Number and location of zero-group-velocity modes.

The frequency-wavenumber spectra of laminated media often exhibit anomalous modes with descending branches whose group velocity is negative, and these terminate at a minimum point at which the group velocity transitions from negative to positive. These minima are associated with resonant conditions in the medium, which have been clearly observed in experiments and in the nondestructive testing of laminated plates. Starting from first principles, this paper provides a theoretical analysis on the number and location of such zero-group-velocity (ZGV) modes for horizontally layered media bounded by any arbitrary combination of external boundaries. It is found that these ZGV points are few in number and show up mostly in low-order modes which are characterized by a negative second derivative at the cutoff frequencies, a condition that can readily be tested. It is also shown that the effective number of ZGVs is small even when the ratio of the dilatational and shear wave velocity is a rational number and there exist coincidences in cutoff frequencies, a condition that at first would suggest that the number of ZGVs is infinite. Finally, it is shown that the number of ZGVs decreases with the Poisson's ratio.

Integrated Analysis of Contractile Kinetics, Force Generation, and Electrical Activity in Single Human Stem Cell-Derived Cardiomyocytes.

The quantitative analysis of cardiomyocyte function is essential for stem cell-based approaches for the in vitro study of human cardiac physiology and pathophysiology. We present a method to comprehensively assess the function of single human pluripotent stem cell-derived cardiomyocyte (hPSC-CMs) through simultaneous quantitative analysis of contraction kinetics, force generation, and electrical activity. We demonstrate that statistical analysis of movies of contracting hPSC-CMs can be used to quantify changes in cellular morphology over time and compute contractile kinetics. Using a biomechanical model that incorporates substrate stiffness, we calculate cardiomyocyte force generation at single-cell resolution and validate this approach with conventional traction force microscopy. The addition of fluorescent calcium indicators or membrane potential dyes allows the simultaneous analysis of contractility and calcium handling or action potential morphology. Accordingly, our approach has the potential for broad application in the study of cardiac disease, drug discovery, and cardiotoxicity screening.