Heleen Fehervary

Planar biaxial testing of soft biological tissue using rakes: A critical analysis of protocol and fitting process

Mechanical characterization of soft biological tissue is becoming more and more prevalent. Despite the growing use of planar biaxial testing for soft tissue characterization, testing conditions and subsequent data analysis have not been standardized and vary widely. This also influences the quality of the result of the parameter fitting. Moreover, the testing conditions and data analysis are often not or incompletely reported, which impedes the proper comparison of parameters obtained from different studies. With a focus on planar biaxial tests using rakes, this paper investigates varying testing conditions and varying data analysis methods and their effect on the quality of the parameter fitting results. By means of a series of finite element simulations, aspects such as number of rakes, rakes׳ width, loading protocol, constitutive model, material stiffness and anisotropy are evaluated based on the degree of homogeneity of the stress field, and on the correlation between the experimentally obtained stress and the stress derived from the constitutive model. When calculating the aforementioned stresses, different definitions of the section width and deformation gradient are used in literature, each of which are looked into. Apart from this degree of homogeneity and correlation, also the effect on the quality of the parameter fitting result is evaluated. The results show that inhomogeneities can be reduced to a minimum for wise choices of testing conditions and analysis methods, but never completely eliminated. Therefore, a new parameter optimization procedure is proposed that corrects for the inhomogeneities in the stress field and induces significant improvements to the fitting results. Recommendations are made for best practice in rake-based planar biaxial testing of soft biological tissues and subsequent parameter fitting, and guidelines are formulated for reporting thereof in publications.

Biomechanical Characterization of Ascending Aortic Aneurysms

Ascending thoracic aortic aneurysms (ATAAs) are a silent disease, ultimately leading to dissection or rupture of the arterial wall. There is a growing consensus that diameter information is insufficient to assess rupture risk, whereas wall stress and strength provide a more reliable estimate. The latter parameters cannot be measured directly and must be inferred through biomechanical assessment, requiring a thorough knowledge of the mechanical behaviour of the tissue. However, for healthy and aneurysmal ascending aortic tissues, this knowledge remains scarce. This study provides the geometrical and mechanical properties of the ATAA of six patients with unprecedented detail. Prior to their ATAA repair, pressure and diameter were acquired non-invasively, from which the distensibility coefficient, pressure–strain modulus and wall stress were calculated. Uniaxial tensile tests on the resected tissue yielded ultimate stress and stretch values. Parameters for the Holzapfel–Gasser–Ogden material model were estimated based on the pre-operative pressure–diameter data and the post-operative stress–stretch curves from planar biaxial tensile tests. Our results confirmed that mechanical or geometrical information alone cannot provide sufficient rupture risk estimation. The ratio of physiological to ultimate wall stress seems a more promising parameter. However, wall stress estimation suffers from uncertainties in wall thickness measurement, for which our results show large variability, between patients but also between measurement methods. Our results also show a large strength variability, a value which cannot be measured non-invasively. Future work should therefore be directed towards improved accuracy of wall thickness estimation, but also towards the large-scale collection of ATAA wall strength data.

Biomechanical evaluation of a personalized external aortic root support applied in the Ross procedure

A commonly heard concern in the Ross procedure, where a diseased aortic valve is replaced by the patients own pulmonary valve, is the possibility of pulmonary autograft dilatation. We performed a biomechanical investigation of the use of a personalized external aortic root support or exostent as a possibility for supporting the autograft. In ten sheep a short length of pulmonary artery was interposed in the descending aorta, serving as a simplified version of the Ross procedure. In seven of these cases, the autograft was supported by an external mesh or so-called exostent. Three sheep served as control, of which one was excluded from the mechanical testing. The sheep were sacrificed six months after the procedure. Samples of the relevant tissues were obtained for subsequent mechanical testing: normal aorta, normal pulmonary artery, aorta with exostent, pulmonary artery with exostent, and pulmonary artery in aortic position for six months. After mechanical testing, the material parameters of the Gasser-Ogden-Holzapfel model were determined for the different tissue types. Stress-strain curves of the different tissue types show significantly different mechanical behavior. At baseline, stress-strain curves of the pulmonary artery are lower than aortic stress-strain curves, but at the strain levels at which the collagen fibers are recruited, the pulmonary artery behaves stiffer than the aorta. After being in aortic position for six months, the pulmonary artery tends towards aorta-like behavior, indicating that growth and remodeling processes have taken place. When adding an exostent around the pulmonary autograft, the mechanical behavior of the composite artery (exostent + artery) differs from the artery alone, the non-linearity being more evident in the former.

Should We Ignore What We Cannot Measure? How Non-Uniform Stretch, Non-Uniform Wall Thickness and Minor Side Branches Affect Computational Aortic Biomechanics in Mice

In order to advance the state-of-the-art in computational aortic biomechanics, we investigated the influence of (i) a non-uniform wall thickness, (ii) minor aortic side branches and (iii) a non-uniform axial stretch distribution on the location of predicted hotspots of principal strain in a mouse model for dissecting aneurysms. After 3 days of angiotensin II infusion, a murine abdominal aorta was scanned in vivo with contrast-enhanced micro-CT. The animal was subsequently sacrificed and its aorta was scanned ex vivo with phase-contrast X-ray tomographic microscopy (PCXTM). An automatic morphing framework was developed to map the non-pressurized, non-stretched PCXTM geometry onto the pressurized, stretched micro-CT geometry. The output of the morphing model was a structural FEM simulation where the output strain distribution represents an estimation of the wall deformation, not only due to the pressurization, but also due to the local axial stretch field. The morphing model also included minor branches and a mouse-specific wall thickness. A sensitivity study was then performed to assess the influence of each of these novel features on the outcome of the simulations. The results were supported by comparing the computed hotspots of principal strain to hotspots of early vascular damage as detected on PCXTM. Non-uniform axial stretch, non-uniform wall thickness and minor subcostal arteries significantly alter the locations of calculated hotspots of maximal principal strain. Even if experimental data on these features are often not available in clinical practice, one should be aware of the important implications that simplifications in the model might have on the final simulated result.

Biomechanical characterization of human dura mater

A reliable computational model of the human head is necessary for better understanding of the physical mechanisms of traumatic brain injury (TBI), car-crash investigation, development of protective head gear and advancement of dural replacement materials. The performance and biofidelity of these models depend largely on the material description of the different structures present in the head. One of these structures is the dura mater, the protective layer around the brain. We tested five human dura mater specimens, with samples at different locations, using planar biaxial tests. We describe the resulting stress-strain curves using both the anisotropic Gasser-Ogden-Holzapfel (GOH) model and the isotropic one-term Ogden model. The low-strain section of the curves is also described using a Neo-Hookean formulation. The obtained stress-strain curves reveal highly nonlinear but isotropic behaviour. A significant amount of inter- and intra-specimen variability is noticed, whereby the latter does not seem to be influenced by location. The GOH model achieves the best fit of the individual test data. A simple Neo-Hookean model can only be used with extreme caution, as it does not manage to capture the nonlinear effects present even at low strains.

Characterisation of Mechanical Properties of Human Pulmonary and Aortic Tissue

The aim of this study is to characterise the mechanical properties of aortic and pulmonary arterial tissue, thereby comparing both tissue types and investigating the effect of lung-affecting disease on the mechanical behaviour of pulmonary arteries. Force-controlled, planar biaxial tensile tests were performed on human tissue samples collected from donors and receptors undergoing lung transplantation. In total 8 pulmonary donor, 6 pulmonary receptor and 6 aortic donor samples were tested and analysed. Donor samples are considered to be healthy, while receptors provided pathological tissue. The stiffness and strength of each sample were calculated from the stress-strain curves and a statistical analysis was performed between the three tissue groups (pulmonary donor, pulmonary receptor and aortic donor). The stiffness of aortic donor tissue was found to be significantly higher than for pulmonary donor tissue (p < 0.01) at physiological systolic stresses. The same could be observed for the strength (p < 0.05). Pulmonary samples were, however, significantly stiffer than aortic samples at stresses in the physiological range of aorta (p < 0.01). There was no significant difference found between the donors and receptors for pulmonary samples. The fact that the physiological pressure in the aorta is fivefold higher than in the pulmonary artery is also reflected in its stiffness and strength.

Comparison of in vivo vs. ex situ obtained material properties of sheep common carotid artery

Patient-specific biomechanical modelling can improve preoperative surgical planning. This requires patient-specific geometry as well as patient-specific material properties as input. The latter are, however, still quite challenging to estimate in vivo. This study focuses on the estimation of the mechanical properties of the arterial wall. Firstly, in vivo pressure, diameter and thickness of the arterial wall were acquired for sheep common carotid arteries. Next, the animals were sacrificed and the tissue was stored for mechanical testing. Planar biaxial tests were performed to obtain experimental stress-stretch curves. Finally, parameters for the hyperelastic Mooney-Rivlin and Gasser-Ogden-Holzapfel (GOH) material model were estimated based on the in vivo obtained pressure-diameter data as well as on the ex situ experimental stress-stretch curves. Both material models were able to capture the in vivo behaviour of the tissue. However, in the ex situ case only the GOH model provided satisfactory results. When comparing different fitting approaches, in vivo vs. ex situ, each of them showed its own advantages and disadvantages. The in vivo approach estimates the properties of the tissue in its physiological state while the ex situ approach allows to apply different loadings to properly capture the anisotropy of the tissue. Both of them could be further enhanced by improving the estimation of the stress-free state, i.e. by adding residual circumferential stresses in vivo and by accounting for the flattening effect of the tested samples ex vivo. • Competing interests: none declared • Word count: 4716.

How important is sample alignment in planar biaxial testing of anisotropic soft biological tissues? A finite element study

Finite element models of biomedical applications increasingly use anisotropic hyperelastic material formulations. Appropriate material parameters are essential for a reliable outcome of these simulations, which is why planar biaxial testing of soft biological tissues is gaining importance. However, much is still to be learned regarding the ideal methodology for performing this type of test and the subsequent parameter fitting procedure. This paper focuses on the effect of an unknown sample orientation or a mistake in the sample orientation in a planar biaxial test using rakes. To this end, finite element simulations were conducted with various degrees of misalignment. Variations to the test method and subsequent fitting procedures are compared and evaluated. For a perfectly aligned sample and for a slightly misaligned sample, the parameters of the Gasser-Ogden-Holzapfel model can be found to a reasonable accuracy using a planar biaxial test with rakes and 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. For a sample with unknown sample orientation, material parameters could theoretically be obtained by increasing the degrees of freedom along which test data is obtained, e.g. by adding the data of a rail shear test. However, in the situation and the material model studied here, the inhomogeneous boundary conditions of the test set-ups render it impossible to obtain the correct parameters, even when using the parameter fitting method that takes into account boundary conditions. To conclude, it is always important to carefully track the sample orientation during harvesting and preparation and to minimize the misalignment during mounting. For transversely isotropic samples with an unknown orientation, we advise against parameter fitting based on a planar biaxial test, even when combined with a rail shear test.