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GPU accelerated registration of a statistical shape model of the lumbar spine to 3D ultrasound images. Khallaghi, Siavash 2011

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GPU Accelerated Registration of a Statistical Shape Model of the Lumbar Spine to 3D Ultrasound Images Siavash Khallaghia, Purang Abolmaesumib, Ren Hui Gongc, Elvis Chenc, Sean Gillc, Jonathan Boisverte, David Pichorad, Dan Borschneckd, Gabor Fichtingerc, Parvin Mousavic a Dept. of Electrical and Computer Engineering, Queen’s University, Kingston, ON, Canada; b Dept. of Electrical and Computer Engineering, University of British Columbia, Vancouver, BC, Canada; c School of Computing, Queen’s University, Kingston, ON, Canada d Kingston General Hospital, Kingston, ON, Canada e National Research Council, Ottawa, ON, Canada ABSTRACT We present a parallel implementation of a statistical shape model registration to 3D ultrasound images of the lumbar vertebrae (L2-L4). Covariance Matrix Adaptation Evolution Strategy optimization technique, along with Linear Correlation of Linear Combination similarity metric have been used, to improve the robustness and capture range of the registration approach. Instantiation and ultrasound simulation have been implemented on a graphics processing unit for a faster registration. Phantom studies show a mean target registration error of 3.2 mm, while 80% of all the cases yield target registration error of below 3.5 mm. Keywords: Graphics Processing Unit, Statistical Shape Model, Ultrasound, Registration, Spine 1. INTRODUCTION Spinal needle injections, such as epidurals and facet joint injections, are performed on a regular basis in radiology clinics and hospitals. Traditionally these percutaneous procedures are performed under fluoro or CT guidance. This exposes both the patient and the physician to hazardous radiation. In order to remove the ionizing radiation, many papers suggest the registration of Statistical Shape Models (SSM) with intra-operative ultrasound (US) images.1–3 A statistical shape model is a mathematical entity, which captures the statistical information, including the mean and variations, of a group of objects. It not only represents the objects within the population of the constructed SSM, but can also produce new instances of the objects from a linear combination of the principal modes of variations. Existing SSMs can be divided into two categories: geometrical SSMs,4–6 which describe the outline of images, and volumetric SSMs,1,7, 8 which model both the internal intensity and geometrical information. While geometrical SSMs are computationally less expensive, they are prone to bone surface segmentation errors. Prior work proposes several approaches for SSM to CT,9 SSM to MRI10 and SSM to US registration.1 The feasibility of US registration to SSMs of bony anatomy has been previously investigated.3,11 Barratt et al.1 and Foroughi et al.2 built SSMs for the femur and pelvis, which are subsequently repositioned and deformed to fit a cloud of bone surface points extracted from a set of tracked US images. Schumann et al.12 further improved their technique to compensate for variations in the speed of sound between calibration and intra-operative use. Typically the most time-consuming components of a non-rigid registration algorithm are the transformation of the moving image and the calculation of the similarity metric. To alleviate this problem, several techniques base on parallel implementation of the registration technique have been proposed. Depending on the application, either of these blocks may be the bottleneck for the registration algorithm. Crookes et al.13 implements an affine registration on the graphics processing unit. Ozcelik et al.14 presents a parallel implementation of Thirion’s Demons algorithm by applying four consecutive CUDA kernels: gradient, deformation, displacement smoothing and correlation. Rehman et al.15 is another example of GPU-based deformable registration. Medical Imaging 2011: Visualization, Image-Guided Procedures, and Modeling, edited by Kenneth H. Wong, David R. Holmes III, Proc. of SPIE Vol. 7964, 79642W © 2011 SPIE · CCC code: 1605-7422/11/$18 · doi: 10.1117/12.878377 Proc. of SPIE Vol. 7964  79642W-1 Downloaded from SPIE Digital Library on 16 Aug 2011 to Terms of Use:  http://spiedl.org/terms / Template /_ /cT1/ / CT1 / Rigid Registration Deform able Registration I Mean Deformation Vector SSM Rigid Deformable Registration Registration Eigenvalues 1' P CARigid Deform able Eigenvectors ARegistration Registration / CT1 / t I Figure 1. Outline of the SSM construction method from a set of CT images for an individual vertebra. The SSM of the ensemble of vertebra is created from three similar workflows for the L2, L3 and L4 respectively. Multi-modality registration between CT and US images, due to to the different nature of input images, tends to be a time-consuming and complex task. Hence, the use of GPUs to accelerate the registration process is a natural choice. Kutter et al.16 presents a modular design for the simulation of US images from CT data on the GPU. They further extend the approach to a multi-modality registration technique between US and CT data using a variation of the Linear Correlation of Linear Combination (LC2) similarity metric, originally proposed by Wein et al.17 These works demonstrate a significant improvement in the registration runtime using the parallel implementation on the GPU, making it an affordable and available alternative for real-time applications. In this paper we present a parallel implementation of an SSM to US registration method we proposed before,3 for the alignment of an SSM of lumbar spine to 3D US data. Using the deformable B-spline transform, a statistical shape model for each of the L2-L4 vertebrae is constructed. For a faster registration, instantiation and ultrasound simulation have been implemented on the GPU. The registration is validated on three tissue mimicking phantoms with realistic spinal curvature. 2. METHODOLOGY 2.1 CT Data Collection The CT data were collected at a local hospital under the approval of the Research Ethics Board. A set of CT images, acquired from 38 patients (19 male and 19 female), was used where the L2, L3 and L4 vertebrae were semi-automatically segmented using ITK-Snap and resampled into 120× 200× 100 voxels with an isotropic spacing of 0.6 mm. The patient data was divided into two groups: 35 for constructing the SSM (hereafter referred to as training data), and three for validation (two male and one female). 2.2 Statistical Shape Model Construction A SSM is contructed for each vertebra seperately as shown in Figure 1. For each SSM, a random patient CT volume is initially chosen as the template, It. Each training example, Ik , is registered to the template by a rigid registration followed by a B-spline deformable registration, such that It ≈ T kdef(T krigid(Ik)) , where T(.) denotes a transformation. B-spline registration is performed in a 40×30×30 grid using the mutual information metric.7 To reduce the deformable registration time, a three stage multi-resolution approach is implemented. With the deformable transformation of all the training examples known with respect to the template, principal component analysis (PCA) is performed to construct the SSM. Proc. of SPIE Vol. 7964  79642W-2 Downloaded from SPIE Digital Library on 16 Aug 2011 to Terms of Use:  http://spiedl.org/terms Figure 2. Registration workflow After the SSM is constructed, it is used to generate new instances of the population. A new instance of the SSM, defined by the deformation vector Dnew is produced by a linear combination of the mean deformation vector, φ̄, SSM weights, wi, and the eigenvectors of the covariance matrix generated from all the deformation fields, vi: Dnew = φ̄+ N∑ i=1 wivi. (1) The SSM weights in equation (1) provide a compact description of the transformation needed to deform the mean shape into the shape of the new instance. In our case the first 12 eigenvectors cover 95% of variations in shape. 2.3 Registration Framework This section describes the SSM to US registration method. The registration problem is solved in two steps: first rigid and then deformable. At the rigid stage, starting from six random initial rigid parameters (three for rotatation and three for translation, i.e. the pose) and zero SSM weights, the algorithm solves for the optimal rigid parameters. Subsequently, at the deformable stage, the algorithm finds 12 optimal deformable parameters (i.e. the SSM weights). Using the updated rigid and deformable parameters, the algorithm iterates through the rigid and deformable phases until convergence is achieved. For optimization, Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is used because it yields convergence in an irregular search space.18 Decoupling the problem into rigid and deformable registration phases, not only decreases the complexity of the problem, but also allows for a faster convergence by decreasing the population size of the CMA-ES optimizer. Figure 2 illustrates the general registration workflow. First, we set the initial SSM weights to zero, and generate an instance of each of the vertebra. Then, using a random initial rigid transformation, each generated instance is perturbed to an initial pose. Following that, a ray-casting based ultrasound simulation is applied to the reconstructed volume. Assuming that the Hounsfield units can be related to the acoustic impedance values used to calculate ultrasound transmission and reflection, each ultrasound beam is modeled as a ray passing down the columns of the image. Next, the LC217 metric is calculated. This similarity measure is fed to the CMA-ES optimizer until all the rigid parameters converge. A similar approach is employed for the deformable registration phase. The registration iterates between deformable and rigid phases until the correct pose and shape of the SSM are found. Running the proposed registration algorithm on a desktop personal computer, will take approximately a day for a single registration. To speed the algorithm up, we have implemented a parallel version of our registration algorithm on an nVidia GTX 285 Graphical Processing Unit (GPU), details of which has been presented in this work. Proc. of SPIE Vol. 7964  79642W-3 Downloaded from SPIE Digital Library on 16 Aug 2011 to Terms of Use:  http://spiedl.org/terms Figure 3. Parallel implementation of the instantiation block on the GPU. 2.3.1 GPU Accelerated Instance Generation Figure 2 illustrates the parallel instance generation algorithm. Given the SSM weights, a linear combination of eigenvectors is set as the B-spline grid node vectors. The SSM template and grid node vectors are uploaded from the global memory to the device memory and stored in a CUDA-3D-arrays. A 3D-texture is also bound to each array, enabling the algorithm to read and manipulate data in the 3D-arrays. We have implemented the instantiation in two steps. The first kernel, interpolates the B-spline grid nodes to produce the deformation field at each voxel. This is done by placing a 2D grid that spans each slice and then going through the slices one at a time to produce the deformation vector. Subsequently, the second kernel transforms each voxel from the index representation to the physical coordinate system, applies the deformation vector and transforms it back to the index representation. In the case of unassigned voxels in the final volume, the empty voxel is filled with a default value. Finally the deformed volume is downloaded to global memory. Table 2 illustrates timing tests for instance generation on the CPU and the GPU. 2.3.2 GPU Accelerated Ultrasound Simulation The ultrasound simulation is based on the work presented by Wein et al.17 and Kutter et al.16 Figure 4 illustrates the parallel implementation of ultrasound simulation on the GPU. First, the input CT volume is uploaded to the device memory and stored as a CUDA array. Then, a 2D grid is placed on top of the CT volume parallel to the coronal plane. the ultrasound is simulated in two steps: The first CUDA kernel computes the ultrasound reflection image, each ultrasound ray is assigned one CUDA-thread, traveling down the CT volume. The second kernel, computes the mapped CT image. The two images are fused together to produce the simulated ultrasound. The result of the ultrasound simulation is then downloaded to the global memory. 3. RESULTS AND DISCUSSION 3.1 Ultrasound Data Acquisition As mentioned in subsection 2.1, we excluded three CT volumes from the patient data for validation. The three excluded CT volumes were used to construct 3D models of the entire lumbar spine, including L1 to L5. These Proc. of SPIE Vol. 7964  79642W-4 Downloaded from SPIE Digital Library on 16 Aug 2011 to Terms of Use:  http://spiedl.org/terms Figure 4. Parallel implementation of US simulation on the GPU. virtual models were printed using a Cimetrix 3D shape printer (Cimetrix Solutions, Oshawa, ON, Canada). Three spine phantoms were constructed by submerging the printed vertebrae in an agar-gelatine-based gel. The resulting phantoms simulated the appearance of vertebrae and soft tissue in ultrasound. A high-resolution CT image (0.46 × 0.46 × 0.625 mm) and an ultrasound volume were acquired from each phantom from a freehand sweep with a linear-array transducer at 6.6 MHz with an imaging depth of 5.5 cm. Nine fiducial markers, mounted on the exterior of the phantom box, were localized with a tracked pointer and transformed to the US space. The CT and ultrasound volumes were aligned using these markers. 3.2 Results The SSM mean shape and the ultrasound volumes were brought to an initial position by rigidly registering the mean shape to the corresponding phantom CT volume. For each phantom, thirty experiments were performed with perturbing the mean shape using a transformation generated from a uniform random distribution in the interval of [0,10] mm translation along each axis and [0-10]◦ rotation about each axis. To evaluate the accuracy of the registration, an expert orthopedic surgeon was asked to identify five cor- responding landmarks, three on the spinous process and two on the facet joints, on the registered SSM, the ultrasound volume and the corresponding CT. The average distance of these five landmarks is chosen as a mea- sure of the final Target Registration Error (TRE). A registration is considered failed if the final TRE is more than 3.5 mm, as the clinically accepted error. Registration results are shown in Table 1 and an example of the initial misalignment and the registration result is illustrated in Figure 5. The registration results are sufficient for various spinal interventions, such as facet joint injections and epidural anesthesia, which are the primary focus of our research. Results in Table 2 show a 350 speed up gain for the GPU implementation of the instance generation in comparison to the CPU implementation. The speed up gain is in agreement with the results presented by Gong et al.19 Also by simulating the US on the device, the entire registration algorithm was implemented on the GPU which allowed for minimal interaction between the CPU and the GPU. This allowed the registration run-time to decrease from the order 8 hours to 20 minutes, a 24x improvement. Proc. of SPIE Vol. 7964  79642W-5 Downloaded from SPIE Digital Library on 16 Aug 2011 to Terms of Use:  http://spiedl.org/terms Figure 5. Transverse (left), coronal (center), and sagittal (right) slices of the original US volume overlaid with the bone contours of the misaligned (top) and registered (bottom) SSM volumes. Table 1. Registration results for the SSM to US registration. SR (Success Rate) is defined as the ratio of the registrations where the overall TRE is less than 3.5 mm. SR is presented for each phantom with the maximum initial misalignment of 10 mm. L2 L3 L4 Phantom Mean STD SR Mean STD SR Mean STD SR 1 3.10 0.29 85% 3.38 0.42 81% 3.22 0.33 82% 2 3.05 0.43 80% 3.48 0.33 79% 3.41 0.45 78% 3 3.23 0.36 75% 3.25 0.45 82% 3.24 0.26 85% Several factors limit the success rate of the registration. Due to partial volume occlusion, it is impossible to visualize the superior articular process in ultrasound images. Also, deforming the SSM to capture the sharp corners of the spinous and transverse processes is a challenging task. While the former is intrinsic to ultrasound imaging, the latter can be substantially improved by increasing the number of training images and using a denser grid in the construction of the SSM. With the deformation implemented on the GPU, denser B-spline grids are more accessible for real-time applications. Table 2. CPU vs. GPU instantiation run-time and the performance gain computed as CPU/GPU. A total of 100 speed tests were performed on the CPU and the GPU. In each test a random combination of SSM weights was passed to the instantiation block. SSM Average CPU Time Average GPU Time Gain sec msec L2 2.3 8.4 273 L3 2.4 7.2 342 L4 2.5 8.2 308 Proc. of SPIE Vol. 7964  79642W-6 Downloaded from SPIE Digital Library on 16 Aug 2011 to Terms of Use:  http://spiedl.org/terms 4. CONCLUSIONS In this paper, we present a novel parallel implementation of the SSM to ultrasound registration of the lumbar vertebrae (L2-L4), which brings our previous report3 closer to clinical applicability. 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