafts and applying an intra-myocardial pump model [7] to explain the systolic flow.…”

Mathematical Modeling of Cardiovascular System Dynamics Using a Lumped Parameter Method

“…Some models are based on lumped parameter representations of the arterial networks [32][33][34][35][36][37][38], and others model vessel hemodynamics by using the fluid dynamic equations that govern flow through a distributed, compliant network [39][40][41][42]. Lumped parameter models are generally successful in illuminating the complex interaction of the major hemodynamic elements and the control system.…”