Characterizing white matter tissue in large strain via asymmetric indentation and inverse finite element modeling

Macro-indentation testing of soft biological materials and assessment of hyper-elastic material models from inverse finite element analysis

Mechanical characterization of hydrogels and ultra-soft tissues is a challenging task both from an experimental and material parameter estimation perspective because they are much softer than many biological materials, ceramics, or polymers. The elastic modulus of such materials is within the 1 - 100 kPa range, behaving as a hyperelastic solid with strain hardening capability at large strains. In the current study, indentation experiments have been performed on agarose hydrogels, bovine liver, and bovine lymph node specimens. This work reports on the reliable determination of the elastic modulus by indentation experiments carried out at the macro-scale (mm) using a spherical indenter. However, parameter identification of the hyperelastic material properties usually requires an inverse finite element analysis due to the lack of an analytical contact model of the indentation test. Hence a comprehensive study on the spherical indentation of hyperelastic soft materials is carried out through robust computational analysis. Neo-Hookean and first-order Ogden hyperelastic material models were found to be most suitable. A case study on known anisotropic hyperelastic material showed the inability of the inverse finite element method to uniquely identify the whole material parameter set.

Region-Dependent Mechanical Properties of Human Brain Tissue Under Large Deformations Using Inverse Finite Element Modeling

This study aims to facilitate intracranial simulation of traumatic events by determining the mechanical properties of different anatomical structures of the brain. Our experimental indentation paradigm used fresh, post-operative human tissue, which is highly advantageous in determining mechanical properties without being affected by postmortem time. This study employed an inverse finite element approach coupled with experimental indentation data to characterize mechanical properties of the human hippocampus (CA1, CA3, dentate gyrus), cortex white matter, and cortex grey matter. We determined that an uncoupled viscoelastic Ogden constitutive formulation was most appropriate to represent the mechanical behavior of these different regions of brain. Anatomical regions were significantly different in their mechanical properties. The cortex white matter was stiffer than cortex grey matter, and the CA1 and dentate gyrus were both stiffer than cortex grey matter. Although no sex dependency was observed, there were trends indicating that male brain regions were generally stiffer than corresponding female regions. In addition, there were no statistically significant age dependent differences. This study provides a structure-specific description of fresh human brain tissue mechanical properties, which will be an important step toward explicitly modeling the heterogeneity of brain tissue deformation during TBI through finite element modeling.

Inverse identification of region-specific hyperelastic material parameters for human brain tissue

The identification of material parameters accurately describing the region-dependent mechanical behavior of human brain tissue is crucial for computational models used to assist, e.g., the development of safety equipment like helmets or the planning and execution of brain surgery. While the division of the human brain into different anatomical regions is well established, knowledge about regions with distinct mechanical properties remains limited. Here, we establish an inverse parameter identification scheme using a hyperelastic Ogden model and experimental data from multi-modal testing of tissue from 19 anatomical human brain regions to identify mechanically distinct regions and provide the corresponding material parameters. We assign the 19 anatomical regions to nine governing regions based on similar parameters and microstructures. Statistical analyses confirm differences between the regions and indicate that at least the corpus callosum and the corona radiata should be assigned different material parameters in computational models of the human brain. We provide a total of four parameter sets based on the two initial Poisson's ratios of 0.45 and 0.49 as well as the pre- and unconditioned experimental responses, respectively. Our results highlight the close interrelation between the Poisson's ratio and the remaining model parameters. The identified parameters will contribute to more precise computational models enabling spatially resolved predictions of the stress and strain states in human brains under complex mechanical loading conditions.

Development, validation and a case study: The female finite element head model (FeFEHM)

BACKGROUND AND OBJECTIVE

Traumatic brain injuries are one of the leading causes of death and disability in the world. To better understand the interactions and forces applied in different constituents of the human head, several finite element head models have been developed throughout the years, for offering a good cost-effective and ethical approach compared to experimental tests. Once validated, the female finite element head model (FeFEHM) will allow a better understanding of injury mechanisms resulting in neuronal damage, which can later evolve into neurodegenerative diseases.

METHODS

This work encompasses the approached methodology starting from medical images and finite element modelling until the validation process using novel experimental data of brain displacements conducted on human cadavers. The material modelling of the brain is performed using an age-specific characterization of the brain using microindentation at dynamic rates and under large deformation, with a similar age to the patient used to model the FeFEHM.

RESULTS

The numerical displacement curves are in good accordance with the experimental data, displaying similar peak times and values, in all three anatomical planes. The case study result shows a similarity between the pressure fields of the FeFEHM compared to another model, highlighting the future potential of the model.

CONCLUSIONS

The initial objective was met, and a new female finite element head model has been developed with biofidelic brain motion. This model will be used for the assessment of repetitive impact scenarios and its repercussions on the female brain.

A transversely isotropic viscohyperelastic-damage model for the brain tissue with strain rate sensitivity

Understanding the mechanical behaviors and properties of brain tissue are crucial to study the mechanisms of traumatic brain injury (TBI). Such injury may be associated with high rate loading conditions and the large deformation of brain tissue. Thus, constitutive models that consider the rate dependent large deformation of brain tissue and its possible damage initiation and evolution may help uncover the related mechanisms of TBI. Motivated from this, in this paper we present a fully three-dimensional large strain viscohyperelastic-damage model with the purpose of reproducing the experimentally observed rate sensitive elastic and damage-induced stress softening behaviors of brain tissue. The parameters of the proposed model can be identified using the experimental data from simple monotonic tests such as uniaxial tension, compression and simple shear. The proposed model is validated by comparing its prediction with experimental data. Good agreement between predictive results and experimental data is achieved indicating the potential of the proposed model in characterizing the mechanical behaviors of brain tissue considering rate dependence and damage effect.

Modeling the damage-induced softening behavior of brain white matter using a coupled hyperelasticty-damage model

White matter in the brain is structurally anisotropic consisting of large bundle of aligned axonal fibers. Hyperelastic, transversely isotropic constitutive models are typically used in the modeling and simulation of such tissues. However, most studies constrain the material models to describe the mechanical behavior of white matter in the limit of small deformation, without considering the experimentally observed damage initiation and damage-induced material softening in large strain regime. In this study, we extend a previously developed transversely isotropic hyperelasticity model for white matter by coupling it with damage equations within the framework of thermodynamics and using continuum damage mechanics method. Two homogeneous deformation cases are used to demonstrate the proposed model's capability in capturing the damage-induced softening behaviors of white matter under uniaxial loading and simple shear, along with the investigation of fiber orientation effect on such behaviors and material stiffness. As a demonstration case of inhomogeneous deformation, the proposed model is also implemented into finite element codes to reproduce the experimental data (nonlinear material behavior and damage initiation) from an indentation configuration of porcine white matter. Good agreement between numerical results and experimental data is achieved indicating the potential of the proposed model in characterizing the mechanical behaviors of white matter considering damage at large strain.

Poro-viscoelastic material parameter identification of brain tissue-mimicking hydrogels

Understanding and characterizing the mechanical and structural properties of brain tissue is essential for developing and calibrating reliable material models. Based on the Theory of Porous Media, a novel nonlinear poro-viscoelastic computational model was recently proposed to describe the mechanical response of the tissue under different loading conditions. The model contains parameters related to the time-dependent behavior arising from both the viscoelastic relaxation of the solid matrix and its interaction with the fluid phase. This study focuses on the characterization of these parameters through indentation experiments on a tailor-made polyvinyl alcohol-based hydrogel mimicking brain tissue. The material behavior is adjusted to ex vivo porcine brain tissue. An inverse parameter identification scheme using a trust region reflective algorithm is introduced and applied to match experimental data obtained from the indentation with the proposed computational model. By minimizing the error between experimental values and finite element simulation results, the optimal constitutive model parameters of the brain tissue-mimicking hydrogel are extracted. Finally, the model is validated using the derived material parameters in a finite element simulation.

Bidirectional hyperelastic characterization of brain white matter tissue

Biomechanical study of brain injuries originated from mechanical damages to white matter tissue requires detailed information on mechanical characteristics of its main components, the axonal fibers and extracellular matrix, which is very limited due to practical difficulties of direct measurement. In this paper, a new theoretical framework was established based on microstructural modeling of brain white matter tissue as a soft composite for bidirectional hyperelastic characterization of its main components. First the tissue was modeled as an Ogden hyperelastic material, and its principal Cauchy stresses were formulated in the axonal and transverse directions under uniaxial and equibiaxial tension using the theory of homogenization. Upon fitting these formulae to the corresponding experimental test data, direction-dependent hyperelastic constants of the tissue were obtained. These directional properties then were used to estimate the strain energy stored in the homogenized model under each loading scenario. A new microstructural composite model of the tissue was also established using principles of composites micromechanics, in which the axonal fibers and surrounding matrix are modeled as different Ogden hyperelastic materials with unknown constants. Upon balancing the strain energies stored in the homogenized and composite models under different loading scenarios, fully coupled nonlinear equations as functions of unknown hyperelastic constants were derived, and their optimum solutions were found in a multi-parametric multi-objective optimization procedure using the response surface methodology. Finally, these solutions were implemented, in a bottom-up approach, into a micromechanical finite element model to reproduce the tissue responses under the same loadings and predict the tissue responses under unseen non-equibiaxial loadings. Results demonstrated a very good agreement between the model predictions and experimental results in both directions under different loadings. Moreover, the axonal fibers with hyperelastic characteristics stiffer than the extracellular matrix were shown to play the dominant role in directional reinforcement of the tissue.

Morphological changes in glial cells arrangement under mechanical loading: A quantitative study

The mechanical properties and microstructure of brain tissue, as its two main physical parameters, could be affected by mechanical stimuli. In previous studies, microstructural alterations due to mechanical loading have received less attention than the mechanical properties of the tissue. Therefore, the current study aimed to investigate the effect of ex-vivo mechanical forces on the micro-architecture of brain tissue including axons and glial cells. A three-step loading protocol (i.e., loading-recovery-loading) including eight strain levels from 5% to 40% was applied to bovine brain samples with axons aligned in one preferred direction (each sample experienced only one level of strain). After either the first or secondary loading step, the samples were fixed, cut in planes parallel and perpendicular to the loading direction, and stained for histology. The histological images were analyzed to measure the end-to-end length of axons and glial cell-cell distances. The results showed that after both loading steps, as the strain increased, the changes in the cell nuclei arrangement in the direction parallel to axons were more significant compared to the other two perpendicular directions. Based on this evidence, we hypothesized that the spatial pattern of glial cells is highly affected by the orientation of axonal fibers. Moreover, the results revealed that in both loading steps, the maximum cell-cell distance occurred at 15% strain, and this distance decreased for higher strains. Since 15% strain is close to the previously reported brain injury threshold, this evidence could suggest that at higher strains, the axons start to rupture, causing a reduction in the displacement of glial cells. Accordingly, it was concluded that more attention to glial cells' architecture during mechanical loading may lead to introduce a new biomarker for brain injury.

Correlating the microstructural architecture and macrostructural behaviour of the brain

The computational simulation of pathological conditions and surgical procedures, for example the removal of cancerous tissue, can contribute crucially to the future of medicine. Especially for brain surgery, these methods can be important, as the ultra-soft tissue controls vital functions of the body. However, the microstructural interactions and their effects on macroscopic material properties remain incompletely understood. Therefore, we investigated the mechanical behaviour of brain tissue under three different deformation modes, axial tension, compression, and semi-confined compression, in different anatomical regions, and for varying axon orientation. In addition, we characterised the underlying microstructure in terms of myelin, cells, glial cells and neuron area fraction, and density. The correlation of these quantities with the material parameters of the anisotropic Ogden model reveals a decrease in shear modulus with increasing myelin area fraction. Strikingly, the tensile shear modulus correlates positively with cell and neuronal area fraction (Spearman's correlation coefficient of r_s=0.40 and r_s=0.33), whereas the compressive shear modulus decreases with increasing glial cell area (r_s=-0.33). Our study finds that tissue non-linearity significantly depends on the myelin area fraction (r_s=0.47), cell density (r_s=0.41) and glial cell area (r_s=0.49). Our results provide an important step towards understanding the micromechanical load transfer that leads to the non-linear macromechanical behaviour of the brain. STATEMENT OF SIGNIFICANCE: Within this article, we investigate the mechanical behaviour of brain tissue under three different deformation modes, in different anatomical regions, and for varying axon orientation. Further, we characterise the underlying microstructure in terms of various constituents. The correlation of these quantities with the material parameters of the anisotropic Ogden model reveals a decrease in shear modulus with increasing myelin area fraction. Strikingly, the tensile shear modulus correlates positively with cell and neuronal area fraction, whereas the compressive shear modulus decreases with increasing glial cell area. Our study finds that tissue non-linearity significantly depends on the myelin area fraction, cell density, and glial cell area. Our results provide an important step towards understanding the micromechanical load transfer that leads to the non-linear macromechanical behaviour of the brain.

Anisotropy profoundly alters stress fields within contractile cells and cell aggregates

Many biological phenomena such as cell proliferation and death are correlated with stress fields within cells. Stress fields are quantified using computational methods which rely on fundamental assumptions about local mechanical properties. Most existing methods such as Monolayer Stress Microscopy assume isotropic properties, yet experimental observations strongly suggest anisotropy. We first model anisotropy in circular cells analytically using Eshelby's inclusion method. Our solution reveals that uniform anisotropy cannot exist in cells due to the occurrence of substantial stress concentration in the central region. A more realistic non-uniform anisotropy model is then introduced based on experimental observations and implemented numerically which interestingly clears out stress concentration. Stresses within the entire aggregate also drastically change compared to the isotropic case, resulting in better agreement with observed biomarkers. We provide a physics-based mechanism to explain the low alignment of stress fibers in the center of cells, which might explain certain biological phenomena e.g., existence of disrupted rounded cells, and higher apoptosis rate at the center of circular aggregates.

Tissue-Scale Biomechanical Testing of Brain Tissue for the Calibration of Nonlinear Material Models

Brain tissue is one of the most complex and softest tissues in the human body. Due to its ultrasoft and biphasic nature, it is difficult to control the deformation state during biomechanical testing and to quantify the highly nonlinear, time-dependent tissue response. In numerous experimental studies that have investigated the mechanical properties of brain tissue over the last decades, stiffness values have varied significantly. One reason for the observed discrepancies is the lack of standardized testing protocols and corresponding data analyses. The tissue properties have been tested on different length and time scales depending on the testing technique, and the corresponding data have been analyzed based on simplifying assumptions. In this review, we highlight the advantage of using nonlinear continuum mechanics based modeling and finite element simulations to carefully design experimental setups and protocols as well as to comprehensively analyze the corresponding experimental data. We review testing techniques and protocols that have been used to calibrate material model parameters and discuss artifacts that might falsify the measured properties. The aim of this work is to provide standardized procedures to reliably quantify the mechanical properties of brain tissue and to more accurately calibrate appropriate constitutive models for computational simulations of brain development, injury and disease. Computational models can not only be used to predictively understand brain tissue behavior, but can also serve as valuable tools to assist diagnosis and treatment of diseases or to plan neurosurgical procedures. © 2022 The Authors. Current Protocols published by Wiley Periodicals LLC.

Development and Validation of a New Anisotropic Visco-Hyperelastic Human Head Finite Element Model Capable of Predicting Multiple Brain Injuries

This paper reports on the latest refinement of the Finite Element Global Human Body Models Consortium 50th percentile (GHBMC M50) adult male head model by the development and incorporation of a new material model into the white matter tissue of the brain. The white matter is represented by an anisotropic visco-hyperelastic material model capable of simulating direction-dependent response of the brain tissue to further improve the bio-fidelity and injury predictive capability of the model. The parameters representing the material were optimized by comparing model responses to seven experimentally reported strain responses of brains of postmortem human subjects (PMHS) subjected to head impact. The head model was subjected to rigorous validation against experimental data on force–deflection responses in the skull and face, intracranial pressure, and brain strain responses from over 34 PMHS head impact experiments. Crash-induced injury indices (CIIs) for facial bone fracture, skull fracture, cerebral contusion, acute subdural hematomas (ASDHs), and diffuse brain injury were developed by reconstructing 32 PMHS and real-world injury cases with the model. Model predicted maximum principal strain (MPS) and stress were determined as fracture CIIs for compact bone and spongy bones, respectively, in the skull and face. Brain responses in terms of MPS, MPS rates, and pressure distribution in injury producing experimental impacts were determined using the model and analyzed with logistic regression and survival analysis to develop CIIs for brain contusions, diffuse brain injuries, and ASDH. The statistical models using logistic regression and survival analysis showed high accuracy with area under the receiver operating curve greater than 0.8. Because of lack of sufficient moderate diffuse brain injury data, a statistical model was not created, but all indications are that the MPS rate is an essential brain response that discriminates between moderate and severe brain injuries. The authors stated that the current GHBMC M50 v.6.0 is an advanced tool for injury prediction and mitigation of injuries in automotive crashes, sports, recreational, and military environments.

Insights into Infusion-Based Targeted Drug Delivery in the Brain: Perspectives, Challenges and Opportunities

Targeted drug delivery in the brain is instrumental in the treatment of lethal brain diseases, such as glioblastoma multiforme, the most aggressive primary central nervous system tumour in adults. Infusion-based drug delivery techniques, which directly administer to the tissue for local treatment, as in convection-enhanced delivery (CED), provide an important opportunity; however, poor understanding of the pressure-driven drug transport mechanisms in the brain has hindered its ultimate success in clinical applications. In this review, we focus on the biomechanical and biochemical aspects of infusion-based targeted drug delivery in the brain and look into the underlying molecular level mechanisms. We discuss recent advances and challenges in the complementary field of medical robotics and its use in targeted drug delivery in the brain. A critical overview of current research in these areas and their clinical implications is provided. This review delivers new ideas and perspectives for further studies of targeted drug delivery in the brain.

A Machine Learning Approach to Investigate the Uncertainty of Tissue-Level Injury Metrics for Cerebral Contusion

Controlled cortical impact (CCI) on porcine brain is often utilized to investigate the pathophysiology and functional outcome of focal traumatic brain injury (TBI), such as cerebral contusion (CC). Using a finite element (FE) model of the porcine brain, the localized brain strain and strain rate resulting from CCI can be computed and compared to the experimentally assessed cortical lesion. This way, tissue-level injury metrics and corresponding thresholds specific for CC can be established. However, the variability and uncertainty associated with the CCI experimental parameters contribute to the uncertainty of the provoked cortical lesion and, in turn, of the predicted injury metrics. Uncertainty quantification via probabilistic methods (Monte Carlo simulation, MCS) requires a large number of FE simulations, which results in a time-consuming process. Following the recent success of machine learning (ML) in TBI biomechanical modeling, we developed an artificial neural network as surrogate of the FE porcine brain model to predict the brain strain and the strain rate in a computationally efficient way. We assessed the effect of several experimental and modeling parameters on four FE-derived CC injury metrics (maximum principal strain, maximum principal strain rate, product of maximum principal strain and strain rate, and maximum shear strain). Next, we compared the in silico brain mechanical response with cortical damage data from in vivo CCI experiments on pig brains to evaluate the predictive performance of the CC injury metrics. Our ML surrogate was capable of rapidly predicting the outcome of the FE porcine brain undergoing CCI. The now computationally efficient MCS showed that depth and velocity of indentation were the most influential parameters for the strain and the strain rate-based injury metrics, respectively. The sensitivity analysis and comparison with the cortical damage experimental data indicate a better performance of maximum principal strain and maximum shear strain as tissue-level injury metrics for CC. These results provide guidelines to optimize the design of CCI tests and bring new insights to the understanding of the mechanical response of brain tissue to focal traumatic brain injury. Our findings also highlight the potential of using ML for computationally efficient TBI biomechanics investigations.

Mechanical properties of whole-body soft human tissues: a review

The mechanical properties of soft tissues play a key role in studying human injuries and their mitigation strategies. While such properties are indispensable for computational modelling of biological systems, they serve as important references in loading and failure experiments, and also for the development of tissue simulants. To date, experimental studies have measured the mechanical properties of peripheral tissues (e.g. skin)in-vivoand limited internal tissuesex-vivoin cadavers (e.g. brain and the heart). The lack of knowledge on a majority of human tissues inhibit their study for applications ranging from surgical planning, ballistic testing, implantable medical device development, and the assessment of traumatic injuries. The purpose of this work is to overcome such challenges through an extensive review of the literature reporting the mechanical properties of whole-body soft tissues from head to toe. Specifically, the available linear mechanical properties of all human tissues were compiled. Non-linear biomechanical models were also introduced, and the soft human tissues characterized using such models were summarized. The literature gaps identified from this work will help future biomechanical studies on soft human tissue characterization and the development of accurate medical models for the study and mitigation of injuries.

Microscale characterisation of the time-dependent mechanical behaviour of brain white matter

Brain mechanics is a topic of deep interest because of the significant role of mechanical cues in both brain function and form. Specifically, capturing the heterogeneous and anisotropic behaviour of cerebral white matter (WM) is extremely challenging and yet the data on WM at a spatial resolution relevant to tissue components are sparse. To investigate the time-dependent mechanical behaviour of WM, and its dependence on local microstructural features when subjected to small deformations, we conducted atomic force microscopy (AFM) stress relaxation experiments on corpus callosum (CC), corona radiata (CR) and fornix (FO) of fresh ovine brain. Our experimental results show a dependency of the tissue mechanical response on axons orientation, with e.g. the stiffness of perpendicular and parallel samples is different in all three regions of WM whereas the relaxation behaviour is different for the CC and FO regions. An inverse modelling approach was adopted to extract Prony series parameters of the tissue components, i.e. axons and extra cellular matrix with its accessory cells, from experimental data. Using a bottom-up approach, we developed analytical and FEA estimates that are in good agreement with our experimental results. Our systematic characterisation of sheep brain WM using a combination of AFM experiments and micromechanical models provide a significant contribution for predicting localised time-dependent mechanics of brain tissue. This information can lead to more accurate computational simulations, therefore aiding the development of surgical robotic solutions for drug delivery and accurate tissue mimics, as well as the determination of criteria for tissue injury and predict brain development and disease progression.

The effect of fiber-matrix interaction on the kinking instability arising in the torsion of stretched fibrous biofilaments

The response of fibrous soft tissues undergoing torsional deformations is a topic of current interest. Such deformations are common in ligaments and tendons and are also of particular interest in cardiac mechanics. The problem of torsion superimposed on extension of incompressible hyperelastic solid circular cylinders is a classic problem of nonlinear elasticity that has been considered by many authors in the context of rubber elasticity particularly for isotropic materials. A striking feature of such problems is the instability that arises with sufficiently large twist where a kink and then a knot suddenly appears. An energy approach to examining this instability when the extension and twist are prescribed was described by Gent and Hua (2004) and illustrated there for a neo-Hookean isotropic elastic material. The theoretical results were compared with experimental observations on natural rubber rods. Murphy (2015) has shown that the approach of Gent and Hua (2004) for isotropic materials can be simplified when the rods are assumed to be thin and this theory was applied to transversely isotropic materials by Horgan and Murphy (2016). In contrast with the case for isotropic materials, it was shown there that the kinking instability occurs even in the absence of stretch, i.e., for the case of pure torsion. Here we are concerned with the implications of this simplified thin rod instability theory for fiber-reinforced transversely isotropic materials that reflect fiber-matrix interaction. It is again shown that the kinking instability occurs even in the absence of stretch, i.e., for the case of pure torsion. The results are illustrated for a specific strain-energy density function that models fiber-matrix interaction. It is shown that the critical twist at which kinking occurs decreases as a measure of fiber-matrix interaction is increased so that the fiber-matrix interaction has a destabilizing effect. The results are illustrated using experimental data of other authors for skeletal muscles and for porcine brain white matter tissue.

Compression and tension behavior of the prosthetic foam materials polyurethane, EVA, Pelite™ and a combination of polyurethane and EVA: a preliminary study

Materials with low-strength and low-impedance properties, such as elastomers and polymeric foams are major contributors to prosthetic liner design. Polyethylene-Light (Pelite™) is a foam liner that is the most frequently used in prosthetics but it does not cater to all amputees' limb and skin conditions. The study aims to investigate the newly modified Foam Liner, a combination of two different types of foams (EVA + PU + EVA) as the newly modified Foam Liner in terms of compressive and tensile properties in comparison to Pelite™, polyurethane (PU) foam, and ethylene-vinyl acetate (EVA) foam. Universal testing machine (AGS-X, Shimadzu, Kyoto, Japan) has been used to measure the tensile and compressive stress. Pelite™ had the highest compressive stress at 566.63 kPa and tensile stress at 1145 kPa. Foam Liner fell between EVA and Pelite™ with 551.83 kPa at compression and 715.40 kPa at tension. PU foam had the lowest compressive stress at 2.80 kPa and tensile stress at 33.93 kPa. Foam Liner has intermediate compressive elasticity but has high tensile elasticity compared to EVA and Pelite™. Pelite™ remains the highest in compressive and tensile stiffness. Although it is good for amputees with bony prominence, constant pressure might result in skin breakdown or ulcer. Foam Liner would be the best for amputees with soft tissues on the residual limbs to accommodate movement.

The importance of axonal directions in the brainstem injury during neurosurgical interventions

Brainstem, which connects the distal part of the brain and the spinal cord, contains main motor and sensory nerves and facilitates communication between the cerebrum, cerebellum, and spinal cord. Due to the complicated anatomy and neurostructure of brainstem, surgical interventions to resect brainstem tumors are particularly challenging, and new approaches to reduce the risk of surgical brain injury are of utmost importance. Although previous studies have investigated the structural anisotropy of brain white matter, the effect of axonal fibers on the mechanical properties of white matter has not yet been fully understood. The current study aims to compare the effect of axonal orientation on changes in material properties of brainstem under large deformations and failure through a novel approach. Using diffusion tensor imaging (DTI) on ex-vivo bovine brains, we determined the orientation of axons in brainstem. We extracted brainstem samples in two orthogonal directions, parallel and perpendicular to the axons, and subjected to uniaxial tension to reach the failure at loading rates of 50 mm/min and 150 mm/min. The results showed that the tearing energy and failure strain of samples with axons parallel to the force direction were approximately 1.5 times higher than the samples with axons perpendicular to the force direction. The results also revealed that as the sample's initial length increases, its failure strain decreases. These results emphasize the importance of the axon orientation in the mechanical properties of brainstem, and suggest that considering the directional-dependent behavior for this tissue could help to propose new surgical interventions for reducing the risk of injury during tumor resection.

Multi-physics modeling and finite element formulation of corneal UV cross-linking

The UV cross-linking technique applied to the cornea is a popular and effective therapy for eye diseases such as keratoconus and ectatic disorders. The treatment strengthens the cornea by forming new cross-links via photochemical reactions and, in turn, prevents the disease from further developing. To better understand and capture the underlying mechanisms, we develop a multi-physics model that considers the migration of the riboflavin (i.e., the photo-initializer), UV light absorption, the photochemical reaction that forms the cross-links, and biomechanical changes caused by changes to the microstructure. Our model is calibrated to a set of nanoindentation tests on UV cross-linked corneas from the literature. Additionally, we implement our multi-physics model numerically into a commercial finite element software. We also compare our simulation against a set of inflation tests from the literature. The simulation capability allows us to make quantitative predictions of a therapy's outcomes in full 3-D, based on the actual corneal geometry; it also helps medical practitioners with surgical planning.

Analyzing Liver Surface Indentation for In Vivo Refinement of Tumor Location in Minimally Invasive Surgery

Manual palpation to update the position of subsurface tumor(s) is a normal practice in open surgery, but is not possible through the small incisions of minimally invasive surgery (MIS). This paper proposes a method that has the potential to use a simple constant-force indenter and the existing laparoscopic camera for tumor location refinement in MIS. The indenter floats with organ movement to generate a static surface deformation on the soft tissue, resolving problems of previous studies that require complicated measurement of force and displacement during indentation. By analyzing the deformation profile, we can intraoperatively update the tumor's location in real-time. Indentation experiments were conducted on healthy and "diseased" porcine liver specimens to obtain the deformation surrounding the indenter site. An inverse finite element (FE) algorithm was developed to determine the optimal material parameters of the healthy liver tissue. With these parameters, a computational model of tumorous tissue was constructed to quantitatively evaluate the effects of the tumor location on the induced deformation. By relating the experimental data from the "diseased" liver specimen to the computational results, we estimated the radial distance between the tumor and the indenter, as well as the angular position of the tumor relative to the indenter.

An anatomically detailed and personalizable head injury model: Significance of brain and white matter tract morphological variability on strain

Finite element head (FE) models are important numerical tools to study head injuries and develop protection systems. The generation of anatomically accurate and subject-specific head models with conforming hexahedral meshes remains a significant challenge. The focus of this study is to present two developmental works: first, an anatomically detailed FE head model with conforming hexahedral meshes that has smooth interfaces between the brain and the cerebrospinal fluid, embedded with white matter (WM) fiber tracts; second, a morphing approach for subject-specific head model generation via a new hierarchical image registration pipeline integrating Demons and Dramms deformable registration algorithms. The performance of the head model is evaluated by comparing model predictions with experimental data of brain-skull relative motion, brain strain, and intracranial pressure. To demonstrate the applicability of the head model and the pipeline, six subject-specific head models of largely varying intracranial volume and shape are generated, incorporated with subject-specific WM fiber tracts. DICE similarity coefficients for cranial, brain mask, local brain regions, and lateral ventricles are calculated to evaluate personalization accuracy, demonstrating the efficiency of the pipeline in generating detailed subject-specific head models achieving satisfactory element quality without further mesh repairing. The six head models are then subjected to the same concussive loading to study the sensitivity of brain strain to inter-subject variability of the brain and WM fiber morphology. The simulation results show significant differences in maximum principal strain and axonal strain in local brain regions (one-way ANOVA test, p < 0.001), as well as their locations also vary among the subjects, demonstrating the need to further investigate the significance of subject-specific models. The techniques developed in this study may contribute to better evaluation of individual brain injury and the development of individualized head protection systems in the future. This study also contains general aspects the research community may find useful: on the use of experimental brain strain close to or at injury level for head model validation; the hierarchical image registration pipeline can be used to morph other head models, such as smoothed-voxel models.

The effect of fiber-matrix interaction on the Poynting effect for torsion of fibrous soft biomaterials

The response of fibrous soft tissues undergoing torsional deformations is a topic of considerable current interest. Such deformations are common in ligaments and tendons and are also of particular interest in cardiac mechanics. A well-known context where such issues arise is in understanding the mechanical response of papillary muscles of the heart. Thus the classical torsion problem for solid or hollow cylinders composed of rubber-like materials has received renewed recent attention in the context of anisotropic materials. Here we consider the torsion of a solid circular cylinder composed of a transversely isotropic incompressible fiber-reinforced hyperelastic material. The focus of the work is on examining the effect of fiber-matrix interaction on the axial stress response with emphasis on the Poynting effect. The classic Poynting effect for isotropic rubber-like materials where torsion induces elongation of the cylinder is shown to be significantly different for the transversely isotropic models considered here. For sufficiently small total angles of twist, well within the range of physiological response, a reverse-Poynting effect is shown to hold where the cylinder tends to shorten on twisting while for larger angles of twist, the usual positive Poynting effect occurs. It is shown that the influence of the fiber-matrix interaction is to enhance the reverse Poynting effect. The results are illustrated using experimental data of other authors for skeletal muscles and for brain white matter.

The effect of large deformation on Poisson's ratio of brain white matter: An experimental study

A more Accurate description of the mechanical behavior of brain tissue could improve the results of computational models. While most studies have assumed brain tissue as an incompressible material with constant Poisson's ratio of almost 0.5 and constructed their modeling approach according to this assumption, the relationship between this ratio and levels of applied strains has not yet been studied. Since the mechanical response of the tissue is highly sensitive to the value of Poisson's ratio, this study was designed to investigate the characteristics of the Poisson's ratio of brain tissue at different levels of applied strains. Samples were extracted from bovine brain tissue and tested under unconfined compression at strain values of 5%, 10%, and 30%. Using an image processing method, the axial and transverse strains were measured over a 60-s period to calculate the Poisson's ratio for each sample. The results of this study showed that the Poisson's ratio of brain tissue at strain levels of 5% and 10% was close to 0.5, and assuming brain tissue as an incompressible material is a valid assumption at these levels of strain. For samples under 30% compression, this ratio was higher than 0.5, which could suggest that under strains higher than the brain injury threshold (approximately 18%), tissue integrity was impaired. Based on these observations, it could be concluded that for strain levels higher than the injury threshold, brain tissue could not be assumed as an incompressible material, and new material models need to be proposed to predict the material behavior of the tissue. In addition, the results showed that brain tissue under unconfined compression uniformly stretched in the transverse direction, and the bulging in the samples is negligible.

Dynamic mechanical characterization and viscoelastic modeling of bovine brain tissue

Brain tissue is vulnerable and sensitive, predisposed to potential damage under various conditions of mechanical loading. Although its material properties have been investigated extensively, the frequency-dependent viscoelastic characterization is currently limited. Computational models can provide a non-invasive method by which to analyze brain injuries and predict the mechanical response of the tissue. The brain injuries are expected to be induced by dynamic loading, mostly in compression and measurement of dynamic viscoelastic properties are essential to improve the accuracy and variety of finite element simulations on brain tissue. Thus, the aim of this study was to investigate the compressive frequency-dependent properties of brain tissue and present a mathematical model in the frequency domain to capture the tissue behavior based on experimental results. Bovine brain specimens, obtained from four locations of corona radiata, corpus callosum, basal ganglia and cortex, were tested under compression using dynamic mechanical analysis over a range of frequencies between 0.5 and 35 Hz to characterize the regional and directional response of the tissue. The compressive dynamic properties of bovine brain tissue were heterogenous for regions but not sensitive to orientation showing frequency dependent statistical results, with viscoelastic properties increasing with frequency. The mean storage and loss modulus were found to be 12.41 kPa and 5.54 kPa, respectively. The material parameters were obtained using the linear viscoelastic model in the frequency domain and the numeric simulation can capture the compressive mechanical behavior of bovine brain tissue across a range of frequencies. The frequency-dependent viscoelastic characterization of brain tissue will improve the fidelity of the computational models of the head and provide essential information to the prediction and analysis of brain injuries in clinical treatments.

An anatomically detailed and personalizable head injury model: Significance of brain and white matter tract morphological variability on strain

Finite element head (FE) models are important numerical tools to study head injuries and develop protection systems. The generation of anatomically accurate and subject-specific head models with conforming hexahedral meshes remains a significant challenge. The focus of this study is to present two developmental works: first, an anatomically detailed FE head model with conforming hexahedral meshes that has smooth interfaces between the brain and the cerebrospinal fluid, embedded with white matter (WM) fiber tracts; second, a morphing approach for subject-specific head model generation via a new hierarchical image registration pipeline integrating Demons and Dramms deformable registration algorithms. The performance of the head model is evaluated by comparing model predictions with experimental data of brain-skull relative motion, brain strain, and intracranial pressure. To demonstrate the applicability of the head model and the pipeline, six subject-specific head models of largely varying intracranial volume and shape are generated, incorporated with subject-specific WM fiber tracts. DICE similarity coefficients for cranial, brain mask, local brain regions, and lateral ventricles are calculated to evaluate personalization accuracy, demonstrating the efficiency of the pipeline in generating detailed subject-specific head models achieving satisfactory element quality without further mesh repairing. The six head models are then subjected to the same concussive loading to study the sensitivity of brain strain to inter-subject variability of the brain and WM fiber morphology. The simulation results show significant differences in maximum principal strain and axonal strain in local brain regions (one-way ANOVA test, p < 0.001), as well as their locations also vary among the subjects, demonstrating the need to further investigate the significance of subject-specific models. The techniques developed in this study may contribute to better evaluation of individual brain injury and the development of individualized head protection systems in the future. This study also contains general aspects the research community may find useful: on the use of experimental brain strain close to or at injury level for head model validation; the hierarchical image registration pipeline can be used to morph other head models, such as smoothed-voxel models.

Structural Anisotropy vs. Mechanical Anisotropy: The Contribution of Axonal Fibers to the Material Properties of Brain White Matter

Brain's micro-structure plays a critical role in its macro-structure material properties. Since the structural anisotropy in the brain white matter has been introduced due to axonal fibers, considering the direction of axons in the continuum models has been mediated to improve the results of computational simulations. The aim of the current study was to investigate the role of fiber direction in the material properties of brain white matter and compare the mechanical behavior of the anisotropic white matter and the isotropic gray matter. Diffusion tensor imaging (DTI) was employed to detect the direction of axons in white matter samples, and tensile stress-relaxation loads up to 20% strains were applied on bovine gray and white matter samples. In order to calculate the nonlinear and time-dependent properties of white matter and gray matter, a visco-hyperelastic model was used. The results indicated that the mechanical behavior of white matter in two orthogonal directions, parallel and perpendicular to axonal fibers, are significantly different. This difference indicates that brain white matter could be assumed as an anisotropic material and axons have contribution in the mechanical properties. Also, up to 15% strain, white matter samples with axons parallel to the force direction are significantly stiffer than both the gray matter samples and white matter samples with axons perpendicular to the force direction. Moreover, the elastic moduli of white matter samples with axons both parallel and perpendicular to the loading direction and gray matter samples at 15-20% strain are not significantly different. According to these observations, it is suggested that axons have negligible roles in the material properties of white matter when it is loaded in the direction perpendicular to the axon direction. Finally, this observation showed that the anisotropy of brain tissue not only has effects on the elastic behavior, but also has effects on the viscoelastic behavior.

Experimental study of the Poynting effect in a soft unidirectional fiber-reinforced material under simple shear

The aim of this work was to investigate the shear and lateral normal responses of a soft unidirectional fiber-reinforced material subjected to simple shear. The Poynting effect was also investigated. Soft composites were manufactured from a flexible adhesive reinforced by a single family of parallel and continuous fibers of nylon. Specimens with fibers oriented at an angle (-45°, 0°, 45° and 90°) with respect to the applied shear force were tested. A simple shear test apparatus was developed to measure shear and normal forces simultaneously. A standard reinforcing model based on strain-energy density function was used to verify the mechanical behavior of the soft composite with different fiber orientation. Results showed that the initial stiffness of the composite with fibers oriented at -45° and 45° was approximately the same and was higher than those at 0° and 90°. Also, there was no significant difference between values of initial stiffness for angles of 0° and 90° and the neat matrix. The effect of the stretching resistance of the fibers was more pronounced for fibers oriented at 45° and 90°. There was no Poynting effect for the neat matrix or for the composite with fibers at 0° while positive and negative Poynting effects were observed for fibers oriented at -45° and 45° (and 90°), respectively. The standard reinforcing model was only verified for a limited range of amount of shear due to composite failure. Fiber debonding and fiber buckling were observed in the composites with fibers oriented at 45° (and 90°) and -45°, respectively, at large deformations.

Visco-hyperelastic characterization of human brain white matter micro-level constituents in different strain rates

In this study, we propose a computational characterization technique for obtaining the material properties of axons and extracellular matrix (ECM) in human brain white matter. To account for the dynamic behavior of the brain tissue, data from time-dependent relaxation tests of human brain white matter in different strain rates are extracted and formulated by a visco-hyperelastic constitutive model consisting of the Ogden hyperelastic model and the Prony series expansion. Through micromechanical finite element simulation, a derivative-free optimization framework designed to minimize the difference between the numerical and experimental data is used to identify the material properties of the axons and ECM. The Prony series expansion parameters of axons and ECM are found to be highly affected by the Prony series expansion coefficients of the brain white matter. The optimal parameters of axons and ECM are verified through micromechanical simulation by comparing the averaged numerical response with that of the experimental data. Moreover, the initial shear modulus and the reduced shear modulus of the axons are found for different strain rates of 0.0001, 0.01, and 1 s^-1. Consequently, first- and second-order regressions are used to find relations for the prediction of the shear modulus at the intermediate strain rates. Graphical Abstract The applied procedure for characterization of brain white matter micro-level constituents. The macro-level experimental data in different strain rates are used in the context of simulation-based optimization to obtain the properties of axons and extracellular matrix material.

A pilot in silico modeling-based study of the pathological effects on the biomechanical function of tricuspid valves

Current clinical assessment of functional tricuspid valve regurgitation relies on metrics quantified from medical imaging modalities. Although these clinical methodologies are generally successful, the lack of detailed information about the mechanical environment of the valve presents inherent challenges for assessing tricuspid valve regurgitation. In the present study, we have developed a finite element-based in silico model of one porcine tricuspid valve (TV) geometry to investigate how various pathological conditions affect the overall biomechanical function of the TV. There were three primary observations from our results. Firstly, the results of the papillary muscle (PM) displacement study scenario indicated more pronounced changes in the TV biomechanical function. Secondly, compared to uniform annulus dilation, nonuniform dilation scenario induced more evident changes in the von Mises stresses (83.8-125.3 kPa vs 65.1-84.0 kPa) and the Green-Lagrange strains (0.52-0.58 vs 0.47-0.53) for the three TV leaflets. Finally, results from the pulmonary hypertension study scenario showed opposite trends compared to the PM displacement and annulus dilation scenarios. Furthermore, various chordae rupture scenarios were simulated, and the results showed that the chordae tendineae attached to the TV anterior and septal leaflets may be more critical to proper TV function. This in silico modeling-based study has provided a deeper insight into the tricuspid valve pathologies that may be useful, with moderate extensions, for guiding clinical decisions. NOVELTY STATEMENT: The novelties of the research are summarized below: A comprehensive in silico pilot study of how isolated functional tricuspid regurgitation pathologies and ruptured chordae tendineae would alter the tricuspid valve function; An extensive analysis of the tricuspid valve function, including mechanical quantities (eg, the von Mises stress and the Green-Lagrange strain) and clinically-relevant geometry metrics (eg, the tenting area and the coaptation height); and A developed computational modeling pipeline that can be extended to evaluate patient-specific tricuspid valve geometries and enhance the current clinical diagnosis and treatment of tricuspid regurgitation.

Tension Strain-Softening and Compression Strain-Stiffening Behavior of Brain White Matter

Brain, the most important component of the central nervous system (CNS), is a soft tissue with a complex structure. Understanding the role of brain tissue microstructure in mechanical properties is essential to have a more profound knowledge of how brain development, disease, and injury occur. While many studies have investigated the mechanical behavior of brain tissue under various loading conditions, there has not been a clear explanation for variation reported for material properties of brain tissue. The current study compares the ex-vivo mechanical properties of brain tissue under two loading modes, namely compression and tension, and aims to explain the differences observed by closely examining the microstructure under loading. We tested bovine brain samples under uniaxial tension and compression loading conditions, and fitted hyperelastic material parameters. At 20% strain, we observed that the shear modulus of brain tissue in compression is about 6 times higher than in tension. In addition, we observed that brain tissue exhibited strain-stiffening in compression and strain-softening in tension. In order to investigate the effect of loading modes on the tissue microstructure, we fixed the samples using a novel method that enabled keeping the samples at the loaded stage during the fixation process. Based on the results of histology, we hypothesize that during compressive loading, the strain-stiffening behavior of the tissue could be attributed to glial cell bodies being pushed against surroundings, contacting each other and resisting compression, while during tension, cell connections are detached and the tissue displays softening behavior.

A knowledge map analysis of brain biomechanics: Current evidence and future directions

Although brain, one of the most complex organs in the mammalian body, has been subjected to many studies from physiological and pathological points of view, there remain significant gaps in the available knowledge regarding its biomechanics. This article reviews the research trends in brain biomechanics with a focus on injury. We used published scientific articles indexed by Web of Science database over the past 40 years and tried to address the gaps that still exist in this field. We analyzed the data using VOSviewer, which is a software tool designed for scientometric studies. The results of this study showed that the response of brain tissue to external forces has been one of the significant research topics among biomechanicians. These studies have addressed the effects of mechanical forces on the brain and mechanisms of traumatic brain injury, as well as characterized changes in tissue behavior under trauma and other neurological diseases to provide new diagnostic and monitoring methods. In this study, some challenges in the field of brain injury biomechanics have been identified and new directions toward understanding the gaps in this field are suggested.

Multi-Excitation Magnetic Resonance Elastography of the Brain: Wave Propagation in Anisotropic White Matter

Magnetic resonance elastography (MRE) has emerged as a sensitive imaging technique capable of providing a quantitative understanding of neural microstructural integrity. However, a reliable method for the quantification of the anisotropic mechanical properties of human white matter is currently lacking, despite the potential to illuminate the pathophysiology behind neurological disorders and traumatic brain injury. In this study, we examine the use of multiple excitations in MRE to generate wave displacement data sufficient for anisotropic inversion in white matter. We show the presence of multiple unique waves from each excitation which we combine to solve for parameters of an incompressible, transversely isotropic (ITI) material: shear modulus, μ, shear anisotropy, ϕ, and tensile anisotropy, ζ. We calculate these anisotropic parameters in the corpus callosum body and find the mean values as μ = 3.78 kPa, ϕ = 0.151, and ζ = 0.099 (at 50 Hz vibration frequency). This study demonstrates that multi-excitation MRE provides displacement data sufficient for the evaluation of the anisotropic properties of white matter.

An indentation-based approach to determine the elastic constants of soft anisotropic tissues

Characterization of the mechanical properties of tissue can help to understand tissue mechanobiology, including disease diagnosis and progression. Indentation is increasingly used to measure the local mechanical properties of tissue, but it has not been fully adapted to capture anisotropic properties. This paper presents an indentation-based method to measure elastic constants of soft anisotropic tissues without additional mechanical tests. The approach uses measurement of the indentation modulus and the aspect ratio of the elliptical contact introduced by anisotropic mechanical properties of tissue to determine the elastic constants from finite element analysis. The imprinted area imparted by a fluorescent bead-coated spherical indenter showed the aspect ratio of the contact area, giving a generalized sense of the level of anisotropy, and instrumented indentation determined the indentation modulus. A parametric study using finite element simulation of the indentation tests established the relationship between the aspect ratio of contact and the non-dimensional ratios, E_x/E_y and G_xy/E_y; here, E_x and E_y are the Young's moduli (E_x > E_y) and G_xy is the shear modulus in the xy plane. For strongly anisotropic materials (E_x/E_y > 150), aspect ratio and indentation modulus are sufficient to determine G_xy and E_y. For weakly anisotropic materials, indentation modulus in the transverse direction, E_y, and the aspect ratio of contact in the anisotropic plane can be used to determine the elastic constants. The proposed approach improves the elastic characterization of soft, anisotropic biological materials from indentation and helps to elucidate the complex mechanical behavior of soft anisotropic tissues.

Determining constitutive behavior of the brain tissue using digital image correlation and finite element modeling

Detailed knowledge about the mechanical properties of brain can improve numerical modeling of the brain under various loading conditions. The success of this modeling depends on constitutive model and reliable extraction of its material constants. The isotropy of the brain tissue is a key factor which affects the form of constitutive models. In this study, compression tests were performed on different parts of the sheep brain tissue. Also, the digital image correlation (DIC) method was utilized to investigate the direction dependency of brain parts considering their microstructures. To this aim, the DIC method was employed to measure the transverse strain of two lateral sides of the tissue samples. The results of DIC method revealed that the brain stem and corona radiata were isotropic, while the mixed white and gray matter showed an unrepeatable behavior depending on the extracted sample. To examine and validate DIC method, stress-strain diagrams were also used to investigate the isotropy. It could be concluded that axonal fibers had no reinforcing role in the brain tissue. Furthermore, the DIC method indicated incompressibility of the brain tissue. Then, the significance of using a correct method to extract the material constants of brain was discussed. In other words, the effect of the real boundary conditions in experiments, which was neglected in most previous studies, was taken into account here. Finally, the particle swarm optimization algorithm along with the finite element modeling was used to estimate the hyper-viscoelastic constants of different parts of the brain tissue.

A Non-Linear Model of an All-Elastomer, in-Plane, Capacitive, Tactile Sensor Under the Application of Normal Forces

In this work, a large deformation, non-linear semi-analytical model for an all-elastomer, capacitive tactile unit-sensor is developed. The model is capable of predicting the response of such sensors over their entire sensing range under the application of normal forces. In doing so the finite flat punch indentation model developed earlier is integrated with a capacitance model to predict the change-in-capacitance as a function of applied normal forces. The empirical change-in-capacitance expression, based on the parallel plate capacitance model, is developed to account for the fringe field and saturation effects. The elastomeric layer used as a substrate in these sensors is modeled as an incompressible, non-linear, hyperelastic material. More specifically, the two term Mooney-Rivlin strain energy function is used as a constitutive response to relate the stresses and strains. The developed model assumes both geometrical as well as material non-linearity. Based on the related experimental work presented elsewhere, the inverse analysis, combining finite element (FE) modeling and non-linear optimization, is used to obtain the Mooney-Rivlin material parameters. Finally, to validate the model developed herein the model predictions are compared to the experimental results obtained elsewhere for four different tactile sensors. Great agreements are found to exist between the two which shows the model capabilities in capturing the response of these sensors. The model and methodologies developed in this work, may also help advancing bio-material studies in the determination of biological tissue properties.

Nonlinear Biomechanical Characteristics of the Schneiderian Membrane: Experimental Study and Numerical Modeling

Objective

The aim of this study is to quantify the nonlinear mechanical behavior of the Schneiderian membrane.

Methods

Thirty cadaveric maxillary sinus membrane specimens were divided into the elongation testing group and the perforation testing group. Mechanical experimental measurements were taken via ex vivo experiments. Theoretical curves were compared with experimental findings to assess the effectiveness of the nonlinear mechanical properties. The FE model with nonlinear mechanical properties was used to simulate the detachment of the Schneiderian membrane under loading.

Results

The mean thickness of the membrane samples was 1.005 mm. The mean tensile strength obtained by testing was 6.81 N/mm². In membrane perforation testing, the mean tensile strength and the linear elastic modulus were significantly higher than those in membrane elongation testing (P < 0.05). The mean adhesion force between the Schneiderian membrane and the bone was 0.052 N/mm. By FE modeling, the squared correlation coefficients of theoretical stress-strain curves for the nonlinear and linear models were 0.99065 and 0.94656 compared with the experimental data.

Conclusions

The biomechanical properties of the Schneiderian membrane were implemented into the FE model, which was applied to simulate the mechanical responses of the Schneiderian membrane in sinus floor elevation.

Material properties of the brain in injury-relevant conditions - Experiments and computational modeling

Material properties of the brain have been extensively studied but remain poorly characterized. The vast variations in constitutive models and material constants are well documented. However, no study exists to translate the variations into disparities in impact-induced brain strains most relevant to brain injury. Here, we reviewed a subset of injury-relevant brain material properties either characterized in experiments or adopted in recent head injury models. To highlight how variations in measured brain material properties manifested in simulated brain strains, we selected six experiments that have provided a complete set of brain material model and constants to implement a common head injury model. Responses resulting from two extreme events representing a high-rate cadaveric head impact and a low-rate in vivo head rotation, respectively, varied substantially. We hypothesized, and further confirmed, that the time-varying shear moduli at the appropriate time scales (e.g., ~5 ms and ~40 ms corresponding to the impulse durations of the major acceleration peaks for the two impacts, respectively), rather than the initial or long-term shear moduli, were the most indicative of impact-induced brain strains. These results underscored the need to implement measured brain material properties into an actual head injury model for evaluation. They may also provide guidelines to better characterize brain material properties in future experiments and head injury models. Finally, our finding provided a practical solution to satisfy head injury model validation requirements at both ends of the impact severity spectrum. This would improve the confidence in model simulation performance across a range of time scales relevant to concussion and sub-concussion in the real-world.

A novel method for rapid and quantitative mechanical assessment of soft tissue for diagnostic purposes: A computational study

Biological tissues often experience drastic changes in their microstructure due to their pathophysiological conditions. Such microstructural changes could result in variations in mechanical properties, which can be used in diagnosing or monitoring a wide range of diseases, most notably cancer. This paves the avenue for non-invasive diagnosis by instrumented palpation although challenges remain in quantitatively assessing the amount of diseased tissue by means of mechanical characterization. This paper presents a framework for tissue diagnosis using a quantitative and efficient estimation of the fractions of cancerous and non-cancerous tissue without a priori knowledge of tissue microstructure. First, the sample is tested in a creep or stress relaxation experiment, and the behavior is characterized using a single term Prony series. A rule of mixtures, which relates tumor fraction to the apparent mechanical properties, is then obtained by minimizing the difference between strain energy of a heterogeneous system and an equivalent homogeneous one. Finally, the percentage of each tissue constituent is predicted by comparing the observed relaxation time with that calculated from the rule of mixtures. The proposed methodology is assessed using models reconstructed from histological samples and magnetic resonance imaging of prostate. Results show that estimation of cancerous tissue fraction can be obtained with a maximum error of 12% when samples of different sizes, geometries, and tumor fractions are presented. The proposed framework has the potential to be applied to a wide range of diseases such as rectal polyps, cirrhosis, or breast and prostate cancer whose current primary diagnosis remains qualitative.

Measurement of anisotropic mechanical properties in porcine brain white matter ex vivo using magnetic resonance elastography

The mechanical properties of brain tissue, particularly those of white matter (WM), need to be characterized accurately for use in finite element (FE) models of brain biomechanics and traumatic brain injury (TBI). Magnetic resonance elastography (MRE) is a powerful tool for non-invasive estimation of the mechanical properties of soft tissues. While several studies involving direct mechanical tests of brain tissue have shown mechanical anisotropy, most MRE studies of brain tissue assume an isotropic model. In this study, an incompressible transversely isotropic (TI) material model parameterized by minimum shear modulus (μ₂), shear anisotropy parameter (ϕ), and tensile anisotropy parameter (ζ) is applied to analyze MRE measurements of ex vivo porcine white matter (WM) brain tissue. To characterize shear anisotropy, "slow" (pure transverse) shear waves were propagated at 100, 200 and 300Hz through sections of ex vivo brain tissue including both WM and gray matter (GM). Shear waves were found to propagate with elliptical fronts, consistent with TI material behavior. Shear wave fields were also analyzed within regions of interest (ROI) to find local shear wavelengths parallel and perpendicular to fiber orientation. FE simulations of a TI material with a range of plausible shear modulus (μ₂) and shear anisotropy parameters (ϕ) were run and the results were analyzed in the same fashion as the experimental case. Parameters of the FE simulations which most closely matched each experiment were taken to represent the mechanical properties of that particular sample. Using this approach, WM in the ex vivo porcine brain was found to be mildly anisotropic in shear with estimates of minimum shear modulus (actuation frequencies listed in parenthesis): μ₂= 1.04 ± 0.12 kPa (at 100Hz), μ₂= 1.94 ± 0.29 kPa (at 200Hz), and μ₂= 2.88 ± 0.34 kPa (at 300Hz) and corresponding shear anisotropy factors of ϕ= 0.27 ± 0.09 (at 100Hz), ϕ= 0.29 ± 0.14 (at 200Hz) and ϕ= 0.34 ± 0.13 (at 300Hz). Future MRE studies will focus on tensile anisotropy, which will require both slow and fast shear waves for accurate estimation.

Micromechanical analysis of brain's diffuse axonal injury

Computational models are important tools which help researchers understand traumatic brain injury (TBI). A mechanistic multi-scale numerical approach is introduced to quantify diffuse axonal injury (DAI), the most important mechanism of TBI, induced by a mechanical insult at micro-scale regions of the white matter or voxels where fiber orientations are the same. Using the mechanical properties of a single axon with a viscoelastic constitutive relation and its functional failure in terms of electrophysiological impairment, a numerical 2D micro-level lattice method is implemented to directly analyze the percentage of injured axons in a voxel containing a bundle of axons all with the same orientation under biaxial stretches. Reference micro-injury maps are then developed with the input parameters based on the principal strain or stretch values and their direction with respect to axons, which provide the percentage of injured axons in the voxel of interest as the output. The methodology is independent of any statistical analyses of the accident data and medical reports to derive probabilistic injury risk curves for DAI. Avoiding a structurally detailed full finite element head model, this study proposes a micro-mechanical approach which considers the anatomical structure of neural axons in the white matter together with their mechanical properties using a numerical lattice method to analyze the brain's diffuse axonal injury. This work has the potential to help develop safer prevention tools and more effective diagnosis methods for DAI.

Models and tissue mimics for brain shift simulations

Capturing the deformation of human brain during neurosurgical operations is an extremely important task to improve the accuracy or surgical procedure and minimize permanent damage in patients. This study focuses on the development of an accurate numerical model for the prediction of brain shift during surgical procedures and employs a tissue mimic recently developed to capture the complexity of the human tissue. The phantom, made of a composite hydrogel, was designed to reproduce the dynamic mechanical behaviour of the brain tissue in a range of strain rates suitable for surgical procedures. The use of a well-controlled, accessible and MRI compatible alternative to real brain tissue allows us to rule out spurious effects due to patient geometry and tissue properties variability, CSF amount uncertainties, and head orientation. The performance of different constitutive descriptions is evaluated using a brain-skull mimic, which enables 3D deformation measurements by means of MRI scans. Our combined experimental and numerical investigation demonstrates the importance of using accurate constitutive laws when approaching the modelling of this complex organic tissue and supports the proposal of a hybrid poro-hyper-viscoelastic material formulation for the simulation of brain shift.