Computational modeling of the arterial wall based on layer-specific histological data

Evaluation of a multi-scale discrete fiber model for analyzing arterial failure

So far, the prevalent rupture risk quantification of aortic aneurysms does not consider information of the underlying microscopic mechanisms. Uniaxial tension tests were performed on imaged aorta samples oriented in circumferential and longitudinal directions. To account for local heterogeneity in collagen fiber architecture, SHG imaging was performed on tissues at several locations prior to mechanical testing. This enabled the quantification of micro-scale information including organization of collagen fibers using relevant probability density functions. Two different modeling approaches are presented in this study for the sake of comparison. A multi-scale mechanical model was developed using this micro-structural information with collagen fibers as main components. accounting for non-affine fiber kinematics. Simultaneously, an embedded element model that accounts for affine fiber kinematics was developed in Abaqus using the same micro-structural information. Numerical simulations emulating uniaxial tension experiments were performed on the developed models. Global mechanical response of both models agreed well with the experimental data, although leading to mismatched material properties. The models present a rudimentary yet better than before representation of structure based description of aortic-tissue failure mechanics. reinforcing the importance of structural organization of micro-scale constituents and their kinematics in determining tissue failure.

A computational framework for biomaterials containing three-dimensional random fiber networks based on the affine kinematics

Understanding the structure-function relationship of biomaterials can provide insights into different diseases and advance numerous biomedical applications. This paper presents a finite element-based computational framework to model biomaterials containing a three-dimensional fiber network at the microscopic scale. The fiber network is synthetically generated by a random walk algorithm, which uses several random variables to control the fiber network topology such as fiber orientations and tortuosity. The geometric information of the generated fiber network is stored in an array-like data structure and incorporated into the nonlinear finite element formulation. The proposed computational framework adopts the affine fiber kinematics, based on which the fiber deformation can be expressed by the nodal displacement and the finite element interpolation functions using the isoparametric relationship. A variational approach is developed to linearize the total strain energy function and derive the nodal force residual and the stiffness matrix required by the finite element procedure. Four numerical examples are provided to demonstrate the capabilities of the proposed computational framework, including a numerical investigation about the relationship between the proposed method and a class of anisotropic material models, a set of synthetic examples to explore the influence of fiber locations on material local and global responses, a thorough mesh-sensitivity analysis about the impact of mesh size on various numerical results, and a detailed case study about the influence of material structures on the performance of eggshell-membrane-hydrogel composites. The proposed computational framework provides an efficient approach to investigate the structure-function relationship for biomaterials that follow the affine fiber kinematics.

Geometrically nonlinear modelling of pre-stressed viscoelastic fibre-reinforced composites with application to arteries

Mechanical behaviour of pre-stressed fibre-reinforced composites is modelled in a geometrically exact setting. A general approach which includes two different reference configurations is employed: one configuration corresponds to the load-free state of the structure and another one to the stress-free state of each material particle. The applicability of the approach is demonstrated in terms of a viscoelastic material model; both the matrix and the fibre are modelled using a multiplicative split of the deformation gradient tensor; a transformation rule for initial conditions is elaborated and specified. Apart from its simplicity, an important advantage of the approach is that well-established numerical algorithms can be used for pre-stressed inelastic structures. The interrelation between the advocated approach and the widely used "opening angle" approach is clarified. A full-scale FEM simulation confirms the main predictions of the "opening angle" approach. A locking effect is discovered: in some cases the opening angle of the composite is essentially smaller than the opening angles of its individual layers. Thus, the standard cutting test typically used to analyse pre-stresses does not carry enough information and more refined experimental techniques are needed.

A computational model for understanding the micro-mechanics of collagen fiber network in the tunica adventitia

Abdominal aortic aneurysm is a prevalent cardiovascular disease with high mortality rates. The mechanical response of the arterial wall relies on the organizational and structural behavior of its microstructural components, and thus, a detailed understanding of the microscopic mechanical response of the arterial wall layers at loads ranging up to rupture is necessary to improve diagnostic techniques and possibly treatments. Following the common notion that adventitia is the ultimate barrier at loads close to rupture, in the present study, a finite element model of adventitial collagen network was developed to study the mechanical state at the fiber level under uniaxial loading. Image stacks of the rabbit carotid adventitial tissue at rest and under uniaxial tension obtained using multi-photon microscopy were used in this study, as well as the force-displacement curves obtained from previously published experiments. Morphological parameters like fiber orientation distribution, waviness, and volume fraction were extracted for one sample from the confocal image stacks. An inverse random sampling approach combined with a random walk algorithm was employed to reconstruct the collagen network for numerical simulation. The model was then verified using experimental stress-stretch curves. The model shows the remarkable capacity of collagen fibers to uncrimp and reorient in the loading direction. These results further show that at high stretches, collagen network behaves in a highly non-affine manner, which was quantified for each sample. A comprehensive parameter study to understand the relationship between structural parameters and their influence on mechanical behavior is presented. Through this study, the model was used to conclude important structure-function relationships that control the mechanical response. Our results also show that at loads close to rupture, the probability of failure occurring at the fiber level is up to 2%. Uncertainties in usually employed rupture risk indicators and the stochastic nature of the event of rupture combined with limited knowledge on the microscopic determinants motivate the development of such an analysis. Moreover, this study will advance the study of coupling microscopic mechanisms to rupture of the artery as a whole.

A deep learning approach to estimate chemically-treated collagenous tissue nonlinear anisotropic stress-strain responses from microscopy images

Biological collagenous tissues comprised of networks of collagen fibers are suitable for a broad spectrum of medical applications owing to their attractive mechanical properties. In this study, we developed a noninvasive approach to estimate collagenous tissue elastic properties directly from microscopy images using Machine Learning (ML) techniques. Glutaraldehyde-treated bovine pericardium (GLBP) tissue, widely used in the fabrication of bioprosthetic heart valves and vascular patches, was chosen to develop a representative application. A Deep Learning model was designed and trained to process second harmonic generation (SHG) images of collagen networks in GLBP tissue samples, and directly predict the tissue elastic mechanical properties. The trained model is capable of identifying the overall tissue stiffness with a classification accuracy of 84%, and predicting the nonlinear anisotropic stress-strain curves with average regression errors of 0.021 and 0.031. Thus, this study demonstrates the feasibility and great potential of using the Deep Learning approach for fast and noninvasive assessment of collagenous tissue elastic properties from microstructural images.

STATEMENT OF SIGNIFICANCE

In this study, we developed, to our best knowledge, the first Deep Learning-based approach to estimate the elastic properties of collagenous tissues directly from noninvasive second harmonic generation images. The success of this study holds promise for the use of Machine Learning techniques to noninvasively and efficiently estimate the mechanical properties of many structure-based biological materials, and it also enables many potential applications such as serving as a quality control tool to select tissue for the manufacturing of medical devices (e.g. bioprosthetic heart valves).