Compressive properties and constitutive modeling of different regions of 8-week-old pediatric porcine brain under large strain and wide strain rates

Frequency and time dependent viscoelastic characterization of pediatric porcine brain tissue in compression

Understanding the viscoelastic behavior of pediatric brain tissue is critical to interpret how external mechanical forces affect head injury in children. However, knowledge of the viscoelastic properties of pediatric brain tissue is limited, and this reduces the biofidelity of developed numeric simulations of the pediatric head in analysis of brain injury. Thus, it is essential to characterize the viscoelastic behavior of pediatric brain tissue in various loading conditions and to identify constitutive models. In this study, the pediatric porcine brain tissue was investigated in compression with determine the viscoelasticity under small and large strain, respectively. A range of frequencies between 0.1 and 40 Hz was applied to determine frequency-dependent viscoelastic behavior via dynamic mechanical analysis, while brain samples were divided into three strain rate groups of 0.01/s, 1/s and 10/s for compression up to 0.3 strain level and stress relaxation to obtain time-dependent viscoelastic properties. At frequencies above 20 Hz, the storage modulus did not increase, while the loss modulus increased continuously. With strain rate increasing from 0.01/s to 10/s, the mean stress at 0.1, 0.2 and 0.3 strain increased to approximate 6.8, 5.6 and 4.4 times, respectively. The brain compressive response was sensitive to strain rate and frequency. The characterization of brain tissue will be valuable for development of head protection systems and prediction of brain injury.

Experimental testing combined with inverse-FE for mechanical characterisation of penile tissues

Erectile dysfunction (ED) predominantly affects men in their 40-70s and can lead to poor quality of life. One option for ED treatment is surgical implantation of an inflatable penile prosthesis (IPP). However, they can be associated with negative outcomes including infection, migration or fibrosis. To improve outcomes, the interaction between the IPP device and surrounding tissues needs further investigation and this could be achieved using pre-clinical testbeds, but they need to be informed by extensive tissue testing. In this study, an experimental approach is adopted to characterise the mechanics of horse penile tissue and establish a testing protocol for penile tissue. The whole penis segments were tested in plate compression tests to obtain whole penis behaviour which is necessary for validation of a pre-clinical testbed, whilst tensile and compression tests were performed on individual penile tissues, namely corpus cavernosa and tunica albuginea. The second part of the paper deals with the development of a computational model employing an inverse finite element approach to estimate the material parameters of each tissue layer. These material parameters are in good agreement with the experimental results obtained from the individual tissue layers and whole organ tissue tests. This paper presents the first study proposing realistic nonlinear elastic material parameters for penile tissues and offers a validated testbed for IPPs. STATEMENT OF SIGNIFICANCE: Erectile Dysfunction (ED) affects over half the male population aged 40-70 potentially leading to poor quality of life. Patients not responding to conventional treatments of ED, are advised to use penile prostheses which can create an erection using implanted inflatable cylinders. A significant drawback of such prostheses, however, is the substantial tissue damage they can induce during their usage. Preclinical testbeds, including computational and bench-top models, could offer an efficient means of improving device designs to mitigate this damage but such testbeds require extensive knowledge of penile tissue properties. In this study, the authors determine penile tissue mechanics and apply an inverse FE approach to characterise the penile material properties required to validate preclinical models of the penis.

Brain Material Properties and Integration of Arachnoid Complex for Biofidelic Impact Response for Human Head Finite Element Model

Finite element head models offer great potential to study brain-related injuries; however, at present may be limited by geometric and material property simplifications required for continuum-level human body models. Specifically, the mechanical properties of the brain tissues are often represented with simplified linear viscoelastic models, or the material properties have been optimized to specific impact cases. In addition, anatomical structures such as the arachnoid complex have been omitted or implemented in a simple lumped manner. Recent material test data for four brain regions at three strain rates in three modes of loading (tension, compression, and shear) was used to fit material parameters for a hyper-viscoelastic constitutive model. The material model was implemented in a contemporary detailed head finite element model. A detailed representation of the arachnoid trabeculae was implemented with mechanical properties based on experimental data. The enhanced head model was assessed by re-creating 11 ex vivo head impact scenarios and comparing the simulation results with experimental data. The hyper-viscoelastic model faithfully captured mechanical properties of the brain tissue in three modes of loading and multiple strain rates. The enhanced head model showed a high level of biofidelity in all re-created impacts in part due to the improved brain-skull interface associated with implementation of the arachnoid trabeculae. The enhanced head model provides an improved predictive capability with material properties based on tissue level data and is positioned to investigate head injury and tissue damage in the future.

Rate- and Region-Dependent Mechanical Properties of Göttingen Minipig Brain Tissue in Simple Shear and Unconfined Compression

Traumatic brain injury (TBI), particularly from explosive blasts, is a major cause of casualties in modern military conflicts. Computational models are an important tool in understanding the underlying biomechanics of TBI but are highly dependent on the mechanical properties of soft tissue to produce accurate results. Reported material properties of brain tissue can vary by several orders of magnitude between studies, and no published set of material parameters exists for porcine brain tissue at strain rates relevant to blast. In this work, brain tissue from the brainstem, cerebellum, and cerebrum of freshly euthanized adolescent male Göttingen minipigs was tested in simple shear and unconfined compression at strain rates ranging from quasi-static (QS) to 300 s-1. Brain tissue showed significant strain rate stiffening in both shear and compression. Minimal differences were seen between different regions of the brain. Both hyperelastic and hyper-viscoelastic constitutive models were fit to experimental stress, considering data from either a single loading mode (unidirectional) or two loading modes together (bidirectional). The unidirectional hyper-viscoelastic models with an Ogden hyperelastic representation and a one-term Prony series best captured the response of brain tissue in all regions and rates. The bidirectional models were generally able to capture the response of the tissue in high-rate shear and all compression modes, but not the QS shear. Our constitutive models describe the first set of material parameters for porcine brain tissue relevant to loading modes and rates seen in blast injury.

Deployment of an electrocorticography system with a soft robotic actuator

Electrocorticography (ECoG) is a minimally invasive approach frequently used clinically to map epileptogenic regions of the brain and facilitate lesion resection surgery and increasingly explored in brain-machine interface applications. Current devices display limitations that require trade-offs among cortical surface coverage, spatial electrode resolution, aesthetic, and risk consequences and often limit the use of the mapping technology to the operating room. In this work, we report on a scalable technique for the fabrication of large-area soft robotic electrode arrays and their deployment on the cortex through a square-centimeter burr hole using a pressure-driven actuation mechanism called eversion. The deployable system consists of up to six prefolded soft legs, and it is placed subdurally on the cortex using an aqueous pressurized solution and secured to the pedestal on the rim of the small craniotomy. Each leg contains soft, microfabricated electrodes and strain sensors for real-time deployment monitoring. In a proof-of-concept acute surgery, a soft robotic electrode array was successfully deployed on the cortex of a minipig to record sensory cortical activity. This soft robotic neurotechnology opens promising avenues for minimally invasive cortical surgery and applications related to neurological disorders such as motor and sensory deficits.

Difference analysis of phenomenological models with two variable forms for soft tissue quasi-static mechanical characterization

It was important to understand the accurate mechanical properties of soft tissue for the evaluation of its injury, provide reliable protective ways or design effective human resist-injury devices. There was little study that clarified the difference between phenomenological models based on strain invariant and the principal stretches variables respectively although some quasi-static constitutive models of soft tissue were developed. In this study, we enumerate several typical hyperelastic models and derive the tensor equation of stress-strain based on continuum mechanics to fit the experimental data of human brain specimens under multiple loading modes in previous studies and give the coefficient of determination based on the least square fitting. It was suggested that two variable forms of phenomenological models with only the first strain invariant are consistent under uniaxial compression and tension, but the Cauchy stress tensor expressed by strain is completely different under simple shear loading. Also, the shear stress derived from the constitutive model based on strain invariants and principal stretchs has multiple relationships related to shear strain. The results in this study would be used to understand the more accurate mechanical characterization of soft tissue, which will allow us to evaluate the injury and develop much accurate injury criteria for soft tissue.

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.

Development and global validation of a 1-week-old piglet head finite element model for impact simulations

PURPOSE

Child head injury under impact scenarios (e.g. falling, vehicle crashing, etc.) is an important topic in the field of injury biomechanics. The head of piglet was commonly used as the surrogate to investigate the biomechanical response and mechanisms of pediatric head injuries because of the similar cellular structures and material properties. However, up to date, piglet head models with accurate geometry and material properties, which have been validated by impact experiments, are seldom. We aimed to develop such a model for future research.

METHODS

In this study, first, the detailed anatomical structures of the piglet head, including the skull, suture, brain, pia mater, dura mater, cerebrospinal fluid, scalp, and soft tissue, were constructed based on CT scans. Then, a structured butterfly method was adopted to mesh the complex geometries of the piglet head to generate high-quality elements and each component was assigned corresponding constitutive material models. Finally, the guided drop tower tests were conducted and the force-time histories were ectracted to validate the piglet head finite element model.

RESULTS

Simulations were conducted on the developed finite element model under impact conditions and the simulation results were compared with the experimental data from the guided drop tower tests and the published literature. The average peak force and duration of the guide drop tower test were similar to that of the simulation, with an error below 10%. The inaccuracy was below 20%. The average peak force and duration reported in the literature were comparable to those of the simulation, with the exception of the duration for an impact energy of 11 J. The results showed that the model was capable to capture the response of the pig head.

CONCLUSION

This study can provide an effective tool for investigating child head injury mechanisms and protection strategies under impact loading conditions.

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.

Investigation of the Compressive Viscoelastic Properties of Brain Tissue Under Time and Frequency Dependent Loading Conditions

The mechanical characterization of brain tissue has been generally analyzed in the frequency and time domain. It is crucial to understand the mechanics of the brain under realistic, dynamic conditions and convert it to enable mathematical modelling in a time domain. In this study, the compressive viscoelastic properties of brain tissue were investigated under time and frequency domains with the same physical conditions and the theory of viscoelasticity was applied to estimate the prediction of viscoelastic response in the time domain based on frequency-dependent mechanical moduli through Finite Element models. Storage and loss modulus were obtained from white and grey matter, of bovine brains, using dynamic mechanical analysis and time domain material functions were derived based on a Prony series representation. The material models were evaluated using brain testing data from stress relaxation and hysteresis in the time dependent analysis. The Finite Element models were able to represent the trend of viscoelastic characterization of brain tissue under both testing domains. The outcomes of this study contribute to a better understanding of brain tissue mechanical behaviour and demonstrate the feasibility of deriving time-domain viscoelastic parameters from frequency-dependent compressive data for biological tissue, as validated by comparing experimental tests with computational simulations.

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

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

Dynamic mechanical characterization and viscoelastic modeling of bovine brain tissue

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

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.

A comprehensive study on the mechanical properties of different regions of 8-week-old pediatric porcine brain under tension, shear, and compression at various strain rates

Young porcine brain is often used as a surrogate for studying the mechanical factors affecting traumatic brain injury in children. However, the mechanical properties of pediatric brain tissue derived from humans and piglets are very scarce, and this seriously detracts from the biofidelity of the developed finite element (FE) models of the pediatric head/brain. The present study addresses this issue by subjecting the cerebrum (white matter and gray matter), cerebellum, and brainstem specimens derived from 8-week-old piglets to tension and shear testing at strain rates of 0.01, 1, and 50/s. The experimental data are combined with the corresponding data derived from a previous study under compression to obtain comprehensive stress-strain curves of the pediatric porcine cerebrum, cerebellum, and brainstem tissue specimens. In general, the average stress level of the white matter is somewhat higher than that of the gray matter under the tension, shear and compression conditions, however, this difference does not reach a significant level. The stiffness of the cerebellum and the cerebrum does not differ significantly under tension and shear conditions, but the stiffness of the cerebellum is greater than that of the cerebrum under compression. The brainstem has significantly higher stiffness than the cerebrum and the cerebellum under all loading modes. In addition, the mechanical properties of brain tissue exhibit significant strain-rate dependences. With increasing strain rate from 0.01/s to 50/s, the average stress at a strain of 0.5 for all of the brain tissue increased by about 2.2 times under tension, about 2.4 times under shearing and about 2.2 times under compression. The variations in the stress as a function of the strain rate for brain tissue specimens were well characterized by exponential functions at strains of 0.25 and 0.5 under all three loading modes. The results of this study are useful for developing biofidelic FE models of the pediatric brain.