Experimental and numerical study on the mechanical behavior of rat brain 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.

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.

Determining constitutive behavior of the brain tissue using digital image correlation and finite element modeling

Detailed knowledge about the mechanical properties of brain can improve numerical modeling of the brain under various loading conditions. The success of this modeling depends on constitutive model and reliable extraction of its material constants. The isotropy of the brain tissue is a key factor which affects the form of constitutive models. In this study, compression tests were performed on different parts of the sheep brain tissue. Also, the digital image correlation (DIC) method was utilized to investigate the direction dependency of brain parts considering their microstructures. To this aim, the DIC method was employed to measure the transverse strain of two lateral sides of the tissue samples. The results of DIC method revealed that the brain stem and corona radiata were isotropic, while the mixed white and gray matter showed an unrepeatable behavior depending on the extracted sample. To examine and validate DIC method, stress-strain diagrams were also used to investigate the isotropy. It could be concluded that axonal fibers had no reinforcing role in the brain tissue. Furthermore, the DIC method indicated incompressibility of the brain tissue. Then, the significance of using a correct method to extract the material constants of brain was discussed. In other words, the effect of the real boundary conditions in experiments, which was neglected in most previous studies, was taken into account here. Finally, the particle swarm optimization algorithm along with the finite element modeling was used to estimate the hyper-viscoelastic constants of different parts of the brain tissue.

A NUMERICAL STUDY ON THE HEMODYNAMIC AND SHEAR STRESS OF DOUBLE ANEURYSM THROUGH S-SHAPED VESSEL

Abdominal aortic aneurysm (AAA) is a degenerative disease defined as the abnormal ballooning of the abdominal aorta (AA) wall which is usually caused by atherosclerosis. The aneurysm grows larger and eventually ruptures if it is not diagnosed and treated. Aneurysms occur mostly in the aorta, the main artery of the chest and abdomen. The aorta carries blood flow from the heart to all parts of the body, including the vital organs, the legs, and feet. The objective of the present study is to investigate the combined effects of aneurysm and curvature on flow characteristics in S-shaped bends with sweep angle of 90° at Reynolds number of 900. The fluid mechanics of blood flow in a curved artery with abnormal aortic is studied through a mathematical analysis and employing Cosmos flow simulation. Blood is modeled as an incompressible non-Newtonian fluid and the flow is assumed to be steady and laminar. Hemodynamic characteristics are analyzed. Grid independence is tested on three successively refined meshes. It is observed that the abrupt expansion induced by AAA results in an immensely disturbed regime. The results may have implications not only for understanding the mechanical behavior of the blood flow inside an aneurysm artery but also for investigating the mechanical behavior of the blood flow in different arterial diseases, such as atherosclerosis.

A COMBINATION OF EXPERIMENTAL AND NUMERICAL ANALYSES TO MEASURE THE COMPRESSIVE MECHANICAL PROPERTIES OF TENNIS BALL

Tennis is almost a newly born sport (1859) that can be played individually against a single opponent (singles) or between two teams of two players each, namely doubles. Materially, tennis balls were made of cloth strips stitched together from thread. They have also been made of hollow rubber with a felt coating appearing in different colors from traditionally white to yellow in the recent years to permit their visibility. Although the most common injuries associated with tennis have been reported to be related to rotator cuff, elbow, wrist, anterior knee pain, and ankle, the injury that a tennis ball can cause, for example, for eye is still not clear. However, as the tennis ball can reach to a speed of 260 km/h, it seems vital to understand its mechanical properties to have a deep insight into the injury that can happen during playing. Therefore, this study aimed to perform an experimental study to evaluate the linear elastic and nonlinear hyperelastic mechanical properties of the tennis ball under compressive loading. To do this, 40 numbers of approved tennis balls by international tennis federation (ITF) were prepared and subjected to a series of compressive loadings. The strain of the balls was measured via a pair of CCD cameras using digital image correlation (DIC) technique. The results revealed the mean elastic modulus, maximum stress, and strain of 336.69 kPa, 410.15 kPa, and 66%, for the tennis balls, respectively. The nonlinear mechanical behavior of the tennis balls were also computationally investigated through a hyperelastic material model, namely Ogden. Finally, a finite element (FE) model was executed to verify the hyperelastic data with that of experimental and, interestingly, the numerical data were in good agreement with experimental ones. The findings of this study may have implications not only for understanding the compressive mechanical properties of the tennis ball, but also for investigating the injury that can occur in the human body by tennis ball, especially the eye.

Mechanics of Biological Tissues and Biomaterials: Current Trends

Investigation of the mechanical behavior of biological tissues and biomaterials has been an active area of research for several decades. However, in recent years, the enthusiasm in understanding the mechanical behavior of biological tissues and biomaterials has increased significantly due to the development of novel biomaterials for new fields of application, along with the emergence of advanced computational techniques. The current Special Issue is a collection of studies that address various topics within the general theme of “mechanics of biomaterials”. This editorial aims to present the context within which the studies of this Special Issue could be better understood. I, therefore, try to identify some of the most important research trends in the study of the mechanical behavior of biological tissues and biomaterials.

An experimental-nonlinear finite element study of a balloon expandable stent inside a realistic stenotic human coronary artery to investigate plaque and arterial wall injury

The stresses induced within plaque tissues and arterial layers during stent expansion inside an atherosclerotic artery can be exceeded from the yield stresses of those tissues and, consequently, lead to plaque or arterial wall rupture. The distribution and magnitude of the stresses in the plaque-artery-stent structure might be distinctly different for different plaque types. In this study, the mechanical properties of six healthy and atherosclerotic human coronary arteries were determined for application in plaque and arterial vulnerability assessment. A nonlinear finite element simulation based on an Ogden material model was established to investigate the effect of plaque types on the stresses induced in the arterial wall during implantation of a balloon expandable coronary stent. The atherosclerotic artery was assumed to consist of a plaque and normal arterial tissues on its outer side. The results indicated a significant influence of plaque types on the maximum stresses induced within the plaque wall and arterial wall during stenting but not when computing maximum stress on the stent. The stress on the stiffest calcified plaque wall was 3.161 MPa, whereas cellular and hypocellular plaques showed relatively less stress on their wall. The highest von Mises stresses within the arterial wall were observed on the hypocellular plaque, whereas the lowest stresses were seen to be located in the calcified and cellular plaques. Although the computed stresses on the arterial wall for the calcified and cellular plaques were not high enough to invoke a rupture, the stress on the hypocellular plaque was relatively higher than that of the strength of the arterial wall. These findings may have implications not only for understanding the stresses induced in plaque and the arterial wall, but also for developing surgeries such as balloon-angioplasty and stenting.

Measurement of the axial and circumferential mechanical properties of rat skin tissue at different anatomical locations

Skin tissue is not only responsible for thermoregulation but also for protecting the human body from mechanical, bacterial, and viral insults. The mechanical properties of skin tissue may vary according to the anatomical locations in the body. However, the linear elastic and nonlinear hyperelastic mechanical properties of the skin in different anatomical regions and at different loading directions (axial and circumferential) so far have not been determined. In this study, the mechanical properties during tension of the rat abdomen and back were calculated at different loading directions using linear elastic and nonlinear hyperelastic material models. The skin samples were subjected to a series of tensile tests. The elastic modulus and maximum stress of the skin tissues were measured before the incidence of failure. The nonlinear mechanical behavior of the skin tissues was also computationally investigated through a constitutive equation. Hyperelastic strain energy density function was calibrated using the experimental data. The results revealed the anisotropic mechanical behavior of the abdomen and the isotropic mechanical response of the back skin. The highest elastic modulus was observed in the abdomen skin under the axial direction (10 MPa), while the lowest one was seen in the back skin under axial loading (5 MPa). The Mooney-Rivlin material model closely addressed the nonlinear mechanical behavior of the skin at different loading directions, which can be implemented in the future biomechanical models of skin tissue. The results might have implications not only for understanding of the isotropic and anisotropic mechanical behavior of skin tissue at different anatomical locations but also for providing more information for a diversity of disciplines, including dermatology, cosmetics industry, clinical decision making, and clinical intervention.

A comparative study on the uniaxial mechanical properties of the umbilical vein and umbilical artery using different stress-strain definitions

The umbilical cord is part of the fetus and generally includes one umbilical vein (UV) and two umbilical arteries (UAs). As the saphenous vein and UV are the most commonly used veins for the coronary artery disease treatment as a coronary artery bypass graft (CABG), understating the mechanical properties of UV has a key asset in its performance for CABG. However, there is not only a lack of knowledge on the mechanical properties of UV and UA but there is no agreement as to which stress-strain definition should be implemented to measure their mechanical properties. In this study, the UV and UA samples were removed after caesarean from eight individuals and subjected to a series of tensile testing. Three stress definitions (second Piola-Kichhoff stress, engineering stress, and true stress) and four strain definitions (Almansi-Hamel strain, Green-St. Venant strain, engineering strain, and true strain) were employed to determine the linear mechanical properties of UVs and UAs. The nonlinear mechanical behavior of UV/UA was computationally investigated using hyperelastic material models, such as Ogden and Mooney-Rivlin. The results showed that the effect of varying the stress definition on the maximum stress measurements of the UV/UA is significant but not when calculating the elastic modulus. In the true stress-strain diagram, the maximum strain of UV was 92 % higher, while the elastic modulus and maximum stress were 162 and 42 % lower than that of UA. The Mooney-Rivlin material model was designated to represent the nonlinear mechanical behavior of the UV and UA under uniaxial loading.

An experimental study on the mechanical properties of rat brain tissue using different stress-strain definitions

There are different stress-strain definitions to measure the mechanical properties of the brain tissue. However, there is no agreement as to which stress-strain definition should be employed to measure the mechanical properties of the brain tissue at both the longitudinal and circumferential directions. It is worth knowing that an optimize stress-strain definition of the brain tissue at different loading directions may have implications for neuronavigation and surgery simulation through haptic devices. This study is aimed to conduct a comparative study on different results are given by the various definitions of stress-strain and to recommend a specific definition when testing brain tissues. Prepared cylindrical samples are excised from the parietal lobes of rats' brains and experimentally tested by applying load on both the longitudinal and circumferential directions. Three stress definitions (second Piola-Kichhoff stress, engineering stress, and true stress) and four strain definitions (Almansi-Hamel strain, Green-St. Venant strain, engineering strain, and true strain) are used to determine the elastic modulus, maximum stress and strain. The highest non-linear stress-strain relation is observed for the Almansi-Hamel strain definition and it may overestimate the elastic modulus at different stress definitions at both the longitudinal and circumferential directions. The Green-St. Venant strain definition fails to address the non-linear stress-strain relation using different definitions of stress and triggers an underestimation of the elastic modulus. The results suggest the application of the true stress-true strain definition for characterization of the brain tissues mechanics since it gives more accurate measurements of the tissue's response using the instantaneous values.

A nonlinear finite element simulation of balloon expandable stent for assessment of plaque vulnerability inside a stenotic artery

The stresses induced on plaque wall during stent implantation inside a stenotic artery are associated with plaque rupture. The stresses in the plaque-artery-stent structure appear to be distinctly different for different plaque types in terms of both distribution and magnitude. In this study, a nonlinear finite element simulation was executed to analyze the influence of plaque composition (calcified, cellular, and hypocellular) on plaque, artery layers (intima, media, and adventitia), and stent stresses during implantation of a balloon expandable coronary stent into a stenosed artery. The atherosclerotic artery was assumed to consist of a plaque and normal arterial tissues on its outer side. The results revealed a significant influence of plaque types on the maximum stresses induced within plaque wall and artery layers during stenting, but not when calculating maximum stress on stent. The stress on stiffer calcified plaque wall was in the fracture level (2.21 MPa), whereas cellular and hypocellular plaques play a protective role by displaying less stress on their wall. The highest von Mises stresses were observed on less stiff media layer. The findings of this study suggest a lower risk of arterial vascular injury for calcified plaque, while higher risk of plaque ruptures for cellular and hypocellular plaques.

Finite element simulation of an artificial intervertebral disk using fiber reinforced laminated composite model

Degeneration of intervertebral disk (IVD) has been increased in recent years. The lumbar herniation can be cured using conservative and surgical procedures. Surgery is considered after failure of conservative treatment. Partial discectomy, fusion, and total disk replacement (TDR) are also common surgical treatments for degenerative disk disease. However, due to limitations and disadvantages of the current treatments, many studies have been carried out to approach the best design of mimicking natural disk. Recently, a new method of TDRs has been introduced using nature deformation of IVD by reinforced fibers of annulus fibrosis. Nonetheless, owing to limitations of experimental works on the human body, numerical studies of IVD may help to understand load transfer and biomechanical properties within the disks with reinforced fibers. In this study, a three-dimensional (3D) finite element model of the L2-L3 disk vertebrae unit with 12 vertical fibers embedded into annulus fibrosis was constructed. The IVD was subjected to compressive force, bending moment, and axial torsion. The most important parameters of disk failures were compared to that of experimental data. The results showed that the addition of reinforced fibers into the disk invokes a significant decrease of stress in the nucleus and annulus. The findings of this study may have implications not only for developing IVDs with reinforced fibers but also for the application of fiber reinforced IVD in orthopedics surgeries as a suitable implant.

A comparative study on the elastic modulus of polyvinyl alcohol sponge using different stress-strain definitions

There have been different stress-strain definitions to measure the elastic modulus of spongy materials, especially polyvinyl alcohol (PVA) sponge. However, there is no agreement as to which stress-strain definition should be implemented. This study was aimed to show how different results are given by the various definitions of stress-strain used, and to recommend a specific definition when testing spongy materials. A fabricated PVA sponge was subjected to a series of tensile tests in order to measure its mechanical properties. Three stress definitions (second Piola-Kichhoff stress, engineering stress, and true stress) and four strain definitions (Almansi-Hamel strain, Green-St. Venant strain, engineering strain, and true strain) were used to determine the elastic modulus. The results revealed that the Almansi-Hamel strain definition exhibited the highest non-linear stress-strain relation and, as a result, may overestimate the elastic modulus at different stress definitions (second Piola-Kichhoff stress, engineering stress, and true stress). The Green-St. Venant strain definition failed to address the non-linear stress-strain relation using different definitions of stress and invoked an underestimation of the elastic modulus values. Engineering stress and strain definitions were only valid for small strains and displacements, which make them impractical when analyzing spongy materials. The results showed that the effect of varying the stress definition on the maximum stress measurements was significant but not when calculating the elastic modulus. It is important to consider which stress-strain definition is employed when characterizing the mechanical properties of spongy materials. Although the true stress-true strain definition exhibits a non-linear relation, we favor it in spongy materials mechanics as it gives more accurate measurements of the material's response using the instantaneous values.

Material properties in unconfined compression of gelatin hydrogel for skin tissue engineering applications

Gelatin (Gel) has been reported as a promising candidate in tissue engineering owing to its easy availability, biocompatibility, and biodegradability. Gel hydrogel is of potential to be cross-linked with different materials to enhance their biocompatibility for cell culture for tissue engineering applications. The mechanical properties of this versatile material, however, have not been thoroughly determined. In this study, the linear elastic (Young’s modulus and maximum stress) and non-linear hyperelastic (hyperelastic coefficients) mechanical properties of prepared hydrogels at different contents of Gel (wt%) were measured, and its Young’s modulus was compared with that of skin tissue. The prepared cylindrical Gel hydrogels were subjected to a series of unconfined compression tests. The hyperelastic strain energy density function was calibrated using the compressive experimental data. The potential ability of the Yeoh hyperelastic constitutive equation, which has been proposed as the best material model to represent the non-linear behavior of hydrogels, was verified using finite element (FE) simulations. The results revealed that the Young’s modulus and maximum stress of hydrogels are increased by the addition of Gel. The highest Young’s modulus (81 kPa) and maximum stress (24 kPa) were observed for hydrogels with 15 wt% Gel. Results also showed that the hydrogels with a relatively lower content (<7.5 wt%) of Gel have suitable Young’s modulus compared with those with a higher content (>7.5 wt%) for skin tissue engineering. The Yeoh material model was closely fitted with the experimental data and could be used in further biomechanical simulations of the hydrogels. The experimental results were also compared well with those predicted by the FE models. The results of this study might have implications not only for the understanding of the mechanical properties of Gel hydrogel but also for the fabrication of polymeric substrate materials suitable for skin tissue engineering applications.