R. J. Okamoto Department of Mechanical Engineering, Washington University, St. Louis, MO 63130 M. J. Moulton Division of Cardiothoracic Surgery, Washington University, St. Louis, MO 63130 S. J. Peterson Department of Mechanical Engineering, Washington University, St. Louis, MO 63130 D. Li Mallinckrodt Institute of Radiology, Washington University, St. Louis, MO 63130 M. K. Pasque Division of Cardiothoracic Surgery, Washington University, St. Louis, MO 63130 J. M. Guccione Department of Mechanical Engineering, Division of Cardiothoracic Surgery, Washington University, St. Louis, MO 63130 Epicardial Suction: A New Approach to Mechanical Testing of the Passive Ventricular Wall The lack of an appropriate three-dimensional constitutive relation for stress in passive ventricular myocardium currently limits the utility of existing mathematical models for experimental and clinical applications. Previous experiments used to estimate parameters in three-dimensional constitutive relations, such as biaxial testing of excised myocardial sheets or passive inflation of the isolated arrested heart, have not included significant transverse shear deformation or in-plane compression. Therefore, a new approach has been developed in which suction is applied locally to the ventricular epicardium to intro- duce a complex deformation in the region of interest, with transmural variations in the magnitude and sign of nearly all six strain components. The resulting deformation is measured throughout the region of interest using magnetic resonance tagging. A nonlin- ear, three-dimensional, finite element model is used to predict these measurements at several suction pressures. Parameters defining the material properties of this model are optimized by comparing the measured and predicted myocardial deformations. We used this technique to estimate material parameters of the intact passive canine left ventricular free wall using an exponential, transversely isotropic constitutive relation. We tested two possible models of the heart wall: first, that it was homogeneous myocardium, and sec- ond, that the myocardium was covered with a thin epicardium with different material properties. For both models, in agreement with previous studies, we found that myocar- dium was nonlinear and anisotropic with greater stiffness in the fiber direction. We obtained closer agreement to previously published strain data from passive filling when the ventricular wall was modeled as having a separate, isotropic epicardium. These results suggest that epicardium may play a significant role in passive ventricular mechan- ics. S0148-07310000305-8 Keywords: Constitutive Relations, Finite Elements, Stress Analysis Introduction Mathematical models are needed to provide a sound basis for interpreting the nonhomogeneous changes in cardiac mechanical function that occur in regional pathological disorders, such as is- chemic heart disease 1, in terms of changes in the local proper- ties of the heart muscle. Existing models incorporate detailed de- scriptions of the three-dimensional ventricular topology, the internal fibrous architecture of the ventricular walls, and informa- tion about the ventricular pressures 2,3. The ability of these models to predict the mechanical behavior of the heart accurately depends, however, on an accurate description of the intrinsic ma- terial properties of the ventricular wall. In vitro biaxial testing protocols performed on isolated sheets of ventricular muscle suggest that passive myocardium is nonlinear, anisotropic, nearly elastic, and possibly regionally heterogeneous 4–7. These sheets are cut so that the muscle-fiber axis lies in the plane of the section and the fiber orientation is relatively uniform through the thickness of the sample, but the extent to which these results reflect the material properties of intact myocardium re- mains uncertain. In order to make these tests, it is necessary to disrupt the structural integrity of the myocardium, and the speci- men may be further damaged by contracture induced by ischemia or by calcium released from cells injured during the cutting pro- cess 6. Moreover, it is not possible to reproduce either the com- pressive loading or the shear loading that occurs in vivo using this testing method. Passive material properties of intact ventricular wall have been estimated using the conservation laws of continuum mechanics 8,9, but only under the assumption of material homogeneity. However, neither type of experiment provides information on transverse shearing properties in the circumferential–radial and longitudinal–radial planes because transverse shear strains are negligible in the isolated, arrested heart undergoing passive infla- tion 10. These material properties are needed not only for math- ematical models of passive ventricular filling. They are also very important for models of the beating heart in which systolic con- traction is modeled by defining the stress tensor as the sum of the passive three-dimensional stress and an active fiber-directed stress 11. Significant circumferential–radial and longitudinal–radial transverse shear strains during systole were reported by Waldman and co-workers 12. Therefore, the purpose of this study was to use a new approach, termed epicardial suction, to quantify the material properties of intact canine left ventricular wall, especially those related to trans- verse shear. Methods An overview of the approach is shown in Fig. 1. Epicardial suction is a new technique that produces local deformation in an intact heart. In contrast to experiments using beating hearts or passive inflation of isolated, arrested hearts, the deformation oc- curs primarily in the region of the left ventricle LV where the suction cup is placed. The suction pressure is varied periodically, producing a repeatable pattern of deformation. The deformation is measured using a magnetic resonance imaging MRI technique known as MR tagging. This technique allows noninvasive mea- surement of displacements at numerous locations in the image Contributed by the Bioengineering Division for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received by the Bioengineering Divi- sion April 27, 1999; revised manuscript received May 30, 2000. Associate Technical Editor: J. D. Humphrey. Copyright © 2000 by ASME Journal of Biomechanical Engineering OCTOBER 2000, Vol. 122 Õ 479