Walking-induced inertial effects on the cardiovascular system

During exercise, the cardiovascular, respiratory, and locomotor systems interplay dynamically, yet the specific mechanisms of cardiovascular and locomotor interaction during simple rhythmic exercise like walking remain unclear. Computational models constitute a powerful tool to investigate the interplay of networked physiological systems, but while gravitational and postural effects on circulation have been explored, the influence of inertial forces from body motion on hemodynamics has not been addressed.

Here, we present a closed-loop cardiovascular model that incorporates inertial effects during walking. The lumped parameter model includes 25 vascular compartments, a four-chamber heart with valves, pericardial and intrathoracic pressures, interventricular septal dynamics, and a baroreflex mechanism. Inertial effects are modeled as additional hydrodynamic pressure sources in each vascular segment, equivalent to the acceleration of blood mass, caused by gravity and motion. Three protocols are used: a head-up tilt test to validate baroreflex and gravity effects; a synthetic walking simulation with controlled heart rate (HR) and step rate (SR); and a human walking experiment (n=2) linking beat-wise simulated aortic pressure to measured brachial pressure using recorded HR and body acceleration. Beat-wise morphology similarity (K-stat) between experimental and simulated hemodynamic waveforms is quantified with a two-sample Kolmogorov-Smirnov test.

The model reproduces expected physiological responses to head-up tilt. During synthetic walking, inertial effects result in pressure augmentation, increasing systolic or diastolic pressure depending on the phase between HR and SR. With SR > HR, phase variability produces a low-frequency "beating" in the pressure waveforms and mean arterial pressure, corresponding to the difference between SR and HR. In the human subject experiment, the model accurately replicates beat-wise pressure changes at varying phase shifts between HR and SR. Quantitative comparison shows a substantial increase in similarity of waveform when hydrodynamic pressure is included (K-stat: 0.123 vs. 0.029 for P1; 0.164 vs. 0.059 for P2).

Introducing contributions of body acceleration as an additional hydrodynamic pressure source in the vascular compartments seems a valid way to capture walking-induced inertial effects. This work contributes to the broader effort to characterize physiological network adaptations to exercise and offers a foundation for future research studying and optimizing cardiac-locomotor interaction.