Mechanics of Cardiovascular Soft Tissues

Researcher:Jonas Stålhand
Funding:The Swedish Research Councile (VR)


Soft tissues are complex, anisotropic materials subjected to large, nonlinear, incompressible deformations. It was, therefore, not until the 1960s that the mechanical modelling of soft tissues really took off, following the pioneering work in nonlinear continuum mechanics in the 1940-1960s by E. Erikson, A.E. Green, W. Noll, R.S. Rivlin and C. Truesdell. One of the first hypotheses with far-reaching consequences for the mechanical modelling of soft tissues was made by Y.C. Fung. He proposed that the strain-energy of soft tissues could be described by a relatively simple exponential function in the strains [1].

Since then, the mechanical models have evolved owing to a combination of in vitro (laboratory) experiments and application of nonlinear continuum mechanics. The development has led to the introduction of more mathematically advanced theories [2] and sophisticated devices that can measure a variety of responses under controlled conditions. Unfortunately, the associated increase in complexity has to some extent distanced the state-of-the-art mechanical models from the clinical application. The clinical measurements are generally conducted in vivo (in the body) and are therefore restricted in what can be measured. The measurable quantities in vivo are quite simply in conflict with the required in-data to a state-of-the-art mechanical model. Nevertheless, since the ultimate goal is to apply the mechanical models to improve methods for diagnosing and treating diseases, it is paramount to find methods that can bridge this gap.


The objective with this research project is to study the mechanical properties of the cardiovascular system. The research programme is based on a method recently developed by our research group, see references [3-6]. In the previous research, the artery is treated as a fibre-reinforced, incompressible cylinder subjected to an internal pressure. In general, the artery is not a perfect cylinder, however, and its geometry and composition of different tissues, e.g., collagen, elastin, and smooth muscles, may play an important role for the mechanical behaviour. In order to study the effects of the geometry and structure, the model will be adapted to use true human geometrical data for arteries, for instance from CT, MR, or ultrasonic measurements. In addition to the above mentioned difficulties, soft tissues is are capable of active contraction and continuous structural adaptation (both growth and structural re-organization) in response to changing local and functional requirements. All these aspects are important that need to be considered to truly understand the mechanical behaviour of cardiovascular soft tissues.


[1] Fung Y.C. (1993) Biomechanics. Mechanical Properties of Living Tissues, 2ed., Springer-Verlag, New York

[2] Holzapfel G.A., Gasser T.C., Ogden R.W. (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. Elasticity 61: 1-48

[3] Stålhand J., Klarbring A. (2005) Aorta in vivo parameter identification using an axial force constraint. Biomechan Model Mechanobiol 3: 191-199

[4] Stålhand J., Klarbring A. (2006) Parameter identification in arteries using constraints. In: Holzapfel GA, Ogden RW (eds.) Mechanics of Biological Tissue. Springer -Verlag, Wien, pp. 295-305

[5] Olsson T., Stålhand J., Klarbring A. (2006) Modeling Initial Strain Distribution in Soft Tissues with Application to Arteries. Biomechan Model Mechanobiol 5: 27-38

[6] Stålhand J., Klarbring A., Karlsson M. (2004) Towards in vivo aorta material identification and stress estimation. Biomechan Model Mechanobiol 2: 169-186

Page responsible: Jonas Stålhand
Last updated: 2008-02-20