A composite micromechanical model for connective tissues: Part II--Application to rat tail tendon and joint capsule.

A micromechanical model of fibrous soft tissue has been developed which predicts upper and lower bounds on mechanical properties based on the structure and properties of tissue components by Ault and Hoffman [3, 4]. In this paper, two types of biological tissue are modeled and the results compared to experimental test data. The highly organized structure of rat tail tendon is modeled using the upper bound aggregation rule which predicts uniform strain behavior in the composite material. This model fits the experimental data and results in a correlation coefficient of 0.98. Applied to cat knee joint capsule, the lower bound aggregation rule of the model correlates with the data and predicts uniform stress within this more loosely organized tissue structure. These studies show that the nature of the interactions between the components in tissue differs depending upon its structure and that the biomechanical model is capable of analyzing such differences in structure.     

Generating elastic, biodegradable polyurethane/poly(lactide-co-glycolide) fibrous sheets with controlled antibiotic release via two-stream electrospinning

Damage control laparotomy is commonly applied to prevent compartment syndrome following trauma but is associated with new risks to the tissue, including infection. To address the need for biomaterials to improve abdominal laparotomy management, we fabricated an elastic, fibrous composite sheet with two distinct submicrometer fiber populations: biodegradable poly(ester urethane) urea (PEUU) and poly(lactide-co-glycolide) (PLGA), where the PLGA was loaded with the antibiotic tetracycline hydrochloride (PLGA-tet). A two-stream electrospinning setup was developed to create a uniform blend of PEUU and PLGA-tet fibers. Composite sheets were flexible with breaking strains exceeding 200%, tensile strengths of 5-7 MPa, and high suture retention capacity. The blending of PEUU fibers markedly reduced the shrinkage ratio observed for PLGA-tet sheets in buffer from 50% to 15%, while imparting elastomeric properties to the composites. Antibacterial activity was maintained for composite sheets following incubation in buffer for 7 days at 37 degrees C. In vivo studies demonstrated prevention of abscess formation in a contaminated rat abdominal wall model with the implanted material. These results demonstrate the benefits derivable from a two-stream electrospinning approach wherein mechanical and controlled-release properties are contributed by independent fiber populations and the applicability of this composite material to abdominal wall closure.     

A theoretical model for the elastic properties of very soft tissues.

A theoretical model is developed to predict the elastic properties of very soft tissues such as glands, tumors and brain. Tissues are represented as regular arrays of polyhedral (cubic or tetrakaidecahedral) cells, surrounded by extracellular spaces of uniform width. Cells are assumed to be incompressible, with very low resistance to shear deformation. Tissue shear rigidity is assumed to result mainly from the extracellular matrix, which is treated as a compressible elastic mesh of interconnected fibers. Small-strain elastic properties of tissue are predicted using a finite-element method and an analytical method. The model can be used to estimate the compressibility of a very soft tissue based on its Young's modulus and extracellular volume fraction.     

A microstructurally driven model for pulmonary artery tissue

A new constitutive model for elastic, proximal pulmonary artery tissue is presented here, called the total crimped fiber model. This model is based on the material and microstructural properties of the two main, passive, load-bearing components of the artery wall, elastin, and collagen. Elastin matrix proteins are modeled with an orthotropic neo-Hookean material. High stretch behavior is governed by an orthotropic crimped fiber material modeled as a planar sinusoidal linear elastic beam, which represents collagen fiber deformations. Collagen-dependent artery orthotropy is defined by a structure tensor representing the effective orientation distribution of collagen fiber bundles. Therefore, every parameter of the total crimped fiber model is correlated with either a physiologic structure or geometry or is a mechanically measured material property of the composite tissue. Further, by incorporating elastin orthotropy, this model better represents the mechanics of arterial tissue deformation. These advancements result in a microstructural total crimped fiber model of pulmonary artery tissue mechanics, which demonstrates good quality of fit and flexibility for modeling varied mechanical behaviors encountered in disease states.     

Structural three-dimensional constitutive law for the passive myocardium

A three-dimensional constitutive law is proposed for the myocardium. Its formulation is based on a structural approach in which the total strain energy of the tissue is the sum of the strain energies of its constituents: the muscle fibers, the collagen fibers and the fluid matrix which embeds them. The ensuing material law expresses the specific structural and mechanical properties of the tissue, namely, the spatial orientation of the comprising fibers, their waviness in the unstressed state and their stress-strain behavior when stretched. Having assumed specific functional forms for the distribution of the fibers spatial orientation and waviness, the results of biaxial mechanical tests serve for the estimation of the material constants appearing in the constitutive equations. A very good fit is obtained between the measured and the calculated stresses, indicating the suitability of the proposed model for describing the mechanical behavior of the passive myocardium. Moreover, the results provide general conclusions concerning the structural basis for the tissue overall mechanical properties, the main of which is that the collagen matrix, though comprising a relatively small fraction of the whole tissue volume, is the dominant component accounting for its stiffness.     

A constitutive model for vascular tissue that integrates fibril, fiber and continuum levels with application to the isotropic and passive properties of the infrarenal aorta

A fundamental understanding of the mechanical properties of the extracellular matrix (ECM) is critically important to quantify the amount of macroscopic stress and/or strain transmitted to the cellular level of vascular tissue. Structural constitutive models integrate histological and mechanical information, and hence, allocate stress and strain to the different microstructural components of the vascular wall. The present work proposes a novel multi-scale structural constitutive model of passive vascular tissue, where collagen fibers are assembled by proteoglycan (PG) cross-linked collagen fibrils and reinforce an otherwise isotropic matrix material. Multiplicative kinematics account for the straightening and stretching of collagen fibrils, and an orientation density function captures the spatial organization of collagen fibers in the tissue. Mechanical and structural assumptions at the collagen fibril level define a piece-wise analytical stress-stretch response of collagen fibers, which in turn is integrated over the unit sphere to constitute the tissue's macroscopic mechanical properties. The proposed model displays the salient macroscopic features of vascular tissue, and employs the material and structural parameters of clear physical meaning. Likewise, the constitutive concept renders a highly efficient multi-scale structural approach that allows for the numerical analysis at the organ level. Model parameters were estimated from isotropic mean-population data of the normal and aneurysmatic aortic wall and used to predict in-vivo stress states of patient-specific vascular geometries, thought to demonstrate the robustness of the particular Finite Element (FE) implementation. The collagen fibril level of the multi-scale constitutive formulation provided an interface to integrate vascular wall biology and to account for collagen turnover.     

On the design of composite protein-quantum dot biomaterials via self-assembly

Incorporation of nanoparticles during the hierarchical self-assembly of protein-based materials can impart function to the resulting composite materials. Herein we demonstrate that the structure and nanoparticle distribution of composite fibers are sensitive to the method of nanoparticle addition and the physicochemical properties of both the nanoparticle and the protein. Our model system consists of a recombinant enhanced green fluorescent protein-Ultrabithorax (EGFP-Ubx) fusion protein and luminescent CdSe-ZnS core-shell quantum dots (QDs), allowing us to optically assess the distribution of both the protein and nanoparticle components within the composite material. Although QDs favorably interact with EGFP-Ubx monomers, the relatively rough surface morphology of composite fibers suggests EGFP-Ubx-QD conjugates impact self-assembly. Indeed, QDs templated onto EGFP-Ubx film post-self-assembly can be subsequently drawn into smooth composite fibers. Additionally, the QD surface charge impacts QD distribution within the composite material, indicating that surface charge plays an important role in self-assembly. QDs with either positively or negatively charged coatings significantly enhance fiber extensibility. Conversely, QDs coated with hydrophobic moieties and suspended in toluene produce composite fibers with a heterogeneous distribution of QDs and severely altered fiber morphology, indicating that toluene severely disrupts Ubx self-assembly. Understanding factors that impact the protein-nanoparticle interaction enables manipulation of the structure and mechanical properties of composite materials. Since proteins interact with nanoparticle surface coatings, these results should be applicable to other types of nanoparticles with similar chemical groups on the surface.     

Biomimetic and bioactive nanofibrous scaffolds from electrospun composite nanofibers

Electrospinning is an enabling technology that can architecturally (in terms of geometry, morphology or topography) and biochemically fabricate engineered cellular scaffolds that mimic the native extracellular matrix (ECM). This is especially important and forms one of the essential paradigms in the area of tissue engineering. While biomimesis of the physical dimensions of native ECM's major constituents (eg, collagen) is no longer a fabrication-related challenge in tissue engineering research, conveying bioactivity to electrospun nanofibrous structures will determine the efficiency of utilizing electrospun nanofibers for regenerating biologically functional tissues. This can certainly be achieved through developing composite nanofibers. This article gives a brief overview on the current development and application status of employing electrospun composite nanofibers for constructing biomimetic and bioactive tissue scaffolds. Considering that composites consist of at least two material components and phases, this review details three different configurations of nanofibrous composite structures by using hybridizing basic binary material systems as example. These are components blended composite nanofiber, core-shell structured composite nanofiber, and nanofibrous mingled structure.     

Fibrin-fiber architecture influences cell spreading and differentiation

ABSTRACT

The mechanical and structural properties of the extracellular matrix (ECM) play an important role in regulating cell fate. The natural ECM has a complex fibrillar structure and shows nonlinear mechanical properties, which are both difficult to mimic synthetically. Therefore, systematically testing the influence of ECM properties on cellular behavior is very challenging. In this work we show two different approaches to tune the fibrillar structure and mechanical properties of fibrin hydrogels. Addition of extra thrombin before gelation increases the protein density within the fibrin fibers without significantly altering the mechanical properties of the resulting hydrogel. On the other hand, by forming a composite hydrogel with a synthetic biomimetic polyisocyanide network the protein density within the fibrin fibers decreases, and the mechanics of the composite material can be tuned by the PIC/fibrin mass ratio. The effect of the changes in gel structure and mechanics on cellular behavior are investigated, by studying human mesenchymal stem cell (hMSC) spreading and differentiation on these gels. We find that the trends observed in cell spreading and differentiation cannot be explained by the bulk mechanics of the gels, but correlate to the density of the fibrin fibers the gels are composed of. These findings strongly suggest that the microscopic properties of individual fibers in fibrous networks play an essential role in determining cell behavior.     

Inflation of an artery leading to aneurysm formation and rupture

Formation and rupture of aneurysms due to the inflation of an artery with collagen fibers distributed in two preferred directions, subjected to internal pressure and axial stretch are examined within the framework of nonlinear elasticity. A two layer tube model with a fiber-reinforced composite based incompressible anisotropic hyperelastic constitutive material is employed to model the stress-strain behavior of the artery wall with distributed collagen fibers. The artery wall takes up a uniform inflation deformation, and there are no aneurysms in the artery under the normal condition. But an aneurysm may be formed in arteries when the stiffness of the fibers is decreased to a certain value or the direction of the fibers is changed to a certain degree towards the circumferential direction. The aneurysm may expand to much large extent and become complex in shape. One portion of the aneurysm becomes highly distended as a bubble while the rest remains lightly inflated. The rupture of the aneurysm is discussed along with the distribution of stresses. Critical pressures and the rupture pressures are given for different collagen fiber orientations or stiffness. Furthermore, the stability of the solutions is discussed to explain the formation of aneurysm.     

Micromechanical Modeling Study of Mechanical Inhibition of Enzymatic Degradation of Collagen Tissues

This study investigates how the collagen fiber structure influences the enzymatic degradation of collagen tissues. We developed a micromechanical model of a fibrous collagen tissue undergoing enzymatic degradation based on two central hypotheses. The collagen fibers are crimped in the undeformed configuration. Enzymatic degradation is an energy activated process and the activation energy is increased by the axial strain energy density of the fiber. We determined the intrinsic degradation rate and characteristic energy for mechanical inhibition from fibril-level degradation experiments and applied the parameters to predict the effect of the crimped fiber structure and fiber properties on the degradation of bovine cornea and pericardium tissues under controlled tension. We then applied the model to examine the effect of the tissue stress state on the rate of tissue degradation and the anisotropic fiber structures that developed from enzymatic degradation.     

Composite Scaffolds of Interfacial Polyelectrolyte Fibers for Temporally Controlled Release of Biomolecules

Various scaffolds used in tissue engineering require a controlled biochemical environment to mimic the physiological cell niche. Interfacial polyelectrolyte complexation (IPC) fibers can be used for controlled delivery of various biological agents such as small molecule drugs, cells, proteins and growth factors. The simplicity of the methodology in making IPC fibers gives flexibility in its application for controlled biomolecule delivery. Here, we describe a method of incorporating IPC fibers into two different polymeric scaffolds, hydrophilic polysaccharide and hydrophobic polycaprolactone, to create a multi-component composite scaffold. We showed that IPC fibers can be easily embedded into these polymeric structures, enhancing the capability for sustained release and improved preservation of biomolecules. We also created a composite polymeric scaffold with topographical cues and sustained biochemical release that can have synergistic effects on cell behavior. Composite polymeric scaffolds with IPC fibers represent a novel and simple method of recreating the cellular niche.     

Collagen fiber alignment does not explain mechanical anisotropy in fibroblast populated collagen gels

Many load-bearing soft tissues exhibit mechanical anisotropy. In order to understand the behavior of natural tissues and to create tissue engineered replacements, quantitative relationships must be developed between the tissue structures and their mechanical behavior. We used a novel collagen gel system to test the hypothesis that collagen fiber alignment is the primary mechanism for the mechanical anisotropy we have reported in structurally anisotropic gels. Loading constraints applied during culture were used to control the structural organization of the collagen fibers of fibroblast populated collagen gels. Gels constrained uniaxially during culture developed fiber alignment and a high degree of mechanical anisotropy, while gels constrained biaxially remained isotropic with randomly distributed collagen fibers. We hypothesized that the mechanical anisotropy that developed in these gels was due primarily to collagen fiber orientation. We tested this hypothesis using two mathematical models that incorporated measured collagen fiber orientations: a structural continuum model that assumes affine fiber kinematics and a network model that allows for nonaffine fiber kinematics. Collagen fiber mechanical properties were determined by fitting biaxial mechanical test data from isotropic collagen gels. The fiber properties of each isotropic gel were then used to predict the biaxial mechanical behavior of paired anisotropic gels. Both models accurately described the isotropic collagen gel behavior. However, the structural continuum model dramatically underestimated the level of mechanical anisotropy in aligned collagen gels despite incorporation of measured fiber orientations; when estimated remodeling-induced changes in collagen fiber length were included, the continuum model slightly overestimated mechanical anisotropy. The network model provided the closest match to experimental data from aligned collagen gels, but still did not fully explain the observed mechanics. Two different modeling approaches showed that the level of collagen fiber alignment in our uniaxially constrained gels cannot explain the high degree of mechanical anisotropy observed in these gels. Our modeling results suggest that remodeling-induced redistribution of collagen fiber lengths, nonaffine fiber kinematics, or some combination of these effects must also be considered in order to explain the dramatic mechanical anisotropy observed in this collagen gel model system.     

About the equilibrium shape of fibred structures, and biological shapes

Biological morphogenesis has often been modeled with reaction-diffusion models [A.M. Turing, The chemical basis of morphogenesis, Phil. Trans. R. Soc. Lond. B 237 (1952) 37-72]. The interplay of bio-chemical fields is supposed to generate shapes by positional information carried by the values in the field. However, the structure of the biological tissue at the microscopic scale is absent from these models. We show that the fibred nature of biological tissue induces specific morphogenic properties. Fibred shapes can be calculated from physical principles borrowed from the theory of crystallogenesis. These give an intuitive insight into the shape of fruits or vegetables, buds and pins in botany, fingers, muscles, insects abdomen and heart in the animal realm, and also into other fibred structures such as the mitotic spindle. We predict the existence of bumps, apices or cusps at poles of fibred structures. An extrapolation to out-of-equilibrium growth predicts that these structures grow forward in the direction of the cusp, and that fibred organs should have a regular branching ordering. However, our model does not take into account the elasto-plastic properties, or the composite nature of the living material.     

Elastic anisotropy of articular cartilage is associated with the microstructures of collagen fibers and chondrocytes

Chondrocyte shape and volumetric concentration change as a function of depth in articular cartilage. A given chondrocyte shape produces different effects on the global material properties depending on the structure of the collagen fiber network. The shape and volumetric concentration of chondrocytes in articular cartilage appear to be related to the mechanical stability of the matrix. The present study was aimed to investigate, theoretically, the effects of the structural arrangement of the collagen fiber network, and the shape and distribution of chondrocytes, on the global material behavior of articular cartilage. Articular cartilage was assumed to be a four-phasic composite comprised of a matrix (associated with the properties of the proteoglycan structure), vertically and horizontally distributed collagen fibers, and spheroidal inclusions representing chondrocytes. A solution for composite materials was used to estimate the global, effective material properties of cartilage. Only the elasticity of the solid phase was investigated in the present study. Our simulations suggest that a soft, spheroidal cell inclusion in a fiber-reinforced proteoglycan matrix affects the material properties differently depending on the shape of the spheroidal inclusions. If the long axis of the inclusions is parallel to the collagen fibers, as in the deep zone, the soft inclusions increase the stiffness of the composite in the fiber direction, and reduce the stiffness of the composite in the direction normal to the fibers. Furthermore, we found that Young's modulus normal to the contact surface increases from the superficial to the deep zone in articular cartilage by a factor of 10-50, a finding that agrees well with experimental observations. Our analysis suggests that the combination of proteoglycan matrix, fiber orientation, and shape of chondrocytes are intimately related and are likely adapted to optimize the mechanical stability and load carrying capacity of the structure.     

The cell as a material

To elucidate the dynamic and functional role of a cell within the tissue it belongs to, it is essential to understand its material properties. The cell is a viscoelastic material with highly unusual properties. Measurements of the mechanical behavior of cells are beginning to probe the contribution of constituent components to cell mechanics. Reconstituted cytoskeletal protein networks have been shown to mimic many aspects of the mechanical properties of cells, providing new insight into the origin of cellular behavior. These networks are highly nonlinear, with an elastic modulus that depends sensitively on applied stress. Theories can account for some of the measured properties, but a complete model remains elusive.     

Contributions of Glycosaminoglycans to Collagen Fiber Recruitment in Constitutive Modeling of Arterial Mechanics

The contribution of glycosaminoglycans (GAGs) to the biological and mechanical functions of biological tissue has emerged as an important area of research. GAGs provide structural basis for the organization and assembly of extracellular matrix (ECM). The mechanics of tissue with low GAG content can be indirectly affected by the interaction of GAGs with collagen fibers, which have long been known to be one of the primary contributors to soft tissue mechanics. Our earlier study showed that enzymatic GAG depletion results in straighter collagen fibers that are recruited at lower levels of stretch, and a corresponding shift in earlier arterial stiffening (Mattson et al., 2016). In this study, the effect of GAGs on collagen fiber recruitment was studied through a structure-based constitutive model. The model incorporates structural information, such as fiber orientation distribution, content, and recruitment of medial elastin, medial collagen, and adventitial collagen fibers. The model was first used to study planar biaxial tensile stress-stretch behavior of porcine descending thoracic aorta. Changes in elastin and collagen fiber orientation distribution, and collagen fiber recruitment were then incorporated into the model in order to predict the stress-stretch behavior of GAG depleted tissue. Our study shows that incorporating early collagen fiber recruitment into the model predicts the stress-stretch response of GAG depleted tissue reasonably well (rms = 0.141); considering further changes of fiber orientation distribution does not improve the predicting capability (rms = 0.149). Our study suggests an important role of GAGs in arterial mechanics that should be considered in developing constitutive models.     

A methodology for developing anisotropic AAA phantoms via additive manufacturing

An Abdominal Aortic Aneurysm (AAA) is a permanent focal dilatation of the abdominal aorta at least 1.5 times its normal diameter. The criterion of maximum diameter is still used in clinical practice, although numerical studies have demonstrated the importance of biomechanical factors for rupture risk assessment. AAA phantoms could be used for experimental validation of the numerical studies and for pre-intervention testing of endovascular grafts. We have applied multi-material 3D printing technology to manufacture idealized AAA phantoms with anisotropic mechanical behavior. Different composites were fabricated and the phantom specimens were characterized by biaxial tensile tests while using a constitutive model to fit the experimental data. One composite was chosen to manufacture the phantom based on having the same mechanical properties as those reported in the literature for human AAA tissue; the strain energy and anisotropic index were compared to make this choice. The materials for the matrix and fibers of the selected composite are, respectively, the digital materials FLX9940 and FLX9960 developed by Stratasys. The fiber proportion for the composite is equal to 0.15. The differences between the composite behavior and the AAA tissue are small, with a small difference in the strain energy (0.4%) and a maximum difference of 12.4% in the peak Green strain ratio. This work represents a step forward in the application of 3D printing technology for the manufacturing of AAA phantoms with anisotropic mechanical behavior.     

A transversely isotropic, transversely homogeneous microstructural-statistical model of articular cartilage

Articular cartilage is a multi-phasic, composite, fibre-reinforced material. Therefore, its mechanical properties are determined by the tissue microstructure. The presence of cells (chondrocytes) and collagen fibres within the proteoglycan matrix influences, at a local and a global level, the material symmetries. The volumetric concentration and shape of chondrocytes, and the volumetric concentration and spatial arrangement of collagen fibres have been observed to change as a function of depth in articular cartilage. In particular, collagen fibres are perpendicular to the bone-cartilage interface in the deep zone, their orientation is almost random in the middle zone, and they are parallel to the surface in the superficial zone. The aim of this work is to develop a model of elastic properties of articular cartilage based on its microstructure. In previous work, we addressed this problem based on Piola's notation for fourth-order tensors. Here, mathematical tools initially developed for transversely isotropic composite materials comprised of a statistical orientation of spheroidal inclusions are extended to articular cartilage, while taking into account the dependence of the elastic properties on cartilage depth. The resulting model is transversely isotropic and transversely homogeneous (TITH), the transverse plane being parallel to the bone-cartilage interface and the articular surface. Our results demonstrate that the axial elastic modulus decreases from the deep zone to the articular surface, a result that is in good agreement with experimental findings. Finite element simulations were carried out, in order to explore the TITH model's behaviour in articular cartilage compression tests. The force response, fluid flow and displacement fields obtained with the TITH model were compared with the classical linear elastic, isotropic, homogeneous (IH) model, showing that the IH model is unable to predict the non-uniform behaviour of the tissue. Based on considerations that the mechanical stability of the tissue depends on its topological and microstructural properties, our long-term goal is to clearly understand the stability conditions in topological terms, and the relationship with the growth and remodelling mechanisms in the healthy and diseased tissue.