Transverse stiffness: A method for estimation of myocardial wall stress

Abstract

Determination of regional ventricular wall stress would allow quantification of both regional contractile state and its interplay with global function. Current methods for quantifying regional stress include mathematical modelling and measurements with strain gauges. Both methods are difficult to validate. We hypothesized that transverse stiffness (i.e., the ratio of indentation stress to strain as the ventricular wall is indented in the direction perpendicular to the wall) would be proportional to the stresses in the plane of the wall and could be used to estimate the latter. To test this hypothesis, 6 arterially perfused canine ventricular septa were mounted in an apparatus that could exert biaxial load in the plane of the wall. A servo system maintained the central third of the septa isometric during active contractions while the septa were paced at 30-60 pulses/min. In the center of the isometric region, a probe of 7 mm diameter indented the septa while the transverse indentation stress and strain were measured. For values of peak systolic in-plane stress from 0.56 to 2.6 g/mm2, the transverse stiffness varied from 1.2 to 11.7 g/mm2 and was linearly related to the in-plane wall stress in each septum (p < 0.001, ANOVA). After cardioplegia, the transverse stiffness also correlated with passively applied wall stress for each dog (p < 0.001). The slopes of the individual relations between transverse stiffness and wall stress from active contractions were similar to those from passively applied stress (mean ± SEM; 1.82 ± 0.36 versus 1.45 ± 0.31, NS). The intercepts with the transverse stiffness axis from active contractions, however, were greater than those from passively applied stress (2.23 ± 0.57 versus - 0.16 ± 0.12 g/mm2, p < 0.015). Moreover, at similar wall stresses, the transverse stiffness for active contractions was greater than that for passively applied stress (3.1 ± 0.7 versus 1.1 ± 0.2 g/mm2, p < 0.005). Thus, regional transverse stiffness appears to allow quantitative estimation of regional in-plane stresses and can distinguish between actively generated and passively applied stress. This approach may allow one to accurately quantify the regional contractile state and to determine whether regional dysfunction is due to abnormal muscle that is not generating stress or to muscle capable of generating stress but which is abnormally loaded.