Hyperelastic modelling of arterial layers with distributed collagen fibre orientations

A Computational Investigation of Microstructural Damage of the Acl Under High Loading of the Knee Joint

The anterior cruciate ligament plays a major role in maintaining the stability of the knee joint, is susceptible to injury under strenuous activity. ACL injuries can lead to joint instability and complications such as osteoarthritis. Despite this, there is a lack of material models capable of predicting damage at a localized fiber level, hindering our ability to understand how damage develops in real-time. The present work develops a continuum-damage material model of the ACL and applies the model to a finite element simulation of the knee undergoing high quadriceps tendon loading. Using quadriceps tendon loadings of 1000, 1500, and 2000 N, the development of microstructural damage within the ACL tissue was examined, and the effects of localized damage on the joint kinematics were investigated. Damage tended to develop in the mid-substance of the ACL in the present model in the anterior medial bundle region and could induce significant changes in the joint kinematics. Using this model, new insights into the development of ACL injury mechanisms can be investigated.

Microstructure and mechanics of the bovine trachea: Layer specific investigations through SHG imaging and biaxial testing

The trachea is a complex tissue made up of hyaline cartilage, fibrous tissue, and muscle fibers. Currently, the knowledge of microscopic structural organization of these components and their role in determining the tissue's mechanical response is very limited. The purpose of this study is to provide data on the microstructure of the tracheal components and its influence on tissue's mechanical response. Five bovine tracheae were used in this study. Adventitia, cartilage, mucosa/submucosa, and trachealis muscle layers were methodically cut out from the whole tissue. Second-harmonic generation(SHG) via multi-photon microscopy (MPM) enabled imaging of collagen fibers and muscle fibers. Simultaneously, a planar biaxial test rig was used to record the mechanical behavior of each layer. In total 60 samples were tested and analyzed. Fiber architecture in the adventitia and mucosa/submucosa layer showed high degree of anisotropy with the mean fiber angle varying from sample to sample. The trachealis muscle displayed neat layers of fibers organized in the longitudinal direction. The cartilage also displayed a structure of thick mesh-work of collagen type II organized predominantly towards the circumferential direction. Further, mechanical testing demonstrated the anisotropic nature of the tissue components. The cartilage was identified as the stiffest component for strain level < 20% and hence the primary load bearing component. The other three layers displayed a non-linear mechanical response which could be explained by the structure and organization of their fibers. This study is useful in enhancing the utilization of structurally motivated material models for predicting tracheal overall mechanical response.

Correlation between age, location, orientation, loading velocity and delamination strength in the human aorta

Aortic dissection is a biomechanical phenomenon associated with a failure of internal cohesion, which manifests itself through the delamination of the aortic wall. The goal of this study is to deepen our knowledge of the delamination strength of the aorta. To achieve this, 661 peeling experiments were carried out with strips of the human aorta collected from 46 cadavers. The samples were ordered into groups with respect to (1) anatomical location, (2) orientation of the sample, and (3) extension rate used within the experiment. The obtained results are in accordance with the hypothesis that delamination resistance is not sensitive to the extension rates 0.1, 1, 10, and 50 mms^-1. We arrived at this conclusion for all positions along the aorta investigated in our study. These were the thoracic ascending (AAs), thoracic descending (ADs), and the abdominal aorta (AAb), simultaneously considering both the longitudinal (L) as well as the circumferential (C) orientations of the samples. On the other hand, our results showed that the delamination strength differs significantly with respect to the anatomical position and orientation of the sample. The medians of the delamination strength were as follows, 4.1 in AAs-L, 3.2 in AAs-C, 3.1 in ADs-L, 2.4 in ADs-C, AAb-L in 3.6, and 2.7 in AAb-C case (all values are in 0.01·Nmm^-1). This suggests that resistance to crack propagation should be an anisotropic property and that the aorta is inhomogeneous along its length from the point of view of delamination resistance. Finally, correlation analysis proved that the delamination strength of the human aorta significantly decreases with age.

Design and Simulation of the Biomechanics of Multi-Layered Composite Poly(Vinyl Alcohol) Coronary Artery Grafts

Coronary artery disease is among the primary causes of death worldwide. While synthetic grafts allow replacement of diseased tissue, mismatched mechanical properties between graft and native tissue remains a major cause of graft failure. Multi-layered grafts could overcome these mechanical incompatibilities by mimicking the structural heterogeneity of the artery wall. However, the layer-specific biomechanics of synthetic grafts under physiological conditions and their impact on endothelial function is often overlooked and/or poorly understood. In this study, the transmural biomechanics of four synthetic graft designs were simulated under physiological pressure, relative to the coronary artery wall, using finite element analysis. Using poly(vinyl alcohol) (PVA)/gelatin cryogel as the representative biomaterial, the following conclusions are drawn: (I) the maximum circumferential stress occurs at the luminal surface of both the grafts and the artery; (II) circumferential stress varies discontinuously across the media and adventitia, and is influenced by the stiffness of the adventitia; (III) unlike native tissue, PVA/gelatin does not exhibit strain stiffening below diastolic pressure; and (IV) for both PVA/gelatin and native tissue, the magnitude of stress and strain distribution is heavily dependent on the constitutive models used to model material hyperelasticity. While these results build on the current literature surrounding PVA-based arterial grafts, the proposed method has exciting potential toward the wider design of multi-layer scaffolds. Such finite element analyses could help guide the future validation of multi-layered grafts for the treatment of coronary artery disease.

Association of 3-Year All-Cause Mortality and Peak Wall Stresses of Ascending Thoracic Aortic Aneurysms in Veterans

Risk of aortic dissection in ascending thoracic aortic aneurysms is not sufficiently captured by size-based metrics. From a biomechanical perspective, dissection may be initiated when wall stress exceeds wall strength. Our objective was to assess the association between aneurysm peak wall stresses and 3-year all-cause mortality. Finite element analysis was performed in 273 veterans with chest computed tomography for surveillance of ascending thoracic aortic aneurysms. Three-dimensional geometries were reconstructed and models developed accounting for prestress geometries. A fiber-embedded hyperelastic material model was applied to obtain circumferential and longitudinal wall stresses under systolic pressure. Patients were followed up to 3 years following the scan to assess aneurysm repair and all-cause mortality. Fine-Gray subdistribution hazards were estimated for all-cause mortality based on age, aortic diameter, and peak wall stresses, treating aneurysm repair as a competing risk. When accounting for age, subdistribution hazard of mortality was not significantly increased by peak circumferential stresses (p = 0.30) but was significantly increased by peak longitudinal stresses (p = 0.008). Aortic diameter did not significantly increase subdistribution hazard of mortality in either model (circumferential model: p = 0.38; longitudinal model: p = 0.30). The effect of peak longitudinal stresses on subdistribution hazard of mortality was maximized at a binary threshold of 355kPa, which captured 34 of 212(16%) patients with diameter <5 cm, 11 of 36(31%) at 5.0-5.4 cm, and 11 of 25(44%) at ≥5.5 cm. Aneurysm peak longitudinal stresses stratified by age and diameter were associated with increased hazard of 3-year all-cause mortality in a veteran cohort. Risk prediction may be enhanced by considering peak longitudinal stresses.

Engineering analysis of aortic wall stress and root dilatation in the V-shape surgery for treatment of ascending aortic aneurysms

OBJECTIVES

The study objective was to evaluate the aortic wall stress and root dilatation before and after the novel V-shape surgery for the treatment of ascending aortic aneurysms and root ectasia.

METHODS

Clinical cardiac computed tomography images were obtained for 14 patients [median age, 65 years (range, 33-78); 10 (71%) males] who underwent the V-shape surgery. For 10 of the 14 patients, the computed tomography images of the whole aorta pre- and post-surgery were available, and finite element simulations were performed to obtain the stress distributions of the aortic wall at pre- and post-surgery states. For 6 of the 14 patients, the computed tomography images of the aortic root were available at 2 follow-up time points post-surgery (Post 1, within 4 months after surgery and Post 2, about 20-52 months from Post 1). We analysed the root dilatation post-surgery using change of the effective diameter of the root at the two time points and investigated the relationship between root wall stress and root dilatation.

RESULTS

The mean and peak max-principal stresses of the aortic root exhibit a significant reduction, P=0.002 between pre- and post-surgery for both root mean stress (median among the 10 patients presurgery, 285.46 kPa; post-surgery, 199.46 kPa) and root peak stress (median presurgery, 466.66 kPa; post-surgery, 342.40 kPa). The mean and peak max-principal stresses of the ascending aorta also decrease significantly from pre- to post-surgery, with P=0.004 for the mean value (median presurgery, 296.48 kPa; post-surgery, 183.87 kPa), and P=0.002 for the peak value (median presurgery, 449.73 kPa; post-surgery, 282.89 kPa), respectively. The aortic root diameter after the surgery has an average dilatation of 5.01% in total and 2.15%/year. Larger root stress results in larger root dilatation.

CONCLUSIONS

This study marks the first biomechanical analysis of the novel V-shape surgery. The study has demonstrated significant reduction in wall stress of the aortic root repaired by the surgery. The root was able to dilate mildly post-surgery. Wall stress could be a critical factor for the dilatation since larger root stress results in larger root dilatation. The dilated aortic root within 4 years after surgery is still much smaller than that of presurgery.

Arterial Stiffness Probed by Dynamic Ultrasound Elastography Characterizes Waveform of Blood Pressure

The clinical and economic burdens of cardiovascular diseases pose a global challenge. Growing evidence suggests an early assessment of arterial stiffness can provide insights into the pathogenesis of cardiovascular diseases. However, it remains difficult to quantitatively characterize local arterial stiffness in vivo. Here we utilize guided axial waves continuously excited and detected by ultrasound to probe local blood pressures and mechanical properties of common carotid arteries simultaneously. In a pilot study of 17 healthy volunteers, we observe a  ∼ 20 % variation in the group velocities of the guided axial waves (5.16 ± 0.55 m/s in systole and 4.31 ± 0.49 m/s in diastole) induced by the variation of the blood pressures. A linear relationship between the square of group velocity and blood pressure is revealed by the experiments and finite element analysis, which enables us to measure the waveform of the blood pressures by the group velocities. Furthermore, we propose a wavelet analysis-based method to extract the dispersion relations of the guided axial waves. We then determined the shear modulus by fitting the dispersion relations in diastole with the leaky Lamb wave model. The average shear modulus of all the volunteers is 166.3 ± 32.8 kPa. No gender differences are found. This study shows the group velocity and dispersion relation of the guided axial waves can be utilized to probe blood pressure and arterial stiffness locally in a noninvasive manner and thus promising for early diagnosis of cardiovascular diseases.

How suture networks improve the protective function of natural structures: A multiscale investigation

Myriad natural protective structures consist of bone plates joined by convoluted unmineralized (soft) collagenous sutures. Examples of such protective structures include: shells of turtles, craniums of almost all animals (including humans), alligator armour, armadillo armour, and others. The function of sutures has been well researched. However, whether, and if so how, sutures improve protective performance during a predator attack has received limited attention. Sutures are ubiquitous in protective structures, and this motivates the question as to whether sutures optimize the protective function of the structure. Hence, in this work the behaviour of structures that contain sutures during predator attacks is investigated. We show that sutures decrease the maximum strain energy density that turtle shells experience during predator attacks by more than an order of magnitude. Hence, sutures make turtle shells far more resilient to material failure, such as, fracture, damage, and plastic deformations. Additionally, sutures increase the viscous behaviour of the shell causing increased dissipation of energy during predator attacks. Further investigations into the influence of sutures on behaviour during locomotion and breathing are also presented. The results presented in this work motivate the inclusion of sutures in biomimetically designed protective structures, such as helmets and protective clothing. STATEMENT OF SIGNIFICANCE: Myriad bony protective structures contain networks of sutures, that is con- voluted soft collagenous tissue. Their ubiquity motivates the question, whether, and if so how, sutures improve protective performance. Hence, this work inves- tigates how sutures affect protective performance using computational experi- ments. Due to the length scale of sutures being far smaller than the structures in which they reside, classical modelling approaches are prohibitively expensive. Hence, in this work, a multiscale approach is taken. To our knowledge, this is the first multiscale investigation of structures that contain sutures. Among other insights, we show that sutures decrease the maximum strain energy density in structures during predator attacks by over an order of mag- nitude. Hence, sutures make structures far more resilient to failure.

Predicting and understanding arterial elasticity from key microstructural features by bidirectional deep learning

Microstructural features and mechanical properties are closely related in all soft biological tissues. Both yet exhibit considerable inter-individual differences and are affected by factors such as aging and disease and its progression. Histological analysis, modern in situ imaging, and biomechanical testing have deepened our understanding of these complex interrelations, yet two key questions remain: (1) Given the specific microstructure, can one predict the macroscopic mechanical properties without mechanical testing? (2) Can one quantify individual contributions of the different microstructural features to the macroscopic mechanical properties in an automated, systematic and largely unbiased way? Here we propose a bidirectional deep learning architecture to address these two questions. Our architecture uses data from standard histological analyses, two-photon microscopy and biaxial biomechanical testing. Its capabilities are demonstrated by predicting with high accuracy (R²=0.92) the evolving mechanical properties of the murine aorta during maturation and aging. Moreover, our architecture reveals that the extracellular matrix composition and organization are the most prominent factors governing the macroscopic mechanical properties of the tissues studied herein. STATEMENT OF SIGNIFICANCE:  .

Efficient Finite Element Modeling of Steel Cables in Reinforced Rubber

Spiral steel cables feature complex deformation behavior due to their wound geometry. In applications where the cables are used to reinforce rubber components, modeling the cables is not trivial, because the cable’s outer surface must be connected to the surrounding rubber material. There are several options for modeling steel cables using beam and/or solid elements for the cable. So far, no study that lists and evaluates the performance of such approaches can be found in the literature. This work investigates such modeling options for a simple seven-wire strand that is regarded as a cable. The setup, parameter calibration, and implementation of the approaches are described. The accuracy of the obtained deformation behavior is assessed for a three-cable specimen using a reference model that features the full geometry of the wires in the three cables. It is shown that a beam approach with anisotropic beam material gives the most accurate stiffness results. The results of the three-cable specimen model indicate that such a complex cable model is quite relevant for the specimen’s deformation. However, there is no single approach that is well suited for all applications. The beam with anisotropic material behavior is well suited if the necessary simplifications in modeling the cable–rubber interface can be accepted. The present work thus provides a guide not only for calibrating but also for selecting the cable-modeling approach. It is shown how such modeling approaches can be used in commercial FE software for applications such as conveyor belts.

On the Lagrangian-Eulerian Coupling in the Immersed Finite Element/Difference Method

The immersed boundary (IB) method is a non-body conforming approach to fluid-structure interaction (FSI) that uses an Eulerian description of the momentum, viscosity, and incompressibility of a coupled fluid-structure system and a Lagrangian description of the deformations, stresses, and resultant forces of the immersed structure. Integral transforms with Dirac delta function kernels couple the Eulerian and Lagrangian variables, and in practice, discretizations of these integral transforms use regularized delta function kernels. Many different kernel functions have been proposed, but prior numerical work investigating the impact of the choice of kernel function on the accuracy of the methodology has often been limited to simplified test cases or Stokes flow conditions that may not reflect the method's performance in applications, particularly at intermediate-to-high Reynolds numbers, or under different loading conditions. This work systematically studies the effect of the choice of regularized delta function in several fluid-structure interaction benchmark tests using the immersed finite element/difference (IFED) method, which is an extension of the IB method that uses a finite element structural discretization combined with a Cartesian grid finite difference method for the incompressible Navier-Stokes equations. Whereas the conventional IB method spreads forces from the nodes of the structural mesh and interpolates velocities to those nodes, the IFED formulation evaluates the regularized delta function on a collection of interaction points that can be chosen to be denser than the nodes of the Lagrangian mesh. This opens the possibility of using structural discretizations with wide node spacings that would produce gaps in the Eulerian force in nodally coupled schemes (e.g., if the node spacing is comparable to or broader than the support of the regularized delta functions). Earlier work with this methodology suggested that such coarse structural meshes can yield improved accuracy for shear-dominated cases and, further, found that accuracy improves when the structural mesh spacing is increased. However, these results were limited to simple test cases that did not include substantial pressure loading on the structure. This study investigates the effect of varying the relative mesh widths of the Lagrangian and Eulerian discretizations in a broader range of tests. Our results indicate that kernels satisfying a commonly imposed even-odd condition require higher resolution to achieve similar accuracy as kernels that do not satisfy this condition. We also find that narrower kernels are more robust, in the sense that they yield results that are less sensitive to relative changes in the Eulerian and Lagrangian mesh spacings, and that structural meshes that are substantially coarser than the Cartesian grid can yield high accuracy for shear-dominated cases but not for cases with large normal forces. We verify our results in a large-scale FSI model of a bovine pericardial bioprosthetic heart valve in a pulse duplicator.

3D Modeling of the Crystalline Lens Complex under Pseudoexfoliation

Pseudoexfoliation, one of the most frequent crystalline lens complex disorders, is prevalent in up to 30% of individuals older than 60 years old. This disease can lead to severe conditions, such as subluxation or dislocation of the lens, due to the weakening of the zonules. The goal for the present study was to understand the relevant biomechanical features that can lead to the worsening of an individual’s visual capacity under pseudoexfoliation. To this end, finite element models based on a 62-year-old lens complex were developed, composed by the capsular bag, cortex, nucleus, anterior, equatorial, and posterior zonular fibers. Healthy and pseudoexfoliative conditions were simulated, varying the location of the zonulopathy (inferior/superior) and the degenerated layer. The accommodative capacity of the models with inferior dialysis of the zonular fibers was, on average, 4.7% greater than for the cases with superior dialysis. If the three sets of zonules were disrupted, this discrepancy increased to 14.9%. The present work provides relevant data to be further analyzed in clinical scenarios, as these models (and their future extension to a wider age range) can help in identifying the most influential regions for the reduction of the visual capacity of the lens.

Differences in Collagen Fiber Diameter and Waviness between Healthy and Aneurysmal Abdominal Aortas

Collagen plays a key role in the strength of aortic walls, so studying micro-structural changes during disease development is critical to better understand collagen reorganization. Second-harmonic generation microscopy is used to obtain images of human aortic collagen in both healthy and diseased states. Methods are being developed in order to efficiently determine the waviness, that is, tortuosity and amplitude, as well as the diameter, orientation, and dispersion of collagen fibers, and bundles in healthy and aneurysmal tissues. The results show layer-specific differences in the collagen of healthy tissues, which decrease in samples of aneurysmal aortic walls. In healthy tissues, the thick collagen bundles of the adventitia are characterized by greater waviness, both in the tortuosity and in the amplitude, compared to the relatively thin and straighter collagen fibers of the media. In contrast, most aneurysmal tissues tend to have a more uniform structure of the aortic wall with no significant difference in collagen diameter between the luminal and abluminal layers. An increase in collagen tortuosity compared to the healthy media is also observed in the aneurysmal luminal layer. The data set provided can help improve related material and multiscale models of aortic walls and aneurysm formation.

Biomechanical constitutive modeling of the gastrointestinal tissues: a systematic review

The gastrointestinal (GI) tract is a continuous channel through the body that consists of the esophagus, the stomach, the small intestine, the large intestine, and the rectum. Its primary functions are to move the intake of food for digestion before storing and ultimately expulsion of feces. The mechanical behavior of GI tissues thus plays a crucial role for GI function in health and disease. The mechanical properties are characterized by a biomechanical constitutive model, which is a mathematical representation of the relation between load and deformation in a tissue. Hence, validated biomechanical constitutive models are essential to characterize and simulate the mechanical behavior of the GI tract. Here, a systematic review of these constitutive models is provided. This review is limited to studies where a model of the strain energy function is proposed to characterize the stress-strain relation of a GI tissue. Several needs are identified for more advanced modeling including: 1) Microstructural models that provide actual structure-function relations; 2) Validation of coupled electro-mechanical models accounting for active muscle contractions; 3) Human data to develop and validate models. The findings from this review provide guidelines for using existing constitutive models as well as perspective and directions for future studies.

Bio-inspired hydrogels with fibrous structure: A review on design and biomedical applications

Numerous tissues in the human body have fibrous structures, including the extracellular matrix, muscles, and heart, which perform critical biological functions and have exceptional mechanical strength. Due to their high-water content, softness, biocompatibility and elastic nature, hydrogels resemble biological tissues. Traditional hydrogels, on the other hand, have weak mechanical properties and lack tissue-like fibrous structures, limiting their potential applications. Thus, bio-inspired hydrogels with fibrous architectures have piqued the curiosity of biomedical researchers. Here, we review fabrication strategies for fibrous hydrogels and their recent progress in the biomedical fields of wound dressings, drug delivery, tissue engineering scaffolds and bioadhesives. Challenges and future perspectives are also discussed.

Bayesian inference on a microstructural, hyperelastic model of tendon deformation

Microstructural models of soft-tissue deformation are important in applications including artificial tissue design and surgical planning. The basis of these models, and their advantage over their phenomenological counterparts, is that they incorporate parameters that are directly linked to the tissue's microscale structure and constitutive behaviour and can therefore be used to predict the effects of structural changes to the tissue. Although studies have attempted to determine such parameters using diverse, state-of-the-art, experimental techniques, values ranging over several orders of magnitude have been reported, leading to uncertainty in the true parameter values and creating a need for models that can handle such uncertainty. We derive a new microstructural, hyperelastic model for transversely isotropic soft tissues and use it to model the mechanical behaviour of tendons. To account for parameter uncertainty, we employ a Bayesian approach and apply an adaptive Markov chain Monte Carlo algorithm to determine posterior probability distributions for the model parameters. The obtained posterior distributions are consistent with parameter measurements previously reported and enable us to quantify the uncertainty in their values for each tendon sample that was modelled. This approach could serve as a prototype for quantifying parameter uncertainty in other soft tissues.

Experimental investigations of the human oesophagus: anisotropic properties of the embalmed muscular layer under large deformation

The oesophagus is a primarily mechanical organ whose material characterisation would aid in the investigation of its pathophysiology, help in the field of tissue engineering, and improve surgical simulations and the design of medical devices. However, the layer-dependent, anisotropic properties of the organ have not been investigated using human tissue, particularly in regard to its viscoelastic and stress-softening behaviour. Restrictions caused by the COVID-19 pandemic meant that fresh human tissue was not available for dissection. Therefore, in this study, the layer-specific material properties of the human oesophagus were investigated through ex vivo experimentation of the embalmed muscularis propria layer. For this, a series of uniaxial tension cyclic tests with increasing stretch levels were conducted at two different strain rates. The muscular layers from three different cadaveric specimens were tested in both the longitudinal and circumferential directions. The results displayed highly nonlinear and anisotropic behaviour, with both time- and history-dependent stress-softening. The longitudinal direction was found to be stiffer than the circumferential direction at both strain rates. Strain rate-dependent behaviour was apparent, with an increase in strain rate resulting in an increase in stiffness in both directions. Histological analysis was carried out via various staining methods; the results of which were discussed with regard to the experimentally observed stress-stretch response. Finally, the behaviour of the muscularis propria was simulated using a matrix-fibre model able to capture the various mechanical phenomena exhibited, the fibre orientation of which was driven by the histological findings of the study.

The Role of Layer-Specific Residual Stresses in Arterial Mechanics: Analysis via a Novel Modelling Framework

The existence of residual stresses in unloaded arteries has long been known. However, their effect is often neglected in experimental studies. Using a recently developed modelling framework, we aimed to investigate the role of residual stresses in the mechanical behaviour of the tri-layered wall of the pig thoracic aorta. The mechanical behaviour of the intact wall and isolated layers of n = 3 pig thoracic aortas was investigated via uniaxial tensile testing. After modelling the layer-specific mechanical data using a hyperelastic strain energy function, the layer-specific deformations in the unloaded vessel were estimated so that the mechanical response of the computationally assembled tri-layered flat wall would match that measured experimentally. Physiological tension–inflation of the cylindrical tri-layered vessel was then simulated, analysing changes in the distribution of stresses in the three layers when neglecting residual stresses. In the tri-layered model with residual stresses, layers exhibited comparable stresses throughout the physiological range of pressure. At 100 mmHg, intimal, medial, and adventitial circumferential load bearings were 16 $$\pm$$ ±  3%, 59 $$\pm$$ ± 4%, and 25 $$\pm$$ ± 2%, respectively. Adventitial stiffening at high pressures produced a shift in load bearing from the media to the adventitia. When neglecting residual stresses, in vivo stresses were highest at the intima and lowest at the adventitia. Consequently, the intimal and adventitial load bearings, 23 $$\pm$$ ± 2% and 18 $$\pm$$ ± 3% at 100 mmHg, were comparable at all pressures. Residual stresses play a crucial role in arterial mechanics guaranteeing a uniform distribution of stresses through the wall thickness. Neglecting these leads to incorrect interpretation of the layers’ role in arterial mechanics.

Implementing computational modeling in tissue engineering: where disciplines meet

In recent years, the mathematical and computational sciences have developed novel methodologies and insights that can aid in designing advanced bioreactors, microfluidic set-ups or organ-on-chip devices, in optimizing culture conditions, or predicting long-term behavior of engineered tissues in vivo. In this review, we introduce the concept of computational models and how they can be integrated in an interdisciplinary workflow for Tissue Engineering and Regenerative Medicine (TERM). We specifically aim this review of general concepts and examples at experimental scientists with little or no computational modeling experience. We also describe the contribution of computational models in understanding TERM processes and in advancing the TERM field by providing novel insights.

Biomechanical and structural responses of the aorta to intermittent hypobaric hypoxia in a rat model

High altitude hypoxia is a condition experienced by diverse populations worldwide. In addition, several jobs require working shifts where workers are exposed to repetitive cycles of hypobaric hypoxia and normobaric normoxia. Currently, few is known about the biomechanical cardiovascular responses of this condition. In the present study, we investigate the cycle-dependent biomechanical effects of intermittent hypobaric hypoxia (IHH) on the thoracic aorta artery, in terms of both structure and function. To determine the vascular effects of IHH, functional, mechanical and histological approaches were carried out in the thoracic aorta artery, using uniaxial, pre-stretch, ring opening, myography, and histological tests. Three groups of rats were established: control (normobaric normoxia, NN), 4-cycles of intermittent hypoxia (short-term intermittent hypobaric hypoxia, STH), and 10-cycles of intermittent hypoxia (long-term intermittent hypobaric hypoxia, LTH). The pre-stretch and ring opening tests, aimed at quantifying residual strains of the tissues in longitudinal and circumferential directions, showed that the hypoxia condition leads to an increase in the longitudinal stretch and a marked decrease of the circumferential residual strain. The uniaxial mechanical tests were used to determine the elastic properties of the tissues, showing that a general stiffening process occurs during the early stages of the IH (STH group), specially leading to a significative increase in the high strain elastic modulus ([Formula: see text]) and an increasing trend of low strain elastic modulus ([Formula: see text]). In contrast, the LTH group showed a more control-like mechanical behavior. Myography test, used to assess the vasoactive function, revealed that IH induces a high sensitivity to vasoconstrictor agents as a function of hypoxic cycles. In addition, the aorta showed an increased muscle-dependent vasorelaxation on the LTH group. Histological tests, used to quantify the elastic fiber, nuclei, and geometrical properties, showed that the STH group presents a state of vascular fibrosis, with a significant increase in elastin content, and a tendency towards an increase in collagen fibers. In addition, advanced stages of IH (LTH), showed a vascular remodeling effect with a significant increase of internal and external diameters. Considering all the multidimensional vascular effects, we propose the existence of a long-term passive adaptation mechanism and vascular dysfunction as cycle-dependent effects of intermittent exposures to hypobaric hypoxia.

Fluid Flow and Structural Numerical Analysis of a Cerebral Aneurysm Model

Intracranial aneurysms (IA) are dilations of the cerebral arteries and, in most cases, have no symptoms. However, it is a very serious pathology, with a high mortality rate after rupture. Several studies have been focused only on the hemodynamics of the flow within the IA. However, besides the effect of the flow, the development and rupture of the IA are also associated with a combination of other factors such as the wall mechanical behavior. Thus, the objective of this work was to analyze, in addition to the flow behavior, the biomechanical behavior of the aneurysm wall. For this, CFD simulations were performed for different Reynolds numbers (1, 100, 500 and 1000) and for two different rheological models (Newtonian and Carreau). Subsequently, the pressure values of the fluid simulations were exported to the structural simulations in order to qualitatively observe the deformations, strains, normal stresses and shear stress generated in the channel wall. For the structural simulations, a hyperelastic constitutive model (5-parameter Mooney–Rivlin) was used. The results show that with the increase in the Reynolds number (Re), the recirculation phenomenon is more pronounced, which is not seen for Re = 1. The higher the Re, the higher the strain, displacement, normal and shear stresses values.

Heterogeneous microstructural changes of the cervix influence cervical funneling

The cervix acts as a dynamic barrier between the uterus and vagina, retaining the fetus during pregnancy and allowing birth at term. Critical to this function, the physical properties of the cervix change, or remodel, but abnormal remodeling can lead to preterm birth (PTB). Although cervical remodeling has been studied, the complex 3D cervical microstructure has not been well-characterized. In this complex, dynamic, and heterogeneous tissue microenvironment, the microstructural changes are likely also heterogeneous. Using quantitative, 3D, second-harmonic generation microscopy, we demonstrate that rat cervical remodeling during pregnancy is not uniform across the cervix; the collagen fibers orient progressively more perpendicular to the cervical canals in the inner cervical zone, but do not reorient in other regions. Furthermore, regions that are microstructurally distinct early in pregnancy become more similar as pregnancy progresses. We use a finite element simulation to show that heterogeneous regional changes influence cervical funneling, an important marker of increased risk for PTB; the internal cervical os shows ∼6.5x larger radial displacement when fibers in the inner cervical zone are parallel to the cervical canals compared to when fibers are perpendicular to the canals. Our results provide new insights into the microstructural and tissue-level cervical changes that have been correlated with PTB and motivate further clinical studies exploring the origins of cervical funneling. STATEMENT OF SIGNIFICANCE: Cervical funneling, or dilation of the internal cervical os, is highly associated with increased risk of preterm birth. This study explores the 3D microstructural changes of the rat cervix during pregnancy and illustrates how these changes influence cervical funneling, assuming similar evolution in rats and humans. Quantitative imaging showed that microstructural remodeling during pregnancy is nonuniform across cervical regions and that initially distinct regions become more similar. We report, for the first time, that remodeling of the inner cervical zone can influence the dilation of the internal cervical os and allow the cervix to stay closed despite increased intrauterine pressure. Our results suggest a possible relationship between the microstructural changes of this zone and cervical funneling, motivating further clinical investigations.

Experimental Investigation of the Anisotropic Mechanical Response of the Porcine Thoracic Aorta

Knowledge of the mechanical properties of blood vessels and determining appropriate constitutive relations are essential in developing methodologies for accurate prognosis of vascular diseases. We examine the directional variation of the mechanical properties of the porcine thoracic aorta by performing uniaxial extension tests on dumbbell-shaped specimens cut at five different orientations with respect to the circumferential direction of the aorta. Specimens in all the orientations considered exhibit a nonlinear constitutive response that is typical of collagenous soft tissues. Shear strain under uniaxial extension demonstrates clearly discernible anisotropy of the mechanical response of the porcine aorta, and samples oriented at 45[Formula: see text] and 60[Formula: see text] with respect to the circumferential direction show a peculiar crescent-shaped shear strain-nominal stretch response not displayed by axial and circumferential specimens. Failure stress indicates decreasing tensile strength of the porcine aortic wall from the circumferential direction to the longitudinal direction. Furthermore, we determine the material parameters for the four-fiber-family and Gasser-Holzapfel-Ogden models from the mechanical response data of the circumferential and longitudinal specimens. It is shown how the material parameters derived from the uniaxial tests on circumferential and longitudinal specimens are insufficient to characterize the response of off-axis specimens.

Maturation Fetus Ascending Aorta Elastic Properties: Circumferential Strain and Longitudinal Strain by Velocity Vector Imaging

Objective

This study aimed to assess the circumferential and longitudinal strain of the fetal ascending aortic (AA) wall and establish a gestational age-associated longitudinal reference for aortic wall strain during the second half of pregnancy.

Methods

Singleton fetuses with gestational age (GA) at 20 + 0 to 24 + 6 weeks were prospectively collected from a low-risk population. Global circumferential strain (GCS) and mean longitudinal strain (MLS) of the ascending aorta were measured serially at 4-week intervals using the velocity vector imaging (VVI) technique. Fractional polynomials were conducted to obtain the best-fitting curves between GA and AA strains. GA-specific reference percentiles of GCS and MLS were established by multilevel modeling.

Results

A total of 223 fetuses with a total of 1,127 serial observations were enrolled. GCS presented a second-degree fractional polynomial smoothing regression along GA (R2 = 0.635, P &lt; 0.05). Fetal aortic GCS remained unchanged at ~27.29% (20.36–35.6%) before 31 weeks and increased significantly from 31.36% (26.38–37.12%) at 31 weeks to 43.29% (30.5–56.78%) at term. MLS presented a third-degree fractional polynomial smoothing regression along GA (R2 = 0.465, P &lt; 0.05). MLS remained steady at ~10.03% (3.28–17.62%) between 20 and 31 weeks and then increased significantly from 12.68% (7.42–20.1%) at 32 weeks to 17.5% (9.67–25.34%) at term. The GCS was significantly higher than the MLS in the ascending aorta wall (p &lt; 0.001).

Conclusion

The fetal ascending aorta wall demonstrates obviously greater circumferential strain than longitudinal strain. Both strains remained steady before the late trimester and then gradually increased until delivery, suggesting progressive maturation of aortic elasticity mechanics.

Physiological basis for longitudinal motion of the arterial wall

As opposed to arterial distension in the radial plane, longitudinal wall motion (LWM) is a multiphasic and bidirectional displacement of the arterial wall in the anterograde (i.e., in the direction of blood flow) and retrograde (i.e., opposing direction of blood flow) directions. While initially disregarded as imaging artifact, LWM has been consistently reported in ultrasound investigations in the last decade and is reproducible beat-to-beat, albeit with large inter-individual variability across healthy and diseased populations. Emerging literature has sought to examine the mechanistic control of LWM to explain the shape and variability of the motion pattern but lacks considerations for key foundational vascular principles at the level of the arterial wall ultrastructure. The purpose of this review is to summarize the potential factors that underpin the causes and control of arterial LWM, spanning considerations from the arterial extracellular matrix to systems-level integrative theories. First, an overview of LWM and relevant aspects wall composition will be discussed, including major features of the multiphasic pattern, arterial wall extracellular components, tunica fiber orientations, and arterial longitudinal pre-stretch. Second, current theories on the systems-level physiological mechanisms driving LWM will be discussed in the context of available evidence including experimental human research, porcine studies, and mathematical models. Throughout, we discuss implications of these observations with suggestions for future priority research areas.

Effects of dispersed fibres in myocardial mechanics, Part II: active response

This work accompanies the first part of our study "effects of dispersed fibres in myocardial mechanics: Part I passive response" with a focus on myocardial active contraction. Existing studies have suggested that myofibre architecture plays an important role in myocardial active contraction. Following the first part of our study, we firstly study how the general fibre architecture affects ventricular pump function by varying the mean myofibre rotation angles, and then the impact of fibre dispersion along the myofibre direction on myocardial contraction in a left ventricle model. Dispersed active stress is described by a generalised structure tensor method for its computational efficiency. Our results show that both the myofibre rotation angle and its dispersion can significantly affect cardiac pump function by redistributing active tension circumferentially and longitudinally. For example, larger myofibre rotation angle and higher active tension along the sheet-normal direction can lead to much reduced end-systolic volume and higher longitudinal shortening, and thus a larger ejection fraction. In summary, these two studies together have demonstrated that it is necessary and essential to include realistic fibre structures (both fibre rotation angle and fibre dispersion) in personalised cardiac modelling for accurate myocardial dynamics prediction.

A Strain-Rate Dependent Constitutive Model for Göttingen Minipig Cerebral Arteries

Computational simulations of traumatic brain injury (TBI) are commonly used to advance understanding of the injury-pathology relationship, tissue damage thresholds, and design of protective equipment such as helmets. Both human and animal TBI models have developed substantially over recent decades, partially due to the inclusion of more detailed brain geometry and representation of tissues like cerebral blood vessels. Explicit incorporation of vessels dramatically affects local strain and enables researchers to investigate TBI-induced damage to the vasculature. While some studies have indicated that cerebral arteries are rate-dependent, no published experimentally based, rate-sensitive constitutive models of cerebral arteries exist. In the present work, we characterize the mechanical properties of axially failed porcine arteries, both quasi-statically (0.01 s-1) and at high rate (<100 s-1), and propose a rate-sensitive model to fit the data. We find that the quasi-static and high-rate stress-stretch curves become significantly different (p>0.05) above a stretch of 1.23. We additionally find a significant change in both failure stretch and stress as a result of strain rate. The stress-stretch curve is then modeled as a Holzapfel-Gasser-Ogden material, with a Prony series added to capture the effects of viscoelasticity. Ultimately, this paper demonstrates that rate dependence should be considered in the material properties of cerebral arteries undergoing high strain-rate deformations and provides a ready-to-use model for finite element implementation.

Effects of dispersed fibres in myocardial mechanics, Part I: passive response

It is widely acknowledged that an imbalanced biomechanical environment can have significant effects on myocardial pathology, leading to adverse remodelling of cardiac function if it persists. Accurate stress prediction essentially depends on the strain energy function which should have competent descriptive and predictive capabilities. Previous studies have focused on myofibre dispersion, but not on fibres along other directions. In this study, we will investigate how fibre dispersion affects myocardial biomechanical behaviours by taking into account both the myofibre dispersion and the sheet fibre dispersion, with a focus on the sheet fibre dispersion. Fibre dispersion is incorporated into a widely-used myocardial strain energy function using the discrete fibre bundle approach. We first study how different dispersion affects the descriptive capability of the strain energy function when fitting to ex vivo experimental data, and then the predictive capability in a human left ventricle during diastole. Our results show that the chosen strain energy function can achieve the best goodness-of-fit to the experimental data by including both fibre dispersion. Furthermore, noticeable differences in stress can be found in the LV model. Our results may suggest that it is necessary to include both dispersion for myofibres and the sheet fibres for the improved descriptive capability to the ex vivo experimental data and potentially more accurate stress prediction in cardiac mechanics.

Towards a Digital Twin of Coronary Stenting: A Suitable and Validated Image-Based Approach for Mimicking Patient-Specific Coronary Arteries

Considering the field of application involving stent deployment simulations, the exploitation of a digital twin of coronary stenting that can reliably mimic the patient-specific clinical reality could lead to improvements in individual treatments. A starting step to pursue this goal is the development of simple, but at the same time, robust and effective computational methods to obtain a good compromise between the accuracy of the description of physical phenomena and computational costs. Specifically, this work proposes an approach for the development of a patient-specific artery model to be used in stenting simulations. The finite element model was generated through a 3D reconstruction based on the clinical imaging (coronary Optical Coherence Tomography (OCT) and angiography) acquired on the pre-treatment patient. From a mechanical point of view, the coronary wall was described with a suitable phenomenological model, which is consistent with more complex constitutive approaches and accounts for the in vivo pressurization and axial pre-stretch. The effectiveness of this artery modeling method was tested by reproducing in silico the stenting procedures of two clinical cases and comparing the computational results with the in vivo lumen area of the stented vessel.

Personalized Pre- and Post-Operative Hemodynamic Assessment of Aortic Coarctation from 3D Rotational Angiography

PURPOSE

Coarctation of Aorta (CoA) is a congenital disease consisting of a narrowing that obstructs the systemic blood flow. This proof-of-concept study aimed to develop a framework for automatically and robustly personalizing aortic hemodynamic computations for the assessment of pre- and post-intervention CoA patients from 3D rotational angiography (3DRA) data.

METHODS

We propose a framework that combines hemodynamic modelling and machine learning (ML) based techniques, and rely on 3DRA data for non-invasive pressure computation in CoA patients. The key features of our framework are a parameter estimation method for calibrating inlet and outlet boundary conditions, and regional mechanical wall properties, to ensure that the computational results match the patient-specific measurements, and an improved ML based pressure drop model capable of predicting the instantaneous pressure drop for a wide range of flow conditions and anatomical CoA variations.

RESULTS

We evaluated the framework by investigating 6 patient datasets, under pre- and post-operative setting, and, since all calibration procedures converged successfully, the proposed approach is deemed robust. We compared the peak-to-peak and the cycle-averaged pressure drop computed using the reduced-order hemodynamic model with the catheter based measurements, before and after virtual and actual stenting. The mean absolute error for the peak-to-peak pressure drop, which is the most relevant measure for clinical decision making, was 2.98 mmHg for the pre- and 2.11 mmHg for the post-operative setting. Moreover, the proposed method is computationally efficient: the average execution time was of only [Formula: see text] minutes on a standard hardware configuration.

CONCLUSION

The use of 3DRA for hemodynamic modelling could allow for a complete hemodynamic assessment, as well as virtual interventions or surgeries and predictive modeling. However, before such an approach can be used routinely, significant advancements are required for automating the workflow.

Passive biaxial mechanical behavior of newborn mouse aorta with and without elastin

Aortic wall material properties are needed for computational models and for comparisons across developmental and disease states. There has been abundant work in comparing aortic material properties across disease states, but limited work across developmental states. We performed passive biaxial mechanical testing on newborn mouse aorta with (Eln^+/+) and without (Eln^-/-) elastin. Elastin provides elasticity to the aortic wall and is necessary for survival beyond birth in the mouse. Mechanically functional elastin is challenging to create in vitro and so Eln^-/- aorta can be a comparison for tissue engineered arteries with limited elastin amounts. We found that a traditional arterial strain energy function provided reasonable fits to newborn mouse aorta and generally predicted lower material constants in Eln^-/- compared to Eln^+/+ aorta. At physiologic pressures, the circumferential stresses and moduli trended lower in Eln^-/- compared to Eln^+/+ aorta. Increased blood pressure in Eln^-/- mice helps to alleviate the differences in stresses and moduli. Increased blood pressure also serves to partially offload stresses in the isotropic compared to the anisotropic component of the wall. The baseline material parameters can be used in computational models of growth and remodeling to improve understanding of developmental mechanobiology and tissue engineering strategies.

A Nonparametric Approach for Estimating Three-Dimensional Fiber Orientation Distribution Functions (ODFs) in Fibrous Materials

Many biological tissues contain an underlying fibrous microstructure that is optimized to suit a physiological function. The fiber architecture dictates physical characteristics such as stiffness, diffusivity, and electrical conduction. Abnormal deviations of fiber architecture are often associated with disease. Thus, it is useful to characterize fiber network organization from image data in order to better understand pathological mechanisms. We devised a method to quantify distributions of fiber orientations based on the Fourier transform and the Qball algorithm from diffusion MRI. The Fourier transform was used to decompose images into directional components, while the Qball algorithm efficiently converted the directional data from the frequency domain to the orientation domain. The representation in the orientation domain does not require any particular functional representation, and thus the method is nonparametric. The algorithm was verified to demonstrate its reliability and used on datasets from microscopy to show its applicability. This method increases the ability to extract information of microstructural fiber organization from experimental data that will enhance our understanding of structure-function relationships and enable accurate representation of material anisotropy in biological tissues.

Simulating progressive intramural damage leading to aortic dissection using DeepONet: an operator-regression neural network

Aortic dissection progresses mainly via delamination of the medial layer of the wall. Notwithstanding the complexity of this process, insight has been gleaned by studying in vitro and in silico the progression of dissection driven by quasi-static pressurization of the intramural space by fluid injection, which demonstrates that the differential propensity of dissection along the aorta can be affected by spatial distributions of structurally significant interlamellar struts that connect adjacent elastic lamellae. In particular, diverse histological microstructures may lead to differential mechanical behaviour during dissection, including the pressure-volume relationship of the injected fluid and the displacement field between adjacent lamellae. In this study, we develop a data-driven surrogate model of the delamination process for differential strut distributions using DeepONet, a new operator-regression neural network. This surrogate model is trained to predict the pressure-volume curve of the injected fluid and the damage progression within the wall given a spatial distribution of struts, with in silico data generated using a phase-field finite-element model. The results show that DeepONet can provide accurate predictions for diverse strut distributions, indicating that this composite branch-trunk neural network can effectively extract the underlying functional relationship between distinctive microstructures and their mechanical properties. More broadly, DeepONet can facilitate surrogate model-based analyses to quantify biological variability, improve inverse design and predict mechanical properties based on multi-modality experimental data.

Predicting the Effect of Localized ACL Damage on Neighbor Ligament Mechanics via Finite Element Modeling

The anterior cruciate ligament (ACL) plays a pivotal role in support of the knee under loading. When damaged, it is known that substantial changes in the mechanics of the neighboring ligaments can be observed. However, a localized damage approach to investigating how ACL deficiency influences the neighboring ligaments has not been carried out. To do this, a finite element model, incorporating a continuum damage material model of the ACL, was implemented. Localized ACL damage was induced using high quadriceps force loading. Once damaged, anterior shear forces or tibial torque loadings were applied to the knee joint. The relative changes in stress contour and average mid-substance stress were examined for each of the neighboring ligaments following localized ACL damage. It was observed that localized ACL damage could produce notable changes in the mechanics of the neighboring knee ligaments, with non-homogenous stress contour shape changes and average stress magnitude being observed to increase in most cases, with a notable exception occurring in the MCL for both loading modes. In addition, the ligament bearing the most loading also changed with ACL deficiency. These changes carry implications as to morphological effects that may be induced following localized ACL damage, indicating that early diagnosis of ACL injury may be helpful in mitigating other complications post injury.

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

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

Role of smooth muscle activation in the static and dynamic mechanical characterization of human aortas

The rupture of aortic aneurysms causes around 10,000 deaths each year in the United States. Prosthetic tubes for aortic repair present a large mismatch of mechanical properties with the natural aorta, which has negative consequences for perfusion. This motivates research into the mechanical characterization of human aortas to develop a new generation of mechanically compatible aortic grafts. Experimental data and a suitable material model for human aortas with vascular smooth muscle (VSM) activation are not available. Hence, the present study provides experimental data that are needed. These data made it possible to develop a precise structure-based model of active aortic tissue. The results show the importance of VSM activation on the static and dynamic mechanical response of human aortas.

Experimental data and a suitable material model for human aortas with smooth muscle activation are not available in the literature despite the need for developing advanced grafts; the present study closes this gap. Mechanical characterization of human descending thoracic aortas was performed with and without vascular smooth muscle (VSM) activation. Specimens were taken from 13 heart-beating donors. The aortic segments were cooled in Belzer UW solution during transport and tested within a few hours after explantation. VSM activation was achieved through the use of potassium depolarization and noradrenaline as vasoactive agents. In addition to isometric activation experiments, the quasistatic passive and active stress–strain curves were obtained for circumferential and longitudinal strips of the aortic material. This characterization made it possible to create an original mechanical model of the active aortic material that accurately fits the experimental data. The dynamic mechanical characterization was executed using cyclic strain at different frequencies of physiological interest. An initial prestretch, which corresponded to the physiological conditions, was applied before cyclic loading. Dynamic tests made it possible to identify the differences in the viscoelastic behavior of the passive and active tissue. This work illustrates the importance of VSM activation for the static and dynamic mechanical response of human aortas. Most importantly, this study provides material data and a material model for the development of a future generation of active aortic grafts that mimic natural behavior and help regulate blood pressure.

Fluid-structure interaction simulation of tissue degradation and its effects on intra-aneurysm hemodynamics

Tissue degradation plays a crucial role in vascular diseases such as atherosclerosis and aneurysms. Computational modeling of vascular hemodynamics incorporating both arterial wall mechanics and tissue degradation has been a challenging task. In this study, we propose a novel finite element method-based approach to model the microscopic degradation of arterial walls and its interaction with blood flow. The model is applied to study the combined effects of pulsatile flow and tissue degradation on the deformation and intra-aneurysm hemodynamics. Our computational analysis reveals that tissue degradation leads to a weakening of the aneurysmal wall, which manifests itself in a larger deformation and a smaller von Mises stress. Moreover, simulation results for different heart rates, blood pressures and aneurysm geometries indicate consistently that, upon tissue degradation, wall shear stress increases near the flow-impingement region and decreases away from it. These findings are discussed in the context of recent reports regarding the role of both high and low wall shear stress for the progression and rupture of aneurysms.

A Review on Damage and Rupture Modelling for Soft Tissues

Computational modelling of damage and rupture of non-connective and connective soft tissues due to pathological and supra-physiological mechanisms is vital in the fundamental understanding of failures. Recent advancements in soft tissue damage models play an essential role in developing artificial tissues, medical devices/implants, and surgical intervention practices. The current article reviews the recently developed damage models and rupture models that considered the microstructure of the tissues. Earlier review works presented damage and rupture separately, wherein this work reviews both damage and rupture in soft tissues. Wherein the present article provides a detailed review of various models on the damage evolution and tear in soft tissues focusing on key conceptual ideas, advantages, limitations, and challenges. Some key challenges of damage and rupture models are outlined in the article, which helps extend the present damage and rupture models to various soft tissues.

Biomechanical characterization and constitutive modeling of the layer-dissected residual strains and mechanical properties of abdominal porcine aorta

We analyze the residual stresses and mechanical properties of layer-dissected infrarenal abdominal aorta (IAA). We measured the axial pre-stretch and opening angle and performed uniaxial tests to study and compare the mechanical behavior of both intact and layer-dissected porcine IAA samples under physiological loads. Finally, some of the most popular anisotropic hyperelastic constitutive models (GOH and microfiber models) were proposed to estimate the mechanical properties of the abdominal aorta by least-square fitting of the recorded in-vitro uniaxial test results. The results show that the residual stresses are layer dependent. In all cases, we found that the OA in the media layer is lower than in the whole artery, the intima and the adventitia. For the axial pre-stretch, we found that the adventitia and the media were slightly stretched in the environment of the intact arterial strip, whereas the intima appears to be compressed. Regarding the mechanical properties, the media seems to be the softest layer over the whole deformation domain showing high anisotropy, while the intima and adventitia exhibit considerable stiffness and a lower anisotropy response. Finally, all the hyperelastic anisotropic models considered in this study provided a reasonable approximation of the experimental data. The GOH model showed the best fitting.