Hyperelastic modelling of arterial layers with distributed collagen fibre orientations

A novel tube law analysis under anisotropic external load

Mathematical and physical modeling of flows in collapsible pipes often relates the flow area to the difference between the internal and the external pressures (i.e. the transmural pressure). The relation is used to model the conduits of the human body transporting biological fluids, is called tube law and usually considers the transmural pressure resulting from isotropic external pressure only. We provide a new empirical tube law considering anisotropic conditions of the external load; our formulation is based on the hypothesis, supported by clinical and experimental findings, that in physiological conditions both isotropic and anisotropic stresses are combined in the external load acting on vessels. The proposed mathematical model was validated through laboratory experiments reproducing the flow through a collapsible tube representing the physiological conditions of male urethra during micturition. The proposed tube law better agrees with the experimental observations, in comparison to classic formulations available in literature, thus showing that the proposed model better describes the physiological condition of flow in collapsible tubes subjected to anisotropic external load. The application of our model can be readily extended to several types of vessels.

Genesis of intimal thickening due to hemodynamical shear stresses

This paper investigates intimal growth in arteries, induced by hemodynamical shear stress, through finite element simulation using the FEniCS computational environment. In our model, the growth of the intima depends on cross-section geometry and shear stress. In this work, the arterial wall is modeled as three distinct layers: the intima, the media and the adventitia, each with different mechanical properties. We assume that the cross-section of the vessel does not change in the axial direction. We further assume that the blood flow is steady, non-turbulent and unidirectional. Blood flow induces shear stress on the endothelium and stimulates the release of platelet derived growth factor (PDGF) which drives the growth. We simulate intimal growth for three distinct arterial cross section geometries. We show that the qualitative nature of intimal thickening varies depending on arterial geometry. For cross section geometries that are annular, the growth of the intima is uniform in the angular direction, and the endothelium stays circular as the intima grows. For non-annular cross section geometries, the intima grows more quickly where it is thicker, and shear stress and intimal thickening are negatively correlated with the distance from the flow center, where the flow velocity is maximal. Over time, the maxima and minima of the curvature increase and decrease, respectively, the PDGF concentration increases and the lumen becomes more polygonal. The model provides a framework for coupling hemodynamics simulations to mathematical descriptions of atherosclerosis, both of which have been modeled separately in great detail.

Traction-separation law parameters for the description of age-related changes in the delamination strength of the human descending thoracic aorta

Aortic dissection is a life-threatening disease that consists in the development of a tear in the wall of the aorta. The initial tear propagates as a discontinuity leading to separation within the aortic wall, which can result in the creation of a so-called false lumen. A fatal threat occurs if the rupture extends through the whole thickness of the aortic wall, as blood may then leak. It is generally accepted that the dissection, which can sometime extend along the entire length of the aorta, propagates via a delamination mechanism. The aim of the present paper is to provide experimentally validated parameters of a mathematical model for the description of the wall's cohesion. A model of the peeling experiment was built in Abaqus. The delamination interface was described by a piecewise linear traction-separation law. The bulk behavior of the aorta was assumed to be nonlinearly elastic, anisotropic, and incompressible. Our simulations resulted in estimates of the material parameters for the traction-separation law of the human descending thoracic aorta, which were obtained by minimizing the differences between the FEM predictions and the delamination force given by the regression of the peeling experiments. The results show that the stress at damage initiation, Tc, should be understood as an age-dependent quantity, and under the assumptions of our model this dependence can be expressed by linear regression as Tc =  - 13.03·10-4·Age + 0.2485 if the crack front advances in the axial direction, and Tc =  - 7.58·10-4·Age + 0.1897 if the crack front advances in the direction of the aortic circumference (Tc [MPa], Age [years]). Other model parameters were the stiffness K and the separation at failure, δf-δc (K = 0.5 MPa/mm, δf-δc = 0.1 mm). The material parameters provided by our study can be used in numerical simulations of the biomechanics of dissection propagation through the aorta especially when age-associated phenomena are studied.

Three-dimensional anisotropic unified continuum model for simulating the healing of damaged soft biological tissues

The soft biological tissues have the ability to heal and self-repair after damage or injury. During the healing process, damaged tissues are replaced by newly produced undamaged tissue to restore homeostasis. Computational modeling serves as an effective tool for simulating the healing process and understanding the underlying mechanisms. In previous work, we developed the first unified continuum damage model for the healing of soft biological tissues. However, the initial theory lacked generalizability to more realistic scenarios and applicability to biomechanical problems due to the simplicity of the isotropic constitutive model and two-dimensional simulations. Therefore, we further improve our approach by developing a three-dimensional anisotropic unified healing model to address more realistic challenges. By using the Holzapfel-Gasser-Ogden model as the hyperelastic term, the influence of the collagen fibers is considered and the reorientation of fibers in healing is simulated. Three numerical examples related to hypertension, aneurysm, and restenosis of the atherosclerotic artery after balloon angioplasty are presented to demonstrate the effectiveness of the proposed model. By comparing numerical solutions and reference solutions, we demonstrate the ability of the proposed model in simulating long-term tissue healing process and analyze the impact of anisotropic terms.

Comparative analysis of Zero Pressure Geometry and prestress methods in cardiovascular Fluid-Structure Interaction

BACKGROUND AND OBJECTIVE

Modelling patient-specific aortic biomechanics with advanced computational techniques, such as Fluid-Structure Interaction (FSI), can be crucial to provide effective decision-making indices to enhance current clinical practices. To effectively simulate Ascending Thoracic Aortic Aneurysms (ATAA), the stress-free configuration must be defined. The Zero Pressure Geometry (ZPG) and the Prestress Tensor (PT) are two of the main approaches to tackle this issue. However, their impact on the numerical results is yet to be analysed. Computed Tomography Angiography (CTA) and Magnetic Resonance Imaging (MRI) data were used to develop patient-specific 2-way FSI frameworks.

METHODS

Three models were developed considering different tissue prestressing approaches to account for the reference configuration and their numerical results were compared. The selected approaches were: (i) ZPG, (ii) PT and (iii) a combination of the PT approach with a regional mapping of material properties (PTCAL).

RESULTS

The pressure fields estimated by all models were equivalent. The estimation of Wall Shear Stress (WSS) based metrics revealed good correspondence between all models except the Relative Residence Time (RRT). Regarding ATAA wall mechanics, the proposed extension to the PT approach presented a closer agreement with the ZPG model than its counterpart. Additionally, the PT and PTCAL approaches required around 60% fewer iterations to achieve cycle-to-cycle convergence than the ZPG algorithm.

CONCLUSION

Using a regional mapping of material properties in combination with the PT method presented a better correspondence with the ZPG approach. The outcomes of this study can pave the way for advancing the accuracy and convergence of ATAA numerical models using the PT methodology.

Age-related changes in the biochemical composition of the human aorta and their correlation with the delamination strength

Various studies have correlated the mechanical properties of the aortic wall with its biochemical parameters and inner structure. Very few studies have addressed correlations with the cohesive properties, which are crucial for understanding fracture phenomena such as aortic dissection, i.e. a life-threatening process. Aimed at filling this gap, we conducted a comprehensive biochemical and histological analysis of human aortas (the ascending and descending thoracic and infrarenal abdominal aorta) from 34 cadavers obtained post-mortem during regular autopsies. The pentosidine, hydroxyproline and calcium contents, calcium/phosphorus molar ratio, degree of atherosclerosis, area fraction of elastin, collagen type I and III, alpha smooth muscle actin, vasa vasorum, vasa vasorum density, aortic wall thickness, thicknesses of the adventitia, media and intima were determined and correlated with the delamination forces in the longitudinal and circumferential directions of the vessel as determined from identical cadavers. The majority of the parameters determined did not indicate significant correlation with age, except for the calcium content and collagen maturation (enzymatic crosslinking). The main results concern differences between enzymatic and non-enzymatic crosslinking and those caused by the presence of atherosclerosis. The enzymatic crosslinking of collagen increased with age and was accompanied by a decrease in the delamination strength, while non-enzymatic crosslinking tended to decrease with age and was accompanied by an increase in the delamination strength. As the rate of calcification increased, the presence of atherosclerosis led to the formation of calcium phosphate plaques with higher solubility than the tissue without or with only mild signs of atherosclerosis. STATEMENT OF SIGNIFICANCE: This study presents a detailed biochemical and histological analysis of human aortic samples (ascending thoracic aorta, descending thoracic aorta and infrarenal abdominal aorta) taken from 34 cadavers. The contribution of this scientific study lies in the detailed biochemical comparison of the enzymatic and non-enzymatic glycosylation-derived crosslinks of vascular tissues and their influence on the delamination strength of the human aorta since, to the best of our knowledge, no such comprehensive studies exist in the literature. A further benefit concerns the notification of the limitations of the various analytical methods applied; an important factor that must be taken into account in such studies.

Machine learning reveals correlations between brain age and mechanics

Our brain undergoes significant micro- and macroscopic changes throughout its life cycle. It is therefore crucial to understand the effect of aging on the mechanical properties of the brain in order to develop accurate personalized simulations and diagnostic tools. Here we systematically probed the mechanical behavior of n=439 brain tissue samples in tension and compression, in different anatomical regions, for different axon orientations, across five age groups. We used Bayesian statistics to characterize the relation between brain age and mechanical properties and quantify uncertainties. Our results, based on our experimental data and material parameters for the isotropic Ogden and the anisotropic Gasser-Ogden-Holzapfel models, reveal a non-linear relationship between age and mechanics across the life cycle of the porcine brain. Both tensile and compressive shear moduli reached peak values ranging from 0.4-1.0 kPa in tension to 0.16-0.32 kPa in compression at three years of age. Anisotropy was most pronounced at six months, and then decreased. These results represent an important step in understanding age-dependent changes in the mechanical properties of brain tissue and provide the scientific basis for more accurate and realistic computational brain simulations. STATEMENT OF SIGNIFICANCE: In this paper, we investigate the age-dependent mechanical properties of brain tissue based on different deformation modes, anatomical regions, and axon orientations. Hierarchical Bayesian modeling was used to identify isotropic and anisotropic material parameters. The study reveals a nonlinear relationship between shear modulus, degree of anisotropy, and tension-compression asymmetry over the life cycle of the brain. By demonstrating the non-linearity of these relationships, the study fills a significant knowledge gap in current research. This work is a fundamental step in accurately characterizing the complex relationship between brain aging and mechanical properties.

Allogeneic abdominal non-vascularized rectus fascia transplantation without immunosuppression equals syngeneic transplantation in a rabbit model at short-term follow-up

Complex abdominal wall repair remains a major surgical challenge. In transplant patients, non-vascularized rectus fascia (NVRF) is successfully used to bridge the defect. To extrapolate this to non-transplant patients, we developed a rabbit model of NVRF-transplantation without immunosuppression comparing syngeneic versus allogeneic transplants. Short-term outcome (4 weeks) was evaluated macroscopically (ingrowth, seroma/hematoma, herniation, and infection), histologically at the graft interface and center (inflammation, neovascularization, and collagen deposition) and by mechanical testing. In both groups a similar macroscopic ingrowth of the NVRF was observed. In the syn-group, one seroma and one hematoma was seen. Two small herniations were detected at the suture line in the allo-group. No surgical site infections were observed. Histologically, graft neovascularization was observed in all animals. Infiltration of T-lymphocytes was seen at the graft interface in both groups, but more in the allo-group (p < 0.0001). Deposition of collagen was not different between groups. Macrophages were present in both groups around sutures and in the center more abundantly in the allo-group (p = 0.0001). Graft stiffness and strength were similar for both groups. With this model, we showed that allogeneic transplantation without immunosuppression results in favorable short-term inflammatory and mechanical outcomes. Long-term experiments are needed to further evaluate the effect on graft integration and hernia development.

Evaluation of an Inverse Method for Quantifying Spatially Variable Mechanics

Soft biological tissues often function as highly deformable membranes in vivo and exhibit impressive mechanical behavior effectively characterized by planar biaxial testing. The Generalized Anisotropic Inverse Mechanics (GAIM) method links full-field deformations and boundary forces from mechanical testing to quantify material properties of soft, anisotropic, heterogeneous tissues. In this study, we introduced an orthotropic constraint to GAIM to improve the quality and physical significance of its mechanical characterizations. We evaluated the updated GAIM method using simulated and experimental biaxial testing datasets obtained from soft tissue analogs (PDMS and TissueMend) with well-defined mechanical properties. GAIM produced stiffnesses (first Kelvin moduli, K1) that agreed well with previously published Young's moduli of PDMS samples. It also matched the stiffness moduli determined via uniaxial testing for TissueMend, a collagen-rich patch intended for tendon repair. We then conducted the first biaxial testing of TissueMend and confirmed that the sample was mechanically anisotropic via a relative anisotropy metric produced by GAIM. Next, we demonstrated the benefits of full-field laser micrometry in distinguishing between spatial variations in thickness and stiffness. Finally, we conducted an analysis to verify that results were independent of partitioning scheme. The success of the newly implemented constraints on GAIM suggests notable potential for applying this tool to soft tissues, particularly following the onset of pathologies that induce mechanical and structural heterogeneities.

Fibrotaxis: gradient-free, spontaneous and controllable droplet motion on soft solids

Most passive droplet transport strategies rely on spatial variations of material properties to drive droplet motion, leading to gradient-based mechanisms with intrinsic length scales that limit the droplet velocity or the transport distance. Here, we propose droplet fibrotaxis, a novel mechanism that leverages an anisotropic fiber-reinforced deformable solid to achieve spontaneous and gradient-free droplet transport. Using high-fidelity simulations, we identify the fluid wettability, fiber orientation, anisotropy strength and elastocapillary number as critical parameters that enable controllable droplet velocity and long-range droplet transport. Our results highlight the potential of fibrotaxis as a droplet transport mechanism that can have a strong impact on self-cleaning surfaces, water harvesting and medical diagnostics.

Finite element-based evaluation of the supraspinatus tendon biomechanical environment necessitates better clinical management based on tear location and thickness

Partial-thickness rotator cuff tears are a common cause of pain and disability and are central to developing full-thickness rotator cuff tears. However, limited knowledge exists regarding the alterations to the mechanical environment due to these lesions. Computational models that study the alterations to the mechanical environment of the supraspinatus tendon can help advance clinical management to avoid tear progression and provide a basis for surgical intervention. In this study, we use three-dimensional validated finite element models from six intact specimens to study the effects of low- and high-grade tears originating on the articular and bursal surfaces of the supraspinatus tendon. Bursal-sided tears generally had a lower failure load, modulus, and strain than articular-sided tears. Thus, caution should be taken when managing bursal-sided tears as they may be more susceptible to tear progression.

Adaptive integration of history variables in constrained mixture models for organ-scale growth and remodeling

In the last decades, many computational models have been developed to predict soft tissue growth and remodeling (G&R). The constrained mixture theory describes fundamental mechanobiological processes in soft tissue G&R and has been widely adopted in cardiovascular models of G&R. However, even after two decades of work, large organ-scale models are rare, mainly due to high computational costs (model evaluation and memory consumption), especially in long-range simulations. We propose two strategies to adaptively integrate history variables in constrained mixture models to enable large organ-scale simulations of G&R. Both strategies exploit that the influence of deposited tissue on the current mixture decreases over time through degradation. One strategy is independent of external loading, allowing the estimation of the computational resources ahead of the simulation. The other adapts the history snapshots based on the local mechanobiological environment so that the additional integration errors can be controlled and kept negligibly small, even in G&R scenarios with severe perturbations. We analyze the adaptively integrated constrained mixture model on a tissue patch for a parameter study and show the performance under different G&R scenarios. To confirm that adaptive strategies enable large organ-scale examples, we show simulations of different hypertension conditions with a real-world example of a biventricular heart discretized with a finite element mesh. In our example, adaptive integrations sped up simulations by a factor of three and reduced memory requirements to one-sixth. The reduction of the computational costs gets even more pronounced for simulations over longer periods. Adaptive integration of the history variables allows studying more finely resolved models and longer G&R periods while computational costs are drastically reduced and largely constant in time.

Non-invasive regional parameter identification of degenerated human meniscus

Accurate identification of local changes in the biomechanical properties of the normal and degenerative meniscus is critical to better understand knee joint osteoarthritis onset and progression. Ex-vivo material characterization is typically performed on specimens obtained from different locations, compromising the tissue's structural integrity and thus altering its mechanical behavior. Therefore, the aim of this in-silico study was to establish a non-invasive method to determine the region-specific material properties of the degenerated human meniscus. In a previous experimental magnetic resonance imaging (MRI) study, the spatial displacement of the meniscus and its root attachments in mildly degenerated (n = 12) and severely degenerated (n = 12) cadaveric knee joints was determined under controlled subject-specific axial joint loading. To simulate the experimental response of the lateral and medial menisci, individual finite element models were created utilizing a transverse isotropic hyper-poroelastic constitutive material formulation. The superficial displacements were applied to the individual models to calculate the femoral reaction force in an inverse finite element analysis. During particle swarm optimization, the four most sensitive material parameters were varied to minimize the error between the femoral reaction force and the force applied in the MRI loading experiment. Individual global and regional parameter sets were identified. In addition to in-depth model verification, prediction errors were determined to quantify the reliability of the identified parameter sets. Both compressibility of the solid meniscus matrix (+141 %, p ≤ 0.04) and hydraulic permeability (+53 %, p ≤ 0.04) were significantly increased in the menisci of severely degenerated knees compared to mildly degenerated knees, irrespective of the meniscus region. By contrast, tensile and shear properties were unaffected by progressive knee joint degeneration. Overall, the optimization procedure resulted in reliable and robust parameter sets, as evidenced by mean prediction errors of <1 %. In conclusion, the proposed approach demonstrated high potential for application in clinical practice, where it might provide a non-invasive diagnostic tool for the early detection of osteoarthritic changes within the knee joint.

Analysis of material parameter uncertainty propagation in preoperative flap suture simulation

Skin flap transplantation is the most commonly used method to repair tissue defect and cover the wound. In clinic, finite element method is often used to design the pre-operation scheme of flap suture. However, the material parameters of skin flap are uncertain due to experimental errors and differences in body parts. How to consider the influence of material parameter uncertainty on the mechanical response of flap suture in the finite element modeling is an urgent problem to be solved at present. Therefore, the influence of material parameter uncertainty propagation in skin flap suture simulation was studied, Firstly, the geometric model of clinical patient's hand wound was constructed by using reverse modeling technology, the patient's three-dimensional wound was unfolded into a flat surface by using curved surface expansion method, yielding a preliminary design contour for the patient's transplant flap. Based on the acquired patient wound geometry model, the finite element model of flap suture with different fiber orientations and different sizes was constructed in Abaqus, and the uncertainty propagation analysis method based on Monte Carlo simulation combined with surrogate model technology was further used to analyze the stress response of flap suture considering the uncertainty of material parameters. Results showed that the overall stress value was relatively lower when the average fiber orientation was 45°. which could be used as the optimal direction for the flap excision. when the preliminary design contour of the flap was scaled down within 90%, the stress value after flap suturing remained within a safe range.

Tissue expansion mitigates radiation-induced skin fibrosis in a porcine model

Tissue expansion (TE) is the primary method for breast reconstruction after mastectomy. In many cases, mastectomy patients undergo radiation treatment (XR). Radiation is known to induce skin fibrosis and is one of the main causes for complications during post-mastectomy breast reconstruction. TE, on the other hand, induces a pro-regenerative response that culminates in growth of new skin. However, the combined effect of XR and TE on skin mechanics is unknown. Here we used the porcine model of TE to study the effect of radiation on skin fibrosis through biaxial testing, histological analysis, and kinematic analysis of skin deformation over time. We found that XR leads to stiffening of skin compared to control based on a shift in the transition stretch (transition between a low stiffness and an exponential stress-strain region characteristic of collagenous tissue) and an increase in the high modulus (modulus computed with stress-stretch data past the transition point). The change in transition stretch can be explained by thicker, more aligned collagen fiber bundles measured in histology images. Skin subjected to both XR+TE showed similar microstructure to controls as well as similar biaxial response, suggesting that physiological remodeling of collagen induced by TE partially counteracts pro-fibrotic XR effects. Skin growth was indirectly assessed with a kinematic approach that quantified increase in permanent area changes without reduction in thickness, suggesting production of new tissue driven by TE even in the presence of radiation treatment. Future work will focus on the detailed biological mechanisms by which TE counteracts radiation induced fibrosis. STATEMENT OF SIGNIFICANCE: Breast cancer is the most prevalent in women and its treatment often results in total breast removal (mastectomy), followed by reconstruction using tissue expanders. Radiation, which is used in about a third of breast reconstruction cases, can lead to significant complications. The timing of radiation treatment remains controversial. Radiation is known to cause immediate skin damage and long-term fibrosis. Tissue expansion leads to a pro-regenerative response involving collagen remodeling. Here we show that tissue expansion immediately prior to radiation can reduce the level of radiation-induced fibrosis. Thus, we anticipate that this new evidence will open up new avenues of investigation into how the collagen remodeling and pro-regenerative effects of tissue expansion can be leverage to prevent radiation-induced fibrosis.

Fluid-structure interaction analysis of a healthy aortic valve and its surrounding haemodynamics

The opening and closing dynamics of the aortic valve (AV) has a strong influence on haemodynamics in the aortic root, and both play a pivotal role in maintaining normal physiological functions of the valve. The aim of this study was to establish a subject-specific fluid-structure interaction (FSI) workflow capable of simulating the motion of a tricuspid healthy valve and the surrounding haemodynamics under physiologically realistic conditions. A subject-specific aortic root was reconstructed from magnetic resonance (MR) images acquired from a healthy volunteer, whilst the valve leaflets were built using a parametric model fitted to the subject-specific aortic root geometry. The material behaviour of the leaflets was described using the isotropic hyperelastic Ogden model, and subject-specific boundary conditions were derived from 4D-flow MR imaging (4D-MRI). Strongly coupled FSI simulations were performed using a finite volume-based boundary conforming method implemented in FlowVision. Our FSI model was able to simulate the opening and closing of the AV throughout the entire cardiac cycle. Comparisons of simulation results with 4D-MRI showed a good agreement in key haemodynamic parameters, with stroke volume differing by 7.5% and the maximum jet velocity differing by less than 1%. Detailed analysis of wall shear stress (WSS) on the leaflets revealed much higher WSS on the ventricular side than the aortic side and different spatial patterns amongst the three leaflets.

Comparing continuum and direct fiber models of soft tissues: An ocular biomechanics example reveals that continuum models may artificially disrupt the strains at both the tissue and fiber levels

Collagen fibers are the main load-bearing component of soft tissues but difficult to incorporate into models. Whilst simplified homogenization models suffice for some applications, a thorough mechanistic understanding requires accurate prediction of fiber behavior, including both detailed fiber-level strains and long-distance transmission. Our goal was to compare the performance of a continuum model of the optic nerve head (ONH) built using conventional techniques with a fiber model we recently introduced which explicitly incorporates the complex 3D organization and interaction of collagen fiber bundles [1]. To ensure a fair comparison, we constructed the continuum model with identical geometrical, structural, and boundary specifications as for the fiber model. We found that: 1) although both models accurately matched the intraocular pressure (IOP)-induced globally averaged displacement responses observed in experiments, they diverged significantly in their ability to replicate specific 3D tissue-level strain patterns. Notably, the fiber model faithfully replicated the experimentally observed depth-dependent variability of radial strain, the ring-like pattern of meridional strain, and the radial pattern of circumferential strain, whereas the continuum model failed to do so; 2) the continuum model disrupted the strain transmission along each fiber, a feature captured well by the fiber model. These results demonstrate limitations of the conventional continuum models that rely on homogenization and affine deformation assumptions, which render them incapable of capturing some complex tissue-level and fiber-level deformations. Our results show that the strengths of explicit fiber modeling help capture intricate ONH biomechanics. They potentially also help modeling other fibrous tissues. STATEMENT OF SIGNIFICANCE: Understanding the mechanics of fibrous tissues is crucial for advancing knowledge of various diseases. This study uses the ONH as a test case to compare conventional continuum models with fiber models that explicitly account for the complex fiber structure. We found that the fiber model captured better the biomechanical behaviors at both the tissue level and the fiber level. The insights gained from this study demonstrate the significant potential of fiber models to advance our understanding of not only glaucoma pathophysiology but also other conditions involving fibrous soft tissues. This can contribute to the development of therapeutic strategies across a wide range of applications.

A viscoelastic constitutive framework for aging muscular and elastic arteries

The evolution of arterial biomechanics and microstructure with age and disease plays a critical role in understanding the health and function of the cardiovascular system. Accurately capturing these adaptative processes and their effects on the mechanical environment is critical for predicting arterial responses. This challenge is exacerbated by the significant differences between elastic and muscular arteries, which have different structural organizations and functional demands. In this study, we aim to shed light to these adaptive processes by comparing the viscoelastic mechanics of autologous thoracic aortas (TA) and femoropopliteal arteries (FPA) in different age groups. We have extended our fractional viscoelastic framework, originally developed for FPA, to both types of arteries. To evaluate this framework, we analyzed experimental mechanical data from TA and FPA specimens from 21 individuals aged 13 to 73 years. Each specimen was subjected to a multi-ratio biaxial mechanical extension and relaxation test complemented by bidirectional histology to quantify the structural density and microstructural orientations. Our new constitutive model accurately captured the mechanical responses and microstructural differences of the tissues and closely matched the experimentally measured densities. It was found that the viscoelastic properties of collagen and smooth muscle cells (SMCs) in both the FPA and TA remained consistent with age, but the viscoelasticity of the SMCs in the FPA was twice that of the TA. Additionally, changes in collagen nonlinearity with age were similar in both TA and FPA. This model provides valuable insights into arterial mechanophysiology and the effects of pathological conditions on vascular biomechanics. STATEMENT OF SIGNIFICANCE: Developing durable treatments for arterial diseases necessitates a deeper understanding of how mechanical properties evolve with age in response to mechanical environments. In this work, we developed a generalized viscoelastic constitutive model for both elastic and muscular arteries and analyzed both the thoracic aorta (TA) and the femoropopliteal artery (FPA) from 21 donors aged 13 to 73. The derived parameters correlate well with histology, allowing further examination of how viscoelasticity evolves with age. Correlation between the TA and FPA of the same donors suggest that the viscoelasticity of the FPA may be influenced by the TA, necessitating more detailed analysis. In summary, our new model proves to be a valuable tool for studying arterial mechanophysiology and exploring pathological impacts.

Collagen Induces Anisotropy in Fingertip Subcutaneous Tissues During Contact

The subcutaneous mechanical response of the fingertip is highly anisotropic due to the presence of a network of collagen fibers linking the outer skin layer to the bone. The impact of this anisotropy on the fingerpad deformation, which had not been studied until now, is here demonstrated using a two-dimensional finite element model of a transverse section of the finger. Different distributions of fiber orientations are considered: radial (physiologic), circumferential, and random (isotropic). The three variants of the model are assessed using experimental observations of a finger pressed on a flat surface. Predictions relying on the physiological orientation of fibers best reproduce experimental trends. Our results show that the orientation of fibers significantly influences the distribution of internal strains and stresses. This leads to a sudden change in the profile of contact pressure when transitioning from sticking to slipping. Interpreted in terms of tactile perception or sensation, these variations might represent important sensory cues for partial slip detection. This is also valuable information for the development of haptic devices.

Multiscale structure and function of the aortic valve apparatus

Whereas studying the aortic valve in isolation has facilitated the development of life-saving procedures and technologies, the dynamic interplay of the aortic valve and its surrounding structures is vital to preserving their function across the wide range of conditions encountered in an active lifestyle. Our view is that these structures should be viewed as an integrated functional unit, here referred to as the aortic valve apparatus (AVA). The coupling of the aortic valve and root, left ventricular outflow tract, and blood circulation is crucial for AVA's functions: unidirectional flow out of the left ventricle, coronary perfusion, reservoir function, and support of left ventricular function. In this review, we explore the multiscale biological and physical phenomena that underlie the simultaneous fulfillment of these functions. A brief overview of the tools used to investigate the AVA, such as medical imaging modalities, experimental methods, and computational modeling, specifically fluid-structure interaction (FSI) simulations, is included. Some pathologies affecting the AVA are explored, and insights are provided on treatments and interventions that aim to maintain quality of life. The concepts explained in this article support the idea of AVA being an integrated functional unit and help identify unanswered research questions. Incorporating phenomena through the molecular, micro, meso, and whole tissue scales is crucial for understanding the sophisticated normal functions and diseases of the AVA.

Review of Machine Learning Techniques in Soft Tissue Biomechanics and Biomaterials

BACKGROUND AND OBJECTIVE

Advanced material models and material characterization of soft biological tissues play an essential role in pre-surgical planning for vascular surgeries and transcatheter interventions. Recent advances in heart valve engineering, medical device and patch design are built upon these models. Furthermore, understanding vascular growth and remodeling in native and tissue-engineered vascular biomaterials, as well as designing and testing drugs on soft tissue, are crucial aspects of predictive regenerative medicine. Traditional nonlinear optimization methods and finite element (FE) simulations have served as biomaterial characterization tools combined with soft tissue mechanics and tensile testing for decades. However, results obtained through nonlinear optimization methods are reliable only to a certain extent due to mathematical limitations, and FE simulations may require substantial computing time and resources, which might not be justified for patient-specific simulations. To a significant extent, machine learning (ML) techniques have gained increasing prominence in the field of soft tissue mechanics in recent years, offering notable advantages over conventional methods. This review article presents an in-depth examination of emerging ML algorithms utilized for estimating the mechanical characteristics of soft biological tissues and biomaterials. These algorithms are employed to analyze crucial properties such as stress-strain curves and pressure-volume loops. The focus of the review is on applications in cardiovascular engineering, and the fundamental mathematical basis of each approach is also discussed.

METHODS

The review effort employed two strategies. First, the recent studies of major research groups actively engaged in cardiovascular soft tissue mechanics are compiled, and research papers utilizing ML and deep learning (DL) techniques were included in our review. The second strategy involved a standard keyword search across major databases. This approach provided 11 relevant ML articles, meticulously selected from reputable sources including ScienceDirect, Springer, PubMed, and Google Scholar. The selection process involved using specific keywords such as "machine learning" or "deep learning" in conjunction with "soft biological tissues", "cardiovascular", "patient-specific," "strain energy", "vascular" or "biomaterials". Initially, a total of 25 articles were selected. However, 14 of these articles were excluded as they did not align with the criteria of focusing on biomaterials specifically employed for soft tissue repair and regeneration. As a result, the remaining 11 articles were categorized based on the ML techniques employed and the training data utilized.

RESULTS

ML techniques utilized for assessing the mechanical characteristics of soft biological tissues and biomaterials are broadly classified into two categories: standard ML algorithms and physics-informed ML algorithms. The standard ML models are then organized based on their tasks, being grouped into Regression and Classification subcategories. Within these categories, studies employ various supervised learning models, including support vector machines (SVMs), bagged decision trees (BDTs), artificial neural networks (ANNs) or deep neural networks (DNNs), and convolutional neural networks (CNNs). Additionally, the utilization of unsupervised learning approaches, such as autoencoders incorporating principal component analysis (PCA) and/or low-rank approximation (LRA), is based on the specific characteristics of the training data. The training data predominantly consists of three types: experimental mechanical data, including uniaxial or biaxial stress-strain data; synthetic mechanical data generated through non-linear fitting and/or FE simulations; and image data such as 3D second harmonic generation (SHG) images or computed tomography (CT) images. The evaluation of performance for physics-informed ML models primarily relies on the coefficient of determinationR 2 . In contrast, various metrics and error measures are utilized to assess the performance of standard ML models. Furthermore, our review includes an extensive examination of prevalent biomaterial models that can serve as physical laws for physics-informed ML models.

CONCLUSION

ML models offer an accurate, fast, and reliable approach for evaluating the mechanical characteristics of diseased soft tissue segments and selecting optimal biomaterials for time-critical soft tissue surgeries. Among the various ML models examined in this review, physics-informed neural network models exhibit the capability to forecast the mechanical response of soft biological tissues accurately, even with limited training samples. These models achieve highR 2 values ranging from 0.90 to 1.00. This is particularly significant considering the challenges associated with obtaining a large number of living tissue samples for experimental purposes, which can be time-consuming and impractical. Additionally, the review not only discusses the advantages identified in the current literature but also sheds light on the limitations and offers insights into future perspectives.

Mechanical modeling of the petiole-lamina transition zone of peltate leaves

Plant leaves have to deal with various environmental influences. While the mechanical properties of petiole and lamina are generally well studied, only few studies focused on the properties of the transition zone joining petiole and lamina. Especially in peltate leaves, characterised by the attachment of the petiole to the abaxial side of the lamina, the 3D leaf architecture imposes specific mechanical stresses on the petiole and petiole-lamina transition zone. Several principles of internal anatomical organisation have been identified. Since the mechanical characterisation of the transition zone by direct measurements is difficult, we explored the mechanical properties and load-bearing mechanisms by finite-element simulations. We simulate the petiole-lamina transition zone with five different fibre models that were abstracted from CT data. For comparison, three different load cases were defined and tested in the simulation. In the proposed model, the fibres are represented in a smeared sense, where we considered transverse isotropic behavior in elements containing fibres. In a pre-processing step, we determined the fibre content, direction, and dispersion and fed them into our model. The simulations show that initially, matrix and fibres carry the load together. After relaxation of the stresses in the matrix, the fibres carry most of the load. Load dissipation and stiffness differ according to fibre arrangement and depend, among other things, on orientation and cross-linking of the fibres and fibre amount. Even though the presented method is a simplified approach, it is able to show the different load-bearing capacities of the presented fibre arrangements. STATEMENT OF SIGNIFICANCE: In plant leaves, the petiole-lamina transition zone is an important structural element facilitating water and nutrient transport, as well as load dissipation from the lamina into the petiole. Especially in peltate leaves, the 3D leaf architecture imposes specific mechanical stresses on the petiole-lamina transition zone. This study aims at investigating its mechanical behavior using finite-element simulations. The proposed continuum mechanical anisotropic viscoelastic material model is able to simulate the transition zone under different loads while also considering different fibre arrangements. The simulations highlight the load-bearing mechanisms of different fibre organisations, show the mechanical significance of the petiole-lamina transition zone and can be used in the design of a future biomimetic junction in construction.

Does free tendon length influence the injury risk of the Achilles tendon? A finite element study

Purpose

The Achilles tendon is a common injury site, but anatomical risk factors for injury are relatively unexplored in the literature. This study aimed to evaluate whether changes in free tendon length would influence the results of a simulated rupture of the Achilles tendon.

Methods

Using a previously validated 3D finite element model of the free and aponeurotic Achilles tendon as a basis, two additional finite element models with 25% decreased and increased free tendon lengths were created. The finite element models were sequentially loaded from 2500 to 3500N in 100N increments, and the total volume of elements exhibiting a maximal principal strain above 10% was recorded. An Achilles tendon rupture was considered to have occurred when a continuous group of elements with a volume of at least 3 mm3 exhibited a maximum principal strain above 10%. Models were compared regarding the smallest load that met the rupture criterion and plots of the percentage of elements exhibiting maximum principal strains above 10% across the loading range. Sensitivity analyses assessed the influence of subtendon division variations and subtendon sliding restriction on the results.

Results

Rupture loads and plots of the percentage of elements with maximum principal strains above 10% were similar between models, regardless of the free tendon length. No models met the rupture criterion when simulations were run without subtendon sliding. Rupture loads in the subtendon division variation models were correlated with the subtendon cross-sectional areas.

Conclusions

The simulated rupture results of the Achilles tendon were sensitive to variations in subtendon cross-sectional areas but not in free tendon length.

Level of Evidence

Level V.

A universal material model subroutine for soft matter systems

Soft materials play an integral part in many aspects of modern life including autonomy, sustainability, and human health, and their accurate modeling is critical to understand their unique properties and functions. Today's finite element analysis packages come with a set of pre-programmed material models, which may exhibit restricted validity in capturing the intricate mechanical behavior of these materials. Regrettably, incorporating a modified or novel material model in a finite element analysis package requires non-trivial in-depth knowledge of tensor algebra, continuum mechanics, and computer programming, making it a complex task that is prone to human error. Here we design a universal material subroutine, which automates the integration of novel constitutive models of varying complexity in non-linear finite element packages, with no additional analytical derivations and algorithmic implementations. We demonstrate the versatility of our approach to seamlessly integrate innovative constitutive models from the material point to the structural level through a variety of soft matter case studies: a frontal impact to the brain; reconstructive surgery of the scalp; diastolic loading of arteries and the human heart; and the dynamic closing of the tricuspid valve. Our universal material subroutine empowers all users, not solely experts, to conduct reliable engineering analysis of soft matter systems. We envision that this framework will become an indispensable instrument for continued innovation and discovery within the soft matter community at large.

Foundational Engineering of Artificial Blood Vessels' Biomechanics: The Impact of Wavy Geometric Designs

The design of wavy structures and their mechanical implications on artificial blood vessels (ABVs) have been insufficiently studied in the existing literature. This research aims to explore the influence of various wavy geometric designs on the mechanical properties of ABVs and to establish a foundational framework for advancing and applying these designs. Computer-aided design (CAD) and finite element method (FEM) simulations, in conjunction with physical sample testing, were utilized. A geometric model incorporating concave and convex curves was developed and analyzed with a symbolic mathematical tool. Subsequently, a total of ten CAD models were subjected to increasing internal pressures using a FEM simulation to evaluate the expansion of internal areas. Additionally, physical experiments were conducted further to investigate the expansion of ABV samples under pressure. The results demonstrated that increased wave numbers significantly enhance the flexibility of ABVs. Samples with 22 waves exhibited a 45% larger area under 24 kPa pressure than those with simple circles. However, the increased number of waves also led to undesirable high-pressure gradients at elevated pressures. Furthermore, a strong correlation was observed between the experimental outcomes and the simulation results, with a notably low error margin, ranging from 19.88% to 3.84%. Incorporating wavy designs into ABVs can effectively increase both vessel flexibility and the internal area under pressure. Finally, it was found that expansion depending on the wave number can be efficiently modeled with a simple linear equation, which could be utilized in future designs.

Comparing continuum and direct fiber models of soft tissues. An ocular biomechanics example reveals that continuum models may artificially disrupt the strains at both the tissue and fiber levels

Collagen fibers are the main load-bearing component of soft tissues but difficult to incorporate into models. Whilst simplified homogenization models suffice for some applications, a thorough mechanistic understanding requires accurate prediction of fiber behavior, including both detailed fiber-level strains and long-distance transmission. Our goal was to compare the performance of a continuum model of the optic nerve head (ONH) built using conventional techniques with a fiber model we recently introduced which explicitly incorporates the complex 3D organization and interaction of collagen fiber bundles [1]. To ensure a fair comparison, we constructed the continuum model with identical geometrical, structural, and boundary specifications as for the fiber model. We found that: 1) although both models accurately matched the intraocular pressure (IOP)-induced globally averaged displacement responses observed in experiments, they diverged significantly in their ability to replicate specific 3D tissue-level strain patterns. Notably, the fiber model faithfully replicated the experimentally observed depth-dependent variability of radial strain, the ring-like pattern of meridional strain, and the radial pattern of circumferential strain, whereas the continuum model failed to do so; 2) the continuum model disrupted the strain transmission along each fiber, a feature captured well by the fiber model. These results demonstrate limitations of the conventional continuum models that rely on homogenization and affine deformation assumptions, which render them incapable of capturing some complex tissue-level and fiber-level deformations. Our results show that the strengths of explicit fiber modeling help capture intricate ONH biomechanics. They potentially also help modeling other fibrous tissues.

Biomechanics of annulus fibrosus: Elastic fiber simplification and degenerative impact on damage initiation and propagation

This study addresses three primary objectives related to lumbar intervertebral disc (IVD) biomechanics under ramping quasi-static loading conditions. First, we explore the conditions justifying the simplification of axisymmetric elastic fiber families into single fiber bundles through discretized strain energy functions. Simulations reveal that a concentration factor exceeding 10 allows for a consistent deviation below 10% between simplified and non-simplified responses. Second, we investigate the impact of elastic fibers on the physiological stiffness in IVDs, revealing minimal influence on biological motions but significant effects on degeneration. Lastly, we examine the initiation and progression of annulus fibrosus (AF) damage. Our findings confirm the validity of simplifying elastic fiber families and underscore the necessity of considering elastic fiber damage in biomechanical studies of AF tissues. Elastic fibers contribute to increased biaxial stretch stiffness, and their damage significantly affects the loading capacity of the inner AF. Additionally, degeneration significantly alters the susceptibility to damage in the AF, with specific regions exhibiting higher vulnerability. Damage tends to extend circumferentially and radially, emphasizing the regional variations in collagen and elastic fiber properties. This study offers useful insights for refining biomechanical models, paving the way for a more comprehensive understanding of IVD responses and potential clinical implications.

Effect of bioprosthetic leaflet anisotropy on stent dynamics of Transcatheter Aortic Valve Replacement devices

The assessment of stent fatigue in Transcatheter Aortic Valve Replacement (TAVR) systems is critical for the design of next-generation devices, both in vitro and in vivo. The mechanical properties of the bioprosthetic heart valves (BHVs) have a significant impact on the fatigue life of the metallic stent and thus must be taken into consideration when evaluating new TAVR device designs. This study aims to investigate the relationship between BHV anisotropic behaviour and the asymmetric deflections of the stent frame observed during in vitro testing. An explicit dynamics finite element model of the nitinol stent with attached bioprosthetic valve leaflets was developed to evaluate the deflections of the TAVR device under haemodynamic loading. Our results demonstrate that pericardium behaviour plays a dominant role in determining stent frame deflection. The anisotropic behaviour of the leaflets, resulting from collagen fibre orientation, affects the extent of deflection encountered by each commissure of the frame. This leads to asymmetric variation in frame deflection that can influence the overall fatigue life of the nitinol stent. This study highlights the importance of considering both the flexible nature of the metallic stent as well as the leaflet anisotropic behaviour in the design and fatigue assessment of TAVR systems.

Significance of Dynamic Axial Stretching on Estimating Biomechanical Behavior and Properties of the Human Ascending Aorta

Contrary to most vessels, the ascending thoracic aorta (ATA) not only distends but also elongates in the axial direction. The purpose of this study is to investigate the biomechanical behavior of the ascending thoracic aorta (ATA) in response to dynamic axial stretching during the cardiac cycle. In addition, the implications of neglecting this dynamic axial stretching when estimating the constitutive model parameters of the ATA are investigated. The investigations were performed through in silico simulations by assuming a Gasser-Ogden-Holzapfel (GOH) constitutive model representative of ATA tissue material. The GOH model parameters were obtained from biaxial tests performed on four human ATA tissues in a previous study. Pressure-diameter curves were simulated as synthetic data to assess the effect of neglecting dynamic axial stretching on estimating constitutive model parameters. Our findings reveal a significant increase in axial stress (~ 16%) and stored strain energy (~ 18%) in the vessel when dynamic axial stretching is considered, as opposed to assuming a fixed axial stretch. All but one artery showed increased volume compliance while considering a dynamic axial stretching condition. Furthermore, we observe a notable difference in the estimated constitutive model parameters when dynamic axial stretching of the ATA is neglected, compared to the ground truth model parameters. These results underscore the critical importance of accounting for axial deformations when conducting in vivo biomechanical characterization of the ascending thoracic aorta.

Universal phase-field mixture representation of thermodynamics and shock-wave mechanics in porous soft biologic continua

A continuum mixture theory is formulated for large deformations, thermal effects, phase interactions, and degradation of soft biologic tissues suitable at high pressures and low to very high strain rates. Tissues consist of one or more solid and fluid phases and can demonstrate nonlinear anisotropic elastic, viscoelastic, thermoelastic, and poroelastic physics. Under extreme deformations or shock loading, tissues may fracture, tear, or rupture. Existing models do not account for all physics simultaneously, and most poromechanics and soft-tissue models assume incompressibility of some or all constituents, generally inappropriate for modeling shock waves or extreme compressions. Motivated by these prior limitations, a thermodynamically consistent formulation that combines a continuum theory of mixtures, compressible nonlinear anisotropic thermoelasticity, viscoelasticity, and phase-field mechanics of fracture is constructed to resolve the pertinent physics. A metric tensor of generalized Finsler space supplies geometric insight on effects of rearrangements of microstructure, for example degradation, growth, and remodeling. Shocks are modeled as singular surfaces. Hugoniot states and shock decay are analyzed: Solutions account for concurrent viscoelasticity, fracture, and interphase momentum and energy exchange not all contained in previous analyses. Suitability of the framework for representing blood, skeletal muscle, and liver is demonstrated by agreement with experimental data and observations across a range of loading rates and pressures. Insight into previously unresolved physics is obtained, for example importance of rate sensitivity of damage and quantification of effects of dissipation from viscoelasticity and phase interactions on shock decay.

Calibration of Holzapfel-Gasser-Ogden collateral ligament properties in a hybrid post-arthroplasty knee joint model for laxity testing

Knee collateral ligaments play a vital role in providing frontal-plane stability in post-total knee arthroplasty (TKA) knees. Finite element models can utilize computationally efficient one-dimensional springs or more physiologically accurate three-dimensional continuum elements like the Holzapfel-Gasser-Ogden (HGO) formulation. However, there is limited literature defining subject-specific mechanical properties, particularly for the HGO model. In this study, we propose a co-simulation framework to obtain subject-specific material parameters for an HGO-based finite element ligament model integrated into a rigid-body model of the post-TKA knee. Our approach achieves comparable accuracy to spring formulations while significantly reducing coefficient calibration time and demonstrating improved correlation with reference knee kinematics and ligament strains throughout the tested loading range.

Lung Mechanics: Material Characterization of Pulmonary Constituents for an Experimentally Informed Computational Pipeline

The lung comprises multiple components including the parenchyma, airways, and visceral pleura, where each constituent displays specific material properties that together govern the whole organ's properties. The structural and mechanical complexity of the lung has historically undermined its comprehensive characterization, especially compared to other biological organs, such as the heart or bones. This knowledge void is particularly remarkable when considering that pulmonary disease is one of the leading causes of morbidity and mortality across the globe. Establishing the mechanical properties of the lung is central to formulating a baseline understanding of its operation, which can facilitate investigations of diseased states and how the lung will potentially respond to clinical interventions. Here, we present established and widely accepted experimental protocols for pulmonary material quantification, specifying how to extract, prepare, and test each type of lung constituent under planar biaxial tensile loading to investigate the mechanical properties, such as physiological stress-strain profiles, anisotropy, and viscoelasticity. These methods are presented across an array of commonly studied species (murine, rat, and porcine). Additionally, we highlight how such material properties may inform the construction of an inverse finite element model, which is central to implementing predictive computational tools for accurate disease diagnostics and optimized medical treatments. These presented methodologies are aimed at supporting research advancements in the field of pulmonary biomechanics and to help inaugurate future novel studies. © 2024 The Author(s). Current Protocols published by Wiley Periodicals LLC. Basic Protocol 1: General procedures in lung biaxial testing Alternate Protocol 1: Parenchymal-specific preparation and loading procedures Alternate Protocol 2: Airway-specific preparation and loading procedures Alternate Protocol 3: Visceral pleura-specific preparation and loading procedures Basic Protocol 2: Computational analysis.

Effect of Tear Size and Location on Supraspinatus Tendon Strain During Activities of Daily Living and Physiotherapy

The supraspinatus tendon plays a crucial role in shoulder abduction, making it one of the common structures affected by injury. Clinically, crescent-shaped tears are the most commonly seen tear shape. By developing six specimen-specific, three-dimensional, supraspinatus-infraspinatus finite element model with heterogeneous material properties, this study aimed to examine the changes in tissue deformation (maximum principal strain) of the supraspinatus tendon due to specimen-specific material properties and rotator cuff tear size. FE models with small- and medium-sized full-thickness crescent-shaped tears were subjected to loads seen during activities of daily living and physiotherapy. Six fresh-frozen cadaveric shoulders were dissected to mechanically test the supraspinatus tendon and develop and validate FE models that can be used to assess changes in strain due to small (< 1 cm, equivalent to 20-30% of the tendon width) and medium-sized (1-3 cm, equivalent to 40-50% of the tendon width) tears that are located in the middle and posterior regions of the supraspinatus tendon. FE predictions of maximum principal strain at the tear tips were examined to determine whether failure strain was reached during activities of daily living (drinking and brushing teeth) and physiotherapy exercises (prone abduction and external rotation at 90° abduction). No significant differences were observed between the middle and posterior tear failure loads for small- and medium-sized tears. For prone abduction, there was a potential risk for tear progression (exceeded failure strain) for medium-sized tears in the supraspinatus tendon's middle and posterior regions. For external rotation at 90° abduction, one model with a middle tear and two with posterior tears experienced failure. For all daily activity loads, the strain never exceeded the failure strain. Our three-dimensional supraspinatus-infraspinatus FE model shows that small tears appear unlikely to progress based on the regional strain response; however, medium-sized tears are at higher risk during more strenuous physiotherapy exercises. Furthermore, differences in patient-specific tendon material properties are important in determining whether the tear will progress. Therefore, patient-specific management plans based on tear size may be beneficial to improve clinical outcomes.

Progression of partial to complete ruptures of the Achilles tendon during rehabilitation: A study using a finite element model

Substantial research on complete Achilles tendon ruptures is available, but guidance on partial ruptures is comparatively sparse. Conservative management is considered acceptable in partial tendon ruptures affecting less than 50% of the tendon's width, but supporting experimental evidence is currently lacking. Using a previously validated finite element model of the Achilles tendon, this study aimed to assess whether loading conditions simulating an early functional rehabilitation protocol could elicit progression to a complete rupture in partial ruptures of varying severity. In silico tendon rupture simulations were performed to locate the most likely rupture site for least, moderate, and extreme subtendon twist configurations. These three models were split at the corresponding rupture site and two sets of partial ruptures were created for each, starting from the medial and lateral sides, and ranging from 10% to 50% loss of continuity. Simulations were conducted with material parameters from healthy and tendinopathic tendons. Partial ruptures were considered to progress if the volume of elements showing a maximum principal strain above 10% exceeded 3 mm3. To assess whether the tendinopathic tendons typical geometric characteristics could compensate for the inferior material properties found in tendinopathy, an additional model with increased cross-sectional area in the free tendon region was developed. Progression to complete ruptures occurred even with less than a 50% loss of continuity, regardless of subtendon twisting, and material parameters. The tendinopathic tendon model with increased cross-sectional area showed similar results. These findings suggest the current criteria for surgical treatment of partial ruptures should be reconsidered. Statement of clinical significance: The clinical significance and most appropriate treatment of partial ruptures of the Achilles tendon is unclear. Despite the widespread use of the "50% rule" in treatment decisions of partial tendon ruptures, experimental evidence supporting it is missing. The present study provides new data, from a validated aponeurotic and free Achilles tendon finite element model, showing that partial ruptures may progress to complete ruptures under loading conditions elicited from functional rehabilitation protocols, even for partial ruptures affecting less than 50% of the tendon's width. Under these novel findings, the current criteria for surgical treatment of partial ruptures should be reconsidered.

Characterisation of human penile tissue properties using experimental testing combined with multi-target inverse finite element modelling

This paper presents an inverse finite element (FE) approach aimed at estimating multi-layered human penile tissues. The inverse FE approach integrates experimental force-displacement and boundary deformation data of penile tissues with a developed FE model and uses new experimental data on human penile tissue. The experimental study encompasses whole organ plate-compression tests and individual layer tensile and compression tests, providing comprehensive insights into the tissue's mechanical behaviour. The biomechanical characterisation of penile tissue is of crucial significance for understanding its mechanical behaviour under various physiological and pathological conditions. The FE model is constructed using the realistic geometry of the penile segment and appropriate constitutive models for each tissue layer to leverage the accuracy and consistency of the model. Through systematic variation of tissue parameters in the inverse FE algorithm, simulations achieve the best match with both force-displacement and deformed boundary results obtained from the whole organ plate-compression tests. Test results from individual tissue layers are also utilised to assess the estimated parameters. The proposed inverse FE approach allows for the estimation of penile tissue parameters with high precision and reliability, shedding light on the mechanical properties of this complex biological organ. This work has applications not only in urology but also for researchers in various disciplines of biomechanics. As a result, our study contributes to advancing the understanding of human penile tissue mechanics whilst the methodology could also be applied to a range of other soft biological tissues. STATEMENT OF SIGNIFICANCE: This research uses a multi-target inverse finite element (FE) approach for estimating the material parameters of human penile tissues. By integrating experimental data and a realistic FE model, this study achieves high-precision constitutive model parameter estimation, offering key insights into penile tissue mechanics under various loading conditions. The significance of this work lies in the use of this inverse FE approach for fresh-frozen human penile tissues, to identify the mechanical properties and constitutive models for both segregated tunica albuginea and corpus cavernosum as well as intact penile tissue segments. The study's scientific impact lies in its advancement of the understanding of human urological tissue mechanics, impacting researchers and clinicians alike.

Preliminary establishment and validation of the inversion method for growth and remodeling parameters of patient-specific abdominal aortic aneurysm

Traditional medical imaging and biomechanical studies have challenges in analyzing the long-term evolution process of abdominal aortic aneurysm (AAA). The homogenized constrained mixture theory (HCMT) allows for quantitative analysis of the changes in the multidimensional morphology and composition of AAA. However, the accuracy of HCMT still requires further clinical verification. This study aims to establish a patient-specific AAA growth model based on HCMT, simulate the long-term growth and remodeling (G&R) process of AAA, and validate the feasibility and accuracy of the method using two additional AAA cases with five follow-up datasets. The media and adventitia layers of AAA were modeled as mixtures composed of elastin, collagen fibers, and smooth muscle cells (SMCs). The strain energy function was used to describe the continuous deposition and degradation effect of the mixture during the AAA evolution. Multiple sets of growth parameters were applied to finite element simulations, and the simulation results were compared with the follow-up data for gradually selecting the optimal growth parameters. Two additional AAA patients with different growth rates were used for validating this method, the optimal growth parameters were obtained using the first two follow-up imaging data, and the growth model was applied to simulate the subsequent four time points. The differences between the simulated diameters and the follow-up diameters of AAA were compared to validate the accuracy of the mechanistic model. The growth parameters, especially the stress-mediated substance deposition gain factor, are highly related to the AAA G&R process. When setting the optimal growth parameters to simulate AAA growth, the proportion of simulation results within the distance of less than 0.5 mm from the baseline models is above 80%. For the validating cases, the mean difference rates between the simulated diameter and the real-world diameter are within 2.5%, which basically meets the clinical demand for quantitatively predicting the AAA growth in maximum diameters. This study simulated the growth process of AAA, and validated the accuracy of this mechanistic model. This method was proved to be used to predict the G&R process of AAA caused by dynamic changes in the mixtures of the AAA vessel wall during long-term, assisting accurately and quantitatively predicting the multidimensional morphological development and mixtures evolution process of AAA in the clinic.

Twisting the theory on the origin of human umbilical cord coiling featuring monozygotic twins

The human umbilical cord (hUC) is the lifeline that connects the fetus to the mother. Hypercoiling of the hUC is associated with pre- and perinatal morbidity and mortality. We investigated the origin of hUC hypercoiling using state-of-the-art imaging and omics approaches. Macroscopic inspection of the hUC revealed the helices to originate from the arteries rather than other components of the hUC. Digital reconstruction of the hUC arteries showed the dynamic alignment of two layers of muscle fibers in the tunica media aligning in opposing directions. We observed that genetically identical twins can be discordant for hUC coiling, excluding genetic, many environmental, and parental origins of hUC coiling. Comparing the transcriptomic and DNA methylation profile of the hUC arteries of four twin pairs with discordant cord coiling, we detected 28 differentially expressed genes, but no differentially methylated CpGs. These genes play a role in vascular development, cell-cell interaction, and axis formation and may account for the increased number of hUC helices. When combined, our results provide a novel framework to understand the origin of hUC helices in fetal development.

Critical role of arterial constitutive model in predicting blood pressure from pulse wave velocity

BACKGROUND

A promising approach to cuff-less, continuous blood pressure monitoring is to estimate blood pressure (BP) from Pulse Wave Velocity (PWV). However, most existing PWV-based methods rely on empirical BP-PWV relations and have large prediction errors, which may be caused by the implicit assumption of thin-walled, linear elastic arteries undergoing small deformations. Our objective is to understand the BP-PWV relationship in the absence of such limiting assumptions.

METHOD

We performed Fluid-Structure Interaction (FSI) simulations of the radial artery and the common carotid artery under physiological flow conditions. In these dynamic simulations, we employed two constitutive models for the arterial wall: the linear elastic model, implying a thin-walled linear elastic artery undergoing small deformations, and the Holzapfel-Gasser-Ogden (HGO) model, accounting for the nonlinear effects of collagen fibers and their orientations on the large arterial deformation.

RESULTS

Despite the changing BP, the linear elastic model predicts a constant PWV throughout a cardiac cycle, which is not physiological. The HGO model correctly predicts a positive BP-PWV correlation by capturing the nonlinear deformation of the artery, showing up to 50 % variations of PWV in a cardiac cycle.

CONCLUSION

Dynamic FSI simulations reveal that the BP-PWV relationship strongly depends on the arterial constitutive model, especially in the radial artery. To infer BP from PWV, one must account for the varying PWV, a consequence of the nonlinear arterial response due to collagen fibers. Future efforts should be directed towards robust measurement of time-varying PWV if it is to be used to predict BP.

Guidelines for mechanistic modeling and analysis in cardiovascular research

Computational, or in silico, models are an effective, noninvasive tool for investigating cardiovascular function. These models can be used in the analysis of experimental and clinical data to identify possible mechanisms of (ab)normal cardiovascular physiology. Recent advances in computing power and data management have led to innovative and complex modeling frameworks that simulate cardiovascular function across multiple scales. While commonly used in multiple disciplines, there is a lack of concise guidelines for the implementation of computer models in cardiovascular research. In line with recent calls for more reproducible research, it is imperative that scientists adhere to credible practices when developing and applying computational models to their research. The goal of this manuscript is to provide a consensus document that identifies best practices for in silico computational modeling in cardiovascular research. These guidelines provide the necessary methods for mechanistic model development, model analysis, and formal model calibration using fundamentals from statistics. We outline rigorous practices for computational, mechanistic modeling in cardiovascular research and discuss its synergistic value to experimental and clinical data.

Fracture mechanics modeling of aortic dissection

Aortic dissection, a critical cardiovascular condition with life-threatening implications, is distinguished by the development of a tear and its propagation within the aortic wall. A thorough understanding of the initiation and progression of these tears, or cracks, is essential for accurate diagnosis and effective treatment. This paper undertakes a fracture mechanics approach to delve into the mechanics of tear propagation in aortic dissection. Our objective is to elucidate the impact of geometric and material parameters, providing valuable insights into the determinants of this pivotal cardiovascular event. Through our investigation, we have gained an understanding of how various parameters influence the energy release rate for tear propagation in both longitudinal and circumferential directions, aligning our findings with clinical data.

Hemodynamic evaluation of biomaterial-based surgery for Tetralogy of Fallot using a biorobotic heart, in silico, and ovine models

Tetralogy of Fallot is a congenital heart disease affecting newborns and involves stenosis of the right ventricular outflow tract (RVOT). Surgical correction often widens the RVOT with a transannular enlargement patch, but this causes issues including pulmonary valve insufficiency and progressive right ventricle failure. A monocusp valve can prevent pulmonary regurgitation; however, valve failure resulting from factors including leaflet design, morphology, and immune response can occur, ultimately resulting in pulmonary insufficiency. A multimodal platform to quantitatively evaluate the effect of shape, size, and material on clinical outcomes could optimize monocusp design. This study introduces a benchtop soft biorobotic heart model, a computational fluid model of the RVOT, and a monocusp valve made from an entirely biological cell-assembled extracellular matrix (CAM) to tackle the multifaceted issue of monocusp failure. The hydrodynamic and mechanical performance of RVOT repair strategies was assessed in biorobotic and computational platforms. The monocusp valve design was validated in vivo in ovine models through echocardiography, cardiac magnetic resonance, and catheterization. These models supported assessment of surgical feasibility, handling, suturability, and hemodynamic and mechanical monocusp capabilities. The CAM-based monocusp offered a competent pulmonary valve with regurgitation of 4.6 ± 0.9% and a transvalvular pressure gradient of 4.3 ± 1.4 millimeters of mercury after 7 days of implantation in sheep. The biorobotic heart model, in silico analysis, and in vivo RVOT modeling allowed iteration in monocusp design not now feasible in a clinical environment and will support future surgical testing of biomaterials for complex congenital heart malformations.

Temporal evolution of ascending aortic aneurysm wall stress predicts all-cause mortality

OBJECTIVES

Diameter-based risk stratification for elective repair of ascending aortic aneurysm fails to prevent type A dissection in many patients. Aneurysm wall stresses may contribute to risk prediction; however, rates of wall stress change over time are poorly understood. Our objective was to examine aneurysm wall stress changes over 3-5 years and subsequent all-cause mortality.

METHODS

Male veterans with <5.5 cm ascending aortic aneurysms and computed tomography at baseline and 3- to 5-year follow-up underwent three-dimensional aneurysm model construction. Peak circumferential and longitudinal wall stresses at systole were calculated using finite element analysis. Temporal trends were assessed by mixed-effects modelling. Changes in aortic wall stresses, diameter and length over time were evaluated as predictors of subsequent 3-year all-cause mortality by Cox proportional hazards modelling.

RESULTS

Sixty-two male veterans were included in the study. Yearly changes in geometric and biomechanical measures were 0.12 mm/year (95% confidence interval, 0.04-0.20) for aortic diameter, 0.41 mm/year (0.12-0.71) for aortic length, 1.19 kPa/year -5.94 to 8.33) for peak circumferential stress, and 0.48 kPa/year (-3.89 to 4.84) for peak longitudinal stress. Yearly change in peak circumferential stress was significantly associated with hazard of death-hazard ratio for peak circumferential stress growth per 10 kPa/year, 1.27 (95% CI, 1.02-1.60; P = 0.037); hazard ratio for peak circumferential stress growth ≥ 32 kPa/year, 8.47 (95% CI, 2.42-30; P < 0.001).

CONCLUSIONS

In this population of nonsurgical aneurysm patients, large temporal changes in peak circumferential stress, but not aortic diameter or length, was associated with all-cause mortality. Biomechanical stress and stress changes over time may be beneficial as additional risk factors for elective surgery in small aneurysms.

Aortic tissue stiffness and tensile strength are correlated with density changes following proteolytic treatment

INTRODUCTION

Dissection or rupture of the aorta is accompanied by high mortality rates, and there is a pressing need for better prediction of these events for improved patient management and clinical outcomes. Biomechanically, these events represent a situation wherein the locally acting wall stress exceed the local tissue strength. Based on recent reports for polymers, we hypothesized that aortic tissue failure strength and stiffness are directly associated with tissue mass density. The objective of this work was to test this novel hypothesis for porcine thoracic aorta.

METHODS

Three tissue specimens from freshly harvested porcine thoracic aorta were treated with either collagenase or elastase to selectively degrade structural proteins in the tissue, or with phosphate buffer saline (control). The tissue mass and volume of each specimen were measured before and after treatment to allow for density calculation, then mechanically tested to failure under uniaxial extension.

RESULTS

Protease treatments resulted in statistically significant tissue density reduction (sham vs. collagenase p = 0.02 and sham vs elastase p = 0.003), which in turn was significantly and directly correlated with both ultimate tensile strength (sham vs. collagenase p = 0.02 and sham vs elastase p = 0.03) and tangent modulus (sham vs. collagenase p = 0.007 and sham vs elastase p = 0.03).

CONCLUSIONS

This work demonstrates for the first time that tissue stiffness and tensile strength are directly correlated with tissue density in proteolytically-treated aorta. These findings constitute an important step towards understanding aortic tissue failure mechanisms and could potentially be leveraged for non-invasive aortic strength assessment through density measurements, which could have implications to clinical care.

Nonlinear Elasticity of Blood Vessels and Vascular Grafts

The transplantation of vascular grafts has emerged as a prevailing approach to address vascular disorders. However, the development of small-diameter vascular grafts is still in progress, as they serve in a more complicated mechanical environment than their counterparts with larger diameters. The biocompatibility and functional characteristics of small-diameter vascular grafts have been well developed; however, mismatch in mechanical properties between the vascular grafts and native arteries has not been accomplished, which might facilitate the long-term patency of small-diameter vascular grafts. From a point of view in mechanics, mimicking the nonlinear elastic mechanical behavior exhibited by natural blood vessels might be the state-of-the-art in designing vascular grafts. This review centers on elucidating the nonlinear elastic behavior of natural blood vessels and vascular grafts. The biological functionality and limitations associated with as-reported vascular grafts are meticulously reviewed and the future trajectory for fabricating biomimetic small-diameter grafts is discussed. This review might provide a different insight from the traditional design and fabrication of artificial vascular grafts.

Mechanical characterization and torsional buckling of pediatric cardiovascular materials

In complex cardiovascular surgical reconstructions, conduit materials that avoid possible large-scale structural deformations should be considered. A fundamental mode of mechanical complication is torsional buckling which occurs at the anastomosis site due to the mechanical instability, leading surgical conduit/patch surface deformation. The objective of this study is to investigate the torsional buckling behavior of commonly used materials and to develop a practical method for estimating the critical buckling rotation angle under physiological intramural vessel pressures. For this task, mechanical tests of four clinically approved materials, expanded polytetrafluoroethylene (ePTFE), Dacron, porcine and bovine pericardia, commonly used in pediatric cardiovascular surgeries, are conducted (n = 6). Torsional buckling initiation tests with n = 4 for the baseline case (L = 7.5 cm) and n = 3 for the validation of ePTFE (L = 15 cm) and Dacron (L = 15 cm and L = 25 cm) for each are also conducted at low venous pressures. A practical predictive formulation for the buckling potential is proposed using experimental observations and available theory. The relationship between the critical buckling rotation angle and the lumen pressure is determined by balancing the circumferential component of the compressive principal stress with the shear stress generated by the modified critical buckling torque, where the modified critical buckling torque depends linearly on the lumen pressure. While the proposed technique successfully predicted the critical rotation angle values lying within two standard deviations of the mean in the baseline case for all four materials at all lumen pressures, it could reliably predict the critical buckling rotation angles for ePTFE and Dacron samples of length 15 cm with maximum relative errors of 31% and 38%, respectively, in the validation phase. However, the validation of the performance of the technique demonstrated lower accuracy for Dacron samples of length 25 cm at higher pressure levels of 12 mmHg and 15 mmHg. Applicable to all surgical materials, this formulation enables surgeons to assess the torsional buckling potential of vascular conduits noninvasively. Bovine pericardium has been found to exhibit the highest stability, while Dacron (the lowest) and porcine pericardium have been identified as the least stable with the (unitless) torsional buckling resistance constants, 43,800, 12,300 and 14,000, respectively. There was no significant difference between ePTFE and Dacron, and between porcine and bovine pericardia. However, both porcine and bovine pericardia were found to be statistically different from ePTFE and Dacron individually (p < 0.0001). ePTFE exhibited highly nonlinear behavior across the entire strain range [0, 0.1] (or 10% elongation). The significant differences among the surgical materials reported here require special care in conduit construction and anastomosis design.

Hemodynamics and wall shear metrics in a pulmonary autograft: Comparing a fluid-structure interaction and computational fluid dynamics approach

OBJECTIVE

In young patients, aortic valve disease is often treated by placement of a pulmonary autograft (PA) which adapts to its new environment through growth and remodeling. To better understand the hemodynamic forces acting on the highly distensible PA in the acute phase after surgery, we developed a fluid-structure interaction (FSI) framework and comprehensively compared hemodynamics and wall shear-stress (WSS) metrics with a computational fluid dynamic (CFD) simulation.

METHODS

The FSI framework couples a prestressed non-linear hyperelastic arterial tissue model with a fluid model using the in-house coupling code CoCoNuT. Geometry, material parameters and boundary conditions are based on in-vivo measurements. Hemodynamics, time-averaged WSS (TAWSS), oscillatory shear index (OSI) and topological shear variation index (TSVI) are evaluated qualitatively and quantitatively for 3 different sheeps.

RESULTS

Despite systolic-to-diastolic volumetric changes of the PA in the order of 20 %, the point-by-point correlation of TAWSS and OSI obtained through CFD and FSI remains high (r > 0.9, p < 0.01) for TAWSS and (r > 0.8, p < 0.01) for OSI). Instantaneous WSS divergence patterns qualitatively preserve similarities, but large deformations of the PA leads to a decrease of the correlation between FSI and CFD resolved TSVI (r < 0.7, p < 0.01). Moderate co-localization between FSI and CFD is observed for low thresholds of TAWSS and high thresholds of OSI and TSVI.

CONCLUSION

FSI might be warranted if we were to use the TSVI as a mechano-biological driver for growth and remodeling of PA due to varying intra-vascular flow structures and near wall hemodynamics because of the large expansion of the PA.

The predictive capability of aortic stiffness index for aortic dissection among dilated ascending aortas

OBJECTIVE

We created a finite element model to predict the probability of dissection based on imaging-derived aortic stiffness and investigated the link between stiffness and wall tensile stress using our model.

METHODS

Transthoracic echocardiogram measurements were used to calculate aortic diameter change over the cardiac cycle. Aortic stiffness index was subsequently calculated based on diameter change and blood pressure. A series of logistic models were developed to predict the binary outcome of aortic dissection using 1 or more series of predictor parameters such as aortic stiffness index or patient characteristics. Finite element analysis was performed on a subset of diameter-matched patients exhibiting patient-specific material properties.

RESULTS

Transthoracic echocardiogram scans of patients with type A aortic dissection (n = 22) exhibited elevated baseline aortic stiffness index when compared with aneurysmal patients' scans with tricuspid aortic valve (n = 83, P < .001) and bicuspid aortic valve (n = 80, P < .001). Aortic stiffness index proved an excellent discriminator for a future dissection event (area under the curve, 0.9337, odds ratio, 2.896). From the parametric finite element study, we found a correlation between peak longitudinal wall tensile stress and stiffness index (ρ = .6268, P < .001, n = 28 pooled).

CONCLUSIONS

Noninvasive transthoracic echocardiogram-derived aortic stiffness measurements may serve as an impactful metric toward predicting aortic dissection or quantifying dissection risk. A correlation between longitudinal stress and stiffness establishes an evidence-based link between a noninvasive stiffness parameter and stress state of the aorta with clinically apparent dissection events.

Implications of preoperative arterial stiffness for patients treated with endovascular repair of abdominal aortic aneurysms

Arterial stiffening is associated with adverse cardiovascular patient outcomes; stiffness may also be associated with postsurgical events and has been suggested to be a fundamental mechanism in the pathogenesis of aortic aneurysms. Although open repair of aneurysms decreases aortic stiffness, implantation of a rigid endograft is associated with increased aortic stiffness after endovascular aneurysm repair (EVAR). This review provides an overview of aortic wall physiology and the contemporary understanding of aortic stiffness and its implications for patients undergoing abdominal aortic aneurysm repair. Recent data suggests that increased central arterial stiffness, estimated preoperatively using the pulse wave velocity (PWV), may predict aneurysm sac behavior after EVAR, with elevated preoperative PWV associated with less sac shrinkage, and even sac enlargement, after EVAR. With the development of several simple noninvasive methods to measure PWV, such as brachial-ankle PWV and single cuff brachial oscillometry, there may be a role for monitoring ambulatory PWV to predict outcomes after EVAR. Additionally, because aortic stiffness is associated with adverse cardiovascular outcomes, and EVAR increases aortic stiffness, assessment of aortic stiffness before aortic interventions may help to guide therapeutic decisions as well as surveillance protocols, leading to optimized patient outcomes.

In Vivo Optical Coherence Elastography Unveils Spatial Variation of Human Corneal Stiffness

OBJECTIVE

The mechanical properties of corneal tissues play a crucial role in determining corneal shape and have significant implications in vision care. This study aimed to address the challenge of obtaining accurate in vivo data for the human cornea.

METHODS

We have developed a high-frequency optical coherence elastography (OCE) technique using shear-like antisymmetric (A0)-mode Lamb waves at frequencies above 10 kHz.

RESULTS

By incorporating an anisotropic, nonlinear constitutive model and utilizing the acoustoelastic theory, we gained quantitative insights into the influence of corneal tension on wave speeds and elastic moduli. Our study revealed significant spatial variations in the shear modulus of the corneal stroma on healthy subjects for the first time. Over an age span from 21 to 34 (N = 6), the central corneas exhibited a mean shear modulus of 87 kPa, while the corneal periphery showed a significant decrease to 44 kPa. The central cornea's shear modulus decreases with age with a slope of -19 +/- 8 kPa per decade, whereas the periphery showed non-significant age dependence. The limbus demonstrated an increased shear modulus exceeding 100 kPa. We obtained wave displacement profiles that are consistent with highly anisotropic corneal tissues.

CONCLUSION

Our approach enabled precise measurement of corneal tissue elastic moduli in situ with high precision (<7%) and high spatial resolution (<1 mm). Our results revealed significant stiffness variation from the central to peripheral corneas.

SIGNIFICANCE

The high-frequency OCE technique holds promise for biomechanical evaluation in clinical settings, providing valuable information for refractive surgeries, degenerative disorder diagnoses, and intraocular pressure assessments.

Identification of Vivo Material Parameters of Arterial Wall Based on Improved Niching Genetic Algorithm and Neural Networks

Cardiovascular diseases are seriously threatening human health and the incidence rate is high. Many scholars are devoted to studying arterial mechanical properties and material parameters. In this study, the bovine artery was selected as the experimental object and the uniaxial tensile test was carried out by cutting the specimens along its axial, circumferential and [Formula: see text] directions. The finite element software ABAQUS and hyperelastic Holzapfel Gasser Ogden (HGO) constitutive model were used to simulate the experimental process. Niche technology is introduced on the basis of genetic algorithm, and the program of Improved Niche Genetic Algorithm for material parameter identification is compiled based on Python language. In addition, BP Neural Network was constructed based on Tensorflow mathematical system. The material parameters of the constitutive model of bovine artery in different directions were identified by finite element method and experimental data. The results show that Improved Niche Genetic Algorithm and Neural Network, respectively, combined with finite element are both effective and accurate methods for predicting the parameters of arterial vascular hyperelastic materials, which can provide reference and help for the study of arterial vascular mechanical properties.