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

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.

A novel constitutive model considering the role of elastic lamellae' structural heterogeneity in homogenizing transmural stress distribution in arteries

Understanding how the homeostatic stress state can be reached in arterial tissues can provide new insights into vascular physiology. Even though the function of maintaining homeostasis is often linked to the concentric layers of medial elastic lamellae, how the lamellae are capable of evenly distributing the stress transmurally remains to be understood. The recent microstructural study by Yu et al. (2018 J. R. Soc. Interface 15, 20180492) revealed that, circumferentially, lamellar layers closer to the lumen are wavier than the ones further away from it and, thus, experience more unfolding when subjected to blood pressure. Motivated by this peculiar finding, the current study, for the first time, proposes a novel approach to model elastic lamellae and such structural heterogeneity using the extensible worm-like chain model. When implemented into the material description of the conventional two-layer artery model, in which adventitial collagen is modelled using the inextensible worm-like chain model, it is demonstrated that structural heterogeneity in elastic lamellae plays an important role in dictating transmural stress distribution and, therefore, the homeostasis of the arterial wall.

Are ovine and porcine carotid arteries equivalent animal models for experimental cardiac surgery: A quantitative histological comparison

BACKGROUND

Coronary artery bypass grafting (CABG) is a common cardiac surgery. Manufacturing small-diameter (2-5mm) vascular grafts for CABG is important for patients who lack first-choice autologous arterial, or venous conduits. Ovine and porcine common carotid arteries (CCAs) are used as large animal models for in vivo testing of newly developed tissue-engineered arterial grafts. It is unknown to what extent these models are interchangeable and whether the left and right arteries of the same subjects can be used as experimental controls. Therefore, we compared the microscopic structure of paired left and right ovine and porcine CCAs in the proximodistal direction and compared these animal model samples to samples of human coronary arteries (CAs) and human internal thoracic arteries (ITAs).

METHODS

We compared the histological composition of whole CCAs of sheep (n=22 animals) with whole porcine CCAs (n=21), segments of human CAs (n=21), and human ITAs (n=21). Using unbiased sampling and stereological methods, we quantified the fractions of elastin, total collagen, type I collagen, type III collagen, smooth muscle actin (SMA) and chondroitin sulfate (CS) A, B, and C. We also quantified the densities and distributions of nuclear profiles, nervi vasorum and vasa vasorum as well as the thickness of the intima-media and total wall thickness.

RESULTS

The differences between the paired samples of left and right CCAs in sheep were substantially greater than the differences in laterality in porcine CCAs. The right ovine CCAs had a smaller fraction of elastin (p<0.001), greater fraction of SMA (p<0.01), and greater intima-media thickness (p<0.001) than the paired left side CCAs. In pigs, the right CCAs had a greater fraction of elastin (p<0.05) and a greater density of vasa vasorum in the media (p<0.001) than the left-side CCAs. The fractions of elastin and CS decreased and the fraction of SMA increased in the proximodistal direction in both the ovine (p<0.001) and porcine (p<0.001) CCAs. Ovine CCAs had a muscular phenotype along their entire length, but porcine CCAs were elastic-type arteries in the proximal segments but muscular type arteries in middle and distal segments. The CCAs of both animals differed from the human CAs and ITAs in most parameters, but the ovine CCAs had a comparable fraction of elastin and CS to human ITAs.

CONCLUSIONS

From a histological point of view, ovine and porcine CCAs were not equivalent in most quantitative parameters to human CAs and ITAs. Left and right ovine CCAs did not have the same histological composition, which is limiting for their mutual equivalence as sham-operated controls in experiments. These differences should be taken into account when designing and interpreting experiments using these models in cardiac surgery. The complete morphometric data obtained by quantitative evaluation of arterial segments were provided to facilitate the power analysis necessary for justification of the minimum number of samples when planning further experiments. The middle or distal segments of ovine and porcine CCAs remain the most realistic and the best characterized large animal models for testing artificial arterial CABG conduits.

Variation of Passive Biomechanical Properties of the Small Intestine along Its Length: Microstructure-Based Characterization

Multiaxial testing of the small intestinal wall is critical for understanding its biomechanical properties and defining material models, but limited data and material models are available. The aim of the present study was to develop a microstructure-based material model for the small intestine and test whether there was a significant variation in the passive biomechanical properties along the length of the organ. Rat tissue was cut into eight segments that underwent inflation/extension testing, and their nonlinearly hyper-elastic and anisotropic response was characterized by a fiber-reinforced model. Extensive parametric analysis showed a non-significant contribution to the model of the isotropic matrix and circumferential-fiber family, leading also to severe over-parameterization. Such issues were not apparent with the reduced neo-Hookean and (axial and diagonal)-fiber family model, that provided equally accurate fitting results. Absence from the model of either the axial or diagonal-fiber families led to ill representations of the force- and pressure-diameter data, respectively. The primary direction of anisotropy, designated by the estimated orientation angle of diagonal-fiber families, was about 35° to the axial direction, corroborating prior microscopic observations of submucosal collagen-fiber orientation. The estimated model parameters varied across and within the duodenum, jejunum, and ileum, corroborating histologically assessed segmental differences in layer thicknesses.

Alterations with age in the biomechanical behavior of human ureteral wall: Microstructure-based modeling

The human ureters have not been thoroughly explored from the biomechanics perspective, despite the wealth of such data for other soft-tissue types. This study was motivated by the need to use relevant biomechanical data from human ureters and microstructure-based material formulations for simulations of ureteral peristalsis and stenting. Our starting choice was the four-fiber family model that has proven its validity as a descriptor of the multiaxial response of cardiovascular tissues. The degree of model complexity, required for rigorous fits to passive quasi-static pressure-diameter-force data at several axial stretches, was systematically investigated. Ureteral segments from sixteen human autopsy subjects were evaluated. A diagonal and axial family model allowed equally-good fits as the full model for all age groups and ureteral regions; considerably better than those allowed by the phenomenological Fung-type model whose root-mean-square error of fitting was three-fold greater. This reduced model mimicked the structure seen in histologic sections, namely plentiful diagonal collagen fibers in the lamina propria and axial fibers in the muscle and adventitia. The paucity of elastin fibers and mixed muscle orientation justified the use of isotropic muscle-dominated matrix with small neo-Hookean parameter values. The significantly thicker lamina propria in the lower than the upper ureter of young subjects (312 ± 27 vs. 232 ± 26 μm; mean ± standard error) corroborated the significant regional differences in diagonal-fiber family parameter values. The significant muscle thickening with age (upper ureter: 373 ± 48 vs. 527 ± 67 μm; middle: 388 ± 29 vs. 575 ± 69 μm; lower: 440 ± 21 vs. 602 ± 71 μm) corroborated the significant age-related increase in axial-fiber family parameter values.

Histological mapping of porcine carotid arteries - An animal model for the assessment of artificial conduits suitable for coronary bypass grafting in humans

BACKGROUND

Using animal models in experimental medicine requires mapping of their anatomical variability. Porcine common carotid arteries (CCA) are often preferred for the preclinical testing of vascular grafts due to their anatomical and physiological similarity to human small-diameter arteries. Comparing the microscopic structure of animal model organs to their human counterparts reveals the benefits and limitations of translational medicine.

METHODS

Using quantitative histology and stereology, we performed an extensive mapping of the regional proximodistal differences in the fractions of elastin, collagen, and smooth muscle actin as well as the intima-media and wall thicknesses among 404 segments (every 1 cm) of porcine CCAs collected from male and female pigs (n = 21). We also compared the microscopic structure of porcine CCAs with segments of human coronary arteries and one of the preferred arterial conduits used for the coronary artery bypass grafting (CABG), namely, the internal thoracic artery (ITA) (n = 21 human cadavers).

RESULTS

The results showed that the histological structure of left and right porcine CCA can be considered equivalent, provided that gross anatomical variations of the regular branching patterns are excluded. The proximal elastic carotid (51.2% elastin, 4.2% collagen, and 37.2% actin) transitioned to more muscular middle segments (23.5% elastin, 4.9% collagen, 54.3% actin) at the range of 2-3 centimeters and then to even more muscular distal segments (17.2% elastin, 4.9% collagen, 64.0% actin). The resulting morphometric data set shows the biological variability of the artery and is made available for biomechanical modeling and for performing a power analysis and calculating the minimum number of samples per group when planning further experiments with this widely used large animal model.

CONCLUSIONS

Comparison of porcine carotids with human coronary arteries and ITA revealed the benefits and the limitations of using porcine CCAs as a valid model for testing bioengineered small-diameter CABG vascular conduits. Morphometry of human coronary arteries and ITA provided more realistic data for tailoring multilayered artificial vascular prostheses and the ranges of values within which the conduits should be tested in the future. Despite their limitations, porcine CCAs remain a widely used and well-characterized large animal model that is available for a variety of experiments in vascular surgery.

Biaxial biomechanical properties of the nonpregnant murine cervix and uterus

From a biomechanical perspective, female reproductive health is an understudied area of research. There is an incomplete understanding of the complex function and interaction between the cervix and uterus. This, in part, is due to the limited research into multiaxial biomechanical functions and geometry of these organs. Knowledge of the biomechanical function and interaction between these organs may elucidate etiologies of conditions such as preterm birth. Therefore, the objective of this study was to quantify the multiaxial biomechanical properties of the murine cervix and uterus using a biaxial testing set-up. To accomplish this, an inflation-extension testing protocol (n = 15) was leveraged to quantify biaxial biomechanical properties while preserving native matrix interactions and geometry. Ultrasound imaging and histology (n = 10) were performed to evaluate regional geometry and microstructure, respectively. Histological analysis identified a statistically significant greater collagen content and significantly smaller smooth muscle content in the cervix as compared to the uterus. No statistically significant differences in elastic fibers were identified. Analysis of bilinear fits revealed a significantly stiffer response from the circumferentially orientated ECM fibers compared to axially orientated fibers in both organs. Bilinear fits and a two-fiber family constitutive model showed that the cervix was significantly less distensible than the uterus. We submit that the regional biaxial information reported in this study aids in establishing an appropriate reference configuration for mathematical models of the uterine-cervical complex. Thus, may aid future work to elucidate the biomechanical mechanisms leading to cervical or uterine conditions.

Mechanobiological model of arterial growth and remodeling

A coupled agent-based model (ABM) and finite element analysis (FEA) computational framework is developed to study the interplay of bio-chemo-mechanical factors in blood vessels and their role in maintaining homeostasis. The agent-based model implements the power of REPAST Simphony libraries and adapts its environment for biological simulations. Coupling a continuum-level model (FEA) to a cellular-level model (ABM) has enabled this computational framework to capture the response of blood vessels to increased or decreased levels of growth factors, proteases and other signaling molecules (on the micro scale) as well as altered blood pressure. Performance of the model is assessed by simulating porcine left anterior descending artery under normotensive conditions and transient increases in blood pressure and by analyzing sensitivity of the model to variations in the rule parameters of the ABM. These simulations proved that the model is stable under normotensive conditions and can recover from transient increases in blood pressure. Sensitivity studies revealed that the model is most sensitive to variations in the concentration of growth factors that affect cellular proliferation and regulate extracellular matrix composition (mainly collagen).

Effect of ovariectomy and Sideritis euboea extract administration on large artery mechanics, morphology, and structure in middle-aged rats

BACKGROUND

Arterial function is regulated by estrogen, but no consistent pattern of arterial mechanical remodeling in response to depleted estrogen levels is available.

OBJECTIVE

To examine long-term effects of ovariectomy (OVX) on the mechanical properties, morphology, and histological structure of the carotid artery in middle-aged rats and a potentially protective effect of Sideritis euboea extract (SID), commonly consumed as "mountain tea".

METHODS

10-month-old female Wistar rats were allocated into control (sham-operated), OVX, OVX+SID, and OVX+MALT (maltodextrin; excipient used for dilution of SID) groups. They were sacrificed after 6 months and their carotid arteries were submitted to inflation/extension tests and to dimensional and histological evaluation.

RESULTS

Remodeling in OVX rats was characterized by a decreased in situ axial extension ratio, along with increased opening angle, thickness, and area of the vessel wall and of its medial layer, but unchanged lumen diameter. Compositional changes involved increased elastin/collagen densities. Characterization by the "four-fiber" microstructure-motivated model revealed similar in situ biaxial response of carotid arteries in OVX and control rats.

CONCLUSIONS

Carotid artery remodeling in OVX rats was largely consistent with hypertensive remodeling, despite the minor arterial pressure changes found, and was not altered by administration of SID, despite previous evidence of its osteo-protective effect.

A nonlinear anisotropic inverse method for computational dissection of inhomogeneous planar tissues

Quantification of the mechanical behavior of soft tissues is challenging due to their anisotropic, heterogeneous, and nonlinear nature. We present a method for the 'computational dissection' of a tissue, by which we mean the use of computational tools both to identify and to analyze regions within a tissue sample that have different mechanical properties. The approach employs an inverse technique applied to a series of planar biaxial experimental protocols. The aggregated data from multiple protocols provide the basis for (1) segmentation of the tissue into regions of similar properties, (2) linear analysis for the small-strain behavior, assuming uniform, linear, anisotropic behavior within each region, (3) subsequent nonlinear analysis following each individual experimental protocol path and using local linear properties, and (4) construction of a strain energy data set W(E) at every point in the material by integrating the differential stress-strain functions along each strain path. The approach has been applied to simulated data and captures not only the general nonlinear behavior but also the regional differences introduced into the simulated tissue sample.

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.

Layer- and region-specific material characterization of ascending thoracic aortic aneurysms by microstructure-based models

Material characterization of ascending thoracic aortic aneurysms is indispensable for the determination of stress distributions across wall thickness and the different aneurysm regions that may be responsible for their catastrophic rupture or dissection, but only few studies have addressed this issue hitherto. In this article, we are presenting our findings of implementing microstructure-based formulations for characterizing layer- and region-specific variations in wall properties, which is a reasonable consensus today. Together, we performed image-based analysis to derive collagen-fiber orientation angles that may serve as validation of the preferred candidate for a fiber-reinforced constitutive descriptor. We considered a four-fiber model with dispersions of fiber angles about the main directions, based on our histological observations, demonstrating a wide distribution of fiber orientations spanning circumferential to longitudinal directions, and its successful implementation to our biomechanical data from tensile testing. However, an in-depth parametric analysis showed that a condensed model without longitudinal-fiber family described the data just as well and did not omit essential histological organization of collagen fibers, while reserving a smaller number of parameters, which makes it advantageous for computational applications. A major aberration from almost all existing models in the literature is the hypothesis made that fibers can support compressive stresses. Such a hypothesis needs further examination but it has the benefits of allowing improved fits to the vanishing transverse stresses under uniaxial test conditions and of properly reflecting the exponential nature of the compressive stress-strain response of aortic tissue, being consistent with observations of collagen being under compression in the unloaded wall.

Characterization of regional deformation and material properties of the intact explanted vein by microCT and computational analysis

PURPOSE

Detailed mechanical information of the vein is important to better understand remodeling of the vessel in disease states, but has been difficult to obtain due to its thinness, unique geometry, and limitations of mechanical testing. This study presents a novel method for characterizing deformation of the intact explanted vein under physiological loads and determining its material properties by combining high-resolution imaging and computational analysis.

METHODS

High-resolution CT (microCT) was used to image an iodine-stained, excised porcine internal jugular vein sample under extension to 100% and 120% of in situ length, and inflation and 2, 10, 20 mmHg of pressure, inside a microCT-compatible hydrostatic loading chamber. Regional strains were measured with the finite element (FE) image registration method known as Hyperelastic Warping. Material properties were approximated with inverse FE characterization by optimizing stiffness-related coefficients so to match simulated strains to the experimental measurements.

RESULTS

The observed morphology and regional strain of the vein were found to be relatively heterogeneous. The regional variability in the measured strain was primarily driven by geometry. Although iodine treatment may result in tissue stiffening, which requires additional investigation, it is effective in allowing detailed detection of vein geometry.

CONCLUSIONS

The feasibility and utility of using microCT and computational analysis to characterize mechanical responses and material properties of the vein were demonstrated. The presented method is a promising alternative or addition to mechanical testing for characterizing veins or other similarly delicate vessels in their native anatomical configuration under a wide range of realistic or simulated environmental and loading conditions.

Passive biaxial mechanical properties and in vivo axial pre-stretch of the diseased human femoropopliteal and tibial arteries

Surgical and interventional therapies for atherosclerotic lesions of the infrainguinal arteries are notorious for high rates of failure. Frequently, this leads to expensive reinterventions, return of disabling symptoms or limb loss. Interaction between the artery and repair material likely plays an important role in reconstruction failure, but data describing the mechanical properties and functional characteristics of human femoropopliteal and tibial arteries are currently not available. Diseased superficial femoral (SFA, n = 10), popliteal (PA, n = 8) and tibial arteries (TA, n = 3) from 10 patients with critical limb ischemia were tested to determine passive mechanical properties using planar biaxial extension. All specimens exhibited large nonlinear deformations and anisotropy. Under equibiaxial loading, all arteries were stiffer in the circumferential direction than in the longitudinal direction. Anisotropy and longitudinal compliance decreased distally, but circumferential compliance increased, possibly to maintain a homeostatic multiaxial stress state. Constitutive parameters for a four-fiber family invariant-based model were determined for all tissues to calculate in vivo axial pre-stretch that allows the artery to function in the most energy efficient manner while also preventing buckling during extremity flexion. Calculated axial pre-stretch was found to decrease with age, disease severity and more distal arterial location. Histological analysis of the femoropopliteal artery demonstrated a distinct sub-adventitial layer of longitudinal elastin fibers that appeared thicker in healthier arteries. The femoropopliteal artery characteristics and properties determined in this study may assist in devising better diagnostic and treatment modalities for patients with peripheral arterial disease.

Time-course of venous wall biomechanical adaptation in pressure and flow-overload: assessment by a microstructure-based material model

Arteriovenous fistulae have been previously created by our group, through implantation of e-PTFE grafts between the carotid artery and jugular vein in healthy pigs, to gather comprehensive data on the time-course of the adapted geometry, composition, and biomechanical properties of the venous wall exposed to chronic increases in pressure and flow. The aim of this study was to mathematically assess the biomechanical adaptation of venous wall, by characterizing our previous in vitro inflation/extension testing data obtained 2, 4, and 12 weeks post-fistula, using a microstructure-based material model. Our choice for such a model considered a quadratic function for elastin with a four-fiber family term for collagen, and permitted realistic data characterization for both overloaded and control veins. As structural validation to the hemodynamically-driven differences in the material response, computerized histology was employed to quantitate the composition and orientation of collagen and elastin-fiber networks. The parameter values optimized showed marked differences among the overloaded and control veins, namely decrease in the quadratic function parameters and increase in the four-fiber family parameters. Differences among the two vein types were highlighted with respect to the underlying microstructure, namely the reduced elastin and increased collagen contents induced by pressure and flow-overload. Explicit correlations were found of the material parameters with the two basic scleroprotein contents, substantiating the material model used and the characterization findings presented. Our results are expected to improve the current understanding of the dynamics of venous adaptation under sustained pressure- and flow-overload conditions, for which data are largely unavailable and contradictory.

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.