Layer-specific fiber distribution in arterial tissue modeled as a constrained mixture.

Collagen fibers and their orientation greatly influence an artery's mechanical characteristics, determining its transversely isotropic behavior. It is generally assumed that these fibers are deposited along a preferred direction to maximize the load bearing capacity of the vessel wall. This implies a large spatial variation in collagen orientation which can be reconstructed in numerical models using so-called reorientation algorithms. Until now, these algorithms have used the classical continuum mechanics modeling framework which requires knowledge of tissue-level parameters and the artery's stress-free reference state, which is inaccessible in a clinical context. We present an algorithm to compute the preferred fiber distribution compatible with the constrained mixture theory, which orients two collagen fiber families according to the loading experienced by the isotropic non-collagenous extracellular matrix, without requiring prior knowledge of the stress-free state. Because consensus is lacking whether stress or stretch is the determining factor behind the preferred fiber distribution, we implemented both approaches and compared the results with experimental microstructural data of an abdominal aorta. The stress-based algorithm was able to describe several experimentally observed transitions of the fiber distribution across the intima, media and adventitia.

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.

Growth and remodeling in the pulmonary autograft: Computational evaluation using kinematic growth models and constrained mixture theory.

Computational investigations of how soft tissues grow and remodel are gaining more and more interest and several growth and remodeling theories have been developed. Roughly, two main groups of theories for soft tissues can be distinguished: kinematic-based growth theory and theories based on constrained mixture theory. Our goal was to apply these two theories on the same experimental data. Within the experiment, a pulmonary artery was exposed to systemic conditions. The change in diameter was followed-up over time. A mechanical and microstructural analysis of native pulmonary artery and pulmonary autograft was conducted. Whereas the kinematic-based growth theory is able to accurately capture the growth of the tissue, it does not account for the mechanobiological processes causing this growth. The constrained mixture theory takes into account the mechanobiological processes including removal, deposition and adaptation of all structural constituents, allowing us to simulate a changing microstructure and mechanical behavior.

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.

A Chemomechanobiological Model of the Long-Term Healing Response of Arterial Tissue to a Clamping Injury.

Vascular clamping often causes injury to arterial tissue, leading to a cascade of cellular and extracellular events. A reliable in silico prediction of these processes following vascular injury could help us to increase our understanding thereof, and eventually optimize surgical techniques or drug delivery to minimize the amount of long-term damage. However, the complexity and interdependency of these events make translation into constitutive laws and their numerical implementation particularly challenging. We introduce a finite element simulation of arterial clamping taking into account acute endothelial denudation, damage to extracellular matrix, and smooth muscle cell loss. The model captures how this causes tissue inflammation and deviation from mechanical homeostasis, both triggering vascular remodeling. A number of cellular processes are modeled, aiming at restoring this homeostasis, i.e., smooth muscle cell phenotype switching, proliferation, migration, and the production of extracellular matrix. We calibrated these damage and remodeling laws by comparing our numerical results to in vivo experimental data of clamping and healing experiments. In these same experiments, the functional integrity of the tissue was assessed through myograph tests, which were also reproduced in the present study through a novel model for vasodilator and -constrictor dependent smooth muscle contraction. The simulation results show a good agreement with the in vivo experiments. The computational model was then also used to simulate healing beyond the duration of the experiments in order to exploit the benefits of computational model predictions. These results showed a significant sensitivity to model parameters related to smooth muscle cell phenotypes, highlighting the pressing need to further elucidate the biological processes of smooth muscle cell phenotypic switching in the future.

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.

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.

Reinforcing the pulmonary artery autograft in the aortic position with a textile mesh: a histological evaluation.

OBJECTIVES: The Ross procedure involves replacing a patient's diseased aortic valve with their own pulmonary valve. The most common failure mode is dilatation of the autograft. Various strategies to reinforce the autograft have been proposed. Personalized external aortic root support has been shown to be effective in stabilizing the aortic root in Marfan patients. In this study, the use of a similar external mesh to support a pulmonary artery autograft was evaluated. METHODS: The pulmonary artery was translocated as an interposition autograft in the descending thoracic aortas of 10 sheep. The autograft was reinforced with a polyethylene terephthalate mesh (n = 7) or left unreinforced (n = 3). After 6 months, a computed tomography scan was taken, and the descending aorta was excised and histologically examined using the haematoxylin-eosin and Elastica van Gieson stains. RESULTS: The autograft/aortic diameter ratio was 1.59 in the unreinforced group but much less in the reinforced group (1.11) (P < 0.05). A fibrotic sheet, variable in thickness and containing fibroblasts, neovessels and foreign body giant cells, was incorporated in the mesh. Histological examination of the reinforced autograft and the adjacent aorta revealed thinning of the vessel wall due to atrophy of the smooth muscle cells. Potential spaces between the vessel wall and the mesh were filled with oedema. CONCLUSIONS: Reinforcing an interposition pulmonary autograft in the descending aorta with a macroporous mesh showed promising results in limiting autograft dilatation in this sheep model. Histological evaluation revealed atrophy of the smooth muscle cell and consequently thinning of the vessel wall within the mesh support.

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.