Nonlinear structural and material properties and models: the pulmonary trunk

Scholarly review of geometry and compliance: biomechanical perspectives on vascular injury and healing

Mechanical stress and strain upon cardiovascular tissue are important factors that influence the ultimate configuration of clinically observed disease entities. Although mechanical forces can stimulate cellular changes and response, structural or geometric alterations introduced by disease processes can, in turn, influence local hemodynamic conditions. Dynamic interactions of structural parameters, such as arterial compliance and geometry, can further contribute to the final determination of the mechanical conditions and outcome of the vessel. Manipulation of vascular compliance and geometry may, therefore, have desirable effects. In this article, fundamental vascular biomechanical forces are defined and their association with cellular response and clinical disease processes are introduced. The interplay between vascular geometry and compliance is emphasized, and the potential for mechanical solutions to vascular diseases are explored.

Stress reduction by geometric compliance matching at vascular graft anastomoses

An analysis is presented of stresses developed with different junctional configurations of end-to-end vascular graft anastomoses with severe compliance mismatch. Junctions of circular transverse sections and junctions by bias cuts (beveled ends) are compared with an anastomosis of a graft constructed with an elliptical transverse section and a bevel end cut vessel. This latter substitutes midwall inextensional deformations for extensional deformations that occur with the former, conventional configurations. Applications to end-to-side anastomoses are also discussed. A range of parameters are considered: i.e., vascular wall thickness/radius ratios between 0.1 and 0.5, locations from the anastomotic plane between 1/2 and 3/2 times the vascular wall thickness, host vessel axial stretch by external forces between 0 and 15%, maximal vascular circumferential stretch distal from the anastomosis between 0 and 25%, and perimeter locations at the anastomotic junction between 0 degree and 90 degrees. The graft constructed with an elliptic cross-section developed peak stresses that are orders of magnitude lower than those developed with conventional configurations. The introduction of matching geometric compliance that dominates at the anastomotic junction minimizes consequences of material mismatch between graft and vessel and has the potential to reduce suture line stress greatly. This analysis may suggest designs for experimental studies to confirm relationships between neointimal hyperplasia and suture line stress levels, and provide a relatively simple solution for reduction of such stresses at the anastomotic junction. Choices may be permitted of graft materials with optimal surface properties despite less favorable elastic properties.

Diastolic mechanics and the origin of the third heart sound

The third heart sound (S3) is observed for various hemodynamic conditions in both the normal and diseased heart. A theory is proposed in which myocardial viscoelasticity is primarily responsible for S3. A mathematical model is developed based on the mechanical aspects of diastolic function: nonlinear elasticity, viscoelasticity, and pressure generation. The model is provided as an electrical analogy of the left ventricle and circulatory system. S3 is predicted for the normal heart and the heart with dilated cardiomyopathy. An elevation of S3 intensity is indicated for cardiomyopathy, as is often observed in the clinic. S3 is produced experimentally by volume loading of the open-chest canine preparation and mathematically by imposing the conditions of volume loading on the model. Consistency of theory and experiment imply that it is valid to attribute S3 to myocardial viscoelasticity. The animal whose heart possessed the largest constant of viscoelasticity produced the greatest level of S3, in both cases. Nonlinear ventricular compliance is not found to be an essential requirement for sound generation, although increased compliance led to an increase in sound. S3 is predicted to change in response to venous return, ventricular stiffness, contractility, heart rate, and duration of contraction, as observed by others. In general, the coupling of these quantities to S3 is explained in terms of an excitation of viscous properties of the ventricle.