Hyperelastic modelling of arterial layers with distributed collagen fibre orientations

Synergistic Integration of Deep Neural Networks and Finite Element Method with Applications of Nonlinear Large Deformation Biomechanics

Patient-specific finite element analysis (FEA) holds great promise in advancing the prognosis of cardiovascular diseases by providing detailed biomechanical insights such as high-fidelity stress and deformation on a patient-specific basis. Albeit feasible, FEA that incorporates three-dimensional, complex patient-specific geometry can be time-consuming and unsuitable for time-sensitive clinical applications. To mitigate this challenge, machine learning (ML) models, e.g., deep neural networks (DNNs), have been increasingly utilized as potential alternatives to finite element method (FEM) for biomechanical analysis. So far, efforts have been made in two main directions: (1) learning the input-to-output mapping of traditional FEM solvers and replacing FEM with data-driven ML surrogate models; (2) solving equilibrium equations using physics-informed loss functions of neural networks. While these two existing strategies have shown improved performance in terms of speed or scalability, ML models have not yet provided practical advantages over traditional FEM due to generalization issues. This has led us to the question: instead of abandoning or replacing the traditional FEM framework that can reliably solve biomechanical problems, can we integrate FEM and DNNs to enhance performance? In this study, we propose a synergistic integration of DNNs and FEM to overcome their individual limitations. Using biomechanical analysis of the human aorta as the test bed, we demonstrated two novel integrative strategies in forward and inverse problems. For the forward problem, we developed DNNs with state-of-the-art architectures to predict a nodal displacement field, and this initial DNN solution was then updated by a FEM-based refinement process, yielding a fast and accurate computing framework. For the inverse problem of heterogeneous material parameter identification, our method employs DNN as a regularizer of the spatial distribution of material parameters, aiding the optimizer in locating the optimal solution. In our demonstrative examples, despite that the DNN-only forward models yielded small displacement errors in most test cases; stress errors were considerably large, and for some test cases, the peak stress errors were greater than 50%. Our DNN-FEM integration eliminated these non-negligible errors in DNN-only models and was magnitudes faster than the FEM-only approach. Additionally, compared to FEM-only inverse method with errors greater than 50%, our DNN-FEM inverse approach significantly improved the parameter identification accuracy and reduced the errors to less than 1%.

Patient-specific finite element analysis of human corneal lenticules: An experimental and numerical study

The number of elective refractive surgeries is constantly increasing due to the drastic increase in myopia prevalence. Since corneal biomechanics are critical to human vision, accurate modeling is essential to improve surgical planning and optimize the results of laser vision correction. In this study, we present a numerical model of the anterior cornea of young patients who are candidates for laser vision correction. Model parameters were determined from uniaxial tests performed on lenticules of patients undergoing refractive surgery by means of lenticule extraction, using patient-specific models of the lenticules. The models also took into account the known orientation of collagen fibers in the tissue, which have an isotropic distribution in the corneal plane, while they are aligned along the corneal curvature and have a low dispersion outside the corneal plane. The model was able to reproduce the experimental data well with only three parameters. These parameters, determined using a realistic fiber distribution, yielded lower values than those reported in the literature. Accurate characterization and modeling of the cornea of young patients is essential to study better refractive surgery for the population undergoing these treatments, to develop in silico models that take corneal biomechanics into account when planning refractive surgery, and to provide a basis for improving visual outcomes in the rapidly growing population undergoing these treatments.

Effect of Nonlinear Hyperelastic Property of Arterial Tissues on the Pulse Wave Velocity Based on the Unified-Fiber-Distribution (UFD) Model

Pulse wave velocity (PWV) is a key, independent risk factor for future cardiovascular events. The Moens-Korteweg equation describes the relation between PWV and the stiffness of arterial tissue with an assumption of isotopic linear elastic property of the arterial wall. However, the arterial tissue exhibits highly nonlinear and anisotropic mechanical behaviors. There is a limited study regarding the effect of arterial nonlinear and anisotropic properties on the PWV. In this study, we investigated the impact of the arterial nonlinear hyperelastic properties on the PWV, based on our recently developed unified-fiber-distribution (UFD) model. The UFD model considers the fibers (embedded in the matrix of the tissue) as a unified distribution, which expects to be more physically consistent with the real fiber distribution than existing models that separate the fiber distribution into two/several fiber families. With the UFD model, we fitted the measured relation between the PWV and blood pressure which obtained a good accuracy. We also modeled the aging effect on the PWV based on observations that the stiffening of arterial tissue increases with aging, and the results agree well with experimental data. In addition, we did parameter studies on the dependence of the PWV on the arterial properties of fiber initial stiffness, fiber distribution, and matrix stiffness. The results indicate the PWV increases with increasing overall fiber component in the circumferential direction. The dependences of the PWV on the fiber initial stiffness, and matrix stiffness are not monotonic and change with different blood pressure. The results of this study could provide new insights into arterial property changes and disease information from the clinical measured PWV data.

An investigation of how specimen dimensions affect biaxial mechanical characterizations with CellScale BioTester and constitutive modeling of porcine tricuspid valve leaflets

Biaxial mechanical characterizations are the accepted approach to determine the mechanical response of many biological soft tissues. Although several computational and experimental studies have examined how experimental factors (e.g., clamped vs. suture mounting) affect the acquired tissue mechanical behavior, little is known about the role of specimen dimensions in data acquisition and the subsequent modeling. In this study, we combined our established mechanical characterization framework with an iterative size-reduction protocol to test the hypothesis that specimen dimensions affect the observed mechanical behavior of biaxial characterizations. Our findings indicated that there were non-significant differences in the peak equibiaxial stretches of tricuspid valve leaflets across four specimen dimensions ranging from 4.5×4.5mm to 9 × 9mm. Further analyses revealed that there were significant differences in the low-tensile modulus of the circumferential tissue direction. These differences resulted in significantly different constitutive model parameters for the Tong-Fung model between different specimen dimensions of the posterior and septal leaflets. Overall, our findings demonstrate that specimen dimensions play an important role in experimental characterizations, but not necessarily in constitutive modeling of soft tissue mechanical behavior during biaxial testing with the commercial CellScale BioTester.

Fiber orientation and crimp level might control the auxetic effect of biological tissues

We propose an analytical micromechanical model for studying the lamellar-composite-like structure of fibrous soft tissue. The tissue under consideration is made up of several lamellae, and is designed to resemble the annulus fibrosus (AF) tissue or media layer of arterial tissue, for example. The collagen fibers are arranged in parallel in each lamella and the fiber orientation differs from one lamella to its neighbors. The parallel fibers in each lamella of AF tissue, for example, have been observed to have a crimped microstructure. The proposed model incorporates this quality, considering fiber waviness as a sinusoidal shape and taking into account the fiber dispersion in different layers, where both fiber and matrix are considered as solid phases. We find that collagen-fiber waviness and layer orientation have a significant influence on Poisson's ratio. The effective Poisson's ratio predicted by the proposed model demonstrates that the crimped collagen fiber microstructure might weaken the auxetic effect of fibrous soft tissue, which might explain why, as the literature suggests, the auxetic behavior is more difficult to observe than large Poisson's ratios. As opposed to the many studies that use the well-known hyperelastic fiber-based constitutive model, in which out-of-plane expansion is often observed, the present work explains the auxetic response found in modeling and in experimental data from the perspective of collagen fiber microstructure.

Numerical investigation of cavitation in periodontal Pockets: Insights for enhancing cleaning efficiency

Ultrasonic dental scalers are indispensable instruments for efficient dental cleaning through the generation of cavitation. To gain valuable insights and enhance the cavitation cleaning effects, a numerical investigation is conducted using the finite element method via ABAQUS. Numerical results are compared with the experimental cavitation image for a scaler undergoes vibrations near a wall. We then analyse how the amplitude, frequency, and cross-sectional shape of the scaler affect cavitation generation. Numerical results indicate that cavitation is more pronounced for a scaler oscillating near a nearly rigid boundary than a soft boundary. It increases with the vibration amplitude because of higher ultrasonic energy transferring to the liquid and generating stronger pressure waves. The resonant frequency of the scaler coincides with the maximum cavitation and scaler tip amplitude. Reducing the dimension of the cross-section of the scaler in its oscillation direction increases both the scaler tip amplitude and the cavitation generated. This finding offers a potential design approach for enhancing the scaler cavitation and its cleaning effects. These insights provide practical guidance for optimising dental scaler settings, which can improve oral hygiene and prevent complications related to dental implants.

Development of in silico models to guide the experimental characterisation of penile tissue and inform surgical treatment of erectile dysfunction

This paper presents a computational study to investigate the mechanical properties of human penile tissues. Different experimental testing regimes, namely indentation and plate-compression tests, are compared to establish the most suitable testing regime for establishing the mechanical properties of the different penile tissues. An idealised MRI-based geometry of the penis, containing different tissue layers, is simulated using the finite element (FE) method to enable realistic predictions of the deformation of the penis. Unlike the linear elastic models used in the literature to-date, hyperelastic isotropic/anisotropic material models are used to capture material nonlinearity and anisotropy. The influence of material properties, morphological variations, material nonlinearity and anisotropy are investigated. Moreover, the implantation of an inflatable penile prosthesis (IPP) is simulated to assess the effects of the implantation procedure, material nonlinearity, and anisotropy on tissue stresses. The results indicate that the interior layers of the penis do not affect the overall stiffness of the penis in the indentation test, while the plate-compression test is able to capture the effects of these layers. Tunica Albuginea (TA) is found to have the most significant contribution to the total stiffness of the penis under load. It can also be observed that buckling occurs in the septum of the penis during the compression tests, and different morphologies dictate different compressive behaviours. There is a clear need for future experimental studies on penile tissues given the lack of relevant test data in the literature. Based on this study, plate-compression testing would offer the most insightful experimental data for such tissue characterisation.

Constituent-based quasi-linear viscoelasticity: a revised quasi-linear modelling framework to capture nonlinear viscoelasticity in arteries

Arteries exhibit fully nonlinear viscoelastic behaviours (i.e. both elastically and viscously nonlinear). While elastically nonlinear arterial models are well established, effective mathematical descriptions of nonlinear viscoelasticity are lacking. Quasi-linear viscoelasticity (QLV) offers a convenient way to mathematically describe viscoelasticity, but its viscous linearity assumption is unsuitable for whole-wall vascular applications. Conversely, application of fully nonlinear viscoelastic models, involving deformation-dependent viscous parameters, to experimental data is impractical and often reduces to identifying specific solutions for each tested loading condition. The present study aims to address this limitation: By applying QLV theory at the wall constituent rather than at the whole-wall level, the deformation-dependent relative contribution of the constituents allows to capture nonlinear viscoelasticity with a unique set of deformation-independent model parameters. Five murine common carotid arteries were subjected to a protocol of quasi-static and harmonic, pseudo-physiological biaxial loading conditions to characterise their viscoelastic behaviour. The arterial wall was modelled as a constrained mixture of an isotropic elastin matrix and four families of collagen fibres. Constituent-based QLV was implemented by assigning different relaxation functions to collagen- and elastin-borne parts of the wall stress. Nonlinearity in viscoelasticity was assessed via the pressure dependency of the dynamic-to-quasi-static stiffness ratio. The experimentally measured ratio increased with pressure, from 1.03 [Formula: see text] 0.03 (mean [Formula: see text] standard deviation) at 80-40 mmHg to 1.58 [Formula: see text] 0.22 at 160-120 mmHg. Constituent-based QLV captured well this trend by attributing the wall viscosity predominantly to collagen fibres, whose recruitment starts at physiological pressures. In conclusion, constituent-based QLV offers a practical and effective solution to model arterial viscoelasticity.

On a three-dimensional model for the description of the passive characteristics of skeletal muscle tissue

In this work, a three-dimensional model was developed to describe the passive mechanical behaviour of anisotropic skeletal muscle tissue. To validate the model, orientation-dependent axial ([Formula: see text], [Formula: see text], [Formula: see text]) and semi-confined compression experiments (mode I, II, III) were performed on soleus muscle tissue from rabbits. In the latter experiments, specimen deformation is prescribed in the loading direction and prevented in an additional spatial direction, fibre compression at [Formula: see text] (mode I), fibre elongation at [Formula: see text] (mode II) and a neutral state of the fibres at [Formula: see text] where their length is kept constant (mode III). Overall, the model can adequately describe the mechanical behaviour with a relatively small number of model parameters. The stiffest tissue response during orientation-dependent axial compression ([Formula: see text] kPa) occurs when the fibres are oriented perpendicular to the loading direction ([Formula: see text]) and are thus stretched during loading. Semi-confined compression experiments yielded the stiffest tissue ([Formula: see text] kPa) in mode II when the muscle fibres are stretched. The extensive data set collected in this study allows to study the different error measures depending on the deformation state or the combination of deformation states.

Contribution of Elastic and Collagen Fibers to the Mechanical Behavior of Bovine Nuchal Ligament

Ligamentum nuchae is a highly elastic tissue commonly used to study the structure and mechanics of elastin. This study combines imaging, mechanical testing, and constitutive modeling to examine the structural organization of elastic and collagen fibers and their contributions to the nonlinear stress-strain behavior of the tissue. Rectangular samples of bovine ligamentum nuchae cut in both longitudinal and transverse directions were tested in uniaxial tension. Purified elastin samples were also obtained and tested. It was observed that the stress-stretch response of purified elastin tissue follows a similar curve as the intact tissue initially, but the intact tissue shows a significant stiffening behavior for stretches above 1.29 with collagen engagement. Multiphoton and histology images confirm the elastin-dominated bulk of ligamentum nuchae interspersed with small bundles of collagen fibrils and sporadic collagen-rich regions with cellular components and ground substance. A transversely isotropic constitutive model that considers the longitudinal organization of elastic and collagen fibers was developed to describe the mechanical behavior of both intact and purified elastin tissue under uniaxial tension. These findings shed light on the unique structural and mechanical roles of elastic and collagen fibers in tissue mechanics and may aid in future use of ligamentum nuchae in tissue grafting.

Patient-specific computational simulations of wound healing following midline laparotomy closure

In the current study, we developed a new computational methodology to simulate wound healing in soft tissues. We assumed that the injured tissue recovers partially its mechanical strength and stiffness by gradually increasing the volume fraction of collagen fibers. Following the principles of the constrained mixture theory, we assumed that new collagen fibers are deposited at homeostatic tension while the already existing tissue undergoes a permanent deformation due to the effects of remodeling. The model was implemented in the finite-element software Abaqus® through a VUMAT subroutine and applied to a complex and realistic case: simulating wound healing following midline laparotomy closure. The incidence of incisional hernia is still quite significant clinically, and our goal was to investigate different conditions hampering the success of these procedures. We simulated wound healing over periods of 6 months on a patient-specific geometry. One of the outcomes of the finite-element simulations was the width of the wound tissue, which was found to be clinically correlated with the development of incisional hernia after midline laparotomy closure. We studied the impact of different suturing modalities and the effects of situations inducing increased intra-abdominal pressure or its intermittent variations such as coughing. Eventually, the results showed that the main risks of developing an incisional hernia mostly depend on the elastic strains reached in the wound tissue after degradation of the suturing wires. Despite the need for clinical validation, these results are promising for establishing a digital twin of wound healing in midline laparotomy incision.

Regional biomechanical characterization of human ascending aortic aneurysms: Microstructure and biaxial mechanical response

The ascending thoracic aortic aneurysm (ATAA) is a permanent dilatation of the vessel with a high risk of adverse events, and shows heterogeneous properties. To investigate regional differences in the biomechanical properties of ATAAs, tissue samples were collected from 10 patients with tricuspid aortic valve phenotype and specimens from minor, anterior, major, and posterior regions were subjected to multi-ratio planar biaxial extension tests and second-harmonic generation (SHG) imaging. Using the data, parameters of a microstructure-motivated constitutive model were obtained considering fiber dispersion. SHG imaging showed disruptions in the organization of the layers. Structural and material parameters did not differ significantly between regions. The non-symmetric fiber dispersion model proposed by Holzapfel et al. [25] was used to fit the data. The mean angle of collagen fibers was negatively correlated between minor and anterior regions, and the parameter associated with collagen fiber stiffness was positively correlated between minor and major regions. Furthermore, correlations were found between the stiffness of the ground matrix and the mean fiber angle, and between the parameter associated with the collagen fiber stiffness and the out-of-plane dispersion parameter in the posterior and minor regions, respectively. The experimental data collected in this study contribute to the biomechanical data available in the literature on human ATAAs. Region-specific parameters for the constitutive models are fundamental to improve the current risk stratification strategies, which are mainly based on aortic size. Such investigations can facilitate the development of more advanced finite element models capable of capturing the regional heterogeneity of pathological tissues. STATEMENT OF SIGNIFICANCE: Tissue samples of human ascending thoracic aortic aneurysms (ATAA) were collected. Samples from four regions underwent multi-ratio planar biaxial extension tests and second-harmonic generation imaging. Region-specific parameters of a microstructure-motivated model considering fiber dispersion were obtained. Structural and material parameters did not differ significantly between regions, however, the mean fiber angle was negatively correlated between minor and anterior regions, and the parameter associated with collagen fiber stiffness was positively correlated between minor and major regions. Furthermore, correlations were found between the stiffness of the ground matrix and the mean fiber angle, and between the parameter associated with the collagen fiber stiffness and the out-of-plane dispersion parameter in the posterior and minor regions, respectively. This study provides a unique set of mechanical and structural data, supporting the microstructural influence on the tissue response. It may facilitate the development of better finite element models capable of capturing the regional tissue heterogeneity.

Glisson's capsule matrix structure and function is altered in patients with cirrhosis irrespective of aetiology

Background & Aims

Glisson's capsule is the interstitial connective tissue that surrounds the liver. As part of its normal physiology, it withstands significant daily changes in liver size. The pathophysiology of the capsule in disease is not well understood. The aim of this study was to characterise the changes in capsule matrix, cellular composition, and mechanical properties that occur in liver disease and to determine whether these correlate with disease severity or aetiology.

Methods

Samples from ten control patients, and six with steatosis, seven with moderate fibrosis, and 37 with cirrhosis were collected from autopsies, intraoperative biopsies, and liver explants. Matrix proteins and cell markers were assessed by staining and second harmonic generation imaging. Mechanical tensile testing was performed on a test frame.

Results

Capsule thickness was significantly increased in cirrhotic samples compared with normal controls irrespective of disease aetiology (70.12 ± 14.16 μm and 231.58 ± 21.82 μm, respectively), whereas steatosis and moderate fibrosis had no effect on thickness (90.91 ± 11.40 μm). Changes in cirrhosis included an increase in cell number (fibroblasts, vascular cells, infiltrating immune cells, and biliary epithelial cells). Key matrix components (collagens 1 and 3, hyaluronan, versican, and elastin) were all deposited in the lower capsule, although only the relative amounts per area of hyaluronan and versican were increased. Organisational features, including crimping and alignment of collagen fibres, were also altered in cirrhosis. Unexpectedly, capsules from cirrhotic livers had decreased resistance to loading compared with controls.

Conclusions

The liver capsule, similar to the parenchyma, is an active site of disease, demonstrating changes in matrix and cell composition as well as mechanical properties.

Impact and implications

We assessed the changes in composition and response to stretching of the liver outer sheath, the capsule, in human liver disease. We found an increase in key structural components and numbers of cells as well as a change in matrix organisation of the capsule during the later stages of disease. This allows the diseased capsule to stretch more under any given force, suggesting that it is less stiff than healthy tissue.

Damage and Fracture Mechanics of Porcine Subcutaneous Tissue Under Tensile Loading

Subcutaneous injection, which is a preferred delivery method for many drugs, causes deformation, damage, and fracture of the subcutaneous tissue. Yet, experimental data and constitutive modeling of these dissipation mechanisms in subcutaneous tissue remain limited. Here we show that subcutaneous tissue from the belly and breast anatomical regions in the swine show nonlinear stress-strain response with the characteristic J-shaped behavior of collagenous tissue. Additionally, subcutaneous tissue experiences damage, defined as a decrease in the strain energy capacity, as a function of the previously experienced maximum deformation. The elastic and damage response of the tissue are accurately described by a microstructure-driven constitutive model that relies on the convolution of a neo-Hookean material of individual fibers with a fiber orientation distribution and a fiber recruitment distribution. The model fit revealed that subcutaneous tissue can be treated as initially isotropic, and that changes in the fiber recruitment distribution with loading are enough to explain the dissipation of energy due to damage. When tested until failure, subcutaneous tissue that has undergone damage fails at the same peak stress as virgin samples, but at a much larger stretch, overall increasing the tissue toughness. Together with a finite element implementation, these data and constitutive model may enable improved drug delivery strategies and other applications for which subcutaneous tissue biomechanics are relevant.

Analysis of the geometrical influence of ring-opening samples on arterial circumferential residual stress reconstruction

This work consists of analyzing the impact of geometrical features (thickness and curvature) on the estimation of circumferential residual stresses in arteries. For this purpose, a specific sample of lamb abdominal artery is chosen for analysis and, through computational tools based on Python libraries, the stress-free geometry is captured after the ring opening test. Numerical simulations are then used to reconstruct the sample in order to estimate the circumferential residual stresses. Then, four stress-free geometry models are analyzed: an ideal geometry, i.e., constant curvature and thickness; a constant curvature and variable thickness geometry; a variable curvature and constant thickness geometry; and a variable curvature and thickness geometry. The numerical results show that models perform well from a geometric point of view, where the most different feature was the closed outer perimeter that differs about 14% from the closed real sample. As far as residual stress is concerned, differences up to 198% were found in more realistic models taking a constant curvature and thickness model as reference. Thus, the analysis of a realistic geometry with highly variable curvature and thickness can introduce, compared to an idealized geometry, significant differences in the estimation of residual stresses. This could indicate that the characterization of arterial residual stresses is not sufficient when considering only the opening angle and, therefore, it is also necessary to incorporate more geometrical variables.

Simultaneous tensile and shear measurement of the human cornea in vivo using S0- and A0-wave optical coherence elastography

Understanding corneal stiffness is valuable for improving refractive surgery, detecting corneal abnormalities, and assessing intraocular pressure. However, accurately measuring the elastic properties, particularly the tensile and shear moduli that govern mechanical deformation, has been challenging. To tackle this issue, we have developed guided-wave optical coherence elastography that can simultaneously excite and analyze symmetric (S0) and anti-symmetric (A0) elastic waves in the cornea at frequencies around 10 kHz and allows us to extract tensile and shear properties from measured wave dispersion curves. By applying acoustoelastic theory that incorporates corneal tension and a nonlinear constitutive tissue model, we verified the technique using elastomer phantoms and ex vivo porcine corneas and investigated the dependence on intraocular pressure. For two healthy human subjects, we measured a mean tensile modulus of 3.6 MPa and a mean shear modulus of 76 kPa in vivo with estimated errors of < 4%. This technique shows promise for the quantitative biomechanical assessment of the cornea in a clinical setting.

Comparison of multilayer and single-layer coronary plaque models on stress/strain calculations based on optical coherence tomography images

Mechanical stress and strain conditions are closely related to atherosclerotic plaque progression and rupture and have been under intensive investigations in recent years. It is well known that arteries have a three-layer structure: intima, media and adventitia. However, in vivo image-based multilayer plaque models are not available in the current literature due to lack of multilayer image segmentation data. A multilayer segmentation and repairing technique was introduced to segment coronary plaque optical coherence tomography (OCT) image to obtain its three-layer vessel structure. A total of 200 OCT slices from 20 patients (13 male; 7 female) were used to construct multilayer and single-layer 3D thin-slice models to calculate plaque stress and strain and compare model differences. Our results indicated that the average maximum plaque stress values of 20 patients from multilayer and single-layer models were 385.13 ± 110.09 kPa and 270.91 ± 95.86 kPa, respectively. The relative difference was 42.2%, with single-layer stress serving as the base value. The average mean plaque stress values from multilayer and single-layer models were 129.59 ± 32.77 kPa and 93.27 ± 18.20 kPa, respectively, with a relative difference of 38.9%. The maximum and mean plaque strain values obtained from the multilayer models were 11.6% and 19.0% higher than those from the single-layer models. Similarly, the maximum and mean cap strains showed increases of 9.6% and 12.9% over those from the single-layer models. These findings suggest that use of multilayer models could improve plaque stress and strain calculation accuracy and may have large impact on plaque progression and vulnerability investigation and potential clinical applications. Further large-scale studies are needed to validate our findings.

On the identification of the ultra-structural organization of elastic fibers and their effects on the integrity of annulus fibrosus

Due to the complicated structure of the elastic fiber network in annulus fibrosus, existing in-silico studies either simplified or just overlooked its distribution pattern. Nonetheless, experimental and simulation results have proven that elastic fibers are of great importance to maintaining the structural integrity of annulus fibrosus and therefore to ensuring the load-bearing ability of intervertebral discs. Such needs call for a fine model. This work aims at developing a biphasic annulus fibrosus model by incorporating the accurate distribution pattern of collagen and elastic fibers. Both the structural parameters and intrinsic mechanical parameters were successfully identified using single lamella and inter-lamella microscopy anatomy and micromechanical testing data. The proposed model was then used to implement finite element simulations on various anterior and posterolateral multi-lamellae annulus fibrosus specimens. In general, simulation results agree well with available experimental and simulation data. On this basis, the effects of elastic fibers on the integrity of annulus fibrosus were further investigated. It was found that elastic fibers significantly influence the free swelling, radial stretching and circumferential shear performances of annulus fibrosus. Nonetheless, no significant effects were found for the circumferential stretching capability. The proposed biphasic model considers for the first time the distribution characteristics of elastic fibers at two scales, including both the principal orientations of all fiber families and the detailed distribution pattern within each family. Better understandings on the functions of collagen and elastic fibers can therefore be realized. To further enhance its prediction capability, the current model can be extended in the future by taking the fiber-matrix interaction as well as progressive damages into consideration.

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.

PyTorch-FEA: Autograd-enabled finite element analysis methods with applications for biomechanical analysis of human aorta

BACKGROUND AND OBJECTIVES

Finite-element analysis (FEA) is widely used as a standard tool for stress and deformation analysis of solid structures, including human tissues and organs. For instance, FEA can be applied at a patient-specific level to assist in medical diagnosis and treatment planning, such as risk assessment of thoracic aortic aneurysm rupture/dissection. These FEA-based biomechanical assessments often involve both forward and inverse mechanics problems. Current commercial FEA software packages (e.g., Abaqus) and inverse methods exhibit performance issues in either accuracy or speed.

METHODS

In this study, we propose and develop a new library of FEA code and methods, named PyTorch-FEA, by taking advantage of autograd, an automatic differentiation mechanism in PyTorch. We develop a class of PyTorch-FEA functionalities to solve forward and inverse problems with improved loss functions, and we demonstrate the capability of PyTorch-FEA in a series of applications related to human aorta biomechanics. In one of the inverse methods, we combine PyTorch-FEA with deep neural networks (DNNs) to further improve performance.

RESULTS

We applied PyTorch-FEA in four fundamental applications for biomechanical analysis of human aorta. In the forward analysis, PyTorch-FEA achieved a significant reduction in computational time without compromising accuracy compared with Abaqus, a commercial FEA package. Compared to other inverse methods, inverse analysis with PyTorch-FEA achieves better performance in either accuracy or speed, or both if combined with DNNs.

CONCLUSIONS

We have presented PyTorch-FEA, a new library of FEA code and methods, representing a new approach to develop FEA methods to forward and inverse problems in solid mechanics. PyTorch-FEA eases the development of new inverse methods and enables a natural integration of FEA and DNNs, which will have numerous potential applications.

A review on the biomechanical behaviour of the aorta

Large aortic aneurysm and acute and chronic aortic dissection are pathologies of the aorta requiring surgery. Recent advances in medical intervention have improved patient outcomes; however, a clear understanding of the mechanisms leading to aortic failure and, hence, a better understanding of failure risk, is still missing. Biomechanical analysis of the aorta could provide insights into the development and progression of aortic abnormalities, giving clinicians a powerful tool in risk stratification. The complexity of the aortic system presents significant challenges for a biomechanical study and requires various approaches to analyse the aorta. To address this, here we present a holistic review of the biomechanical studies of the aorta by categorising articles into four broad approaches, namely theoretical, in vivo, experimental and combined investigations. Experimental studies that focus on identifying mechanical properties of the aortic tissue are also included. By reviewing the literature and discussing drawbacks, limitations and future challenges in each area, we hope to present a more complete picture of the state-of-the-art of aortic biomechanics to stimulate research on critical topics. Combining experimental modalities and computational approaches could lead to more comprehensive results in risk prediction for the aortic system.

The effects of axial twisting and material non-symmetry on arterial bent buckling

Artery buckling occurs due to hypertensive lumen pressure or reduced axial tension and other pathological conditions. Since arteries in vivo often experience axial twisting and the collagen fiber alignment in the arterial wall may become nonsymmetric, it is imperative to know how axial twisting and nonsymmetric collagen alignment would affect the buckling behavior of arteries. To this end, the objective of this study was to determine the effect of axial twisting and nonsymmetric collagen fiber distribution on the critical pressure of arterial bent buckling. The buckling model analysis was generalized to incorporate an axial twist angle and nonsymmetric fiber alignment. The effect of axial twisting on the critical pressure was simulated and experimentally tested in a group of porcine carotid arteries. Our results showed that axial twisting tends to reduce the critical pressure depending on the axial stretch ratio and twist angle. In addition, nonsymmetric fiber alignment reduces the critical pressure. Experimental results confirmed that a twist angle of 90° reduces the critical pressure significantly (p < 0.05). It was concluded that axial twisting and non-axisymmetric collagen fibers distribution could make arteries prone to bent buckling. These results enrich our understanding of artery buckling and vessel tortuosity. The model analysis and results could also be applicable to other fiber reinforced tubes under lumen pressure and axial twisting.

Modelling Cell Orientation Under Stretch: The Effect of Substrate Elasticity

When cells are seeded on a cyclically deformed substrate like silicon, they tend to reorient their major axis in two ways: either perpendicular to the main stretching direction, or forming an oblique angle with it. However, when the substrate is very soft such as a collagen gel, the oblique orientation is no longer observed, and the cells align either along the stretching direction, or perpendicularly to it. To explain this switch, we propose a simplified model of the cell, consisting of two elastic elements representing the stress fiber/focal adhesion complexes in the main and transverse directions. These elements are connected by a torsional spring that mimics the effect of crosslinking molecules among the stress fibers, which resist shear forces. Our model, consistent with experimental observations, predicts that there is a switch in the asymptotic behaviour of the orientation of the cell determined by the stiffness of the substratum, related to a change from a supercritical bifurcation scenario, whereby the oblique configuration is stable for a sufficiently large stiffness, to a subcritical bifurcation scenario at a lower stiffness. Furthermore, we investigate the effect of cell elongation and find that the region of the parameter space leading to an oblique orientation decreases as the cell becomes more elongated. This implies that elongated cells, such as fibroblasts and smooth muscle cells, are more likely to maintain an oblique orientation with respect to the main stretching direction. Conversely, rounder cells, such as those of epithelial or endothelial origin, are more likely to switch to a perpendicular or parallel orientation on soft substrates.

Fracture of the porcine aorta. Part 2: FEM modelling and inverse parameter identification

The mechanics of vascular tissue, particularly its fracture properties, are crucial in the onset and progression of vascular diseases. Vascular tissue properties are complex, and the identification of fracture mechanical properties relies on robust and efficient numerical tools. In this study, we propose a parameter identification pipeline to extract tissue properties from force-displacement and digital image correlation (DIC) data. The data has been acquired by symconCT testing porcine aorta wall specimens. Vascular tissue is modelled as a non-linear viscoelastic isotropic solid, and an isotropic cohesive zone model describes tissue fracture. The model closely replicated the experimental observations and identified the fracture energies of 1.57±0.82 kJ m^-2 and 0.96±0.34 kJ m^-2 for rupturing the porcine aortic media along the axial and circumferential directions, respectively. The identified strength was always below 350 kPa, a value significantly lower than identified through classical protocols, such as simple tension, and sheds new light on the resilience of the aorta. Further refinements to the model, such as considering rate effects in the fracture process zone and tissue anisotropy, could have improved the simulation results. STATEMENT OF SIGNIFICANCE: This paper identified porcine aorta's biomechanical properties using data acquired through a previously developed experimental protocol, the symmetry-constraint compact tension test. An implicit finite element method model mimicked the test, and a two-step approach identified the material's elastic and fracture properties directly from force-displacement curves and digital image correlation-based strain measurements. Our findings show a lower strength of the abdominal aorta as compared to the literature, which may have significant implications for the clinical evaluation of the risk of aortic rupture.

Assessment of the aortic tunica media histological changes in relation with the cause of death

AIM

The authors set out to evaluate the correlations between three of the main morphological aortic parameters (elastic fibers - FE, collagen fibers - FCOL, and smooth muscle fibers - FM) and the cause of death.

MATERIALS AND METHODS

Study groups included 25 cases died of a vascular disease (V_P), 37 cases died of a non-vascular disease (NV_P) and 28 cases died of a violent/suspect non-pathological cause of death (V_Dth), the latter group representing also the control group. Four aortic cross-sections (base, arch, thoracic, and abdominal regions) were collected during autopsy from the selected cases, fixed in 10% buffered formalin and first of all photographed together with a calibrating ruler. Then, they were embedded in paraffin, sectioned off at 4 μm and stained with Hematoxylin-Eosin (HE) and Orcein. The obtained histological slides were transformed into virtual slides. Fibrillary components amounts were using a custom-made software, developed in MATLAB (MathWorks, USA). Statistical tools used were Pearson's correlation test, t-test (two-sample assuming equal variances) and one-way analysis of variance (ANOVA) test.

RESULTS AND DISCUSSIONS

The amounts of the three fibrillary components of the aortic tunica media had a synchronous variation in all aortic regions in each of the three groups, excepting FCOL in the group of patients died from vascular pathology, which presented only a trend of synchronous variation along the aorta. FE had their lowest values and FCOL had their highest values in patients died from vascular pathology. FCOL had always higher levels than FE in people died from any pathological condition, vascular or non-vascular. FM had always at least two times lower level than that of the other types of fibers, regardless of whether the person died due to a pathological condition or not.

CONCLUSIONS

The different pathological conditions causing death are influencing the fibrillary composition of aortic tunica media. Further studies are required to reveal other changes in the morphology of aortic wall in particular and vascular wall in general that could be related with different pathological conditions affecting the entire organism.

Mitral valve geometrical echocardiographic analysis and 3D computational modeling of a normal mitral valve

Aim: This research aims to develop a consistent computational model of a normal mitral valve (MV) and describe mitral regurgitation (MR) geometry based on Carpentier's classification. Materials & methods: MV geometry was assessed by 2D transthoracic echocardiogram in 100 individuals. A 3D parametric geometric model of the MV was developed. A computational model of a normal MV was performed. Results: The simulation of the valve function was successfully accomplished and its kinematics was analyzed. Differences in geometry were revealed between normal and type III MR. Conclusion: 3D computational models of the normal MV can be constructed relying on standard measurements performed by 2D echocardiography. Certain geometrical differences exist among the normal and the most severe type of MR.

A multiphysics-based artificial neural networks model for atherosclerosis

Atherosclerosis is a medical condition involving the hardening and/or thickening of arteries' walls. Mathematical multi-physics models have been developed to predict the development of atherosclerosis under different conditions. However, these models are typically computationally expensive. In this study, we used machine learning techniques, particularly artificial neural networks (ANN), to enhance the computational efficiency of these models. A database of multi-physics Finite Element Method (FEM) simulations was created and used for training and validating an ANN model. The model is capable of quick and accurate prediction of atherosclerosis development. A remarkable computational gain is obtained using the ANN model compared to the original FEM simulations.

Effect of Aging, Sex, and Gene (Fbln5) on Arterial Stiffness of Mice: 20 Weeks Adult Fbln5-knockout Mice Have Older Arteries than 100 Weeks Wild-Type Mice

The arterial stiffening is a strong independent predictor of cardiovascular risk and has been used to characterize the biological age of arteries ('arterial age'). Here we revealed that the Fbln5 gene knockout (Fbln5 ^-/- ) significantly increases the arterial stiffening for both male and female mice. We also showed that the arterial stiffening increases with natural aging, but the stiffening effect of Fbln5 ^-/- is much more severe than aging. The arterial stiffening of 20 weeks old mice with Fbln5 ^-/- is much higher than that at 100 weeks in wild-type (Fbln5 ^+/+ ) mice, which indicates that 20 weeks mice (equivalent to ∼26 years old humans) with Fbln5 ^-/- have older arteries than 100 weeks wild-type mice (equivalent to ∼77 years humans). Histological microstructure changes of elastic fibers in the arterial tissue elucidate the underlying mechanism of the increase of arterial stiffening due to Fbln5-knockout and aging. These findings provide new insights to reverse 'arterial age' due to abnormal mutations of Fbln5 gene and natural aging. This work is based on a total of 128 biaxial testing samples of mouse arteries and our recently developed unified-fiber-distribution (UFD) model. The UFD model considers the fibers in the arterial tissue as a unified distribution, which is more physically consistent with the real fiber distribution of arterial tissues than the popular fiber-family-based models (e.g., the well-know Gasser-Ogden-Holzapfel [GOH] model) that separate the fiber distribution into several fiber families. Thus, the UFD model achieves better accuracies with less material parameters. To our best knowledge, the UFD model is the only existing accurate model that could capture the property/stiffness differences between different groups of the experimental data discussed here.

Crimped fiber composites: mechanics of a finite-length crimped fiber embedded in a soft matrix

Composites comprising crimped fibers of finite length embedded in a soft matrix have the potential to mimic the strain-hardening behavior of tissues containing fibrous collagen. Unlike continuous fiber composites, such chopped fiber composites would be flow-processable. Here, we study the fundamental mechanics of stress transfer between a single crimped fiber and the embedding matrix subjected to tensile strain. Finite element simulations show that fibers with large crimp amplitude and large relative modulus straighten significantly at small strain without bearing significant load. At large strain, they become taut and hence bear increasing load. Analogous to straight fiber composites, there is a region near the ends of each fiber which bears much lower stress than the midsection. We show that the stress-transfer mechanics can be captured by a shear lag model where the crimped fiber can be replaced with an equivalent straight fiber whose effective modulus is lower than that of the crimped fiber, but increases with applied strain. This allows estimating the modulus of a composite at low fiber fraction. The degree of strain hardening and the strain needed for strain hardening can be tuned by changing relative modulus of the fibers and the crimp geometry.

Fabrication of bio-inspired anisotropic structures from biopolymers for biomedical applications: A review

The anisotropic features play indispensable roles in regulating various life activities in different organisms. Increasing efforts have been made to learn and mimic various tissues' intrinsic anisotropic structure or functionality for broad applications in different areas, especially in biomedicine and pharmacy. This paper discusses the strategies for fabricating biomaterials using biopolymers for biomedical applications with the case study analysis. Biopolymers, including different polysaccharides, proteins, and their derivates, that have been confirmed with sound biocompatibility for different biomedical applications are summarized, with a special focus on nanocellulose. Advanced analytical techniques for understanding and characterizing the biopolymer-based anisotropic structures for various biomedical applications are also summarized. Challenges still exist in precisely constructing biopolymers-based biomaterials with anisotropic structures from molecular to macroscopic levels and fitting the dynamic processes in native tissue. It is foreseeable that with the advancement of biopolymers' molecular functionalization, biopolymer building block orientation manipulation strategies, and structural characterization techniques, developing anisotropic biopolymer-based biomaterials for different biomedical applications would significantly contribute to a friendly disease-curing and healthcare experience.

A model of fluid-structure and biochemical interactions for applications to subclinical leaflet thrombosis

Subclinical leaflet thrombosis (SLT) is a potentially serious complication of aortic valve replacement with a bioprosthetic valve in which blood clots form on the replacement valve. SLT is associated with increased risk of transient ischemic attacks and strokes and can progress to clinical leaflet thrombosis. SLT following aortic valve replacement also may be related to subsequent structural valve deterioration, which can impair the durability of the valve replacement. Because of the difficulty in clinical imaging of SLT, models are needed to determine the mechanisms of SLT and could eventually predict which patients will develop SLT. To this end, we develop methods to simulate leaflet thrombosis that combine fluid-structure interaction and a simplified thrombosis model that allows for deposition along the moving leaflets. Additionally, this model can be adapted to model deposition or absorption along other moving boundaries. We present convergence results and quantify the model's ability to realize changes in valve opening and pressures. These new approaches are an important advancement in our tools for modeling thrombosis because they incorporate both adhesion to the surface of the moving leaflets and feedback to the fluid-structure interaction.

A Validated Three-Dimensional, Heterogenous Finite Element Model of the Rotator Cuff and The Effects of Collagen Orientation

Continuum mechanics-based finite element models of the shoulder aim to quantify the mechanical environment of the joint to aid in clinical decision-making for rotator cuff injury and disease. These models allow for the evaluation of the internal loading of the shoulder, which cannot be measured in-vivo. This study uses human cadaveric rotator cuff samples with surface tendon strain estimates, to validate a heterogeneous finite element model of the supraspinatus-infraspinatus complex during various load configurations. The computational model was considered validated when the absolute difference in average maximum principal strain for the articular and bursal sides for each load condition estimated by the model was no greater than 3% compared to that measured in the biomechanical study. The model can predict the strains for varying infraspinatus loads allowing for the study of load sharing between these two tightly coordinated tendons. The future goal is to use the modularity of this validated model to study the initiation and propagation of rotator cuff tear and other rotator cuff pathologies to ultimately improve care for rotator cuff tear patients.

Changes in the microstructure of the human aortic adventitia under biaxial loading investigated by multi-photon microscopy

Among the three layers of the aortic wall, the media is primarily responsible for its mechanical properties, but the adventitia prevents the aorta from overstretching and rupturing. The role of the adventitia is therefore crucial with regard to aortic wall failure, and understanding the load-induced changes in tissue microstructure is of high importance. Specifically, the focus of this study is on the changes in collagen and elastin microstructure in response to macroscopic equibiaxial loading applied to the aortic adventitia. To observe these changes, multi-photon microscopy imaging and biaxial extension tests were performed simultaneously. In particular, microscopy images were recorded at 0.02 stretch intervals. The microstructural changes of collagen fiber bundles and elastin fibers were quantified with the parameters of orientation, dispersion, diameter, and waviness. The results showed that the adventitial collagen was divided from one into two fiber families under equibiaxial loading conditions. The almost diagonal orientation of the adventitial collagen fiber bundles remained unchanged, but the dispersion was substantially reduced. No clear orientation of the adventitial elastin fibers was observed at any stretch level. The waviness of the adventitial collagen fiber bundles decreased under stretch, but the adventitial elastin fibers showed no change. These original findings highlight differences between the medial and adventitial layers and provide insight into the stretching process of the aortic wall. STATEMENT OF SIGNIFICANCE: To provide accurate and reliable material models, it is essential to understand the mechanical behavior of the material and its microstructure. Such understanding can be enhanced with tracking of the microstructural changes caused by mechanical loading of the tissue. This study provides therefore a unique dataset of structural parameters of the human aortic adventitia obtained under equibiaxial loading. The structural parameters describe orientation, dispersion, diameter, and waviness of collagen fiber bundles and elastin fibers. Eventually, the microstructural changes in the human aortic adventitia are compared with the microstructural changes in the human aortic media from a previous study. This comparison reveals the cutting-edge findings on the differences in the response to the loading between these two human aortic layers.

Synergistic Integration of Deep Neural Networks and Finite Element Method with Applications for Biomechanical Analysis of Human Aorta

Motivation: Patient-specific finite element analysis (FEA) has the potential to aid in the prognosis of cardiovascular diseases by providing accurate stress and deformation analysis in various scenarios. It is known that patient-specific FEA is time-consuming and unsuitable for time-sensitive clinical applications. To mitigate this challenge, machine learning (ML) techniques, including deep neural networks (DNNs), have been developed to construct fast FEA surrogates. However, due to the data-driven nature of these ML models, they may not generalize well on new data, leading to unacceptable errors.

Methods

We propose a synergistic integration of DNNs and finite element method (FEM) to overcome each other’s limitations. We demonstrated this novel integrative strategy in forward and inverse problems. For the forward problem, we developed DNNs using state-of-the-art architectures, and DNN outputs were then refined by FEM to ensure accuracy. For the inverse problem of heterogeneous material parameter identification, our method employs a DNN as regularization for the inverse analysis process to avoid erroneous material parameter distribution.

Results

We tested our methods on biomechanical analysis of the human aorta. For the forward problem, the DNN-only models yielded acceptable stress errors in majority of test cases; yet, for some test cases that could be out of the training distribution (OOD), the peak stress errors were larger than 50%. The DNN-FEM integration eliminated the large errors for these OOD cases. Moreover, the DNN-FEM integration was magnitudes faster than the FEM-only approach. For the inverse problem, the FEM-only inverse method led to errors larger than 50%, and our DNN-FEM integration significantly improved performance on the inverse problem with errors less than 1%.

Modeling planar response of vascular tissues using quadratic functions of effective strain

Simulation-based studies of the cardiovascular structure such as aorta have become increasingly popular for many biomedical problems such as predictions of aneurysm rupture. A critical step in these simulations is the development of constitutive models that accurately describe the tissue's mechanical behavior. In this work, we present a new constitutive model, which explicitly accounts for the gradual recruitment of collagen fibers. The recruitment is considered using an effective stretch, which is a continuum-scale kinematic variable measuring the uncrimped stretch of the tissue in an average sense. The strain energy of a fiber bundle is described by a quadratic function of the effective strain. Constitutive models formulated in this manner are applied to describe the responses of ascending thoracic aortic aneurysm and porcine thoracic aorta tissues. The heterogeneous properties of the ATAA tissue are extracted from bulge inflation test data, and then used in finite element analysis to simulate the inflation test. The descriptive and predictive capabilities are further assessed using planar testing data of porcine thoracic aortic tissues. It is found that the constitutive model can accurately describe the stress-strain relations. In particular, the finite element simulation replicates the displacement, strain, and stress distributions with excellent fidelity.

Effect of aging on the biaxial mechanical behavior of human descending thoracic aorta: Experiments and constitutive modeling considering collagen crosslinking

Collagen crosslinking, an important contributor to the stiffness of soft tissues, was found to increase with aging in the aortic wall. Here we investigated the mechanical properties of human descending thoracic aorta with aging and the role of collagen crosslinking through a combined experimental and modeling approach. A total of 32 samples from 17 donors were collected and divided into three age groups: <40, 40-60 and > 60 years. Planar biaxial tensile tests were performed to characterize the anisotropic mechanical behavior of the aortic samples. A recently developed constitutive model incorporating collagen crosslinking into the two-fiber family model (Holzapfel and Ogden, 2020) was modified to accommodate biaxial deformation of the aorta, in which the extension and rotation kinematics of bonded fibers and crosslinks were decoupled. The mechanical testing results show that the aorta stiffens with aging with a more drastic change in the longitudinal direction, which results in altered aortic anisotropy. Our results demonstrate a good fitting capability of the constitutive model considering crosslinking for the biaxial aortic mechanics of all age groups. Furthermore, constitutive modeling results suggest an increased contribution of crosslinking and strain energy density to the biaxial stress-stretch behaviors with aging and point to excessive crosslinking as a prominent contributor to aortic stiffening.

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.

Computational modeling of electromechanical coupling in human cardiomyocyte applied to study hypertrophic cardiomyopathy and its drug response

BACKGROUND AND OBJECTIVE

Knowledge of electromechanical coupling in cardiomyocyte and how it is influenced by various pathophysiological factors is fundamental to understanding the pathogenesis of myocardial disease and its response to medication, which is however hard to be thoroughly addressed by clinical/experimental studies due to technical limitations. At this point, computational modeling offers an alternative approach. The main objective of the study was to develop a computational model capable of simulating the process of electromechanical coupling and quantifying the roles of various factors in play in the human left ventricular cardiomyocyte.

METHODS

A new electrophysiological model was firstly built by combining several existing electrophysiological models and incorporating the mechanism of electrophysiological homeostasis, which was subsequently coupled to models representing the cross-bridge dynamics and active force generation during excitation-contraction coupling and the passive mechanical properties of cardiomyocyte to yield an integrative electromechanical model. Model parameters were calibrated or optimized based on a large amount of experimental data. The resulting model was applied to delineate the characteristics of electromechanical coupling and explore underlying determinant factors in hypertrophic cardiomyopathy (HCM) cardiomyocyte, as well as quantify their changes in response to different medications.

RESULTS

Model predictions captured the major electromechanical characteristics of cardiomyocyte under both normal physiological and HCM conditions. In comparison with normal cardiomyocyte, HCM cardiomyocyte suffered from systemic changes in both electrophysiological and mechanical variables. Numerical simulations of drug response revealed that Mavacamten and Metoprolol could both reduce the active contractility and alleviate calcium overload but had marked differential influences on many other electromechanical variables, which theoretically explained why the two drugs have differential therapeutic effects. In addition, our numerical experiments demonstrated the important role of compensatory ion transport in maintaining electrophysiological homeostasis and regulating cytoplasmic volume.

CONCLUSIONS

A sophisticated computational model has the advantage of providing quantitative and integrative insights for understanding the pathogenesis and drug responses of HCM or other myocardial diseases at the level of cardiomyocyte, and hence may contribute as a useful complement to clinical/experimental studies. The model may also be coupled to tissue- or organ-level models to strengthen the physiological implications of macro-scale numerical simulations.

Mechanical Behavior and Collagen Structure of Degenerative Mitral Valve Leaflets and a Finite Element Model of Primary Mitral Regurgitation

Degenerative mitral valve disease is the main cause of primary mitral regurgitation with two phenotypes: fibroelastic deficiency (FED) often with localized myxomatous degeneration and diffuse myxomatous degeneration or Barlow's disease. Myxomatous degeneration disrupts the microstructure of the mitral valve leaflets, particularly the collagen fibers, which affects the mechanical behavior of the leaflets. The present study uses biaxial mechanical tests and second harmonic generation microscopy to examine the mechanical behavior of Barlow and FED tissue. Three tissue samples were harvested from a FED patient and one sample is from a Barlow patient. Then we use an appropriate constitutive model by excluding the collagen fibers under compression. Finally, we built an FE model based on the echocardiography of patients diagnosed with FED and Barlow and the characterized material model and collagen fiber orientation. The Barlow sample and the FED sample from the most affected segment showed different mechanical behavior and collagen structure compared to the other two FED samples. The FE model showed very good agreement with echocardiography with 2.02±1.8 mm and 1.05±0.79 mm point-to-mesh distance errors for Barlow and FED patients, respectively. It has also been shown that the exclusion of collagen fibers under compression provides versatility for the material model; it behaves stiff in the belly region, preventing excessive bulging, while it behaves very softly in the commissures to facilitate folding. STATEMENT OF SIGNIFICANCE: None.

The study on the impact of AAA wall motion on the hemodynamics based on 4D CT image data

Purpose: To analyze the effect of the physiological deformation of the vessel wall on the hemodynamics in the abdominal aortic aneurysm (AAA), this paper compared the hemodynamics in AAA based on the moving boundary (MB) simulation and the rigid wall (RW) simulation. Method: Patient-specific models were reconstructed to generate mesh based on four-dimensional computed tomography angiography (4D CT) data. The dynamic mesh technique was used to achieve deformation of the vessel wall, surface mesh and volume mesh of the fluid domain were successively remeshed at each time step. Besides, another rigid wall simulation was performed. Hemodynamics obtained from these two simulations were compared. Results: Flow field and wall shear stress (WSS) distribution are similar. When using the moving boundary method (MBM), mean time-averaged wall shear stress (TAWSS) is lower, mean oscillatory shear index (OSI) and mean relative residence time (RRT) are higher. When using the 10th and 20th percentile values for TAWSS and 80th and 90th percentile values for RRT, the ratios of areas with low TAWSS, high OSI and high RRT to the entire vessel wall are higher than those assuming the vessel as rigid. In addition, one overlapping region of low TAWSS, high OSI and high RRT by using the MBM is consistent with the location of thrombus obtained from the follow-up imaging data. Conclusion: The hemodynamics results by using the MBM reflect a higher blood retention effect. This paper presents a potential tool to assess the risk of intraluminal thrombus (ILT) formation based on the MBM.

PyTorch-FEA: Autograd-enabled Finite Element Analysis Methods with Applications for Biomechanical Analysis of Human Aorta

Motivation

Finite-element analysis (FEA) is widely used as a standard tool for stress and deformation analysis of solid structures, including human tissues and organs. For instance, FEA can be applied at a patient-specific level to assist in medical diagnosis and treatment planning, such as risk assessment of thoracic aortic aneurysm rupture/dissection. These FEA-based biomechanical assessments often involve both forward and inverse mechanics problems. Current commercial FEA software packages (e.g., Abaqus) and inverse methods exhibit performance issues in either accuracy or speed.

Methods

In this study, we propose and develop a new library of FEA code and methods, named PyTorch-FEA, by taking advantage of autograd, an automatic differentiation mechanism in PyTorch. We develop a class of PyTorch-FEA functionalities to solve forward and inverse problems with improved loss functions, and we demonstrate the capability of PyTorch-FEA in a series of applications related to human aorta biomechanics. In one of the inverse methods, we combine PyTorch-FEA with deep neural networks (DNNs) to further improve performance.

Results

We applied PyTorch-FEA in four fundamental applications for biomechanical analysis of human aorta. In the forward analysis, PyTorch-FEA achieved a significant reduction in computational time without compromising accuracy compared with Abaqus, a commercial FEA package. Compared to other inverse methods, inverse analysis with PyTorch-FEA achieves better performance in either accuracy or speed, or both if combined with DNNs.

Analysis of Fatigue Strength and Reliability of Lower Limb Arterial Stent at Different Vascular Stenosis Rates and Stent-to-Artery Ratios

In order to study the influence of different vascular stenosis rates and stent-to-artery ratios on the fatigue strength and reliability of lower limb arterial stents, numerical simulation was conducted for the fatigue strength of complete SE stents under pulsating loads using a finite element method. Then, fracture mechanics and conditional probability theory were adopted for mathematical modeling, whereby analyzing the crack growth rate and reliability with stents of different thickness (0.12, 0.15, and 0.18 mm) at different vascular stenosis rates (30, 50, and 70%) and stent-to-artery ratios (80, 85, and 90%). The study found: all three stents of different thickness failed to meet 10-year service life at three vascular stenosis rates; all three stents of different thickness met 10-year service life at three stent-to-artery ratios. With increased vascular stenosis rate, the elastic strain of stents was increased, while the fatigue strength was decreased; with increased stent-to-artery ratio, the elastic strain of the stent was increased, while the reliability of the stent was reduced. After the stent with an initial crack was implanted into the vessel, the crack length underwent non-linear growth with increased pulsating cyclic loads. When the pulsating load reached 3 × 10⁸, the growth rate of the crack on the stent surface increased exponentially, leading to a rapid decrease in reliability. Vascular stenosis rate, stent release ratio, and support thickness have significant effects on crack length propagation rate and reliability. Determining the influence of vascular stenosis rate and stent-to-artery ratio on the fatigue strength and reliability of stents provides a valuable reference for evaluating the fracture failure rate and safety of stents.

Fracture toughness of fibrin gels as a function of protein volume fraction: Mechanical origins

The mechanical stability of blood clots necessary for their functions is provided by fibrin, a fibrous gel. Rupture of clots leads to life-threatening thrombotic embolization, which is little understood. Here, we combine experiments and simulations to determine the toughness of plasma clots as a function of fibrin content and correlate toughness with fibrin network structure characterized by confocal and scanning electron microscopy. We develop fibrin constitutive laws that scale with fibrin concentration and capture the force-stretch response of cracked clot specimens using only a few material parameters. Toughness is calculated from the path-independent J* integral that includes dissipative effects due to fluid flow and uses only the constitutive model and overall stretch at crack propagation as input. We show that internal fluid motion, which is not directly measurable, contributes significantly to clot toughness, with its effect increasing as fibrin content increases, because the reduced gel porosity at higher density results in greater expense of energy in fluid motion. Increasing fibrin content (1→10mg/mL) results in a significant increase in clot toughness (3→15 N/m) in accordance with a power law relation reminiscent of cellular solids and elastomeric gels. These results provide a basis for understanding and predicting the tendency for thrombotic embolization. STATEMENT OF SIGNIFICANCE: Fibrin, a naturally occurring biomaterial, is the major determinant of the structural and mechanical integrity of blood clots. We determined that increasing the fibrin content in clots, as in some thrombi and fibrin-based anti-bleeding sealants, results in an increase in clot toughness. Toughness corresponds to the ability to resist rupturing in the presence of a defect. We couple bulk mechanical testing, microstructural measurements, and finite element modeling to capture the force-stretch response of fibrin clots and compute toughness. We show that increased fibrin content in clots reduces porosity and limits fluid motion and that fluid motion drastically alters the clot toughness. These results provide a fundamental understanding of blood clot rupture and could help in rational design of fibrin-containing biomaterials.

Roadmap for an imaging and modelling paediatric study in rural NZ

Our study methodology is motivated from three disparate needs: one, imaging studies have existed in silo and study organs but not across organ systems; two, there are gaps in our understanding of paediatric structure and function; three, lack of representative data in New Zealand. Our research aims to address these issues in part, through the combination of magnetic resonance imaging, advanced image processing algorithms and computational modelling. Our study demonstrated the need to take an organ-system approach and scan multiple organs on the same child. We have pilot tested an imaging protocol to be minimally disruptive to the children and demonstrated state-of-the-art image processing and personalized computational models using the imaging data. Our imaging protocol spans brain, lungs, heart, muscle, bones, abdominal and vascular systems. Our initial set of results demonstrated child-specific measurements on one dataset. This work is novel and interesting as we have run multiple computational physiology workflows to generate personalized computational models. Our proposed work is the first step towards achieving the integration of imaging and modelling improving our understanding of the human body in paediatric health and disease.

Tri-layered constitutive modelling unveils functional differences between the pig ascending and lower thoracic aorta

The arterial wall's tri-layered macroscopic and layer-specific microscopic structure determine its mechanical properties, which vary at different arterial locations. Combining layer-specific mechanical data and tri-layered modelling, this study aimed to characterise functional differences between the pig ascending (AA) and lower thoracic aorta (LTA). AA and LTA segments were obtained for n=9 pigs. For each location, circumferentially and axially oriented intact wall and isolated layer strips were tested uniaxially and the layer-specific mechanical response modelled using a hyperelastic strain energy function. Then, layer-specific constitutive relations and intact wall mechanical data were combined to develop a tri-layered model of an AA and LTA cylindrical vessel, accounting for the layer-specific residual stresses. AA and LTA behaviours were then characterised for in vivo pressure ranges while stretched axially to in vivo length. The media dominated the AA response, bearing>2/3 of the circumferential load both at physiological (100 mmHg) and hypertensive pressures (160 mmHg). The LTA media bore most of the circumferential load at physiological pressure only (57±7% at 100 mmHg), while adventitia and media load bearings were comparable at 160 mmHg. Furthermore, increased axial elongation affected the media/adventitia load-bearing only at the LTA. The pig AA and LTA presented strong functional differences, likely reflecting their different roles in the circulation. The media-dominated compliant and anisotropic AA stores large amounts of elastic energy in response to both circumferential and axial deformations, which maximises diastolic recoiling function. This function is reduced at the LTA, where the adventitia shields the artery against supra-physiological circumferential and axial loads.

Design and validation of a finite element model of the aponeurotic and free Achilles tendon

The Achilles tendon (AT) is a common injury site. Ruptures are usually located in the free tendon but may cross the myotendinous junction into the aponeurotic region. Considering the possibility of aponeurotic region involvement in AT ruptures, a novel three dimensional (3D) finite element (FE) model that includes both the aponeurotic and free AT regions and features subtendon twisting and sliding was developed. It was hypothesized that the model would be able to predict in vivo data collected from the literature, thus being considered valid, and that model outputs would be most sensitive to subtendon twist configurations. The 3D model was constructed using magnetic resonance images. The model was divided into soleus and gastrocnemius subtendons. In addition to a frictionless contact condition, the interaction between subtendons was modeled using two contact formulations: sliding with anisotropic friction and no sliding. Loads were applied on the tendon's most proximal cross-section and anterior surface, with magnitudes estimated from in vivo studies. Model outputs were compared with experimental data regarding 3D deformation, transverse plane rotation, and nodal displacements in the free tendon. The FE model adequately simulated the free tendon behavior regarding longitudinal strain, cross-section area variation, transverse plane rotation, and sagittal nodal displacements, provided that subtendon sliding was allowed. The frictionless model exhibited noticeable medial transverse sliding of the soleus subtendon, which was present to a much lesser degree in the anisotropic friction model. Model outputs were most sensitive to variations in subtendon twist and dispersion of the collagen fiber orientations. Clinical Significance: This Achilles tendon finite element model, validated using in vivo experimental data, may be used to study its mechanical behavior, injury mechanisms, and rupture risk factors.

Characterization and modeling of the in-plane collagen fiber distribution in the porcine dermis

The structural arrangement of collagen fibers in the plane of the dermis layer plays a critical role in accurately predicting the mechanical behavior of skin tissues. This paper combines a histological analysis with statistical modeling to characterize and model the in-plane collagen fiber distribution in the porcine dermis. The histology data reveals that the fiber distribution in the plane of the porcine dermis is non-symmetric. The histology data forms the basis of our model, which employs a combination of two π-periodic von-Mises distribution density functions to create a non-symmetric distribution. We demonstrate that a non-symmetric in-plane fiber distribution is a significant improvement over a symmetric distribution.

Biaxial hyperelastic and anisotropic behaviors of the corneal anterior central stroma along the preferential fibril orientations. Part II: Quantitative computational analysis of mechanical response of stromal components

To study the hyperelastic and anisotropic behaviors of the central anterior stroma for patients with myopia, 40 corneal stromal specimens extracted after small incision lenticule extraction (SMILE) surgery were used in the biaxial extension test along two preferential fibril orientations. An improved collagen fibril crimping constitutive model with a specific physical meaning was proposed to analyze the hyperelasticity and anisotropy of the stroma. The effective elastic modulus of the two families of preferentially oriented collagen fibrils and the stiffness of the non-collagenous matrix along all three directions were compared according to the specific physical meaning of the parameters. Anisotropic behavior was found in the hyperelastic properties of the corneal anterior central stroma in the preferential fibril orientations. The stiffness of non-collagenous matrix is significantly larger in the optical axis direction than in the nasal-temporal (NT) and superior-inferior (SI) directions. Moreover, individual differences between males and females slightly impact on hyperelastic and anisotropic behaviors. The differences of these behaviors were significant in the comparison of the left and right eyes. These results have a guiding significance for the accurate design of surgical plans for refractive surgery according to a patient's condition and have a driving value for the further exploration of the biomechanical properties of the whole cornea.

Mechanical characterization of human umbilical arteries by thick-walled models: Enhanced vascular compliance by removing an abluminal lining

The decellularized human umbilical artery (HUA) is considered as a promising option for small-diameter, tissue-engineered vascular grafts (TEVGs). Our previous study showed that the HUA bears a thin, watertight lining on its outermost abluminal surface. Removal of this abluminal lining layer improves efficacy of the perfusion-assisted decellularization of the HUA and increases its compliance. As stress across the wall is believed to affect growth and remodeling of the TEVG, it is imperative to mechanically characterize the HUA using thick-walled models. Combining inflation experiments and computational methods, we investigate the mechanical properties of the HUA before and after the abluminal lining removal to examine the HUA's wall mechanics. The inflation tests of five HUAs were performed to obtain the mechanical and geometrical response of the vessel wall before and after the lining layer removal. Using nonlinear hyperelastic models, the same responses are obtained computationally using the thick-walled models. The experimental data are incorporated into the computational models to estimate the mechanical and orientation parameters of the fibers and isotropic matrix of different layers in the HUAs. The parameter fitting of both thick-walled models (before and after the abluminal lining removal) results in most of the R-squared values for measuring the goodness of fitting to be over 0.90 for all samples. The compliance of the HUA increases from a mean value of 2.60% per 100 mmHg before the removal of the lining to a mean value of 4.21% per 100 mmHg after the removal. The results reveal that, although the abluminal lining is thin, it is stiff and capable of supporting majority of the high luminal pressure, and that the inner layer is far less stressed than the abluminal lining. Computational simulations also show that removal of the abluminal lining increases the circumferential wall stress by up to 280 kPa under the in vivo luminal pressure. The integrated computational and experimental approaches provide more accurate estimates of the material behaviors of HUAs employed in grafts and, in turn, the study enhances our understanding of interactions between the graft and the native vessel on vascular growth and remodeling.

Orientation-dependent indentation reveals the crosslink-mediated deformation mechanisms of collagen fibrils

The spatial arrangement and interactions of the extracellular matrix (ECM) components control the mechanical behavior of tissue at multiple length scales. Changes in microscale deformation mechanisms affect tissue function and are often hallmarks of remodeling and disease. Despite their importance, the deformation mechanisms that modulate the mechanical behavior of collagenous tissue, particularly in indentation and compression modes of deformation, remain poorly understood. Here, we develop an integrated computational and experimental approach to investigate the deformation mechanisms of collagenous tissue at the microscale. While the complex deformation arising from indentation with a spherical probe is often considered a pitfall rather than an opportunity, we leverage this orientation-dependent deformation to examine the shear-regulated interactions of collagen fibrils and the role of crosslinks in modulating these interactions. We specifically examine tendon and cervix, two tissues rich in collagen with quite different microstructures and mechanical functions. We find that interacting, crosslinked collagen fibrils resist microscale longitudinal compressive forces, while widely used constitutive models fail to capture this behavior. The reorientation of collagen fibrils tunes the compressive stiffness of complex tissues like cervix. This study offers new insights into the mechanical behavior of collagen fibrils during indentation, and more generally, under longitudinal compressive forces, and illustrates the mechanisms that contribute to the experimentally observed orientation-dependent mechanical behavior. STATEMENT OF SIGNIFICANCE: Remodeling and disease can affect the deformation and interaction of tissue constituents, and thus mechanical function of tissue. Yet, the microscale deformation mechanisms are not well characterized in many tissues. Here, we develop a combined experimental-computational approach to infer the microscale deformation mechanisms of collagenous tissues with very different functions: tendon and cervix. Results show that collagen fibrils resist microscale forces along their length, though widely-used constitutive models do not account for this mechanism. This deformation process partially modulates the compressive stiffness of complex tissues such as cervix. Computational modeling shows that crosslink-mediated shear deformations are central to this unexpected behavior. This study offers new insights into the deformation mechanisms of collagenous tissue and the function of collagen crosslinkers.