A passive strain-energy function for elastic and muscular arteries: correlation of material parameters with histological data

Experimental Protocols to Test Aortic Soft Tissues: A Systematic Review

Experimental protocols are fundamental for quantifying the mechanical behaviour of soft tissue. These data are crucial for advancing the understanding of soft tissue mechanics, developing and calibrating constitutive models, and informing the development of more accurate and predictive computational simulations and artificial intelligence tools. This paper offers a comprehensive review of experimental tests conducted on soft aortic tissues, employing the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) methodology, based on the Scopus, Web of Science, IEEE, Google Scholar and PubMed databases. This study includes a detailed overview of the test method protocols, providing insights into practical methodologies, specimen preparation and full-field measurements. The review also briefly discusses the post-processing methods applied to extract material parameters from experimental data. In particular, the results are analysed and discussed providing representative domains of stress-strain curves for both uniaxial and biaxial tests on human aortic tissue.

Review paper: The importance of consideration of collagen cross-links in computational models of collagen-based tissues

Collagen as the main protein in Extra Cellular Matrix (ECM) is the main load-bearing component of fibrous tissues. Nanostructure and architecture of collagen fibrils play an important role in mechanical behavior of these tissues. Extensive experimental and theoretical studies have so far been performed to capture these properties, but none of the current models realistically represent the complexity of network mechanics because still less is known about the collagen's inner structure and its effect on the mechanical properties of tissues. The goal of this review article is to emphasize the significance of cross-links in computational modeling of different collagen-based tissues, and to reveal the need for continuum models to consider cross-links properties to better reflect the mechanical behavior observed in experiments. In addition, this study outlines the limitations of current investigations and provides potential suggestions for the future work.

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).

The mechanical behavior of bovine spinal cord white matter under various strain rate conditions: tensile testing and visco-hyperelastic constitutive modeling

The mechanical behavior of the white matter is important for estimating the damage of the spinal cord during accidents. In this study, we conducted uniaxial tension testing in vitro of bovine spinal cord white matter under extremely high strain rate conditions (up to 100 s^-1). A visco-hyperelastic constitutive law for modeling the strain rate-dependent behavior of the bovine spinal cord white matter was developed. A set of material constants was obtained using a Levenberg-Marquardt fitting algorithm to match the uniaxial tension experimental data with various strain rates. Our experimental data confirmed that the modulus and tensile strength increased when the strain rate is higher. For the extremely high strain rate condition (100 s^-1), we found that both the modulus and failure stress significantly increased compared with the low strain rate case. These new data in terms of mechanical response at high strain rate provide insight into the spine injury mechanism caused by high-speed impact. Moreover, the developed constitutive model will allow researchers to perform more realistic finite element modeling and simulation of spinal cord injury damage under various complicated conditions.

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

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

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.

Insights into Biomechanical and Proteomic Characteristics of Small Diameter Vascular Grafts Utilizing the Human Umbilical Artery

The gold standard vascular substitutes, used in cardiovascular surgery, are the Dacron or expanded polytetrafluoroethylene (ePTFE)-derived grafts. However, major adverse reactions accompany their use. For this purpose, decellularized human umbilical arteries (hUAs) may be proven as a significant source for the development of small diameter conduits. The aim of this study was the evaluation of a decellularization protocol in hUAs. To study the effect of the decellularization to the hUAs, histological analysis was performed. Then, native and decellularized hUAs were biochemically and biomechanically evaluated. Finally, broad proteomic analysis was applied. Histological analysis revealed the successful decellularization of the hUAs. Furthermore, a great amount of DNA was removed from the decellularized hUAs. Biomechanical analysis revealed statistically significant differences in longitudinal direction only in maximum stress (p < 0.013) and strain (p < 0.001). On the contrary, all parameters tested for circumferential direction exhibited significant differences (p < 0.05). Proteomic analysis showed the preservation of the extracellular matrix and cytoskeletal proteins in both groups. Proteomic data are available via ProteomeXchange with identifier PXD020187. The above results indicated that hUAs were efficiently decellularized. The tissue function properties of these conduits were well retained, making them ideal candidates for the development of small diameter vascular grafts.

Characterization of chemoelastic effects in arteries using digital volume correlation and optical coherence tomography

Understanding stress-strain relationships in arteries is important for fundamental investigations in mechanobiology. Here we demonstrate the essential role of chemoelasticity in determining the mechanical properties of arterial tissues. Stepwise stress-relaxation uniaxial tensile tests were carried out on samples of porcine thoracic aortas immersed in a hyperosmotic solution. The tissue deformations were tracked using optical coherence tomography (OCT) during the tensile tests and digital volume correlation (DVC) was used to obtain measurements of depth-resolved strains across the whole thickness of the tested aortas. The hyperosmotic solution exacerbated chemoelastic effects, and we were able to measure different manifestations of these chemoelastic effects: swelling of the media inducing a modification of its optical properties, and existence of a transverse tensile strain. For the first time ever to our best knowledge, 3D strains induced by chemoelastic effects in soft tissues were quantified thanks to the OCT-DVC method. Without doubt, chemoelasticity plays an essential role in arterial mechanobiology in vivo and future work should focus on characterizing chemoelastic effects in arterial walls under physiological and disease conditions. STATEMENT OF SIGNIFICANCE: Chemoelasticity, coupling osmotic phenomena and mechanical stresses, is essential in soft tissue mechanobiology. For the first time ever, we measure and analyze 3D strain fields induced by these chemoelastic effects thanks to the unique combination of OCT imaging and digital volume correlation.

Microstructural quantification of collagen fiber orientations and its integration in constitutive modeling of the porcine carotid artery

BACKGROUND

Mechanical characteristics of vascular tissue may play a role in different arterial pathologies, which, amongst others, requires robust constitutive descriptions to capture the vessel wall's anisotropic and non-linear properties.Specifically, the complex 3D network of collagen and its interaction with other structural elements has a dominating effect of arterial properties at higher stress levels.The aim of this study is to collect quantitative collagen organization as well as mechanical properties to facilitate structural constitutive models for the porcine carotid artery.This helps the understanding of the mechanics of swine carotid arteries, being a standard in clinical hypothesis testing, in endovascular preclinical trials for example.

METHOD

Porcine common carotid arteries (n=10) were harvested and used to (i) characterize the collagen fiber organization with polarized light microscopy, and (ii) the biaxial mechanical properties by inflation testing.The collagen organization was quantified by the Bingham orientation density function (ODF), which in turn was integrated in a structural constitutive model of the vessel wall.A one-layered and thick-walled model was used to estimate mechanical constitutive parameters by least-square fitting the recorded in vitro inflation test results.Finally, uniaxial data published elsewhere were used to validate the mean collagen organization described by the Bingham ODF.

RESULTS

Thick collagen fibers, i.e.the most mechanically relevant structure, in the common carotid artery are dispersed around the circumferential direction.In addition, almost all samples showed two distinct families of collagen fibers at different elevation, but not azimuthal, angles.Collagen fiber organization could be accurately represented by the Bingham ODF (κ1,2,3=[13.5,0.0,25.2] and κ1,2,3=[14.7,0.0,26.6]; average error of about 5%), and their integration into a structural constitutive model captured the inflation characteristics of individual carotid artery samples.Specifically, only four mechanical parameters were required to reasonably (average error from 14% to 38%) cover the experimental data over a wide range of axial and circumferential stretches.However, it was critical to account for fibrilar links between thick collagen fibers.Finally, the mean Bingham ODF provide also good approximation to uniaxial experimental data.

CONCLUSIONS

The applied structural constitutive model, based on individually measured collagen orientation densities, was able to capture the biaxial properties of the common carotid artery. Since the model required coupling amongst thick collagen fibers, the collagen fiber orientations measured from polarized light microscopy, alone, seem to be insufficient structural information. Alternatively, a larger dispersion of collagen fiber orientations, that is likely to arise from analyzing larger wall sections, could have had a similar effect, i.e. could have avoided coupling amongst thick collagen fibers.

STATEMENT OF SIGNIFICANCE

The applied structural constitutive model, based on individually measured collagen orientation densities, was able to capture the biaxial and uniaxial properties of the common carotid artery. Since the model required coupling amongst thick collagen fibers, an effective orientation density that accounts for cross-links between the main collagen fibers has been porposed. The model provides a good approximation to the experimental data.

Using Digital Image Correlation to Characterize Local Strains on Vascular Tissue Specimens

Characterization of the mechanical behavior of biological and engineered soft tissues is a central component of fundamental biomedical research and product development. Stress-strain relationships are typically obtained from mechanical testing data to enable comparative assessment among samples and in some cases identification of constitutive mechanical properties. However, errors may be introduced through the use of average strain measures, as significant heterogeneity in the strain field may result from geometrical non-uniformity of the sample and stress concentrations induced by mounting/gripping of soft tissues within the test system. When strain field heterogeneity is significant, accurate assessment of the sample mechanical response requires measurement of local strains. This study demonstrates a novel biomechanical testing protocol for calculating local surface strains using a mechanical testing device coupled with a high resolution camera and a digital image correlation technique. A series of sample surface images are acquired and then analyzed to quantify the local surface strain of a vascular tissue specimen subjected to ramped uniaxial loading. This approach can improve accuracy in experimental vascular biomechanics and has potential for broader use among other native soft tissues, engineered soft tissues, and soft hydrogel/polymeric materials. In the video, we demonstrate how to set up the system components and perform a complete experiment on native vascular tissue.

Experimental investigation and constitutive modeling of the 3D histomechanical properties of vein tissue

Numerous studies have provided material models of arterial walls, but limited information is available on the pseudo-elastic response of vein walls and their underlying microstructure, and only few constitutive formulations have been proposed heretofore. Accordingly, we identified the histomechanics of healthy porcine jugular veins by applying an integrated approach of inflation/extension tests and histomorphometric evaluation. Several alternate phenomenological and microstructure-based strain-energy functions (SEF) were attempted to mimic the material response. Evaluation of their descriptive/predictive capacities showed that the exponential Fung-type SEF alone or in tandem with the neo-Hookean term did not capture the deformational response at high pressures. This problem was solved to a degree with the neo-Hookean and two-fiber (diagonally arranged) family SEF, but altogether the least reliable fit was generated. Fitting precision was much improved with the four-fiber (diagonally, circumferentially, longitudinally arranged) family model, as the inability of neo-Hookean function with force data was alleviated by use of the longitudinal-fiber family. Implementation of a quadratic term as a descriptor of low-pressure anisotropy facilitated the simulation of low-pressure and force data, and the four-fiber families simulated more faithfully than the two-fiber families the physiologic and high-pressure response. Importantly, this SEF was consistent with vein angioarchitecture, namely the occurrence of extensive elastin fibers along the longitudinal axis and few orthogonal fibers attached to them and of three collagen sets with circumferential, longitudinal, and diagonal arrangement, respectively. Our findings help to establish the relationship between vein microstructure and its biomechanical response, yet additional observations are obligatory prior to endeavoring generalizations to other veins.

Biomechanical behavior and histological organization of the three-layered passive esophagus as a function of topography

The zero-stress state of the mucosa-submucosa and two muscle esophageal layers has been delineated, but their multi-axial response has not, because muscle dissection may not leave tubular specimens intact for inflation/extension testing. The histomechanical behavior of the three-layered porcine esophagus was investigated in this study, through light microscopic examination and uniaxial tension, with two-dimensional strain measurement in pairs of orthogonally oriented specimens. The two-dimensional Fung-type strain–energy function described suitably the pseudo-elastic tissue response, affording faithful simulations to our data. Differences in the scleroprotein content and configuration were identified as a function of layer, topography, and orientation, substantiating the macromechanical differences found. In view of the failure and optimized material parameters, the mucosa-submucosa was stronger and stiffer than muscle, associating it with a higher collagen content. A notable topographical distribution was apparent, with data for the abdominal region differentiated from that for the cervical region, owing to the existence of inner muscle with a circumferential arrangement and of outer muscle with a longitudinal arrangement in the former region, and of both muscle layers with oblique arrangement in the latter region, with thoracic esophagus being a transition zone. Tissue from the mucosa-submucosa was stronger and stiffer longitudinally, relating with a preferential collagen reinforcement along that axis, but more extensible in the orthogonal axis.

Analysis of femoral artery intima-media thickness during the cardiac cycle

BACKGROUND

Variations in the intima-media thickness (IMT) of the carotid artery during the cardiac cycle are well established. The change in femoral IMT during the cardiac cycle is largely unknown. This study focuses on the variation of femoral IMT, vessel diameter, and cross-sectional area (CSA) of the IMT during the cardiac cycle.

METHODS

Video clips of the femoral artery were obtained using B-mode ultrasonography in 60 patients between the ages of 18 and 50. IMT and diameter measurements were made using automated software, and CSA was subsequently calculated. Triplicate measurements of each femoral artery were made at three points in the cardiac cycle: the R wave, the T wave, and at the point of maximal vessel diameter falling after the T wave and before the following P wave.

RESULTS

Femoral IMT, diameter, and CSA did not show a statistically significant difference with measurement on the R versus the T wave (P>0.36, P>0.28, and P>0.76, respectively). Interestingly, when comparing measurements on the R or T wave with measurements taken at the maximum vessel diameter, there was a statistically significant difference in vessel diameter (P<0.001) and CSA (P<0.005) but not in femoral IMT (P>0.2).

CONCLUSIONS

Unlike studies of the carotid artery, there were no statistically significant differences between measurements made at the R versus the T wave. There were, however, statistically significant differences noted in diameter and CSA when measurements were taken at a point later in the cardiac cycle. This has ramifications for future studies on vascular remodeling.

Differential histomechanical response of carotid artery in relation to species and region: mathematical description accounting for elastin and collagen anisotropy

The selection of a mathematical descriptor for the passive arterial mechanical behavior has been long debated in the literature and customarily constrained by lack of pertinent data on the underlying microstructure. Our objective was to analyze the response of carotid artery subjected to inflation/extension with phenomenological and microstructure-based candidate strain-energy functions (SEFs), according to species (rabbit vs. pig) and region (proximal vs. distal). Histological variations among segments were examined, aiming to explicitly relate them with the differential material response. The Fung-type model could not capture the biphasic response alone. Combining a neo-Hookean with a two-fiber family term alleviated this restraint, but force data were poorly captured, while consideration of low-stress anisotropy via a quadratic term allowed improved simulation of both pressure and force data. The best fitting was achieved with the quadratic and Fung-type or four-fiber family SEF. The latter simulated more closely than the two-fiber family the high-stress response, being structurally justified for all artery types, whereas the quadratic term was justified for transitional and muscular arteries exhibiting notable elastin anisotropy. Diagonally arranged fibers were associated with pericellular medial collagen, and circumferentially and longitudinally arranged fibers with medial and adventitial collagen bundles, evidenced by the significant correlations of SEF parameters with quantitative histology.

A structural constitutive model considering angular dispersion and waviness of collagen fibres of rabbit facial veins

Background

Structural constitutive models of vascular wall integrate information on composition and structural arrangements of tissue. In blood vessels, collagen fibres are arranged in coiled and wavy bundles and the individual collagen fibres have a deviation from their mean orientation. A complete structural constitutive model for vascular wall should incorporate both waviness and orientational distribution of fibres. We have previously developed a model, for passive properties of vascular wall, which considers the waviness of collagen fibres. However, to our knowledge there is no structural model of vascular wall which integrates both these features.

Methods

In this study, we have suggested a structural strain energy function that incorporates not only the waviness but also the angular dispersion of fibres. We studied the effect of parameters related to the orientational distribution on macro-mechanical behaviour of tissue during inflation-extension tests. The model was further applied on experimental data from rabbit facial veins.

Results

Our parametric study showed that the model is less sensitive to the orientational dispersion when fibres are mainly oriented circumferentially. The macro-mechanical response is less sensitive to changes in the mean orientation when fibres are more dispersed. The model accurately fitted the experimental data of veins, while not improving the quality of the fit compared to the model without dispersion. Our results showed that the orientational dispersion of collagen fibres could be compensated by a less abrupt and shifted to higher strain collagen engagement pattern. This should be considered when the model is fitted to experimental data and model parameters are used to study structural modifications of collagen fibre network in physiology and disease.

Conclusions

The presented model incorporates structural features related to waviness and orientational distribution of collagen fibres and thus offers possibilities to better understand the relation between structure and function in the vascular wall. Also, the model can be used to further study mechanically induced collagen remodelling in vascular tissue in health and disease.

New interpretation of arterial stiffening due to cigarette smoking using a structurally motivated constitutive model

Cigarette smoking is the leading self-inflicted risk factor for cardiovascular diseases; it causes arterial stiffening with serious sequelea including atherosclerosis and abdominal aortic aneurysms. This work presents a new interpretation of arterial stiffening caused by smoking based on data published for rat pulmonary arteries. A structurally motivated "four fiber family" constitutive relation was used to fit the available biaxial data and associated best-fit values of material parameters were estimated using multivariate nonlinear regression. Results suggested that arterial stiffening caused by smoking was reflected by consistent increase in an elastin-associated parameter and moreover by marked increase in the collagen-associated parameters. That is, we suggest that arterial stiffening due to cigarette smoking appears to be isotropic, which may allow simpler phenomenological models to capture these effects using a single stiffening parameter similar to the approach in isotropic continuum damage mechanics. There is a pressing need, however, for more detailed histological information coupled with more complete biaxial mechanical data for a broader range of systemic arteries.