Determination of friction coefficient in unconfined compression of brain tissue

Review of the Brain's Behaviour after Injury and Disease for Its Application in an Agent-Based Model (ABM)

The brain is the most complex organ in the human body and, as such, its study entails great challenges (methodological, theoretical, etc.). Nonetheless, there is a remarkable amount of studies about the consequences of pathological conditions on its development and functioning. This bibliographic review aims to cover mostly findings related to changes in the physical distribution of neurons and their connections-the connectome-both structural and functional, as well as their modelling approaches. It does not intend to offer an extensive description of all conditions affecting the brain; rather, it presents the most common ones. Thus, here, we highlight the need for accurate brain modelling that can subsequently be used to understand brain function and be applied to diagnose, track, and simulate treatments for the most prevalent pathologies affecting the brain.

Water quality modelling using principal component analysis and artificial neural network

The study investigates the latent pollution sources and most significant parameters that cause spatial variation and develops the best input for water quality modelling using principal component analysis (PCA) and artificial neural network (ANN). The dataset, 22 water quality parameters were obtained from Department of Environment Malaysia (DOE). The PCA generated six significant principal component scores (PCs) which explained 65.40 % of the total variance. Parameters for water quality variation are mainlyrelated to mineral components, anthropogenic activities, and natural processes. However, in ANN three input combination models (ANN A, B, and C) were developed to identify the best model that can predict water quality index (WQI) with very high precision. ANN A model appears to have the best prediction capacity with a coefficient of determination (R²) = 0.9999 and root mean square error (RMSE) = 0.0537. These results proved that the PCA and ANN methods can be applied as tools for decision-making and problem-solving for better managing of river quality.

Techniques for characterizing mechanical properties of soft tissues

The characterization of soft tissues remains a vital need for various bioengineering and medical fields. Developing areas such as regenerative medicine, robot-aided surgery, and surgical simulations all require accurate knowledge about the mechanical properties of soft tissues to replicate their mechanics. Mechanical properties can be characterized through several different characterization techniques such as atomic force microscopy, compression testing, and tensile testing. However, many of these methods contain considerable differences in ability to accurately characterize the mechanical properties of soft tissues. As a result of these variations, there are often discrepancies in the reported values for numerous studies. This paper reviews common characterization methods that have been applied to obtain the mechanical properties of soft tissues and highlights their advantages as well as disadvantages. The limitations, accuracies, repeatability, in-vivo testing capability, and types of properties measurable for each method are also discussed.

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.

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.

A Hyper-Viscoelastic Continuum-Level Finite Element Model of the Spinal Cord Assessed for Transverse Indentation and Impact Loading

Finite Element (FE) modelling of spinal cord response to impact can provide unique insights into the neural tissue response and injury risk potential. Yet, contemporary human body models (HBMs) used to examine injury risk and prevention across a wide range of impact scenarios often lack detailed integration of the spinal cord and surrounding tissues. The integration of a spinal cord in contemporary HBMs has been limited by the need for a continuum-level model owing to the relatively large element size required to be compatible with HBM, and the requirement for model development based on published material properties and validation using relevant non-linear material data. The goals of this study were to develop and assess non-linear material model parameters for the spinal cord parenchyma and pia mater, and incorporate these models into a continuum-level model of the spinal cord with a mesh size conducive to integration in HBM. First, hyper-viscoelastic material properties based on tissue-level mechanical test data for the spinal cord and hyperelastic material properties for the pia mater were determined. Secondly, the constitutive models were integrated in a spinal cord segment FE model validated against independent experimental data representing transverse compression of the spinal cord-pia mater complex (SCP) under quasi-static indentation and dynamic impact loading. The constitutive model parameters were fit to a quasi-linear viscoelastic model with an Ogden hyperelastic function, and then verified using single element test cases corresponding to the experimental strain rates for the spinal cord (0.32–77.22 s⁻¹) and pia mater (0.05 s⁻¹). Validation of the spinal cord model was then performed by re-creating, in an explicit FE code, two independent ex-vivo experimental setups: 1) transverse indentation of a porcine spinal cord-pia mater complex and 2) dynamic transverse impact of a bovine SCP. The indentation model accurately matched the experimental results up to 60% compression of the SCP, while the impact model predicted the loading phase and the maximum deformation (within 7%) of the SCP experimental data. This study quantified the important biomechanical contribution of the pia mater tissue during spinal cord deformation. The validated material models established in this study can be implemented in computational HBM.

Study on the Effect of Sample Temperature on the Uniaxial Compressive Mechanical Properties of the Brain Tissue

Craniocerebral injury has been a research focus in the field of injury biomechanics. Although experimental endeavors have made certain progress in characterizing the material behavior of the brain, the temperature dependency of brain mechanics appears to be inconclusive thus far. To partially address this knowledge gap, the current study measured the brain material behavior via unconstrained uniaxial compression tests under low strain rate (0.0083 s^-1) and high strain rate (0.83 s^-1) at four different sample temperatures (13°C, 20°C, 27°C, and 37°C). Each group has 9~12 samples. One-way analysis of variance method was used to study the influence of sample temperature on engineering stress. The results show that the effect of sample temperature on the mechanical properties of brain tissue is significant under the high strain rate, especially at low temperature (13°C), in which the hardening of the brain tissue is very obvious. At the low strain rate, no temperature dependency of brain mechanics is noted. Therefore, the current results highlight that the temperature of the brain sample should be ensured to be in accordance with the living subject when studying the biomechanical response of living tissue.

Anisotropic Mechanical Properties of the Human Uterus Measured by Spherical Indentation

The mechanical function of the uterus is critical for a successful pregnancy. During gestation, uterine tissue grows and stretches to many times its size to accommodate the growing fetus, and it is hypothesized the magnitude of uterine tissue stretch triggers the onset of contractions. To establish rigorous mechanical testing protocols for the human uterus in hopes of predicting tissue stretch during pregnancy, this study measures the anisotropic mechanical properties of the human uterus using optical coherence tomography (OCT), instrumented spherical indentation, and video extensometry. In this work, we perform spherical indentation and digital image correlation to obtain the tissue's force and deformation response to a ramp-hold loading regimen. We translate previously reported fiber architecture, measured via optical coherence tomography, into a constitutive fiber composite material model to describe the equilibrium material behavior during indentation. We use an inverse finite element method integrated with a genetic algorithm (GA) to fit the material model to our experimental data. We report the mechanical properties of human uterine specimens taken across different anatomical locations and layers from one non-pregnant (NP) and one pregnant (PG) patient; both patients had pathological uterine tissue. Compared to NP uterine tissue, PG tissue has a more dispersed fiber distribution and equivalent stiffness material parameters. In both PG and NP uterine tissue, the mechanical properties differ significantly between anatomical locations.

Correlating Tissue Mechanics and Spinal Cord Injury: Patient-Specific Finite Element Models of Unilateral Cervical Contusion Spinal Cord Injury in Non-Human Primates

Non-human primate (NHP) models are the closest approximation of human spinal cord injury (SCI) available for pre-clinical trials. The NHP models, however, include broader morphological variability that can confound experimental outcomes. We developed subject-specific finite element (FE) models to quantify the relationship between impact mechanics and SCI, including the correlations between FE outcomes and tissue damage. Subject-specific models of cervical unilateral contusion SCI were generated from pre-injury MRIs of six NHPs. Stress and strain outcomes were compared with lesion histology using logit analysis. A parallel generic model was constructed to compare the outcomes of subject-specific and generic models. The FE outcomes were correlated more strongly with gray matter damage (0.29 < R2 < 0.76) than white matter (0.18 < R2 < 0.58). Maximum/minimum principal strain, Von-Mises and Tresca stresses showed the strongest correlations (0.31 < R2 < 0.76) with tissue damage in the gray matter while minimum principal strain, Von-Mises stress, and Tresca stress best predicted white matter damage (0.23 < R2 < 0.58). Tissue damage thresholds varied for each subject. The generic FE model captured the impact biomechanics in two of the four models; however, the correlations between FE outcomes and tissue damage were weaker than the subject-specific models (gray matter [0.25 < R2 < 0.69] and white matter [R2 < 0.06] except for one subject [0.26 < R2 < 0.48]). The FE mechanical outputs correlated with tissue damage in spinal cord white and gray matters, and the subject-specific models accurately mimicked the biomechanics of NHP cervical contusion impacts.

Mechanical characterization of porcine liver properties for computational simulation of indentation on cancerous tissue

An accurate characterization of soft biological tissue properties is essential for a realistic simulation of surgical procedures. Unconfined uniaxial compression tests with specimens affixed to the fixtures are often performed to characterize the stress-stretch curves of soft biological tissues, with which the material parameters can be obtained. However, the constrained boundary condition causes non-uniform deformation during the uniaxial test, posing challenges for accurate measurement of tissue deformation. In this study, we measured the deformation locally at the middle of liver specimens and obtained the corresponding stress-stretch curves. Since the effect of the constrained boundary condition on the local deformation of specimen is minimized, the stress-stretch curves are thus more realistic. Subsequently, we fitted the experimental stress-stretch curves with several constitutive models and found that the first-order Ogden hyperelastic material model was most suitable for characterizing the mechanical properties of porcine liver tissues. To further verify the characterized material properties, we carried out indentation tests on porcine liver specimens and compared the experimental data with computational results by using finite element simulations. A good agreement was achieved. Finally, we constructed computational models of liver tissue with a tumor and investigated the effect of the tumor on the mechanical response of the tissue under indentation. The computational results revealed that the liver specimen with tumor shows a stiffer response if the distance between the tumor and the indenter is small.

Data mining the effects of testing conditions and specimen properties on brain biomechanics

Traumatic brain injury is highly prevalent in the United States. However, despite its frequency and significance, there is little understanding of how the brain responds during injurious loading. A confounding problem is that because testing conditions vary between assessment methods, brain biomechanics cannot be fully understood. Data mining techniques, which are commonly used to determine patterns in large datasets, were applied to discover how changes in testing conditions affect the mechanical response of the brain. Data at various strain rates were collected from published literature and sorted into datasets based on strain rate and tension vs. compression. Self-organizing maps were used to conduct a sensitivity analysis to rank the testing condition parameters by importance. Fuzzy C-means clustering was applied to determine if there were any patterns in the data. The parameter rankings and clustering for each dataset varied, indicating that the strain rate and type of deformation influence the role of these parameters in the datasets.

Compressive mechanical characterization of non-human primate spinal cord white matter

The goal of developing computational models of spinal cord injury (SCI) is to better understand the human injury condition. However, finite element models of human SCI have used rodent spinal cord tissue properties due to a lack of experimental data. Central nervous system tissues in non human primates (NHP) closely resemble that of humans and therefore, it is expected that material constitutive models obtained from NHPs will increase the fidelity and the accuracy of human SCI models. Human SCI most often results from compressive loading and spinal cord white matter properties affect FE predicted patterns of injury; therefore, the objectives of this study were to characterize the unconfined compressive response of NHP spinal cord white matter and present an experimentally derived, finite element tractable constitutive model for the tissue. Cervical spinal cords were harvested from nine male adult NHPs (Macaca mulatta). White matter biopsy samples (3 mm in diameter) were taken from both lateral columns of the spinal cord and were divided into four strain rate groups for unconfined dynamic compression and stress relaxation (post-mortem <1-hour). The NHP spinal cord white matter compressive response was sensitive to strain rate and showed substantial stress relaxation confirming the viscoelastic behavior of the material. An Ogden 1st order model best captured the non-linear behavior of NHP white matter in a quasi-linear viscoelastic material model with 4-term Prony series. This study is the first to characterize NHP spinal cord white matter at high (>10/sec) strain rates typical of traumatic injury. The finite element derived material constitutive model of this study will increase the fidelity of SCI computational models and provide important insights for transferring pre-clinical findings to clinical treatments.

STATEMENT OF SIGNIFICANCE

Spinal cord injury (SCI) finite element (FE) models provide an important tool to bridge the gap between animal studies and human injury, assess injury prevention technologies (e.g. helmets, seatbelts), and provide insight into the mechanisms of injury. Although, FE model outcomes depend on the assumed material constitutive model, there is limited experimental data for fresh spinal cords and all was obtained from rodent, porcine or bovine tissues. Central nervous system tissues in non human primates (NHP) more closely resemble humans. This study characterizes fresh NHP spinal cord material properties at high strains rates and large deformations typical of SCI for the first time. A constitutive model was defined that can be readily implemented in finite strain FE analysis of SCI.

The estimation method of friction in unconfined compression tests of liver tissue

In traditional unconfined compression tests, the friction between platform and specimen is often considered negligible or minimized by lubrication or other means. However, friction can affect the estimation of material parameters. The percentage difference in radial deformation was investigated in this study. A novel friction estimation method was established and verified using a finite element method. The proposed method was based on the radial deformation during the compression process. Three different hyperelastic material parameters of liver tissue were applied in the simulations. The hyperelastic parameters H1 were obtained by no-slip compression tests, while the others were extracted from the literature. The results showed that the percentage difference in radial deformation was mainly influenced by the friction coefficient and diameter-to-height ( d/ h) ratio of the specimen in unconfined compression tests. The percentage difference increased as the friction coefficient and d/ h increased. Different d/ h and friction coefficient values were tested to validate the proposed method, and the accuracy was estimated to exceed 86%. An optimization strategy for material parameters in unconfined compression tests was proposed accordingly.

ADAPTIVE UNSCENTED KALMAN FILTER FOR ONLINE SOFT TISSUES CHARACTERIZATION

Online soft tissue characterization is important for robotic-assisted minimally invasive surgery to achieve precise and stable robotic control with haptic feedback. This paper presents a new adaptive unscented Kalman filter based on the nonlinear Hunt–Crossley model for online soft tissue characterization without requiring the characteristics of system noise. This filter incorporates the concept of Sage windowing in the traditional unscented Kalman filter to adaptively estimate system noise covariance using predicted residuals within a time window. In order to account for the inherent relationship between the current and previous states of soft tissue deformation involved in robotic-assisted surgery and improve the estimation performance, a recursive estimation of system noise covariance is further constructed by introducing a fading scaling factor to control the contributions between noise covariance estimations at current and previous time points. The proposed adaptive unscented Kalman filter overcomes the limitation of the traditional unscented Kalman filter in requiring the characteristics of system noise. Simulations and comparisons show the efficacy of the suggested nonlinear adaptive unscented Kalman filter for online soft tissue characterization.

The mechanical importance of myelination in the central nervous system

Neurons in the central nervous system are surrounded and cross-linked by myelin, a fatty white substance that wraps around axons to create an electrically insulating layer. The electrical function of myelin is widely recognized; yet, its mechanical importance remains underestimated. Here we combined nanoindentation testing and histological staining to correlate brain stiffness to the degree of myelination in immature, pre-natal brains and mature, post-natal brains. We found that both gray and white matter tissue stiffened significantly (p≪0.001) upon maturation: the gray matter stiffness doubled from 0.31±0.20kPa pre-natally to 0.68±0.20kPa post-natally; the white matter stiffness tripled from 0.45±0.18kPa pre-natally to 1.33±0.64kPa post-natally. At the same time, the white matter myelin content increased significantly (p≪0.001) from 58±2% to 74±9%. White matter stiffness and myelin content were correlated with a Pearson correlation coefficient of ρ=0.92 (p≪0.001). Our study suggests that myelin is not only important to ensure smooth electrical signal propagation in neurons, but also to protect neurons against physical forces and provide a strong microstructural network that stiffens the white matter tissue as a whole. Our results suggest that brain tissue stiffness could serve as a biomarker for multiple sclerosis and other forms of demyelinating disorders. Understanding how tissue maturation translates into changes in mechanical properties and knowing the precise brain stiffness at different stages of life has important medical implications in development, aging, and neurodegeneration.

Extracellular matrix-based intracortical microelectrodes: Toward a microfabricated neural interface based on natural materials

Extracellular matrix (ECM)-based implantable neural electrodes (NEs) were achieved using a microfabrication strategy on natural-substrate-based organic materials. The ECM-based design minimized the introduction of non-natural products into the brain. Further, it rendered the implants sufficiently rigid for penetration into the target brain region and allowed them subsequently to soften to match the elastic modulus of brain tissue upon exposure to physiological conditions, thereby reducing inflammatory strain fields in the tissue. Preliminary studies suggested that ECM-NEs produce a reduced inflammatory response compared with inorganic rigid and flexible approaches. In vivo intracortical recordings from the rat motor cortex illustrate one mode of use for these ECM-NEs.

On a staggered iFEM approach to account for friction in compression testing of soft materials

An inverse finite element method (iFEM) to estimate material parameters from compression tests of soft materials is presented, where alginate hydrogel was used as a phantom material. The method applies if the boundary conditions at the loaded surfaces are not ideal, i.e. neither free of friction nor fully constrained, as it may be the case in most realistic testing set-ups. Assuming a linear friction law, the friction coefficient μ was considered unknown and estimated in a first step by minimising the difference between the contours of the sample, obtained by optical measurements, and the simulated shape. Force-displacement data were used in a second step to determine the parameters of the constitutive law. Staggering these two steps, both friction and material parameters were identified by optimisation. Skipping the first step and predefining μ instead, a unique parameter set could only be clearly identified if the deviations of the contours were considered in addition to the deviations in the force-displacement data. Finally, forward FEM calculations with differently shaped specimens were used to verify the goodness of the obtained parameter sets.