Modeling lamellar disruption within the aortic wall using a particle-based approach.

Aortic dissections associate with medial degeneration, thus suggesting a need to understand better the biophysical interactions between the cells and matrix that constitute the middle layer of the aortic wall. Here, we use a recently extended "Smoothed Particle Hydrodynamics" formulation to examine potential mechanisms of aortic delamination arising from smooth muscle cell (SMC) dysfunction or apoptosis, degradation of or damage to elastic fibers, and pooling of glycosaminoglycans (GAGs), with associated losses of medial collagen in the region of the GAGs. First, we develop a baseline multi-layered model for the healthy aorta that delineates medial elastic lamellae and intra-lamellar constituents. Next, we examine stress fields resulting from the disruption of individual elastic lamellae, lost SMC contractility, and GAG production within an intra-lamellar space, focusing on the radial transferal of loading rather than on stresses at the tip of the delaminated tissue. Results suggest that local disruptions of elastic lamellae transfer excessive loads to nearby intra-lamellar constituents, which increases cellular vulnerability to dysfunction or death. Similarly, lost SMC function and accumulations of GAGs increase mechanical stress on nearby elastic lamellae, thereby increasing the chance of disruption. Overall these results suggest a positive feedback loop between lamellar disruption and cellular dropout with GAG production and lost medial collagen that is more pronounced at higher distending pressures. Independent of the initiating event, this feedback loop can catastrophically propagate intramural delamination.

A computational model to predict cell traction-mediated prestretch in the mitral valve.

Prestretch is observed in many soft biological tissues, directly influencing the mechanical behavior of the tissue in question. The development of this prestretch occurs through complex growth and remodeling phenomena, which yet remain to be elucidated. In the present study it was investigated whether local cell-mediated traction forces can explain the development of global anisotropic tissue prestretch in the mitral valve. Towards this end, a model predicting actin stress fiber-generated traction forces was implemented in a finite element framework of the mitral valve. The overall predicted magnitude of prestretch induced valvular contraction after release of in vivo boundary constraints was in good agreement with data reported on valvular retraction after excision from the heart. Next, by using a systematic variation of model parameters and structural properties, a more anisotropic prestretch development in the valve could be obtained, which was also similar to physiological values. In conclusion, this study shows that cell-generated traction forces could explain prestretch magnitude and anisotropy in the mitral valve.

Tricuspid valve leaflet strains in the beating ovine heart.

The tricuspid leaflets coapt during systole to facilitate proper valve function and, thus, ensure efficient transport of deoxygenated blood to the lungs. Between their open state and closed state, the leaflets undergo large deformations. Quantification of these deformations is important for our basic scientific understanding of tricuspid valve function and for diagnostic or prognostic purposes. To date, tricuspid valve leaflet strains have never been directly quantified in vivo. To fill this gap in our knowledge, we implanted four sonomicrometry crystals per tricuspid leaflet and six crystals along the tricuspid annulus in a total of five sheep. In the beating ovine hearts, we recorded crystal coordinates alongside hemodynamic data. Once recorded, we used a finite strain kinematic framework to compute the temporal evolutions of area strain, radial strain, and circumferential strain for each leaflet. We found that leaflet strains were larger in the anterior leaflet than the posterior and septal leaflets. Additionally, we found that radial strains were larger than circumferential strains. Area strains were as large as 97% in the anterior leaflet, 31% in the posterior leaflet, and 31% in the septal leaflet. These data suggest that tricuspid valve leaflet strains are significantly larger than those in the mitral valve. Should our findings be confirmed they could suggest either that the mechanobiological equilibrium of tricuspid valve resident cells is different than that of mitral valve resident cells or that the mechanotransductive apparatus between the two varies. Either phenomenon may have important implications for the development of tricuspid valve-specific surgical techniques and medical devices.

Particle-based computational modelling of arterial disease.

Accumulated glycosaminoglycans (GAGs) can sequester water and induce swelling within the intra-lamellar spaces of the medial layer of an artery. It is increasingly believed that stress concentrations caused by focal swelling can trigger the damage and delamination that is often seen in thoracic aortic disease. Here, we present computational simulations using an extended smoothed particle hydrodynamics approach to examine potential roles of pooled GAGs in initiating and propagating intra-lamellar delaminations. Using baseline models of the murine descending thoracic aorta, we first calculate stress distributions in a healthy vessel. Next, we examine increases in mechanical stress in regions surrounding GAG pools. The simulations show that smooth muscle activation can partially protect the wall from swelling-associated damage, consistent with experimental observations, but the wall can yet delaminate particularly in cases of smooth muscle dysfunction or absence. Moreover, pools of GAGs located at different but nearby locations can extend and coalesce, thus propagating a delamination. These findings, combined with a sensitivity study on the input parameters of the model, suggest that localized swelling can alter aortic mechanics in ways that eventually can cause catastrophic damage within the wall. There is, therefore, an increased need to consider roles of GAGs in aortic pathology.

Modeling Soft Tissue Damage and Failure Using a Combined Particle/Continuum Approach.

Biological soft tissues experience damage and failure as a result of injury, disease, or simply age; examples include torn ligaments and arterial dissections. Given the complexity of tissue geometry and material behavior, computational models are often essential for studying both damage and failure. Yet, because of the need to account for discontinuous phenomena such as crazing, tearing, and rupturing, continuum methods are limited. Therefore, we model soft tissue damage and failure using a particle/continuum approach. Specifically, we combine continuum damage theory with Smoothed Particle Hydrodynamics (SPH). Because SPH is a meshless particle method, and particle connectivity is determined solely through a neighbor list, discontinuities can be readily modeled by modifying this list. We show, for the first time, that an anisotropic hyperelastic constitutive model commonly employed for modeling soft tissue can be conveniently implemented within a SPH framework and that SPH results show excellent agreement with analytical solutions for uniaxial and biaxial extension as well as finite element solutions for clamped uniaxial extension in 2D and 3D. We further develop a simple algorithm that automatically detects damaged particles and disconnects the spatial domain along rupture lines in 2D and rupture surfaces in 3D. We demonstrate the utility of this approach by simulating damage and failure under clamped uniaxial extension and in a peeling experiment of virtual soft tissue samples. In conclusion, SPH in combination with continuum damage theory may provide an accurate and efficient framework for modeling damage and failure in soft tissues.

Histological and biomechanical changes in a mouse model of venous thrombus remodeling.

BACKGROUND: Deep vein thrombosis and the risk of pulmonary embolism are significant causes of morbidity and mortality. Much remains unclear, however, about the mechanisms by which a venous thrombus initiates, progresses, or resolves. In particular, there is a pressing need to characterize the evolving mechanical properties of a venous thrombus for its mechanical integrity is fundamental to many disease sequelae. OBJECTIVE: The primary goal of the present study was to initiate a correlation between evolving histological changes and biomechanical properties of venous thrombus. METHODS: We employed an inferior vena cava ligation model in mice to obtain cylindrical samples of thrombus that were well suited for mechanical testing and that could be explanted at multiple times following surgery. Using uniaxial micro-mechanical testing, we collected stress-stretch data that were then fit with a microstructurally-inspired material model before submitting the samples to immunohistological examination. RESULTS: We found that venous thrombus underwent a radially inward directed replacement of fibrin with collagen between 2 weeks and 4 weeks of development, which was accompanied by the infiltration of inflammatory and mesenchymal cells. These histological changes correlated with a marked increase in material stiffness. CONCLUSIONS: We demonstrated that 2 to 4 week old venous thrombus undergoes drastic remodeling from a fibrin-dominated mesh to a collagen-dominated microstructure and that these changes are accompanied by dramatic changes in biomechanical behavior.

Heterogeneous growth-induced prestrain in the heart.

Even when entirely unloaded, biological structures are not stress-free, as shown by Y.C. Fung׳s seminal opening angle experiment on arteries and the left ventricle. As a result of this prestrain, subject-specific geometries extracted from medical imaging do not represent an unloaded reference configuration necessary for mechanical analysis, even if the structure is externally unloaded. Here we propose a new computational method to create physiological residual stress fields in subject-specific left ventricular geometries using the continuum theory of fictitious configurations combined with a fixed-point iteration. We also reproduced the opening angle experiment on four swine models, to characterize the range of normal opening angle values. The proposed method generates residual stress fields which can reliably reproduce the range of opening angles between 8.7±1.8 and 16.6±13.7 as measured experimentally. We demonstrate that including the effects of prestrain reduces the left ventricular stiffness by up to 40%, thus facilitating the ventricular filling, which has a significant impact on cardiac function. This method can improve the fidelity of subject-specific models to improve our understanding of cardiac diseases and to optimize treatment options.

Computational modeling of growth: systemic and pulmonary hypertension in the heart.

We introduce a novel constitutive model for growing soft biological tissue and study its performance in two characteristic cases of mechanically induced wall thickening of the heart. We adopt the concept of an incompatible growth configuration introducing the multiplicative decomposition of the deformation gradient into an elastic and a growth part. The key feature of the model is the definition of the evolution equation for the growth tensor which we motivate by pressure-overload-induced sarcomerogenesis. In response to the deposition of sarcomere units on the molecular level, the individual heart muscle cells increase in diameter, and the wall of the heart becomes progressively thicker. We present the underlying constitutive equations and their algorithmic implementation within an implicit nonlinear finite element framework. To demonstrate the features of the proposed approach, we study two classical growth phenomena in the heart: left and right ventricular wall thickening in response to systemic and pulmonary hypertension.