Dan Ruan

Real-time prediction of respiratory motion based on local regression methods

Recent developments in modulation techniques enable conformal delivery of radiation doses to small, localized target volumes. One of the challenges in using these techniques is real-time tracking and predicting target motion, which is necessary to accommodate system latencies. For image-guided-radiotherapy systems, it is also desirable to minimize sampling rates to reduce imaging dose. This study focuses on predicting respiratory motion, which can significantly affect lung tumours. Predicting respiratory motion in real-time is challenging, due to the complexity of breathing patterns and the many sources of variability. We propose a prediction method based on local regression. There are three major ingredients of this approach: (1) forming an augmented state space to capture system dynamics, (2) local regression in the augmented space to train the predictor from previous observation data using semi-periodicity of respiratory motion, (3) local weighting adjustment to incorporate fading temporal correlations. To evaluate prediction accuracy, we computed the root mean square error between predicted tumor motion and its observed location for ten patients. For comparison, we also investigated commonly used predictive methods, namely linear prediction, neural networks and Kalman filtering to the same data. The proposed method reduced the prediction error for all imaging rates and latency lengths, particularly for long prediction lengths.

Inference of hysteretic respiratory tumor motion from external surrogates: a state augmentation approach

It is important to monitor tumor movement during radiotherapy. Respiration-induced motion affects tumors in the thorax and abdomen (in particular, those located in the lung region). For image-guided radiotherapy (IGRT) systems, it is desirable to minimize imaging dose, so external surrogates are used to infer the internal tumor motion between image acquisitions. This process relies on consistent correspondence between the external surrogate signal and the internal tumor motion. Respiratory hysteresis complicates the external/internal correspondence because two distinct tumor positions during different breathing phases can yield the same external observation. Previous attempts to resolve this ambiguity often subdivided the data into inhale/exhale stages and restricted the estimation to only one of these directions. In this study, we propose a new approach to infer the internal tumor motion from external surrogate signal using state augmentation. This method resolves the hysteresis ambiguity by incorporating higher-order system dynamics. It circumvents the segmentation of the internal/external trajectory into different phases, and estimates the inference map based on all the available external/internal correspondence pairs. Optimization of the state augmentation is investigated. This method generalizes naturally to adaptive on-line algorithms.

Mean position tracking of respiratory motion

Modeling and predicting tumor motion caused by respiration is challenging due to temporal variations in breathing patterns. Treatment approaches such as gating or adaptive bed adjustment/ alignment may not require full knowledge of instantaneous position, but might benefit from tracking the general trend of the motion. One simple method for tracking mean tumor position is to apply moving average filters with window sizes corresponding to the breathing periods. Yet respiratory motion is only semiperiodic, so such methods require reliable phase estimation, which is difficult in the presence of noise. This article describes a robust method to track the mean position of respiratory motion without explicitly estimating instantaneous phase. We form a state vector from the respiration signal values at the current instant and at a previous time, and fit an ellipse model to training data. Ellipse eccentricity and orientation potentially capture hysteresis in respiratory motion. Furthermore, we provide two recursive online algorithms for real time mean position tracking: a windowed version with an adaptive window size and another one with temporal discounting. We test the proposed method with simulated breathing traces, as well as with real time-displacement (RPM, Varian) signals. Estimation traces are compared with retrospectively generated moving average results to illustrate the performance of the proposed approach.

Exploring breathing pattern irregularity with projection-based method

Accurate descriptions of organ motion due to breathing are highly desirable for radiation treatment planning. This paper proposes an index that quantifies the irregularity of a signal related to respiratory motion. The method works by finding the periodic band-limited signal that best fits the signal samples, and then computing the root mean squared (RMS) residual error. The fitted signal itself may be useful for treatment planning. Using clinical data describing amplitude-time relationships (RPM, Varian) from twelve patients, we correlated the proposed index against relevant metrics from various treatment planning schemes. Simulation results demonstrate a reasonable match with all treatment methods considered, suggesting that the proposed irregularity index is suitable for a variety of treatment methods. Compared to the modified cosine function, which was investigated previously for breathing pattern models, the proposed approach is more representative, flexible, and computationally efficient.

Nonrigid Registration Using Regularization that Accomodates Local Tissue Rigidity

Regularized nonrigid medical image registration algorithms usually estimate the deformation by minimizing a cost function, consisting of a similarity measure and a penalty term that discourages unreasonable deformations. Conventional regularization methods enforce homogeneous smoothness properties of the deformation field; less work has been done to incorporate tissue-type-specific elasticity information. Yet ignoring the elasticity differences between tissue types can result in non-physical results, such as bone warping. Bone structures should move rigidly (locally), unlike the more elastic deformation of soft issues. Existing solutions for this problem either treat different regions of an image independently, which requires precise segmentation and incurs boundary issues; or use an empirical spatial varying filter to correct the deformation field, which requires the knowledge of a stiffness map and departs from the cost-function formulation. We propose a new approach to incorporate tissue rigidity information into the nonrigid registration problem, by developing a space variant regularization function that encourages the local Jacobian of the deformation to be a nearly orthogonal matrix in rigid image regions, while allowing more elastic deformations elsewhere. For the case of X-ray CT data, we use a simple monotonic increasing function of the CT numbers (in HU) as a rigidity index since bones typically have the highest CT numbers. Unlike segmentation-based methods, this approach is flexible enough to account for partial volume effects. Results using a B-spline deformation parameterization illustrate that the proposed approach improves registration accuracy in inhale-exhale CT scans with minimal computational penalty.

Discriminative sliding preserving regularization in medical image registration

Sliding effects often occur along tissue/organ boundaries. For instance, it is widely observed that the lung and diaphragm slide against the rib cage and the atria during breathing. Conventional homogeneous smooth registration methods fail to address this issue. Some recent studies preserve motion discontinuities by either using joint registration/segmentation or utilizing robust regularization energy on the motion field. However, allowing all types of discontinuities is not strict enough for physical deformations. In particular, flows that generate local vacuums or mass collisions should be discouraged by the energy functional. In this study, we propose a regularization energy that encodes a discriminative treatment of different types of motion discontinuities. The key idea is motivated by the Helmholtz-Hodge decomposition, and regards the underlying motion flow as a superposition of a solenoidal component, an irrotational component and a harmonic part. The proposed method applies a homogeneous penalty on the divergence, discouraging local volume change caused by the irrotational component, thus avoiding local vacuum or collision; it regularizes the curl field with a robust functional so that the resulting solenoidal component vanishes almost everywhere except on a singular set where the large shear values are preserved. This singularity set corresponds to sliding interfaces. Preliminary tests with both simulated and clinical data showed promising results.

TU‐C‐ValA‐04: Deformable Registration Using Regularization That Accommodates Local Tissue Rigidity

Purpose: Existing methods for deformable image registration typically use homogeneous regularization to encourage global smoothness. Less work has been done to incorporate voxel‐level tissue‐specific elasticity information. Ignoring differences in elasticity can, however, result in non‐physiological registrations, such as bone warping. We propose an approach to incorporate tissue rigidity information using a spatial variant regularization. Method and Materials: Regularized image registration algorithms estimate the deformation by minimizing a cost function, consisting of a dis‐similarity metric and regularization. To account for tissue‐type‐dependent rigidity information, we incorporate into the cost function a non‐rigidity penalty: an integral of stiffness index for local deformation weighted by spatial variant regularization factor depending on tissue type. For CT data, a simple monotonic increasing function of the CT number is used as a rigidity index for local tissue type. A necessary and sufficient condition for stiff local deformation is derived, and the local non‐stiffness is measured by the deviation of local Jacobian from orthnormality using the Frobenius norm. Tensor B‐Splines are used to parameterize the deformation field. A multi‐resolution scheme and gradient‐based approach are applied for optimization. Performance was accessed by registering 3D thorax CT‐images obtained from different breathing phases. Results: Experiments with clinical data demonstrate higher accuracy for inhale‐exhale thorax CT registration with the proposed approach. We observe comparable intensity match as the unregularized approaches, but more physiologically reasonable results with respect to different tissue types; in particular bone warping phenomena is eliminated in general. Conclusion: This work provides a way to incorporate tissue‐type‐dependent information into deformable registration framework with regularization design. Inference from image intensity avoids explicit segmentation, and is robust to partial volume effect. Our formulation based on local Jacobian and Frobenius norm provides analytical expression for the regularization and its derivative. More physiological results are achieved with minor computation expense. Supported by NIH P01‐CA59827.

TU‐C‐M100J‐08: Objective Characterization, Estimation and Prediction for Modeling Breathing‐Related Movement

Purpose: To propose a hierarchical model for estimation, tracking, and prediction of respiratory tumor motion. To incorporate modeling on different scales: semi‐reproducibility globally and slow frequency/displacement variation locally. Method and Materials: The problem is formulated with a hierarchy of scales: On the finer scale, a databased approach is used to estimate the local variation of both displacement and frequency, utilizing classic control and chaostheory. A warping procedure is used to “counteract” local variation, resulting in a much more regular post‐warping signal. On the global level, the post‐warping (phase‐synchronized) signal is modeled as a noisy observation of an intrinsic periodic system, and the best periodic pattern is estimated within a nonparametric optimization setting. For tracking and prediction purposes, the locally estimated warping map (together with proper interpolation or extrapolation, whichever applies) is used to un‐warp the globally obtained periodic pattern. A recursive method is devised to further improve the efficiency for real‐time processing. Results: The obtained estimation/prediction signal demonstrates similar local variation as the raw observation, while semi‐periodicity is incorporated to decrease its noise sensitivity and enhance prediction accuracy. Verification using RPM data shows that the proposed method reduces 1‐period look‐ahead prediction error (RMSE) by more than 50% compared to perfect periodic modeling. Conventional local linear models generally fail in such long‐term prediction tasks. Conclusions: This work provides an infrastructure for incorporating information on different knowledge levels, and offers the flexibility to adaptively balance the roles of physical prior knowledge and data fidelity. The model‐based method on the global level incorporates the well‐recognized semi‐periodicity pattern of respiratory motion, overcoming the myopia of local state models. Data‐driven local phase map estimation used in warping and un‐warping fully utilizes the observation and enjoys the freedom of nonparametric setup. This work is sponsored by NIH P01‐CA59827.

SU‐E‐T‐608: Integrated Beam Orientation and Fluence Map Optimization in Radiation Therapy Treatment Planning

PURPOSEnTo efficiently select high-quality coplanar or non-coplanar beam orientations for IMRT treatments while formally and explicitly incorporating the effect of the selected beam orientations on the quality of the dose distribution obtained by the treatment plan optimization model.nnnMETHODSnBeam orientation models consider a discrete set of potential coplanar and/or non-coplanar beam locations around the patient. A new greedy algorithm is proposed to solve a model that integrates beam orientation optimization (BOO) and fluence map optimization (FMO). The algorithm iteratively adds beams to a FMO model. In each iteration, an attractiveness measure is associated with each remaining candidate beam orientation. This attractiveness measure is based explicitly on an optimal dose distribution that allows only the currently selected set of beams to be used. Several alternate attractiveness measures are considered which use either first-order information or both first and second-order information. Performance of the algorithm was assessed on a clinical lung cancer case.nnnRESULTSnThe developed beam selection algorithm was applied to a lung cancer case using either coplanar beams or both coplanar and non-coplanar beams. In the coplanar case, beam orientations were found that produce a superior dose distribution to that using an equal number of equi-spaced beams. In the non-coplanar case it was found that fewer beams were needed to produce a dose distribution of comparable quality to that found in the coplanar case.nnnCONCLUSIONSnThe developed solution approach showcases the potential benefits of integrating different steps in the treatment plan optimization process. By integrating the BOO and FMO models, treatment plan quality was explicitly incorporated into the beam selection process. BOO can be automated and implemented efficiently, which eliminates the guesswork involved in manually adjusting beam orientations in IMRT treatment planning.

SU‐D‐211‐02: A Framework for 4pi Radiotherapy

PURPOSEnInclusion of highly non-coplanar treatment angles increases radiations dose conformality and critical organ sparing. However, implementation of this treatment strategy has been hampered by inaccurate solution space modeling, limited automated beam selection methods, the lack of efficient beam sequencing program and integrated collision prevention. The aim is to develop a 4pi radiotherapy paradigm that takes full advantage of modern computer-controlled robotic C-arm linear accelerators.nnnMETHODSnThe beam geometry solution space was modeled by 3D surface scanning of the couch, gantry and patient. In order to utilize the entire solution space and optimize MLC resolution, variable source-to-tumor distances were introduced. Conformai radiation doses were computed using convolution/superposition from uniformly distributed solid angles. Beam orientation optimization was performed using a column generation and pricing approach, which was also used to optimize beam fluence intensity modulation. A level set method was then employed to automatically sequence beams so the treatment time and couch motion can be minimized while avoiding collision on the path.nnnRESULTSnThe machine and patient surface was accurately measured and a cocoon shaped solution space was created with an integrated gap buffer of 4 cm. 14 conformai beams were typically selected to maximize target dose coverage and minimize critical organ doses. Compared with manual non-coplanar and coplanar volumetric modulated arc therapy plans, an average 20% improvement was observed in high dose spillage, defined as the 50% isodose volume divided by the target volume, in a wide range of clinical cases including brain, lung, liver and partial breast cancer.nnnCONCLUSIONSnWe have established a framework that overcomes major technical difficulties associated with automated planning and delivery of highly non-coplanar treatment on the widely available C-arm linacs. Compared with coplanar volumetric modulated arc therapy plans, 4pi plans improve nearly all aspects of the dosimetry while remain highly deliverable.