Stability analysis of one-dimensional dynamical systems applied to an isolated beating heart

Area of Science:

• Computational Biology
• Mathematical Modeling
• Non-linear Dynamics

Background:

• Understanding the complex dynamics of cardiac function is crucial for diagnosing and treating heart conditions.
• Existing models may not fully capture the transition from normal to abnormal heart rhythms.
• Non-linear discrete dynamical systems offer a powerful framework for analyzing complex biological systems.

Purpose of the Study:

• To propose and analyze a novel one-dimensional non-linear discrete dynamical system model for an isolated beating heart.
• To investigate the dynamic properties and stability of the proposed model across various parameter domains.
• To correlate model dynamics with physiological states of normal and abnormal heart beating.

Main Methods:

• Development of a one-dimensional non-linear discrete dynamical system model.
• Application of stability analysis to determine attractor domains within the parameter space.
• Identification of bifurcations and their relationship to specific cardiac behaviors.
• Analysis of end-diastolic volumes to differentiate between stable and time-variant states.

Main Results:

• Identified parameter domains corresponding to stable (normal) and unstable (abnormal) heart beating.
• Demonstrated that stable end-diastolic volumes represent normal function, while time-variant volumes indicate abnormal function.
• Observed a bifurcation leading to period-2 orbits, characterizing mechanical alternans in abnormal heartbeats.
• Provided quantitative and qualitative predictions for experimental validation.

Conclusions:

• The proposed dynamical system model effectively simulates isolated heart beating dynamics.
• The model elucidates the transition mechanisms between normal and abnormal cardiac rhythms, including mechanical alternans.
• Findings offer a predictive framework to guide future experimental studies on cardiac electrophysiology and mechanics.