Influence of strain rate on indentation response of porcine brain

An atlas of the heterogeneous viscoelastic brain with local power-law attenuation synthesised using Prony-series

This review addresses the acute need to acknowledge the mechanical heterogeneity of brain matter and to accurately calibrate its local viscoelastic material properties accordingly. Specifically, it is important to compile the existing and disparate literature on attenuation power-laws and dispersion to make progress in wave physics of brain matter, a field of research that has the potential to explain the mechanisms at play in diffuse axonal injury and mild traumatic brain injury in general. Currently, viscous effects in the brain are modelled using Prony-series, i.e., a sum of decaying exponentials at different relaxation times. Here we collect and synthesise the Prony-series coefficients appearing in the literature for twelve regions: brainstem, basal ganglia, cerebellum, corona radiata, corpus callosum, cortex, dentate gyrus, hippocampus, thalamus, grey matter, white matter, homogeneous brain, and for eight different mammals: pig, rat, human, mouse, cow, sheep, monkey and dog. Using this data, we compute the fractional-exponent attenuation power-laws for different tissues of the brain, the corresponding dispersion laws resulting from causality, and the averaged Prony-series coefficients. STATEMENT OF SIGNIFICANCE: Traumatic brain injuries are considered a silent epidemic and finite element methods (FEMs) are used in modelling brain deformation, requiring access to viscoelastic properties of brain. To the best of our knowledge, this work presents 1) the first multi-frequency viscoelastic atlas of the heterogeneous brain, 2) the first review focusing on viscoelastic modelling in both FEMs and experimental works, 3) the first attempt to conglomerate the disparate existing literature on the viscoelastic modelling of the brain and 4) the largest collection of viscoelastic parameters for the brain (212 different Prony-series spanning 12 different tissues and 8 different animal surrogates). Furthermore, this work presents the first brain atlas of attenuation power-laws essential for modelling shear waves in brain.

A Method for Evaluating Brain Deformation Under Sagittal Blunt Impacts Using a Half-Skull Human-Scale Surrogate

Trauma to the brain is a biomechanical problem where the initiating event is a dynamic loading (blunt, inertial, blast) to the head. To understand the relationship between the mechanical parameters of the injury and the spatial and temporal deformation patterns in the brain, there is a need to develop a reusable and adaptable experimental traumatic brain injury (TBI) model that can measure brain motion under varying parameters. In this effort, we aim to directly measure brain deformation (strain and strain rates) in different brain regions in a human head model using a drop tower.

METHODS

Physical head models consisting of a half, sagittal plane skull, brain, and neck were constructed and subjected to crown and frontal impacts at two impact speeds. All tests were recorded with a high-speed camera at 1000 frames per second. Motion of visual markers within brain surrogates were used to track deformations and calculate spatial strain histories in 6 brain regions of interest. Principal strains, strain rates and strain impulses were calculated and reported.

RESULTS

Higher impact velocities corresponded to higher strain values across all impact scenarios. Crown impacts were characterized by high, long duration strains distributed across the parietal, frontal and hippocampal regions whereas frontal impacts were characterized by sharply rising and falling strains primarily found in the parietal, frontal, hippocampal and occipital regions. High strain rates were associated with short durations and impulses indicating fast but short-lived strains. 2.23 m/s (5 mph) crown impacts resulted in 53% of the brain with shear strains higher than 0.15 verses 32% for frontal impacts.

CONCLUSIONS

The results reveal large differences in the spatial and temporal strain responses between crown and forehead impacts. Overall, the results suggest that for the same speed, crown impact leads to higher magnitude strain patterns than a frontal impact. The data provided by this model provides unique insight into the spatial and temporal deformation patterns that have not been provided by alternate surrogate models. The model can be used to investigate how anatomical, material and loading features and parameters can affect deformation patterns in specific regions of interest in the brain.

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.

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.

Distinguishing poroelasticity and viscoelasticity of brain tissue with time scale

Brain tissue is considered to be biphasic, with approximately 80% liquid and 20% solid matrix, thus exhibiting viscoelasticity due to rearrangement of the solid matrix and poroelasticity due to fluid migration within the solid matrix. However, how to distinguish poroelastic and viscoelastic effects in brain tissue remains challenging. In this study, we proposed a method of unconfined compression-isometric hold to measure the force versus time relaxation curves of porcine brain tissue samples with systematically varied sample lengths. Upon scaling the measured relaxation force and relaxation time with different length-dependent physical quantities, we successfully distinguished the poroelasticity and viscoelasticity of the brain tissue. We demonstrated that during isometric hold, viscoelastic relaxation dominated the mechanical behavior of brain tissue in the short-time regime, while poroelastic relaxation dominated in the long-time regime. Furthermore, compared with poroelastic relaxation, viscoelastic relaxation was found to play a more dominant role in the mechanical response of porcine brain tissue. We then evaluated the differences between poroelastic and viscoelastic effects for both porcine and human brain tissue. Because of the draining of pore fluid, the Young's moduli in poroelastic relaxation were lower than those in viscoelastic relaxation; brain tissue changed from incompressible during viscoelastic relaxation to compressible during poroelastic relaxation, resulting in reduced Poisson ratios. This study provides new insights into the physical mechanisms underlying the roles of viscoelasticity and poroelasticity in brain tissue. STATEMENT OF SIGNIFICANCE: Although the poroviscoelastic model had been proposed to characterize brain tissue mechanical behavior, it is difficult to distinguish the poroelastic and viscoelastic behaviors of brain tissue. The study distinguished viscoelasticity and poroelasticity of brain tissue with time scales and then evaluated the differences between poroelastic and viscoelastic effects for both porcine and human brain tissue, which helps to accurate selection of constitutive models suitable for application in certain situations (e.g., pore-dominant and viscoelastic-dominant deformation).

Effects of Different Types of Electric Fields on Mechanical Properties and Microstructure of Ex Vivo Porcine Brain Tissues

Electrotherapy plays a crucial role in regulating neuronal activity. Nevertheless, the relevant therapeutic mechanisms are still unclear; thus, the effects of electric fields on brain tissue's mechanical properties and microstructure need to be explored. In this study, focusing on the changes in mechanical properties and microstructure of ex vivo porcine brain tissues under different types of electric fields, directional and alternating electric fields (frequencies of 5, 20, 50, and 80 Hz, respectively) integrate with a custom-designed indentation device. The experimental results showed that for the ex vivo brain tissue, the directional electric field (DEF) can reduce the elastic properties of brain tissue. Simultaneously, the DEF can increase the cell spacing and reduce the proteoglycan content. The transmission electron microscope (TEM) analysis observed that the DEF can reduce the integrity of the plasma membrane, the endoplasmic reticulum's stress response, and the myelin lamella's separation. The alternating electric field (AEF) can accelerate the stress relaxation process of brain tissue and change the time-dependent mechanical properties of brain tissue. Meanwhile, with the increase in frequency, the cell spacing decreased, and the proteoglycan content gradually approached the control group without electric fields. TEM analysis observed that with the increase in frequency, the integrity of the plasma membrane increases, and the separation of the myelin lamella gradually disappears. Understanding the changes in the mechanical properties and microstructure of brain tissue under AEF and DEF enables a preliminary exploration of the therapeutic mechanism of electrotherapy. Simultaneously, the essential data was provided to support the development of embedded electrodes. In addition, the ex vivo experiments build a solid foundation for future in vivo experiments.

Instrumented nanoindentation in musculoskeletal research

Musculoskeletal tissues, such as bone, cartilage, and muscle, are natural composite materials that are constructed with a hierarchical structure ranging from the cell to tissue level. The component differences and structural complexity, together, require comprehensive multiscale mechanical characterization. In this review, we focus on nanoindentation testing, which is used for nanometer to sub-micrometer length scale mechanical characterization. In the following context, we will summarize studies of nanoindentation in musculoskeletal research, examine the critical factors that affect nanoindentation testing results, and briefly summarize other commonly used techniques that can be conjoined with nanoindentation for synchronized imaging and colocalized characterization.

Long-term recovery behavior of brain tissue in hydrocephalus patients after shunting

The unpredictable complexities in hydrocephalus shunt outcomes may be related to the recovery behavior of brain tissue after shunting. The simulated cerebrospinal fluid (CSF) velocity and intracranial pressure (ICP) over 15 months after shunting were validated by experimental data. The mean strain and creep of the brain had notable changes after shunting and their trends were monotonic. The highest stiffness of the hydrocephalic brain was in the first consolidation phase (between pre-shunting to 1 month after shunting). The viscous component overcame and damped the input load in the third consolidation phase (after the fifteenth month) and changes in brain volume were stopped. The long-intracranial elastance (long-IE) changed oscillatory after shunting and there was not a linear relationship between long-IE and ICP. We showed the long-term effect of the viscous component on brain recovery behavior of hydrocephalic brain. The results shed light on the brain recovery mechanism after shunting and the mechanisms for shunt failure.

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.

The effects of electric fields on the mechanical properties and microstructure of ex vivo porcine brain tissues

As a popular tool for regulating the physiological conditions of the brain and treating brain diseases, electrotherapy has become increasingly mature in clinical applications. However, the mechanical properties and microstructure of the brain that change with weak electric fields are often overlooked. Thus, the mechanical behaviors of the brain tissue, which play a critical role in modulating the brain form and brain function, need to be taken into account. Herein, the direct current electric fields were combined with a customized indentation device and simultaneously focused on the changes in the mechanical properties and microstructure of ex vivo porcine brain tissues under electric fields. The experimental results showed that the electric fields reduced the shear modulus and viscosity and increased the relaxation rate of ex vivo porcine brain tissues. Moreover, electric fields polarized the cell bodies and reduced proteoglycan content in the cortex. The TEM observation confirmed that the electric fields deepened the degree of endoplasmic reticulum expansion and decreased the structural integrity of the cell membrane and myelin sheath. This study confirmed the effect of electric fields on ex vivo brain tissues; concurrently, it created comparable space in microscopic structure/compositions and mechanical parameters for future deeper brain experiments under stress-electric field coupling.

Mechanical properties of brain tissue based on microstructure

Research on the mechanical properties of brain tissue has gradually deepened recently. Two indentation protocols were used here to characterize the mechanical properties of cortical tissues. Further, histological staining was used to explore the correlation between the mechanical properties and microstructure on the basis of the density of cell nuclei and proteoglycan content. No significant difference was observed in transient contact stiffness between the cerebral cortex and cerebellar cortex at the depth interval of 0-600 μm under the cortical surface; however, the average shear modulus of the cerebral cortex was higher than that of the cerebellar cortex. The cerebral cortex responded more quickly to the change in load and released stress more thoroughly than the cerebellar cortex. In addition, the density of cell nuclei was related to both the transient contact stiffness and second time constant of cortical tissues. Proteoglycan content had a more significant impact on the shear modulus, second time constant, and stress relaxation rate of cortical tissues. Exploring mechanical properties thoroughly will provide more detailed mechanical information for future brain chip implantation. Alternatively, linking the mechanical properties of cortical tissues to the microstructure can provide basic data for the design and manufacture of substitute materials for brain tissue.

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.

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.

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.

Indentation response in porcine brain under electric fields

Electric fields in the environment can have profound effects on brain function and behavior. In clinical practice, some noninvasive/microinvasive therapies with electrical fields such as transcranial electrical stimulation (tES), deep brain stimulation (DBS), and electroconvulsive therapy (ECT) have emerged as powerful tools for the treatment of neuropsychiatric disorders and neuromodulation. Nonetheless, currently, most studies focus on the mechanisms and effects of therapies and do not to address the mechanical properties of brain tissue under electric fields. Thus, the mechanical behavior of brain tissue, which plays an important role in modulating both brain form and brain function, should be given attention. The present study addresses this paucity by presenting, for the first time, the mechanical properties of brain tissue under various intensities of direct current electric field (0, 2, 5, 10, 20, and 50 V) using a custom-designed indentation device. Prior to brain indentation, validation tests were performed in different hydrogels to ensure that there was no interference in the electric fields from the indentation device. Subsequently, the load trace data obtained from the indentation-relaxation tests was fitted to both linear elastic and viscoelastic models to characterize the sensitivity of the mechanical behavior of the brain tissue to the electric fields. The brain tissue was found to be softened at a higher electric field level and less viscous, and substantially responded more quickly with an increase in electric field. The explanations for the above behaviors were further discussed based on the analysis of the resistance and thermal responses during the testing process. Understanding the effect of electric fields on brain tissue at the mechanical level can provide a better understanding of the mechanisms of some therapies, which may be beneficial to guide therapy protocols.

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.

Effect of Tissue Material Properties in Blast Loading: Coupled Experimentation and Finite Element Simulation

Computational models of blast-induced traumatic brain injury (bTBI) require a robust definition of the material models of the brain. The mechanical constitutive models of these tissues are difficult to characterize, leading to a wide range of values reported in literature. Therefore, the sensitivity of the intracranial pressure (ICP) and maximum principal strain to variations in the material model of the brain was investigated through a combined computational and experimental approach. A finite element model of a rat was created to simulate a shock wave exposure, guided by the experimental measurements of rats subjected to shock loading conditions corresponding to that of mild traumatic brain injury in a field-validated shock tube. In the numerical model, the properties of the brain were parametrically varied. A comparison of the ICP measured at two locations revealed that experimental and simulated ICP were higher in the cerebellum (p < 0.0001), highlighting the significance of pressure sensor locations within the cranium. The ICP and strain were correlated with the long-term bulk (p < 0.0001) and shear moduli (p < 0.0001), with an 80 MPa effective bulk modulus value matching best with experimental measurements. In bTBI, the solution is sensitive to the brain material model, necessitating robust validation methods.