Biomechanics and Modeling in Mechanobiology

, Volume 10, Issue 6, pp 799–811

Computational modeling of growth: systemic and pulmonary hypertension in the heart


  • M. K. Rausch
    • Department of Mechanical EngineeringStanford University
  • A. Dam
    • Department of Mechanical EngineeringStanford University
  • S. Göktepe
    • Department of Civil EngineeringMiddle East Technical University
  • O. J. Abilez
    • Departments of Bioengineering and SurgeryStanford University
    • Departments of Mechanical Engineering, Bioengineering, and Cardiothoracic SurgeryStanford University
Original Paper

DOI: 10.1007/s10237-010-0275-x

Cite this article as:
Rausch, M.K., Dam, A., Göktepe, S. et al. Biomech Model Mechanobiol (2011) 10: 799. doi:10.1007/s10237-010-0275-x


We introduce a novel constitutive model for growing soft biological tissue and study its performance in two characteristic cases of mechanically induced wall thickening of the heart. We adopt the concept of an incompatible growth configuration introducing the multiplicative decomposition of the deformation gradient into an elastic and a growth part. The key feature of the model is the definition of the evolution equation for the growth tensor which we motivate by pressure-overload-induced sarcomerogenesis. In response to the deposition of sarcomere units on the molecular level, the individual heart muscle cells increase in diameter, and the wall of the heart becomes progressively thicker. We present the underlying constitutive equations and their algorithmic implementation within an implicit nonlinear finite element framework. To demonstrate the features of the proposed approach, we study two classical growth phenomena in the heart: left and right ventricular wall thickening in response to systemic and pulmonary hypertension.


BiomechanicsGrowthRemodelingFinite elementsHypertensionHypertrophy

Copyright information

© Springer-Verlag 2010