Eduard Schreibmann

Model‐based image reconstruction for four‐dimensional PET

Positron emission tonography (PET) is useful in diagnosis and radiation treatment planning for a variety of cancers. For patients with cancers in thoracic or upper abdominal region, the respiratory motion produces large distortions in the tumor shape and size, affecting the accuracy in both diagnosis and treatment. Four-dimensional (4D) (gated) PET aims to reduce the motion artifacts and to provide accurate measurement of the tumor volume and the tracer concentration. A major issue in 4D PET is the lack of statistics. Since the collected photons are divided into several frames in the 4D PET scan, the quality of each reconstructed frame degrades as the number of frames increases. The increased noise in each frame heavily degrades the quantitative accuracy of the PET imaging. In this work, we propose a method to enhance the performance of 4D PET by developing a new technique of 4D PET reconstruction with incorporation of an organ motion model derived from 4D-CT images. The method is based on the well-known maximum-likelihood expectation-maximization (ML-EM) algorithm. During the processes of forward- and backward-projection in the ML-EM iterations, all projection data acquired at different phases are combined together to update the emission map with the aid of deformable model, the statistics is therefore greatly improved. The proposed algorithm was first evaluated with computer simulations using a mathematical dynamic phantom. Experiment with a moving physical phantom was then carried out to demonstrate the accuracy of the proposed method and the increase of signal-to-noise ratio over three-dimensional PET. Finally, the 4D PET reconstruction was applied to a patient case.

Motion correction for improved target localization with on-board cone-beam computed tomography

On-board imager (OBI) based cone-beam computed tomography (CBCT) has become available in radiotherapy clinics to accurately identify the target in the treatment position. However, due to the relatively slow gantry rotation (typically about 60 s for a full 360 degrees scan) in acquiring the CBCT projection data, the patients respiratory motion causes serious problems such as blurring, doubling, streaking and distortion in the reconstructed images, which heavily degrade the image quality and the target localization. In this work, we present a motion compensation method for slow-rotating CBCT scans by incorporating into image reconstruction a patient-specific motion model, which is derived from previously obtained four-dimensional (4D) treatment planning CT images of the same patient via deformable registration. The registration of the 4D CT phases results in transformations representing a temporal sequence of three-dimensional (3D) deformation fields, or in other words, a 4D model of organ motion. The algorithm was developed heuristically in two-dimensional (2D) parallel-beam geometry and extended to 3D cone-beam geometry. By simulations with digital phantoms capable of translational motion and other complex motion, we demonstrated that the algorithm can reduce the motion artefacts locally, and restore the tumour size and shape, which may thereby improve the accuracy of target localization and patient positioning when CBCT is used as the treatment guidance.

Multiobjective Evolutionary optimization of the number of beams, their orientations and weights for intensity-modulated radiation therapy

We propose a hybrid multiobjective (MO) evolutionary optimization algorithm (MOEA) for intensity-modulated radiotherapy inverse planning and apply it to optimize the number of incident beams, their orientations and intensity profiles. The algorithm produces a set of efficient solutions, which represent different clinical trade-offs and contains information such as variety of dose distributions and dose-volume histograms. No importance factors are required and solutions can be obtained in regions not accessible by conventional weighted sum approaches. The application of the algorithm using a test case, a prostate and a head and neck tumour case is shown. The results are compared with MO inverse planning using a gradient-based optimization algorithm.

Multiobjective inverse planning for intensity modulated radiotherapy with constraint-free gradient-based optimization algorithms

We consider the behaviour of the limited memory L-BFGS algorithm as a representative constraint-free gradient-based algorithm which is used for multiobjective (MO) dose optimization for intensity modulated radiotherapy (IMRT). Using a parameter transformation, the positivity constraint problem of negative beam fluences is entirely eliminated: a feature which to date has not been fully understood by all investigators. We analyse the global convergence properties of L-BFGS by searching for the existence and the influence of possible local minima. With a fast simulated annealing (FSA) algorithm we examine whether the L-BFGS solutions are globally Pareto optimal. The three examples used in our analysis are a brain tumour, a prostate tumour and a test case with a C-shaped PTV. In 1% of the optimizations global convergence is violated. A simple mechanism practically eliminates the influence of this failure and the obtained solutions are globally optimal. A single-objective dose optimization requires less than 4 s for 5400 parameters and 40000 sampling points. The elimination of the problem of negative beam fluences and the high computational speed permit constraint-free gradient-based optimization algorithms to be used for MO dose optimization. In this situation, a representative spectrum of possible solutions is obtained which contains information such as the trade-off between the objectives and range of dose values. Using simple decision making tools the best of all the possible solutions can be chosen. We perform an MO dose optimization for the three examples and compare the spectra of solutions, firstly using recommended critical dose values for the organs at risk and secondly, setting these dose values to zero.

Radiation dose reduction in four-dimensional computed tomography.

Four-dimensional (4D) CT is useful in many clinical situations, where detailed abdominal and thoracic imaging is needed over the course of the respiratory cycle. However, it usually delivers a larger radiation dose than the standard three-dimensional (3D) CT, since multiple scans at each couch position are required in order to provide the temporal information. Our purpose in this work is to develop a method to perform 4D CT scans at relatively low current, hence reducing the radiation exposure of the patients. To deal with the increased statistical noise caused by the low current, we proposed a novel 4D penalized weighted least square (4D-PWLS) smoothing method, which can incorporate both spatial and phase information. The 4D images at different phases were registered to the same phase via a deformable model, thereby, a regularization term combining temporal and spatial neighbors can be designed for the 4D-PWLS objective function. The proposed method was tested with phantom experiments and a patient study, and superior noise suppression and resolution preservation were observed. A quantitative evaluation of the benefit of the proposed method to 4D radiotherapy and 4D PET/CT imaging are under investigation.

Image registration with auto-mapped control volumes.

Many image registration algorithms rely on the use of homologous control points on the two input image sets to be registered. In reality, the interactive identification of the control points on both images is tedious, difficult, and often a source of error. We propose a two-step algorithm to automatically identify homologous regions that are used as a priori information during the image registration procedure. First, a number of small control volumes having distinct anatomical features are identified on the model image in a somewhat arbitrary fashion. Instead of attempting to find their correspondences in the reference image through user interaction, in the proposed method, each of the control regions is mapped to the corresponding part of the reference image by using an automated image registration algorithm. A normalized cross-correlation (NCC) function or mutual information was used as the auto-mapping metric and a limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm (L-BFGS) was employed to optimize the function to find the optimal mapping. For rigid registration, the transformation parameters of the system are obtained by averaging that derived from the individual control volumes. In our deformable calculation, the mapped control volumes are treated as the nodes or control points with known positions on the two images. If the number of control volumes is not enough to cover the whole image to be registered, additional nodes are placed on the model image and then located on the reference image in a manner similar to the conventional BSpline deformable calculation. For deformable registration, the established correspondence by the auto-mapped control volumes provides valuable guidance for the registration calculation and greatly reduces the dimensionality of the problem. The performance of the two-step registrations was applied to three rigid registration cases (two PET-CT registrations and a brain MRI-CT registration) and one deformable registration of inhale and exhale phases of a lung 4D CT. Algorithm convergence was confirmed by starting the registration calculations from a large number of initial transformation parameters. An accuracy of approximately 2 mm was achieved for both deformable and rigid registration. The proposed image registration method greatly reduces the complexity involved in the determination of homologous control points and allows us to minimize the subjectivity and uncertainty associated with the current manual interactive approach. Patient studies have indicated that the two-step registration technique is fast, reliable, and provides a valuable tool to facilitate both rigid and nonrigid image registrations.

Feasibility study of beam orientation class-solutions for prostate IMRT.

IMRT is being increasingly used for treatment of prostate cancer. In practice, however, the beam orientations used for the treatments are still selected empirically, without any guideline. The purpose of this work was to investigate interpatient variation of the optimal beam configuration and to facilitate intensity modulated radiation therapy (IMRT) prostate treatment planning by proposing a set of beam orientation class-solutions for a range of numbers of incident beams. We used fifteen prostate cases to generate the beam orientation class-solutions. For each patient and a given number of incident beams, a multiobjective optimization engine was employed to provide optimal beam directions. For the fifteen cases considered, the gantry angle of any of the optimized plans were all distributed within a certain range The angular distributions of the optimal beams were analyzed and the most selected directions are identified as optimal directions. The optimal directions for all patients are averaged to obtain the class-solution. The class-solution gantry angles for prostate IMRT were found to be: three beams (0 degrees, 120 degrees, 240 degrees), five beams (35 degrees, 110 degrees, 180 degrees, 250 degrees, 325 degrees), six beams (0 degrees, 60 degrees, 120 degrees, 180 degrees, 240 degrees, 300 degrees), seven beams (25 degrees, 75 degrees, 130 degrees, 180 degrees, 230 degrees, 285 degrees, 335 degrees), eight beams (20 degrees, 70 degrees, 110 degrees, 150 degrees, 200 degrees, 250 degrees, 290 degrees, 340 degrees), and nine beams (20 degrees, 60 degrees, 100 degrees, 140 degrees, 180 degrees, 220 degrees, 260 degrees, 300 degrees, 340 degrees). The level of validity of the class-solutions was tested using an additional clinical prostate case by comparing with the individually optimized beam configurations. The difference between the plans obtained with class-solutions and patient-specific optimizations was found to be clinically insignificant.

Automated Contour Mapping With a Regional Deformable Model

PURPOSE To develop a regional narrow-band algorithm to auto-propagate the contour surface of a region of interest (ROI) from one phase to other phases of four-dimensional computed tomography (4D-CT). METHODS AND MATERIALS The ROI contours were manually delineated on a selected phase of 4D-CT. A narrow band encompassing the ROI boundary was created on the image and used as a compact representation of the ROI surface. A BSpline deformable registration was performed to map the band to other phases. A Mattes mutual information was used as the metric function, and the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm was used to optimize the function. After registration the deformation field was extracted and used to transform the manual contours to other phases. Bidirectional contour mapping was introduced to evaluate the proposed technique. The new algorithm was tested on synthetic images and applied to 4D-CT images of 4 thoracic patients and a head-and-neck Cone-beam CT case. RESULTS Application of the algorithm to synthetic images and Cone-beam CT images indicates that an accuracy of 1.0 mm is achievable and that 4D-CT images show a spatial accuracy better than 1.5 mm for ROI mappings between adjacent phases, and 3 mm in opposite-phase mapping. Compared with whole image-based calculations, the computation was an order of magnitude more efficient, in addition to the much-reduced computer memory consumption. CONCLUSIONS A narrow-band model is an efficient way for contour mapping and should find widespread application in future 4D treatment planning.

A geometry based optimization algorithm for conformal external beam radiotherapy

A geometric solution of the problem of optimal orientation of beams in conformal external radiotherapy is presented. The method uses geometric derived quantities which consider the intersection volume between organs at risk (OAR) and the beam shape. In comparison to previous geometric methods a true 3D volume computation is used which takes into account beam divergence, concave shapes, as well as treatment settings such as individual beam shaping by blocks or multi-leaf collimators. For standard dosimetric cost functions used by dose optimization algorithms a corresponding set of geometric objective functions is proposed. We compare the correlations between geometric and dosimetric cost functions for two clinical cases, a prostate and a head tumour case. A correlation is observed for the prostate case, whereas for the head case it is less pronounced due to the larger part of overlapping volumes between the beams which cannot be considered by the used objectives. In comparison to not-optimized beam directions the dose distribution is significantly better for the beam directions found by the optimization of a geometric multi-objective cost function. An optimal dose distribution can easily be achieved using the geometric model. This is shown by comparing for the two cases the dose-volume histograms (DVH) of manually optimized plans by experienced planners and the DVHs of the geometrically found optimal solutions. In comparison to the manually optimized plans the solutions found by the geometric method significantly reduce the average dose in the OARs and NT, while maintaining the same PTV coverage. The optimization requires only a few seconds and could be used to improve the performance of inverse planning algorithms in radiotherapy for the determination of the optimal direction of beams.

TU‐D‐J‐6C‐08: Enhancing 4D PET Through Retrospective Stacking

Purpose: Four‐dimensional (4D) PET presents challenges distinct from 4D CT owing to radiotracer dose limitations. A single‐bed field‐of‐view (FOV) PET scan typically requires several minutes to acquire adequate data for reconstruction, necessarily spanning several respiratory cycles and smearing the radiotracer signal within a given lesion over an increased volume. Although prospective or retrospective gating captures the PETimage at a single point in the respiratory cycle, restricting the data to events within the gating interval increases the signal‐to‐noise ratio (SNR). We propose a method, coined “retrospective stacking” (RS), to combine the data from the entire respiratory cycle through deformable registration. In addition, we use the transformation maps to generate a 4D PET with statistics comparable to the single RS image.Method and Materials: A single FOV of a pancreatic cancer patient was acquired via the gated PET mode on a GE Discovery ST PET‐CT scanner. These gated images were registered using a mutual information / B‐splines registration algorithm, and superimposed. A 4D PET series spanning the full respiratory cycle was generated, and fused onto a 4D CT.Results: The SNR of the RS image showed an increase of 15% over a single gated reconstruction. Activity‐volume histograms of radiotracer activity surrounding the pancreatic lesion revealed that the ungated PET showed 33% greater tumor volume (using a 40%‐of‐maximum threshold) than the RS image. The reconstructed 4D PET fused well with the 4D CT, providing a clearer view of radiotracer distribution over the respiratory cycle than was possible using gated reconstructions.Conclusion: Retrospective stacking enabled better integration of temporally varying PET and CT series by reducing radiotracer smearing due to respiratory motion, while at the same time increasing the SNR beyond the poorer statistics inherent in gated PET acquisition. Noise‐reduced 4D PETimages could also be generated for fusion with 4D CT.1