Magnetic Resonance Image-Based Modeling for Neurosurgical Interventions

Surgeries such as implantation of deep brain stimulation devices require accurate placement of devices within the brain. Because placement affects performance, image guidance and robotic assistance techniques have been widely adopted. These methods require accurate prediction of brain deformation during and following implantation. In this study, a magnetic resonance (MR) image-based finite element (FE) model was proposed by using a coupled Eulerian-Lagrangian method. Anatomical accuracy was achieved by mapping image voxels directly to the volumetric mesh space. The potential utility was demonstrated by evaluating the effect of different surgical approaches on the deformation of the corpus callosum (CC) region. The results showed that the maximum displacement of the corpus callosum increase with an increase of interventional angle with respect to the midline. The maximum displacement of the corpus callosum for different interventional locations was predicted, which is related to the brain curvature and the distance between the interventional area and corpus callosum (CC). The estimated displacement magnitude of the CC region followed those obtained from clinical observations. The proposed method provided an automatic pipeline for generating realistic computational models for interventional surgery. Results also demonstrated the potential of constructing patient-specific models for imageguided, robotic neurological surgery.


Introduction
Image-guided surgery can achieve optimal performance with accurate target location in the brain. It can also be integrated with various robotic manipulation systems for remote surgery and delicate operations [1]. Among all forms of surgical procedures, image-guided brain intervention is a common practice for deep brain stimulation (DBS). However, deformation of brain tissue could occur during the interventional process due to its soft and viscoelastic properties. The deformed brain tissue poses a challenge for the current image guidance, which requires registration between the pre-operative and intra-operative images [2]. Therefore, quantification of the brain tissue deformation during the intervention is significant for accurate image guidance.
Intraoperative magnetic resonance (MR) imaging techniques can provide accurate information for image guidance in neurological surgery. Studies on MR imaging techniques for brain intervention can provide quantitative information for both image guidance and device manipulation by considering the brain tissue deformation [3,4]. For different modeling methods of predicting the brain deformation, finite element (FE) method could provide the most accurate estimation [5,6]. In addition, computational results of the FE model can also provide information for force feedback, which is crucial for robotic manipulations.
Most of the current FE models of the brain are based on general anatomical structures, which lack geometrical details of the brain [7]. Although the general brain models could provide important information for quantifying the brain responses during the interventional process, patient-specific models are still needed for clinical applications. In DBS, electrodes, inserted into the brain in specific positions, required accuracy of sub-millimeter. Therefore, with available pre-and intra-operative MR images, a new FE model used for surgery is still needed.
In this study, the estimated displacement magnitude of the corpus callosum (CC) region was evaluated by finite element (FE) simulation of an interventional needle inserted into a brain. In Section 2, an MRimage based finite element (FE) modeling of the brain was proposed with anatomical details. The brain tissues were treated as hyperelastic, viscoelastic materials. The coupled Eulerian-Largrangian (CEL) method was adopted for the fluid environment of the brain tissue. The effects of interventional angles and locations for optimal surgery were studied in Section 3. In Section 4, the interventional results were presented and discussed. Preliminary results provided the suggestions of the optimal interventional course for minimal deformation of the brain tissue.

Mesh Generation and Simulation Configuration
The image-based human brain model was generated based on the reconstruction of MR atlas images from UCLA Brain Mapping Center [8]. By considering the biomechanical fidelity, the anatomical regions of white matter (WM), gray matter (GM), brain stem (BS), cerebellum (CB), cerebro-spinal-fluid (CSF), corpus callosum (CC), and blood vessel (VE) were segmented from brain MR images and constructed in the model. Briefly, each voxel from the MR image was extracted and mapped into a physical coordinate system. Then the connections of each node were established to build the mesh. The 2 mm isotropic hexahedron meshes for different brain regions were generated in this study. The details of the brain model generation process are shown in Fig. 1.
For the interventional FE model construction, a rigid interventional needle was constructed and inserted aligned with midline position perpendicular to the brain transverse plane. Both the brain and needle were placed in a fluid environment by using the Eulerian domain, which is shown in Fig. 2(a). For the FE simulation, the total intervention depth was 10 mm simulated with an increment of 1 mm, the brain stem was fixed as a boundary condition, which is shown in Fig. 2(b). In order to study the interaction between the interventional needle and surrounding CSF of brain, the coupled Eulerian-Largrangian (CEL) analysis method was introduced. For the CEL method, the complex material distributions in an Eulerian element mesh was assigned with the help of volume fraction tool in Abaqus/CAE. All simulations in the current study were conducted with ABAQUS/Explict 6.17 (Simulia, Providence, RI).

Model Computation
Considering large deformation of and rate effect of the brain tissue, a hyper-viscoelastic material model was employed [9][10][11]. In current study, a second-order Ogden model was employed to describe the hyperelastic behavior of brain tissue [12] = ∑ ( 1 + 2 + 3 ) where µi and αi are the material constants, K is the bulk modulus, λi are the three principal stretches and the Jacobian J = detF = λ1λ2λ3. The total second Piola-Kirchhoff stress in the brain can be obtained as [13] = + , where is the hyperelastic part of the second Piola-Kirchhoff stress, it can be calculated directly from Eq. (1). The viscous part of the second Piola-Kirchhoff stress can be described as [14] = where Ekl are the components of the Green-Lagrangian strain tensor, Gijkl are the stress relaxation functions, and t is the current time. The general form of Gijkl can be further written as [13,14] where g1(t) and g2(t) are two independent relaxation functions. Each of the relaxation functions can be described using a Prony series equation [15] g ( ) = where G0 is the instantaneous shear relaxation modulus, N is the number of term, gi is the relaxation modulus, and τi is the relaxation time. The material parameters are given in Tab. 1 and Tab. 2.  In current study, CSF was described as hyperplastic material using Neo-Hookean model, the material parameters are given in Tab. 3.
where p is the current pressure, ρ0 is the initial density, η is the nominal volumetric strain, c0, s and Γ 0 are materials constants, and Em is the internal energy per unit mass of the fluid. c0 and s have the following relation where Us is the shock velocity and Up is the particle velocity (Tab. 4). The interventional needle is treated as a rigid body in the model (Tab. 5).

Effect of Interventional Angles for Optimal Surgery
Interventional angles ranging from 0 to 45 degrees with an increment of 10 degrees were simulated ( Figure 3). As a demonstration, displacement distribution of the CC region was compared. It is seen from Fig. 3 that the maximum displacement values in CC increase with an increase of interventional angles with respect to the midline.

Effect of Interventional Locations for Optimal Surgery
The brain deformation under different interventional locations was investigated by varying the interventional positions on top of brain with an incline angle of 30 degrees (Figure 4). It is seen from Fig.  4 that interventional location close to the midline (P1) had the largest magnitude of displacement for the CC region, followed by locations of P2, P7, P5, P4, and P3. The smallest deformation of CC was from the interventional location at P6.

Discussion and Conclusions
Brain deformation during the interventional process affects the accuracy and performance of the surgery. To accurately quantify the deformation of the brain during the intervention, a model construction scheme based on MR images was proposed. Intervention process was simulated based on the FE model generated from the MR images. By varying the angles and locations of the intervention, deformation of the CC region was quantified and analyzed.
For varying angle of the intervention, simulation results showed that the largest deformation of CC resulted from the insert angle of 45 degrees direction parallel to the midline. This indicates that the smaller insert angle will have smaller displacement of corpus callosum during the interventional process. For varying intervention positions, simulation results from the CC region showed a decreasing order of the displacement for locations of P1, P2, and P3, which should be related to both the decreased inclined angles with the curvature effect and the shorter distance between insert needle and corpus callosum of P2 and P3. Similarly, locations P7, P4, and P6 has decrease trends due to the brain curvature effect. Location P4 and P5 have similar displacement of corpus callosum due to the symmetry of the brain. According to the simulation results, location P6 has the smallest displacement value of corpus callosum, which may be the optimal location for interventional surgery.
In this paper, a workflow to construct brain interventional FE model based on MR images was proposed. Within this framework, patient-specific models could be constructed for specific surgical applications. For illustration, the deformation of the corpus callosum is investigated. Using CEL modeling, brain deformation was quantified with improved computational accuracy. Results showed that the maximum displacement of CC region increased with an increase of interventional angles with respect to the midline. However, the maximum displacement of CC for different interventional locations depended on the brain curvature and interventional depth. This study demonstrated the potential of using MR image-based modeling for optimal interventional planning of image-guided, robotic neurological surgery.