Calibration of Holzapfel-Gasser-Ogden collateral ligament properties in a hybrid post-arthroplasty knee joint model for laxity testing.

Knee collateral ligaments play a vital role in providing frontal-plane stability in post-total knee arthroplasty (TKA) knees. Finite element models can utilize computationally efficient one-dimensional springs or more physiologically accurate three-dimensional continuum elements like the Holzapfel-Gasser-Ogden (HGO) formulation. However, there is limited literature defining subject-specific mechanical properties, particularly for the HGO model. In this study, we propose a co-simulation framework to obtain subject-specific material parameters for an HGO-based finite element ligament model integrated into a rigid-body model of the post-TKA knee. Our approach achieves comparable accuracy to spring formulations while significantly reducing coefficient calibration time and demonstrating improved correlation with reference knee kinematics and ligament strains throughout the tested loading range.

Stiffness matters: Improved failure risk assessment of ascending thoracic aortic aneurysms.

Objectives: Rupture and dissection are feared complications of ascending thoracic aortic aneurysms caused by mechanical failure of the wall. The current method of using the aortic diameter to predict the risk of wall failure and to determine the need for surgical resection lacks accuracy. Therefore, this study aims to identify reliable and clinically measurable predictors for aneurysm rupture or dissection by performing a personalized failure risk analysis, including clinical, geometrical, histologic, and mechanical data. Methods: The study cohort consisted of 33 patients diagnosed with ascending aortic aneurysms without genetic syndromes. Uniaxial tensile tests until failure were performed to determine the wall strength. Material parameters were fitted against ex vivo planar biaxial data and in vivo pressure-diameter relationships at diastole and systole, which were derived from multiphasic computed tomography (CT) scans. Using the resulting material properties and in vivo data, the maximal in vivo stress at systole was calculated, assuming a thin-walled axisymmetric geometry. The retrospective failure risk was calculated by comparing the peak wall stress at suprasystolic pressure with the wall strength. Results: The distensibility coefficient, reflecting aortic compliance and derived from blood pressure measurements and multiphasic CT scans, outperformed predictors solely based on geometrical features in assessing the risk of aneurysm failure. Conclusions: In a clinical setting, multiphasic CT scans followed by the calculation of the distensibility coefficient are of added benefit in patient-specific, clinical decision-making. The distensibility derived from the aneurysm volume change has the best predictive power, as it also takes the axial stretch into account.

An improved parameter fitting approach of a planar biaxial test including the experimental prestretch.

Planar biaxial testing is a popular experimental technique for characterizing and comparing biological soft tissues. A correct identification of the different stress states of the tissue sample is therefore essential. However, the difference between the zero-stress reference state and the sample state prior to the loading cycle caused by the mounting, preconditioning and preloading is often not considered. The importance of this difference, caused by prestretch, is investigated by simulating virtual planar biaxial experiments, either assuming an ideal test with a single deformation gradient or using finite element modeling to simulate a rake-based experiment. Multiple parameter fitting methods are used to estimate the material properties based on the available experimental data. These methods vary based on how they approximate the zero-stress state: either the prestretch is ignored, or the loads are zeroed after the preload has been reached, or the unknown prestretch values are included into the optimization function. The results reveal the high necessity of assessing the stress-free state when analyzing a planar biaxial test. The material fitting including the prestretch outperforms the other methods in terms of correctly describing the mechanical behavior of the tested material. It can be extended to correct for the boundary effects induced by the gripping mechanisms, providing a more accurate, yet more computationally expensive estimate of the material properties.

Alterations in Human Mitral Valve Mechanical Properties Secondary to Left Ventricular Remodeling: A Biaxial Mechanical Study.

Secondary mitral regurgitation occurs when a left ventricular problem causes leaking of the mitral valve. The altered left ventricular geometry changes the orientation of the subvalvular apparatus, thereby affecting the mechanical stress on the mitral valve. This in turn leads to active remodeling of the mitral valve, in order to compensate for the ventricular remodeling. In this study, a biomechanical analysis was performed on eight human mitral valves with secondary mitral regurgitation and ten healthy human mitral valves to better understand this pathophysiology and its effect on the mechanical properties of these tissues. Samples were obtained from the anterior and posterior leaflet and used for planar biaxial mechanical experiments. Uniaxial experiments were performed on four groups of mitral valve chords: anterior basal, anterior marginal, posterior basal and posterior marginal chords. The mechanical response of the mitral valve leaflets was fitted to the May-Newman and Yin constitutive model, whereas the material parameters of the third order Ogden model were determined for the chord samples. Next, stiffnesses calculated at low and high stress levels were statistically analyzed. Leaflet samples with secondary mitral regurgitation showed a small thickness increase and a change in anisotropy index compared to healthy control valves. Diseased leaflets were more compliant circumferentially and stiffer radially, resulting in anisotropic samples with the radial direction being stiffest. In addition, chord samples were slightly thicker and less stiff at high stress in secondary mitral regurgitation, when grouped per leaflet type and insertion region. These results confirm mechanical alterations due to the pathophysiological valvular changes caused by left ventricular remodeling. It is important that these changes in mechanical behavior are incorporated into computational models of the mitral valve.

Mechanical properties and cellular content of leukocyte- and platelet-rich fibrin membranes of patients on antithrombotic drugs.

INTRODUCTION: The aim of this study was to examine the potential influence of antithrombotics on leukocyte- and platelet-rich fibrin (L-PRF) membranes. METHODS: Tensile tests and cell counts were performed with L-PRF membranes originating from patients on anticoagulants and antiplatelets versus patients not taking antithrombotics. RESULTS: For the tensile tests, 13 control patients, 12 on anticoagulants, and 10 on antiplatelets donated blood. Compared to controls, membranes from anticoagulated donors were weaker (strength 0.57 ± 0.24 MPa vs. 0.80 ± 0.27 MPa, p = .03) and could not be stretched as far (1.8 ± 0.3 vs. 2.1 ± 0.3 times the initial length, p = .01). For the cell counting, 23 control patients, 16 on anticoagulants, and 16 on antiplatelets donated blood. The percentage of platelets was ±50% in the three groups. The percentage of leukocytes was lower in the anticoagulant group compared with controls (69 ± 10% vs. 78 ± 8%, p = .04). However, because of the unknown error of method, it is questionable whether the statistical significance is meaningful. There was no difference between membranes from the control group and the group on antiplatelets. CONCLUSION: Our results indicate that L-PRF membranes originating from patients on anticoagulants are weaker, stretch less far, and contain less leukocytes than L-PRF membranes of patients not taking these drugs.

How to implement user-defined fiber-reinforced hyperelastic materials in finite element software.

Finite element modeling is often used in biomechanical engineering to evaluate medical devices, treatments and diagnostic tools. Using an adequate material model that describes the mechanical behavior of biological tissues is essential for a reliable outcome of the simulation. Pre-programmed material models for biological tissues are available in many finite element software packages. However, since these pre-programmed models are presented to the user as a black box, without the possibility to modify the material description, many researchers turn to implementing their own material formulations. This is a complex undertaking, requiring extensive knowledge while documentation is limited. This paper provides a detailed description, at the level of the biomedical engineer, of the implementation of a nonlinear hyperelastic material model using user subroutines in Abaqus®, in casuUANISOHYPER_INV and UMAT. The Gasser-Ogden-Holzapfel material model is used as an example, resulting in four implementation variations: the built-in implementation, a UANISOHYPER_INV formulation, a UMAT with analytical tangent stiffness formulation and a UMAT with numerical tangent stiffness formulation. In addition, three different element formulations are used: a continuum compressible, a continuum incompressible and a plane stress incompressible. All cases are thoroughly verified by applying a series of deformations on a single cube element and by simulating an extension-inflation experiment with non-homogeneous deformations and multiple elements. In these test cases, stresses, displacements, reaction forces, the required number of iterations and the total CPU time were compared. The results show that the four implementation variations are very similar, with total relative errors between 10-3 and 10-15, number of iterations that varied by maximum one iteration, and a comparable CPU time. In addition to this detailed overview, the user subroutines are added as supplementary material to this tutorial, which can be used as the ideal starting point for biomechanical engineers to implement their own material models at different levels of complexity.

Mechano-biological adaptation of the pulmonary artery exposed to systemic conditions.

Cardiac surgeries may expose pulmonary arterial tissue to systemic conditions, potentially resulting in failure of that tissue. Our goal was to quantitatively assess pulmonary artery adaptation due to changes in mechanical environment. In 17 sheep, we placed a pulmonary autograft in aortic position, with or without macroporous mesh reinforcement. It was exposed to systemic conditions for 6 months. All sheep underwent 3 ECG-gated MRI's. Explanted tissue was subjected to mechanical and histological analysis. Results showed progressive dilatation of the unreinforced autograft, while reinforced autografts stabilized after two months. Some unreinforced pulmonary autograft samples displayed more aorta-like mechanical behavior with increased collagen deposition. The mechanical behavior of reinforced autografts was dominated by the mesh. The decrease in media thickness and loss of vascular smooth muscle cells was more pronounced in reinforced than in unreinforced autografts. In conclusion, altering the mechanical environment of a pulmonary artery causes changes in its mechano-biological properties.

Constrained mixture modeling affects material parameter identification from planar biaxial tests.

The constrained mixture theory is an elegant way to incorporate the phenomenon of residual stresses in patient-specific finite element models of arteries. This theory assumes an in vivo reference geometry, obtained from medical imaging, and constituent-specific deposition stretches in the assumed reference state. It allows to model residual stresses and prestretches in arteries without the need for a stress-free reference configuration, most often unknown in patient-specific modeling. A finite element (FE) model requires material parameters, which are classically obtained by fitting the constitutive model to experimental data. The characterization of arterial tissue is often based on planar biaxial test data, to which nonlinear elastic fiber-reinforced material parameters are fitted. However, the introduction of the constrained mixture theory requires an adapted approach to parameter fitting. Therefore, we introduce an iterative fitting method, alternating between nonlinear least squares parameter optimization and an FE prestressing algorithm to obtain the correct constrained mixture material state during the mechanical test. We verify the method based on numerically constructed planar biaxial test data sets, containing ground truth sets of material parameters. The results show that the method converges to the correct parameter sets in just a few iterations. Next, the iterative fitting approach is applied to planar biaxial test data of ovine pulmonary artery tissue. The obtained results demonstrate a convergence towards constrained mixture compatible parameters, which differ significantly from classically obtained parameters. We show that this new modeling approach yields in vivo wall stresses similar to when using classically obtained parameters. However, due to the numerous advantages of constrained mixture modeling, our fitting method is relevant to obtain compatible material parameters, that may not be confused with parameters obtained in a classical way.

Development of an improved parameter fitting method for planar biaxial testing using rakes.

A correct estimation of the material parameters from a planar biaxial test is crucial since they will affect the outcome of the finite element model in which they are used. In a virtual planar biaxial experiment, a difference can be noticed in the stress calculated from the force measured experimentally at the rakes and the actual stress at the center of the sample. As a consequence, a classic parameter fitting does not result in a correct estimation of the material parameters. This difference is caused by the boundary conditions of the set-up and is among others dependent on the sample material. To overcome this problem, a new parameter fitting procedure is proposed that takes this difference into account by calculating a finite element-based correction vector. This paper describes the methodology to apply this new parameter fitting procedure on real experimental data from a planar biaxial test using rakes. To this end, image processing is used to extract the experiment characteristics. This information is used to construct a finite element model. Two variations of the new parameter fitting procedure are investigated using two human aortic samples: a basic approach and an image-based approach. The performance of the method is assessed by the difference between the force measured at the rakes during the experiment and the force at the rakes obtained from the finite element simulation. Both approaches of the new parameter fitting procedure lead to an improved estimation of the sample behavior compared with the classic approach.

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.

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.

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.

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 patient's 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 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.

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.