M Matej Hrapko

Mechanical properties of brain tissue by indentation: Interregional variation

Although many studies on the mechanical properties of brain tissue exist, some controversy concerning the possible differences in mechanical properties of white and gray matter tissues remains. Indentation experiments are conducted on white and gray matter tissues of various regions of the cerebrum and on tissue from the thalamus and the midbrain to study interregional differences. An advantage of indentation, when compared to standard rheological tests as often used for the characterization of brain tissue, is that it is a local test, requiring only a small volume of tissue to be homogeneous. Indentation tests are performed at different speeds and the force relaxation after a step indent is measured as well. White matter tissue is found to be stiffer than gray matter and to show more variation in response between different samples which is consistent with structural differences between white matter and gray matter. In addition to differences between white matter and gray matter, also different regions of brain tissue are compared.

The influence of test conditions on characterization of the mechanical properties of brain tissue.

To understand brain injuries better, the mechanical properties of brain tissue have been studied for 50 years; however, no universally accepted data set exists. The variation in material properties reported may be caused by differences in testing methods and protocols used. An overview of studies on the mechanical properties of brain tissue is given, focusing on testing methods. Moreover, the influence of important test conditions, such as temperature, anisotropy, and precompression was experimentally determined for shear deformation. The results measured at room temperature show a stiffer response than those measured at body temperature. By applying the time-temperature superposition, a horizontal shift factor a(T)=8.5-11 was found, which is in agreement with the values found in literature. Anisotropy of samples from the corona radiata was investigated by measuring the shear resistance for different directions in the sagittal, the coronal, and the transverse plane. The results measured in the coronal and the transverse plane were 1.3 and 1.25 times stiffer than the results obtained from the sagittal plane. The variation caused by anisotropy within the same plane of individual samples was found to range from 25% to 54%. The effect of precompression on shear results was investigated and was found to stiffen the sample response. Combinations of these and other factors (postmortem time, donor age, donor type, etc.) lead to large differences among different studies, depending on the different test conditions.

Characterisation of the mechanical behaviour of brain tissue in compression and shear.

No validated, generally accepted data set on the mechanical properties of brain tissue exists, not even for small strains. Most of the experimental and methodological issues have previously been addressed for linear shear loading. The objective of this work was to obtain a consistent data set for the mechanical response of brain tissue to either compression or shear. Results for these two deformation modes were obtained from the same samples to reduce the effect of inter-sample variation. Since compression tests are not very common, the influence of several experimental conditions for the compression measurements was analysed in detail. Results with and without initial contact of the sample with the loading plate were compared. The influence of a fluid layer surrounding the sample and the effect of friction were examined and were found to play an important role during compression measurements.To validate the non-linear viscoelastic constitutive model of brain tissue that was developed in Hrapko et al. (Biorheology 43 (2006), 623-636) and has shown to provide a good prediction of the shear response, the model has been implemented in the explicit Finite Element code MADYMO. The model predictions were compared to compression relaxation results up to 15% strain of porcine brain tissue samples. Model simulations with boundary conditions varying within the physical ranges of friction, initial contact and compression rate are used to interpret the compression results.

Optical characterization of acceleration-induced strain fields in inhomogeneous brain slices

The aim of this study was to measure high-resolution strain fields in planar sections of brain tissue during translational acceleration to obtain validation data for numerical simulations. Slices were made from fresh, porcine brain tissue, and contained both grey and white matter as well as the complex folding structure of the cortex. The brain slices were immersed in artificial cerebrospinal fluid (aCSF) and were encapsulated in a rigid cavity representing the actual shape of the skull. The rigid cavity sustained an acceleration of about 900m/s(2) to a velocity of 4m/s followed by a deceleration of more than 2000m/s(2). During the experiment, images were taken using a high-speed video camera and Von Mises strains were calculated using a digital image correlation technique. The acceleration of the sampleholder was determined using the same digital image correlation technique. A rotational motion of the brain slice relative to the sampleholder was observed, which may have been caused by a thicker posterior part of the slice. Local variations in the displacement field were found, which were related to the sulci and the grey and white matter composition of the slice. Furthermore, higher Von Mises strains were seen in the areas around the sulci.

Mechanical Properties of Brain Tissue: Characterisation and Constitutive Modelling

The head is often considered as the most critical region of the human body for life-threatening injuries sustained in accidents. In order to develop effective protective measures, a better understanding of the process of injury development in the brain is required. Finite Element (FE) models are being developed, in order to predict the mechanical response of the contents of the head during impact. To obtain accurate predictions of the mechanical response of the brain, an accurate description of the mechanical behaviour of brain tissue is required. However, up to now no universally accepted data set for the constitutive response of brain tissue exists. The large variation in material properties reported may be caused by differences in testing methods and protocols used. An overview of studies on the mechanical properties of brain tissue is presented, focusing on testing methods. Furthermore, the large strain mechanical response of brain tissue as well as modelling approaches for this behaviour are discussed.

On the consequences of non linear constitutive modelling of brain tissue for injury prediction with numerical head models

The objective of this work was to investigate the influences of constitutive non linearities of brain tissue in numerical head model simulations by comparing the performance of a recently developed non linear constitutive model [10, 11] with a simplified version, based on neo-Hookean elastic behaviour, and with a previously developed constitutive model [6]. Numerical simulation results from an existing 3D head model in the explicit Finite Element code MADYMO were compared. A head model containing a sliding interface between the brain and the skull was used and results were compared with the results obtained with a previously validated version possessing a tied skull-brain interface. For these head models, the effects of different constitutive models were systematically investigated for different loading directions and varying loading amplitudes in both translation and rotation. In the case of the simplified and fully non linear version of the model of Hrapko et al. [10, 11], the response predicted with a head model for varying conditions (i.e. severity and type of loading) varies consistently with the constitutive behaviour. Consequently, when used in a finite element head model, the response can be scaled according to the constitutive model used. However, the differences found when using the non linear model of Brands et al. [5] were dependent on the loading conditions. Hence this model is less suitable for use in a numerical head model.

Constitutive Modelling of Brain Tissue for Prediction of Traumatic Brain Injury

To develop protective measures for crash situations, an accurate assessment of injury risk is required. By using a Finite Element model of the head, the mechanical behaviour of the brain can be predicted for any acceleration and improved injury criteria can be developed and implemented into safety standards. Many head models are based on a detailed geometrical description of the anatomical components. However, for reliable predictions of injury, also an accurate constitutive model for brain tissue is required that is applicable for large deformations and complex loading conditions that occur during an impact to the head. This chapter deals with constitutive modelling of brain tissue. Different approaches towards modelling of the mechanical response of biological tissues are discussed. A short overview of the large strain behaviour of brain tissue and constitutive models that have been developed for this material is given. A non-linear viscoelastic model for brain tissue is then discussed in more detail. The model is based on a multi-mode Maxwell model and consists of a non-linear elastic mode in combination with a number of viscoelastic modes. For this model, also a numerical implementation scheme is given. The influences of constitutive non-linearities of brain tissue in numerical head model simulations are shown by comparing the performance of the model of Hrapko et al. with a simplified version, based on neo-Hookean elastic behaviour, and a third non-linear constitutive model from literature.