Analysis of coronary-sinus-occlusion pressure by iterating the convolution integral

Area of Science:

• Cardiovascular Physiology
• Mathematical Biology
• Medical Engineering

Background:

• Intermittent coronary sinus occlusion (ICSO) is a technique investigated for reducing myocardial infarct size and improving cardiac function.
• The efficacy of ICSO is dependent on precise timing of coronary sinus occlusion and release intervals.
• Understanding coronary hemodynamics during ICSO is crucial for optimizing the procedure.

Purpose of the Study:

• To investigate the coronary hemodynamic reactions to intermittent coronary sinus occlusion (ICSO).
• To develop a mathematical model to predict coronary sinus pressure (CSP) responses to ICSO.
• To correlate mathematical model parameters with different physiological states of the myocardium.

Main Methods:

• Analysis of coronary sinus pressure (CSP) measurements in anesthetized dogs under normal perfusion, induced infarction, and reperfusion.
• Development of a mathematical model using a convolution integral and a memory function g(x) to represent CSP reactions.
• Numerical techniques employed to evaluate the memory function g(x) and reproduce measured CSP data.

Main Results:

• Distinct memory functions g(x) were derived for normal perfusion, infarction, and reperfusion states.
• The derived memory functions accurately reproduced measured CSP data, indicating their validity.
• Differences in g(x) were found to correlate with known characteristics of normal and diseased myocardium.

Conclusions:

• A mathematical model incorporating a memory function can effectively describe CSP responses to ICSO.
• The model provides a universal method to predict CSP reactions for various ICSO patterns, potentially reducing animal studies.
• Understanding the link between cardiovascular physiology and mathematical representations aids in selecting therapeutic interventions.