Multiscale model of fatigue of collagen gels

The non-affine fiber network solver: A multiscale fiber network material model for finite-element analysis

Multiscale mechanical models in biomaterials research have largely relied on simplifying the microstructure in order to make large-scale simulations tractable. The microscale simplifications often rely on approximations of the constituent distributions and assumptions on the deformation of the constituents. Of particular interest in biomechanics are fiber embedded materials, where simplified fiber distributions and assumed affinity in the fiber deformation greatly influence the mechanical behavior. The consequences of these assumptions are problematic when dealing with microscale mechanical phenomena such as cellular mechanotransduction in growth and remodeling, and fiber-level failure events during tissue failure. In this work, we propose a technique for coupling non-affine network models to finite element solvers, allowing for simulation of discrete microstructural phenomena within macroscopically complex geometries. The developed plugin is readily available as an open-source library for use with the bio-focused finite element software FEBio, and the description of the implementation allows for the adaptation to other finite element solvers.

Hybrid Discrete-Continuum Multiscale Model of Tissue Growth and Remodeling

Tissue growth and remodeling (G&R) is often central to disease etiology and progression, so understanding G&R is essential for understanding disease and developing effective therapies. While the state-of-the-art in this regard is animal and cellular models, recent advances in computational tools offer another avenue to investigate G&R. A major challenge for computational models is bridging from the cellular scale (at which changes are actually occurring) to the macroscopic, geometric-scale (at which physiological consequences arise). Thus, many computational models simplify one scale or another in the name of computational tractability. In this work, we develop a discrete-continuum modeling scheme for analyzing G&R, in which we apply changes directly to the discrete cell and extracellular matrix (ECM) architecture and pass those changes up to a finite-element macroscale geometry. We demonstrate the use of the model in three case-study scenarios: the media of a thick-walled artery, and the media and adventitia of a thick-walled artery, and chronic dissection of an arterial wall. We analyze each case in terms of the new and insightful data that can be gathered from this technique, and we compare our results from this model to several others. STATEMENT OF SIGNIFICANCE: This work is significant in that it provides a framework for combining discrete, microstructural- and cellular-scale models to the growth and remodeling of large tissue structures (such as the aorta). It is a significant advance in that it couples the microscopic remodeling with an existing macroscopic finite element model, making it relatively easy to use for a wide range of conceptual models. It has the potential to improve understanding of many growth and remodeling processes, such as organ formation during development and aneurysm formation, growth, and rupture.

A Hybrid Microstructural-Continuum Multiscale Approach for Modeling Hyperelastic Fibrous Soft Tissue

The heterogeneous, nonlinear, anisotropic material behavior of biological tissues makes precise definition of an accurate constitutive model difficult. One possible solution to this issue would be to define microstructural elements and perform fully coupled multiscale simulation. However, for complex geometries and loading scenarios, the computational costs of such simulations can be prohibitive. Ideally then, we should seek a method that contains microstructural detail, but leverages the speed of classical continuum-based finite-element (FE) modeling. In this work, we demonstrate the use of the Holzapfel-Gasser-Ogden (HGO) model [1, 2] to fit the behavior of microstructural network models. We show that Delaunay microstructural networks can be fit to the HGO strain energy function by calculating fiber network strain energy and average fiber stretch ratio. We then use the HGO constitutive model in a FE framework to improve the speed of our hybrid model, and demonstrate that this method, combined with a material property update scheme, can match a full multiscale simulation. This method gives us flexibility in defining complex FE simulations that would be impossible, or at least prohibitively time consuming, in multiscale simulation, while still accounting for microstructural heterogeneity.

Biomechanics of infarcted left ventricle: a review of modelling

Mathematical modelling in biomechanics of infarcted left ventricle (LV) serves as an indispensable tool for remodelling mechanism exploration, LV biomechanical property estimation and therapy assessment after myocardial infarction (MI). However, a review of mathematical modelling after MI has not been seen in the literature so far. In the paper, a systematic review of mathematical models in biomechanics of infarcted LV was established. The models include comprehensive cardiovascular system model, essential LV pressure-volume and stress-stretch models, constitutive laws for passive myocardium and scars, tension models for active myocardium, collagen fibre orientation optimization models, fibroblast and collagen fibre growth/degradation models and integrated growth-electro-mechanical model after MI. The primary idea, unique characteristics and key equations of each model were identified and extracted. Discussions on the models were provided and followed research issues on them were addressed. Considerable improvements in the cardiovascular system model, LV aneurysm model, coupled agent-based models and integrated electro-mechanical-growth LV model are encouraged. Substantial attention should be paid to new constitutive laws with respect to stress-stretch curve and strain energy function for infarcted passive myocardium, collagen fibre orientation optimization in scar, cardiac rupture and tissue damage and viscoelastic effect post-MI in the future.

Connectivity and plasticity determine collagen network fracture

Collagen forms the structural scaffold of connective tissues in all mammals. Tissues are remarkably resistant against mechanical deformations because collagen molecules hierarchically self-assemble in fibrous networks that stiffen with increasing strain. Nevertheless, collagen networks do fracture when tissues are overloaded or subject to pathological conditions such as aneurysms. Prior studies of the role of collagen in tissue fracture have mainly focused on tendons, which contain highly aligned bundles of collagen. By contrast, little is known about fracture of the orientationally more disordered collagen networks present in many other tissues such as skin and cartilage. Here, we combine shear rheology of reconstituted collagen networks with computer simulations to investigate the primary determinants of fracture in disordered collagen networks. We show that the fracture strain is controlled by the coordination number of the network junctions, with less connected networks fracturing at larger strains. The hierarchical structure of collagen fine-tunes the fracture strain by providing structural plasticity at the network and fiber level. Our findings imply that low connectivity and plasticity provide protective mechanisms against network fracture that can optimize the strength of biological tissues.

In silico study of cuspid' periodontal ligament damage under parafunctional and traumatic conditions of whole-mouth occlusions. A patient-specific evaluation

BACKGROUND AND OBJECTIVE

Although traumatic loading has been associated with periodontal ligament (PDL) damage and therefore with several oral disorders, the damage phenomena and the traumatic loads involved are still unclear. The complex composition and extremely thin size of the PDL make experimentation difficult, requiring computational studies that consider the macroscopic loading conditions, the microscopic composition and fine detailed geometry of the tissue. In this study, a new methodology to analyse the damage phenomena in the collagen network and the extracellular matrix of the PDL caused by parafunctional and traumatic occlusal forces was proposed.

METHODS

The entire human mandible and a portion thereof containing a full cuspid tooth were separately modelled using finite element analysis based on computed tomography and micro-computed tomography images, respectively. The first model was experimentally validated by occlusion analysis and subjected to the muscle loads produced during hard and soft chewing, traumatic cuspid occlusion, grinding, clenching, and simultaneous grinding and clenching. The occlusal forces computed by the first model were subsequently applied to the single tooth model to evaluate damage to the collagen network and the extracellular matrix of the PDL.

RESULTS

Early occlusal contact on the left cuspid tooth guided the mandible to the more occluded side (16.5% greater in the right side) and absorbed most of the lateral load. The intrusive occlusal loads on the posterior teeth were 0.77-13.3% greater than those on the cuspid. According to our findings, damage to the collagen network and the extracellular matrix of the PDL could occur in traumatic and grinding conditions, mainly due to fibre overstretching (>60%) and interstitial fluid overpressure (>4.7 kPa), respectively.

CONCLUSIONS

Our findings provide important biomechanical insights into the determination of damage mechanisms which are caused by mechanical loading and the key role of the porous-fibrous behaviour of the PDL in parafunctional and traumatic loading scenarios. Besides, the 3D loading conditions computed from occlusal contacts will help future studies in the design of new orthodontics appliances and encourage the application of computing methods in medical practice.

Effects of Collagen Heterogeneity on Myocardial Infarct Mechanics in a Multiscale Fiber Network Model

The scar that forms after a myocardial infarction is often characterized by a highly disordered architecture but generally exhibits some degree of collagen fiber orientation, with a resulting mechanical anisotropy. When viewed in finer detail, however, the heterogeneity of the sample is clear, with different subregions exhibiting different fiber orientations. In this work, we used a multiscale finite element model to explore the consequences of the heterogeneity in terms of mechanical behavior. To do so, we used previously obtained fiber alignment maps of rat myocardial scar slices (n = 15) to generate scar-specific finite element meshes that were populated with fiber models based on the local alignment state. These models were then compared to isotropic models with the same sample shape and fiber density, and to homogeneous models with the same sample shape, fiber density, and average fiber alignment as the scar-specific models. All simulations involved equibiaxial extension of the sample with free motion in the third dimension. We found that heterogeneity led to a lower degree of mechanical anisotropy and a higher level of local stress concentration than the corresponding homogeneous model, and also that fibers failed in the heterogeneous model at much lower macroscopic strains than in the isotropic and homogeneous models. Taken together, these results suggest that scar heterogeneity may impair myocardial mechanical function both in terms of anisotropy and strength, and that individual variations in scar heterogeneity could be an important consideration for understanding scar remodeling and designing therapeutic interventions for patients after myocardial infarction.