scholarly journals A Coupled Fiber-Matrix Model Demonstrates Highly Inhomogeneous Microstructural Interactions in Soft Tissues Under Tensile Load

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
Lijuan Zhang ◽  
Spencer P. Lake ◽  
Victor K. Lai ◽  
Catalin R. Picu ◽  
Victor H. Barocas ◽  
...  
Keyword(s):  
Stress Field ◽  
Matrix Model ◽  
Collagen Fiber ◽  
Soft Tissues ◽  
Computational Cost ◽  
Parallel Model ◽  
Fiber Network ◽  
Detailed Model ◽  
The Matrix ◽  
Fiber Matrix

A soft tissue's macroscopic behavior is largely determined by its microstructural components (often a collagen fiber network surrounded by a nonfibrillar matrix (NFM)). In the present study, a coupled fiber-matrix model was developed to fully quantify the internal stress field within such a tissue and to explore interactions between the collagen fiber network and nonfibrillar matrix (NFM). Voronoi tessellations (representing collagen networks) were embedded in a continuous three-dimensional NFM. Fibers were represented as one-dimensional nonlinear springs and the NFM, meshed via tetrahedra, was modeled as a compressible neo-Hookean solid. Multidimensional finite element modeling was employed in order to couple the two tissue components and uniaxial tension was applied to the composite representative volume element (RVE). In terms of the overall RVE response (average stress, fiber orientation, and Poisson's ratio), the coupled fiber-matrix model yielded results consistent with those obtained using a previously developed parallel model based upon superposition. The detailed stress field in the composite RVE demonstrated the high degree of inhomogeneity in NFM mechanics, which cannot be addressed by a parallel model. Distributions of maximum/minimum principal stresses in the NFM showed a transition from fiber-dominated to matrix-dominated behavior as the matrix shear modulus increased. The matrix-dominated behavior also included a shift in the fiber kinematics toward the affine limit. We conclude that if only gross averaged parameters are of interest, parallel-type models are suitable. If, however, one is concerned with phenomena, such as individual cell-fiber interactions or tissue failure that could be altered by local variations in the stress field, then the detailed model is necessary in spite of its higher computational cost.

Elucidation of Microstructural Interactions Between Collagen and Non-Fibrillar Matrix in Soft Tissue Using a Coupled Fiber-Matrix Model

2012 ◽  
Author(s):  
Lijuan Zhang ◽  
Spencer P. Lake ◽  
Victor K. Lai ◽  
Victor H. Barocas ◽  
Mark S. Shephard
Keyword(s):  
Soft Tissues ◽  
Mechanical Response ◽  
Tensile Load ◽  
Matrix Composites ◽  
Collagen Network ◽  
Fiber Network ◽  
Matrix Modeling ◽  
Microscale Model ◽  
Fiber Matrix

The mechanical properties of soft connective tissues are governed by their collagen fiber network and surrounding non-fibrillar matrix (e.g., proteoglycans, cells, elastin, etc.). In order to understand how healthy tissues function, and how properties change in injury and disease, it is necessary to quantify the mechanical response of both the collagen network and the non-fibrillar matrix (NFM), as well as the nature of the interaction between these tissue constituents. Using collagen-agarose co-gels as a simple experimental tissue analog system, we have demonstrated how NFM contributes to the mechanical and organizational properties of soft tissues in indentation and tension [1–2]. Furthermore, we used a network-based microscale model to examine how specific NFM properties alter the response of fiber-matrix composites under load [3]. This model fit our experimental data well and provided insight into the role of NFM in tensile mechanics. Since it was constructed according to the conventional approach of superposition of the two constituents (collagen network and NFM), however, the model could not specifically examine local interactions between collagen fibers and the surrounding NFM, which could be critical in assessing tissue damage or cell-matrix interactions. Therefore, we developed and evaluated a fiber-matrix modeling scheme to characterize the microstructural interactions between tissue constituents, as well as to quantify the role of individual tissue components in the behavior of soft tissues under tensile load. For validation, the new model (‘coupled’) was compared to our previous model (‘parallel’) and to experimental co-gel data.

Collagen-Agarose Co-Gels as a Model for Collagen-Matrix Interaction in Soft Tissue

2011 ◽  
Author(s):  
Spencer P. Lake ◽  
Sadie Doggett ◽  
Victor H. Barocas
Keyword(s):  
Collagen Fiber ◽  
Type I Collagen ◽  
Soft Tissues ◽  
Experimental System ◽  
Model System ◽  
Type I ◽  
Collagen Gels ◽  
Fiber Network ◽  
Fibrillar Material

Connective soft tissues have complex mechanical properties that are determined by their collagen fiber network and surrounding non-fibrillar material. The mechanical role of non-fibrillar material and the nature of its interaction with the collagen network remain poorly understood, in part because of the lack of a simple experimental model system to examine and quantify these properties. The development of a simple but representational experimental system will allow for greater insight into the interaction between fibers and the non-fibrillar matrix. Reconstituted Type I collagen gels are an attractive model tissue for exploring micro- and macroscale relationships between constituents (e.g., [1–2]), but standard collagen gels lack the non-fibrillar components (i.e., proteoglycan, minor collagens, etc.) present in native tissue. A recent study [3] added low quantities of agarose to collagen gels, which dramatically increased the shear storage modulus with minimal changes to the collagen fiber network. In this study, we suggest that collagen-agarose co-gels can serve as a model system to investigate the mechanical role of non-fibrillar ECM. Even though agarose is relatively compliant at low concentrations, and collagen fibers are very stiff in tension, we hypothesized that the presence of agarose in co-gels would have a pronounced effect on structural response and mechanical behavior in tensile loading. Therefore, the objective of this study was to examine the properties of collagen-agarose co-gels to understand better the nature of, and the relationships between, the collagen fiber network and non-fibrillar matrix of simplified tissue analogs.

scholarly journals Surface Instability of Sheared Soft Tissues

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
M. Destrade ◽  
M. D. Gilchrist ◽  
D. A. Prikazchikov ◽  
G. Saccomandi
Keyword(s):  
Experimental Data ◽  
Collagen Fiber ◽  
Soft Tissues ◽  
Surface Instability ◽  
Fiber Bundles ◽  
Parallel Fibers ◽  
Naked Eye ◽  
The Matrix ◽  
Use Values ◽  
Biological Soft Tissue

When a block made of an elastomer is subjected to a large shear, its surface remains flat. When a block of biological soft tissue is subjected to a large shear, it is likely that its surface in the plane of shear will buckle (appearance of wrinkles). One factor that distinguishes soft tissues from rubberlike solids is the presence—sometimes visible to the naked eye—of oriented collagen fiber bundles, which are stiffer than the elastin matrix into which they are embedded but are nonetheless flexible and extensible. Here we show that the simplest model of isotropic nonlinear elasticity, namely, the incompressible neo-Hookean model, suffers surface instability in shear only at tremendous amounts of shear, i.e., above 3.09, which corresponds to a 72deg angle of shear. Next we incorporate a family of parallel fibers in the model and show that the resulting solid can be either reinforced or strongly weakened with respect to surface instability, depending on the angle between the fibers and the direction of shear and depending on the ratio E∕μ between the stiffness of the fibers and that of the matrix. For this ratio we use values compatible with experimental data on soft tissues. Broadly speaking, we find that the surface becomes rapidly unstable when the shear takes place “against” the fibers and that as E∕μ increases, so does the sector of angles where early instability is expected to occur.

Developing the basis of the matrix model of the regional innovation subsystem

2020 ◽  
Vol 18 (11) ◽  
pp. 2183-2204
Author(s):  
E.I. Moskvitina
Keyword(s):  
Russian Federation ◽  
Matrix Model ◽  
Federal District ◽  
Assessment Method ◽  
Expert Assessment ◽  
Regional Innovation ◽  
Regional Strategies ◽  
Analysis And Synthesis ◽  
The Matrix ◽  
The Russian Federation

Subject. This article deals with the issues related to the formation and implementation of the innovation capacity of the Russian Federation subjects. Objectives. The article aims to develop the organizational and methodological foundations for the formation of a model of the regional innovation subsystem. Methods. For the study, I used the methods of analysis and synthesis, economics and statistics analysis, and the expert assessment method. Results. The article presents a developed basis of the regional innovation subsystem matrix model. It helps determine the relationship between the subjects and the parameters of the regional innovation subsystem. To evaluate the indicators characterizing the selected parameters, the Volga Federal District regions are considered as a case study. The article defines the process of reconciliation of interests between the subjects of regional innovation. Conclusions. The results obtained can be used by regional executive bodies when developing regional strategies for the socio-economic advancement of the Russian Federation subjects.

scholarly journals Exact 1/N expansion of Wilson loop correlators in $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Wolfgang Mück
Keyword(s):  
Matrix Model ◽  
Wilson Loop ◽  
Model Solution ◽  
Wilson Loops ◽  
Combinatorial Formula ◽  
Expectation Value ◽  
Yang Mills ◽  
Hooft Coupling ◽  
The Matrix ◽  
Super Yang Mills Theory

Abstract Supersymmetric circular Wilson loops in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills theory are discussed starting from their Gaussian matrix model representations. Previous results on the generating functions of Wilson loops are reviewed and extended to the more general case of two different loop contours, which is needed to discuss coincident loops with opposite orientations. A combinatorial formula representing the connected correlators of multiply wound Wilson loops in terms of the matrix model solution is derived. Two new results are obtained on the expectation value of the circular Wilson loop, the expansion of which into a series in 1/N and to all orders in the ’t Hooft coupling λ was derived by Drukker and Gross about twenty years ago. The connected correlators of two multiply wound Wilson loops with arbitrary winding numbers are calculated as a series in 1/N. The coefficient functions are derived not only as power series in λ, but also to all orders in λ by expressing them in terms of the coefficients of the Drukker and Gross series. This provides an efficient way to calculate the 1/N series, which can probably be generalized to higher-point correlators.

scholarly journals Divergent ⇒ complex amplitudes in two dimensional string theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Matrix Model ◽  
Two Dimensional ◽  
Full Matrix ◽  
Instanton Contribution ◽  
The Matrix ◽  
Theory Result ◽  
The One ◽  
Remarkable Agreement

Abstract In a recent paper, Balthazar, Rodriguez and Yin found remarkable agreement between the one instanton contribution to the scattering amplitudes of two dimensional string theory and those in the matrix model to the first subleading order. The comparison was carried out numerically by analytically continuing the external energies to imaginary values, since for real energies the string theory result diverges. We use insights from string field theory to give finite expressions for the string theory amplitudes for real energies. We also show analytically that the imaginary parts of the string theory amplitudes computed this way reproduce the full matrix model results for general scattering amplitudes involving multiple closed strings.

scholarly journals Why Is the Matrix Model Correct?

1997 ◽  
Vol 79 (19) ◽  
pp. 3577-3580 ◽  
Author(s):  
Nathan Seiberg
Keyword(s):  
Matrix Model ◽  
The Matrix

scholarly journals Enhanced osteoprogenitor elongated collagen fiber matrix formation by bioactive glass ionic silicon dependent on Sp7 (osterix) transcription

2016 ◽  
Vol 104 (10) ◽  
pp. 2604-2615 ◽  
Author(s):  
Venu G. Varanasi ◽  
Tetsurou Odatsu ◽  
Timothy Bishop ◽  
Joyce Chang ◽  
Jeremy Owyoung ◽  
...  
Keyword(s):  
Bioactive Glass ◽  
Collagen Fiber ◽  
Fiber Matrix

scholarly journals Recurrent Multi-Fiber Network for 3D MRI Brain Tumor Segmentation

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 320
Author(s):  
Yue Zhao ◽  
Xiaoqiang Ren ◽  
Kun Hou ◽  
Wentao Li
Keyword(s):  
Brain Tumor ◽  
Network Architecture ◽  
Contextual Information ◽  
Computational Cost ◽  
Disease Diagnosis ◽  
Tumor Segmentation ◽  
Brain Tumor Segmentation ◽  
Fiber Network ◽  
3D Network ◽  
The Brain

Automated brain tumor segmentation based on 3D magnetic resonance imaging (MRI) is critical to disease diagnosis. Moreover, robust and accurate achieving automatic extraction of brain tumor is a big challenge because of the inherent heterogeneity of the tumor structure. In this paper, we present an efficient semantic segmentation 3D recurrent multi-fiber network (RMFNet), which is based on encoder–decoder architecture to segment the brain tumor accurately. 3D RMFNet is applied in our paper to solve the problem of brain tumor segmentation, including a 3D recurrent unit and 3D multi-fiber unit. First of all, we propose that recurrent units segment brain tumors by connecting recurrent units and convolutional layers. This quality enhances the model’s ability to integrate contextual information and is of great significance to enhance the contextual information. Then, a 3D multi-fiber unit is added to the overall network to solve the high computational cost caused by the use of a 3D network architecture to capture local features. 3D RMFNet combines both advantages from a 3D recurrent unit and 3D multi-fiber unit. Extensive experiments on the Brain Tumor Segmentation (BraTS) 2018 challenge dataset show that our RMFNet remarkably outperforms state-of-the-art methods, and achieves average Dice scores of 89.62%, 83.65% and 78.72% for the whole tumor, tumor core and enhancing tumor, respectively. The experimental results prove our architecture to be an efficient tool for brain tumor segmentation accurately.

scholarly journals Effective Action and Measure in Matrix Model of IIB Superstrings

1997 ◽  
Vol 12 (31) ◽  
pp. 2331-2340 ◽  
Author(s):  
L. Chekhov ◽  
K. Zarembo
Keyword(s):  
Matrix Model ◽  
Effective Action ◽  
Continuum Limit ◽  
Auxiliary Field ◽  
Large N ◽  
The Matrix ◽  
Reparametrization Invariance ◽  
The Continuum ◽  
Induced Measure

We calculate an effective action and measure induced by the integration over the auxiliary field in the matrix model recently proposed to describe IIB superstrings. It is shown that the measure of integration over the auxiliary matrix is uniquely determined by locality and reparametrization invariance of the resulting effective action. The large-N limit of the induced measure for string coordinates is discussed in detail. It is found to be ultralocal and, thus, is possibly irrelevant in the continuum limit. The model of the GKM type is considered in relation to the effective action problem.

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