CALCULATION OF LEFT-VENTRICULAR WALL STRESS

Chamber-stress equations relate wall stresses to pressure and wall dimensions. Such equations play a central role in the analysis and understanding of heart-chamber function. Over the past three decades, several stress equations giving radically different results have been derived, used, and/or espoused. They can be classified into two categories, according to the definition of stress underlying the equation. The stresses in one class of equations are total forces per unit normal area, excluding ambient pressure but including pressure in the wall exerted by more external elements of the wall. The stresses in the other class of equations are fiber-pulling forces per unit normal area, that is, total forces per unit normal area excluding all pressure. The validity of stress equations can be tested at least three ways: 1) Do they predict that the pressure inside a small chamber nested in a larger chamber would be the sum of transmural pressures of the two chambers? Do they satisfy the expectation from Laplace's law that a sphere with a given circular stress and thickness/radius ratio would exert twice the pressure of acylinder with the same circular stress and thickness/radius ratio? Do they predict that the ratio of principle stresses depends on chamber shape but not on wall/cavity ratio, with the circular/longitudinal stress ratio of a cylinder being 2 and that of a prolate spheroid being between 1 and 2? Stress equations of the first class fail all of these tests by large margins, whereas those of the second class pass all of these tests exactly. When selecting a stress equation, one should consider these distinctions as they might affect 1) evaluation of stress afterload and stress preload, 2) evaluation of contractility, 3) understanding the role of contractility and wall/cavity ratio as determinants of pressure-making ability, 4) understanding the role of fiber orientation as a determinant of chamber shape, and 5) translations between pressure-volume relations and stress-length relations.