- Email: [email protected]
Distortion corrected MRI for radiotherapy
Proceedings of the 44th Annual ASTRO Meeting
Purpose/Objective: The process of planning and delivering variants of three-dimensional conformal radiation therapy and intensity-modulated radiation therapy depends on the localization and digitization of anatomical structures. The extraction of data sufficient to produce a three-dimensional surface surrounding an anatomical structure, such as a liver or the rectum, has become known as segmentation. Although various tools have been provided to assist radiation oncologists with manual segmentation, the exercise remains a time-consuming bottleneck in the treatment planning procedure. In recent years, computer scientists, engineers and mathematicians have been investigating automated algorithms for image segmentation. The purpose of this work is to investigate the application of level set techniques based on solving partial differential equations (PDEs) for automating the segmentation phase in radiotherapy treatment planning. Materials/Methods: Level set methods provide a natural mathematical representation for dealing with complicated structures such as vascular trees [1]. The level set technique involves solving a PDE in which a discrete time variable can represent, e.g., different CT scans. In such methods, the boundary of an organ, which is a curve in a three-dimensional space, is implicitly represented as a zero level set of a four dimensional surface. The representation of the boundary of the organ in different scans can be then obtained by solving a nonlinear PDE of the form (t,x,y) ⫹ K兩ⵜ兩 ⫽ 0 where (t,x,y) represents a gray-scale image evaluated for parameter value t, and K is a so-called speed function, that can depend on and its derivatives. The underlying concept is to find a speed function K such that the parameter t will provide the best fit of a set of contours generated by the zero level set of at different times t, to the gray-scale pattern produced by the structure in a given reconstruction plane. A more advanced level set representation method is the “tracking and morphing active contours method” [2,3]. There, the goal is to detect and track objects that are moving in a scene, which in our case amounts to tracking the boundaries of a given organ in different scans. We propose new non-blind segmentation algorithms that improve the standard level set and morphing active contours methods. The key idea is to incorporate the structure of the target organ into the segmentation, while processing three-dimensional data. In this investigation we used data sets acquired during routine clinical operations with a Marconi PQ5000 spiral computerized tomography scanner. In particular we investigated segmentation of vascular structure in the liver. In order to identify lymph nodes, we investigated segmentation of a section of vessels consisting of the abdominal aorta, the common iliac arteries, the internal and external iliac arteries, and the companion venous structures. Automated segmentations were compared with manual segmentations using the kappa parameter [4]. Three liver cases and three abdominal/pelvic vessel cases were included in the study. A human user who identified the approximate location and orientation of the target structures initiated the algorithm. Results: The new algorithms we developed were able to segment the target structures in most cases to within the variance among human segmentations of the same structures. Conclusions: Image processing techniques that are based on solving PDEs provide a promising avenue to explore for applications in radiation oncology treatment planning. Additional investigations are needed to determine the variants of the underlying differential equations to be used for specific applications. [1] Sethian J.A., Level Set Methods and Fast Marching Methods, Second Edition, Cambridge Univ. Press, Cambridge, UK, 1999 [2] Sapiro G., Geometric Partial Differential Equations and Image Analysis, Cambridge Univ. Press, Cambridge, UK, 2001 [3] Paragios N., Deriche R., A PDE-Based Level Set Approach for Detection and Tracking of Moving Objects, Proc. Int. Comf. Comp. Vision ’98, IEEE, Los Alamitos, CA, 1998 [4] Fleiss J.L., Statistical Methods for Rates and Proportions, John Wiley & Sons, New York, 1981
140
Distortion Corrected MRI for Radiotherapy
H.P. Shukla1, P. Vaisanen2, M. Steckner1 1 Philips Medical, Cleveland, OH, 2Philips, Helsinki, Finland Purpose/Objective: Minimizing spatial errors in MRI has significant implications for interventional procedures, including planning of radiation therapy dose. [1] MRI datasets are commonly registered to datasets from other modalities (e.g., CT). In general, no attempts are made to minimize nor quantify the degree of MR spatial error. An algorithm to automatically minimize a particular type of distortion (gradient induced) has been implemented an ‘open’ geometry magnet, which has been shown particularly conducive for Radiation Oncology. [2] We show results of gradient correction in a quantitative manner using a custom-made test tool that allows an assessment regarding spatial ‘volumes-of-confidence’. The data analysis leads directly to discussion of clinical implications for systematic reduction of spatial distortion in the context of radiotherapy. [1] Khoo, V., BJR, 73, 2000 [2] Popowski, Y, IJROBP, 47:3, 2000 Materials/Methods: A diagnostic 0.23 Tesla open magnet (Panorama, Philips) was the target platform for the Gradient Distortion Correction (GDC) algorithm. This magnet uses bi-shielded multiplanar gradient coils, and has a 46 cm gap for the accommodation of oncology patients and immobilization devices. A Large-Body phased array coil of dimensions 50 ⫻ 35 cm was used to collect data from a grid phantom for analysis of GDC. A custom-made 45 ⫻ 35 cm grid phantom (1 cm thick) was embedded with 220 wheat germ 9 mm spheres. The capsules (73% oil) were positioned 25 mm apart within the grid, separated by PVC. The capsules were NOT placed in the corner areas of the phantom, so that the final outline of the capsules was quasi-elliptical. The phantom was interrogated with a Field-Echo pulse sequence at 9.8 MHz. To collapse the data into a 2D plane and minimize gradient interaction, slice thickness was set to be much greater than the phantom thickness, at 45 cm. Data from the phantom was collected before and after GDC correction in the three primary orthogonal planes. Analysis was done quantitatively by contour and scatterplots. Scatterplots show absolute error as a function of radius. RMS error is calculated within an isocentric sphere for both 36 cm and 40 cm diameters. Finally, a maximum radius is calculated for which a 95% confidence level is attained for spatial errors of 2 mm or less. Results: The pre and post-GDC corrected images display considerable improvement in spatial fidelity away from isocenter. Contour plots show an expansion of iso-lines in all directions, indicating an expanded error-free volume. Scatterplots of absolute error as a function of isocentric distance in each plane also show marked improvement of spatial fidelity, particularly for spherical volumes greater than 24 cm in diameter. Values for RMS error and maximum error at two spherical diameters are
83
84
I. J. Radiation Oncology
● Biology ● Physics
Volume 54, Number 2, Supplement, 2002
tabulated for each plane below. For this phantom, a 95% confidence level at 2 mm error can be achieved at a diameter of 33 cm (sagittal), 37 cm (coronal), and 39 cm (axial). Conclusions: Significant improvements in spatial fidelity can be achieved on an open geometry MRI by an algorithms to correct for gradient distortions. This leads to improved positional confidence within a quasi-elliptical volume approximated by a sphere 36 cm in diameter. In addition, object-based distortions (e.g., chemical-shift and susceptibility) can also be minimized at low magnetic field, and possibly constrained within a single pixel or voxel. Thus, GDC and other systematic considerations for reduction of spatial distortion benefits the quality of rigid-body registration between MRI and other modalities, regardless of the methodology used to perform the registration and the criteria used for evaluation. Furthermore, for certain patient sizes and pathologies where MRI provides definitive anatomical information (e.g., soft tissue sarcomas), MRI can now seriously be considered as a source of independent datasets for complete radiation therapy simulation and planning.[3] [3] Shukla, HP, AAPM, 1999 GDC
No
Yes
No
Yes
No
Yes
Sagittal Coronal Axial
RMS Error 8.1 8.5 7.5
RMS Error 2.0 1.5 1.8
Max.Error ⬍36 cm diameter 7.5 8.5 7.1
Max.Error ⬍36 cm diameter 2.4 1.8 1.3
Max.Error ⬍40 cm diameter 12 13 11
Max.Error ⬍40 cm diameter 3.0 3.4 2.2
141
Routine Clinical Use of Mutual Information for Automated 3D Registration of Anatomic and Functional Image Data
M.L. Kessler1, P. Archer1, C. Meyer2, S. Narayan1, A. Eisbruch1, H. Sandler1, T. Lawrence1 1 Department of Radiation Oncology, The University of Michigan Medical School, Ann Arbor, MI, 2Department of Radiology, The University of Michigan Medical School, Ann Arbor, MI Purpose/Objective: In order to fully exploit data from anatomic and functional imaging studies for radiotherapy, these data must be spatially registered to the primary treatment planning imaging study. To carry out this process in an automated and robust fashion, we have implemented a mutual information-based image registration system that can handle a wide variety of imaging situations and anatomic sites. The details and routine clinical use of this system are described here. Materials/Methods: The mutual information-based image registration system was implemented on an OpenVMS Alpha-based workstation (Compaq Computer Corp, Houston, TX) using the “C” programming language for all computations and the Application Visual System (Advanced Visual Systems Inc, Waltham, MA) for all user interaction and display. The input to the system is any pair of 3D image volumes that have some degree of anatomic overlap. Simple image processing tools such as volumetric cropping and contrast manipulation are provided to allow the user to specify the relevant features/regions of the two image datasets to register, if needed. The system supports rigid, full affine and thin-plate spline spatial transformations. In clinical practice, the two datasets are selected from a database and displayed in a side-by-side fashion using 3D views constructed from three orthogonal image planes. Using a mouse pointing device, the user interactively specifies some number of roughly corresponding points. At least three pairs of points are required for rigid transformations and at least five pairs for thin-plate spline transformations. After this initialization, registration of the datasets is completely automated. A Nelder-Mead simplex algorithm is used to iteratively perturb the individual locations of one set of points. A candidate transformation is computed from the pairs of points and this is used to reformat the higher resolution dataset at the voxel locations of the lower resolution dataset. The mutual information (MI) between the native lower resolution dataset and the re-sampled higher resolution dataset is computed directly from the image intensities and compared to that of the previous iteration. This process continues until the change in MI between successive iterations falls below a threshold value. The accuracy of the resulting transformation is accessed using a set of interactive display tools such as split screen display, composite color-gel images and contour overlays. Once registered, information defined from one dataset, such as tumor volumes, normal structure outlines or computed dose can be mapped to the other dataset and vice-versa. Similarly, structures defined independently on both datasets can be combined using 3D Boolean operations. Results: This system has been in routine clinical use for over a year and has been used to register 3D image data from anatomic and functional imaging studies for over 150 patients with tumors in the brain, lung, and pelvis. In many of these cases, the additional information from MR and PET helped resolve ambiguities in the treatment planing CT study and resulted in treatment plans that irradiated significantly less normal tissue. The accuracy of registration was consistently near or below the voxel size of the lower resolution dataset and the overall time involved was typically less than ten minutes per pair of datasets. In cases outside the brain, the ability to discard image data (via cropping) that was either not represented in both studies or involved excessive anatomic or machine distortions proved to be an important tool for successful registrations. Conclusions: The mutual information metric has proven to be an accurate and robust metric for registering 3D image data. Because the metric uses the image data directly, rather than extracted anatomic features, many of the limitations of the more common geometric-based metrics are avoided and a much wider variety of anatomic and functional imaging studies can be accurately registered and used in treatment planning. Supported in part by NIH P01 CA59827.
142
Comparison of an Image Registration Technique Based on Normalized Mutual Information with a Standard Method Utilizing Implanted Markers in the Staged Treatment of Large Arteriovenous Malformations
J.E. Bond1, V. Smith2, N.J. Yue1, J. Knisely1, A.C. de Lotbiniere3 1 Department of Therapeutic Radiology, Yale University School of Medicine, New Haven, CT, 2Department of Radiation Oncology, University of California San Francisco, San Francisco, CA, 3Department of Neurosurgery, Yale University School of Medicine, New Haven, CT
Purpose/Objective: The process of planning and delivering variants of three-dimensional conformal radiation therapy and intensity-modulated radiation therapy depends on the localization and digitization of anatomical structures. The extraction of data sufficient to produce a three-dimensional surface surrounding an anatomical structure, such as a liver or the rectum, has become known as segmentation. Although various tools have been provided to assist radiation oncologists with manual segmentation, the exercise remains a time-consuming bottleneck in the treatment planning procedure. In recent years, computer scientists, engineers and mathematicians have been investigating automated algorithms for image segmentation. The purpose of this work is to investigate the application of level set techniques based on solving partial differential equations (PDEs) for automating the segmentation phase in radiotherapy treatment planning. Materials/Methods: Level set methods provide a natural mathematical representation for dealing with complicated structures such as vascular trees [1]. The level set technique involves solving a PDE in which a discrete time variable can represent, e.g., different CT scans. In such methods, the boundary of an organ, which is a curve in a three-dimensional space, is implicitly represented as a zero level set of a four dimensional surface. The representation of the boundary of the organ in different scans can be then obtained by solving a nonlinear PDE of the form (t,x,y) ⫹ K兩ⵜ兩 ⫽ 0 where (t,x,y) represents a gray-scale image evaluated for parameter value t, and K is a so-called speed function, that can depend on and its derivatives. The underlying concept is to find a speed function K such that the parameter t will provide the best fit of a set of contours generated by the zero level set of at different times t, to the gray-scale pattern produced by the structure in a given reconstruction plane. A more advanced level set representation method is the “tracking and morphing active contours method” [2,3]. There, the goal is to detect and track objects that are moving in a scene, which in our case amounts to tracking the boundaries of a given organ in different scans. We propose new non-blind segmentation algorithms that improve the standard level set and morphing active contours methods. The key idea is to incorporate the structure of the target organ into the segmentation, while processing three-dimensional data. In this investigation we used data sets acquired during routine clinical operations with a Marconi PQ5000 spiral computerized tomography scanner. In particular we investigated segmentation of vascular structure in the liver. In order to identify lymph nodes, we investigated segmentation of a section of vessels consisting of the abdominal aorta, the common iliac arteries, the internal and external iliac arteries, and the companion venous structures. Automated segmentations were compared with manual segmentations using the kappa parameter [4]. Three liver cases and three abdominal/pelvic vessel cases were included in the study. A human user who identified the approximate location and orientation of the target structures initiated the algorithm. Results: The new algorithms we developed were able to segment the target structures in most cases to within the variance among human segmentations of the same structures. Conclusions: Image processing techniques that are based on solving PDEs provide a promising avenue to explore for applications in radiation oncology treatment planning. Additional investigations are needed to determine the variants of the underlying differential equations to be used for specific applications. [1] Sethian J.A., Level Set Methods and Fast Marching Methods, Second Edition, Cambridge Univ. Press, Cambridge, UK, 1999 [2] Sapiro G., Geometric Partial Differential Equations and Image Analysis, Cambridge Univ. Press, Cambridge, UK, 2001 [3] Paragios N., Deriche R., A PDE-Based Level Set Approach for Detection and Tracking of Moving Objects, Proc. Int. Comf. Comp. Vision ’98, IEEE, Los Alamitos, CA, 1998 [4] Fleiss J.L., Statistical Methods for Rates and Proportions, John Wiley & Sons, New York, 1981
140
Distortion Corrected MRI for Radiotherapy
H.P. Shukla1, P. Vaisanen2, M. Steckner1 1 Philips Medical, Cleveland, OH, 2Philips, Helsinki, Finland Purpose/Objective: Minimizing spatial errors in MRI has significant implications for interventional procedures, including planning of radiation therapy dose. [1] MRI datasets are commonly registered to datasets from other modalities (e.g., CT). In general, no attempts are made to minimize nor quantify the degree of MR spatial error. An algorithm to automatically minimize a particular type of distortion (gradient induced) has been implemented an ‘open’ geometry magnet, which has been shown particularly conducive for Radiation Oncology. [2] We show results of gradient correction in a quantitative manner using a custom-made test tool that allows an assessment regarding spatial ‘volumes-of-confidence’. The data analysis leads directly to discussion of clinical implications for systematic reduction of spatial distortion in the context of radiotherapy. [1] Khoo, V., BJR, 73, 2000 [2] Popowski, Y, IJROBP, 47:3, 2000 Materials/Methods: A diagnostic 0.23 Tesla open magnet (Panorama, Philips) was the target platform for the Gradient Distortion Correction (GDC) algorithm. This magnet uses bi-shielded multiplanar gradient coils, and has a 46 cm gap for the accommodation of oncology patients and immobilization devices. A Large-Body phased array coil of dimensions 50 ⫻ 35 cm was used to collect data from a grid phantom for analysis of GDC. A custom-made 45 ⫻ 35 cm grid phantom (1 cm thick) was embedded with 220 wheat germ 9 mm spheres. The capsules (73% oil) were positioned 25 mm apart within the grid, separated by PVC. The capsules were NOT placed in the corner areas of the phantom, so that the final outline of the capsules was quasi-elliptical. The phantom was interrogated with a Field-Echo pulse sequence at 9.8 MHz. To collapse the data into a 2D plane and minimize gradient interaction, slice thickness was set to be much greater than the phantom thickness, at 45 cm. Data from the phantom was collected before and after GDC correction in the three primary orthogonal planes. Analysis was done quantitatively by contour and scatterplots. Scatterplots show absolute error as a function of radius. RMS error is calculated within an isocentric sphere for both 36 cm and 40 cm diameters. Finally, a maximum radius is calculated for which a 95% confidence level is attained for spatial errors of 2 mm or less. Results: The pre and post-GDC corrected images display considerable improvement in spatial fidelity away from isocenter. Contour plots show an expansion of iso-lines in all directions, indicating an expanded error-free volume. Scatterplots of absolute error as a function of isocentric distance in each plane also show marked improvement of spatial fidelity, particularly for spherical volumes greater than 24 cm in diameter. Values for RMS error and maximum error at two spherical diameters are
83
84
I. J. Radiation Oncology
● Biology ● Physics
Volume 54, Number 2, Supplement, 2002
tabulated for each plane below. For this phantom, a 95% confidence level at 2 mm error can be achieved at a diameter of 33 cm (sagittal), 37 cm (coronal), and 39 cm (axial). Conclusions: Significant improvements in spatial fidelity can be achieved on an open geometry MRI by an algorithms to correct for gradient distortions. This leads to improved positional confidence within a quasi-elliptical volume approximated by a sphere 36 cm in diameter. In addition, object-based distortions (e.g., chemical-shift and susceptibility) can also be minimized at low magnetic field, and possibly constrained within a single pixel or voxel. Thus, GDC and other systematic considerations for reduction of spatial distortion benefits the quality of rigid-body registration between MRI and other modalities, regardless of the methodology used to perform the registration and the criteria used for evaluation. Furthermore, for certain patient sizes and pathologies where MRI provides definitive anatomical information (e.g., soft tissue sarcomas), MRI can now seriously be considered as a source of independent datasets for complete radiation therapy simulation and planning.[3] [3] Shukla, HP, AAPM, 1999 GDC
No
Yes
No
Yes
No
Yes
Sagittal Coronal Axial
RMS Error 8.1 8.5 7.5
RMS Error 2.0 1.5 1.8
Max.Error ⬍36 cm diameter 7.5 8.5 7.1
Max.Error ⬍36 cm diameter 2.4 1.8 1.3
Max.Error ⬍40 cm diameter 12 13 11
Max.Error ⬍40 cm diameter 3.0 3.4 2.2
141
Routine Clinical Use of Mutual Information for Automated 3D Registration of Anatomic and Functional Image Data
M.L. Kessler1, P. Archer1, C. Meyer2, S. Narayan1, A. Eisbruch1, H. Sandler1, T. Lawrence1 1 Department of Radiation Oncology, The University of Michigan Medical School, Ann Arbor, MI, 2Department of Radiology, The University of Michigan Medical School, Ann Arbor, MI Purpose/Objective: In order to fully exploit data from anatomic and functional imaging studies for radiotherapy, these data must be spatially registered to the primary treatment planning imaging study. To carry out this process in an automated and robust fashion, we have implemented a mutual information-based image registration system that can handle a wide variety of imaging situations and anatomic sites. The details and routine clinical use of this system are described here. Materials/Methods: The mutual information-based image registration system was implemented on an OpenVMS Alpha-based workstation (Compaq Computer Corp, Houston, TX) using the “C” programming language for all computations and the Application Visual System (Advanced Visual Systems Inc, Waltham, MA) for all user interaction and display. The input to the system is any pair of 3D image volumes that have some degree of anatomic overlap. Simple image processing tools such as volumetric cropping and contrast manipulation are provided to allow the user to specify the relevant features/regions of the two image datasets to register, if needed. The system supports rigid, full affine and thin-plate spline spatial transformations. In clinical practice, the two datasets are selected from a database and displayed in a side-by-side fashion using 3D views constructed from three orthogonal image planes. Using a mouse pointing device, the user interactively specifies some number of roughly corresponding points. At least three pairs of points are required for rigid transformations and at least five pairs for thin-plate spline transformations. After this initialization, registration of the datasets is completely automated. A Nelder-Mead simplex algorithm is used to iteratively perturb the individual locations of one set of points. A candidate transformation is computed from the pairs of points and this is used to reformat the higher resolution dataset at the voxel locations of the lower resolution dataset. The mutual information (MI) between the native lower resolution dataset and the re-sampled higher resolution dataset is computed directly from the image intensities and compared to that of the previous iteration. This process continues until the change in MI between successive iterations falls below a threshold value. The accuracy of the resulting transformation is accessed using a set of interactive display tools such as split screen display, composite color-gel images and contour overlays. Once registered, information defined from one dataset, such as tumor volumes, normal structure outlines or computed dose can be mapped to the other dataset and vice-versa. Similarly, structures defined independently on both datasets can be combined using 3D Boolean operations. Results: This system has been in routine clinical use for over a year and has been used to register 3D image data from anatomic and functional imaging studies for over 150 patients with tumors in the brain, lung, and pelvis. In many of these cases, the additional information from MR and PET helped resolve ambiguities in the treatment planing CT study and resulted in treatment plans that irradiated significantly less normal tissue. The accuracy of registration was consistently near or below the voxel size of the lower resolution dataset and the overall time involved was typically less than ten minutes per pair of datasets. In cases outside the brain, the ability to discard image data (via cropping) that was either not represented in both studies or involved excessive anatomic or machine distortions proved to be an important tool for successful registrations. Conclusions: The mutual information metric has proven to be an accurate and robust metric for registering 3D image data. Because the metric uses the image data directly, rather than extracted anatomic features, many of the limitations of the more common geometric-based metrics are avoided and a much wider variety of anatomic and functional imaging studies can be accurately registered and used in treatment planning. Supported in part by NIH P01 CA59827.
142
Comparison of an Image Registration Technique Based on Normalized Mutual Information with a Standard Method Utilizing Implanted Markers in the Staged Treatment of Large Arteriovenous Malformations
J.E. Bond1, V. Smith2, N.J. Yue1, J. Knisely1, A.C. de Lotbiniere3 1 Department of Therapeutic Radiology, Yale University School of Medicine, New Haven, CT, 2Department of Radiation Oncology, University of California San Francisco, San Francisco, CA, 3Department of Neurosurgery, Yale University School of Medicine, New Haven, CT