Validation of an arterial constitutive model accounting for collagen content and crosslinking

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.

Effect of aging on the biaxial mechanical behavior of human descending thoracic aorta: Experiments and constitutive modeling considering collagen crosslinking

Collagen crosslinking, an important contributor to the stiffness of soft tissues, was found to increase with aging in the aortic wall. Here we investigated the mechanical properties of human descending thoracic aorta with aging and the role of collagen crosslinking through a combined experimental and modeling approach. A total of 32 samples from 17 donors were collected and divided into three age groups: <40, 40-60 and > 60 years. Planar biaxial tensile tests were performed to characterize the anisotropic mechanical behavior of the aortic samples. A recently developed constitutive model incorporating collagen crosslinking into the two-fiber family model (Holzapfel and Ogden, 2020) was modified to accommodate biaxial deformation of the aorta, in which the extension and rotation kinematics of bonded fibers and crosslinks were decoupled. The mechanical testing results show that the aorta stiffens with aging with a more drastic change in the longitudinal direction, which results in altered aortic anisotropy. Our results demonstrate a good fitting capability of the constitutive model considering crosslinking for the biaxial aortic mechanics of all age groups. Furthermore, constitutive modeling results suggest an increased contribution of crosslinking and strain energy density to the biaxial stress-stretch behaviors with aging and point to excessive crosslinking as a prominent contributor to aortic stiffening.

Characteristics of Collagen Changes in Small Intestine Anastomoses Induced by High-Frequency Electric Field Welding

High-frequency electric field welding-induced tissue fusion has been explored as an advanced surgical method for intestinal anastomoses; however, intrinsic mechanisms remain unclear. The aim of this study was to investigate microcosmic changes of collagen within the fusion area, with various parameters. Ex vivo small intestine was fused with mucosa-mucosa. Four levels of compressive pressure (100 kPa, 150 kPa, 200 kPa, 250 kPa) were applied for 10 s in order to fuse the colons under a power level of 140 W. Then, collagen fibers of the fusion area were examined by fibrillar collagen alignment and TEM. Three levels of power (90 W, 110 W, 140 W) and three levels of time (5 s, 10 s, 20 s) were applied in order to fuse colons at 250 kPa, and then collagen within the fusion area was examined by Raman spectroscopy. Fibrillar collagen alignment analysis showed that with the increase in compression pressure, alignment of the collagen in the fusion area gradually increased, and the arrangement of collagen fibers tended to be consistent, which was conducive to the adhesion of collagen fibers. TEM showed that pressure changed the distribution and morphology of collagen fibers. Raman spectroscopy showed that increased power and time within a certain range contributed to collagen cross linking. Peak positions of amide I band and amide III band changed. These results suggested that higher power and a longer amount of time resulted in a decrease in non-reducible cross links and an increase in reducible cross links. Compression pressure, power, and time can affect the state of collagen, but the mechanisms are different. Compressive pressure affected the state of collagen by changing its orientation; power and time denatured collagen by increasing temperature and improved the reducible cross linking of collagen to promote tissue fusion.

Three-Dimensional Anisotropic Hyperelastic Constitutive Model Describing the Mechanical Response of Human and Mouse Cervix

The mechanical function of the uterine cervix is critical for a healthy pregnancy. During pregnancy, the cervix undergoes significant softening to allow for a successful delivery. Abnormal cervical remodeling is suspected to contribute to preterm birth. Material constitutive models describing known biological shifts in pregnancy are essential to predict the mechanical integrity of the cervix. In this work, the material response of human cervical tissue under spherical indentation and uniaxial tensile tests loaded along different anatomical directions is experimentally measured. A deep-learning segmentation tool is applied to capture the tissue deformation during the uniaxial tensile tests. A 3-dimensional, equilibrium anisotropic continuous fiber constitutive model is formulated, considering collagen fiber directionality, fiber bundle dispersion, and the entropic nature of wavy cross-linked collagen molecules. Additionally, the universality of the material model is demonstrated by characterizing previously published mouse cervix mechanical data. Overall, the proposed material model captures the tension-compression asymmetric material responses and the remodeling characteristics of both human and mouse cervical tissue. The pregnant (PG) human cervix (mean locking stretch ζ=2.4, mean initial stiffness ξ=12 kPa, mean bulk modulus κ=0.26 kPa, mean dispersion b=1.0) is more compliant compared with the nonpregnant (NP) cervix (mean ζ=1.3, mean ξ=32 kPa, mean κ=1.4 kPa, mean b=1.4). Creating a validated material model, which describes the role of collagen fiber directionality, dispersion, and crosslinking, enables tissue-level biomechanical simulations to determine which material and anatomical factors drive the cervix to open prematurely. STATEMENT OF SIGNIFICANCE: In this study, we report a 3D anisotropic hyperelastic constitutive model based on Langevin statistic mechanics and successfully describe the material behavior of both human and mouse cervical tissue using this model. This model bridges the connection between the extracellular matrix (ECM) microstructure remodeling and the macro mechanical properties change of the cervix during pregnancy via microstructure-associated material parameters. This is the first model, to our knowledge, to connect the the entropic nature of wavy cross-linked collagen molecules with the mechanical behavior of the cervix. Inspired by microstructure, this model provides a foundation to understand further the relationship between abnormal cervical ECM remodeling and preterm birth. Furthermore, with a relatively simple form, the proposed model can be applied to other fibrous tissues in the future.

A publicly available virtual cohort of four-chamber heart meshes for cardiac electro-mechanics simulations

Computational models of the heart are increasingly being used in the development of devices, patient diagnosis and therapy guidance. While software techniques have been developed for simulating single hearts, there remain significant challenges in simulating cohorts of virtual hearts from multiple patients. To facilitate the development of new simulation and model analysis techniques by groups without direct access to medical data, image analysis techniques and meshing tools, we have created the first publicly available virtual cohort of twenty-four four-chamber hearts. Our cohort was built from heart failure patients, age 67±14 years. We segmented four-chamber heart geometries from end-diastolic (ED) CT images and generated linear tetrahedral meshes with an average edge length of 1.1±0.2mm. Ventricular fibres were added in the ventricles with a rule-based method with an orientation of -60° and 80° at the epicardium and endocardium, respectively. We additionally refined the meshes to an average edge length of 0.39±0.10mm to show that all given meshes can be resampled to achieve an arbitrary desired resolution. We ran simulations for ventricular electrical activation and free mechanical contraction on all 1.1mm-resolution meshes to ensure that our meshes are suitable for electro-mechanical simulations. Simulations for electrical activation resulted in a total activation time of 149±16ms. Free mechanical contractions gave an average left ventricular (LV) and right ventricular (RV) ejection fraction (EF) of 35±1% and 30±2%, respectively, and a LV and RV stroke volume (SV) of 95±28mL and 65±11mL, respectively. By making the cohort publicly available, we hope to facilitate large cohort computational studies and to promote the development of cardiac computational electro-mechanics for clinical applications.

BMPR2 acts as a gatekeeper to protect endothelial cells from increased TGFβ responses and altered cell mechanics

Balanced transforming growth factor-beta (TGFβ)/bone morphogenetic protein (BMP)-signaling is essential for tissue formation and homeostasis. While gain in TGFβ signaling is often found in diseases, the underlying cellular mechanisms remain poorly defined. Here we show that the receptor BMP type 2 (BMPR2) serves as a central gatekeeper of this balance, highlighted by its deregulation in diseases such as pulmonary arterial hypertension (PAH). We show that BMPR2 deficiency in endothelial cells (ECs) does not abolish pan-BMP-SMAD1/5 responses but instead favors the formation of mixed-heteromeric receptor complexes comprising BMPR1/TGFβR1/TGFβR2 that enable enhanced cellular responses toward TGFβ. These include canonical TGFβ-SMAD2/3 and lateral TGFβ-SMAD1/5 signaling as well as formation of mixed SMAD complexes. Moreover, BMPR2-deficient cells express genes indicative of altered biophysical properties, including up-regulation of extracellular matrix (ECM) proteins such as fibrillin-1 (FBN1) and of integrins. As such, we identified accumulation of ectopic FBN1 fibers remodeled with fibronectin (FN) in junctions of BMPR2-deficient ECs. Ectopic FBN1 deposits were also found in proximity to contractile intimal cells in pulmonary artery lesions of BMPR2-deficient heritable PAH (HPAH) patients. In BMPR2-deficient cells, we show that ectopic FBN1 is accompanied by active β1-integrin highly abundant in integrin-linked kinase (ILK) mechano-complexes at cell junctions. Increased integrin-dependent adhesion, spreading, and actomyosin-dependent contractility facilitates the retrieval of active TGFβ from its latent fibrillin-bound depots. We propose that loss of BMPR2 favors endothelial-to-mesenchymal transition (EndMT) allowing cells of myo-fibroblastic character to create a vicious feed-forward process leading to hyperactivated TGFβ signaling. In summary, our findings highlight a crucial role for BMPR2 as a gatekeeper of endothelial homeostasis protecting cells from increased TGFβ responses and integrin-mediated mechano-transduction.

Contributions of elastic fibers, collagen, and extracellular matrix to the multiaxial mechanics of ligament

Elastin is a biopolymer known to provide resilience to extensible biologic tissues through elastic recoil of its highly crosslinked molecular network. Recent studies have demonstrated that elastic fibers in ligament provide significant resistance to tensile and especially shear stress. We hypothesized that the biomechanics of elastic fibers in ligament could be described as transversely isotropic with both fiber and matrix components in a multi-material mixture. Similarly, we hypothesized that material coefficients derived using the experimental tensile response could be used to predict the experimental shear response. Experimental data for uniaxial and transverse tensile testing of control tissues, and those enzymatically digested to disrupt elastin, were used as inputs to a material coefficient optimization algorithm. An additive decomposition of the strain energy was used to model the total stress as the sum of contributions from collagen fibers, elastic fibers, elastic matrix, and ground substance matrix. Matrices were modeled as isotropic Veronda-Westmann hyperelastic materials, whereas fiber families were modeled as piecewise exponential-linear hyperelastic materials. Optimizations provided excellent fits to the tensile experimental data for each treatment case and material model. Given the disparity in magnitude of stresses between longitudinal and transverse/shear tests and agreement between models and experiments, the hypothesized transversely isotropic material of elastin symmetry was supported. In addition, the coefficients derived from uniaxial and transverse tensile experiments provided reasonable predictions of the experimental behavior during shear deformation. The magnitudes of coefficients representing stress, nonlinearity, and stiffness supported the experimental evidence that elastic fibers dominate the low strain tensile and shear response of ligament. These findings demonstrate that the additive decomposition modeling strategy can represent each discrete fiber and matrix constituent and their relative contribution to the material response of the tissue. These experimental data and the validated constitutive model provide essential inputs and a framework to refine existing computational models of ligament and tendon mechanics by explicitly representing the mechanical contributions of elastic fibers.

Influence of coupled hemodynamics-arterial wall interaction on compliance in a realistic pulmonary artery with variable intravascular wall properties

Pulmonary hypertension is characterized by elevation of pulmonary artery (PA) pressure (p) and structural remodeling of the PA wall, leading to reduction in arterial compliance (c). As a step towards improving diagnosis of pulmonary disease, we use the PA branch geometry (main pulmonary artery (MPA) branching into left (LPA) and right (RPA) pulmonary arteries) obtained from MRI in conjunction with an inverse algorithm to obtain the pre-stress level in the artery walls. Next, a coupled blood-wall interaction (BWI) calculation provides hemodynamic information as well as compliance of the PA walls. We show that the computed load-free geometry from the inverse algorithm exhibits a 27.8% lower inner diameter (d) and 18.5% lower outer d compared to the in vivo geometry from MRI. Further, the mean p computed from the BWI computation in the main PA (p_MPA-n) is within 4% of the mean p_MPA-e (n-numerical; e-experimental). Also, the mean Q computed in the left PA (Q_LPA-n) is within 10% of the mean Q_LPA-e. Finally, the compliance c_MPA-n is computed to be 27% lower than c_MPA-e, while the c_LPA-n is computed to be 20.4% lower than c_LPA-e. Importantly, the PA shows significant intra-vascular variation in compliance, with the MPA showing higher overall compliance compared to the LPA (3.5-4 times).

On fibre dispersion modelling of soft biological tissues: a review

Collagen fibres within fibrous soft biological tissues such as artery walls, cartilage, myocardiums, corneas and heart valves are responsible for their anisotropic mechanical behaviour. It has recently been recognized that the dispersed orientation of these fibres has a significant effect on the mechanical response of the tissues. Modelling of the dispersed structure is important for the prediction of the stress and deformation characteristics in (patho)physiological tissues under various loading conditions. This paper provides a timely and critical review of the continuum modelling of fibre dispersion, specifically, the angular integration and the generalized structure tensor models. The models are used in representative numerical examples to fit sets of experimental data that have been obtained from mechanical tests and fibre structural information from second-harmonic imaging. In particular, patches of healthy and diseased aortic tissues are investigated, and it is shown that the predictions of the models fit very well with the data. It is straightforward to use the models described herein within a finite-element framework, which will enable more realistic (and clinically relevant) boundary-value problems to be solved. This also provides a basis for further developments of material models and points to the need for additional mechanical and microstructural data that can inform further advances in the material modelling.

Novel Biomedical Applications of Crosslinked Collagen

Collagen is one of the most useful biopolymers because of its low immunogenicity and biocompatibility. The biomedical potential of natural collagen is limited by its poor mechanical strength, thermal stability, and enzyme resistance, but exogenous chemical, physical, or biological crosslinks have been used to modify the molecular structure of collagen to minimize degradation and enhance mechanical stability. Although crosslinked collagen-based materials have been widely used in biomedicine, there is no standard crosslinking protocol that can achieve a perfect balance between stability and functional remodeling of collagen. Understanding the role of crosslinking agents in the modification of collagen performance and their potential biomedical applications are crucial for developing novel collagen-based biopolymers for therapeutic gain.

Methods for Quantifying Fibrillar Collagen Alignment

Recent evidence has implicated collagen, particularly fibrillar collagen, in a number of diseases ranging from osteogenesis imperfecta and asthma to breast and ovarian cancer. A key property of collagen that has been correlated with disease has been the alignment of collagen fibers. Collagen can be visualized using a variety of imaging techniques including second-harmonic generation (SHG) microscopy, polarized light microscopy, and staining with dyes or antibodies. However, there exists a great need to easily and robustly quantify images from these modalities for individual fibers in specified regions of interest and with respect to relevant boundaries. Most currently available computational tools rely on calculation of pixel-wise orientation or global window-wise orientation that do not directly calculate or give visible fiber-wise information and do not provide relative orientation against boundaries. We describe and detail how to use a freely available, open-source MATLAB software framework that includes two separate but linked packages "CurveAlign" and "CT-FIRE" that can address this need by either directly extracting individual fibers using an improved fiber tracking algorithm or directly finding optimal representation of fiber edges using the curvelet transform. This curvelet-based framework allows the user to measure fiber alignment on a global, region of interest, and fiber basis. Additionally, users can measure fiber angle relative to manually or automatically segmented boundaries. This tool does not require prior experience of programming or image processing and can handle multiple files, enabling efficient quantification of collagen organization from biological datasets.

Bioinspired Engineering of Poly(ethylene glycol) Hydrogels and Natural Protein Fibers for Layered Heart Valve Constructs

Layered constructs from poly(ethylene glycol) (PEG) hydrogels and chicken eggshell membranes (ESMs) are fabricated, which can be further cross-linked by glutaraldehyde (GA) to form GA-PEG-ESM composites. Our results indicate that ESMs composed of protein fibrous networks show elastic moduli ∼3.3-5.0 MPa and elongation percentages ∼47-56%, close to human heart valve leaflets. Finite element simulations reveal obvious stress concentration on a partial number of fibers in the GA-cross-linked ESM (GA-ESM) samples, which can be alleviated by efficient stress distribution among multiple layers of ESMs embedded in PEG hydrogels. Moreover, the polymeric networks of PEG hydrogels can prevent mineral deposition and enzyme degradation of protein fibers from incorporated ESMs. The fibrous structures of ESMs retain in the GA-PEG-ESM samples after subcutaneous implantation for 4 weeks, while those from ESM and GA-ESM samples show early degradation to certain extent, suggesting the prevention of enzymatic degradation of protein fibers by the polymeric network of PEG hydrogels in vivo. Thus, these GA-PEG-ESM layered constructs show heterogenic structures and mechanical properties comparable to heart valve leaflets, as well as improved functions to prevent progressive calcification and enzymatic degeneration, which are likely used for artificial heart valves.

Pulmonary arterial strain- and remodeling-induced stiffening are differentiated in a chronic model of pulmonary hypertension

Pulmonary hypertension (PH) is a debilitating vascular disease that leads to pulmonary artery (PA) stiffening, which is a predictor of patient mortality. During PH development, PA stiffening adversely affects right ventricular function. PA stiffening has been investigated through the arterial nonlinear elastic response during mechanical testing using a canine PH model. However, only circumferential properties were reported and in the absence of chronic PH-induced PA remodeling. Remodeling can alter arterial nonlinear elastic properties via chronic changes in extracellular matrix (ECM) content and geometry. Here, we used an established constitutive model to demonstrate and differentiate between strain-stiffening, which is due to nonlinear elasticity, and remodeling-induced stiffening, which is due to ECM and geometric changes, in a canine model of chronic thromboembolic PH (CTEPH). To do this, circumferential and axial tissue strips of large extralobar PAs from control and CTEPH tissues were tested in uniaxial tension, and data were fit to a phenomenological constitutive model. Strain-induced stiffening was evident from mechanical testing as nonlinear elasticity in both directions and computationally by a high correlation coefficient between the mechanical data and model (R²=0.89). Remodeling-induced stiffening was evident from a significant increase in the constitutive model stress parameter, which correlated with increased PA collagen content and decreased PA elastin content as measured histologically. The ability to differentiate between strain- and remodeling-induced stiffening in vivo may lead to tailored clinical treatments for PA stiffening in PH patients.

Biaxial Properties of the Left and Right Pulmonary Arteries in a Monocrotaline Rat Animal Model of Pulmonary Arterial Hypertension

In a monocrotaline (MCT) induced-pulmonary arterial hypertension (PAH) rat animal model, the dynamic stress–strain relation was investigated in the circumferential and axial directions using a linear elastic response model within the quasi-linear viscoelasticity theory framework. Right and left pulmonary arterial segments (RPA and LPA) were mechanically tested in a tubular biaxial device at the early stage (1 week post-MCT treatment) and at the advanced stage of the disease (4 weeks post-MCT treatment). The vessels were tested circumferentially at the in vivo axial length with matching in vivo measured pressure ranges. Subsequently, the vessels were tested axially at the mean pulmonary arterial pressure by stretching them from in vivo plus 5% of their length. Parameter estimation showed that the LPA and RPA remodel at different rates: axially, both vessels decreased in Young's modulus at the early stage of the disease, and increased at the advanced disease stage. Circumferentially, the Young's modulus increased in advanced PAH, but it was only significant in the RPA. The damping properties also changed in PAH; in the LPA relaxation times decreased continuously as the disease progressed, while in the RPA they initially increased and then decreased. Our modeling efforts were corroborated by the restructuring organization of the fibers imaged under multiphoton microscopy, where the collagen fibers become strongly aligned to the 45 deg angle in the RPA from an uncrimped and randomly organized state. Additionally, collagen content increased almost 10% in the RPA from the placebo to advanced PAH.

Development of Mechanical and Failure Properties in Sheep Cerebral Arteries

Traumatic brain injury (TBI) is a devastating problem for people of all ages, but the nature of the response to such injury is often different in children than in adults. Cerebral vessel damage and dysfunction are common following TBI, but age-dependent, large-deformation vessel response has not been characterized. Our objective was to investigate the mechanical properties of cerebral arteries as a function of development. Sheep middle cerebral arteries from four age groups (fetal, newborn, juvenile, and adult) were subjected to biaxial loading around physiological conditions and then to failure in the axial direction. Results show little difference among age groups under physiological loading conditions, but response varied significantly with age in response to large axial deformation. Vessels from all age groups reached the same ultimate stretch level, but the amount of stress carried at a given level of stretch increased significantly with age through the developmental period (fetal to juvenile). Our results are the first to identify changes in cerebral vessel response to large deformations with age and may lead to new insights regarding differences in response to TBI with age.