Analog Electrical Model of the Coronary Circulation in Case of Multiple Revascularizations

Abstract

In this work, we propose an analog electrical model of the coronary circulation for patients with obstructive disease undergoing revascularization. In this clinical situation, the collateral circulation to the occluded artery is difficult to ascertain via preoperative measurements and well-developed collaterals might induce long-term restenosis of the revascularized artery due to flow competition mechanisms. The proposed model allows an original biomechanical analysis of per-operative hemodynamic data in order to assess quantitative evaluation of pressures and flows inside the native stenosed arteries, the collateral network and the bypass grafts. Average cardiac cycle values are analysed. In the case of 3-vessel disease and chronic occlusion of the right coronary artery, the quantitative results confirm the protective effects of the collateral flows in the pathological situation, but also show that the revascularization of the occluded right artery is fully justified since the collateral flows remain low, even when the left territory is revascularized. The model thus provides a computational tool to evaluate therapeutic strategies for each patient.

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

“…Collateral resistances, which are usually among the most important parameters for arterial and collateral flows, become almost negligible under the 1G and 3G cases. As previously observed by [15], revascularization through the right graft reduces the pressure difference between the right and left branches of the coronary tree, hence the reperfusion through collateral vessels is reduced. Although significantly diminished, collateral flow is still present, since P w results in Figure 5 show that this right territory pressure is still slightly sensitive to changes in the capillaries of the left territory and proximal collaterals.…”

“…Previous works attempting the hal-00961247, version 1 -19 Mar 2014 creation of personalized models of the coronary circulation in CAD, focus on the calculation of capillary and collateral resistances, assuming that collateral resistances are represented by a common parameter for each patient. This approach, presented by Maasrani et al [15], considers the measured graft flows for the 2G and 3G graft scenarios. Capillary resistances are calculated analytically under the 3G case since the left and right pressures are similar and the collateral flows are negligible; collaterals are estimated numerically in the 2G case, using the difference between the simulated and measured P w .…”

“…Capillary resistances were limited to the ranges shown in Table II. 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.…”

“…These differences are accounted by the fact that the two estimation procedures are fundamentally different. Maasrani's estimation procedure, explained in [15] calculates R LADc and R LCxc by using the measured graft flow in the case 3G, while assuming a negligible collateral flow and constant collateral resistances. The sensitivity analysis results showed that these assumptions are not necessarily true.…”

“…In this sense, previous works of our team proposed an extension of Pietrabissa's model, by integrating collateral circulation and the right coronary artery [15]. Also, an initial validation of the proposed model in the CAD context has been performed, by reproducing the mean blood flows and pressures obtained from clinical data [16].…”