In the few tens of milliseconds around the R wave—the transition from diastole to systole—the interventricular septum (IVS) exhibits a mechanical traveling wave distinct from electrical activation. Using phase‑tracking ultrasonic imaging, this study non‑invasively captured that high‑speed, large‑amplitude wave and visualized, with high spatiotemporal resolution, its phase pattern and amplitude dip (“hole”) as it propagated longitudinally from apex to base.
Experimental findings
Despite an almost zero wavenumber before and after the wave front, a local phase jump coexisted with an amplitude depression, forming a homoclinic hole structure—qualitatively different from the antiphase Lamb wave observed at aortic‑valve closure.
Theoretical analysis
Numerical simulations of the one‑dimensional complex Ginzburg–Landau equation (CGLE) with periodic boundaries reproduced the observed phase‑and‑amplitude pattern, matching the homoclinic plane‑wave solution of the CGLE.
Although the CGLE is a standard framework for Benjamin–Feir instability and defect turbulence in nonlinear media, experimental validation in cardiac tissue has been scarce. This work suggests that living myocardium can indeed belong to the CGLE universality class, opening a route to interpret heartbeat mechanics through nonlinear‑wave theory.
The homoclinic hole is interpreted as a local phase defect that suppresses amplitude via the elastic‑viscous properties of muscle fibers. The defect velocity was estimated at ~ 0.04 mm · ms⁻¹, within the velocity range allowed by plane‑wave branches of the CGLE. These insights are valuable for elucidating abnormal wave propagation in diseased myocardium—where elasticity changes owing to ischemia or fibrosis—and for understanding how microscopic sarcomeric oscillations (SPOC/HSOs) manifest at the macroscopic scale.
Article information & citation
Naoaki Bekki, Seine A. Shintani, Shin’ichi Ishiwata, Hiroshi Kanai. A Model for Measured Traveling Waves at End-Diastole in Human Heart Wall by Ultrasonic Imaging Method. Journal of the Physical Society of Japan 85, 044802 (2016).