Joshua H. Smith

Fitted hyperelastic parameters for Human brain tissue from reported tension, compression, and shear tests.

The mechanical properties of human brain tissue are the subject of interest because of their use in understanding brain trauma and in developing therapeutic treatments and procedures. To represent the behavior of the tissue, we have developed hyperelastic mechanical models whose parameters are fitted in accordance with experimental test results. However, most studies available in the literature have fitted parameters with data of a single type of loading, such as tension, compression, or shear. Recently, Jin et al. (Journal of Biomechanics 46:2795-2801, 2013) reported data from ex vivo tests of human brain tissue under tension, compression, and shear loading using four strain rates and four different brain regions. However, they do not report parameters of energy functions that can be readily used in finite element simulations. To represent the tissue behavior for the quasi-static loading conditions, we aimed to determine the best fit of the hyperelastic parameters of the hyperfoam, Ogden, and polynomial strain energy functions available in ABAQUS for the low strain rate data, while simultaneously considering all three loading modes. We used an optimization process conducted in MATLAB, calling iteratively three finite element models developed in ABAQUS that represent the three loadings. Results showed a relatively good fit to experimental data in all loading modes using two terms in the energy functions. Values for the shear modulus obtained in this analysis (897-1653Pa) are in the range of those presented in other studies. These energy-function parameters can be used in brain tissue simulations using finite element models.

A biphasic hyperelastic model for the analysis of fluid and mass transport in brain tissue.

A biphasic hyperelastic finite element model is proposed for the description of the mechanical behavior of brain tissue. The model takes into account finite deformations through an Ogden-type hyperelastic compressible function and a hydraulic conductivity dependent on deformation. The biphasic equations, implemented here for spherical symmetry using an updated Lagrangian algorithm, yielded radial coordinates and fluid velocities that were used with the convective–diffusive equation in order to predict mass transport in the brain. Results of the model were equal to those of a closed-form solution under infinitesimal deformations, however, for a wide range of material parameters, the model predicted important increments in the infusion sphere, reductions of the fluid velocities, and changes in the species content distribution. In addition, high localized deformation and stresses were obtained at the infusion sphere. Differences with the infinitesimal solution may be mainly attributed to geometrical nonlinearities related to the increment of the infusion sphere and not to material nonlinearities.

A nonlinear biphasic model of flow-controlled infusion in brain: Fluid transport and tissue deformation analyses

A biphasic nonlinear mathematical model is proposed for the concomitant fluid transport and tissue deformation that occurs during constant flow rate infusions into brain tissue. The model takes into account material and geometrical nonlinearities, a hydraulic conductivity dependent on strain, and nonlinear boundary conditions at the infusion cavity. The biphasic equations were implemented in a custom written code assuming spherical symmetry and using an updated Lagrangian finite element algorithm. Results of the model showed that both, geometric and material nonlinearities play an important role in the physics of infusions, yielding important differences from infinitesimal analyses. Geometrical nonlinearities were mainly due to the significant enlargement of the infusion cavity, while variations of the parameters that describe the degree of nonlinearity of the stress-strain curve yielded significant differences in all distributions. For example, a parameter set showing stiffening under tension yielded maximum values of radial displacement and porosity not localized at the infusion cavity. On the other hand, a parameter set showing softening under tension yielded a slight decrease in the fluid velocity for a three-fold increase in the flow rate, which can be explained by the substantial increase of the infusion cavity, not considered in linear analyses. This study strongly suggests that significant enlargement of the infusion cavity is a real phenomenon during infusions that may produce collateral damage to brain tissue. Our results indicate that more experimental tests have to be undertaken in order to determine material nonlinearities of brain tissue over a range of strains. With better understanding of these nonlinear effects, clinicians may be able to develop protocols that can minimize the damage to surrounding tissue.

A nonlinear biphasic model of flow-controlled infusions in brain: mass transport analyses.

A biphasic nonlinear mathematical model is proposed for the mass transport that occurs during constant flow-rate infusions into brain tissue. The model takes into account geometric and material nonlinearities and a hydraulic conductivity dependent upon strain. The biphasic and convective-diffusive transport equations were implemented in a custom-written code assuming spherical symmetry and using an updated Lagrangian finite element algorithm. Results of the model indicate that the inclusion of these nonlinearities produced modest changes in the interstitial concentration but important variations in drug penetration and bulk concentration. Increased penetration of the drug but smaller bulk concentrations were obtained at smaller strains caused by combination of parameters such as increased Youngs modulus and initial hydraulic conductivity. This indicates that simulations of constant flow-rate infusions under the assumption of infinitesimal deformations or rigidity of the tissue may yield lower bulk concentrations near the infusion cavity and over-predictions of the penetration of the infused agent. The analyses also showed that decrease in the infusion flow rate of a fixed amount of drug results in increased penetration of the infused agent. From the clinical point-of-view, this may promote a safer infusion that delivers the therapeutic range over the desired volume while avoiding damage to the tissue by minimizing deformation and strain.

A patient-specific, finite element model for noncommunicating hydrocephalus capable of large deformation.

A biphasic model for noncommunicating hydrocephalus in patient-specific geometry is proposed. The model can take into account the nonlinear behavior of brain tissue under large deformation, the nonlinear variation of hydraulic conductivity with deformation, and contact with a rigid, impermeable skull using a recently developed algorithm. The model was capable of achieving over a 700 percent ventricular enlargement, which is much greater than in previous studies, primarily due to the use of an anatomically realistic skull recreated from magnetic resonance imaging rather than an artificial skull created by offsetting the outer surface of the cerebrum. The choice of softening or stiffening behavior of brain tissue, both having been demonstrated in previous experimental studies, was found to have a significant effect on the volume and shape of the deformed ventricle, and the consideration of the variation of the hydraulic conductivity with deformation had a modest effect on the deformed ventricle. The model predicts that noncommunicating hydrocephalus occurs for ventricular fluid pressure on the order of 1300 Pa.

Implications of Transvascular Fluid Exchange in Nonlinear, Biphasic Analyses of Flow-Controlled Infusion in Brain

A nonlinear, coupled biphasic-mass transport model that includes transvascular fluid exchange is proposed for flow-controlled infusions in brain tissue. The model accounts for geometric and material nonlinearities, a hydraulic conductivity dependent on deformation, and transvascular fluid exchange according to Starling’s law. The governing equations were implemented in a custom-written code assuming spherical symmetry and using an updated Lagrangian finite-element algorithm. Results of the model indicate that, using normal physiological values of vascular permeability, transvascular fluid exchange has negligible effects on tissue deformation, fluid pressure, and transport of the infused agent. As vascular permeability may be increased artificially through methods such as administering nitric oxide, a parametric study was conducted to determine how increased vascular permeability affects flow-controlled infusion. Increased vascular permeability reduced both tissue deformation and fluid pressure, possibly reducing damage to tissue adjacent to the infusion catheter. Furthermore, the loss of fluid to the vasculature resulted in a significantly increased interstitial fluid concentration but a modestly increased tissue concentration. From a clinical point of view, this increase in concentration could be beneficial if limited to levels below which toxicity would not occur. However, the modestly increased tissue concentration may make the increase in interstitial fluid concentration difficult to assess in vivo using co-infused radiolabeled agents.

Constitutive Modeling of Brain Tissue using Ogden-type Strain Energy Functions

Initial experimental characterization of brain tissue assumed it was a single-phase material and modeled the nonlinear mechanical behavior observed under finite deformation using the incompressible Ogden strain energy function. For the modeling of some diseases of the brain, it is necessary to represent brain tissue as a biphasic medium with solid and fluid phases. Two forms of a compressible Ogden-like strain energy functions are currently available in the popular finite element solvers FEBIO and ABAQUS. We assessed the ability of these functions to reproduce physically expected behavior under uniaxial, biaxial, and triaxial loading. For some nonlinear material parameter sets, the compressible Ogden-type strain energy function of ABAQUS yielded stiffening behavior in tension for uniaxial loading that became markedly softer for triaxial deformation. In contrast, the compressible Ogden-type strain energy function of FEBIO showed no such reversal of the trends. Considering that stress fields in brain tissue are rarely uniaxial, a complete evaluation of compressible strain energy functions under multiaxial loading is necessary for accurate modeling of biphasic brain tissue.

Predictions of Drug Distribution During Infusions Into the Brain Using an Axisymmetric Finite Element Biphasic Model That Includes Backflow

Convection-enhanced delivery is a technique to infuse therapeutic agents into the brain under positive pressure for the treatment of disorders of the central nervous system. Recent clinical trials [1] have shown limited efficacy of this procedure, attributed to poor distribution of the infused agent that may be due to backflow, in which the infused fluid preferentially flows along the outside of the catheter toward the surface of the brain.Copyright

A Nonlinear Biphasic Hyperelastic Model for Acute Hydrocephalus

The cerebrospinal fluid present in the central nervous system plays an important role in the physiological activities and protection of the brain. Disruptions of CSF flow lead to different forms of a disease known as hydrocephalus, characterized by a significant increment of the ventricular space. In acute hydrocephalus the Sylvius aqueduct is blocked and ventricular pressure is greatly increased.Copyright

A Flow-Controlled Finite Element Model of Noncommunicating Hydrocephalus

Cerebrospinal fluid (CSF) is produced at a constant rate in the choroid plexuses of the lateral and third ventricles, and it predominately drains through the Sylvius aqueduct to the fourth ventricle. If the Sylvius aqueduct becomes obstructed, such as caused by a growing tumor adjacent to it, CSF accumulates in the ventricles and the ventricles expand significantly, leading to a medical condition known as noncommunicating, hydrocephalus.Copyright