A differentiable, periodic function for pulsatile cardiac output based on heart rate and stroke volume

Area of Science:

• Physiology
• Biomedical Engineering
• Mathematical Modeling

Background:

• Mathematical models of human hemodynamics require realistic cardiac output functions.
• Existing models often lack continuity, differentiability, or periodicity, hindering analysis.
• Accurate modeling of pressure and flow pulses in the circulatory system is crucial.

Purpose of the Study:

• To develop a cardiac output function that is realistic and analytically tractable.
• To create a function that captures essential features of measured hemodynamic data.
• To provide a continuous, differentiable, and periodic model for hemodynamic simulations.

Main Methods:

• Developed a novel cardiac output function based on left ventricle dynamics.
• The function is specified by parameters like heart rate and peak-to-mean flow ratio.
• Expressed the function as a product of two continuous, differentiable, and periodic factors.

Main Results:

• The function accurately models flow into the ascending aorta.
• It is defined by minimal, standard physiological parameters.
• The Fourier expansion results in a finite Fourier series with explicit coefficients.

Conclusions:

• The developed cardiac output function meets the needs for realistic and analytical hemodynamic modeling.
• It offers an accurate representation of physical flow data.
• The function's mathematical properties facilitate advanced model analysis and simulation.