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Simulation of coronary circulation with special regard to the venous bed and coronary sinus occlusion
W Schreiner1, F Neumann, W Mohl
1Second Surgical Department, University of Vienna, Austria.
Insights
This study models coronary artery blood flow using differential equations. Coronary sinus occlusion significantly alters intramyocardial flow dynamics, providing insights into therapeutically important but unmeasurable hemodynamic quantities.
Area of Science:
- Cardiovascular Physiology
- Biomedical Engineering
- Mathematical Modeling
Background:
- Understanding coronary blood flow is crucial for diagnosing and treating cardiovascular diseases.
- Existing models often simplify the complex interactions within the coronary vascular bed.
- Accurate hemodynamic predictions are needed for therapeutic interventions.
Purpose of the Study:
- To develop and validate a mathematical model of the left circumflex and left anterior descending coronary arteries.
- To investigate the hemodynamic effects of coronary sinus occlusion.
- To analyze the impact of myocardial contractility and vessel collapse on coronary blood flow.
Main Methods:
- Coupled differential equations were used to model arterial, capillary, and venous sections of coronary arteries.
- Experimental data from normal perfusion and coronary sinus occlusion were used for parameter assessment.
- Numerical integration was performed to simulate blood flow dynamics.
Main Results:
- A non-linear pressure-volume relationship for venous distensibility was essential for accurate modeling.
- Coronary sinus occlusion reduced total mean flow by 18%.
- Intramyocardial flow was divided into forward (3.03 ml/s) and backward (-1.54 ml/s) components during occlusion, offering a novel hemodynamic prediction.
Conclusions:
- The developed model accurately reproduces coronary hemodynamics under normal and occlusive conditions.
- The study provides a predictive tool for inaccessible hemodynamic parameters, aiding therapeutic strategies.
- Myocardial contractility and vessel collapse significantly influence intra-myocardial flow patterns.
Abstract:
The vascular beds of the left circumflex and the left anterior descending coronary arteries are modelled by means of coupled differential equations that consider an arterial, a capillary and a venous section. In a stepwise procedure, experimental data from normal coronary perfusion and coronary sinus occlusion are used to assess the model parameters. For venous distensibility, a non-linear form of pressure-volume relationship proved vital to reproduce the characteristics of the rise in venous pressure after the onset of coronary sinus occlusion. Numerical integration was carried out for normal perfusion and for coronary sinus occlusion, yielding time courses of flows, volumes and pressures within large coronary arteries, capillaries and coronary veins. Coronary sinus occlusion reduces total mean flow by 18% and divides intramyocardial flow between the capillaries and the veins into a forward component of 3.03 mls-1 and a backward component of -1.54 mls-1. This result represents a prediction for a haemodynamic quantity which is therapeutically important but inaccessible to measurement. Varying degrees of systolic myocardial squeezing are studied to display the impact of myocardial contractility and vessel collapse on the mean values and phasic components of intra-myocardial flows.