Transmural Distribution of Coronary Perfusion and Myocardial Work Density Due to Alterations in Ventricular Loading, Geometry and Contractility

FIGURE 1. Schematic of the cardiac-coronary computational framework. The LV FE model (with dimension given in the inset) is connected to four coronary networks located at different transmural location across the myocardial wall. Each network consists of 400 vessels with different vessel radius (see inset).

FIGURE 2. Flow models in a single vessel and vessel bifurcation. (A) Electrical non-linear analog of the segment lumped model; (B) Single bifurcation three-vessel network.

FIGURE 3. Model predicted results. (A) Pressures, (B) LV volume, (C) IMP, (D) Coronary flow rate, (E) ecc, and (F) ell waveforms. LV pressure and volume, and ecc and ell are plotted together with measurements from 3D echocardiography (dots and stars), and were in agreement with clinical measurements in Gorcsan and Tanaka (2011), Hoit (2011) and Smiseth et al. (2016), Shavik et al. (2019), respectively. “e” in panels (A–D) indicates “ejection phase.”

FIGURE 4. Transmural distribution. (A) IMP that normalized against LV pressure, is comparable to experimental measurements (Heineman and Grayson, 1985); (B) Total coronary flow over a cardiac cycle that is normalized by flow at the endocardium (R = 0), is comparable to the measurements in a canine model under maximal coronary vasodilation (Vatner and Hittinger, 1993); (C) Work done over a cardiac cycle Wf.(D) Average Sff−Eff loop at the endocardial (R = 0), mid-wall and epicardial (R = 1) regions. ⋅ denotes experimental measurements.

FIGURE 5. Effects of myocardial contractility on (A) Pressure waveforms; (B) LV pressure-volume loop; Transmural distribution of (C) IMP; (D) Total coronary flow over a cardiac cycle; (E) Work density over a cardiac cycle Wf; (F) Work density-perfusion mismatch index ratio Wf/Q. “-Tmax,” “base,” and “+Tmax″ denote Tmax = 65, 130, and 205 kPa.

FIGURE 6. Effects of afterload on (A) Pressure waveforms; (B) LV pressure-volume loop; Transmural distribution of (C) IMP; (D) Total coronary flow over a cardiac cycle; (E) Work density over a cardiac cycle Wf; (F) Work density-perfusion mismatch index ratio Wf/Q. “-afterload,” “base,” and “+afterload” denote reduced afterload, baseline, and increased afterload cases.

FIGURE 7. Effects of preload on (A) Pressure waveforms; (B) LV pressure-volume loop; (C) Transmural distribution of IMP; (D) Total coronary flow over a cardiac cycle; (E) Work density over a cardiac cycle Wf; (F) Work density-perfusion mismatch index ratio Wf/Q. “-preload,” “base,” and “+preload” denote reduced preload, baseline, and increased preload cases.

FIGURE 8. Effects of wall thickness on (A) Pressure waveforms; (B) LV pressure-volume loop; Transmural distribution of (C) IMP; (D) Total coronary flow over a cardiac cycle; (E) Work density over a cardiac cycle Wf; (F) Work density-perfusion mismatch index ratio Wf/Q. “–thickness,” “base,” and “+thickness” denote reduced thickness, baseline, and increased thickness cases.

FIGURE 9. Effects of cavity volume on (A) Pressure waveforms; (B) LV pressure-volume loop; Transmural distribution of (C) IMP; (D) Total coronary flow over a cardiac cycle; (E) Work density over a cardiac cycle Wf; (F) Work density-perfusion mismatch index ratio Wf/Q. “-cav vol,” “base,” and “+cav vol” denote reduced cavity volume, baseline, and increased cavity volume cases.