Carstensen’s contributions to shear stress in strain and tissues

Abstract

Some of Edwin Carstensen's final papers considered elastographic shear waves, which had opened up a new set of questions regarding stress and strain in tissues. Carstensen, from his commanding perspective overlooking nearly 70 years of fields and waves in tissues, could uniquely make the following statement: “At present, no consensus group has undertaken a systematic evaluation of the biological effects of low-frequency strains…Thanks to developments in the field of elastography over the last two decades, we now have the tools needed to measure low-frequency strains in tissues directly…Despite the fundamental importance of strain in bioeffects, no bioeffects investigators to our knowledge have taken advantage of these techniques. In fact, strain is rarely mentioned in the bioeffects literature” (Carstensen et al., “Biological effects of low-frequency shear strain: physical descriptors,” Ultrasound Med Biol 42(1)1-15, 2016). Indeed, with this topic, his “voyage of exploration and illumination” had truly come full circle, returning to some earlier questions but under new circumstances. We explore the deep issues Carstensen uncovered, including special forms of shear waves, the implications of Ostreicher's work, tissue viscoelastic response to shear stresses, and the inherent puzzles of linear hysteresis models.