Mechanical characterisation of brain tissue up to 35% strain at 1, 10, and 100/s using a custom-built micro-indentation apparatus

Computational modeling and uncertainty prediction of hyperelastic constitutive responses of damaged brain tissue under different temperature and strain rates

The effect of strain rate and temperature on the hyperelastic material stress-strain characteristics of the damaged porcine brain tissue is evaluated in this present work. The desired constitutive responses are obtained using the commercially available finite element (FE) tool ABAQUS, utilizing 8-noded brick elements. The model's accuracy has been verified by comparing the results from the previously published literature. Further, the stress-strain behavior of the brain tissue is evaluated by varying the damages at various strain rates and temperatures (13, 20, 27, and 37°C) under compression test. Additionally, the sensitivity analysis of the model is computed to check the effect of input parameters, that is, the temperature, strain rate, and damages on the material properties (shear modulus). The modeling and discussion sections enumerate the inclusive features and model capabilities.

Approach for contact medical device development via integrated testing, skeletal muscle modeling, and finite element analysis

Development of novel medical devices for the treatment of musculoskeletal pain associated with neuro-muscular trigger points requires a model for relating the mechanical responses of in vivo biological tissues to applied palliative physical pressures and a method to design treatments for optimal effects. It is reasonable to hypothesize that the efficacy of therapeutic treatment is proportional to the maximum tensile strain at trigger point locations. This work presents modeling of the mechanical behavior of biological tissue structures and treatment simulations, supported by indentation experiments and finite element (FE) modeling. The steady-state indentation responses of the tissue structure of the posterior neck were measured with a testing device, and an FE model was constructed using a first-order Ogden hyperelastic material model and calibrated with the experimental data. The error between experimental and FE-generated displacement-load curves was minimized via a two-stage optimization process comprised of an Optimal Latin Hypercube design-of-experiments analysis and a Bayesian optimization loop. The optimized Ogden model had an initial shear modulus (μ) of 5.16 kPa and a deviatoric exponent (α) of 11.90. Another FE model was developed to simulate the deformation of the tissue structures in the posterior neck adjacent to the C3 vertebrae in response to indentation loading, in order to determine the optimal location and angle to apply an indentation force for maximum therapeutic benefit. The optimal location of indentation was determined to be 28° lateral from the sagittal plane along the surface of the skin, measured from the centerline of the spine, at an angle of 8° counterclockwise from the surface normal vector. The optimized spatial orientation of the indentation corresponded to the average of the maximum principal strain across the deep muscle region of the model.

Dynamic strain fields of the mouse brain during rotation

Mouse models are used to better understand brain injury mechanisms in humans, yet there is a limited understanding of biomechanical relevance, beginning with how the murine brain deforms when the head undergoes rapid rotation from blunt impact. This problem makes it difficult to translate some aspects of diffuse axonal injury from mouse to human. To address this gap, we present the two-dimensional strain field of the mouse brain undergoing dynamic rotation in the sagittal plane. Using a high-speed camera with digital image correlation measurements of the exposed mid-sagittal brain surface, we found that pure rotations (no direct impact to the skull) of 100-200 rad/s are capable of producing complex strain fields that evolve over time with respect to rotational acceleration and deceleration. At the highest rotational velocity tested, the largest tensile strains (≥ 21% elongation) in selected regions of the mouse brain approach strain thresholds previously associated with axonal injury in prior work. These findings provide a benchmark to validate the mechanical response in biomechanical computational models predicting diffuse axonal injury, but much work remains in correlating tissue deformation patterns from computational models with underlying neuropathology.

Shear shock wave injury in vivo: High frame-rate ultrasound observation and histological assessment

Using high frame-rate ultrasound and ¡1μm sensitive motion tracking we previously showed that shear waves at the surface of ex vivo and in situ brains develop into shear shock waves deep inside the brain, with destructive local accelerations. However post-mortem tissue cannot develop injuries and has different viscoelastodynamic behavior from in vivo tissue. Here we present the ultrasonic measurement of the high-rate shear shock biomechanics in the in vivo porcine brain, and histological assessment of the resulting axonal pathology. A new biomechanical model of brain injury was developed consisting of a perforated mylar surface attached to the brain and vibrated using an electromechanical shaker. Using a custom sequence with 8 interleaved wide beam emissions, brain imaging and motion tracking were performed at 2900 images/s. Shear shock waves were observed for the first time in vivo wherein the shock acceleration was measured to be 2.6 times larger than the surface acceleration ( 95g vs. 36g). Histopathology showed axonal damage in the impacted side of the brain from the brain surface, accompanied by a local shock-front acceleration of >70g. This shows that axonal injury occurs deep in the brain even though the shear excitation was at the brain surface, and the acceleration measurements support the hypothesis that shear shock waves are responsible for deep traumatic brain injuries.

Accuracy meets simplicity: A constitutive model for heterogenous brain tissue

We present a general, hyperelastic, stretch-based potential that shows promise for modeling the mechanics of brain tissue. A specific four-parameter model derived from this general potential outperforms alternative models, such as the modified Ogden model, the Gent model, Demiray model, and machine-learning models, in capturing brain tissue elasticity. Specifically, the stretch-based model achieved R2 values of 0.997, 0.992, and 0.993 (tension, compression, and shear) for the cortex, 0.995, 0.983, and 0.983 for the basal ganglia, 0.994, 0.929, and 0.970 for the corona radiata, and 0.990, 0.896, and 0.969 for the corpus callosum. This work has the potential to advance our understanding of brain tissue mechanics and provides a valuable tool to improve finite element models for the investigation of brain development, injuries, and disease.

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.

A finite element model of contusion spinal cord injury in rodents

Traumatic spinal cord injuries result from high impact forces acting on the spine and are proceeded by an extensive secondary inflammatory response resulting in motor, sensory, and autonomic dysfunction. Experimental in vivo traumatic spinal cord injuries in rodents using a contusion model have been extremely useful in elucidating the underlying pathophysiology of these injuries. However, the relationship between the pathophysiology and the biomechanical factors is still not well understood. Therefore, the aim of this research is to provide a comprehensive analysis of the biomechanics of traumatic spinal cord injury in a rat contusion model. This is achieved through the development and validation of a finite element model of the thoracic rat spinal cord and subsequently simulating controlled cortical impact-induced traumatic spinal cord injury. The effects of impactor velocity, depth, and geometry on the resulting stresses and strains within the spinal cord are investigated. Our results show that increasing impactor depth results in larger stresses and strains within the spinal cord tissue as expected. Further, for the first time ever our results show that impactor geometry (spherical versus cylindrical) plays an important role in the distribution and magnitude of stresses and strains within the cord. Therefore, finite element modelling can be a powerful tool used to predict stresses and strains that occur in spinal cord tissue during trauma.

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.

The impact of horizontal eye movements versus intraocular pressure on optic nerve head biomechanics: A tridimensional finite element analysis study

It has been proposed that eye movements could be related to glaucoma development. This research aimed to compare the impact of intraocular pressure (IOP) versus horizontal duction on optic nerve head (ONH) strains. Thus, a tridimensional finite element model of the eye including the three tunics of the eye, all of the meninges, and the subarachnoid space (SAS) was developed using a series of medical tests and anatomical data. The ONH was divided into 22 subregions, and the model was subjected to 21 different eye pressures, as well as 24 different degrees of adduction and abduction ranging from 0.5° to 12°. Mean deformations were documented along anatomical axes and in principal directions. Additionally, the impact of tissue stiffness was assessed. The results show no statistically significant differences between the lamina cribrosa (LC) strains due to eye rotation and IOP variation. However, when assessing LC regions some experienced a reduction in principal strains following a 12° duction, while after the IOP reached 12 mmHg, all LC subzones showed an increase in strains. From an anatomical perspective, the effect on the ONH following 12° duction was opposite to that observed after a rise in IOP. Moreover, high strain dispersion inside the ONH subregions was obtained with lateral eye movements, which was not observed with increased IOP and variation. Finally, SAS and orbital fat stiffness strongly influenced ONH strains during eye movements, while SAS stiffness was also influential under ocular hypertension. Even if horizontal eye movements cause large ONH deformations, their biomechanical effect would be markedly distinct from that induced by IOP. It could be predicted that, at least in physiological conditions, their potential to cause axonal injury would not be so relevant. Thus, a causative role in glaucoma does not appear likely. By contrast, an important role of SAS would be expectable.

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.

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.

Region-Dependent Viscoelastic Properties of Human Brain Tissue Under Large Deformations

This study characterizes the mechanical properties of human brain tissue resected during the course of surgery under multistep indentation loading up to 30% strain. The experimental characterization using fresh, post-operative, human brain tissue is highly advantageous since postmortem times can affect its biomechanical behavior. Although the quasilinear theory of viscoelasticity (QLV) approach has been widely used to model brain tissue mechanical properties, our analysis concluded that the linear viscoelastic approach provided a better fit to the experimental data overall. The only statistically significant regional difference in observed stiffness was between the cortex gray and dentate gyrus. There were no statistically significant age or sex dependent differences, although the data suggested that the cortex white matter in males was stiffer than that in females. Our results can help improve the accuracy of finite element models of brain tissue deformation to predict its response to traumatic brain injury.

Effect of axonal fiber architecture on mechanical heterogeneity of the white matter-a statistical micromechanical model

A diffusion tensor imaging (DTI) -based statistical micromechanical model was developed to study the effect of axonal fiber architecture on the inter- and intra-regional mechanical heterogeneity of the white matter. Three characteristic regions within the white matter, i.e., corpus callosum, brain stem, and corona radiata, were studied considering the previous observations of locations of diffuse axonal injury. The embedded element technique was used to create a fiber-reinforced model, where the fiber was characterized by a Holzapfel hyperelastic material model with variable dispersion of axonal orientations. A relationship between the fractional anisotropy and the dispersion parameter of the hyperelastic model was used to introduce the statistical DTI data into the representative volume element. The FA-informed statistical micromechanical models of three characteristic regions of white matter were developed by deriving the corresponding probabilistic measures of FA variations. Comparison of the model predictions and experimental data indicated a good agreement, suggesting that the model could reasonably capture the inter-regional heterogeneity of white matter. Moreover, the standard deviations of experimental results correlated well with the model predictions, suggesting that the model could capture the intra-regional mechanical heterogeneity for different regions of white matter.

Mechanical Properties of the Cranial Meninges: A Systematic Review

The meninges are membranous tissues that are pivotal in maintaining homeostasis of the central nervous system. Despite the importance of the cranial meninges in nervous system physiology and in head injury mechanics, our knowledge of the tissues' mechanical behavior and structural composition is limited. This systematic review analyzes the existing literature on the mechanical properties of the meningeal tissues. Publications were identified from a search of Scopus, Academic Search Complete, and Web of Science and screened for eligibility according to Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines. The review details the wide range of testing techniques employed to date and the significant variability in the observed experimental findings. Our findings identify many gaps in the current literature that can serve as a guide for future work for meningeal mechanics investigators. The review identifies no peer-reviewed mechanical data on the falx and tentorium tissues, both of which have been identified as key structures in influencing brain injury mechanics. A dearth of mechanical data for the pia-arachnoid complex also was identified (no experimental mechanics studies on the human pia-arachnoid complex were identified), which is desirable for biofidelic modeling of human head injuries. Finally, this review provides recommendations on how experiments can be conducted to allow for standardization of test methodologies, enabling simplified comparisons and conclusions on meningeal mechanics.

Shear-deformation based continuum-damage constitutive modeling of brain tissue

Traumatic brain injury (TBI) is a leading cause of death in the United States. Depending on the severity of injury, complications such as memory loss and emotional changes are common. While the exact mechanisms are still unclear, these cognitive deficiencies are thought to arise from microstructural damages to the brain tissue, such as in diffuse-axonal injury where neuron fibers are sheared. Constitutive models can predict such damage at a microstructural level and allow for insight into the mechanisms of injury initiating at lower length scales. In this study, we developed a continuum damage model of brain tissue that is validated by experimental quasi-static stress-strain tests in tension, compression, and shear. The present work shows that damage is most present in the shear stress state, making the tissue suitable for damage modeling via shear interaction terms. Using this model, new insights into microstructural breakdown due to shear stresses and strains can be gained by application to simulations.

Sex- and age-specific mechanical properties of liver tissue under dynamic loading conditions

The liver is the most commonly injured abdominal organ following either blunt or penetrating impact. Current mechanical properties available in the literature are typically only measured at low strain rates, low strains, or use linear viscoelastic models. There is also a dearth of high-rate, large strain, viscoelastic data available for liver tissue which are required to model the deformation of the liver during high-rate impacts. Furthermore, the issue of whether mouse liver's mechanical properties are sex-dependent has not been addressed previously. Here, we present the first in vitro sex- and age-controlled mechanical characterisation of mixed-strain (C57BL and wild-type) mouse liver tissue at a localised length scale using large-deformation and high strain rate micro-indentation. We also investigated the effects of age on the mechanical properties of liver tissue. Force-relaxation experiments were performed on both male and female mouse livers up to 35% strain at 10/s and allowed to relax for 1s. The neo-Hookean based quasi-linear viscoelastic model was fitted to the experimental data to determine the large-strain behaviour of the tissue. A comprehensive statistical analysis was performed to determine whether any significant differences existed for (i) the short-term shear moduli and (ii) long-term shear moduli between 10 weeks-old male and female mouse livers, and (iii) the short-term and (iv) long-term shear moduli for 6, 10, and 56 weeks-old mouse livers. No significant differences were found between the mechanical properties in the sex groups. The 56 weeks-old liver tissue was found to be significantly stiffer than the 6 weeks-old liver tissue, but not the 10 weeks-old.

Nanoindentation of Soft Biological Materials

Nanoindentation techniques, with high spatial resolution and force sensitivity, have recently been moved into the center of the spotlight for measuring the mechanical properties of biomaterials, especially bridging the scales from the molecular via the cellular and tissue all the way to the organ level, whereas characterizing soft biomaterials, especially down to biomolecules, is fraught with more pitfalls compared with the hard biomaterials. In this review we detail the constitutive behavior of soft biomaterials under nanoindentation (including AFM) and present the characteristics of experimental aspects in detail, such as the adaption of instrumentation and indentation response of soft biomaterials. We further show some applications, and discuss the challenges and perspectives related to nanoindentation of soft biomaterials, a technique that can pinpoint the mechanical properties of soft biomaterials for the scale-span is far-reaching for understanding biomechanics and mechanobiology.