Relationship between structural modeling and hyperelastic material behavior: application to CNS white matter

 Recent measurements of the material properties of brain tissue allow an examination of the underlying microstructural basis in both physiological and pathophysiological conditions. The purpose of this study is to develop a mathematical relationship between microstructurally based models of the central nervous system (CNS) white matter and equivalent hyperelastic material models. For simplicity, time dependent material behavior is not included in this formulation. The microstructural representation is used to formulate structural property relationships for highly oriented white matter, and is mathematically compared to one isotropic and two anisotropic hyperelastic formulations. For the anisotropic characterizations, the population of axons in the white matter is assumed to align along one preferred direction of the material, yielding a transversely isotropic formulation. Relatively simple strain–energy functions incorporating material anisotropy provide sufficient flexibility to model the nonlinear behavior predicted from structurally based models, although the tangential stiffness of the hyperelastic approaches does not follow completely the behavior of the structurally based formulations. This analysis is an initial step towards linking microstructural aspects of the tissue to material models commonly used for large deformations, and may be an important step in relating predicted tissue deformation to the deformation and stress of cellular and subcellular structures. Received: 15 October 2001 / Accepted: 30 September 2002 Funds for this work were provided by CDC grant R49/CCR312712 and NIH grants P50 NS08803, NICHD RO1 41699, and NINDS RO1 35712.     

Measurement of the hyperelastic properties of ex vivo brain tissue slices

The elastic and hyperelastic properties of brain tissue are of interest to the medical research community as there are several applications where accurate characterization of these properties is crucial for an accurate outcome. The linear response is applicable to brain elastography, while the non-linear response is of interest for surgical simulation programs. Because of the biological differences between gray and white matter, it is reasonable to expect a difference in their mechanical properties. The goal of this work is to characterize the elastic and hyperelastic properties of the brain gray and white matter. In this method, force-displacement data of these tissues were acquired from 25 different brain samples using an indentation apparatus. These data were processed with an inverse problem algorithm using finite element method as the forward problem solver. Young's modulus and the hyperelastic parameters corresponding to the commonly used Polynomial, Yeoh, Arruda-Boyce, and Ogden models were obtained. The parameters characterizing the linear and non-linear mechanical behavior of gray and white matters were found to be significantly different. Young's modulus was 1787±186 and 1195±157Pa for white matter and gray matter, respectively. Among hyperelastic models, due to its accuracy, fewer parameters and shorter computational time requirements, Yeoh model was found to be the most suitable. Due to the significant differences between the linear and non-linear tissue response, we conclude that incorporating these differences into brain biomechanical models is necessary to increase accuracy.     

Inverse identification of region-specific hyperelastic material parameters for human brain tissue

The identification of material parameters accurately describing the region-dependent mechanical behavior of human brain tissue is crucial for computational models used to assist, e.g., the development of safety equipment like helmets or the planning and execution of brain surgery. While the division of the human brain into different anatomical regions is well established, knowledge about regions with distinct mechanical properties remains limited. Here, we establish an inverse parameter identification scheme using a hyperelastic Ogden model and experimental data from multi-modal testing of tissue from 19 anatomical human brain regions to identify mechanically distinct regions and provide the corresponding material parameters. We assign the 19 anatomical regions to nine governing regions based on similar parameters and microstructures. Statistical analyses confirm differences between the regions and indicate that at least the corpus callosum and the corona radiata should be assigned different material parameters in computational models of the human brain. We provide a total of four parameter sets based on the two initial Poisson’s ratios of 0.45 and 0.49 as well as the pre- and unconditioned experimental responses, respectively. Our results highlight the close interrelation between the Poisson’s ratio and the remaining model parameters. The identified parameters will contribute to more precise computational models enabling spatially resolved predictions of the stress and strain states in human brains under complex mechanical loading conditions.

     

De-N-acetyllactotriaosylceramide as a novel cationic glycosphingolipid of bovine brain white matter: isolation and characterization

A novel cationic lipid was separated from bovine brain white matter by a series of chromatographies on carboxymethyl-Sephadex and silica gel in chloroform and methanol. Its structure was identified unambiguously as de-N-acetyllactotriaosylceramide (deNAcLc(3)Cer) by mass spectrometry and (1)H NMR. The natural occurrence of this glycolipid in white matter extract was detected by immunostaining of thin-layer chromatography with monoclonal antibody 5F5, which is directed to deNAcLc(3)Cer and recognizes the terminal beta-glucosaminyl (GlcNH(2)) residue, having a free NH(2) group. A de-N-acetylase capable of hydrolyzing the N-acetyl group of Lc(3)Cer was detected in bovine brain extract using N-[(14)C]acetyl-labeled Lc(3)Cer as a substrate. The biogenesis and possible functional significance of deNAcLc(3)Cer are discussed.     

Differential development of human brain white matter tracts

Neuroscience is increasingly focusing on developmental factors related to human structural and functional connectivity. Unfortunately, to date, diffusion-based imaging approaches have only contributed modestly to these broad objectives, despite the promise of diffusion-based tractography. Here, we report a novel data-driven approach to detect similarities and differences among white matter tracts with respect to their developmental trajectories, using 64-direction diffusion tensor imaging. Specifically, using a cross-sectional sample comprising 144 healthy individuals (7 to 48 years old), we applied k-means cluster analysis to separate white matter voxels based on their age-related trajectories of fractional anisotropy. Optimal solutions included 5-, 9- and 14-clusters. Our results recapitulate well-established tracts (e.g., internal and external capsule, optic radiations, corpus callosum, cingulum bundle, cerebral peduncles) and subdivisions within tracts (e.g., corpus callosum, internal capsule). For all but one tract identified, age-related trajectories were curvilinear (i.e., inverted 'U-shape'), with age-related increases during childhood and adolescence followed by decreases in middle adulthood. Identification of peaks in the trajectories suggests that age-related losses in fractional anisotropy occur as early as 23 years of age, with mean onset at 30 years of age. Our findings demonstrate that data-driven analytic techniques may be fruitfully applied to extant diffusion tensor imaging datasets in normative and neuropsychiatric samples.     

Proteomic studies on the white matter of human brain

Limited information on the protein expression profiles of the different components of mammalian brain is available to date. In the present study, proteomic analysis was performed on 32 white matter samples obtained from 8 different regions of brains of four post mortem cases. Proteins were separated by 2D gel electrophoresis and identified by mass spectrometry. Most of the protein spots (98%) are reproducibly present in all the samples analyzed. A total of 64 different proteins were identified and divided into seven functional groups. These include metabolic proteins (33%), structural proteins (9%), proteins involved in signal transduction (9%), blood proteins (8%), stress related proteins (23%), and proteins involved in the ubiquitin mediated proteolysis (6%). This protein database obtained from the white matter of human brain contributes to deepen our knowledge on the molecular mechanisms that control several pathologies affecting this key component of the brain.     

Dynamic mechanical response of bovine gray matter and white matter brain tissues under compression

Dynamic responses of brain tissues are needed for predicting traumatic brain injury (TBI). We modified a dynamic experimental technique for characterizing high strain-rate mechanical behavior of brain tissues. Using the setup, the gray and white matters from bovine brains were characterized under compression to large strains at five different strain rates ranging from 0.01 to 3000/s. The white matter was examined both along and perpendicular to the coronal section for anisotropy characterization. The results show that both brain tissue matters are highly strain-rate sensitive. Differences between the white matter and gray matter in their mechanical responses are recorded. The white matter shows insignificant anisotropy over all strain rates. These results will lead to rate-dependent material modeling for dynamic event simulations.     

A real time hyperelastic tissue model

Real-time soft tissue modeling has a potential application in medical training, procedure planning and image-guided therapy. This paper characterizes the mechanical properties of organ tissue using a hyperelastic material model, an approach which is then incorporated into a real-time finite element framework. While generalizable, in this paper we use the published mechanical properties of pig liver to characterize an example application. Specifically, we calibrate the parameters of an exponential model, with a least-squares method (LSM) using the assumption that the material is isotropic and incompressible in a uniaxial compression test. From the parameters obtained, the stress–strain curves generated from the LSM are compared to those from the corresponding computational model solved by ABAQUS and also to experimental data, resulting in mean errors of 1.9 and 4.8%, respectively, which are considerably better than those obtained when employing the Neo-Hookean model. We demonstrate our approach through the simulation of a biopsy procedure, employing a tetrahedral mesh representation of human liver generated from a CT image. Using the material properties along with the geometric model, we develop a nonlinear finite element framework to simulate the behaviour of liver during an interventional procedure with a real-time performance achieved through the use of an interpolation approach.     

A real time hyperelastic tissue model

Real-time soft tissue modeling has a potential application in medical training, procedure planning and image-guided therapy. This paper characterizes the mechanical properties of organ tissue using a hyperelastic material model, an approach which is then incorporated into a real-time finite element framework. While generalizable, in this paper we use the published mechanical properties of pig liver to characterize an example application. Specifically, we calibrate the parameters of an exponential model, with a least-squares method (LSM) using the assumption that the material is isotropic and incompressible in a uniaxial compression test. From the parameters obtained, the stress-strain curves generated from the LSM are compared to those from the corresponding computational model solved by ABAQUS and also to experimental data, resulting in mean errors of 1.9 and 4.8%, respectively, which are considerably better than those obtained when employing the Neo-Hookean model. We demonstrate our approach through the simulation of a biopsy procedure, employing a tetrahedral mesh representation of human liver generated from a CT image. Using the material properties along with the geometric model, we develop a nonlinear finite element framework to simulate the behaviour of liver during an interventional procedure with a real-time performance achieved through the use of an interpolation approach.     

A model for diffusion in white matter in the brain

Diffusion of molecules in brain and other tissues is important in a wide range of biological processes and measurements ranging from the delivery of drugs to diffusion-weighted magnetic resonance imaging. Diffusion tensor imaging is a powerful noninvasive method to characterize neuronal tissue in the human brain in vivo. As a first step toward understanding the relationship between the measured macroscopic apparent diffusion tensor and underlying microscopic compartmental geometry and physical properties, we treat a white matter fascicle as an array of identical thick-walled cylindrical tubes arranged periodically in a regular lattice and immersed in an outer medium. Both square and hexagonal arrays are considered. The diffusing molecules may have different diffusion coefficients and concentrations (or densities) in different domains, namely within the tubes' inner core, membrane, myelin sheath, and within the outer medium. Analytical results are used to explore the effects of a large range of microstructural and compositional parameters on the apparent diffusion tensor and the degree of diffusion anisotropy, allowing the characterization of diffusion in normal physiological conditions as well as changes occurring in development, disease, and aging. Implications for diffusion tensor imaging and for the possible in situ estimation of microstructural parameters from diffusion-weighted MR data are discussed in the context of this modeling framework.     

Phosphoethanolamine and phosphocholine transferases in gray matter and white matter from developing rat brain

We have studied the activities of 2′,3′-cyclic nucleotide 3′-phosphohydrolase, 1,2-diacylglycerol: CDPethanolamine phosphoethanolamine transferase (EC 2.7.8.1), and 1,2-diacylglycerol: CDPcholine phosphocholine transferase (EC 2.7.8.2) in developing rat brain gray matter and white matter. The specific activity of cyclic nucleotide phosphohydrolase was 5–8 fold higher in white matter than in gray matter at all ages. No significant changes were observed during development. The specific activity of phosphocholine transferase was 2 to 3 fold higher than phosphoethanolamine transferase at all ages both in gray and white matter. Both phosphocholine transferase and phosphoethanolamine transferase increased more than 2 fold in specific activity between 14 and 90 days of age. The total activity of phosphocholine transferase also showed an increase during development. The apparentK _m values for nucleotides and dicaprin were similar in gray matter and white matter. Except for lowK _m values for nucleotides at 14 days of age, no significant changes were observed during development. Changes in rates of glycerophospholipid synthesis may be partly due to the specific activities of these enzymes but are also determined by the quantities of substrates and inhibitors and by affinities for the substrates. Special Issue dedicated to Dr. Eugene Kreps.     

Long-chain acyl CoA synthetase in microsomes from rat brain gray matter and white matter

Long-chain acyl coenzyme A (CoA) synthetase in homogenates and microsomes from rat brain gray and white matter was studied. The formation of the thioesters of CoA was studied upon addition of [1-¹⁴C]-labeled fatty acids. The maximal activities were seen with linoleic acid, followed by arachidonic, palmitic, and docosahexaenoic acids in both gray and white matter homogenates and microsomes. The specific activities in microsomes were 3–5 times higher than in homogenates. The presence of Triton X-100 in the assay system enhanced the activity of long-chain acyl CoA synthetase in homogenates. The effect was more pronounced in palmitic and docosahexaenoic acid activation. The apparentK _m values andV _max values for palmitic and docosahexaenoic acids were much lower than for linoleic and arachidonic acids. The presence of Triton X-100 in the medium caused a definite decrease in the apparentK _m and Vmax values for all the fatty acid except palmitic acid in which case the reverse was true. There were no significant differences observed in the kinetic measurements between gray and white matter microsomes. These findings are similar to those resulting from the known interference of Triton X-100 in the measurement of kinetic variables of long-chain acyl CoA synthetase of liver microsomes. In this work, no correlation was observed between the fatty acid composition of gray and white matter and the capacity of these tissues for the activation of different fatty acids.