Elastic Registration of Prostate MR Images Based on State Estimation of Dynamical Systems

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1 Elastic Registration of Prostate MR Images Based on State Estimation of Dynamical Systems Bahram Marami a,b,c, Suha Ghoul a, Shahin Sirouspour c, David W. Capson d, Sean R. H. Davidson e, John Trachtenberg f and Aaron Fenster a,b,g a Imaging Research Laboratories, Robarts Research Institute, London, Ontario, Canada b Biomedical Engineering Graduate Program, The University of Western Ontario, Canada c Department of Electrical and Computer Engineering, McMaster University, Canada d Department of Electrical and Computer Engineering, University of Victoria, Canada e Ontario Cancer Institute, University Health Network, Toronto, Ontario, Canada f Department of Surgical Oncology, University Health Network, Toronto, Ontario, Canada g Department of Medical Biophysics, University of Western Ontario, London, Ontario, Canada ABSTRACT Magnetic resonance imaging (MRI) is being increasingly used for image-guided biopsy and focal therapy of prostate cancer. A combined rigid and deformable registration technique is proposed to register pre-treatment diagnostic 3 T magnetic resonance (MR) images, with the identified target tumor(s), to the intra-treatment 1.5 T MR images. The pre-treatment 3 T images are acquired with patients in strictly supine position using an endorectal coil, while 1.5 T images are obtained intra-operatively just before insertion of the ablation needle with patients in the lithotomy position. An intensity-based registration routine rigidly aligns two images in which the transformation parameters is initialized using three pairs of manually selected approximate corresponding points. The rigid registration is followed by a deformable registration algorithm employing a generic dynamic linear elastic deformation model discretized by the finite element method (FEM). The model is used in a classical state estimation framework to estimate the deformation of the prostate based on a similarity metric between pre- and intra-treatment images. Registration results using 1 sets of prostate MR images showed that the proposed method can significantly improve registration accuracy in terms of target registration error (TRE) for all prostate substructures. The root mean square (RMS) TRE of 46 manually identified fiducial points was found to be 2.4±1.2 mm, 2.51±1.2 mm, and 2.28±1.22 mm for the whole gland (WG), central gland (CG), and peripheral zone (PZ), respectively after deformable registration. These values are improved from 3.15±1.6 mm, 3.9±1.5 mm, and 3.2±1.73 mm in the WG, CG and PZ, respectively resulted from rigid registration. Registration results are also evaluated based on the Dice similarity coefficient (DSC), mean absolute surface distances (MAD) and maximum absolute surface distances (MAXD) of the WG and CG in the prostate images. Keywords: Prostate MR image registration, elastic model-based registration, motion compensation, focal ablation therapy, finite element method 1. INTRODUCTION Prostate cancer is the most frequently diagnosed non-skin cancer and the third leading cause of cancer death among males in the developed countries. 1 Early detection and treatment can significantly reduce morality rate from prostate cancer. Accurate delivery of treatment is extremely important in localized prostate cancer therapy. Due to the superior performance in differentiating soft tissue structures, MRI systems are employed in imageguided interventions such as prostate biopsy, and radiation and focal therapy of prostate cancer. 2, 3 High-field MRI systems with an endorectal coil can provide detailed images with ability to visualize substructures of the prostate, i.e., central gland (CG) and peripheral zone (PZ), and their margins. These images also allow accurate localizing of the tumor for use in guiding the biopsy needles 2 and focal ablation therapy techniques. 3, 4 Medical Imaging 214: Image Processing, edited by Sebastien Ourselin, Martin A. Styner, Proc. of SPIE Vol. 934, 934F 214 SPIE CCC code: /14/$18 doi: / Proc. of SPIE Vol F-1

2 START ˆx Time Update/Prediction J k no J k 1 ˆx k 1 J Measurement Update k ˆx k yes FINISH ˆx k Preoperative Images Deformation, Transformation and Interpolation T [u ] k _ Intra-operative Images + R Similarity Measure dx c Figure 1: Block diagram of the iterative registration algorithm based on the concept of dynamic state estimation. Focal ablation procedures performed within the bore of the MR scanner are time sensitive, requiring acquisition of the images in a short time. We acquired intra-treatment images using MRI systems with a field-strength of 1.5 T for ablation procedures. 3 Thus, the intra-treatment images acquired by our interventional MRI system had a lower signal-to-noise ratio (SNR), spatial resolution and contrast than those of diagnostic images acquired at 3 T. Accurate registration of the diagnostic pre-treatment images with delineated tumor(s) to intra-treatment images is instrumental in guiding the focal ablation applicators to the identified target and ensuring that the ablation zone covers the target tumor. Prostate tissue usually undergoes non-rigid deformation between imaging sessions due to the presence and absence of the endorectal coil, different inflation volumes of the endorectal coil balloon, patient s position and different bladder volume. Therefore, deformable registration methods are required to align pre-treatment and intra-treatment images. A 3D-3D deformable registration method based on the concept of state estimation for dynamical systems is proposed in this paper. The registration method employs a general linear elastic finite element (FE)-based deformation model. The registration is achieved through a Kalman-like filtering process, which incorporates information from the deformation model and an observation error computed from an intensity-based similarity metric, namely, modality independent neighborhood descriptor (MIND). 5 No specific geometry of the prostate and its substructures is used for constructing the deformation model, rather a cubic volume of tetrahedral finite elements is employed. In the state estimation framework, the estimation process takes into account modeling and observation uncertainties in the form of an unknown process and measurement disturbances. Furthermore, the registration method requires minimal manual intervention of the user and no pre-processing (feature extraction or segmentation) of the images is involved. 2. METHODS The proposed registration method in this paper involves both rigid and deformable registration. In the first step, the pre- and intra-treatment images are rigidly co-registered by minimizing the sum-of-absolute-differences (SAD) of the MINDs between two images. The MIND algorithm extracts distinctive structures in a local neighborhood based on the similarity of small image patches within the image. The extraction of structures using this method is independent from image modalities, contrast, noise and intensity levels of the images. 5 MIND can automatically deal with intensity inhomogeneities around the endorectal coil and no preprocessing of the images is required. In the optimization, the initial values for the rigid transformation parameters are computed based on aligning three manually identified approximate corresponding point pairs in two images. The registration algorithm is robust with respect to the selection of these approximate corresponding points and they are not used for the validation of the registrations. In the second step, the deformation of the prostate is approximated by a dynamic linear elastic model based on a matching criterion between pre- and intra-treatment images using a filtering approach. The dynamics for the tissue deformation are modeled by following discrete-time linear state-space equations x k = Ax k 1 + w k 1 (1a) z k = Hx k + v k (1b) Proc. of SPIE Vol F-2

3 In these equations, x k is the vector of deformation states at time step k, which is comprised of displacements and velocities of the nodal points of the FE mesh, projected to a lower dimensionality. The measurement vector z k is the vector of displacements at control points from their initial positions. Control points, i.e., x c, are evenly distributed inside the FE mesh and their spacing is larger than intra-treatment image voxels. A and H are the state transition and output matrices, respectively, which can be computed based on the dynamic linear elastic FE model 6 and the position of the control points. Moreover, w k and v k are process and measurement noise, and represent uncertainties/errors (model mismatches, unknown external forces, etc) in the deformation dynamics and observation model, respectively. Given any set of pre- and intra-treatment images, the deformable registration is achieved through an iterative routine. The flowchart of the proposed state estimation-based registration algorithm is given in Figure 1 and it involves following steps. 1. Time Update/Prediction: Starting from zero initial states, the vector of state estimates from the previous step ˆx k 1 is updated to ˆx k using ˆx k ˆx k = Aˆx k 1 (2) is an a priori estimate of the states,7 based on which the predicted displacements for the nodal points of the FE mesh, i.e., u k, are computed. 2. Deformation, Transformation and Interpolation: The deformation for the grid of control points x c and intratreatment image R are computed based on the deformation of the FE mesh using elements shape functions. 6 Deformed grids are transformed to the coordinates of the pre-treatment image T using the rigid transformation. The predicted deformed image T [u k ] can then be interpolated from the pre-treatment image volume. 3. Observation Prediction Error: The observation prediction error dx c is computed at control points based on the gradient of the similarity measure as dx c = z k Hˆx k = γ J(R, T [u k ], x c) (3) where J(R, T [u k ], x c) is the SSD between MINDs in two images at x c Measurement Update: The state estimates are updated based on the observation prediction error using ˆx k = ˆx k + Γdx c (4) where Γ is the steady-state Kalman gain, which is computed offline given process and measurement noise covariance matrices. 7 Γ is computed once and can be used in the registration of different image sets. The algorithm terminates when the relative change in the similarity metric between R and T [u] (i.e., J(R, T [u])) is less than a given small number ε or the number of iterations reaches a maximum value. It should be noted that both the deformation and observation models are independent from the image sets. Therefore, γ is the only parameter, which is needed to be tuned for the registration of different image sets. This parameter weights imaged-derived forces to provide a balance between internal elastic energy of the deformation model and external energy defined based on the image similarity measure. A hierarchical multi-level approach (three image resolution levels) is employed in the estimation of non-rigid deformation of the tissue. 3. EXPERIMENTS AND RESULTS The proposed registration algorithm was evaluated in the registration of pre-treatment 3 T T2-weighted MR images of the prostate to their intra-treatment 1.5 T T2-weighted MR images. Ten MR-guided prostate focal laser ablation therapy patients were identified and all patients underwent pre-treatment 3 T MR imaging using a GE Discovery MR75 scanner. Intra-treatment images were obtained using a GE Signa HDxt 1.5 T scanner just before inserting the ablation needle. An endorectal coil was used for acquiring both pre- and intra-treatment images. The pixel sizes in pre- and intra-treatment images were.4.4 mm and mm, respectively and the slice thickness was 3 mm in both image sets. Proc. of SPIE Vol F-3

4 z x 4 2 y 4 (a) (b) Figure 2: (a) Undeformed FE mesh employed in the registration (b) deformed FE mesh after registration of an example image pair. z x y A cubic mesh with 1,476 tetrahedral elements and 2,93 nodal points was employed to construct the deformation model, which is shown in Figure 2a. Using this mesh, an isotropic linear elastic model of deformation with the Young s elasticity modulus E = 15 kpa, Poisson s ratio ν =.49 and a mass density of ρ = 1 g/cm 3 was created. The constructed model is used to estimate the deformation of the prostate in all image pairs. For any given image set, the intra-treatment image volume is scaled and transformed to be placed inside the FE mesh. A regular grid of was also used as control points inside the cube of finite elements. For an example image pair, the deformed 3D FE mesh after registration are given in Figure 2b. Axial views of the registered prostate images with tumor outlines in two different example cases are given in Figure 3. In each row of this figure, pre-treatment images are rigidly (column (a)) and non-rigidly (column (c)) registered to the intra-treatment images in column (b). Tumor outlines were identified by a radiologist in the pre-treatment images. These outlines were transformed and overlaid on the intra-treatment (column (b)) and registered pre-treatment images (column (c)) based on the obtained rigid and non-rigid displacement field. As can be observed from these figures, most of the deformation occurs in the PZ caused by the endorectal coil. For most image cases the tumor cannot be differentiated from the surrounding healthy tissue in the intra-treatment images. These cases demonstrate the need for an algorithm that can accurately register pre-treatment target volumes to intra-treatment images in MRI-guided targeted biopsy or focal ablation therapy. Both pre-treatment and intra-treatment images were manually segmented to determine the volume of the WG and CG in the prostate images and used to evaluate the registration results. The volume of the PZ was computed by subtracting the volume of CG from the WG volume in each image set. Table 1 summarizes the results of both rigid and deformable registrations for the different prostate substructures in terms of average and standard deviations of the TRE, DSC (%), MAD and MAXD. Furthermore, the frequency distribution of TREs for 46 fiducial points (23 points in each region) in the initial rigid alignment and the deformable registration are shown in Figure 4. It is evident from this figure that the distribution of TREs in deformable registration has a higher peak at small values. In contrast, the TRE from the rigid registration is distributed with a wider range. The registration results given in Table 1 and Figure 4 show that deformable registration improves the quality of matching in terms of DSC and TRE especially in the PZ. The average TRE resulted for deformable registration in the PZ is decreased more than that in the CG. This is partly due to the fact that most of the deformation occur in the PZ of the prostate. Also, DSC improvement in the PZ and WG is greater than that in the CG. The average MAD and MAXD results given in Table 1 also show that deformable registration is more effective Proc. of SPIE Vol F-4

5 (a) (b) (c) Figure 3: Axial views of the prostate images with tumor outlines, in each row: (a) rigidly aligned pre-treatment image, (b) intra-treatment image and (c) non-rigidly registered pre-treatment image. Table 1: Summary of registration results (average ± std) based on TRE, DSC, MAD and MAXD TRE (mm) DSC (%) MAD (mm) MAXD (mm) PZ CG WG PZ CG WG CG WG CG WG Rigid 3.2± ± ± ± ± ± ± ± ± ±1.6 Deformable 2.28± ± ± ± ± ± ± ± ± ±.86 in the WG rather than the CG. 4. COMPUTATIONS Computational tasks involved in the proposed registration method can be categorized in two groups: common tasks before starting the registration, which are performed once for all image sets, and tasks for registering each set of images. We implemented all steps of the registration algorithm using MATLAB on a 3.5 GHz Intel(R) Core(TM) i7-397x processor with a 64. GB RAM. Common tasks required 34 min. For the registration of each image set, it required about 2 min to identify three approximate corresponding points in the prostate image pairs, determine the approximate prostate region in the intra-treatment images and rigidly register two images. The time for iterative elastic registration algorithm was about 2 min. After the iterations end, it required 26 sec to compute the deformed pre-treatment image (high-resolution) based on the estimated states of the deformation. Furthermore, the time for finding the deformation of pre-treatment tumor outline and overlaying on the intratreatment images was less than 5 sec. Thus, the total time required is about 5 min to perform both rigid and deformable registration algorithms and compute the deformed registered image. 5. BREAKTHROUG WORK TO BE PRESENTED A novel linear elastic registration method is presented for deformable co-registration of 3D images. An earlier version of the proposed method was evaluated in the registration of breast MR images. 8, 9 In this paper, the method is further developed and generalized. Also, a different similarity measure is employed in the registration. Moreover, the method is evaluated in the registration of prostate MR images. Proc. of SPIE Vol F-5

6 frequency PZ CG frequency PZ CG TRE (mm) TRE (mm) (a) (b) Figure 4: Frequency distribution of TREs in CG and PZ after (a) rigid alignment and (b) deformable registration. 6. CONCLUSIONS A combined rigid and deformable registration approach was proposed to match pre- and intra-treatment MR images in the focal ablation therapy of prostate cancer. The proposed elastic registration method estimates the tissue deformation using a dynamic linear elastic FE-based model through a filtering process. The registration approach involves minimal manual intervention of the user and does not require segmentation of the prostate boundaries. Experimental results showed that the deformable registration improves the quality of matching especially in the PZ where the endorectal coil deforms the prostate during different imaging sessions. ACKNOWLEDGMENTS The authors gratefully acknowledge funding from the Ontario Institute for Cancer Research (OICR) and Canadian Institutes of Health Research (CIHR). A. Fenster holds a Canada Research Chair in Biomedical Engineering, and acknowledges the support of the Canada Research Chair Program. The authors would like to thank Dr. Jeremy Cepek for collecting and analyzing prostate MR image data. REFERENCES [1] Jemal, A., Bray, F., Center, M. M., Ferlay, J., Ward, E., and Forman, D., Global cancer statistics, CA: a cancer journal for clinicians 61(2), 69 9 (211). [2] Hata, N., Jinzaki, M., Kacher, D., Cormak, R., Gering, D., Nabavi, A., Silverman, S. G., DAmico, A. V., Kikinis, R., Jolesz, F. A., et al., MR imaging-guided prostate biopsy with surgical navigation software: Device validation and feasibility, Radiology 22(1), (21). [3] Raz, O., Haider, M. A., Davidson, S. R., Lindner, U., Hlasny, E., Weersink, R., Gertner, M. R., Kucharcyzk, W., McCluskey, S. A., and Trachtenberg, J., Real-time magnetic resonance imaging guided focal laser therapy in patients with low-risk prostate cancer, European urology 58(1), (21). [4] Lindner, U., Lawrentschuk, N., Weersink, R. A., Davidson, S. R., Raz, O., Hlasny, E., Langer, D. L., Gertner, M. R., Van der Kwast, T., Haider, M. A., and Trachtenberg, J., Focal laser ablation for prostate cancer followed by radical prostatectomy: validation of focal therapy and imaging accuracy, European urology 57(6), (21). [5] Heinrich, M. P., Jenkinson, M., Matin, T., Brady, S. M., Schnabel, J. A., and et al., MIND: Modality independent neighbourhood descriptor for multi-modal deformable registration, Med. Im. Anal. (212). [6] Bathe, K., [Finite Element Procedures], Prentice Hall, Englewood Cliffs, NJ (1996). [7] Welch, G. and Bishop, G., An introduction to the kalman filter, (1995). [8] Marami, B., Sirouspour, S., and Capson, D. W., Model-based deformable registration of preoperative 3D to intraoperative low-resolution 3D and 2D sequences of MR images, in [Medical Image Computing and Computer-Assisted Intervention MICCAI 211], , Springer (211). [9] Marami, B., Elastic Registration of Medical Images Using Generic Dynamic Deformation Models, PhD Thesis, McMaster University Library (213). Proc. of SPIE Vol F-6