Finite Element Based Nonlinear Normalization of Human Lumbar Intervertebral Disc Stiffness to Account for Its Morphology

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Ghislain Maquer ◽  
Marc Laurent ◽  
Vaclav Brandejsky ◽  
Michael L. Pretterklieber ◽  
Philippe K. Zysset
Keyword(s):  
Mechanical Properties ◽  
Intervertebral Disc ◽  
Material Properties ◽  
Soft Tissues ◽  
Mechanical Response ◽  
Parameter Study ◽  
Nonlinear Normalization ◽  
Highly Nonlinear ◽  
Flexion Extension ◽  
Linear And Nonlinear

Disc degeneration, usually associated with low back pain and changes of intervertebral stiffness, represents a major health issue. As the intervertebral disc (IVD) morphology influences its stiffness, the link between mechanical properties and degenerative grade is partially lost without an efficient normalization of the stiffness with respect to the morphology. Moreover, although the behavior of soft tissues is highly nonlinear, only linear normalization protocols have been defined so far for the disc stiffness. Thus, the aim of this work is to propose a nonlinear normalization based on finite elements (FE) simulations and evaluate its impact on the stiffness of human anatomical specimens of lumbar IVD. First, a parameter study involving simulations of biomechanical tests (compression, flexion/extension, bilateral torsion and bending) on 20 FE models of IVDs with various dimensions was carried out to evaluate the effect of the disc's geometry on its compliance and establish stiffness/morphology relations necessary to the nonlinear normalization. The computed stiffness was then normalized by height (H), cross-sectional area (CSA), polar moment of inertia (J) or moments of inertia (Ixx, Iyy) to quantify the effect of both linear and nonlinear normalizations. In the second part of the study, T1-weighted MRI images were acquired to determine H, CSA, J, Ixx and Iyy of 14 human lumbar IVDs. Based on the measured morphology and pre-established relation with stiffness, linear and nonlinear normalization routines were then applied to the compliance of the specimens for each quasi-static biomechanical test. The variability of the stiffness prior to and after normalization was assessed via coefficient of variation (CV). The FE study confirmed that larger and thinner IVDs were stiffer while the normalization strongly attenuated the effect of the disc geometry on its stiffness. Yet, notwithstanding the results of the FE study, the experimental stiffness showed consistently higher CV after normalization. Assuming that geometry and material properties affect the mechanical response, they can also compensate for one another. Therefore, the larger CV after normalization can be interpreted as a strong variability of the material properties, previously hidden by the geometry's own influence. In conclusion, a new normalization protocol for the intervertebral disc stiffness in compression, flexion, extension, bilateral torsion and bending was proposed, with the possible use of MRI and FE to acquire the discs' anatomy and determine the nonlinear relations between stiffness and morphology. Such protocol may be useful to relate the disc's mechanical properties to its degree of degeneration.

Nonlinear Dynamic Behaviour of the Intervertebral Disc

2013 ◽  
Author(s):  
Giacomo Marini ◽  
Gerd Huber ◽  
Stephen J. Ferguson
Keyword(s):  
Dynamic Response ◽  
Intervertebral Disc ◽  
High Frequency ◽  
Nonlinear Dynamic ◽  
Mechanical Response ◽  
Numerical Models ◽  
Low Frequency ◽  
Upper Body ◽  
Highly Nonlinear ◽  
Flexion Extension

The intervertebral disc, like many collagen-based tissues, has a mechanical response which is highly nonlinear (1). This characteristic is due to both the arrangement and composition of the tissue constituents of the disc (2). Over the past decades several studies have reported the nonlinear response of the disc for different loading scenarios. In particular, past studies were focused on the quasi-static and low frequency (< 10Hz) response to pure and combined cyclic loading, such as axial compression, shear, flexion/extension moment (3–6). The information provided by these studies has been applied in several fields, from the validation of numerical models to the development of disc prostheses. However, such loading conditions are only partially representative of the in-situ load that the intervertebral disc normally experiences. High frequency dynamics stimuli, such as that experienced while driving a car on a rough surface or driving heavy industrial machinery, are also important. It is well known that long-term exposure to vibrational loading is detrimental to normal disc metabolism (7,8). Despite its relevance only a few studies have investigated the dynamic response of the disc to high frequency vibration (9,10) with sometimes different outcomes. In particular, no study has shown an asymmetric, nonlinear dynamic behavior of the system, even though it is evident in quasi-static testing — the well-known tension / compression asymmetry. This aspect is somehow neglected when building rigid body models of the upper body for impact simulation where a Kelvin-Voigt model with linear stiffness is normally used. The aim of this experimental study was therefore to investigate the nonlinear dynamic response of the intervertebral disc to high frequency loadings, taking different pre-loads and displacement amplitude into account.

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.

Nonlinear Dynamic Viscoelastic Model for Osteoarthritic Cartilage Indentation Force

2011 ◽  
Author(s):  
A. Vidal-Lesso ◽  
E. Ledesma-Orozco ◽  
R. Lesso-Arroyo ◽  
L. Daza-Benitez
Keyword(s):  
Mechanical Properties ◽  
Soft Tissues ◽  
Mechanical Response ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Indentation Test ◽  
Maxwell Model ◽  
Relaxation Curve ◽  
Geometrical Parameters ◽  
Osteoarthritic Cartilage

Biomechanical properties and dynamic response of soft tissues as articular cartilage remains issues for attention. Currently, linear isotropic models are still used for cartilage analysis in spite of its viscoelastic nature. Therefore, the aim of this study was to propose a nonlinear viscoelastic model for cartilage indentation that combines the geometrical parameters and velocity of the indentation test with the thickness of the sample as well as the mechanical properties of the tissue changing over time due to its viscoelastic behavior. Parameters of the indentation test and mechanical properties as a function of time were performed in Laplace space where the constitutive equation for viscoelasticity and the convolution theorem was applied in addition with the Maxwell model and Hayes et al. model for instantaneous elastic modulus. Results of the models were compared with experimental data of indentation tests on osteoarthritic cartilage of a unicompartmental osteoarthritis cases. The models showed a strong fit for the axial indentation nonlinear force in the loading curve (R2 = 0.992) and a good fit for unloading (R2 = 0.987), while an acceptable fit was observed in the relaxation curve (R2 = 0.967). These models may be used to study the mechanical response of osteoarthritic cartilage to several dynamical and geometrical test conditions.

scholarly journals Multi-Scale Structural and Tensile Mechanical Response of Annulus Fibrosus to Osmotic Loading

2012 ◽  
Author(s):  
Woojin M. Han ◽  
Nandan L. Nerurkar ◽  
Lachlan J. Smith ◽  
Nathan T. Jacobs ◽  
Robert L. Mauck ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Intervertebral Disc ◽  
Mechanical Testing ◽  
Biochemical Composition ◽  
Annulus Fibrosus ◽  
Mechanical Response ◽  
Tissue Level ◽  
Multi Scale ◽  
Osmotic Loading

The annulus fibrosus (AF) is a multi-lamellar fibrocartilagenous ring in the intervertebral disc. The variation of biochemical composition from the outer to the inner AF is largely responsible for the heterogeneous mechanical properties. In vitro tissue-level studies require mechanical testing in aqueous buffers to avoid tissue dehydration. The varying glycosaminoglycan (GAG) contents from outer to inner AF suggest that the response to high and low PBS osmolarity may also be different with radial position. Previous studies in tendon and ligament have been conflicting: soaking tendon fascicles in PBS decreased tensile modulus1 and treating ligament in buffer had no effect on modulus.2

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.

Implementation and Validation of Planar Soft Tissue Structural Constitutive Model

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

Constitutive modeling is of fundamental important for numerical simulation and analysis of soft biological tissues. The mechanical behaviors of soft tissues are usually highly nonlinear and anisotropic. The complex behavior is the results from 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. Moreover, 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. The structural model was verified against experiential test data for native bovine pericardium and fetal membrane. In addition to prediction of the mechanical response, we demonstrate how a structural model can provide deeper insights into fiber reorientation and fiber recruitment.

scholarly journals Digital image correlation-based point-wise inverse characterization of heterogeneous material properties of gallbladder in vitro

2014 ◽  
Vol 470 (2167) ◽  
pp. 20140152 ◽  
Author(s):  
Katia Genovese ◽  
Luciana Casaletto ◽  
Jay D. Humphrey ◽  
Jia Lu
Keyword(s):  
Mechanical Properties ◽  
Extracellular Matrix ◽  
Material Properties ◽  
Soft Tissues ◽  
Applied Pressure ◽  
Heterogeneous Material ◽  
Image Correlation ◽  
Surface Geometry ◽  
Stress Strain ◽  
Full Field

Continuing advances in mechanobiology reveal more and more that many cell types, especially those responsible for establishing, maintaining, remodelling or repairing extracellular matrix, are extremely sensitive to their local mechanical environment. Indeed, it appears that they fashion the extracellular matrix so as to promote a ‘mechanical homeostasis’. A natural corollary, therefore, is that cells will try to offset complexities in geometry and applied loads with heterogeneous material properties in order to render their local environment mechanobiologically favourable. There is a pressing need, therefore, for hybrid experimental–computational methods in biomechanics that can quantify such heterogeneities. In this paper, we present an approach that combines experimental information on full-field surface geometry and deformations with a membrane-based point-wise inverse method to infer full-field mechanical properties for soft tissues that exhibit nonlinear behaviours under finite deformations. To illustrate the potential utility of this new approach, we present the first quantification of regional mechanical properties of an excised but intact gallbladder, a thin-walled, sac-like organ that plays a fundamental role in normal digestion. The gallbladder was inflated to a maximum local stretch of 120% in eight pressure increments; at each pressure pause, the entire three-dimensional surface was optically extracted, and from which the surface strains were computed. Wall stresses in each state were predicted from the deformed geometry and the applied pressure using an inverse elastostatic method. The elastic properties of the gallbladder tissue were then characterized locally using point-wise stress–strain data. The gallbladder was found to be highly heterogeneous, with drastically different stiffness between the hepatic and the serosal sides. The identified material model was validated through forward finite-element analysis; both the configurations and the local stress–strain patterns were well reproduced.

scholarly journals Soft-Tissue-Mimicking Using Hydrogels for the Development of Phantoms

Gels ◽  
2022 ◽  
Vol 8 (1) ◽  
pp. 40
Author(s):  
Aitor Tejo-Otero ◽  
Felip Fenollosa-Artés ◽  
Isabel Achaerandio ◽  
Sergi Rey-Vinolas ◽  
Irene Buj-Corral ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Soft Tissues ◽  
Mechanical Response ◽  
Viscoelastic Behavior ◽  
Linear Elastic ◽  
Lack Of Information ◽  
Wide Range ◽  
Significant Difference ◽  
Promising Solution ◽  
Living Tissues

With the currently available materials and technologies it is difficult to mimic the mechanical properties of soft living tissues. Additionally, another significant problem is the lack of information about the mechanical properties of these tissues. Alternatively, the use of phantoms offers a promising solution to simulate biological bodies. For this reason, to advance in the state-of-the-art a wide range of organs (e.g., liver, heart, kidney as well as brain) and hydrogels (e.g., agarose, polyvinyl alcohol –PVA–, Phytagel –PHY– and methacrylate gelatine –GelMA–) were tested regarding their mechanical properties. For that, viscoelastic behavior, hardness, as well as a non-linear elastic mechanical response were measured. It was seen that there was a significant difference among the results for the different mentioned soft tissues. Some of them appear to be more elastic than viscous as well as being softer or harder. With all this information in mind, a correlation between the mechanical properties of the organs and the different materials was performed. The next conclusions were drawn: (1) to mimic the liver, the best material is 1% wt agarose; (2) to mimic the heart, the best material is 2% wt agarose; (3) to mimic the kidney, the best material is 4% wt GelMA; and (4) to mimic the brain, the best materials are 4% wt GelMA and 1% wt agarose. Neither PVA nor PHY was selected to mimic any of the studied tissues.

Importance of Material Properties and Porosity of Bone on Mechanical Response of Articular Cartilage in Human Knee Joint—A Two-Dimensional Finite Element Study

2014 ◽  
Vol 136 (12) ◽  
Author(s):  
Mikko S. Venäläinen ◽  
Mika E. Mononen ◽  
Jukka S. Jurvelin ◽  
Juha Töyräs ◽  
Tuomas Virén ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Articular Cartilage ◽  
Knee Joint ◽  
Trabecular Bone ◽  
Material Properties ◽  
Mechanical Response ◽  
Structural Level ◽  
Two Dimensional ◽  
Local Material Properties

Mechanical behavior of bone is determined by the structure and intrinsic, local material properties of the tissue. However, previously presented knee joint models for evaluation of stresses and strains in joints generally consider bones as rigid bodies or linearly elastic solid materials. The aim of this study was to estimate how different structural and mechanical properties of bone affect the mechanical response of articular cartilage within a knee joint. Based on a cadaver knee joint, a two-dimensional (2D) finite element (FE) model of a knee joint including bone, cartilage, and meniscus geometries was constructed. Six different computational models with varying properties for cortical, trabecular, and subchondral bone were created, while the biphasic fibril-reinforced properties of cartilage and menisci were kept unaltered. The simplest model included rigid bones, while the most complex model included specific mechanical properties for different bone structures and anatomically accurate trabecular structure. Models with different porosities of trabecular bone were also constructed. All models were exposed to axial loading of 1.9 times body weight within 0.2 s (mimicking typical maximum knee joint forces during gait) while free varus–valgus rotation was allowed and all other rotations and translations were fixed. As compared to results obtained with the rigid bone model, stresses, strains, and pore pressures observed in cartilage decreased depending on the implemented properties of trabecular bone. Greatest changes in these parameters (up to −51% in maximum principal stresses) were observed when the lowest modulus for trabecular bone (measured at the structural level) was used. By increasing the trabecular bone porosity, stresses and strains were reduced substantially in the lateral tibial cartilage, while they remained relatively constant in the medial tibial plateau. The present results highlight the importance of long bones, in particular, their mechanical properties and porosity, in altering and redistributing forces transmitted through the knee joint.

In Situ Measurement and Modeling of Human Cadaveric Soft Tissue Mechanical Properties for Use in Real Time Surgical Simulation

2008 ◽  
Author(s):  
Yi-Je Lim ◽  
Dhannanjay Deo ◽  
Suvranu De
Keyword(s):  
Mechanical Properties ◽  
Real Time ◽  
Soft Tissues ◽  
Force Feedback ◽  
Mechanical Response ◽  
Surgical Simulation ◽  
Physical Models ◽  
Nonlinear Viscoelastic ◽  
External Forces ◽  
Surgery Simulator

Development of a realistic surgery simulator that delivers high fidelity visual and haptic (force) feedback, based on the physical models of soft tissues, requires the use of empirical data on the mechanical behavior of intra-abdominal organs under the action of external forces. Measurement of mechanical properties of soft tissues on live human patients presents significant risks, making the use of cadavers a logical alternative. In this paper we present techniques of measuring and modeling the mechanical response of human cadaveric tissue for the purpose of developing a “virtual cadaver” model. The major contribution of this paper is the development of physics-based models of soft tissues that range from linear elastic models to nonlinear viscoelastic models which are efficient for application within the framework of a real time surgery simulator.

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