Isotropic Failure Criteria Are Not Appropriate for Anisotropic Fibrous Biological Tissues

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.

Biomechanical Modeling of Cesarean Section Scars and Scar Defects

Uterine rupture is an intrinsically biomechanical process associated with high maternal and fetal mortality. A previous Cesarean section (C-section) is the main risk factor for uterine rupture in a subsequent pregnancy due to tissue failure at the scar region. Finite element modeling of the uterus and scar tissue presents a promising method to further understand and predict uterine ruptures. Using patient dimensions of an at-term uterus, a C-section scar was modeled with an applied intrauterine pressure to study how scars affect uterine stress. The scar positioning and uterine thickness were varied, and a defect was incorporated into the scar region. The modeled stress distributions confirmed clinical observations as the increased regions of stress due to scar positioning, thinning of the uterine walls, and the presence of a defect are consistent with clinical observations of features that increase the risk of uterine rupture.

An Approach to Quantify Anisotropic Multiaxial Failure of the Annulus Fibrosus

Tears in the annulus fibrosus (AF) of the intervertebral disk (IVD) occur due to multiaxial loading on the spine. However, most existing AF failure studies measure uniaxial stress, not the multiaxial stress at failure. Delamination theory, which requires advanced structural knowledge and knowledge about the interactions between the AF fibers and matrix, has historically been used to understand and predict AF failure. Alternatively, a simple method, the Tsai-Hill yield criteria, could describe multiaxial failure of the AF. This yield criteria uses the known tissue fiber orientation and an equation to establish the multiaxial failure stresses that cause failure. This paper presents a method to test the multiaxial failure stress of the AF experimentally and evaluate the potential for the Tsai-Hill model to predict these failure stresses. Porcine AF was cut into a dogbone shape at three distinct angles relative to the primary lamella direction (parallel, transverse, and oblique). Then, each dogbone was pulled to complete rupture. The Cauchy stress in the material's fiber coordinates was calculated. These multiaxial stress parameters were used to optimize the coefficients of the Tsai-Hill yield. The coefficients obtained for the Tsai-Hill model vary by an order of magnitude between the fiber and transverse directions, and these coefficients provide a good description of the AF multiaxial failure stress. These results establish both an experimental approach and the use of the Tsai-Hill model to explain the anisotropic failure behavior of the tissue.

A review on the biomechanical behaviour of the aorta

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

The Role of the Extrafibrillar Volume on the Mechanical Properties of Molecular Models of Mineralized Bone Microfibrils

Bones are responsible for body support, structure, motion, and several other functions that enable and facilitate life for many different animal species. They exhibit a complex network of distinct physical structures and mechanical properties, which ultimately depend on the fraction of their primary constituents at the molecular scale. However, the relationship between structure and mechanical properties in bones are still not fully understood. Here, we investigate structural and mechanical properties of all-atom bone molecular models composed of type-I collagen, hydroxyapatite (HA), and water by means of fully atomistic molecular dynamics simulations. Our models encompass an extrafibrillar volume (EFV) and consider mineral content in both the EFV and intrafibrillar volume (IFV), consistent with experimental observations. We investigate solvation structures and elastic properties of bone microfibril models with different degrees of mineralization, ranging from highly mineralized to weakly mineralized and nonmineralized models. We find that the local tetrahedral order of water is lost in similar ways in the EFV and IFV regions for all HA containing models, as calcium and phosphate ions are strongly coordinated with water molecules. We also subject our models to tensile loads and analyze the spatial stress distribution over the nanostructure of the material. Our results show that both mineral and water contents accumulate significantly higher stress levels, most notably in the EFV, thus revealing that this region, which has been only recently incorporated in all-atom molecular models, is fundamental for studying the mechanical properties of bones at the nanoscale. Furthermore, our results corroborate the well-established finding that high mineral content makes bone stiffer.

Impact of Wound Dressing on Mechanotransduction within Tissues of Chronic Wounds

Chronic wounds are significant public health problems impacting the health-related quality of individuals' lives (due to disability, decreased productivity, and loss of independence) and an immense economic burden to healthcare systems around the world. In this study, our main objective is to investigate how mechanotransduction can impact the healing process in chronic wounds. We have developed new three-dimensional models of wound tissue to study the distribution of forces within these tissues exerted by wound dressings with different characteristics. The roles of mechanical forces on wound healing have gained significant clinical attention; the application of mechanical forces is expected to influence the physiology of tissue surrounding a wound. We aim to investigate whether the force transmission within wound tissue is impacted by the dressing characteristics and whether this impact may differ with wound tissue's properties. Our results show that wound dressings with lower stiffnesses promote force transmission within a wound tissue. This impact is even more significant on stiffer wound tissues. Furthermore, we show that size of wound dressing alters forces that transmit within the wound tissue where dressings with 9 cm length show higher stresses. The wound tissue stiffening has been associated with healing of a wound. Our results demonstrate that wounds with stiffer tissue experience higher stresses. Taken all together, our findings suggest that low stiffness of wound dressing and its size may be introduced as a criterion to explain parameters predisposing a chronic wound to heal. This study's findings on the role of dressings and tissue characteristics demonstrate that precision dressings are required for wound management and understanding how a dressing impacts mechanotransduction in wound tissue will lead to design of novel dressings promoting healing in chronic wounds.

FINITE ELEMENT EVALUATION OF THE EFFECT OF ADHESIVE CREAMS ON THE STRESS STATE OF DENTURES AND ABUTMENT TEETH

The appropriate fit of removable partial dentures (RPDs) is hypothesized to lead to lower tooth mobility. An adhesive layer between the denture and oral mucosa can facilitate better denture retention and therefore increased stability. Study objectives were to model and compare the response of abutment structures with and without the application of a denture adhesive and to observe the stress response of abutment periodontal ligaments (PDLs) during the application of occlusal force on the RPD. A 3D finite element (FE) model was developed from computer tomography datasets of the mandibular region and the RPD. An adhesive layer was developed by extending the denture surface and using the Prony series approximation of rheological data to implement a viscoelastic material model. FE simulations were performed by applying a bite force on one of the denture segments, with the resulting deformation in PDL compared between the model with the adhesive layer and the base model without. The maximum deformation of 15[Formula: see text][Formula: see text]m was observed in the 2nd molar abutment PDL with the implementation of the adhesive, as compared to 42[Formula: see text][Formula: see text]m for the model without. The lower impact of RPDs on the supporting abutment teeth could potentially reduce the discomfort of denture wearers.

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.

Computation of a probabilistic and anisotropic failure metric on the aortic wall using a machine learning-based surrogate model

Scalar-valued failure metrics are commonly used to assess the risk of aortic aneurysm rupture and dissection, which occurs under hypertensive blood pressures brought on by extreme emotional or physical stress. To compute failure metrics under an elevated blood pressure, a classical patient-specific computer model consists of multiple computation steps involving inverse and forward analyses. These classical procedures may be impractical for time-sensitive clinical applications that require prompt feedback to clinicians. In this study, we developed a machine learning-based surrogate model to directly predict a probabilistic and anisotropic failure metric, namely failure probability (FP), on the aortic wall using aorta geometries at the systolic and diastolic phases. Ascending thoracic aortic aneurysm (ATAA) geometries of 60 patients were obtained from their CT scans, and biaxial mechanical testing data of ATAA tissues from 79 patients were collected. Finite element simulations were used to generate datasets for training, validation, and testing of the ML-surrogate model. The testing results demonstrated that the ML-surrogate can compute the maximum FP failure metric, with 0.42% normalized mean absolute error, in 1 s. To compare the performance of the ML-predicted probabilistic FP metric with other isotropic or deterministic metrics, a numerical case study was performed using synthetic "baseline" data. Our results showed that the probabilistic FP metric had more discriminative power than the deterministic Tsai-Hill metric, isotropic maximum principal stress, and aortic diameter criterion.

The Ring-Pull Assay for Mechanical Properties of Fibrous Soft Tissues - An Analysis of the Uniaxial Approximation and a Correction for Nonlinear Thick-Walled Tissues

BACKGROUND

The ring-pull test, where a ring of tissue is hooked via two pins and stretched, is a popular biomechanical test, especially for small arteries. Although convenient and reliable, the ring test produces inhomogeneous strain, making determination of material parameters non-trivial.

OBJECTIVE

To determine correction factors between ring-pull-estimated and true tissue properties.

METHODS

A finite-element model of ring pulling was constructed for a sample with nonlinear, anisotropic mechanical behavior typical of arteries. The pin force and sample cross-section were used to compute an apparent modulus at small and large strain, which were compared to the specified properties. The resulting corrections were validated with experiments on porcine and ovine arteries. The correction was further applied to experiments on mouse aortic rings to determine material and failure properties.

RESULTS

Calculating strain based on centerline stretch rather than inner-wall or outer-wall stretch afforded better estimation of tissue properties. Additional correction factors were developed based on ring wall thickness H, centerline ring radius R c , and pin radius a. The corrected estimates for tissue properties were in good agreement with uniaxial stretch experiments.

CONCLUSIONS

The computed corrections improved estimation of tissue material properties for both the small-strain (toe) modulus and the large-strain (lockout) modulus. When measuring tensile strength, one should minimize H/a to ensure that peak stress occurs at the sample midplane rather than near the pin. In this scenario, tensile strength can be estimated accurately by using inner-wall stretch at the midplane and the corrected properties.

A Novel Anisotropic Failure Criterion With Dispersed Fiber Orientations for Aortic Tissues

Accurate failure criteria play a fundamental role in biomechanical analyses of aortic wall rupture and dissection. Experimental investigations have demonstrated a significant difference of aortic wall strengths in the circumferential and axial directions. Therefore, the isotropic von Mises stress and maximum principal stress, commonly used in computational analysis of the aortic wall, are inadequate for modeling of anisotropic failure properties. In this study, we propose a novel stress-based anisotropic failure criterion with dispersed fiber orientations. In the new failure criterion, the overall failure metric is computed by using angular integration (AI) of failure metrics in all directions. Affine rotations of fiber orientations due to finite deformation are taken into account in an anisotropic hyperelastic constitutive model. To examine fitting capability of the failure criterion, a set of off-axis uniaxial tension tests were performed on aortic tissues of four porcine individuals and 18 human ascending thoracic aortic aneurysm (ATAA) patients. The dispersed fiber failure criterion demonstrates a good fitting capability with the off-axis testing data. Under simulated biaxial stress conditions, the dispersed fiber failure criterion predicts a smaller failure envelope comparing to those predicted by the traditional anisotropic criteria without fiber dispersion, which highlights the potentially important role of fiber dispersion in the failure of the aortic wall. Our results suggest that the deformation-dependent fiber orientations need to be considered when wall strength determined from uniaxial tests are used for in vivo biomechanical analysis. More investigations are needed to determine biaxial failure properties of the aortic wall.

Investigating Commercial Filaments for 3D Printing of Stiff and Elastic Constructs with Ligament-Like Mechanics

The current gold standard technique for treatment of anterior cruciate ligament (ACL) injury is reconstruction with autograft. These treatments have a relatively high failure and re-tear rate. To overcome this, tissue engineering and additive manufacturing are being used to explore the potential of 3D scaffolds as autograft substitutes. However, mechanically optimal polymers for this have yet to be identified. Here, we use 3D printing technology and various materials with the aim of fabricating constructs better matching the mechanical properties of the native ACL. A fused deposition modeling (FDM) 3D printer was used to microfabricate dog bone-shaped specimens from six different polymers—PLA, PETG, Lay FOMM 60, NinjaFlex, NinjaFlex-SemiFlex, and FlexiFil—at three different raster angles. The tensile mechanical properties of these polymers were determined from stress–strain curves. Our results indicate that no single material came close enough to successfully match reported mechanical properties of the native ACL. However, PLA and PETG had similar ultimate tensile strengths. Lay FOMM 60 displayed a percentage strain at failure similar to reported values for native ACL. Furthermore, raster angle had a significant impact on some mechanical properties for all of the materials except for FlexiFil. We therefore conclude that while none of these materials alone is optimal for mimicking ACL mechanical properties, there may be potential for creating a 3D-printed composite constructs to match ACL mechanical properties. Further investigations involving co-printing of stiff and elastomeric materials must be explored.

Computational modeling of the strength of the ascending thoracic aortic media tissue under physiologic biaxial loading conditions

Type A Aortic Dissection (TAAD) is a life-threatening condition involving delamination of ascending aortic media layers. While current clinical guidelines recommend surgical intervention for aneurysm diameter > 5.5 cm, high incidence of TAAD in patients below this diameter threshold indicates the pressing need for improved evidence-based risk prediction metrics. Construction of such metrics will require the knowledge of the biomechanical failure properties of the aortic wall tissue under biaxial loading conditions. We utilized a fiber-level finite element based structural model of the aortic tissue to quantify the relationship between aortic tissue strength and physiologically relevant biaxial stress state for nonaneurysmal and aneurysmal patient cohorts with tricuspid aortic valve phenotype. We found that the model predicted strength of the aortic tissue under physiologic biaxial loading conditions depends on the stress biaxiality ratio, defined by the ratio of the longitudinal and circumferential components of the tissue stress. We determined that predicted biaxial tissue strength is statistically similar to its uniaxial circumferential strength below biaxiality ratios of 0.68 and 0.69 for nonaneurysmal and aneurysmal cohorts, respectively. Beyond this biaxiality ratio, predicted biaxial strength for both cohorts reduced drastically to a magnitude statistically similar to its longitudinal strength. We identified fiber-level failure mechanisms operative under biaxial stress state governing aforementioned tissue failure behavior. These findings are an important first step towards the development of mechanism-based TAAD risk assessment metrics for early identification of high-risk patients.

Ex Vivo Mechanical Tests and Multiscale Computational Modeling Highlight the Importance of Intramural Shear Stress in Ascending Thoracic Aortic Aneurysms

Ascending thoracic aortic aneurysms (ATAAs) are anatomically complex in terms of architecture and geometry, and both complexities contribute to unpredictability of ATAA dissection and rupture in vivo. The goal of this work was to examine the mechanism of ATAA failure using a combination of detailed mechanical tests on human tissue and a multiscale computational model. We used (1) multiple, geometrically diverse, mechanical tests to characterize tissue properties; (2) a multiscale computational model to translate those results into a broadly usable form; and (3) a model-based computer simulation of the response of an ATAA to the stresses generated by the blood pressure. Mechanical tests were performed in uniaxial extension, biaxial extension, shear lap, and peel geometries. ATAA tissue was strongest in circumferential extension and weakest in shear, presumably because of the collagen and elastin in the arterial lamellae. A multiscale, fiber-based model using different fiber properties for collagen, elastin, and interlamellar connections was specified to match all of the experimental data with one parameter set. Finally, this model was used to simulate ATAA inflation using a realistic geometry. The predicted tissue failure occurred in regions of high stress, as expected; initial failure events involved almost entirely interlamellar connections, consistent with arterial dissection-the elastic lamellae remain intact, but the connections between them fail. The failure of the interlamellar connections, paired with the weakness of the tissue under shear loading, is suggestive that shear stress within the tissue may contribute to ATAA dissection.

FEM-Based Compression Fracture Risk Assessment in Osteoporotic Lumbar Vertebra L1

This paper presents a finite element method (FEM)-based fracture risk assessment in patient-specific osteoporotic lumbar vertebra L1. The influence of osteoporosis is defined by variation of parameters such as thickness of the cortical shell, the bone volume–total volume ratio (BV/TV), and the trabecular bone score (TBS). The mechanical behaviour of bone is defined using the Ramberg–Osgood material model. This study involves the static and nonlinear dynamic calculations of von Mises stresses and follows statistical processing of the obtained results in order to develop the patient-specific vertebra reliability. In addition, different scenarios of parameters show that the reliability of the proposed model of human vertebra highly decreases with low levels of BV/TV and is critical due to the thinner cortical bone, suggesting high trauma risk by reason of osteoporosis.

A Uniaxial Testing Approach for Consistent Failure in Vascular Tissues

Although uniaxial tensile testing is commonly used to evaluate failure properties of vascular tissue, there is no established protocol for specimen shape or gripping method. Large percentages of specimens are reported to fail near the clamp and can potentially confound the studies, or, if discarded will result in sample waste. The objective of this study is to identify sample geometry and clamping conditions that can achieve consistent failure in the midregion of small arterial specimens, even for vessels from older individuals. Failure location was assessed in 17 dogbone specimens from human cerebral and sheep carotid arteries using soft inserts. For comparison with commonly used protocols, an additional 22 rectangular samples were tested using either sandpaper or foam tape inserts. Midsample failure was achieved in 94% of the dogbone specimens, while only 14% of the rectangular samples failed in the midregion, the other 86% failing close to the clamps. Additionally, we found midregion failure was more likely to be abrupt, caused by cracking or necking. In contrast, clamp failure was more likely to be gradual and included a delamination mode not seen in midregion failure. Hence, this work provides an approach that can be used to obtain consistent midspecimen failure, avoiding confounding clamp-related artifacts. Furthermore, with consistent midregion failure, studies can be designed to image the failure process in small vascular samples providing valuable quantitative information about changes to collagen and elastin structure during the failure process.

Multiscale mechanics of the cervical facet capsular ligament, with particular emphasis on anomalous fiber realignment prior to tissue failure

The facet capsular ligaments encapsulate the bilateral spinal facet joints and are common sources of painful injury due to afferent innervation. These ligaments exhibit architectural complexity, which is suspected to contribute to the experimentally observed lack of co-localization between macroscopic strain and microstructural tissue damage. The heterogeneous and multiscale nature of this ligament, combined with challenges in experimentally measuring its microscale mechanics, hinders the ability to understand sensory mechanisms under normal or injurious loading. Therefore, image-based, subject-specific, multiscale finite-element models were constructed to predict the mechanical responses of the human cervical facet capsular ligament under uniaxial tensile stretch. The models precisely simulated the force-displacement responses for all samples ([Formula: see text]) and showed promise in predicting the magnitude and location of peak regional strains at two different displacements. Yet, there was a loss of agreement between the model and experiment in terms of fiber organization at large tissue stretch, possibly due to a lack of accounting for tissue failure. The mean fiber stretch ratio predicted by the models was found to be significantly higher in regions that exhibited anomalous fiber realignment experimentally than in regions with normal realignment ([Formula: see text]). The development of microstructural abnormalities was associated with the predicted fiber-level stretch ([Formula: see text]), but not with the elemental maximum principal stress or maximum principal strain by logistic regression. The multiscale models elucidate a potential mechanical basis for predicting injury-prone tissue domains and for defining the relationships between macroscopic ligament stretch and microscale pathophysiology in the subfailure regime.