Conceptual formulation on four-dimensional inverse planning for intensity modulated radiation therapy

Determining leaf trajectories for dynamic multileaf collimators with consideration of marker visibility: an algorithm study

The purpose of this study was to develop a leaf-setting algorithm for Dynamic Multileaf Collimator-Intensity-Modulated Radiation Therapy (DMLC-IMRT) for optimal marker visibility. Here, a leaf-setting algorithm (called a Delta algorithm) was developed with the objective of maximizing marker visibility so as to improve the tracking effectiveness of fiducial markers during treatment delivery. The initial leaf trajectories were generated using a typical leaf-setting algorithm, then the leaf trajectories were adjusted by Delta algorithm operations (analytical computations and a series of matrix calculations) to achieve the optimal solution. The performance of the Delta algorithm was evaluated with six test fields (with randomly generated intensity profiles) and 15 clinical fields from IMRT plans of three prostate cancer patients. Compared with the initial solution, the Delta algorithm kept the total delivered intensities (TDIs) constant (without increasing the beam delivery time), but improved marker visibility (the percentage ratio of marker visibility time to beam delivery time). For the artificial fields (with three markers), marker visibility increased from 68.00-72.00% for a small field (5 × 5), from 38.46-43.59% for a medium field (10 × 10), and from 28.57-37.14% for a large field (20 × 20). For the 15 clinical fields, marker visibility increased 6-30% for eight fields and > 50% for two fields but did not change for five fields. A Delta algorithm was proposed to maximize marker visibility for DMLC-IMRT without increasing beam delivery time, and this will provide theoretical fundamentals for future studies of 4D DMLC tracking radiotherapy.

Four-dimensional (4D) motion detection to correct respiratory effects in treatment response assessment using molecular imaging biomarkers

Observing early metabolic changes in positron emission tomography (PET) is an essential tool to assess treatment efficiency in radiotherapy. However, for thoracic regions, the use of three-dimensional (3D) PET imaging is unfeasible because the radiotracer activity is smeared by the respiratory motion and averaged during the imaging acquisition process. This motion-induced degradation is similar in magnitude with the treatment-induced changes, and the two occurrences become indiscernible. We present a customized temporal-spatial deformable registration method for quantifying respiratory motion in a four-dimensional (4D) PET dataset. Once the motion is quantified, a motion-corrected (MC) dataset is created by tracking voxels to eliminate breathing-induced changes in the 4D imaging scan. The 4D voxel-tracking data is then summed to yield a 3D MC-PET scan containing only treatment-induced changes. This proof of concept is exemplified on both phantom and clinical data, where the proposed algorithm tracked the trajectories of individual points through the 4D datasets reducing motion to less than 4 mm in all phases. This correction approach using deformable registration can discern motion blurring from treatment-induced changes in treatment response assessment using PET imaging.

Evaluation of dose prediction error and optimization convergence error in four-dimensional inverse planning of robotic stereotactic lung radiotherapy

Inverse optimization of robotic stereotactic lung radiotherapy is typically performed using relatively simple dose calculation algorithm on a single instance of breathing geometry. Variations of patient geometry and tissue density during respiration could reduce the dose accuracy of these 3D optimized plans. To quantify the potential benefits of direct four‐dimensional (4D) optimization in robotic lung radiosurgery, 4D optimizations using 1) ray‐tracing algorithm with equivalent path‐length heterogeneity correction (4EPLopt), and 2) Monte Carlo (MC) algorithm (4MCopt), were performed in 25 patients. The 4EPLopt plans were recalculated using MC algorithm (4MCrecal) to quantify the dose prediction errors (DPEs). Optimization convergence errors (OCEs) were evaluated by comparing the 4MCrecal and 4MCopt dose results. The results were analyzed by dose‐volume histogram indices for selected organs. Statistical equivalence tests were performed to determine the clinical significance of the DPEs and OCEs, compared with a 3% tolerance. Statistical equivalence tests indicated that the DPE and the OCE are significant predominately in GTV D98%. The DPEs in V20 of lung, and D2% of cord, trachea, and esophagus are within 1.2%, while the OCEs are within 10.4% in lung V20 and within 3.5% in trachea D2%. The marked DPE and OCE suggest that 4D MC optimization is important to improve the dosimetric accuracy in robotic‐based stereotactic body radiotherapy, despite the longer computation time.

PACS numbers: 87.53.Ly, 87.55.km

Robust principal component analysis-based four-dimensional computed tomography

The purpose of this paper for four-dimensional (4D) computed tomography (CT) is threefold. (1) A new spatiotemporal model is presented from the matrix perspective with the row dimension in space and the column dimension in time, namely the robust PCA (principal component analysis)-based 4D CT model. That is, instead of viewing the 4D object as a temporal collection of three-dimensional (3D) images and looking for local coherence in time or space independently, we perceive it as a mixture of low-rank matrix and sparse matrix to explore the maximum temporal coherence of the spatial structure among phases. Here the low-rank matrix corresponds to the 'background' or reference state, which is stationary over time or similar in structure; the sparse matrix stands for the 'motion' or time-varying component, e.g., heart motion in cardiac imaging, which is often either approximately sparse itself or can be sparsified in the proper basis. Besides 4D CT, this robust PCA-based 4D CT model should be applicable in other imaging problems for motion reduction or/and change detection with the least amount of data, such as multi-energy CT, cardiac MRI, and hyperspectral imaging. (2) A dynamic strategy for data acquisition, i.e. a temporally spiral scheme, is proposed that can potentially maintain similar reconstruction accuracy with far fewer projections of the data. The key point of this dynamic scheme is to reduce the total number of measurements, and hence the radiation dose, by acquiring complementary data in different phases while reducing redundant measurements of the common background structure. (3) An accurate, efficient, yet simple-to-implement algorithm based on the split Bregman method is developed for solving the model problem with sparse representation in tight frames.

Inverse planning for four-dimensional (4D) volumetric modulated arc therapy

PURPOSE

To develop a 4D volumetric modulated arc therapy (VMAT) inverse planning framework.

METHODS

4D VMAT inverse planning aims to derive an aperture and weight modulated arc therapy treatment plan that optimizes the accumulated dose distribution from all gantry angles and breathing phases. Under an assumption that the gantry rotation and patient breathing are synchronized (i.e., there is a functional relationship between the phase of the patient breathing cycle and the beam angle), the authors compute the contribution from different respiration phases through the registration of the phased CT images. The accumulative dose distribution is optimized by iteratively adjusting the aperture shape and weight of each beam through the minimization of the planning objective function. For comparison, traditional 3D VMAT plans are also performed for the two cases and the performance of the proposed technique is demonstrated.

RESULTS

A framework for 4D VMAT inverse planning has been proposed. With the consideration of the extra dimension of time in VMAT, a tighter target margin can be achieved with a full duty cycle, which is otherwise not achievable simultaneously by either 3D VMAT optimization or gated VMAT.

CONCLUSIONS

The 4D VMAT planning formulism proposed here provides useful insight on how the "time" dimension can be exploited in rotational arc therapy to maximally compensate for the intrafraction organ motion.