Ventricular wall stress.

SUMMARY Quantification of ventricular wall stress is necessary for an understanding of both normal and pathological ventricular mechanics. At present there are no reliable means to measure, directly, wall stresses in the intact ventricle. Thus, we must rely on mathematical models to predict these stresses, knowing that the predictions cannot be validated directly. Since each model employs certain simplifying assumptions, one must be aware of the limitations of stress predictions derived from that model. All of the models currently used to calculate wall stresses were reviewed and the following major conclusions were reached: (1) For most applications, detailed knowledge of the stress distribution across the wall is not essential and cannot be verified by current means. The midwall or stress averaged across the wall is adequate. Hence, the Falsetti et al. (1970) thin-walled or the MJrksy (1969, 1979) thick-walled ellipsoidal formulas derived from a generalized Laplace's law are probably the best compromise in terms of ease of computation, and incorporation of realistic albeit greatly oversimplified geometry. Use of thin-or thick-walled spherical formulas underestimate circumferential stresses by about 20-40% and overestimate longitudinal stresses by about 10-20%, respectively. (2) The wide qualitative and quantitative differences predicted by the various analytical thick-walled formulas make it difficult to judge which gives the most realistic representation of the actual stress distribution across the wall and are, thus, of little practical utility. (3) The finite-element method offers an extremely powerful method for analyzing regional variations in stress. This method can account for variations in material properties , complex geometry, anisotropy, and variations in fiber angle from region to region. However, until faster and better methods of accurate three-dimensional reconstruction of the heart are available and until more data on the multiaxial constitutive properties of myocardium are obtained, this method cannot be utilised to its full capabilities. In addition, the effort and expense involved in using the finite-element method are considerable and will limit its widespread application. (4) Until accurate and reliable methods to measure wall stresses are developed and the predictions of the models are validated, our quantitative knowledge of ventricular wall stress will be incomplete. CARDIOLOGISTS, physiologists, and engineers have long been intensely interested in quantifica-tion of the forces or stresses acting in the wall of the heart. The extent of this interest is evident in the voluminous literature containing references to ventricular wall stress since Woods' publication late in the last century (Woods, 1892). …