Ph.D Thesis

Ph.D StudentEmuna Nir
SubjectBifurcation Phenomena and Sensitivity to Residual
Stresses in Soft Tissues
DepartmentDepartment of Aerospace Engineering
Supervisor PROFESSOR EMERITUS David Durban
Full Thesis textFull thesis text - English Version


Mechanical stability and sensitivity analyses in soft tissues are the two main theses of the present dissertation.

Mechanical stability is one of the underlying mechanisms in either soft tissue developmental (embryogenesis, cortical folding, gastrointestinal patterns), or pathological processes (abnormal cortical folding, arterial tortuosity, mucosal folding). Stability analysis was performed within the context of linear bifurcation theory. We demonstrated that the incremental load behavior at the onset of instability (“rate boundary conditions”) has a significant influence on the critical load and deformation margins. In addition, different rate boundary conditions can give rise to different mode shapes- suggesting not only a possibility of shape transition via mechanical instability, but also of pattern selection via control of rate boundary conditions. We have also found a similar influence of rate interface conditions for layered models, residually stressed by geometric incompatibility- with obvious relevance for layered tissues. One of the examples discussed in this contribution is the possibility of “spontaneous instability” emerging due to geometric incompatibility alone, under no external loads, a phenomenon that can explain pathologies like mucosal folding, for example. Finally, stability analysis was performed to predict arterial instability under combined loading of inflation, axial force, and torsion, and was validated against experimental data. The insights and results of the bifurcation analyses are significant for the increasing number of models used to describe and predict normal and pathological biological processes. In particular, the present contributions of the studies of rate boundary and interface conditions are relevant in soft tissue biomechanics since these conditions are not known with the same certainty as in classic engineering applications. The validated model for arterial instability under torsion offers insights for understanding the pathological condition of arterial tortuosity. It is also clinically relevant for planning of surgical procedures like microanastomosis, and for the development of stents for arteries operating in extreme mechanical environment like the femoropopliteal arteries.

Sensitivity analysis is an emerging research field in soft tissue mechanics with the aim of reducing uncertainties and improving the predictions of biomechanical models. We developed a new, deterministic and straight-forward, method to assess the sensitivities of hyperelastic arterial models to uncertainties in input stress-free geometrical parameters. Applied on experimental data of six different human arteries, this method revealed extreme sensitivities of popular anisotropic arterial models to relatively small (<10%) measurement errors in the opening angle and axial prestretch: constitutive (>160%), descriptive (>30%), and predictive (>200%). The implications of this finding are relevant to the large body of studies involving experimentally based modeling of vascular tissues. The constitutive sensitivity is significant in light of the many studies that use calibrated constitutive parameters to draw conclusions about the underlying microstructure of vascular tissues, their growth and remodeling processes, aging and disease states. The propagation of uncertainties into quantitative predictions of variables like force, luminal pressure, and wall stresses, is of practical importance to the design and execution of clinical devices and interventions.

The present results have been published as four papers in the Journal of Biomechanical Engineering of the ASME.