A STUDY ON THE EFFECT OF COLLAGEN FIBER ORIENTATION ON MECHANICAL RESPONSE OF SOFT BIOLOGICAL TISSUES

2015 ◽  
Vol 76 (7) ◽  
Author(s):  
Farshid Fathi ◽  
Shahrokh Shahi ◽  
Soheil Mohammadi
Keyword(s):  
Finite Element ◽  
Soft Tissues ◽  
Mechanical Response ◽  
Strain Energy Function ◽  
Soft Materials ◽  
Biological Tissues ◽  
Soft Biological Tissues ◽  
Proposed Model ◽  
The Matrix ◽  
Element Approach

Extensive research has been performed in the past decades to study the behavior of soft biological tissues in order to reduce the need for practical experiments. The applicability of these researches, particularly for skin, ligament, muscles and the heart, brings up its importance in various biological science and technology disciplines such as surgery and medicine. Softness and large deformation govern the behavior of soft materials and prohibit the use of small strains solutions in finite element method.In this work, the focus is set on a strain energy function which has the advantage of accurately representing the behavior of a variety of soft tissues with only a few parameters in a finite element approach. The numerical results are verified with a set of tensile experiments to demonstrate the performance of the proposed model. The parameters include the matrix and collagen bundles and their orientation. Different cases are analyzed and discussed for better prediction of different soft tissue responses.  

Finite Elastic Deformation for a Class of Soft Biological Tissues

1977 ◽  
Vol 99 (2) ◽  
pp. 98-103
Author(s):  
Han-Chin Wu ◽  
R. Reiss
Keyword(s):  
Energy Function ◽  
Annulus Fibrosus ◽  
Strain Energy ◽  
Soft Tissues ◽  
Broad Class ◽  
Strain Energy Function ◽  
Biological Tissues ◽  
Tension Test ◽  
Soft Biological Tissues ◽  
Precise Form

The stress response of soft biological tissues is investigated theoretically. The treatment follows the approach of Wu and Yao [1] and is now extended for a broad class of soft tissues. The theory accounts for the anisotropy due to the presence of fibers and also allows for the stretching of fibers under load. As an application of the theory, a precise form for the strain energy function is proposed. This form is then shown to describe the mechanical behavior of annulus fibrosus satisfactorily. The constants in the strain energy function have also been approximately determined from only a uniaxial tension test.

Finite Element Implementation of a Planar Soft Tissue Structural Constitutive Model for Heart Valve Simulations

2013 ◽  
Author(s):  
Rong Fan ◽  
Michael S. Sacks
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Soft Tissues ◽  
Structural Model ◽  
Mechanical Response ◽  
Biological Tissues ◽  
Biaxial Test ◽  
Tissue Microstructure ◽  
Highly Nonlinear ◽  
Insight Into

Constitutive modeling is critical for numerical simulation and analysis of soft biological tissues. The highly nonlinear and anisotropic mechanical behaviors of soft tissues are typically due to the interaction of tissue microstructure. By incorporating information of fiber orientation and distribution at tissue microscopic scale, the structural model avoids ambiguities in material characterization. Moreover, structural models produce much more information than just simple stress-strain results, but can provide much insight into how soft tissues internally reorganize to external loads by adjusting their internal microstructure. It is only through simulation of an entire organ system can such information be derived and provide insight into physiological function. However, accurate implementation and rigorous validation of these models remains very limited. In the present study we implemented a structural constitutive model into a commercial finite element package for planar soft tissues. The structural model was applied to simulate strip biaxial test for native bovine pericardium, and a single pulmonary valve leaflet deformation. In addition to prediction of the mechanical response, we demonstrate how a structural model can provide deeper insights into fiber deformation fiber reorientation and fiber recruitment.

A Micromechanical Model for Fibrous Biological Membranes at Finite Strain

2009 ◽  
Vol 3 ◽  
pp. 1-23 ◽  
Author(s):  
Mauro Borri-Brunetto ◽  
Bernardino Chiaia ◽  
Marco Deambrosi
Keyword(s):  
Mechanical Response ◽  
Micromechanical Model ◽  
Strain Energy Function ◽  
Biological Tissues ◽  
Two Dimensions ◽  
Arterial Walls ◽  
Proposed Model ◽  
Circular Holes ◽  
Definition Of ◽  
Validation Tests

The mechanical model of a number of biological tissues is a membrane, i.e., a sheetlike structure with small thickness, where deformation and stress can be described locally in two dimensions. Many bio-membranes, particularly if subjected to large mechanical loads, present a fibrous structure, with stiff fibers, sometimes with preferential orientations, embedded in a more compliant matrix. Among this tissues are, e.g., the arterial walls, the amniotic membrane, and the skin. The stiff fibers, typically made of collagen, are initially wrinkled and they follow the deformation of the embedding matrix without contributing to the mechanical response until they are fully distended. In this paper, the response of a fibrous membrane is described in the framework of hyperelasticity, with aim to the implementation in an existing finite element code. A micro-mechanical recruitment model, based on the statistical distribution of the activation stretch of the collagen fibers is introduced, leading to the definition of a simple form of the strain-energy function, depending on physically well-defined parameters. After some validation tests performed in homogeneous strain conditions, an application to the study of the stress field around circular holes in large deformation is presented, showing the capabilities of the proposed model.

Constitutive Formulation for Numerical Analysis of Visco-Hyperelastic Damage Phenomena in Soft Biological Tissues

2006 ◽  
Author(s):  
Arturo N. Natali ◽  
Emanuele L. Carniel ◽  
Piero G. Pavan ◽  
Alessio Gasparetto ◽  
Franz G. Sander ◽  
...  
Keyword(s):  
Strain Rate ◽  
Soft Tissues ◽  
Mechanical Response ◽  
Constitutive Models ◽  
Experimental Tests ◽  
Biological Tissues ◽  
Tissue Response ◽  
Time Dependent ◽  
Soft Biological Tissues ◽  
Constitutive Formulation

Soft biological tissues show a strongly non linear and time-dependent mechanical response and undergo large strains under physiological loads. The microstructural arrangement determines specific anisotropic macroscopic properties that must be considered within a constitutive formulation. The characterization of the mechanical behaviour of soft tissues entails the definition of constitutive models capable of accounting for geometric and material non linearity. In the model presented here a hyperelastic anisotropic formulation is adopted as the basis for the development of constitutive models for soft tissues and can be properly arranged for the investigation of viscous and damage phenomena as well to interpret significant aspects pertaining to ordinary and degenerative conditions. Visco-hyperelastic models are used to analyze the time-dependent mechanical response, while elasto-damage models account for the stiffness and strength decrease that can develop under significant loading or degenerative conditions. Experimental testing points out that damage response is affected by the strain rate associated with loading, showing a decrease in the damage limits as the strain rate increases. This phenomena can be investigated by means of a model capable of accounting for damage phenomena in relation to viscous effects. The visco-hyperelastic damage model developed is defined on the basis of a Helmholtz free energy function depending on the strain-damage history. In particular, a specific damage criterion is formulated in order to evaluate the influence of the strain rate on damage. The model can be implemented in a general purpose finite element code. This makes it possible to perform numerical analyses of the mechanical response considering time-dependent effects and damage phenomena. The experimental tests develop investigated tissue response for different strain rate conditions, accounting for stretch situations capable of inducing damage phenomena. The reliability of the formulation is evaluated by a comparison with the results of experimental tests performed on pig periodontal ligament.

Automated Estimation of Elastic Material Parameters of a Transversely Isotropic Material Using Asymmetric Indentation and Inverse Finite Element Analysis

2015 ◽  
Author(s):  
Yuan Feng ◽  
Chung-Hao Lee ◽  
Lining Sun ◽  
Ruth J. Okamoto ◽  
Songbai Ji
Keyword(s):  
Finite Element ◽  
Soft Tissues ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Biological Tissues ◽  
Fiber Reinforced ◽  
Element Analysis ◽  
Soft Biological Tissues ◽  
Tissue Properties ◽  
Brain White Matter

Anisotropy exists in many soft biological tissues. The most common anisotropy is transverse isotropy, which is typical for fiber-reinforced structures, such as the brain white matter, tendon and muscle. Although many methods have been proposed to determine tissue properties, techniques to characterize transversely isotropic materials remain limited. The goal of this study is to investigate the feasibility of asymmetric indentation coupled with numerical optimization based on inverse finite element (FE) simulation to characterize transversely isotropic soft biological tissues. The proposed approach combining indentation and optimization may provide a useful general framework to characterize a variety of fiber-reinforced soft tissues in the future.

FINITE ELEMENT APPROACH TO IMMERSED BOUNDARY METHOD WITH DIFFERENT FLUID AND SOLID DENSITIES

2011 ◽  
Vol 21 (12) ◽  
pp. 2523-2550 ◽  
Author(s):  
DANIELE BOFFI ◽  
NICOLA CAVALLINI ◽  
LUCIA GASTALDI
Keyword(s):  
Finite Element ◽  
Immersed Boundary Method ◽  
Stokes Equations ◽  
Numerical Procedure ◽  
Biological Tissues ◽  
Immersed Boundary ◽  
Fluid Structure ◽  
Finite Element Approach ◽  
Boundary Method ◽  
Element Approach

The Immersed Boundary Method (IBM) has been designed by Peskin for the modeling and the numerical approximation of fluid-structure interaction problems, where flexible structures are immersed in a fluid. In this approach, the Navier–Stokes equations are considered everywhere and the presence of the structure is taken into account by means of a source term which depends on the unknown position of the structure. These equations are coupled with the condition that the structure moves at the same velocity of the underlying fluid. Recently, a finite element version of the IBM has been developed, which offers interesting features for both the analysis of the problem under consideration and the robustness and flexibility of the numerical scheme. Initially, we considered structure and fluid with the same density, as it often happens when dealing with biological tissues. Here we study the case of a structure which can have a density higher than that of the fluid. The higher density of the structure is taken into account as an excess of Lagrangian mass located along the structure, and can be dealt with in a variational way in the finite element approach. The numerical procedure to compute the solution is based on a semi-implicit scheme. In fluid-structure simulations, nonimplicit schemes often produce instabilities when the density of the structure is close to that of the fluid. This is not the case for the IBM approach. In fact, we show that the scheme enjoys the same stability properties as in the case of equal densities.

A Sub-Domain Inverse Finite Element Characterization of Hyperelastic Membranes Including Soft Tissues

2003 ◽  
Vol 125 (3) ◽  
pp. 363-371 ◽  
Author(s):  
Padmanabhan Seshaiyer ◽  
Jay D. Humphrey
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Soft Tissues ◽  
Nonlinear Behavior ◽  
Local Stress ◽  
Biological Tissues ◽  
Material Behavior ◽  
Inverse Finite Element Method ◽  
Complicated Geometry ◽  
Element Method

Quantification of the mechanical behavior of hyperelastic membranes in their service configuration, particularly biological tissues, is often challenging because of the complicated geometry, material heterogeneity, and nonlinear behavior under finite strains. Parameter estimation thus requires sophisticated techniques like the inverse finite element method. These techniques can also become difficult to apply, however, if the domain and boundary conditions are complex (e.g. a non-axisymmetric aneurysm). Quantification can alternatively be achieved by applying the inverse finite element method over sub-domains rather than the entire domain. The advantage of this technique, which is consistent with standard experimental practice, is that one can assume homogeneity of the material behavior as well as of the local stress and strain fields. In this paper, we develop a sub-domain inverse finite element method for characterizing the material properties of inflated hyperelastic membranes, including soft tissues. We illustrate the performance of this method for three different classes of materials: neo-Hookean, Mooney Rivlin, and Fung-exponential.

Equivalent Mixed “PHETS” and “MPHETS” Poroelasttc-Transport-Swelling Finite Element Models for Soft Biological Tissues

1999 ◽  
Author(s):  
B. R. Simon ◽  
S. K. Williams ◽  
J. Liu ◽  
J. W. Nichol ◽  
P. H. Rigby ◽  
...  
Keyword(s):  
Finite Element ◽  
Chemical Potential ◽  
Biological Tissues ◽  
Finite Element Models ◽  
Material Interfaces ◽  
Soft Biological Tissues ◽  
Fibrous Matrix ◽  
Charged Species ◽  
Pressure Fields ◽  
Swelling Model

Abstract A soft hydrated tissue structure can be viewed as a “PETS” (poroelastic-transport-swelling) model, i.e., as a continuum composed of an incompressible porous solid (fibrous matrix with fixed charge density, FCD) that is saturated by a mobile incompressible fluid (water) containing mobile positively (p) and negatively (m) charged species. Previously, we described two PETS models — a “semi-mixed” porohyperelastic PHETS model (Simon et al. 1998) and a “fully mixed” MPHETS model (Simon et al. 1999) using FEMs (finite element models) that included geometric and material nonlinearity and coupled electrical/chemical/mechanical transport of the fluid and charged species. Here, we demonstrate the equivalence of the PHETS and MPHETS formulations that are useful when the solid and fluid materials are incompressible and the electrical-chemical potential and mechanical-osmotic pressure fields are discontinuous at material interfaces.

An Investigation Into the Upper Arm Deformation Under Inflatable Cuff

2008 ◽  
Author(s):  
H. Lan ◽  
A. M. Al-Jumaily ◽  
A. Lowe
Keyword(s):  
Finite Element ◽  
Soft Tissues ◽  
Element Model ◽  
Upper Arm ◽  
Inflatable Cuff ◽  
Proposed Model ◽  
Materials Used ◽  
Tissue Deformations ◽  
Visible Human ◽  
Collapse Process

The human upper arm is simulated using a nonlinear geometrical and physical model. To create a more realistic simulation, the geometry of the model is based on the visible human body dataset. The model consists of four parts, humerus, brachial artery, muscle, and other soft tissues. All the materials used in this model are assumed to be incompressible and hyperelastic. The unique properties of each material are specified and described. Incorporating all of these facts, a finite element model is developed using the commercial programme ABAQUS®. The upper arm tissues’ deformations and artery collapse process under compression are simulated in this model. The proposed model has the potential to simulate the tissue deformations under inflatable cuffs exposed to arm movements.

A Physically-Based Anisotropic Discrete Fiber Model for Fibrous Soft Tissues

2010 ◽  
Author(s):  
C. Flynn ◽  
M. B. Rubin ◽  
P. M. F. Nielsen
Keyword(s):  
Soft Tissues ◽  
Mechanical Response ◽  
Continuous Distribution ◽  
Collagen Fibers ◽  
Fiber Bundles ◽  
Parameter Study ◽  
Rabbit Skin ◽  
Pig Skin ◽  
Proposed Model ◽  
Physically Based

Physically-based fibrous soft tissue models often consider the tissue to be a collection of fibers with a continuous distribution function to represent their orientations. This study proposes a simple model for the response of fibrous connective tissues in terms of a discrete number of fiber bundles. The proposed model consists of six weighted fiber bundles orientated such that they pass through opposing vertices of an icosahedron. A novel aspect of the proposed model is the use of a simple analytical function to represent the undulation distribution of the collagen fibers. The mechanical response of the elastin fiber is represented by a neo-Hookean hyperelastic equation. A parameter study was performed to analyze the effect of each parameter on the overall response of the model. The proposed model accurately simulated the uniaxial stretching of pig skin with an 8% error-of-fit for stretch ratios up to 1.8. The model also accurately simulated the biaxial stretching of rabbit skin with a 10% error-of-fit for stretch ratios up to 1.9. The stiffness of the collagen fibers determined by the model was about 100 MPa for the rabbit skin and 900 MPa for the pig skin, which are comparable with values reported in the literature. The stiffness of the elastin fibers in the model was about 2 kPa.

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