Combining advanced magnetic resonance imaging (MRI) with finite element (FE) analysis for characterising subject-specific injury patterns in the brain after traumatic brain injury

15 Mar.,2023


Do you need Addult 3D Mesh Pillows solution? Choose us as your partner and we will provide you with a solution that will satisfy you.

A combined MRI and computational analysis pipeline was developed using our animal mTBI model. First, mTBI experiments were performed on our sheep TBI model. Advanced MRI scans including diffusion tensor images (DTI) were taken before and after the impact, and then used to analyse damage patterns with a specimen-specific FE model (Fig. 1).

Fig. 1

Overall framework for MRI-based specimen-specific computational analysis of mTBI. Top shows the experimental procedure, the middle row shows the type of analysis performed with advanced MRI images and the bottom shows the FE model generated from the MRI and the cross-sectional view on the coronal and transverse planes

Full size image


Animal experiment

All animal experiments were approved by the University of Auckland’s Animal Ethics Committee and conducted in accordance with the New Zealand Animal Welfare Act 1999. Our ovine TBI model has been previously described [36]. Dry mixed breed Romney ewes (3 years old) were acclimated to a standard pellet diet with food and water supplied ad libitum for at least 1 week prior to the experiment. On the day of the experiment general anesthesia was induced by i.v. thiopental sodium (15 mg/kg) and maintained by (2–3%) isoflurane following intubation. After baseline MRI imaging, with anaesthesia maintained at all times, the animal was brought out of the MRI machine and placed in the sphinx position, with its head supported with a pillow to allow natural recoil movement. An acute impact that constituted a mild TBI was delivered Using a CASH® Special Concussion stunner (Accles & Shelvoke Ltd, UK) with a 1 grain cartridge which produces ~ 76 J of impact energy from a circular impactor (ø = 25 mm). This resulted in non-penetrating injury from a direct impact with unconstrained head motion comparable to previous ovine models of TBI [37, 38]. The stunner was positioned perpendicular to the area between the horn buds, centered above the midsagittal plane. This resulted in an impact to the superior frontal area of the cerebrum (Fig. 1). Post-impact, the animal was returned to the MRI machine for a second round of scanning, which was identical to the baseline sequence.


MR imaging

The MR scanning was performed using a 3 T Siemens (MAGNETOM Skyra, Erlangen, Germany), 32 channel head coil. Multiple MRI sequences were acquired, including T1 MPRAGE and diffusion MRI both of which were used in the FE model generation. Diffusion MRI data were acquired with the following imaging parameters: FOV = 17.4, matrix size: 128 × 128, 70 slices, voxel size = 1.4 × 1.4 × 1.4 mm, TR/TE/flip-angle = 12 s/91 ms/90°, 2 b values with b = 0 s/mm2, 64 with b = 2000s/mm2, scan time = 4:28 min. T1 MPRAGE data were acquired with the following parameters: FOV = 23 cm, matrix size: 256 × 256, 120 slices, voxel size = 0.9 × 0.9 × 0.9 mm, TR/TE/flip-angle = 2 s/3.5 ms/9°, scan time = 4:40 min. FLAIR images were also acquired with TR/TE/flip-angle = 5.5 s/95 ms/150°, inversion time = 1.91, matrix size: 256 × 256, 30 slices, voxel size = 0.6 × 0.6 × 3.3 mm, Echo Train length = 17.


Image analysis

Images were analysed using FSL (FMRIB software library,, version 6.0). Due to the challenges in manually segmenting MRI images [39], we used an established automated methods. First the initial T1-W scan (Fig. 2A) was used to extract the brain using Brain Extraction Tool (BET) in FSL, which accurately segment MRI head images into brain and non-brain parts [40]. After the brain was extracted (Fig. 2B), we used a method called FAST (FMRIB’s Automated Segmentation Tool), which segments MR images of the brain into different tissue types such as white matter, grey matter or CSF, while performing correction for spatial intensity variation in the MR images (Fig. 2C). It is based on a hidden Markov random field model and an associated Expectation–Maximization algorithm [41] and has been quantitatively evaluated for its accuracy [42].

Fig. 2

MRI processing and segmentation. A T1-W image of the sheep head B Extracted brain from T1-W image with BET, C Segmented brain tissues with FAST. Blue: Grey matter, Orange: white matter; Yellow CSF. All images are coronal images

Full size image

Diffusion images, acquired using spin-echo EPI sequence, were processed using FDT (FMRIB's Diffusion Toolbox). First, localized geometric distortion was removed with topup and eddy tools from FDT. Then diffusion tensor information at each voxel was obtained with DTIFIT for our further analysis. These diffusion parameters include radial diffusivity (RD), mean diffusivity (MD), fractional anisotropy (FA), and axial diffusivity (AD), and FA color-coded with principal eigenvector direction (color FA). Then, all this information is transferred to a text file using a custom Matlab script (V. R 2018, The Math Works, Inc., Columbia, MD). The resulting file contains the exact location of each voxel and all other structural (cerebellum, cerebrum, and brain stem, white matter, grey matter, CSF) as well as diffusion information (FA, MD, AD, RD, and color FA that represent the principal diffusion direction) and was used when assigning different material properties to individual elements in the FE model as described later (Fig. 3).

Fig. 3

DTI images of the sheep brain. A FA map, B color FA map, C, D white matter fiber orientation distribution function overlaid on the voxels

Full size image


FE model generation and material property descriptions

A high-fidelity FE model of sheep TBI has been developed directly from MRI. First the MRI segmentations of the skull and the whole brain were exported as surface models. This was then turned into a high-resolution hexahedral mesh using an automated algorithm that uses the free-form deformation technique for matching the outer geometry of a solid mesh to a given cloud of datasets. Specifically, our method is made up of two steps: (1) generation of a template mesh from which subject-specific meshes can be generated and (2) free-form deformation (FFD) of the template mesh to deform the template mesh to subjects’ dataset from medical images such as CT or MRI [43]. FFD method involves embedding a mesh to be customized (called slave mesh) inside a wrapper mesh (called host mesh). The host mesh is deformed according to an objective function to minimize the distance between control points in the ‘least-square’ sense and pass the deformation to the slave mesh. The control points can be placed both on the host and the slave meshes. The objective function is then expressed as the following:

$$F\left( {u_{n} } \right) = \mathop \sum \limits_{d = 1}^{N} w_{d} \left\| {u\left( {\xi_{1d} ,\xi_{2d} } \right) - z_{d}^{2} } \right\| + F_{s} \left( {u_{n} } \right) ,$$


where \({z}_{d}\) are the geometric coordinates of data points d placed on the slave mesh, \({w}_{d}\) is a weight for each data point, \(u\left({\xi }_{1d},{\xi }_{2d}\right)\) are the corresponding mesh points from the host meshes which is obtained via interpolation with the basis function \({u}_{n}\). One unique feature that differentiates our approach to other FFD methods is the inclusion of a Sobolev smoothing term \({F}_{s}\left({u}_{n}\right)\) for additional control over the deformation of the host mesh given below:

$$F_{s} \left( {u_{n} } \right) = \iiint_{{0}}^{{1}} {\left\{ {\gamma _{1} \left\| {\frac{{\partial u}}{{\partial \xi _{1} }}} \right\|^{2} + \gamma _{2} \left\| {\frac{{\partial u}}{{\partial \xi _{2} }}} \right\|^{2} + \gamma _{3} \left\| {\frac{{\partial u}}{{\partial \xi _{3} }}} \right\|^{2} + \gamma _{4} \left\| {\frac{{\partial ^{2} u}}{{\partial \xi _{1}^{2} }}} \right\|^{2} + \gamma _{5} \left\| {\frac{{\partial ^{2} u}}{{\partial \xi _{2}^{2} }}} \right\|^{2} + \gamma _{6} \left\| {\frac{{\partial ^{2} u}}{{\partial \xi _{3}^{2} }}} \right\|^{2} + \gamma _{7} \left\| {\frac{{\partial ^{2} u}}{{\partial \xi _{1} \partial \xi _{2} }}} \right\|^{2} + \gamma _{8} \left\| {\frac{{\partial ^{2} u}}{{\partial \xi _{2} \partial \xi _{3} }}} \right\|^{2} + \gamma _{9} \left\| {\frac{{\partial ^{2} u}}{{\partial \xi _{3} \partial \xi _{1} }}} \right\|^{2} + \gamma _{{10}} \left\| {\frac{{\partial ^{3} u}}{{\partial \xi _{1} \partial \xi _{2} \partial \xi _{3} }}} \right\|^{2} } \right\}d\xi _{1} d\xi _{2} d\xi _{3} }$$


where \({\gamma }_{i} (i=1\cdots 3)\) are the three arc-lengths, \({\gamma }_{i} (i=4\cdots 6)\) are the three curvatures in the \({\xi }_{1,}{\xi }_{2,}{\xi }_{3}\) directions, respectively, and \({\gamma }_{i} (i=7\cdots 9)\) are the three surface area terms for faces \({(\xi }_{1-}{\xi }_{2})\), \({(\xi }_{2-}{\xi }_{3})\) and \({(\xi }_{3-}{\xi }_{1})\), while \({\gamma }_{10}\) is related to the volume, which ensures the shape of the original volume is not too distorted after fitting so that the customized mesh is not anatomically distorted. We have used this method extensively in the past in subject-specific FE model generation for various tissues and joints such as the Achilles tendon and the hip joint [44,45,46]. We applied this to the brain in this study. The number of elements for the template mesh was determined after mesh convergence analysis and the resulting total number of elements was 321,070 consisting of 343,874 nodes. This was then deformed using the FFD described above to generate a subject-specific model by deforming the template mesh to the segmented MR dataset.

We have also incorporated major tissue types in the brain model—the skull (both compact and spongy bones separately), dura mater, pia mater, cerebrospinal fluid and the brain tissue. The material properties used are given in Table 1.

Table 1 Different materials incorporated in our model

Full size table

The brain tissue was modelled using the hyper-viscoelastic fiber-reinforced anisotropic model using the formulation by Gasser, Ogden and Hozapfel (GOH) [48] to incorporate white mater structural anisotropy. This model has been used to describe the anisotropy of the brain by a number of previous works [49,50,51]. In this material formulation, the strain energy function W is defined as the following:

$$W = \frac{G}{2}\left( {\widetilde{{I_{1} }} - 3} \right) + K\left( {\frac{{J^{2} - 1}}{4} - \frac{1}{2}\ln \left( J \right)} \right) + \frac{{k_{1} }}{{k_{2} }}\left( {e^{{k_{2} \left\langle {\tilde{E}_{\alpha } } \right\rangle^{2} }} - 1} \right),$$


where W is the strain energy per unit volume, G is the shear modulus, K is the bulk modulus, J is the determinant of deformation gradient, \({k}_{1}\) and \({k}_{2}\) are the parameters related to the fiber stiffness. The last term in Eq. (1) was from the GOH [37] form with one fiber family, where:

$$\tilde{E}_{\alpha } = k\left( {\tilde{I}_{1} - 3} \right) + \left( {1 - 3k} \right)\left( {\tilde{I}_{4\alpha } - 1} \right),$$


which characterizes the deformation of the fibers with the fiber dispersion parameter k and the function \(\tilde{I}_{4\alpha }\) defined as the following:

$$\tilde{I}_{4\alpha } = \tilde{\user2{C}}:{\varvec{n}}_{{0{\varvec{\alpha}}}} \otimes {\varvec{n}}_{{0{\varvec{\alpha}}}} ,$$


where \(\widetilde{{\varvec{C}}}\) is the isochoric part of the right Cauchy-Green strain tensor and \({{\varvec{n}}}_{0\boldsymbol{\alpha }}\) is the fiber direction unit vector in the undeformed configuration. The viscoelastic behavior was incorporated with the following relaxation function:

$$G\left( t \right) = 1 + \mathop \sum \limits_{i = 1}^{N} g_{i} e^{{\left( {\frac{ - t}{{\tau_{i} }}} \right)}}$$


The fiber dispersion parameter in the GOH model has been linked with FA measures from diffusion MRI by Giordano and Klevin [50] using the following relationship:

$$FA = \frac{{\sqrt {\left( {\frac{1 - 2k}{k} - 1} \right)^{2} } }}{{\sqrt {\left( {\frac{{\left( {1 - 2k} \right)}}{k}} \right)^{2} + 2} }}.$$


We have used this relationship as well as the GOH material law to describe the anisotropy of the brain tissue and have linked it with the FA measurements from MRI (Table 2).

Table 2 FA ranges and corresponding k values for GOH material

Full size table

The viscoelastic behavior was modelled with a relaxation function that was added to the second Piola–Kirchhoff stress as the following:

$$S\left( t \right) = S^{\infty } + \mathop \smallint \limits_{ - \infty }^{t} G\left( {t - s} \right)\frac{{dS^{e} }}{ds}ds,$$


where S is the elastic stress derived from W in Eq. (1) and G is the relaxation function described with the following discrete relaxation spectrum:

$$G\left( t \right) = 1 + \mathop \sum \limits_{i = 1}^{N} \gamma_{i} {\text{exp}}( - t/\tau_{i} ) .$$


The viscoelastic parameters as well as other parameters for the GOH were obtained from Kleiven and Giordano [52].

Each element was automatically assigned with the material property that corresponds to the MRI voxel information using the in-house python code. This is based on the automatic material assignment algorithm that we developed for assigning bone materials to FE models from CT scans [53]. This has been successfully used in assigning different material information to different elements for various types of FE models in the past [23, 44, 46, 54, 55].

This works by searching for the closest voxel to the element of interest by aligning the FE model in the MRI coordinates. This way the correspondence between elements in the FE model and MRI voxels are established, allowing us to assign subject-specific material properties as well as geometry from the MRI scans of the subject (Fig. 4).

Fig. 4

Material property assignments from T1-W and DTI images. Starting with brain segmentation from T1-W image, DTI map was obtained which was used to assign each element in the FE model with corresponding materials the FA values

Full size image

Dynamic simulation was performed with FEBio ( with the boundary condition that mimics the actual load application from the experiment described above. The contact between the brain and meninges layers was modelled with frictionless contact to accurately model the deformation and movements between these two tissues upon impact application.

Three different analyses were performed. First a fully subject-specific analysis was performed with the model that contains both subject-specific geometry and material properties. This was compared with the post-impact MRI scan for model validation. After that, the model was modified to examine (1) the importance of having subject-specific material properties; (2) the importance of incorporating sliding movements between the brain and the skull. The first was examined using a homogeneous material property commonly used in a majority of brain FE models [14, 30, 47]. The second was examined by modifying the contact constraints from frictionless to tied contact, which essentially eliminates sliding between the brain and skull.

For more information Addult 3D Mesh Pillows, please get in touch with us!