title: Comparison of the Young-Laplace law and finite element based calculation of ventricular wall stress: implications for postinfarct and surgical ventricular remodeling.
abstract: BACKGROUND
  Both the Young-Laplace law and finite element (FE) based methods have been used to calculate left ventricular wall stress. We tested the hypothesis that the Young-Laplace law is able to reproduce results obtained with the FE method.
  
  
  METHODS
  Magnetic resonance imaging scans with noninvasive tags were used to calculate three-dimensional myocardial strain in 5 sheep 16 weeks after anteroapical myocardial infarction, and in 1 of those sheep 6 weeks after a Dor procedure. Animal-specific FE models were created from the remaining 5 animals using magnetic resonance images obtained at early diastolic filling. The FE-based stress in the fiber, cross-fiber, and circumferential directions was calculated and compared to stress calculated with the assumption that wall thickness is very much less than the radius of curvature (Young-Laplace law), and without that assumption (modified Laplace).
  
  
  RESULTS
  First, circumferential stress calculated with the modified Laplace law is closer to results obtained with the FE method than stress calculated with the Young-Laplace law. However, there are pronounced regional differences, with the largest difference between modified Laplace and FE occurring in the inner and outer layers of the infarct borderzone. Also, stress calculated with the modified Laplace is very different than stress in the fiber and cross-fiber direction calculated with FE. As a consequence, the modified Laplace law is inaccurate when used to calculate the effect of the Dor procedure on regional ventricular stress.
  
  
  CONCLUSIONS
  The FE method is necessary to determine stress in the left ventricle with postinfarct and surgical ventricular remodeling.
authors.affiliation: Department of Surgery, University of California, San Francisco, Veterans Affairs Medical Center, San Francisco, California 94121, USA.
authors.forename: Zhihong
authors.initials: Z
authors.lastname: Zhang
authors.forename: Amod
authors.initials: A
authors.lastname: Tendulkar
authors.forename: Kay
authors.initials: K
authors.lastname: Sun
authors.forename: David A
authors.initials: DA
authors.lastname: Saloner
authors.forename: Arthur W
authors.initials: AW
authors.lastname: Wallace
authors.forename: Liang
authors.initials: L
authors.lastname: Ge
authors.forename: Julius M
authors.initials: JM
authors.lastname: Guccione
authors.forename: Mark B
authors.initials: MB
authors.lastname: Ratcliffe
mesh_terms: D000465:Algorithms; D000818:Animals; D004195:Disease Models, Animal; D020342:Finite Element Analysis; D006352:Heart Ventricles; D007091:Image Processing, Computer-Assisted; D008279:Magnetic Resonance Imaging; D009203:Myocardial Infarction / Q000150:complications* / Q000473:pathology* / Q000503:physiopathology; D015203:Reproducibility of Results; D012756:Sheep; D013314:Stress, Mechanical; D020257:Ventricular Remodeling / Q000502:physiology*