Biphasic analysis of rat brain slices under creep indentation shows nonlinear tension-compression behavior

Heterogeneous Mechanical Stress and Interstitial Fluid Flow Predictions Derived from DCE-MRI for Rat U251N Orthotopic Gliomas

Mechanical stress and fluid flow influence glioma cell phenotype in vitro, but measuring these quantities in vivo continues to be challenging. The purpose of this study was to predict these quantities in vivo, thus providing insight into glioma physiology and potential mechanical biomarkers that may improve glioma detection, diagnosis, and treatment. Image-based finite element models of human U251N orthotopic glioma in athymic rats were developed to predict structural stress and interstitial flow in and around each animal's tumor. In addition to accounting for structural stress caused by tumor growth, our approach has the advantage of capturing fluid pressure-induced structural stress, which was informed by in vivo interstitial fluid pressure (IFP) measurements. Because gliomas and the brain are soft, elevated IFP contributed substantially to tumor structural stress, even inverting this stress from compressive to tensile in the most compliant cases. The combination of tumor growth and elevated IFP resulted in a concentration of structural stress near the tumor boundary where it has the greatest potential to influence cell proliferation and invasion. MRI-derived anatomical geometries and tissue property distributions resulted in heterogeneous interstitial fluid flow with local maxima near cerebrospinal fluid spaces, which may promote tumor invasion and hinder drug delivery. In addition, predicted structural stress and interstitial flow varied markedly between irradiated and radiation-naïve animals. Our modeling suggests that relative to tumors in stiffer tissues, gliomas experience unusual mechanical conditions with potentially important biological (e.g., proliferation and invasion) and clinical consequences (e.g., drug delivery and treatment monitoring).

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).

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

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

Correlating the microstructural architecture and macrostructural behaviour of the brain

The computational simulation of pathological conditions and surgical procedures, for example the removal of cancerous tissue, can contribute crucially to the future of medicine. Especially for brain surgery, these methods can be important, as the ultra-soft tissue controls vital functions of the body. However, the microstructural interactions and their effects on macroscopic material properties remain incompletely understood. Therefore, we investigated the mechanical behaviour of brain tissue under three different deformation modes, axial tension, compression, and semi-confined compression, in different anatomical regions, and for varying axon orientation. In addition, we characterised the underlying microstructure in terms of myelin, cells, glial cells and neuron area fraction, and density. The correlation of these quantities with the material parameters of the anisotropic Ogden model reveals a decrease in shear modulus with increasing myelin area fraction. Strikingly, the tensile shear modulus correlates positively with cell and neuronal area fraction (Spearman's correlation coefficient of r_s=0.40 and r_s=0.33), whereas the compressive shear modulus decreases with increasing glial cell area (r_s=-0.33). Our study finds that tissue non-linearity significantly depends on the myelin area fraction (r_s=0.47), cell density (r_s=0.41) and glial cell area (r_s=0.49). Our results provide an important step towards understanding the micromechanical load transfer that leads to the non-linear macromechanical behaviour of the brain. STATEMENT OF SIGNIFICANCE: Within this article, we investigate the mechanical behaviour of brain tissue under three different deformation modes, in different anatomical regions, and for varying axon orientation. Further, we characterise the underlying microstructure in terms of various constituents. The correlation of these quantities with the material parameters of the anisotropic Ogden model reveals a decrease in shear modulus with increasing myelin area fraction. Strikingly, the tensile shear modulus correlates positively with cell and neuronal area fraction, whereas the compressive shear modulus decreases with increasing glial cell area. Our study finds that tissue non-linearity significantly depends on the myelin area fraction, cell density, and glial cell area. Our results provide an important step towards understanding the micromechanical load transfer that leads to the non-linear macromechanical behaviour of the brain.

Insights into Infusion-Based Targeted Drug Delivery in the Brain: Perspectives, Challenges and Opportunities

Targeted drug delivery in the brain is instrumental in the treatment of lethal brain diseases, such as glioblastoma multiforme, the most aggressive primary central nervous system tumour in adults. Infusion-based drug delivery techniques, which directly administer to the tissue for local treatment, as in convection-enhanced delivery (CED), provide an important opportunity; however, poor understanding of the pressure-driven drug transport mechanisms in the brain has hindered its ultimate success in clinical applications. In this review, we focus on the biomechanical and biochemical aspects of infusion-based targeted drug delivery in the brain and look into the underlying molecular level mechanisms. We discuss recent advances and challenges in the complementary field of medical robotics and its use in targeted drug delivery in the brain. A critical overview of current research in these areas and their clinical implications is provided. This review delivers new ideas and perspectives for further studies of targeted drug delivery in the brain.

A computational model of glioma reveals opposing, stiffness-sensitive effects of leaky vasculature and tumor growth on tissue mechanical stress and porosity

A biphasic computational model of a growing, vascularized glioma within brain tissue was developed to account for unique features of gliomas, including soft surrounding brain tissue, their low stiffness relative to brain tissue, and a lack of draining lymphatics. This model is the first to couple nonlinear tissue deformation with porosity and tissue hydraulic conductivity to study the mechanical interaction of leaky vasculature and solid growth in an embedded glioma. The present model showed that leaky vasculature and elevated interstitial fluid pressure produce tensile stress within the tumor in opposition to the compressive stress produced by tumor growth. This tensile effect was more pronounced in softer tissue and resulted in a compressive stress concentration at the tumor rim that increased when tumor was softer than host. Aside from generating solid stress, fluid pressure-driven tissue deformation decreased the effective stiffness of the tumor while growth increased it, potentially leading to elevated stiffness in the tumor rim. A novel prediction of reduced porosity at the tumor rim was corroborated by direct comparison with estimates from our in vivo imaging studies. Antiangiogenic and radiation therapy were simulated by varying vascular leakiness and tissue hydraulic conductivity. These led to greater solid compression and interstitial pressure in the tumor, respectively, the former of which may promote tumor infiltration of the host. Our findings suggest that vascular leakiness has an important influence on in vivo solid stress, stiffness, and porosity fields in gliomas given their unique mechanical microenvironment.

Nonlinear plane waves in saturated porous media with incompressible constituents

We consider the propagation of nonlinear plane waves in porous media within the framework of the Biot–Coussy biphasic mixture theory. The tortuosity effect is included in the model, and both constituents are assumed incompressible (Yeoh-type elastic skeleton, and saturating fluid). In this case, the linear dispersive waves governed by Biot’s theory are either of compression or shear-wave type, and nonlinear waves can be classified in a similar way. In the special case of a neo-Hookean skeleton, we derive the explicit expressions for the characteristic wave speeds, leading to the hyperbolicity condition. The sound speeds for a Yeoh skeleton are estimated using a perturbation approach. Then we arrive at the evolution equation for the amplitude of acceleration waves. In general, it is governed by a Bernoulli equation. With the present constitutive assumptions, we find that longitudinal jump amplitudes follow a nonlinear evolution, while transverse jump amplitudes evolve in an almost linearly degenerate fashion.

Dynamic mechanical characterization and viscoelastic modeling of bovine brain tissue

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

A poro-hyper-viscoelastic rate-dependent constitutive modeling for the analysis of brain tissues

In this paper, the dynamic behavior of bovine brain tissue, measured from in-vitro unconfined compression tests, is examined and represented through a viscoelastic biphasic model. The experiments have been carried out under three compression speeds of 10, 100, and 1000 mm/s. The results exhibited significant rate-dependent behavior. The brain tissue is modeled as a biphasic continuum consisting of a compressible solid matrix, fully saturated with an incompressible interstitial fluid. The governing equations based on conservation of mass and momentum are used to describe the solid-fluid interactions. An inverse scheme is employed in which a finite element model runs iteratively to optimize constitutive constants. The obtained material parameters of the proposed biphasic model show relatively good agreement (R² ≥ 0.96) with the experimental tissue mechanical responses at different rates. The model can successfully capture the key aspects of the rate-dependency for both solid and fluid phases under large strain deformation. This poro-hyper viscoelastic model can effectively estimate the global and local rate-dependent tissue deformations, the spatial variations in pore spaces, hydrostatic pressure as well as fluid diffusion through the tissue.