Residual strains in conduit arteries

Mechanical, structural, and morphological differences in the iliac arteries

Iliac arteries play a crucial role in peripheral blood circulation. They are susceptible to various diseases, including aneurysms and atherosclerosis. Structure, material properties, and biomechanical forces acting on different regions of the iliac vasculature may contribute to the localization and progression of these pathologies. We examined 33 arterial specimens from common iliac (CI), external iliac (EI), and internal iliac (II) arteries obtained from 11 human donors (62 ± 12 years). We conducted morphometric, mechanical, and structural analyses using planar biaxial tests, constitutive modeling, and bi-directional histology on transverse and axial sections. The iliac arteries exhibited increased tortuosity and varying disease distribution with age. CI and II arteries displayed non-uniform age-related disease progression around their circumference, while EI remained healthy even in older individuals. Trends in load-free and stress-free thickness varied along the iliac vasculature. Longitudinally, EI exhibited the highest compliance compared to other iliac vessels. In contrast, CI was stiffest longitudinally, and EI was the stiffest circumferentially. Material parameters for all iliac vessels are reported for four common constitutive relations. Elastin near the internal elastic lamina displayed greater waviness in EI and II compared to CI. Also, EI had the least glycosaminoglycans (GAGs) and the highest elastin content. Our findings highlight variations in the morphological, mechanical, and structural properties of iliac arteries along their length. This data can inform vascular disease development and computational studies, and guide the development of biomimetic repair materials and devices tailored to specific iliac locations, improving vascular repair strategies.

Variability in structure, morphology, and mechanical properties of the descending thoracic and infrarenal aorta around their circumference

Aortic diseases, such as aneurysms, atherosclerosis, and dissections, demonstrate a preferential development and progression around the aortic circumference, resulting in a highly heterogeneous disease state around the circumference. Differences in the aorta's structural composition and mechanical properties may be partly responsible for this phenomenon. Our goal in this study was to analyze the mechanical and structural properties of the human aorta at its lateral, anterior, posterior, and medial quadrants in two regions prone to circumferentially inhomogeneous diseases, descending Thoracic Aorta (TA) and Infrarenal Aorta (IFR). Human aortas were obtained from 10 donors (64 ± 11 years) and dissected from their loose surrounding tissue. Mechanical properties were determined in all four quadrants of TA and IFR using planar biaxial testing and fitted to three common constitutive models. The structure of tissues was assessed using Movat Pentachrome stained histology slides. We observed that the anterior quadrant exhibited the greatest thickness, followed by the lateral region, in both the TA and IFR. In TA, the posterior wall appeared as the stiffest location in most samples, while in IFR, the anterior wall was the stiffest. We observed a higher glycosaminoglycans content in the lateral and posterior regions of the IFR. We found elastin density to be similar in TA lateral, anterior, and posterior quadrants, while in IFR, the anterior region demonstrated the highest elastin density. Despite significant variations between subjects, this study highlights the distinct morphometrical, mechanical, and structural properties between the quadrants of both TA and IFR.

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

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

Location specific multi-scale characterization and constitutive modeling of pig aorta

The mechanical and structural behavior of the aorta depend on physiological functions and vary from proximal to distal. Understanding the relation between regionally varying mechanical and multi-scale structural response of aorta can be helpful to assess the disease outcomes. Therefore, this study investigated the variation in mechanical and multi-scale structural properties among the major segments of aorta such as ascending aorta (AA), descending aorta (DA) and abdominal aorta (ABA), and established a relation between mechanical and multi-structural parameters. The obtained results showed significant increase in anisotropy and nonlinearity from proximal to distal aorta. The change in periphery length and radii between load and stress free configuration was also found increasing far from the heart. Opening angle was significantly large for ABA than AA and DA (AA/DA vs ABA; p = 0.001). Mean circumferential residual stretch (ratio of mean periphery length at load and stress free configurations) was found decreasing between AA and DA, and then increasing between DA to ABA and its value was significantly more for ABA (AA vs DA; p = 0.041, AA vs ABA; p = 0.001, DA vs ABA; p = 0.001). The waviness of collagen fibers, collagen fiber content, collagen fibril diameter and total protein content were found significantly increasing from proximal to distal. Pearson correlation test showed a significant linear correlation between variation in mechanical and multi-scale structural parameters over the aortic length. Residual stretch was found positively correlated with collagen fiber content (r = 0.82) whereas opening angel was found positively correlated with total protein content (TPC) (r = 0.76).

Residual strains in ascending thoracic aortic aneurysms: The effect of valve type, layer, and circumferential quadrant

The stress distribution in ascending thoracic aortic aneurysms is determined by the mechanical properties, geometry, loading conditions, and zero-stress state of the aneurysmal aorta. Our objective was to fully characterize the zero-stress state of the aneurysmal aorta in twelve tricuspid aortic valve patients and eight (age/aortic diameter-matched) bicuspid aortic valve patients, for which little data are available. Opening angles and residual stretches were measured for the intact wall and individual layers according to quadrant and were similar in the two patient groups. The intact-wall and medial opening angles were comparable; their circumferential but not their axial ones peaked in the left lateral quadrant, with non-significant regional differences in the other layers. The intima's circumferential opening angles were the highest of all layers (∼300 deg) and the adventitia's the lowest (∼165 deg), with lesser layer differences in the axial opening angles. Upon radially cutting aortic rings, the released circumferential residual stretches were tensile (of large magnitude) externally and compressive (of small magnitude) internally, unlike the axial residual stretches released when cutting intact-wall strips, whose magnitude was small externally and large internally. Nevertheless, large circumferential compressive residual stretches were released in the adventitia upon layer dissection, counteracting the large circumferential tensile stretches of the intact wall externally. Moreover, the large axial tensile residual stretches of the intima counteracted the large axial compressive stretches of the intact wall internally. These layer-specific residual stretches may moderate the in-vivo stress gradients across wall thickness, serving as a protective mechanism against aortic dissection or rupture.

Physical organogenesis of the gut

The gut has been a central subject of organogenesis since Caspar Friedrich Wolff’s seminal 1769 work ‘De Formatione Intestinorum’. Today, we are moving from a purely genetic understanding of cell specification to a model in which genetics codes for layers of physical–mechanical and electrical properties that drive organogenesis such that organ function and morphogenesis are deeply intertwined. This Review provides an up-to-date survey of the extrinsic and intrinsic mechanical forces acting on the embryonic vertebrate gut during development and of their role in all aspects of intestinal morphogenesis: enteric nervous system formation, epithelium structuring, muscle orientation and differentiation, anisotropic growth and the development of myogenic and neurogenic motility. I outline numerous implications of this biomechanical perspective in the etiology and treatment of pathologies, such as short bowel syndrome, dysmotility, interstitial cells of Cajal-related disorders and Hirschsprung disease.

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.

A novel framework for quantifying the subject-specific three-dimensional residual stress field in the aortic wall

BACKGROUND

Quantification of subject-specific residual stress field remains a challenge that prohibits accurate stress analysis and refined understanding of the biomechanical behavior of the aortic wall.

METHOD

This study presents a framework combining experiments, constitutive modeling, and computer simulation to quantify the subject-specific three-dimensional residual stress field of the aortic wall. The material properties and residual deformations were acquired from the same porcine aortic sample, so that the subject-specific residual stress field was quantified analytically. Consequently, a novel stress-driven tissue growth model was developed and incorporated in a finite element aortic model to recover the subject-specific residual stress with the help of analytical solution. We then evaluated the framework's efficacy by simulating the residual stress distribution in the aortic dissection (AD).

RESULT

Subject-specific residual stress field of the aortic sample was quantified analytically. No appreciable discrepancy was observed between the numerically simulated and analytically derived residual stress distributions, indicating the effectiveness of the tissue growth model. Errors arising from the numerically simulated circumferential opening angle and axial bending angle were within 5% relative to experimental results, highlighting that the framework was accurate in terms of subject-specific residual stress estimation. Finally, numerical simulations recovered the buckling behavior of the intimal flap of the dissected aorta and revealed the expansion of the false lumen and compression of the true lumen as the tear propagates circumferentially.

CONCLUSION

The proposed framework is effective in quantifying the three-dimensional subject-specific residual stress field and it is potentially applicable in more sophisticated scenarios involving residual stress.

From Uniaxial Testing of Isolated Layers to a Tri-Layered Arterial Wall: A Novel Constitutive Modelling Framework

Mechanical testing and constitutive modelling of isolated arterial layers yields insight into the individual layers' mechanical properties, but per se fails to recapitulate the in vivo loading state, neglecting layer-specific residual stresses. The aim of this study was to develop a testing/modelling framework that integrates layer-specific uniaxial testing data into a three-layered model of the arterial wall, thereby enabling study of layer-specific mechanics under realistic (patho)physiological conditions. Circumferentially and axially oriented strips of pig thoracic aortas (n = 10) were tested uniaxially. Individual arterial layers were then isolated from the wall, tested, and their mechanical behaviour modelled using a hyperelastic strain energy function. Subsequently, the three layers were computationally assembled into a single flat-walled sample, deformed into a cylindrical vessel, and subjected to physiological tension-inflation. At the in vivo axial stretch of 1.10 ± 0.03, average circumferential wall stress was 75 ± 9 kPa at 100 mmHg, which almost doubled to 138 ± 15 kPa at 160 mmHg. A ~ 200% stiffening of the adventitia over the 60 mmHg pressure increase shifted layer-specific load-bearing from the media (65 ± 10% → 61 ± 14%) to the adventitia (28 ± 9% → 32 ± 14%). Our approach provides valuable insight into the (patho)physiological mechanical roles of individual arterial layers at different loading states, and can be implemented conveniently using simple, inexpensive and widely available uniaxial testing equipment.

Layer-Specific Residual Deformations and Their Variation Along the Human Aorta

This study described the regional distribution of layer-specific residual deformations in fifteen human aortas collected during autopsy. Circumferentially and axially cut strips of standardized dimensions from the anterior quadrant of nine consecutive aortic levels were photographed to obtain the zero-stress state for the intact wall. The strips were then dissected into layers that were also photographed to obtain their zero-stress state. Changes in layer-specific opening angle, residual stretches, and thickness at each aortic level and direction were determined via image analysis. The circumferential and axial opening angles of the intima were ∼240 deg and ∼30 deg, respectively, throughout the aorta; those of the adventitia were ∼150 deg and -20 deg to 70 deg. The opening angles of the intact wall and media were similar in either direction. The circumferential residual stretches of the intima and the axial residual stretches of the media showed high values in the aortic arch, decreasing in the descending thoracic aorta and increasing toward the iliac artery bifurcation, while the axial residual stretches of the adventitia increased distally. The remaining residual stretches did not vary significantly with aortic level, suggesting an intimal role in determining circumferential, as well as medial and adventitial roles in determining axial residual stretches. We conclude that the tensile residual stretches released in the intima and media upon separation, and the compressive residual stretches released in the adventitia may moderate the inverse transmural stress gradients under physiologic loads, resulting from the >180 deg circumferential opening angle of the intact wall.

Photooxidation crosslinking to recover residual stress in decellularized blood vessel

Decellularization method based on trypsin-digestion is widely used to construct small diameter vascular grafts. However, this method will reduce the opening angle of the blood vessel and result in the reduction of residual stress. Residual stress reduced has an adverse effect on the compliance and permeability of small diameter vascular grafts. To improve the situation, acellular blood vessels were treated with glutaraldehyde and photooxidation crosslinking respectively, and the changes of opening angle, circumferential residual strain of native blood vessels, decellularized arteries and crosslinked blood vessels were measured by means of histological examination, scanning electron microscopy (SEM) and transmission electron microscopy (TEM) in this study. The opening angle of decellularized arteries significantly restored after photooxidation crosslinking (P = 0.0216), while that of glutaraldehyde crosslinking blood vessels reduced. The elastic fibers inside the blood vessels became densely rearranged after photooxidation crosslinking. The results of finite element simulation showed that the residual stress increased with the increase of opening angle. In this study, we found at the first time that photooxidation crosslinking method could significantly increase the residual stress of decellularized vessels, which provides biomechanical support for the development of new biomaterials of vascular grafts.

Comparison of morphometric, structural, mechanical, and physiologic characteristics of human superficial femoral and popliteal arteries

Peripheral arterial disease differentially affects the superficial femoral (SFA) and the popliteal (PA) arteries, but their morphometric, structural, mechanical, and physiologic differences are poorly understood. SFAs and PAs from 125 human subjects (age 13-92, average 52±17 years) were compared in terms of radii, wall thickness, and opening angles. Structure and vascular disease were quantified using histology, mechanical properties were determined with planar biaxial extension, and constitutive modeling was used to calculate the physiologic stress-stretch state, elastic energy, and the circumferential physiologic stiffness. SFAs had larger radii than PAs, and both segments widened with age. Young SFAs were 5% thicker, but in old subjects the PAs were thicker. Circumferential (SFA: 96→193°, PA: 105→139°) and longitudinal (SFA: 139→306°, PA: 133→320°) opening angles increased with age in both segments. PAs were more diseased than SFAs and had 11% thicker intima. With age, intimal thickness increased 8.5-fold, but medial thickness remained unchanged (620μm) in both arteries. SFAs had 30% more elastin than the PAs, and its density decreased ~50% with age. SFAs were more compliant than PAs circumferentially, but there was no difference longitudinally. Physiologic circumferential stress and stiffness were 21% and 11% higher in the SFA than in the PA across all ages. The stored elastic energy decreased with age (SFA: 1.4→0.4kPa, PA: 2.5→0.3kPa). While the SFA and PA demonstrate appreciable differences, most of them are due to vascular disease. When pathology is the same, so are the mechanical properties, but not the physiologic characteristics that remain distinct due to geometrical differences.

Review of the Techniques Used for Investigating the Role Elastin and Collagen Play in Arterial Wall Mechanics

The arterial wall is characterised by a complex microstructure that impacts the mechanical properties of the vascular tissue. The main components consist of collagen and elastin fibres, proteoglycans, Vascular Smooth Muscle Cells (VSMCs) and ground matrix. While VSMCs play a key role in the active mechanical response of arteries, collagen and elastin determine the passive mechanics. Several experimental methods have been designed to investigate the role of these structural proteins in determining the passive mechanics of the arterial wall. Microscopy imaging of load-free or fixed samples provides useful information on the structure-function coupling of the vascular tissue, and mechanical testing provides information on the mechanical role of collagen and elastin networks. However, when these techniques are used separately, they fail to provide a full picture of the arterial micromechanics. More recently, advances in imaging techniques have allowed combining both methods, thus dynamically imaging the sample while loaded in a pseudo-physiological way, and overcoming the limitation of using either of the two methods separately. The present review aims at describing the techniques currently available to researchers for the investigation of the arterial wall micromechanics. This review also aims to elucidate the current understanding of arterial mechanics and identify some research gaps.

Mechanical, structural, and physiologic differences in human elastic and muscular arteries of different ages: Comparison of the descending thoracic aorta to the superficial femoral artery

Elastic and muscular arteries differ in structure, function, and mechanical properties, and may adapt differently to aging. We compared the descending thoracic aortas (TA) and the superficial femoral arteries (SFA) of 27 tissue donors (average 41±18 years, range 13-73 years) using planar biaxial testing, constitutive modeling, and bidirectional histology. Both TAs and SFAs increased in size with age, with the outer radius increasing more than the inner radius, but the TAs thickened 6-fold and widened 3-fold faster than the SFAs. The circumferential opening angle did not change in the TA, but increased 2.4-fold in the SFA. Young TAs were relatively isotropic, but the anisotropy increased with age due to longitudinal stiffening. SFAs were 51% more compliant longitudinally irrespective of age. Older TAs and SFAs were stiffer, but the SFA stiffened 5.6-fold faster circumferentially than the TA. Physiologic stresses decreased with age in both arteries, with greater changes occurring longitudinally. TAs had larger circumferential, but smaller longitudinal stresses than the SFAs, larger cardiac cycle stretch, 36% lower circumferential stiffness, and 8-fold more elastic energy available for pulsation. TAs contained elastin sheets separated by smooth muscle cells (SMCs), collagen, and glycosaminoglycans, while the SFAs had SMCs, collagen, and longitudinal elastic fibers. With age, densities of elastin and SMCs decreased, collagen remained constant due to medial thickening, and the glycosaminoglycans increased. Elastic and muscular arteries demonstrate different morphological, mechanical, physiologic, and structural characteristics and adapt differently to aging. While the aortas remodel to preserve the Windkessel function, the SFAs maintain higher longitudinal compliance.

Transient swelling behavior of the bovine caudal disc

The intervertebral disc is an avascular composite structure, comprised of the nucleus pulposus (NP) and the annulus fibrosus (AF). Previous tissue-level experiments either examined relative differences in swelling capacity of the two disc regions at a single time point or tested explant structures that did not replicate in situ boundary conditions. Previous joint-level studies that investigated time-dependent fluid flow into the disc provided limited information about swelling-induced intradiscal strains with respect to time and boundary constraints. Therefore, the objective of this study was to investigate time-dependent swelling behavior of the intervertebral disc ex situ. The first study investigated time-dependent free-swelling response of the whole disc and the disc's subcomponents separately (i.e., NP and AF). Findings from this study showed that the swelling rate and swelling capacity of NP explants under free-swelling conditions were greater than AF explants. The second study evaluated the effect of boundary conditions on in-plane strain distributions of intact discs and AF rings. Swelling-induced strain was highly heterogeneous in AF rings, where negative circumferential strains were observed in the inner AF and tensile circumferential strains were observed in the outer AF. Radial strains in AF rings were an order of magnitude greater than circumferential strains. Restricting fluid flow only to the outer AF periphery reduced the swelling of the inner AF. Swelling of intact discs affected both NP and AF swelling behaviors, where NP hydration decreased by 60%. Furthermore, the presence of the NP reduced peak radial strains in the AF and resulted in uniform strain distribution throughout the AF. In conclusion, these studies highlight that tissue hydration and swelling-induced strains largely depend on regional biochemical composition and geometric boundary constraints.

Variation of Axial Residual Strains Along the Course and Circumference of Human Aorta Considering Age and Gender

Our understanding of aortic biomechanics is customarily limited by lack of information on the axial residual stretches of the vessel in both humans and experimental animals that would facilitate the identification of its actual zero-stress state. The aim of this study was thus to acquire hitherto unreported quantitative knowledge of axial opening angle and residual stretches in different segments and quadrants of the human aorta according to age and gender. Twenty-three aortas were harvested during autopsy from the aortic root to the iliac bifurcation and were divided into ≥12 segments and 4 quadrants. Morphometric measurements were taken in the excised/curled configuration of rectangular strips considered to be under zero-stress using image-analysis software to study the axial/circumferential variation of axial opening angle, internal/external residual stretch, and thickness of the aortic wall. The measured data demonstrated: (1) an axial opening angle peak at the arch branches, decreasing toward the ascending and to a near-constant value in the descending thoracic aorta, and increasing in the abdominal aorta; (2) the variation of residual stretches resembled that of opening angle, but axial differences in external residual stretch were more prominent; (3) wall thickness showed a progressive diminution along the vessel; (4) the highest opening angle/residual stretches were found in the inner quadrant and the lowest in the outer quadrant; (5) the anterior was the thinnest quadrant throughout the aorta; (6) age caused thickening but greatly reduced axial opening angle/residual stretches, without differences between males and females.

Mechanical and structural changes in human thoracic aortas with age

Aortic mechanical and structural characteristics have profound effects on pathophysiology, but many aspects of physiologic stress-stretch state and intramural changes due to aging remain poorly understood in human tissues. While difficult to assess in vivo due to residual stresses and pre-stretch, physiologic stress-stretch characteristics can be calculated using experimentally-measured mechanical properties and constitutive modeling. Mechanical properties of 76 human descending thoracic aortas (TA) from 13 to 78-year-old donors (mean age 51±18 years) were measured using multi-ratio planar biaxial extension. Constitutive parameters were derived for aortas in 7 age groups, and the physiologic stress-stretch state was calculated. Intramural characteristics were quantified from histological images and related to aortic morphometry and mechanics. TA stiffness increased with age, and aortas became more nonlinear and anisotropic. Systolic and diastolic elastic energy available for pulsation decreased with age from 30 to 8 kPa and from 18 to 5 kPa, respectively. Cardiac cycle circumferential stretch dropped from 1.14 to 1.04, and circumferential and longitudinal physiologic stresses decreased with age from 90 to 72 kPa and from 90 to 17 kPa, respectively. Aortic wall thickness and radii increased with age, while the density of elastin in the tunica media decreased. The number of elastic lamellae and circumferential physiologic stress per lamellae unit remained constant with age at 102±10 and 0.85±0.04 kPa, respectively. Characterization of mechanical, physiological, and structural features in human aortas of different ages can help understand aortic pathology, inform the development of animal models that simulate human aging, and assist with designing devices for open and endovascular aortic repairs. STATEMENT OF SIGNIFICANCE: This manuscript describes mechanical and structural changes occurring in human thoracic aortas with age, and presents material parameters for 4 commonly used constitutive models. Presented data can help better understand aortic pathology, inform the development of animal models that simulate human aging, and assist with designing devices for open and endovascular aortic repairs.

Intervertebral disc swelling maintains strain homeostasis throughout the annulus fibrosus: A finite element analysis of healthy and degenerated discs

Tissues in the intervertebral disc have a large capacity to absorb water, partially due to the high glycosaminoglycan (GAG) content, which decreases linearly from the nucleus pulposus (NP) in the center to the outer annulus. Our recent work showed that fiber network and GAG distribution contributes to development of residual stresses and strains that were compressive in the inner annulus to tensile in the outer annulus. GAG loss in the inner annulus, as observed with early to moderate degeneration, reduced swelling capacity and circumferential-direction stress by over 50%. However, our previous model was not capable of evaluating interactions between the NP and annulus fibrosus (AF) during swelling. In this study, we evaluated the effect of degeneration (GAG content or swelling capacity) on residual stress development throughout the disc. Simulations of moderate to severe degeneration showed a 40% decrease in NP swelling capacity, with a 25% decrease in AF and cartilaginous endplate swelling. Together, these changes in tissue swelling resulted in a decrease in NP pressure (healthy = 0.21 MPa; severe degeneration = 0.03 MPa) that was comparable to observations in human discs. There was a 60% decrease in circumferential-direction residual deformations with early degeneration. Radial-direction stretch switched from compressive to tensile with degeneration, which may increase the risk for tears or delamination. Degeneration had a significant impact on residual stress/stretch and fiber stretch in the posterior AF, which is important for understanding herniation risk. In conclusion, degenerative changes in disc geometry and intradiscal deformations was recreated by only altering NP and AF GAG composition. Since most computational models simulate degeneration by altering material stiffness, this work highlights the importance of directly simulating biochemical composition and distribution to study disc biomechanics with degeneration. STATEMENT OF SIGNIFICANCE: Tissues in the intervertebral disc have a large swelling capacity, due to its high glycosaminoglycan content. Our recent work demonstrated the importance of fiber network and glycosaminoglycan distribution residual stresses and strains development. In this study, we evaluated the effect of swelling on intradiscal deformations between the nucleus pulposus and annulus fibrosus. We also investigated the effect of degenerative glycosaminoglycan loss on swelling-based intradiscal deformations of the intact disc and its subcomponents. Decreases in nucleus glycosaminoglycan content resulted in morphological changes observed with degenerated discs and may help to explain mechanisms behind the increases in annular tears and mechanical dysfunction with degeneration.

Molecular-level collagen damage explains softening and failure of arterial tissues: A quantitative interpretation of CHP data with a novel elasto-damage model

The present experimental-modelling study provides a quantitative interpretation of mechanical data and damage measurements obtained from collagen hybridizing peptide (CHP) techniques on overstretched sheep cerebral arterial tissues. To this aim, a structurally-motivated constitutive model is developed in the framework of continuum damage mechanics. The model includes two internal variables for describing the effects of collagen triple-helical unfolding via interstrand delamination: one governs plastic mechanisms in collagen fibers, leading to a stress softening response of the tissue at the macroscale; the other one describes the loss of fiber structural integrity, leading to tissue final failure. The proposed model is calibrated using the obtained mechanical experimental data, showing excellent fitting capabilities. The predicted evolution of internal variables agree well with independent measurements of molecular-level CHP-based damage data, obtaining an independent a posteriori validation of damage predictions. Moreover, available data on inelastic tissue elongation following supraphysiological loads are successfully reproduced. These outcomes further the hypothesis that the accumulation of interstrand delamination is a primary cause for the evolution of inelastic mechanisms in tissues, and in particular of stress softening up to failure.

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.

Finite element simulation of three dimensional residual stress in the aortic wall using an anisotropic tissue growth model

Residual stress is believed to play a significant role in the in vivo stress state of the arterial wall, but quantifying residual stress in vivo is challenging. Based on the well-known assumptions that residual stress is a result of heterogeneous arterial growth and that it homogenizes the transmural distribution of arterial wall stress, we propose a new anisotropic tissue growth model for the aorta to recover the three-dimensional residual stress field in a bi-layer human aortic wall. Finite element simulations showed that the predicted residual stress magnitude with this method are within the documented range for human aorta. Particularly, the homeostatic inter-layer stress difference is identified as a key parameter to quantify the opening angle. To the authors' knowledge, this is the first finite element study employing anisotropic growth of aortic tissue in a bi-layer model to generate three-dimensional residual stress field, and the resultant opening angle can match with the experiments. A parametric study found that inter-layer stress homogeneity, arterial blood pressure, axial pre-stretch, and material stiffness strongly affect the residual stress field.

Mechanical behavior of porcine thoracic aorta in physiological and supra-physiological intraluminal pressures

Understanding the mechanical behavior of aorta under supra-physiological loadings is an important aspect of modeling tissue behavior in various applications that involve large deformations. Utilizing inflation–extension experiments, the mechanical behavior of porcine descending thoracic aortic segments under physiological and supra-physiological intraluminal pressures was investigated. The pressure was changed in the range of 0–70 kPa and the deformation of the segment was determined in three dimensions using a custom-made motion capture system. An orthotropic Fung-type constitutive model was characterized by implementing a novel computationally efficient framework that ensured material stability for numerical simulations. The nonlinear rising trend of circumferential stretch ratio [Formula: see text] from outer toward inner wall was significantly increased at higher pressures. The increase in [Formula: see text] from physiological pressure (13 kPa) to 70 kPa was 13% at the outer wall and 22% at the inner wall; in this pressure range, the longitudinal stretch ratio [Formula: see text] increased 20%. A significant nonlinearity in the material behavior was observed as in the same pressure range, and the circumferential and longitudinal Cauchy stresses at the inner wall were increased 16 and 18 times, respectively. The overall constitutive model was verified in several loading paths in the [Formula: see text] space to confirm its applicability in multi-axial loading conditions.

A Methodology for Verifying Abdominal Aortic Aneurysm Wall Stress

An abdominal aortic aneurysm (AAA) is a permanent focal dilatation of the abdominal aorta of at least 1.5 times its normal diameter. Although the criterion of maximum diameter is still used in clinical practice to decide on a timely intervention, numerical studies have demonstrated the importance of other geometric factors. However, the major drawback of numerical studies is that they must be validated experimentally before clinical implementation. This work presents a new methodology to verify wall stress predicted from the numerical studies against the experimental testing. To this end, four AAA phantoms were manufactured using vacuum casting. The geometry of each phantom was subject to microcomputed tomography (μCT) scanning at zero and three other intraluminal pressures: 80, 100, and 120 mm Hg. A zero-pressure geometry algorithm was used to calculate the wall stress in the phantom, while the numerical wall stress was calculated with a finite-element analysis (FEA) solver based on the actual zero-pressure geometry subjected to 80, 100, and 120 mm Hg intraluminal pressure loading. Results demonstrate the moderate accuracy of this methodology with small relative differences in the average wall stress (1.14%). Additionally, the contribution of geometric factors to the wall stress distribution was statistically analyzed for the four phantoms. The results showed a significant correlation between wall thickness and mean curvature (MC) with wall stress.

Regional distribution of circumferential residual strains in the human aorta according to age and gender

The biomechanical response of the human aorta varies with axial location, but little is known about the respective variation of residual strains. Such data are available for common lab animals, but in the traditional opening angle measurement the aorta is considered as an ideal cylinder and average residual strains are measured, so that the spatial variations of local residual strains are not determined. The present study provides opening angle and residual strain data throughout the course and around the circumference of the aorta harvested during autopsy. Opening angle showed notable topographical variation; the highest value was at the top of aortic arch, declining abruptly toward the ascending aorta and to a near-constant value in the descending aorta, and rising in the abdominal aorta. The variation of curvature and of external but not internal residual stretch resembled that of opening angle. Extensive residual stress and wall thickness differences were evidenced among quadrants, with the more pre-stressed being also the thicker quadrants. Gender had overall minor effects, but aging led to increased parameters, occurring earlier in the distal aorta but at later stages becoming predominant proximally. Differences in caliber were pronounced in older subjects, unlike those in opening angle, residual stretches, and thickness that were striking in middle-aged subjects. By contrast, curvature decreased with aging in relation to the smaller percentwise opening angle differences. Detailed knowledge of the zero-stress/no-load geometry of the human aortic wall is critical for an in-depth understanding of aortic physiology, while providing the basis for comparison with disease.

Energy-based constitutive modelling of local material properties of canine aortas

This study aims at determining the in vitro anisotropic mechanical behaviour of canine aortic tissue. We specifically focused on spatial variations of these properties along the axis of the vessel. We performed uniaxial stretch tests on canine aortic samples in both circumferential and longitudinal directions, as well as histological examinations to derive the tissue's fibre orientations. We subsequently characterized a constitutive model that incorporates both phenomenological and structural elements to account for macroscopic and microstructural behaviour of the tissue. We showed the two fibre families were oriented at similar angles with respect to the aorta's axis. We also found significant changes in mechanical behaviour of the tissue as a function of axial position from proximal to distal direction: the fibres become more aligned with the aortic axis from 46° to 30°. Also, the linear shear modulus of media decreased as we moved distally along the aortic axis from 139 to 64 kPa. These changes derived from the parameters in the nonlinear constitutive model agreed well with the changes in tissue structure. In addition, we showed that isotropic contribution, carried by elastic lamellae, to the total stress induced in the tissue decreases at higher stretch ratios, whereas anisotropic stress, carried by collagen fibres, increases. The constitutive models can be readily used to design computational models of tissue deformation during physiological loading cycles. The findings of this study extend the understanding of local mechanical properties that could lead to region-specific diagnostics and treatment of arterial diseases.

Mechanical analysis of the ring opening test applied to human ascending aortas

This work presents experiments, modelling and numerical simulation aimed at describing the mechanical response of human ascending aortas in the ring opening test. The objective is to quantify, from the opening angles measured in the test, the residual stress distribution along the artery wall and, afterwards, how this stress pattern changes when the artery is subjected to standard physiological pressures. The cases studied correspond to four groups including both healthy and pathological arteries. The tissues are characterized via tensile test measurements that enable to derive the material parameters of two constitutive models adopted in the present analysis. Overall, the numerical results obtained for all groups were found to be a useful data that allow to estimate the residual stress and their influence on the vessels under normal and hypertension physiological conditions.

A Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth

The purpose of this manuscript is to establish a unified theory of porohyperelasticity with transport and growth and to demonstrate the capability of this theory using a finite element model developed in MATLAB. We combine the theories of volumetric growth and mixed porohyperelasticity with transport and swelling (MPHETS) to derive a new method that models growth of biological soft tissues. The conservation equations and constitutive equations are developed for both solid-only growth and solid/fluid growth. An axisymmetric finite element framework is introduced for the new theory of growing MPHETS (GMPHETS). To illustrate the capabilities of this model, several example finite element test problems are considered using model geometry and material parameters based on experimental data from a porcine coronary artery. Multiple growth laws are considered, including time-driven, concentration-driven, and stress-driven growth. Time-driven growth is compared against an exact analytical solution to validate the model. For concentration-dependent growth, changing the diffusivity (representing a change in drug) fundamentally changes growth behavior. We further demonstrate that for stress-dependent, solid-only growth of an artery, growth of an MPHETS model results in a more uniform hoop stress than growth in a hyperelastic model for the same amount of growth time using the same growth law. This may have implications in the context of developing residual stresses in soft tissues under intraluminal pressure. To our knowledge, this manuscript provides the first full description of an MPHETS model with growth. The developed computational framework can be used in concert with novel in-vitro and in-vivo experimental approaches to identify the governing growth laws for various soft tissues.

Inflation and Bi-Axial Tensile Testing of Healthy Porcine Carotid Arteries

Knowledge of the intrinsic material properties of healthy and diseased arterial tissue components is of great importance in diagnostics. This study describes an in vitro comparison of 13 porcine carotid arteries using inflation testing combined with functional ultrasound and bi-axial tensile testing. The measured tissue behavior was described using both a linear, but geometrically non-linear, one-parameter (neo-Hookean) model and a two-parameter non-linear (Demiray) model. The shear modulus estimated using the linear model resulted in good agreement between the ultrasound and tensile testing methods, GUS = 25 ± 5.7 kPa and GTT = 23 ± 5.4 kPa. No significant correspondence was observed for the non-linear model aUS = 1.0 ± 2.7 kPa vs. aTT = 17 ± 8.8 kPa, p ∼ 0); however, the exponential parameters were in correspondence (bUS = 12 ± 4.2 vs. bTT = 10 ± 1.7, p > 0.05). Estimation of more complex models in vivo is cumbersome considering the sensitivity of the model parameters to small changes in measurement data and the absence of intraluminal pressure data, endorsing the use of a simple, linear model in vivo.

Mechanics of Vascular Smooth Muscle

Vascular smooth muscle (VSM; see Table 1 for a list of abbreviations) is a heterogeneous biomaterial comprised of cells and extracellular matrix. By surrounding tubes of endothelial cells, VSM forms a regulated network, the vasculature, through which oxygenated blood supplies specialized organs, permitting the development of large multicellular organisms. VSM cells, the engine of the vasculature, house a set of regulated nanomotors that permit rapid stress-development, sustained stress-maintenance and vessel constriction. Viscoelastic materials within, surrounding and attached to VSM cells, comprised largely of polymeric proteins with complex mechanical characteristics, assist the engine with countering loads imposed by the heart pump, and with control of relengthening after constriction. The complexity of this smart material can be reduced by classical mechanical studies combined with circuit modeling using spring and dashpot elements. Evaluation of the mechanical characteristics of VSM requires a more complete understanding of the mechanics and regulation of its biochemical parts, and ultimately, an understanding of how these parts work together to form the machinery of the vascular tree. Current molecular studies provide detailed mechanical data about single polymeric molecules, revealing viscoelasticity and plasticity at the protein domain level, the unique biological slip-catch bond, and a regulated two-step actomyosin power stroke. At the tissue level, new insight into acutely dynamic stress-strain behavior reveals smooth muscle to exhibit adaptive plasticity. At its core, physiology aims to describe the complex interactions of molecular systems, clarifying structure-function relationships and regulation of biological machines. The intent of this review is to provide a comprehensive presentation of one biomachine, VSM.

Residual deformations in ocular tissues

Residual deformations strongly influence the local biomechanical environment in a number of connective tissues. The sclera is known to be biomechanically important in healthy and diseased eyes, such as in glaucoma. Here, we study the residual deformations of the sclera, as well as the adjacent choroid and retina. Using freshly harvested porcine eyes, we developed two approaches of quantifying residual deformations in the spherically shaped tissues of interest. The first consisted of punching discs from the posterior wall of the eye and quantifying the changes in the area and eccentricity of these samples. The second consisted of cutting a ring from the equatorial sclera and making stress-relieving cuts in it. Measurements of curvature were made before and after the stress-relieving cuts. Using the first approach, we observed a 42% areal contraction of the choroid, but only modest contractions of the sclera and retina. The observed contractions were asymmetric. In the second approach, we observed an opening of the scleral rings (approx. 10% decrease in curvature). We conclude that residual bending deformations are present in the sclera, which we speculate may be due to radially heterogeneous growth and remodelling of the tissue during normal development. Further, residual areal deformations present in the choroid may be due to the network of elastic fibres in this tissue and residual deformations in the constituent vascular bed. Future studies of ocular biomechanics should attempt to include effects of these residual deformations into mechanical models in order to gain a better understanding of the biomechanics of the ocular wall.

A mechanical argument for the differential performance of coronary artery grafts

Coronary artery bypass grafting (CABG) acutely disturbs the homeostatic state of the transplanted vessel making retention of graft patency dependent on chronic remodeling processes. The time course and extent to which remodeling restores vessel homeostasis will depend, in part, on the nature and magnitude of the mechanical disturbances induced upon transplantation. In this investigation, biaxial mechanical testing and histology were performed on the porcine left anterior descending artery (LAD) and analogs of common autografts, including the internal thoracic artery (ITA), radial artery (RA), great saphenous vein (GSV) and lateral saphenous vein (LSV). Experimental data were used to quantify the parameters of a structure-based constitutive model enabling prediction of the acute vessel mechanical response pre-transplantation and under coronary loading conditions. A novel metric Ξ was developed to quantify mechanical differences between each graft vessel in situ and the LAD in situ, while a second metric Ω compares the graft vessels in situ to their state under coronary loading. The relative values of these metrics among candidate autograft sources are consistent with vessel-specific variations in CABG clinical success rates with the ITA as the superior and GSV the inferior graft choices based on mechanical performance. This approach can be used to evaluate other candidate tissues for grafting or to aid in the development of synthetic and tissue engineered alternatives.

A method for incorporating three-dimensional residual stretches/stresses into patient-specific finite element simulations of arteries

The existence of residual stresses in human arteries has long been shown experimentally. Researchers have also demonstrated that residual stresses have a significant effect on the distribution of physiological stresses within arterial tissues, and hence on their development, e.g., stress-modulated remodeling. Through progress in medical imaging, image analysis and finite element (FE) meshing tools it is now possible to construct in vivo patient-specific geometries and thus to study specific, clinically relevant problems in arterial mechanics via FE simulations. Classical continuum mechanics and FE methods assume that constitutive models and the corresponding simulations start from unloaded, stress-free reference configurations while the boundary-value problem of interest represents a loaded geometry and includes residual stresses. We present a pragmatic methodology to simultaneously account for both (i) the three-dimensional (3-D) residual stress distributions in the arterial tissue layers, and (ii) the equilibrium of the in vivo patient-specific geometry with the known boundary conditions. We base our methodology on analytically determined residual stress distributions (Holzapfel and Ogden, 2010, J. R. Soc. Interface 7, 787-799) and calibrate it using data on residual deformations (Holzapfel et al., 2007, Ann. Biomed. Eng. 35, 530-545). We demonstrate our methodology on three patient-specific FE simulations calibrated using experimental data. All data employed here are generated from human tissues - both the aorta and thrombus, and their respective layers - including the geometries determined from magnetic resonance images, and material properties and 3-D residual stretches determined from mechanical experiments. We study the effect of 3-D residual stresses on the distribution of physiological stresses in the aortic layers (intima, media, adventitia) and the layers of the intraluminal thrombus (luminal, medial, abluminal) by comparing three types of FE simulations: (i) conventional calculations; (ii) calculations accounting only for prestresses; (iii) calculations including both 3-D residual stresses and prestresses. Our results show that including residual stresses in patient-specific simulations of arterial tissues significantly impacts both the global (organ-level) deformations and the stress distributions within the arterial tissue (and its layers). Our method produces circumferential Cauchy stress distributions that are more uniform through the tissue thickness (i.e., smaller stress gradients in the local radial directions) compared to both the conventional and prestressing calculations. Such methods, combined with appropriate experimental data, aim at increasing the accuracy of classical FE analyses for patient-specific studies in computational biomechanics and may lead to increased clinical application of simulation tools.

Methods for using 3-D ultrasound speckle tracking in biaxial mechanical testing of biological tissue samples

Being multilayered and anisotropic, biological tissues such as cardiac and arterial walls are structurally complex, making the full assessment and understanding of their mechanical behavior challenging. Current standard mechanical testing uses surface markers to track tissue deformations and does not provide deformation data below the surface. In the study described here, we found that combining mechanical testing with 3-D ultrasound speckle tracking could overcome this limitation. Rat myocardium was tested with a biaxial tester and was concurrently scanned with high-frequency ultrasound in three dimensions. The strain energy function was computed from stresses and strains using an iterative non-linear curve-fitting algorithm. Because the strain energy function consists of terms for the base matrix and for embedded fibers, spatially varying fiber orientation was also computed by curve fitting. Using finite-element simulations, we first validated the accuracy of the non-linear curve-fitting algorithm. Next, we compared experimentally measured rat myocardium strain energy function values with those in the literature and found a matching order of magnitude. Finally, we retained samples after the experiments for fiber orientation quantification using histology and found that the results satisfactorily matched those computed in the experiments. We conclude that 3-D ultrasound speckle tracking can be a useful addition to traditional mechanical testing of biological tissues and may provide the benefit of enabling fiber orientation computation.

Age-related vascular stiffening: causes and consequences

Arterial stiffening occurs with age and is closely associated with the progression of cardiovascular disease. Stiffening is most often studied at the level of the whole vessel because increased stiffness of the large arteries can impose increased strain on the heart leading to heart failure. Interestingly, however, recent evidence suggests that the impact of increased vessel stiffening extends beyond the tissue scale and can also have deleterious microscale effects on cellular function. Altered extracellular matrix (ECM) architecture has been recognized as a key component of the pre-atherogenic state. Here, the underlying causes of age-related vessel stiffening are discussed, focusing on age-related crosslinking of the ECM proteins as well as through increased matrix deposition. Methods to measure vessel stiffening at both the macro- and microscale are described, spanning from the pulse wave velocity measurements performed clinically to microscale measurements performed largely in research laboratories. Additionally, recent work investigating how arterial stiffness and the changes in the ECM associated with stiffening contributed to endothelial dysfunction will be reviewed. We will highlight how changes in ECM protein composition contribute to atherosclerosis in the vessel wall. Lastly, we will discuss very recent work that demonstrates endothelial cells (ECs) are mechano-sensitive to arterial stiffening, where changes in stiffness can directly impact EC health. Overall, recent studies suggest that stiffening is an important clinical target not only because of potential deleterious effects on the heart but also because it promotes cellular level dysfunction in the vessel wall, contributing to a pathological atherosclerotic state.

Correlations between transmural mechanical and morphological properties in porcine thoracic descending aorta

Determination of correlations between transmural mechanical and morphological properties of aorta would provide a quantitative baseline for assessment of preventive and therapeutic strategies for aortic injuries and diseases. A multimodal and multidisciplinary approach was adopted to characterize the transmural morphological properties of descending porcine aorta. Histology and multi-photon microscopy were used for describing the media layer micro-architecture in the circumferential-radial plane, and Fourier Transform infrared imaging spectroscopy was utilized for determining structural protein, and total protein content. The distributions of these quantified properties across the media thickness were characterized and their relationship with the mechanical properties from a previous study was determined. Our findings indicate that there is an increasing trend in the instantaneous Young׳s modulus (E), elastic lamella density (ELD), structural protein (SPR), total protein (TPR), and elastin and collagen circumferential percentage (ECP and CCP) from the inner towards the outer layers. Two regions with equal thickness (inner and outer halves) were determined with significantly different morphological and material properties. The results of this study represent a substantial step toward anatomical characterization of the aortic wall building blocks and establishment of a foundation for quantifying the role of microstructural components on the functionality of aorta.

Noninvasive in vivo determination of residual strains and stresses

Vascular growth and remodeling during embryonic development are associated with blood flow and pressure induced stress distribution, in which residual strains and stresses play a central role. Residual strains are typically measured by performing in vitro tests on the excised vascular tissue. In this paper, we investigated the possibility of estimating residual strains and stresses using physiological pressure-radius data obtained through in vivo noninvasive measurement techniques, such as optical coherence tomography or ultrasound modalities. This analytical approach first tested with in vitro results using experimental data sets for three different arteries such as rabbit carotid artery, rabbit thoracic artery, and human carotid artery based on Fung's pseudostrain energy function and Delfino's exponential strain energy function (SEF). We also examined residual strains and stresses in the human swine iliac artery using the in vivo experimental ultrasound data sets corresponding to the systolic-to-diastolic region only. This allowed computation of the in vivo residual stress information for loading and unloading states separately. Residual strain parameters as well as the material parameters were successfully computed with high accuracy, where the relative errors are introduced in the range of 0-7.5%. Corresponding residual stress distributions demonstrated global errors all in acceptable ranges. A slight discrepancy was observed in the computed reduced axial force. Results of computations performed based on in vivo experimental data obtained from loading and unloading states of the artery exhibited alterations in material properties and residual strain parameters as well. Emerging noninvasive measurement techniques combined with the present analytical approach can be used to estimate residual strains and stresses in vascular tissues as a precursor for growth estimates. This approach is also validated with a finite element model of a general two-layered artery, where the material remodeling states and residual strain generation are investigated.

Non-invasive, energy-based assessment of patient-specific material properties of arterial tissue

The mechanical properties of human biological tissue vary greatly. The determination of arterial material properties should be based on experimental data, i.e. diameter, length, intramural pressure, axial force and stress-free geometry. Currently, clinical data provide only non-invasively measured pressure-diameter data for superficial arteries (e.g. common carotid and femoral artery). The lack of information forces us to take into account certain assumptions regarding the in situ configuration to estimate material properties in vivo. This paper proposes a new, non-invasive, energy-based approach for arterial material property estimation. This approach is compared with an approach proposed in the literature. For this purpose, a simplified finite element model of an artery was used as a mock experimental situation. This method enables exact knowledge of the actual material properties, thereby allowing a quantitative evaluation of material property estimation approaches. The results show that imposing conditions on strain energy can provide a good estimation of the material properties from the non-invasively measured pressure and diameter data.

Residual shear deformations in the coronary artery

Quantifying arterial residual deformations is critical for understanding the stresses and strains within the arterial wall during physiological and pathophysiological conditions. This study presents novel findings on residual shear deformations in the left anterior descending coronary artery. Residual shear deformations are most evident when thin, long axial strips are cut from the artery. These strips deform into helical configurations when placed in isotonic solution. A residual shear angle is introduced as a parameter to quantify the residual shear deformations. Furthermore, a stress analysis is performed to study the effects of residual shear deformations on the intramural shear stress distribution of an artery subjected to pressure, axial stretch, and torsion using numerical simulation. The results from the stress analyses suggest that residual shear deformations can significantly modulate the intramural shear stress across the arterial wall.

Imaging and finite element analysis: a methodology for non-invasive characterization of aortic tissue

Characterization of the mechanical properties of arterial tissues usually involves an invasive procedure requiring tissue removal. In this work we propose a non-invasive method to perform a biomechanical analysis of cardiovascular aortic tissue. This method is based on combining medical imaging and finite element analysis (FEA). Magnetic resonance imaging (MRI) was chosen since it presents relatively low risks for human health. A finite element model was created from the MRI images and loaded with systolic physiological pressures. By means of an optimization routine, the structural material properties were changed until average strains matched those measured by MRI. The method outlined in this work produced an estimate of the in situ properties of cardiovascular tissue based on non-invasive image datasets and finite element analysis.

Implementation and Validation of Aortic Remodeling in Hypertensive Rats

A computational framework was implemented and validated to better understand the hypertensive artery remodeling in both geometric dimensions and material properties. Integrating the stress-modulated remodeling equations into commercial finite element codes allows a better control and visualization of local mechanical parameters. Both arterial thickening and stiffening effects were captured and visualized. An adaptive material remodeling strategy combined with the element birth and death techniques for the geometrical growth were implemented. The numerically predicted remodeling results in terms of the wall thickness, inner diameter, and the ratio of elastin to collagen content of the artery were compared with and fine-tuned by the experimental data from a documented rat model. The influence of time constant on the material remodeling was also evaluated and discussed. In addition, the geometrical growth and material remodeling were isolated to better understand the contributions of each element to the arterial remodeling and their coupling effect. Finally, this framework was applied to an image-based 3D artery generated from computer tomography to demonstrate its heterogeneous remodeling process. Results suggested that hypertension induced arterial remodeling are quite heterogeneous due to both nonlinear geometry and material adaptation process. The developed computational model provided more insights into the evolutions of morphology and material of the artery, which could complement the discrete experimental data for improving the clinical management of hypertension. The proposed framework could also be extended to study other types of stress-driven tissue remodeling including in-stent restenosis and grafting.