"Hands-On, Minds-On, and Science-Up": A Concept-Based Learning Laboratory With a Taste of Research Experience for an Undergraduate Biomedical Engineering Course.

In this paper, we bridged faculty research expertise with concept-based learning pedagogy to design and implement a unique laboratory experience for biomedical engineering undergraduate students enrolled in the biomechanics of tissues course at the University of Calgary. This laboratory aimed to increase student engagement, facilitate deeper understanding of course content, and provide an opportunity for accelerated undergraduate research through "hands-on," "minds-on," and "science-up" learning components, respectively. The laboratory exercise involves testing aortic tissues using a novel miniaturized planar biaxial machine. This type of machine is normally reserved for use in the context of research. The relevance of the proposed laboratory as a teaching tool was assessed using student feedback. Results indicate an overall valuable and positive learning experience for students.

Three-dimensional thoracic aorta principal strain analysis from routine ECG-gated computerized tomography: feasibility in patients undergoing transcatheter aortic valve replacement.

BACKGROUND: Functional impairment of the aorta is a recognized complication of aortic and aortic valve disease. Aortic strain measurement provides effective quantification of mechanical aortic function, and 3-dimenional (3D) approaches may be desirable for serial evaluation. Computerized tomographic angiography (CTA) is routinely performed for various clinical indications, and offers the unique potential to study 3D aortic deformation. We sought to investigate the feasibility of performing 3D aortic strain analysis in a candidate population of patients undergoing transcatheter aortic valve replacement (TAVR). METHODS: Twenty-one patients with severe aortic valve stenosis (AS) referred for TAVR underwent ECG-gated CTA and echocardiography. CTA images were analyzed using a 3D feature-tracking based technique to construct a dynamic aortic mesh model to perform peak principal strain amplitude (PPSA) analysis. Segmental strain values were correlated against clinical, hemodynamic and echocardiographic variables. Reproducibility analysis was performed. RESULTS: The mean patient age was 81±6 years. Mean left ventricular ejection fraction was 52±14%, aortic valve area (AVA) 0.6±0.3 cm2 and mean AS pressure gradient (MG) 44±11 mmHg. CTA-based 3D PPSA analysis was feasible in all subjects. Mean PPSA values for the global thoracic aorta, ascending aorta, aortic arch and descending aorta segments were 6.5±3.0, 10.2±6.0, 6.1±2.9 and 3.3±1.7%, respectively. 3D PSSA values demonstrated significantly more impairment with measures of worsening AS severity, including AVA and MG for the global thoracic aorta and ascending segment (p<0.001 for all). 3D PSSA was independently associated with AVA by multivariable modelling. Coefficients of variation for intra- and inter-observer variability were 5.8 and 7.2%, respectively. CONCLUSIONS: Three-dimensional aortic PPSA analysis is clinically feasible from routine ECG-gated CTA. Appropriate reductions in PSSA were identified with increasing AS hemodynamic severity. Expanded study of 3D aortic PSSA for patients with various forms of aortic disease is warranted.

Collagen structural alterations contribute to stiffening of tissue after split-thickness skin grafting.

The gold standard treatment for full thickness injuries of the skin is autologous split-thickness skin grafting. This involves harvesting the epidermis and superficial dermis from healthy skin and transplanting it onto the prepared wound bed. The donor site regenerates spontaneously, but the appendages and cellular components from the dermal layer are excluded from the graft. As a result, the new tissue is inferior; the healed graft site is dry/itchy, has decreased elasticity, increased fragility, and altered sensory function. Because this dermal layer is composed of collagen and other extracellular matrix proteins, the aim was to characterize the changes in the dermal collagen after split thickness grafting that could contribute to a deficit in functionality. This will serve as a baseline for future studies designed to improve skin function using pharmacological or cell-based therapies for skin repair. A xenograft model whereby human split-thickness grafts were implanted into full-thickness defects on immunocompromised (athymic Nu/Nu) mice was used. The grafts were harvested 4 and 8 weeks later. The collagen microstructure was assessed with second harmonic generation with dual-photon microscopy and light polarization analysis. Collagen fiber stiffness and engagement stretch were estimated by fitting the results of biaxial mechanical tensile tests to a histo-mechanical constitutive model. The stiffness of the collagen fibril-proteoglycan complex increased from 682 ± 226 kPa/sr to 1016 ± 324 kPa/sr between 4 and 8 weeks postgrafting. At the microstructural level there were significant decreases in both thickness of collagen fibers (3.60 ± 0.34 µm vs. 2.10 ± 0.27 µm) and waviness ratio (2.04 ± 0.17 vs. 1.43 ± 0.08) of the collagen fibers postgrafting. The decrease of the macroscopic engagement stretch from 1.19 ± 0.11 to 1.09 ± 0.08 over time postgrafting mirrored the decrease in waviness measured at the microscopic level. This suggested that the integrity of the collagen fibers was compromised and contributed to the functional deficit of the skin postgrafting.

A feature-based morphing methodology for computationally modeled biological structures applied to left atrial fiber directions.

To properly simulate the behavior of biological structures through computer modeling, there exists a need to describe parameters that vary locally. These parameters can be obtained either from literature or from experimental data and they are often assigned to regions in the model as lumped values. Furthermore, parameter values may be obtained on a representative case and may not be available for each specific modeled organ. We describe a semiautomated technique to assign detailed maps of local tissue properties to a computational model of a biological structure. We applied the method to the left atrium of the heart. The orientation of myocytes in the tissue as obtained from histologic analysis was transferred to the 3D model of a porcine left atrium. Finite element method (FEM) dynamic simulations were performed by using an isotropic, neo-Hookean, constitutive model first, then adding an anisotropic, cardiomyocyte oriented, Fung-type component. Results showed higher stresses for the anisotropic material model corresponding to lower stretches in the cardiomyocyte directions. The same methodology can be applied to transfer any map of parameters onto a discretized finite element model.

AI-powered assessment of biomarkers for growth prediction of abdominal aortic aneurysms.

Objective: The purpose of this study was to employ biomechanics-based biomarkers to locally characterize abdominal aortic aneurysm (AAA) tissue and investigate their relation to local aortic growth by means of an artificial intelligence model. Methods: The study focused on a population of 36 patients with AAAs undergoing serial monitoring with electrocardiogram-gated multiphase computed tomography angiography acquisitions. The geometries of the aortic lumen and wall were reconstructed from the baseline scans and used for the baseline assessment of regional aortic weakness with three functional biomarkers, time-averaged wall-shear stress, in vivo principal strain, and intra-luminal thrombus thickness. The biomarkers were encoded as regional averages on axial and circumferential sections perpendicularly to the aortic centerline. Local diametric growth was obtained as difference in diameter between baseline and follow-up at the level of each axial section. An artificial intelligence model was developed to predict accelerated aneurysmal growth with the Extra Trees algorithm used as a binary classifier where the positive class represented regions that grew more than 2.5 mm/year. Additional clinical biomarkers, such as maximum aortic diameter at baseline, were also investigated as predictors of growth. Results: The area under the curve for the constructed receiver operating characteristic curve for the Extra Trees classifier showed a very good performance in predicting relevant aortic growth (area under the curve = 0.92), with the three biomechanics-based functional biomarkers being objectively selected as the main predictors of growth. Conclusions: The use of features based on the functional and local characterization of the aortic tissue resulted in a superior performance in terms of growth prediction when compared with models based on geometrical assessments. With rapid growth linked to increasing risk for patients with AAAs, the ability to access functional information related to tissue weakening and disease progression at baseline has the potential to support early clinical decisions and improve disease management.

A classification approach to improve out of sample predictability of structure-based constitutive models for ascending thoracic aortic tissue.

In this research, a pipeline was developed to assess the out-of-sample predictive capability of structure-based constitutive models of ascending aortic aneurysmal tissue. The hypothesis being tested is that a biomarker can help establish similarities among tissues sharing the same level of a quantifiable property, thus enabling the development of biomarker-specific constitutive models. Biomarker-specific averaged material models were constructed from biaxial mechanical tests of specimens that shared similar biomarker properties such as level of blood-wall shear stress or microfiber (elastin or collagen) degradation in the extracellular matrix. Using a cross-validation strategy commonly used in classification algorithms, biomarker-specific averaged material models were assessed in contrast to individual tissue mechanics of out of sample specimens that fell under the same category but did not contribute to the averaged model's generation. The normalized root means square errors (NRMSE) calculated on out-of-sample data were compared with average models when no categorization was performed versus biomarker-specific models and among different level of a biomarker. Different biomarker levels exhibited statistically different NRMSE when compared among each other, indicating more common features shared by the specimens belonging to the lower error groups. However, no specific biomarkers reached a significant difference when compared to the average model created when No Categorization was performed, possibly on account of unbalanced number of specimens. The method developed could allow for the screening of different biomarkers or combinations/interactions in a systematic manner leading the way to larger datasets and to more individualized constitutive approaches.

Magnetic resonance imaging-based hemodynamic wall shear stress alters aortic wall tissue biomechanics in bicuspid aortic valve patients.

OBJECTIVE: In this study we aimed to conclusively determine whether altered aortic biomechanics are associated with wall shear stress (WSS) independent of region of tissue collection. Elevated WSS in the ascending aorta of patients with bicuspid aortic valve has been shown to contribute to local maladaptive aortic remodeling and might alter biomechanics. METHODS: Preoperative 4-dimensional flow magnetic resonance imaging was performed on 22 patients who underwent prophylactic aortic root and/or ascending aorta replacement. Localized elevated WSS was identified in patients using age-matched healthy atlases (n = 60 controls). Tissue samples (n = 78) were collected and categorized according to WSS (elevated vs normal) and region. Samples were subjected to planar biaxial testing. To fully quantify the nonlinear biomechanical response, the tangential modulus (local stiffness) at a low-stretch (LTM) and high-stretch (HTM) linear region and the onset (TZo) and end stress of the nonlinear transition zone were measured. A linear mixed effect models was implemented to determine statistical relationships. RESULTS: A higher LTM in the circumferential and axial direction was associated with elevated WSS (P = .007 and P = .018 respectively) independent of collection region. Circumferential TZo and HTM were higher with elevated WSS (P = .024 and P = .003); whereas the collection region was associated with variations in axial TZo (P = .013), circumferential HTM (P = .015), and axial HTM (P = .001). CONCLUSIONS: This study shows strong evidence that biomechanical changes in the aorta are strongly associated with hemodynamics, and not region of tissue collection for bicuspid valve aortopathy patients. Elevated WSS is associated with tissue behavior at low stretch ranges (ie, LTM and TZo).

A mechanical characterization of the porcine atria at the healthy stage and after ventricular tachypacing.

Atrial fibrillation (AF) is a cardiac arrhythmia that highly increases the risk of stroke and is associated with significant but still unexplored changes in the mechanical behavior of the tissue. Planar biaxial tests were performed on tissue specimens from pigs at the healthy stage and after ventricular tachypacing (VTP), a procedure applied to reproduce the relevant features of AF. The local arrangement of the fiber bundles in the tissue was investigated on specimens from rabbit atria by means of circularly polarized light. Based on this, mechanical data were fitted to two anisotropic constitutive relationships, including a four-parameter Fung-type model and a microstructurally-motivated model. Accounting for the fiber-induced anisotropy brought average R(2) = 0.807 for the microstructurally-motivated model and average R(2) = 0.949 for the Fung model. Validation of the fitted constitutive relationships was performed by means of FEM simulations coupled to FORTRAN routines. The performances of the two material models in predicting the second Piola-Kirchhoff stress were comparable, with average errors <3.1%. However, the Fung model outperformed the other in the prediction of the Green-Lagrange strain, with 9.2% maximum average error. To increase model generality, a proper averaging procedure accounting for nonlinearities was used to obtain average material parameters. In general, a stiffer behavior after VTP was noted.

Deep-learning method for fully automatic segmentation of the abdominal aortic aneurysm from computed tomography imaging.

Abdominal aortic aneurysm (AAA) is one of the leading causes of death worldwide. AAAs often remain asymptomatic until they are either close to rupturing or they cause pressure to the spine and/or other organs. Fast progression has been linked to future clinical outcomes. Therefore, a reliable and efficient system to quantify geometric properties and growth will enable better clinical prognoses for aneurysms. Different imaging systems can be used to locate and characterize an aneurysm; computed tomography (CT) is the modality of choice in many clinical centers to monitor later stages of the disease and plan surgical treatment. The lack of accurate and automated techniques to segment the outer wall and lumen of the aneurysm results in either simplified measurements that focus on few salient features or time-consuming segmentation affected by high inter- and intra-operator variability. To overcome these limitations, we propose a model for segmenting AAA tissues automatically by using a trained deep learning-based approach. The model is composed of three different steps starting with the extraction of the aorta and iliac arteries followed by the detection of the lumen and other AAA tissues. The results of the automated segmentation demonstrate very good agreement when compared to manual segmentation performed by an expert.

Biomechanics in ascending aortic aneurysms correlate with tissue composition and strength.

Objective: This study correlates low strain tangential modulus (LTM) and transition zone onset (TZo) stress, biomechanical parameters that occur within the physiological range of stress seen in vivo, with tissue strength and histopathologic changes in aneurysmal ascending aortic tissue. Method: Ascending aortic aneurysm tissue samples were collected from 41 patients undergoing elective resection. Samples were subjected to planar biaxial testing to quantify LTM and TZo. These were then correlated with strength assessed from uniaxial testing and with histopathologic quantification of pathologic derangements in elastin, collagen, and proteoglycan (PG). Results: Decreased LTM and TZo were correlated with reduced strength (P < .05), PG content (P < .05), and elastin content (P < .05). Reduced TZo also was correlated with increased elastin fragmentation (P < .05). Conclusions: LTM and TZo are correlated with common biomechanical and histopathologic alterations in ascending aortic aneurysm tissue that are thought to relate to the risk of acute aortic syndromes. LTM and TZo are measured under conditions approximating in vivo physiology and have the potential to be obtained noninvasively using medical imaging techniques. Therefore, they represent parameters that warrant future study as potential contributors to our growing knowledge of pathophysiology, disease progression, and risk stratification of aortic disease.

Elastin integrity in bicuspid valve-associated aortopathy is associated with altered biomechanical properties and influenced by age.

Background: Aortic wall remodelling in bicuspid aortic valve (BAV) patients is heterogeneous and characterized by elastin fiber breakdown alongside impaired biomechanics. However, the relationship between aortic histopathological changes and biomechanics are incompletely understood. We clarify the influence of elastin fiber integrity on ex vivo aortic wall mechanical properties in BAV patients, and explore the influence of patient age. Methods: Aortic tissue samples (N=66) from 19 BAV patients undergoing prophylactic ascending aortic resection surgery were analyzed. Semi-quantitative histopathological analysis was conducted to assess elastin fiber integrity including elastin content and elastic fiber fragmentation. Ex vivo biaxial mechanical testing generated stress-strain curves from which physiological [low-strain tangential modulus (LTM), transition zone onset stress (TZo)] and supraphysiological [transition zone end stress (TZe) and high-strain tangential modulus (HTM)] mechanical properties were obtained. Relationships between histopathology and mechanical properties were determined using a linear mixed effect model. BAV patients were subdivided according to 'younger' and 'older' age groups (i.e., 51-60 and 61-70 years old, respectively). Results: No statistically significant differences in elastin content were observed between younger and older BAV patients. Older patients showed greater elastin fiber fragmentation compared to their younger cohort (74% versus 61%). Elastin fiber histopathology was associated with differences in physiological mechanical properties: elastin fragmentation corresponded with lower LTM (P=0.005) and TZo (P=0.044) in younger BAV patients and higher LTM (P=0.049) and TZo (P=0.001) in older BAV patients. Histopathology changes were significantly associated with supraphysiological mechanical properties only in older BAV patients: decreased elastin integrity was associated with increased TZe (P=0.049) and HTM (P<0.001). Conclusions: Elastin histopathologic changes in BAV aortopathy correspond with differences in mechanical properties and this relationship is influenced by patient age. These novel findings provide additional mechanistic insights into aortic wall remodeling and support a more nuanced stratification of BAV patients by age.

Biomechanical properties of ascending aortic aneurysms: Quantification of inter- and intra-patient variability.

This study investigates the biomechanical properties of ascending aortic aneurysms focusing on the inter-patient differences vs. the heterogeneity within a patient's aneurysm. Each specimen was tested on a biaxial testing device and the resulting stress-strain response was fitted to a four-parameter Fung constitutive model. We postulate that the inter-patient variability (differences between patients) blurs possible intra-patient variability (regional heterogeneity) and, thus, that both effects must be considered to shed light on the role of heterogeneity in aneurysm progression. We propose, demonstrate, and discuss two techniques to assess differences by, first, comparing conventional biomechanical properties and, second, the overall constitutive response. Results show that both inter- and intra-patient variability contribute to errors when using population averaged models to fit individual tissue behaviour. When inter-patient variability was accounted for and its effects excluded, intra-patient heterogeneity could be assessed, showing a wide degree of heterogeneity at the individual patient level. Furthermore, the right lateral region (from the patient's perspective) appeared different (stiffer) than the other regions. We posit that this heterogeneity could be a consequence of maladaptive remodelling due to altered loading conditions that hastens microstructural changes naturally occurring with age. Further validation of these results should be sought from a larger cohort study.

Multidimensional Analysis of Descending Aortic Growth After Acute Type A Aortic Dissection.

BACKGROUND: After repair of acute type A aortic dissection, typical geometric variables of conventional aortic surveillance focus on maximum diameter and its rate of growth, potentially missing important geometric changes elsewhere. We determined additional information provided by a semiautomated, 3-dimensional (3D), nonlinear growth model of the descending thoracic aorta after repair of type A aortic dissection. METHODS: Computed tomographic angiography data were retrospectively collected after hemiarch repair of type A aortic dissection. The descending aorta was systematically reconstructed to generate a 3D model made up of individual segments. The baseline and follow-up diameters were measured semiautomatically for each segment, and the nonlinear interval growth was determined. RESULTS: The fastest growing segment expanded at a rate of 3.8 mm/y (interquartile range, 2.2 to 5.4 mm/y) vs 0.6 mm/y (interquartile range, -0.3 to 1.7 mm/y) when measured at the original site of maximum diameter (P < .01). The maximum baseline diameter was a poor predictor of location with fastest growth (r = 0.10, P > .1). Using the society recommended growth limits, a greater proportion of patients would be considered "at risk" when assessed by our method vs conventional surveillance measures. CONCLUSIONS: Our model identifies areas of rapid aortic growth after repair of type A dissection that would likely be missed using current surveillance techniques. The increased precision, resolution, and reproducibility provided by our technique may improve on limitations of current surveillance techniques, provide novel geometric data on aortic remodeling, and contribute to the pursuit of a comprehensive patient-specific approach to aortic risk stratification.

Biomechanics of Wound Healing in an Equine Limb Model: Effect of Location and Treatment with a Peptide-Modified Collagen-Chitosan Hydrogel.

The equine distal limb wound healing model, characterized by delayed re-epithelialization and a fibroproliferative response to wounding similar to that observed in humans, is a valuable tool for the study of biomaterials poised for translation into both the veterinary and human medical markets. In the current study, we developed a novel method of biaxial biomechanical testing to assess the functional outcomes of healed wounds in a modified equine model and discovered significant functional and structural differences in both unwounded and injured skin at different locations on the distal limb that must be considered when using this model in future work. Namely, the medial skin was thicker and displayed earlier collagen engagement, medial wounds experienced a greater proportion of wound contraction during closure, and proximal wounds produced significantly more exuberant granulation tissue. Using this new knowledge of the equine model of aberrant wound healing, we then investigated the effect of a peptide-modified collagen-chitosan hydrogel on wound healing. Here, we found that a single treatment with the QHREDGS (glutamine-histidine-arginine-glutamic acid-aspartic acid-glycine-serine) peptide-modified hydrogel (Q-peptide hydrogel) resulted in a higher rate of wound closure and was able to modulate the biomechanical function toward a more compliant healed tissue without observable negative effects. Thus, we conclude that the use of a Q-peptide hydrogel provides a safe and effective means of improving the rate and quality of wound healing in a large animal model.

Linking Aortic Mechanical Properties, Gene Expression and Microstructure: A New Perspective on Regional Weakening in Abdominal Aortic Aneurysms.

Background: Current clinical practice for the assessment of abdominal aortic aneurysms (AAA) is based on vessel diameter and does not account for the multifactorial, heterogeneous remodeling that results in the regional weakening of the aortic wall leading to aortic growth and rupture. The present study was conducted to determine correlations between a novel non-invasive surrogate measure of regional aortic weakening and the results from invasive analyses performed on corresponding ex vivo aortic samples. Tissue samples were evaluated to classify local wall weakening and the likelihood of further degeneration based on non-invasive indices. Methods: A combined, image-based fluid dynamic and in-vivo strain analysis approach was used to estimate the Regional Aortic Weakness (RAW) index and assess individual aortas of AAA patients prior to elective surgery. Nine patients were treated with complete aortic resection allowing the systematic collection of tissue samples that were used to determine regional aortic mechanics, microstructure and gene expression by means of mechanical testing, microscopy and transcriptomic analyses. Results: The RAW index was significantly higher for samples exhibiting lower mechanical strength (p = 0.035) and samples classified as low elastin content (p = 0.020). Samples with higher RAW index had the greatest number of genes differentially expressed compared to any constitutive metric. High RAW samples showed a decrease in gene expression for elastin and a down-regulation of pathways responsible for cell movement, reorganization of cytoskeleton, and angiogenesis. Conclusions: This work describes the first AAA index free of assumptions for material properties and accounting for patient-specific mechanical behavior in relation to aneurysm strength. Use of the RAW index captured biomechanical changes linked to the weakening of the aorta and revealed changes in microstructure and gene expression. This approach has the potential to provide an improved tool to aid clinical decision-making in the management of aortic pathology.

Effect of testing conditions on the mechanical response of aortic tissues from planar biaxial experiments: Loading protocol and specimen side.

This study concerns procedural aspects of planar biaxial experiments on aortic tissues that have not been exhaustively addressed in the literature. The following questions are explored. First, is there a difference in the apparent mechanical properties if the experiments are conducted in a force-controlled regime or a displacement-controlled regime. Second, does it matter whether the deformations of the surface are tracked from one side of the tissue or the other (luminal vs. abluminal surface). The study provides answers to these questions with the help of a series of experiments on porcine aortic tissue, constitutive modelling and statistical analysis. It was found that the loading protocol does not substantially affect the constitutive response, while the surface orientation does.

A novel combined fluid dynamic and strain analysis approach identified abdominal aortic aneurysm rupture.

Clinical decision-making for surgical repair of abdominal aortic aneurysms based on maximum aortic diameter presents limitations as rupture can occur below threshold for some aneurysms, whereas others are stable at large sizes. The proposed approach combines hemodynamics and geometric indices with in vivo deformation analysis to assess local weakening of the aortic wall for a case of impending rupture that was confirmed during open surgical repair. A new combined index, the Regional Rupture Potential, is introduced to help the assessment of individual aneurysms and their rupture risk, providing a rationale for clinical decisions.

A Novel Right Ventricular Volume and Pressure Loaded Piglet Heart Model for the Study of Tricuspid Valve Function.

Heart conditions in which the tricuspid valve (TV) faces either increased volume or pressure stressors are associated with premature valve failure. Mechanistic studies to improve our understanding of the underlying pathophysiology responsible for the development of premature TV failure are lacking. Due to the inability to conduct these studies in humans, an animal model is required. In this manuscript, we describe the protocols for a novel chronic recovery infant piglet heart model for the study of changes in the TV when placed under combined volume and pressure stress. In this model, volume loading of the right ventricle and the TV is achieved through the disruption of the pulmonary valve. Then pressure loading is accomplished through the placement of a pulmonary artery band. The success of this model is assessed at four weeks post intervention surgery through echocardiography, intracardiac pressure measurement, and pathologic examination of the heart specimens.

Multi-sector approximation method for arteries: the residual stresses of circumferential rings with non-trivial openings.

The opening angle method is a popular choice in biomechanics to estimate residual stresses in arteries. Experimentally, it means that an artery is cut into rings; then the rings are cut axially or radially allowing them to open into sectors; finally, the corresponding opening angles are measured to give residual stress levels by solving an inverse problem. However, for many tissues, for example in pathological tissues, the ring does not open according to the theory into a neat single circular sector, but rather creates an asymmetric geometry, often with abruptly changing curvature(s). This phenomenon may be due to a number of reasons including variation in thickness, microstructure, mechanical properties, etc. As a result, these samples are often eliminated from studies relying on the opening angle method, which limits progress in understanding and evaluating residual stresses in real arteries. With this work, we propose an effective approach to deal with these non-trivial openings of rings. First, we digitize pictures of opened rings to split them into multiple, connected circular sectors. Then we measure the corresponding opening angles for each sub-sector. Subsequently, we can determine the residual stresses for individual sectors in a closed-ring configuration and, thus, approximate the circumferential residual bending effects.

Anisotropic residual stresses in arteries.

The paper provides a deepened insight into the role of anisotropy in the analysis of residual stresses in arteries. Residual deformations are modelled following Holzapfel and Ogden (Holzapfel and Ogden 2010, J. R. Soc. Interface 7, 787-799. ( doi:10.1098/rsif.2009.0357 )), which is based on extensive experimental data on human abdominal aortas (Holzapfel et al. 2007, Ann. Biomed. Eng. 35, 530-545. ( doi:10.1007/s10439-006-9252-z )) and accounts for both circumferential and axial residual deformations of the individual layers of arteries-intima, media and adventitia. Each layer exhibits distinctive nonlinear and anisotropic mechanical behaviour originating from its unique microstructure; therefore, we use the most general form of strain-energy function (Holzapfel et al. 2015, J. R. Soc. Interface 12, 20150188. ( doi:10.1098/rsif.2015.0188 )) to derive residual stresses for each layer individually. Finally, the systematic experimental data (Niestrawska et al. 2016, J. R. Soc. Interface 13, 20160620. ( doi:10.1098/rsif.2016.0620 )) on both mechanical and structural properties of the different layers of the human abdominal aorta facilitate our discussion on (i) the importance of anisotropy in modelling residual stresses; (ii) the variability of residual stresses within the same class of tissue, the abdominal aorta; (iii) the limitations of conventional opening angle method to account for complex residual deformations; and (iv) the effect of residual stresses on the loaded configuration of the aorta mimicking in vivo conditions.