Comparison of the Young-Laplace Law and Finite Element Based Calculation of Ventricular Wall Stress: Implications for Postinfarct and Surgical Ventricular.

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Comparison of the Young-Laplace Law and Finite Element Based Calculation of Ventricular Wall Stress: Implications for Postinfarct and Surgical Ventricular Remodeling Zhihong Zhang, MS, Amod Tendulkar, MD, Kay Sun, PhD, David A. Saloner, PhD, Arthur W. Wallace, MD, PhD, Liang Ge, PhD, Julius M. Guccione, PhD, Mark B. Ratcliffe, MD The Annals of Thoracic Surgery Volume 91, Issue 1, Pages 150-156 (January 2011) DOI: 10.1016/j.athoracsur.2010.06.132 Copyright © 2011 The Society of Thoracic Surgeons Terms and Conditions

Fig 1 (A) Long-axis magnetic resonance (MR) images from sheep with anteroapical myocardial infarction (MI). (B) Short-axis MR image. Both images were obtained 16 weeks after MI. Both images have noninvasive tissue tags, and both images were obtained at end systole. (MI = dyskinetic infarct; SI = septal infarct.) (A) Reprinted from Zhang, et al, J Thorac Cardiovasc Surg 2007;134:1017–24 [17], with permission from the American Association for Thoracic Surgery. The Annals of Thoracic Surgery 2011 91, 150-156DOI: (10.1016/j.athoracsur.2010.06.132) Copyright © 2011 The Society of Thoracic Surgeons Terms and Conditions

Fig 2 Method of measuring endocardial radius of curvature: r is the radius of curvature, and h is the wall thickness. The Annals of Thoracic Surgery 2011 91, 150-156DOI: (10.1016/j.athoracsur.2010.06.132) Copyright © 2011 The Society of Thoracic Surgeons Terms and Conditions

Fig 3 Finite element model of the left ventricle with anteroapical myocardial infarction. (A) Animal specific contours were generated from magnetic resonance imaging. (B) Solid mesh was broken into three regions (green = remote; brown = borderzone; blue = infarct). The Annals of Thoracic Surgery 2011 91, 150-156DOI: (10.1016/j.athoracsur.2010.06.132) Copyright © 2011 The Society of Thoracic Surgeons Terms and Conditions

Fig 4 Stress calculated with the Laplace and finite element (FE) methods at end diastole by (A) region and (B) layer of the left ventricle wall. Note that both the Young-Laplace law and the modified Laplace law overestimate stress in the circumferential direction and cross-fiber direction in the remote myocardium at end diastole. (Black bars = FE fiber; dark gray bars = FE cross fiber; light gray bars = FE circumferential; white bars = LaPlace; hatched bars = modified LaPlace.) The Annals of Thoracic Surgery 2011 91, 150-156DOI: (10.1016/j.athoracsur.2010.06.132) Copyright © 2011 The Society of Thoracic Surgeons Terms and Conditions

Fig 5 Stress calculated with the Laplace and the finite element (FE) methods at end systole by (A) region and (B) layer of the left ventricle wall. Note that the Young-Laplace law underestimates stress in the fiber direction at end systole. The Young-Laplace law is not different than circumferential stress in the remote myocardium but fails to account for transmural variation in stress. Statistically significant comparisons with cross-fiber stress are not marked. See the text for those details. (White bar = LaPlace; hatched bar = modified LaPlace; black bars = FE fiber; dark gray bars = FE cross fiber; light gray bars = FE circumferential; Endo = endocardium; Epi = epicardium; Mid = midwall.) The Annals of Thoracic Surgery 2011 91, 150-156DOI: (10.1016/j.athoracsur.2010.06.132) Copyright © 2011 The Society of Thoracic Surgeons Terms and Conditions