Planar Biaxial Testing of Soft Biological Tissues

Cardiovascular diseases are the leading cause of death in the developed countries. Since mechanics take a part in the onset, progression and treatment of these diseases, a good understanding of the biomechanical behavior of cardiovascular tissue can help to reduce the mortality associated with these diseases. To this end, mechanical testing of arterial tissue can provide a valuable insight. Moreover, the result of a subsequent parameter fitting can be used in a finite elements simulation of biomechanical problem. A planar biaxial test is a mechanical test that is widely used since its loading is physiologically relevant and it is suitable for small samples. However, variations to the methodology of planar biaxial testing are equally wide. Clearly, the quality of the performed test will influence the quality of the resulting material parameter set and subsequent finite element simulations. Therefore, as the community performing planar biaxial experiments on soft biological tissues is growing, the methodology of this test should be investigated more thoroughly.

The goal of this thesis is to increase the understanding of the mechanics of planar biaxial testing and the subsequent parameter fitting. To this end, the influence of certain variations to the testing conditions, the data processing and the parameter fitting need to be quantified.

In the first part of this thesis a series of variations in a rake-based planar biaxial test was investigated using finite elements. Variations to the testing conditions, such as the number of rakes and the rakes' width, were evaluated based on the inhomogeneity of the stress field and on the correlation between the experimentally measured stress at the rakes and the stress at the center of the sample. These varying testing conditions led to guidelines for best practice of planar biaxial testing. Next, variations to the data processing were evaluated based on the resulting stress-strain curves. The best method for data processing was determined and guidelines for reporting of planar biaxial experiments and parameter fitting were described. Finally, a new parameter fitting procedure was proposed that leads to improved parameter fitting results. This parameter fitting takes the boundary conditions, which are neglected in a classic parameter fitting, into account.

The second part of this thesis investigated the effect of sample orientation in a rake-based planar biaxial test using finite elements. The influence of various degrees of misalignment on the deformation of the sample, on the force measured at the rakes and on the parameter fitting results was studied. For a slightly misaligned sample, the material parameters can be found to a reasonable level of accuracy using a parameter fitting procedure that takes into account the boundary conditions. However, after a certain threshold of misalignment, reliable parameters can no longer be found. The level of this threshold seems to be material dependent. The addition of a rail shear test does not solve this problem. Hence, it is important to carefully track the sample orientation throughout the test protocol.

In the third part of this thesis two gripping mechanisms were compared using finite elements: the pulley-suture system and the rakes. The suture system allows the sample to rotate and shear, while mounting of the sample is more repeatable when rakes are used. For an equal displacement of the actuators, the normal stresses and strains are higher in a rake-based test, while the shear stresses and strains are higher in a suture-based test. The more uniform mounting and higher number of loading points leads to a more homogeneous stress-strain field for rakes compared to sutures. The parameter fitting results of both tests are comparable. 

In the fourth part of this thesis the new parameter fitting procedure that takes into account the boundary conditions, was applied to data from a real planar biaxial experiment using rakes. An image from this experiment was processed to create a sample-specific finite element model of the experiment. A simplified finite element model, for which no image processing was required, was also created. Two human aorta samples were used to compare the classic and two variations (i.e. both finite element models) of the new parameter fitting procedure. Their performance was evaluated based on the correspondence between the force in the biaxial experiment and the force in a finite element simulation of the experiment using the fitted parameters. Both variations of the new parameter fitting procedure lead to an improved estimation of the sample material behavior.

To conclude, the above variations in planar biaxial testing lead to several insights and an improved understanding of the mechanics in the test. This in turn will lead to improved planar biaxial testing of soft biological tissues and eventually towards a standardized method. The parameter fitting results will be more reliable and hence, the outcome of finite element simulations using these material parameters, will be more trustworthy.