The use of strain gradient elasticity in modelling tissues: The case of the human heart

Abstract

In recent years, strain gradient elasticity has been used to capture size effects in stiffness and toughness that appear in structures of different sizes. An important aspect of such theories, often taken of little notice, is the non-classical boundary conditions that appear as couple-stress tractions. Such tractions can provide deformation of the body they are acting on, without the need for classic type of supports that are usually needed when classic tractions are applied. Moreover such tractions seem to be "invisible", since no external pressure is acting and they can be related to non-mechanical sources, like electricity. The human heart seems to stand without support (bones etc), floating in the human body and electric pulses applied to its surface make it vibrate, inflating periodically the various chambers that circulate the blood in the body. We propose a model for the muscle tissues of the heart, in the context of gradient elasticity, relating the power due to the couple stresses with the electric power provided by chemistry. The effect is to provide a model that describes at the surface of the heart couple stress tractions that can be direct functions of the electrocardiogram (ECG) signals. The heart is modeled as a thick spherical shell that deforms under the fore-mentioned boundary conditions and the problem is solved in closed form, providing useful relations that connect the deformation of the walls of the heart with the ECG. Many applications can benefit from the present approach, like pacers and other medical devices. © 2010 World Scientific Publishing Co. Pte. Ltd.