C Yu

Erratum: “GPU-accelerated Monte Carlo convolution/superposition implementation” [].

The MCCS algorithm is the work of Dr. Naqvi et al. and should cite following paper at the beginning of the second-to-last paragraph: S. A. Naqvi, M. Earl, and D. Shepard, “Convolution/superposition using the Monte Carlo method,” Phys. Med. Biol. 48, 2101–2121 (2003). n nFigure 1(b) is reproduced with permission from Physics in Medicine and Biology. The derivation of the extrafocal source distribution function is described in S. A. Naqvi, M. Sarfaraz, T. Holmes, C. X. Yu, and X. A. Li, “Analyzing collimator structure effects in head-scatter calculations for IMRT class fields using scatter raytracing,” Phys. Med. Biol. 46, 2009–2028 (2001).

TU-C-BRB-12: Treatment Plan Validation through Graphical Fingerprint

Purpose: The treatment plan validation by the human is slow and error‐ prone due to the human limitation. We present a possible solution to improve the validation efficiency and quality by adopting graphical fingerprint. We aim to produce a digital fingerprint from various treatment plan parameters and present the fingerprint in a graphical format for easy recognition by human. Method and Materials: Since large amount information exists in the treatment plan, it is not realistic to ask the therapists to verify manually. We resort to use the hash function to generate a fingerprint for each copy of the plan. In this study, Message‐Digest algorithm 5 (MD5) is used mainly due to its relative short output (128bit). To make sure the difference can be readily recognized by human, we adopt the approach used in random art to produce an image (refereed as to graphical fingerprint) for each MD5 output. To ensure there is no result collision, we employed a result checking mechanism to ensure all images produced are valid. Results: 1000 MD5 stings are generated to produce the images we need. The 1000 images are randomly selected to form 20 groups, where each group contains 100 images. Each group is printed out on paper and visually inspected by human. It turns out all groups reach the same conclusion that they contains completely different images and none of the inspections exceeds 2 minutes. Conclusion: Wpresented a possible treatment plan validation approach through graphical fingerprint. It aims to address the human weakness during the manual validation. The approach allows fast recognition of errors by providing an graphical representation for the output of hash functions.

SU‐E‐I‐103: Tissue Dependent Deformation Field Regularization through Collapsed Cone Convolution/Superposition

Purpose Previous Tissue‐dependent deformation field filters incur a relatively high computation cost. We present a collapsed‐cone based adaptive filtering method to reduce the computational overhead. Our proposed method is able to reduce the computational complexity of the superposition process from O(q3N3) to O(MN3) time, where q is the chosen neighborhood size, N is the volume dimension and M is the number of kernel axes. Method and Materials Our proposed filter performs diffusion along chosen kernel axes instead of within a size‐limited cubic neighborhood. During the ray tracing process along the kernel axis, the contribution of a given voxel to its neighbors is exponentially attenuated to simulate the physical characteristics of tissues. During the attenuation, local biomedical information can be naturally incorporated by scaling the ray tracing length according to the underlying tissue stiffness. This scaling makes a voxel within soft tissues more “malleable” with respect to its neighbors movements. Results: We integrated different regularization methods into the same deformable registration approach (Demons algorithm). The kernel size of the Gaussian filter was set to be 5; the number of kernel directions for the CC filter were 4 in 2D and 16 in 3D. The experiments shows that our results produces are no‐worse result with a faster speed than these from other techniques. By investigating the finer details, the proposed method shows better capability of tracking changes. Conclusion Wpresented a collapsed‐cone (CC) based technique for the regularization of the deformation fields in image registration, which provides realistic deformation field and is useful for studying and modelingorgans in motion. Since the CC filter can cover the entire 3D volume of interest, a better maintenance of the overall object shapes can be achieved. The incorporation of tissue information allows the CC filter to adjust its behavior to match the tissue biomedical characteristics.

TH-C-201C-06: Optimal Registration Based on Connected Rubber Model

Purpose We present a new curve evolution model for registering step functions. The proposed model simulates the biological contraction and expansion behaviors of organs and is referred to as the connected rubber model (CRM). Our registration algorithm produces a guaranteed optimal solution in polynomial time.Method and Materials The new connected rubber model (CRM) we propose aims to simulate the contraction and expansion behaviors of organs. Given two step functions the target and source functions of registration to represent the changing boundary of an object our main idea is to deform the source function (i.e. each of its horizontal segments can extend or shrink) such that a best matching with the target function is obtained minimizing a given cost function. We adopt the dynamic programming paradigm to solve this step function registration problem. The derived algorithm is based on the analysis of the model behavior and properties of internal function and it can be theoretically proved to produce the optimal solution within the time complexity of Q (N2) . Results Our CRM algorithm has been applied to two scenarios to verify its effectiveness. The first one is the deformation field initialization for the image registration problem. The initial deformation field generated by CRM is able to reduce the computation time of Demons image registration algorithm by 20%∼40%. The second application is polygon registration where our result demonstrate a fully recovery of deformation complying with our assumption. Conclusion We develop a new registration model for step functions. The guaranteed optimal solution and fast algorithm running time make it an useful tool with great potential for object registration problems. An extension will be made in the future to also allow changes along the vertical direction.

TU‐C‐BRA‐11: Dose Calculation Accelerating: A Comparison Study of GPU and FPGA Based on Collapsed Cone Algorithm

Purpose To provide a fast and practical solution to the dose calculation problem, two implementations of the collapsed cone convolution/superposition (CCCS) algorithm based on different technologies: Graphics Processing Unit (GPU) and Field Programming Gate Array (FPGA), are developed and evaluated. Method and Materials GPU‐based approach and FPGA‐based approach have been two most favorable design choices for application acceleration. However, the answer to the question of which one is better is strongly dependent on the target application domain and the problems computation characteristics. To address this issue, we have implemented both approaches and evaluated them under the same metrics. Both solutions have been thoughoutly optimized to ensure the results reach the limit of hardware.Results Both implementations are compared with a commercial multi‐threaded implementation running on an Intel quad‐core computer with 2.4GHz frequency and 4GB memory. The performance data are collected for different phantom sizes and field sizes. Although the memory technology of the FPGA board is several generations behind the GPU, it still provides same level of speedup. For all test cases, the FPGA board showed a speedup in the range of 21.37–24.26X and the GPU solution (based on GTX260) demonstrates 12.90–16.33X speedup. Some other important design issues, such as cost, system specification, and design efforts are also compared. The anticipated speedups for both platforms are also provided based on the current technology. Conclusion Our results have shown that both implementations achieved significant speedup over a multi‐threaded software implementation on a Quad‐core system. Although FPGA still outperforms GPU in terms of performance, the merits of GPU such as low‐cost and off‐the‐shelf availability make it a preferred solution for many scenarios. Ultra‐high‐performance scenarios would prefer the FPGA solution as it provides a compact and powerful computation engine within a reasonable budget.

TH‐C‐350‐02: Is Dose Rate Variation Crucial for Single‐Arc Radiation Therapy Delivery?

Purpose: Recent arc therapy techniques such as arc‐modulated radiation therapy (AMRT) developed at the University of Maryland and Varians RapidArc™ allow variable segment‐weightings in order to expand the optimization domain. As a result, these plans may require a varying dose rate (DR) for delivery. To evaluate the necessity of DR variation in arc therapy delivery, the variable‐DR plans were translated in such a way that they can be delivered with a constant DR. Method and Materials: Four cases were selected for this study: 1 HN, 1 lung, 1 prostate and 1 brain. A single‐arc AMRT plan was generated for each case. Planning of AMRT started with optimization of ideal intensity maps with 36 equi‐spaced beams in Pinnacle followed by segmentation of the intensity maps into a deliverable AMRT MLC sequence. During leaf‐sequencing, the segment weightings are allowed to vary. In translating variable‐DR AMRT plans into constant‐DR plans, the angular spacing of the original beams were changed from equi‐spacing to spacing according to their weightings. Hence, apertures with more MUs occupy a greater angular range. To account for any field shifting in the process, a field shape correction was applied ensuring proper target coverage. Results and Conclusion: DVH comparisons show that constant‐DR plans were comparable to the corresponding variable‐DR plans in 3 of the 4 cases. Significant degradation occurred in the constant‐DR plan of the prostate case due to the large MU variations in the original variable‐DR plan, causing the beams to deviate significantly from their original positions. The estimated delivery times of the constant‐DR plans are 3 to 30 times longer than the variable‐DR plans due to large MLC shape variation within a small beam interval. It is hereby shown that DR variation is crucial to AMRT delivery in order to maintain excellent plan quality and efficient delivery time.

SU‐GG‐T‐92: Dynamic Leaf Sequencing with Monitor Units Control

Purpose: Our work is motivated by the following observations: (1) Due to MLC leaf transmission, continuous intensity patterns for IMRT cannot be identically reproduced; thus, an objective of dynamic leaf sequencing should be to minimize the error between the delivered and the ideal intensity patterns. (2) The popular sliding‐window algorithm always starts with all MLC leaf pairs closed; substantial reduction in beam‐on time is possible if delivery starts with an open field. This research aims to develop a dynamic leaf sequencing algorithm that produces plans with significantly less MUs while approximating the ideal intensity patterns with the minimum error. Method and Materials: Our new algorithm, called MUCDLS (Monitor Units Controlled Dynamic Leaf Sequencing), solves the following problem: Given an intensity pattern IM and an integer h, calculate the MLC leaf trajectories whose beam‐on time is h MUs and which approximate IM with the minimum error. The trajectories can start at any positions and end at any positions. In MUCDLS, the problem is modeled as a shortest path problem on directed acyclic graphs and solved efficiently. Comparing to the sliding‐window method, MUCDLS has several advantages: (1) It mathematically guarantees the optimality of the solutions; (2) it computes a trade‐off between the MUs and approximation error, offering the flexibility to choose a balanced plan; (3) it incorporates the MLC leaf transmission effect into the optimization.Results: We applied our MUCDLS algorithm to over 100 intensity patterns from 18 clinical cases. Comparisons showed MUCDLS can produce plans of the same quality as that of the sliding‐window plans but with 50–75% less MUs. Sequencing time of 5–10 seconds per intensity pattern was observed. Conclusion: A new dynamic leaf sequencing algorithm that produces plans with significantly less MUs while having the same quality as the sliding‐window algorithm is developed and verified.

SU‐GG‐T‐96: IMRT Leaf Sequencing with Intensity‐Based Segment Weight Optimization

Purpose: Dose distribution based segment weight optimization can significantly improve the quality of IMRT plans after leaf sequencing despite it is computationally very time‐consuming. This research aims to develop a leaf sequencing algorithm that has built‐in intensity‐based segment weight optimization with minimal additional running time. Method and Materials: The new algorithm is named LSWISW (for leaf sequencing with intensity‐based segment weight optimization). Its input includes: (1) (continuous) intensity patterns; (2) MLC leaf leakage ratio (typically ranges from 1% to 3%); either (3) the number of MLC segments, k, specified by the user or (4) an upper bound on the error between the computed intensity pattern and original ideal intensity pattern. If (3) is specified, a plan of k segments that best approximates the ideal intensity pattern is calculated. If (4) is specified, a plan of the minimum number of segments whose error is within the error bound is produced. In LSWISW, the leaf sequencing is modeled as a constrained shortest path problem and solved using dynamic programming; segment weight optimization is modeled and solved as a nonnegative least square optimization.Results: The performance of our leaf sequencing algorithm was tested on three treatment sites (head‐and‐neck, lung, and prostate). Our target delivery system is the Varian LINAC, whose MLC allows interdigitiation. In all the cases, our algorithm produces IMRT plans that rival those from Pinnacle planning system with afterward dose‐based segment weight optimization. Execution times of no more than 1 minute for our algorithm were observed on a laptop computer with a Pentium M Processor of 2.0 GHz. Conclusion: We presented an IMRT leaf sequencing algorithm with built‐in intensity‐based segment weight optimization. Compared with the leaf sequencing and dose‐based segment weight optimization modules from Pinnacle planning system, our new leaf sequencing algorithm is much more effective and efficient.

TH‐C‐AUD‐01: IMAT Leaf Sequencing Using Graph Algorithms

Purpose: To develop an effective and efficient leaf sequencing algorithm for intensity‐modulated arc therapy (IMAT). Methods: The input to our sequencing algorithm includes: (a) A set of (continuous) intensity patterns optimized by a treatment planning system for a sequence of equally spaced beam angles (10 degrees apart); (b) the IMAT maximum leaf motion constraint; (c) the number of arcs, k, that the user specifies based on the complexity of the problem. The output is a set of k treatment arcs that best approximates the set of input intensity patterns at all beam angles. The MLC shapes for each output arc are interconnected to guarantee a smooth delivery without violating the IMAT maximum leaf motion constraint. Our sequencing algorithm consists of two key steps. First, the intensity profiles aligned with each MLC leaf pair at all beam angles are converted into k MLC leaf openings using a k‐link shortest path algorithm, where k is the specified number of arcs for the delivery. The delivered photon flux using these leaf openings best approximates the desired intensity distribution. Second, the leaf openings are connected into k IMAT treatment arcs under the maximum leaf motion constraint using the minimum‐cost matching and shortest path algorithms. Results: The performance of our leaf sequencingsoftware has been tested for four treatment sites (prostate, breast, head‐and‐neck, and lung). In all cases, our leaf sequencing algorithm provides efficient and highly conformal IMAT plans that rival the counterpart tomotherapy plans and significantly improve the IMRT plans. Execution times of our software that range from a few seconds to 2 minutes are observed on a laptop computer equipped with a Pentium M Processor of 2.0 GHz. Conclusion: This research provided strong evidence that IMAT equipped with an effective leaf sequencing algorithm can provide a feasible and high quality implementation of IMRT.