Viscoelastic characterization of injured brain tissue after controlled cortical impact (CCI) using a mouse model

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.

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 Bayesian method with nonlinear noise model to calibrate constitutive parameters of soft tissue

The measured mechanical responses of soft tissue exhibit large variability and errors, especially for the softest brain tissue, while calibrating its constitutive parameters in a deterministic way remains a common practice. Here we implement a Bayesian method considering the nonlinear noise model to calibrate constitutive parameters of brain tissue. A probability model is first developed based on the measured experimental data, likelihood function, and prior function, from which the posterior distributions of model parameters are formulated. The likelihood function considers the nonlinear behaviors of the constitutive response and noise distribution of the experimentally measured data. Meanwhile, the prior predictive distribution is computed to check the probability model preliminarily. Secondly, the Markov Chain Monte Carlo (MCMC) method is used to compute the posterior distributions of model parameters, enabling assessment of parameter uncertainty, correlation, and model calibration error. Finally, the posterior predictive distributions of the overall response, constitutive response, and noise response are computed to validate the probabilistic model, all of which are consistent with the corresponding data. Furthermore, the effect of the prior distribution, experimental data, and noise model on posterior distribution is studied. Our study provides a general approach to calibrating constitutive parameters of soft tissue despite errors and large variability in experimental data.

A position- and time-dependent pressure profile to model viscoelastic mechanical behavior of the brain tissue due to tumor growth

This study proposed a computational framework to calculate the resultant position- and time-dependent pressure profile on the brain tissue due to tumor growth. A finite element (FE) patch of the brain tissue was constructed and an inverse dynamic FE-optimization algorithm was used to calculate its viscoelastic mechanical properties under compressive uniaxial loading. Two patient-specific post-tumor resection FE models were input to the FE-optimization algorithm to calculate the optimized 3rd-order position-dependent and normal distribution time-dependent pressure profile parameters. The optimized viscoelastic material properties, the most suitable simulation time, and the optimized 3rd-order position- and -time-dependent pressure profiles were calculated.

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).

Calponin 1 increases cancer-associated fibroblasts-mediated matrix stiffness to promote chemoresistance in gastric cancer

The mechanical microenvironment regulated by cancer-associated fibroblasts (CAFs) influence tumor progression. Chemotherapeutic interventions including 5-Fluorouracil (5-Fu) are commonly used for primary treatment of patients with advanced gastric cancer (GC), and the development of acquired resistance to 5-Fu limits the clinical efficacy of these chemotherapies. However, if and how the interplay between CAFs and the mechanical microenvironment regulates GC response to 5-Fu is poorly understood. In this study, we demonstrate that high-level expression of calponin 1(CNN1) in gastric CAFs predicts poor clinical outcomes of GC patients, especially for those treated with 5-Fu. CNN1 knockdown in CAFs improves the effectiveness of 5-Fu in reducing tumor growth in a mouse GC model and confers increased sensitivity to 5-Fu in a 3D culture system. Furthermore, CNN1 knockdown impairs CAF contraction and reduces matrix stiffness without affecting the expression of matrix proteins. Mechanistically, CNN1 interacts with PDZ and LIM Domain 7 (PDLIM7) and prevents its degradation by the E3 ubiquitin ligase NEDD4-1, which leads to activation of the ROCK1/MLC pathway. The increased matrix stiffness, in turn, contributes to 5-Fu resistance in GC cells by activating YAP. Taken together, our data reveal a critical role of the mechanical microenvironment in 5-Fu resistance, which is modulated by CNN1^hi CAFs-mediated matrix stiffening, indicating that targeting CAFs may provide a novel option for overcoming drug resistance in GC.

An electromagnetic actuator for brain magnetic resonance elastography with high frequency accuracy

Our goal is to design, test and verify an electromagnetic actuator for brain magnetic resonance elastography (MRE). We proposed a grappler-shaped design that can transmit stable vibrations into the brain. To validate its performance, simulations were carried out to ensure the electromagnetic field generated by the actuator did not interfere with the B₀ field. The actuation vibration spectrum was analyzed to verify the actuation accuracy. Phantom and volunteer experiments were carried out to evaluate the performance of the actuator. Simulation of the magnetic field showed that the proposed actuator has a fringe field of less than 3 G in the imaging region. The phantom experiments showed that the proposed actuator did not interfere with the routine imaging sequences. The measured vibration spectra demonstrated that the frequency offset was about one third that of a pneumatic device and the transmission efficiency was three times higher. The shear moduli estimated from brain MRE were consistent with those from the literature. The actuation frequency of the proposed actuator has less frequency offset and off-center frequency components compared with the pneumatic counterpart. The whole actuator weighted only 980 g. The actuator can carry out multifrequency MRE on the brain with high accuracy. It is easy to use, comfortable for the patient and portable.

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.

Traumatic brain injury-induced cerebral microbleeds in the elderly

Traumatic brain injury (TBI) was shown to lead to the development of cerebral microbleeds (CMBs), which are associated with long term cognitive decline and gait disturbances in patients. The elderly is one of the most vulnerable parts of the population to suffer TBI. Importantly, ageing is known to exacerbate microvascular fragility and to promote the formation of CMBs. In this overview, the effect of ageing is discussed on the development and characteristics of TBI-related CMBs, with special emphasis on CMBs associated with mild TBI. Four cases of TBI-related CMBs are described to illustrate the concept that ageing exacerbates the deleterious microvascular effects of TBI and that similar brain trauma may induce more CMBs in old patients than in young ones. Recommendations are made for future prospective studies to establish the mechanistic effects of ageing on the formation of CMBs after TBI, and to determine long-term consequences of CMBs on clinically relevant outcome measures including cognitive performance, gait and balance function.

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.

A machine learning approach for magnetic resonance image-based mouse brain modeling and fast computation in controlled cortical impact

Computational modeling of the brain is crucial for the study of traumatic brain injury. An anatomically accurate model with refined details could provide the most accurate computational results. However, computational models with fine mesh details could take prolonged computation time that impedes the clinical translation of the models. Therefore, a way to construct a model with low computational cost while maintaining a computational accuracy comparable with that of the high-fidelity model is desired. In this study, we constructed magnetic resonance (MR) image-based finite element (FE) models of a mouse brain for simulations of controlled cortical impact. The anatomical details were kept by mapping each image voxel to a corresponding FE mesh element. We constructed a super-resolution neural network that could produce computational results of a refined FE model with a mesh size of 70 μm from a coarse FE model with a mesh size of 280 μm. The peak signal-to-noise ratio of the reconstructed results was 33.26 dB, while the computational speed was increased by 50-fold. This proof-of-concept study showed that using machine learning techniques, MR image-based computational modeling could be applied and evaluated in a timely fashion. This paved ways for fast FE modeling and computation based on MR images. Results also support the potential clinical applications of MR image-based computational modeling of the human brain in a variety of scenarios such as brain impact and intervention.Graphical abstract MR image-based FE models with different mesh sizes were generated for CCI. The training and testing data sets were computed with 5 different impact locations and 3 different impact velocities. High-resolution strain maps were estimated using a SR neural network with greatly reduced computational cost.

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 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.