Mohammad F. Hadi

Mechanics of a fiber network within a non-fibrillar matrix: Model and comparison with collagen-agarose co-gels

While collagen is recognized as the predominant mechanical component of soft connective tissues, the role of the non-fibrillar matrix (NFM) is less well understood. Even model systems, such as the collagen-agarose co-gel, can exhibit complex behavior, making it difficult to identify relative contributions of specific tissue constituents. In the present study, we developed a two-component microscale model of collagen-agarose tissue analogs and used it to elucidate the interaction between collagen and NFM in uniaxial tension. Collagen fibers were represented with Voronoi networks, and the NFM was modeled as a neo-Hookean solid. Model predictions of total normal stress and Poisson’s ratio matched experimental observations well (including high Poisson’s values of ~3), and the addition of NFM led to composition-dependent decreases in volume change and increases in fiber stretch. Because the NFM was more resistant to volume change than the fiber network, extension of the composite led to pressurization of the NFM. Within a specific range of parameter values (low shear modulus and moderate Poisson’s ratio), the magnitude of the reaction force decreased relative to this pressurization component resulting in a negative (compressive) NFM stress in the loading direction, even though the composite tissue was in tension.

Microscale fiber network alignment affects macroscale failure behavior in simulated collagen tissue analogs

A tissues microstructure determines its failure properties at larger length scales, however, the specific relationship between microstructure and macroscopic failure in native and engineered soft tissues (such as capsular ligaments, aortic aneurysms, or vascular grafts) has proven elusive. In this study, variations in the microscale fiber alignment in collagen gel tissue analogs were modeled in order to understand their effects on macroscale damage and failure outcomes. The study employed a multiscale finite-element (FE) model for damage and failure in collagen-based materials. The model relied on microstructural representative volume elements (RVEs) that consisted of stochastically-generated networks of discrete type-I collagen fibers. Fiber alignment was varied within RVEs and between layers of RVEs in a macroscopic FE model of a notched dogbone geometry. The macroscale stretch and the microscale response of fibers for each of the differently aligned cases were compared as the dogbone was uniaxially extended to failure. Networks with greater fiber alignment parallel to the direction of extension failed at smaller strains (with a 6-22% reduction in the Green strain at failure), however, at greater grip forces (a 28-60% increase) than networks with fibers aligned perpendicular to the extension. Alternating layers of crisscrossed network alignments (aligned ±45 deg to the direction of extension) failed at smaller strains but at greater grip forces than those created using one fiber alignment type. In summary, variations in microscale structure via fiber alignment produced different macroscale failure trends. To conclude, these findings may be significant in the realm of tissue engineering and in soft tissue biomechanics.

Multiscale model predicts tissue-level failure from collagen fiber-level damage.

Excessive tissue-level forces communicated to the microstructure and extracellular matrix of soft tissues can lead to damage and failure through poorly understood physical processes that are multiscale in nature. In this work, we propose a multiscale mechanical model for the failure of collagenous soft tissues that incorporates spatial heterogeneity in the microstructure and links the failure of discrete collagen fibers to the material response of the tissue. The model, which is based on experimental failure data derived from different collagen gel geometries, was able to predict the mechanical response and failure of type I collagen gels, and it demonstrated that a fiber-based rule (at the micrometer scale) for discrete failure can strongly shape the macroscale failure response of the gel (at the millimeter scale). The model may be a useful tool in predicting the macroscale failure conditions for soft tissues and engineered tissue analogs. In addition, the multiscale model provides a framework for the study of failure in complex fiber-based mechanical systems in general.

A Multiscale Approach to Modeling the Passive Mechanical Contribution of Cells in Tissues

In addition to their obvious biological roles in tissue function, cells often play a significant mechanical role through a combination of passive and active behaviors. This study focused on the passive mechanical contribution of cells in tissues by improving our multiscale model via the addition of cells, which were treated as dilute spherical inclusions. The first set of simulations considered a rigid cell, with the surrounding ECM modeled as (1) linear elastic, (2) Neo-Hookean, and (3) a fiber network. Comparison with the classical composite theory for rigid inclusions showed close agreement at low cell volume fraction. The fiber network case exhibited nonlinear stress-strain behavior and Poissons ratios larger than the elastic limit of 0.5, characteristics similar to those of biological tissues. The second set of simulations used a fiber network for both the cell (simulating cytoskeletal filaments) and matrix, and investigated the effect of varying relative stiffness between the cell and matrix, as well as the effect of a cytoplasmic pressure to enforce incompressibility of the cell. Results showed that the ECM network exerted negligible compression on the cell, even when the stiffness of fibers in the network was increased relative to the cell. Introduction of a cytoplasmic pressure significantly increased the stresses in the cell filament network, and altered how the cell changed its shape under tension. Findings from this study have implications on understanding how cells interact with their surrounding ECM, as well as in the context of mechanosensation.

Prefailure and Failure Mechanics of the Porcine Ascending Thoracic Aorta: Experiments and a Multiscale Model

Ascending thoracic aortic aneurysms (ATAA) have a high propensity for dissection, which occurs when the hemodynamic load exceeds the mechanical strength of the aortic media. Despite our recognition of this essential fact, the complex architecture of the media has made a predictive model of medial failure-even in the relatively simple case of the healthy vessel-difficult to achieve. As a first step towards a general model of ATAA failure, we characterized the mechanical behavior of healthy ascending thoracic aorta (ATA) media using uniaxial stretch-to-failure in both circumferential (n = 11) and axial (n = 11) orientations and equibiaxial extensions (n = 9). Both experiments demonstrated anisotropy, with higher tensile strength in the circumferential direction (2510 ± 439.3 kPa) compared to the axial direction (750 ± 102.6 kPa) for the uniaxial tests, and a ratio of 1.44 between the peak circumferential and axial loads in equibiaxial extension. Uniaxial tests for both orientations showed macroscopic tissue failure at a stretch of 1.9. A multiscale computational model, consisting of a realistically aligned interconnected fiber network in parallel with a neo-Hookean solid, was used to describe the data; failure was modeled at the fiber level, with an individual fiber failing when stretched beyond a critical threshold. The best-fit model results were within the 95% confidence intervals for uniaxial and biaxial experiments, including both prefailure and failure, and were consistent with properties of the components of the ATA media.

Combining Displacement Field and Grip Force Information to Determine Mechanical Properties of Planar Tissue With Complicated Geometry

Performing planar biaxial testing and using nominal stress-strain curves for soft-tissue characterization is most suitable when (1) the test produces homogeneous strain fields, (2) fibers are aligned with the coordinate axes, and (3) strains are measured far from boundaries. Some tissue types [such as lamellae of the annulus fibrosus (AF)] may not allow for these conditions to be met due to their natural geometry and constitution. The objective of this work was to develop and test a method utilizing a surface displacement field, grip force-stretch data, and finite-element (FE) modeling to facilitate analysis of such complex samples. We evaluated the method by regressing a simple structural model to simulated and experimental data. Three different tissues with different characteristics were used: Superficial pectoralis major (SPM) (anisotropic, aligned with axes), facet capsular ligament (FCL) (anisotropic, aligned with axes, bone attached), and a lamella from the AF (anisotropic, aligned off-axis, bone attached). We found that the surface displacement field or the grip force-stretch data information alone is insufficient to determine a unique parameter set. Utilizing both data types provided tight confidence regions (CRs) of the regressed parameters and low parameter sensitivity to initial guess. This combined fitting approach provided robust characterization of tissues with varying fiber orientations and boundaries and is applicable to tissues that are poorly suited to standard biaxial testing. The structural model, a set of C++ finite-element routines, and a Matlab routine to do the fitting based on a set of force/displacement data is provided in the on-line supplementary material.

Crack Propagation Versus Fiber Alignment in Collagen Gels: Experiments and Multiscale Simulation

It is well known that the organization of the fibers constituting a collagenous tissue can affect its failure behavior. Less clear is how that effect can be described computationally so as to predict the failure of a native or engineered tissue under the complex loading conditions that can occur in vivo. Toward the goal of a general predictive strategy, we applied our multiscale model of collagen gel mechanics to the failure of a double-notched gel under tension, comparing the results for aligned and isotropic samples. In both computational and laboratory experiments, we found that the aligned gels were more likely to fail by connecting the two notches than the isotropic gels. For example, when the initial notches were 30% of the sample width (normalized tip-to-edge distance = 0.7), the normalized tip-to-tip distance at which the transition occurred from between-notch failure to across-sample failure shifted from 0.6 to 1.0. When the model predictions for the type of failure event (between the two notches versus across the sample width) were compared to the experimental results, the two were found to be strongly covariant by Fishers exact test (p < 0.05) for both the aligned and isotropic gels with no fitting parameters. Although the double-notch system is idealized, and the collagen gel system is simpler than a true tissue, it presents a simple model system for studying failure of anisotropic tissues in a controlled setting. The success of the computational model suggests that the multiscale approach, in which the structural complexity is incorporated via changes in the model networks rather than via changes to a constitutive equation, has the potential to predict tissue failure under a wide range of conditions.

Role of lateral interactions in type IV collagen network mechanics

The basement membrane is a specialized part of the extra-cellular matrix. It is usually characterized as a scaffold for epithelial cells but in some tissues it serves other, mechanical, roles [1]. The mechanical properties of the basement membrane are mainly determined by one of its main constituents — type IV collagen. Unlike the well-known fibrous type I collagen, collagen IV assembles into planar networks (Fig. 1) [2]. The α1(IV) and α2(IV) collagen IV chains assemble into the so-called major chain network, present in all basement membranes. The α3(IV), α4(IV), α5(IV) collagen IV chains form the minor chain network which is found only in the adult basement membranes of the kidney glomerular capillaries (GBM), ocular lens (LBM), cochlea, and the testes [3]. The minor chains have a higher number of cysteine residues, allowing them to form a higher number of lateral interactions. In the minor chain network, the greater potential to interact laterally manifests in the formation of super-coils, which are rarely observed in the major chain network [4]. Increasing the number of cross-links in a polymeric material is known to increase material stiffness; therefore, it is believed that the minor chain network confers basement membranes with additional strength and stability [5]. In the hereditary disease Alport syndrome, a mutation causes the absence of the minor chain network. The GBM and LBM of Alport patients appear weakened and unable to meet their mechanical demands, further supporting this theory [6]. The objective of this study was to evaluate the importance of cross-linking in the minor chains for the mechanical properties of type IV collagen networks, specifically in the GBM and LBM where the absence of the minor chains has an observed mechanical effect.Copyright

Generating random fiber network topologies that mimic previously characterized networks

Fibrous proteins, such as collagen and elastin, form the underlying structure of many soft tissues. These proteins form micrometer-scale networks of varying topology that play a role in governing the mechanics of tissues at larger length scales [1]. The relationship between a network’s topology and its mechanics, however, are poorly understood. This disconnect presents an important challenge in constructing realistic multiscale models of tissues informed by collagen network micrographs and subsequently reconstructed networks [2]. Accurate multiscale simulations may require thousands to millions of such unique networks. It is imperative that a method be developed to generate random networks that are functionally similar to ones derived experimentally. In the current study, we present a probabilistic method for generating de novo networks that mimic the mechanical properties of previously characterized networks. We chose Delaunay and Voronoi networks as model targets because they have been used successfully to model the mechanics of collagenous tissues [3] and since their topologies are well characterized. Understanding the role of topology in network mechanics is fundamental to building improved models of the mechanics of fibrous soft tissues — models that can aid in the rational design of engineered tissues or that can help assess the mechanical impact of damage or disease on native tissues.Copyright

Dissection of porcine ascending aortic media: Mechanical characterization and multiscale model

Ascending thoracic aortic aneurysm (aTAA) is a pathological condition with a high risk of dissection and rupture. Clinically, management of aTAA balances the risk of rupture with that of surgery-related complications. The risk of aneurysm rupture is known to correlate with aneurysm diameter.1,2 Aneurysms greater than 6 cm in diameter have a significantly higher risk of rupture.1 Current guidelines for intervention suggest surgical intervention for aTAA diameters greater than 5.5cm for patients without connective tissue disorders.1Copyright