A structurally-motivated model of coronary hemodynamics across the myocardium

Introduction: Oxygen tissue perfusion is determined by the structure of the capillary network and the upstream (arterial) and downstream (venous) hemodynamics. In most tissue beds capillary pressure and flow are relatively constant; however, the coronary circulation is greatly affected by a spatially and temporally varying intramyocardial pressure. This pressure is thought to cause the diastolic-dominant flows in the coronary arteries and the systolic-dominant flows in the coronary veins. Furthermore, the higher subendocardium (inner-most layer) and lower subepicardium (outer-most layer) intramyocardial pressures suggest that the subendocardium is at higher risk of hypoxia. While coronary blood flow can be measured in large arteries and veins on the epicardial surface of the heart, it is currently not well understood how intramyocardial pressure affects capillary blood flow and subsequent oxygen perfusion.
To model myocardial oxygen perfusion, the following components are needed: (1) an anatomically informed network representing the coronary arteries, veins, and microcirculation at different transmural locations; (2) a model of hemodynamics that accounts for spatially and temporally varying intramyocardial pressure; (3) a 3D model of oxygen transport. In this work, we focus on the first two components. Anatomical information is based on previous literature studies. Hemodynamic solutions are obtained via lumped parameter models (LPMs). This will allow us to understand how myocardial oxygen perfusion is impacted by temporal and transmural changes in intramyocardial pressure.

Materials and

Methods: Generation of Coronary Vasculature: Arterial and venous networks are characterized using a tree structure with a Strahler numbering system. Networks rely on previously reported average branching ratios between generations. Four myocardial locations (subepicardium, mid-layer 1, mid-layer 2, and subendocardium) are specified by bifurcations at arterial generations 8 to 5 and venous generations -5 and -8 (Figure 1). For each myocardial location, all vessels in each generation are lumped into a single 3-element Windkessel model defined by a proximal and distal resistance, and a compliance. Arterial and venous resistances were estimated based on statistics of vessel length and diameter for each generation [1]. Arterial compliances are set from previous estimates of diameter compliance at 100 mmHg by Huo and Kassab [2], and venous compliances are assumed to be 10 times larger than the corresponding arterial compliance for each generation.
The capillary network is assumed periodic in space and is defined following the work of Beard et al. [3]. The structure of this network includes capillaries traveling parallel to the muscle fibers and cross-connecting capillaries. The capillary network is ultimately represented through a weighted undirected connectivity matrix.
Computational Hemodynamic and Perfusion: Hemodynamics through the networks are calculated using a LPM. Physiological pressure conditions are applied to the arterial inlet (generation 11) and venous outlet (generation -12) of the network. Spatially-varying intramyocardial pressures were prescribed at the four different myocardial locations. Three different analyses were conducted: i) steady state; ii) pulsatile analysis with zero intramyocardial pressure; iii) pulsatile analysis with spatially-varying intramyocardial pressure.

Results, Conclusions, and Discussions: The steady-state analysis considered 120 mmHg arterial inlet pressure, 10 mmHg venous outlet pressure, and no transmural pressure. This model was used to compare our results and definition of coronary geometry to previously published computational models. Figure 2a shows the steady state pressure for each arterial and venous generation. The greatest pressure drop is seen in the smaller arteries (generations 1-5). These results are consistent with previous publications, suggesting that the imposed resistances (calculated from statistics on vessel length and diameter across the generations) are physiologically realistic.
The results of the pulsatile analysis with zero intramyocardial pressure are presented in Figure 2b. Prescribed inlet pressure ranged from 120 mmHg systolic to 80 mmHg diastolic. The same constant outlet venous pressure of 10 mmHg was used. Under these assumptions, pulsatility of the flow is only observed in the large vessels (generations 11-6).
Lastly, results for the pulsatile analysis with spatially-varying intramyocardial pressure are presented in Figure 2C. The graphs show the difference between intra-luminal and local intramyocardial pressures for each generation for the subendocardial (left panel) and subepicardial (right panel) regions. The endocardial path experiences high intramyocardial pressures and therefore the effect of this pressure on the network hemodynamics is more pronounced. Negative values indicate larger intramyocardial pressures than intra-luminal pressures and thus suggest vessel compression or collapse.
Further improvements of this model will require refining model parameters for the regions of the network in which the range of the intramyocardial pressure is the largest. Additionally, the representative microvascular model will be included and a model of oxygen transport will be considered.
Lastly, the structure of the microvascular model will be ultimately informed by ongoing work from our group that aims to image and mathematically describe capillary networks extracted from myocardial tissue using confocal microscopy, see microscopy images in Figure 1. These improvements on model assumptions and morphometric data will provide a better understanding of oxygen transport across the myocardium.

[1] Wang et al. Comput Methods Programs Biomed, 243:107908, 2024
[2] Huo and Kassab. J Appl Physiol, 107(2):500-5, 2008
[3] Beard et al. Am J Physiol Heart Circ Physiol, 285(5):H1826-36, 2003

Acknowledgements (Optional): We gratefully acknowledge support from R01-HL158723 and T32-GM150581.