Constitutive Modeling of Brain Tissue: Current Perspectives

2016 ◽  
Vol 68 (1) ◽  
Author(s):  
Rijk de Rooij ◽  
Ellen Kuhl
Keyword(s):  
Brain Tissue ◽  
Mechanical Response ◽  
Deformation Gradient ◽  
Constitutive Models ◽  
Time Dependent ◽  
Elastic Behavior ◽  
Integral Approach ◽  
Mechanical Stimuli ◽  
The Past ◽  
The Brain

Modeling the mechanical response of the brain has become increasingly important over the past decades. Although mechanical stimuli to the brain are small under physiological conditions, mechanics plays a significant role under pathological conditions including brain development, brain injury, and brain surgery. Well calibrated and validated constitutive models for brain tissue are essential to accurately simulate these phenomena. A variety of constitutive models have been proposed over the past three decades, but no general consensus on these models exists. Here, we provide a comprehensive and structured overview of state-of-the-art modeling of the brain tissue. We categorize the different features of existing models into time-independent, time-dependent, and history-dependent contributions. To model the time-independent, elastic behavior of the brain tissue, most existing models adopt a hyperelastic approach. To model the time-dependent response, most models either use a convolution integral approach or a multiplicative decomposition of the deformation gradient. We evaluate existing constitutive models by their physical motivation and their practical relevance. Our comparison suggests that the classical Ogden model is a well-suited phenomenological model to characterize the time-independent behavior of the brain tissue. However, no consensus exists for mechanistic, physics-based models, neither for the time-independent nor for the time-dependent response. We anticipate that this review will provide useful guidelines for selecting the appropriate constitutive model for a specific application and for refining, calibrating, and validating future models that will help us to better understand the mechanical behavior of the human brain.

Development of a Biofidelic Material Model for Brain Tissue

2011 ◽  
Author(s):  
Sandeep Kulathu ◽  
David L. Littlefield
Keyword(s):  
Brain Tissue ◽  
Grey Matter ◽  
Mechanical Response ◽  
Constitutive Models ◽  
Material Model ◽  
Small Sample ◽  
Material Models ◽  
Computational Mesh ◽  
Injury Mechanisms ◽  
The Brain

Computational simulations of brain injury mechanisms have advanced to a level of sophistication where in addition to capturing different anatomic regions, the computational mesh is capable of distinguishing white and grey matter in the brain. Brain tissue is typically modeled as an isotropic, viscoelastic material. Experiments have shown that the mechanical response of brain tissue to an external load varies depending on the location from which the tissue is harvested and also the direction of loading. Some researchers have developed anisotropic constitutive models by appealing to the composite material case wherein cylindrical axon fibers are immersed in a cellular matrix. Though such material models have been developed over a small sample, they have not been applied over the entire brain for simulation purposes.

Uncertainty Quantification in Predicting Behaviour of Rubber-Like Materials in Uni-Axial Loading

2020 ◽  
Author(s):  
Aref Ghaderi ◽  
Vahid Morovati ◽  
Pouyan Nasiri ◽  
Roozbeh Dargazany
Keyword(s):  
Uncertainty Quantification ◽  
Mechanical Response ◽  
Pure Shear ◽  
Constitutive Models ◽  
Material Behavior ◽  
Elastic Behavior ◽  
Deterministic Models ◽  
Data Set ◽  
Material Parameters ◽  
Axial Extension

Abstract Material parameters related to deterministic models can have different values due to variation of experiments outcome. From a mathematical point of view, probabilistic modeling can improve this problem. It means that material parameters of constitutive models can be characterized as random variables with a probability distribution. To this end, we propose a constitutive models of rubber-like materials based on uncertainty quantification (UQ) approach. UQ reduces uncertainties in both computational and real-world applications. Constitutive models in elastomers play a crucial role in both science and industry due to their unique hyper-elastic behavior under different loading conditions (uni-axial extension, biaxial, or pure shear). Here our goal is to model the uncertainty in constitutive models of elastomers, and accordingly, identify sensitive parameters that we highly contribute to model uncertainty and error. Modern UQ models can be implemented to use the physics of the problem compared to black-box machine learning approaches that uses data only. In this research, we propagate uncertainty through the model, characterize sensitivity of material behavior to show the importance of each parameter for uncertainty reduction. To this end, we utilized Bayesian rules to develop a model considering uncertainty in the mechanical response of elastomers. As an important assumption, we believe that our measurements are around the model prediction, but it is contaminated by Gaussian noise. We can make the noise by maximizing the posterior. The uni-axial extension experimental data set is used to calibrate the model and propagate uncertainty in this research.

Mathematical Modeling of Ligaments and Tendons

1993 ◽  
Vol 115 (4B) ◽  
pp. 468-473 ◽  
Author(s):  
S. L.-Y. Woo ◽  
G. A. Johnson ◽  
B. A. Smith
Keyword(s):  
Mathematical Modeling ◽  
Finite Strain ◽  
Mechanical Response ◽  
Time Dependent ◽  
Experimental Investigations ◽  
Display Time ◽  
Viscoelastic Models ◽  
The Past ◽  
Dependent Behavior ◽  
Single Integral

Ligaments and tendons serve a variety of important functions in maintaining the structure of the human body. Although abundant literature exists describing experimental investigations of these tissues, mathematical modeling of ligaments and tendons also contributes significantly to understanding their behavior. This paper presents a survey of developments in mathematical modeling of ligaments and tendons over the past 20 years. Mathematical descriptions of ligaments and tendons are identified as either elastic or viscoelastic, and are discussed in chronological order. Elastic models assume that ligaments and tendons do not display time dependent behavior and thus, they focus on describing the nonlinear aspects of their mechanical response. On the other hand, viscoelastic models incorporate time dependent effects into their mathematical description. In particular, two viscoelastic models are discussed in detail; quasi-linear viscoelasticity (QLV), which has been widely used in the past 20 years, and the recently proposed single integral finite strain (SIFS) model.

Simulation of Brain Response to Noncontact Impacts Using Coupled Eulerian–Lagrangian Method

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Miao Na ◽  
Timothy J. Beavers ◽  
Abhijit Chandra ◽  
Sarah A. Bentil
Keyword(s):  
Brain Tissue ◽  
Mechanical Response ◽  
Brain Regions ◽  
Von Mises Stress ◽  
Fe Model ◽  
Brain Response ◽  
Fe Method ◽  
Angular Velocities ◽  
Von Mises ◽  
The Brain

Abstract Finite element (FE) method has been widely used for gaining insights into the mechanical response of brain tissue during impacts. In this study, a coupled Eulerian−Lagrangian (CEL) formulation is implemented in impact simulations of a head system to overcome the mesh distortion difficulties due to large deformation in the cerebrospinal fluid (CSF) region and provide a biofidelic model of the interaction between the brain and skull. The head system used in our FE model is constructed from the transverse section of the human brain, with CSF modeled by Eulerian elements. Spring connectors are applied to represent the pia-arachnoid connection between the brain and skull. Validations of the CEL formulation and the FE model are performed using the experimental results. The dynamic response of brain tissue under noncontact impacts and the brain regions susceptible to injury are evaluated based on the intracranial pressure (ICP), maximum principal strain (MPS), and von Mises stress. While tracking the critical MPS location on the brain, higher likelihood of contrecoup injury than coup injury is found when sudden brain−skull motion takes place. The accumulation effect of CSF in the ventricle system, under large relative brain−skull motion, is also identified. The FE results show that adding relative angular velocities, to the translational impact model, not only causes a diffuse high strain area, but also cause the temporal lobes to be susceptible to cerebral contusions since the protecting CSF is prone to be squeezed away at the temporal sites due to the head rotations.

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.

scholarly journals The electric response in reflex contractions of spinal and decerebrate preparations

1924 ◽  
Vol 96 (675) ◽  
pp. 243-258 ◽  
Keyword(s):  
Mechanical Response ◽  
Direct Method ◽  
Electrical Response ◽  
Electric Response ◽  
Contracting Muscle ◽  
The Past ◽  
Single Twitch ◽  
Set Up ◽  
The Brain ◽  
String Galvanometer

In a series of communications Liddell and Sherrington (1) have analysed the mechanical response of a muscle stimulated to reflex contraction by rhythmic shocks to an afferent nerve. In particular they have described characteristic differences between the flexor response of the spinal and the extensor response of the decerebrate preparation ( i. e ., the preparation in which the midbrain is left attached to the spinal cord). During the past year we have attempted an analysis of the electrical response of a reflexly contracting muscle. The investigation was concerned in the main with some other points, but it has involved many comparisons of the electrical response of spinal and decerebrate preparations, and as these supplement and generally confirm, the views of Liddell and Sherrington it seems best to publish them as a separate communication. Method of Experiment . The experiments have been made on cats either decapitated under anæsthesia by Sherrington’s method or decerebrated by removal of all the brain above the anterior colliculi. The limb was fixed by a drill through. the lower end of the femur and shielded stimulating electrodes were applied to the popliteal nerve. The muscles whose action currents were recorded were the tibialis anticus for the flexion reflex and the vastocrureus for the crossed extension reflex. In the earlier experiments the tendon of the muscle was fixed by a clamp; in the later it was attached to a rubber tambour which communicated by a leaden pipe 9 feet long with another tambour which carried a pointer moving in the eyepiece of the string galvanometer. A more direct method could not be used owing to the distance between the animal table and the galvanometer. The movement of this pointer, magnified 40 times, was recorded on the same strip of cinematograph film as the movements of the string. Owing to the length of the pipe there is a lag of some hundredths of a second in the movement of the second tambour, and sudden movements ( e. g ., the single twitch of a muscle) set up waves in the pipe which cause oscillations on the record.

A pressure-displacement transducer for measuring brain tissue properties in vivo

1975 ◽  
Vol 38 (1) ◽  
pp. 187-188 ◽  
Author(s):  
Edward K. Walsh ◽  
Alfonso Schettini
Keyword(s):  
Brain Tissue ◽  
Mechanical Response ◽  
Displacement Transducer ◽  
Time Dependent ◽  
Creep Properties ◽  
Tissue Properties ◽  
Short Time ◽  
Made In

A transducer system is described which measures simultaneously the pressure and displacement as the transducer is inserted into the intracranial system. The measurements are made in vivo and with the dura arachnoid membranes intact. The short-time mechanical response of the system as well as the time-dependent relaxation and creep properties can be determined.

Brain tissue elastic behavior and experimental brain compression

1988 ◽  
Vol 255 (5) ◽  
pp. R799-R805 ◽  
Author(s):  
A. Schettini ◽  
E. K. Walsh
Keyword(s):  
Brain Tissue ◽  
Mechanical Response ◽  
Fluid Pressure ◽  
Elastic Parameter ◽  
Elastic Behavior ◽  
Present Observation ◽  
Tissue Elasticity ◽  
Tissue Pressure ◽  
Brain Compression ◽  
Nonlinear Elastic

This study was designed to test the hypothesis that the progressive expansion of an extradural mass causes detectable changes in brain mechanical response properties, in particular the nonlinear elastic behavior, before any significant changes in intracranial cerebrospinal fluid pressure can be detected. In 10 chronically prepared and anesthetized dogs, incremental inflation (0.07 ml/s) of an extradural balloon caused 1) a progressive fall in the brain nonlinear elastic parameter (G0, mmHg/mm2), 2) nonsignificant changes in brain tissue elasticity (G0, mmHg/mm), 3) a disproportionate progressive rise in subpial tension, and 4) a progressive fall in local cerebral blood flow (H2 clearance), despite a modest decrease in cerebral perfusion pressure (extracranial). In previous brain compression experiments (Brain Res. 305: 141-143, 1984) we have shown that the compression site becomes compacted and stiffer (increased G0) and its nonlinear elastic parameter (G0) increases markedly. These earlier findings, coupled with the present observation of a loss in tissue nonlinearity distally to the compression site, are most likely the major mechanisms by which, with a rapidly expanding intracranial mass, tissue pressure gradients and brain displacement, including transtentorial herniation, develop.

A Visco-Hyperelastic-Damage Constitutive Model for the Analysis of the Biomechanical Response of the Periodontal Ligament

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Arturo N. Natali ◽  
Emanuele L. Carniel ◽  
Piero G. Pavan ◽  
Franz G. Sander ◽  
Christina Dorow ◽  
...  
Keyword(s):  
Strain Rate ◽  
Periodontal Ligament ◽  
Soft Tissues ◽  
Mechanical Response ◽  
Experimental Testing ◽  
Constitutive Models ◽  
Biological Tissues ◽  
Time Dependent ◽  
Large Strains ◽  
Free Energy Function

The periodontal ligament (PDL), as other soft biological tissues, shows a strongly non-linear and time-dependent mechanical response and can undergo large strains under physiological loads. Therefore, the characterization of the mechanical behavior of soft tissues entails the definition of constitutive models capable of accounting for geometric and material non-linearity. The microstructural arrangement determines specific anisotropic properties. A hyperelastic anisotropic formulation is adopted as the basis for the development of constitutive models for the PDL and properly arranged for investigating the 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. These 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. The accuracy of the formulation is evaluated by using results of experimental tests performed on animal model, accounting for different strain rates and for strain states capable of inducing damage phenomena. The comparison shows a good agreement between numerical results and experimental data.

Effect of Cerebral Vasculatures on the Mechanical Response of Brain Tissue: A Preliminary Study

2000 ◽  
Author(s):  
Kiyoshi Omori ◽  
Liying Zhang ◽  
King H. Yang ◽  
Albert I. King
Keyword(s):  
Traumatic Brain Injury ◽  
Brain Injury ◽  
Brain Tissue ◽  
Mechanical Response ◽  
Clinical Symptoms ◽  
Anatomical Structure ◽  
Causal Mechanism ◽  
Injury Biomechanics ◽  
Preliminary Study ◽  
The Brain

Abstract Traumatic brain injury (TBI) constitutes a significant portion of all injuries occurring as a result of automotive, motorcycle and sports related injuries. Over the years, a large amount of literature has been devoted to an increased understanding of clinical symptoms, pathological evidence and injury biomechanics for such injuries. However, the precise causal mechanism, which accounts for complex mechanical interactions and responses in an anatomical structure as complex as the brain, is not fully understood.

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