Biomechanics and Modeling in Mechanobiology

, Volume 18, Issue 2, pp 387–398 | Cite as

On the computation of in vivo transmural mean stress of patient-specific aortic wall

  • Minliang Liu
  • Liang Liang
  • Haofei Liu
  • Ming Zhang
  • Caitlin Martin
  • Wei SunEmail author
Original Paper


It is well known that residual deformations/stresses alter the mechanical behavior of arteries, e.g., the pressure–diameter curves. In an effort to enable personalized analysis of the aortic wall stress, approaches have been developed to incorporate experimentally derived residual deformations into in vivo loaded geometries in finite element simulations using thick-walled models. Solid elements are typically used to account for “bending-like” residual deformations. Yet, the difficulty in obtaining patient-specific residual deformations and material properties has become one of the biggest challenges of these thick-walled models. In thin-walled models, fortunately, static determinacy offers an appealing prospect that allows for the calculation of the thin-walled membrane stress without patient-specific material properties. The membrane stress can be computed using forward analysis by enforcing an extremely stiff material property as penalty treatment, which is referred to as the forward penalty approach. However, thin-walled membrane elements, which have zero bending stiffness, are incompatible with the residual deformations, and therefore, it is often stated as a limitation of thin-walled models. In this paper, by comparing the predicted stresses from thin-walled models and thick-walled models, we demonstrate that the transmural mean stress is approximately the same for the two models and can be readily obtained from in vivo clinical images without knowing the patient-specific material properties and residual deformations. Computation of patient-specific mean stress can be greatly simplified by using the forward penalty approach, which may be clinically valuable.


Residual stress Transmural mean stress Membrane stress Forward penalty approach 



This study is supported in part by NIH Grants Nos. HL104080, HL127570 and HL142036. Liang is supported by an American Heart Association postdoctoral fellowship 16POST30210003.

Compliance with ethical standards

Conflict of interest

Dr. Wei Sun serves as the Chief Scientific Advisor of Dura Biotech. He has received compensation and owns equity in the company. The other authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Minliang Liu
    • 1
  • Liang Liang
    • 1
  • Haofei Liu
    • 2
  • Ming Zhang
    • 2
  • Caitlin Martin
    • 1
  • Wei Sun
    • 1
    Email author
  1. 1.Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical EngineeringGeorgia Institute of Technology and Emory UniversityAtlantaUSA
  2. 2.Department of MechanicsTianjin UniversityTianjinChina

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