Numerical simulation of fibrous biomaterials with randomly distributed fiber network structure

A computational framework for biomaterials containing three-dimensional random fiber networks based on the affine kinematics

Understanding the structure-function relationship of biomaterials can provide insights into different diseases and advance numerous biomedical applications. This paper presents a finite element-based computational framework to model biomaterials containing a three-dimensional fiber network at the microscopic scale. The fiber network is synthetically generated by a random walk algorithm, which uses several random variables to control the fiber network topology such as fiber orientations and tortuosity. The geometric information of the generated fiber network is stored in an array-like data structure and incorporated into the nonlinear finite element formulation. The proposed computational framework adopts the affine fiber kinematics, based on which the fiber deformation can be expressed by the nodal displacement and the finite element interpolation functions using the isoparametric relationship. A variational approach is developed to linearize the total strain energy function and derive the nodal force residual and the stiffness matrix required by the finite element procedure. Four numerical examples are provided to demonstrate the capabilities of the proposed computational framework, including a numerical investigation about the relationship between the proposed method and a class of anisotropic material models, a set of synthetic examples to explore the influence of fiber locations on material local and global responses, a thorough mesh-sensitivity analysis about the impact of mesh size on various numerical results, and a detailed case study about the influence of material structures on the performance of eggshell-membrane-hydrogel composites. The proposed computational framework provides an efficient approach to investigate the structure-function relationship for biomaterials that follow the affine fiber kinematics.

Mechanical properties of subisostatic random networks composed of nonlinear fibers

Fibrous protein networks provide structural integrity to different biological materials such as soft tissues. These networks display an unusual exponential strain-stiffening behavior when subjected to mechanical loads. This nonlinear strain-stiffening behavior has so far been explained in terms of the network microstructure and the flexibility of constituting fibers. Here, we conduct a comprehensive computational study to characterize the importance of material properties of individual fibers in the overall nonlinear mechanical response of random fiber networks. To this end, we consider three nonlinear material models, ranging from an almost linear form to a highly nonlinear one, for the fibers of subisostatic disordered networks. We characterize the amount of strain-stiffening as a function of bending rigidity of the fibers, the amount of nonlinearity of the fibers, and the connectivity of random networks. We find that networks composed of highly nonlinear fibers exhibit much more strain-stiffening than networks made up of linear fibers. Furthermore, the local strain distribution becomes more homogenous as the amount of nonlinearity in the material models increases. Increasing the network connectivity signifies the importance of the nonlinear material response of individual fibers in the overall mechanical behavior of networks. The constitutive behavior of fibers plays an important role in defining the failure response of networks particularly in the damage initiation and evolution. These important findings for how the mechanical response of individual fibers affects the overall mechanical properties of random networks could find applications in designing new biomimetic materials and could help scientists better understand the mechanical properties of biological materials.

Role of Ninth Type-III Domain of Fibronectin in the Mediation of Cell-Binding Domain Adsorption on Surfaces with Different Chemistries

The orientation and conformation of adhesive proteins after adsorption play a central role in cell-binding bioactivity. Fibronectin (Fn) holds two peptide sequences that favor cell adhesion: the Arg-Gly-Asp (RGD) loop on the tenth type-III domain (Fn-III₁₀) and the Pro-His-Ser-Arg-Asn (PHSRN) synergy site on the ninth type-III domain (Fn-III₉). Herein, adsorption of Fn fragments (Fn-III₁₀ and Fn-III_9-10) on self-assembled monolayers (SAMs) carrying various functional groups (-COOH, -NH₂, -CH₃, and -OH) was investigated by the Monte Carlo method and molecular dynamics simulation in order to understand its mediation effect on cell adhesion. The results demonstrated that Fn-III₉ could enhance the stiffness of the Fn molecule and further fix the adsorption orientation. The RGD site of the Fn fragment appeared to be deactivated on hydrophobic surfaces (CH₃-SAM) because of the binding of adjacent nonpolar residues on surfaces, whereas charged surfaces (COOH-SAM and NH₂-SAM) and hydrophilic surfaces (OH-SAM) were conducive to the formation of cell-binding-favorable orientation for Fn fragments. The cell adhesion capability of Fn fragments was highly improved on positively charged surfaces (NH₂-SAM) and hydrophilic surfaces because of the advantageous steric structure and orientation of both RGD and PHSRN sites. This work provides an insight into the interplay at the atomic scale between protein adsorption and surface chemistry for designing biologically responsive substrate surfaces.

Nanofibered Gelatin-Based Nonwoven Elasticity Promotes Epithelial Histogenesis

Regarding tissue regeneration, mechanics of biomaterials gains progressive importance. Therefore, this study reports on in situ crosslinked electrospun gelatin nonwoven mats (NWMs) whose distinct modulus of elasticity (ME) promotes epithelial tissue formation in a graded manner. NWMs, comprising fiber diameters in various distributions, yield an ME of about 2.1, 3.2, and 10.9 kPa. A two-step approach of preclinical in vitro validation identifies the elasticity of 3.2 kPa as superior to the other, regarding the histogenetic epithelial outcome. Hence, this 3.2 kPa candidate NWM is colonized with oral mucosal epithelial keratinocytes in the absence or presence of mesenchymal fibroblasts and/or endothelial cells. Evaluation of epithelial histogenesis at days 1 to 10 occurs by colorimetric and fluorescence-based immunohistochemistry (IHCH) of specific biomarkers. These include cytokeratins (CK) 14, CK1, and involucrin that indicate different stages of epithelial differentiation, as well as the basement membrane constituent collagen type IV and Ki-67 as a proliferation marker. Intriguingly, histogenesis and IHCH reveal the best resemblance of the native epithelium by the NWM alone, irrespective of other cell counterparts. These findings prove the gelatin NWM a convenient cell matrix, and evidence that NWM mechanics is important to promote epithelial histogenesis in view of prospective clinical applications.

A deep learning approach to estimate chemically-treated collagenous tissue nonlinear anisotropic stress-strain responses from microscopy images

Biological collagenous tissues comprised of networks of collagen fibers are suitable for a broad spectrum of medical applications owing to their attractive mechanical properties. In this study, we developed a noninvasive approach to estimate collagenous tissue elastic properties directly from microscopy images using Machine Learning (ML) techniques. Glutaraldehyde-treated bovine pericardium (GLBP) tissue, widely used in the fabrication of bioprosthetic heart valves and vascular patches, was chosen to develop a representative application. A Deep Learning model was designed and trained to process second harmonic generation (SHG) images of collagen networks in GLBP tissue samples, and directly predict the tissue elastic mechanical properties. The trained model is capable of identifying the overall tissue stiffness with a classification accuracy of 84%, and predicting the nonlinear anisotropic stress-strain curves with average regression errors of 0.021 and 0.031. Thus, this study demonstrates the feasibility and great potential of using the Deep Learning approach for fast and noninvasive assessment of collagenous tissue elastic properties from microstructural images.

STATEMENT OF SIGNIFICANCE

In this study, we developed, to our best knowledge, the first Deep Learning-based approach to estimate the elastic properties of collagenous tissues directly from noninvasive second harmonic generation images. The success of this study holds promise for the use of Machine Learning techniques to noninvasively and efficiently estimate the mechanical properties of many structure-based biological materials, and it also enables many potential applications such as serving as a quality control tool to select tissue for the manufacturing of medical devices (e.g. bioprosthetic heart valves).

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.