Xin Dou

The matrix orthogonal decomposition problem in intensity-modulated radiation therapy

In this paper, we study an interesting matrix decomposition problem that seeks to decompose a “complicated” matrix into two “simpler” matrices while minimizing the sum of the horizontal complexity of the first sub-matrix and the vertical complexity of the second sub-matrix. The matrix decomposition problem is crucial for improving the “step-and-shoot” delivery efficiency in Intensity-Modulated Radiation Therapy, which aims to deliver a highly conformal radiation dose to a target tumor while sparing the surrounding normal tissues. Our algorithm is based on a non-trivial graph construction scheme, which enables us to formulate the decomposition problem as computing a minimum s-t cut in a 3-D geometric multi-pillar graph. Experiments on randomly generated intensity map matrices and on clinical data demonstrated the efficiency of our algorithm.

Optimal field-splitting algorithm in intensity-modulated radiotherapy: Evaluations using head-and-neck and female pelvic IMRT cases

To develop an optimal field-splitting algorithm of minimal complexity and verify the algorithm using head-and-neck (H&N) and female pelvic intensity-modulated radiotherapy (IMRT) cases. An optimal field-splitting algorithm was developed in which a large intensity map (IM) was split into multiple sub-IMs (≥2). The algorithm reduced the total complexity by minimizing the monitor units (MU) delivered and segment number of each sub-IM. The algorithm was verified through comparison studies with the algorithm as used in a commercial treatment planning system. Seven IMRT, H&N, and female pelvic cancer cases (54 IMs) were analyzed by MU, segment numbers, and dose distributions. The optimal field-splitting algorithm was found to reduce both total MU and the total number of segments. We found on average a 7.9 ± 11.8% and 9.6 ± 18.2% reduction in MU and segment numbers for H&N IMRT cases with an 11.9 ± 17.4% and 11.1 ± 13.7% reduction for female pelvic cases. The overall percent (absolute) reduction in the numbers of MU and segments were found to be on average -9.7 ± 14.6% (-15 ± 25 MU) and -10.3 ± 16.3% (-3 ± 5), respectively. In addition, all dose distributions from the optimal field-splitting method showed improved dose distributions. The optimal field-splitting algorithm shows considerable improvements in both total MU and total segment number. The algorithm is expected to be beneficial for the radiotherapy treatment of large-field IMRT.

TH‐C‐201C‐03: Tumor Segmentation in CT Images Using Globally Optimal Single Surface Detection

Introduction The problem of accurate and reproducible tumor definition is essential for radiation therapy in treatment planning as well as for volumetric assessment of tumor response to therapy. To improve the quality and reproducibility of the tumor definition as well as to accelerate the workflow of the oncologist and radiologist novel automated segmentation tools are needed. Nodule and lesion segmentation remain challenging and are not yet solved satisfactorily. Method and Material Our tumor segmentation algorithm is based on a single surface detection algorithm using regional properties. To use this method for tumor segmentation we created a framework which requires a small amount of user input that is then followed by an ellipsoidal transform on the data. The framework then uses the single surface detection method optimizing the intra‐class variance. The surface detection method utilizes the techniques of shape probing graph search and parametric maximum‐flow. Our algorithm was tested for the segmentation of livertumors from 15 CTimagedata sets and lungtumors from 18 CTimagedata sets.Surface positioning error and volume measures compared with expert‐traced results were computed. Results Our segmentation method demonstrated low surface positioning errors and robust performance compared with the expert‐traced results. The average signed and unsigned positioning errors for liver lesions were −0.07±0.31 and 0.77±0.16 voxels. For lungtumors the average signed and unsigned positioning errors were −0.03±0.10 and 0.78±0.13 voxels. Volume measures also showed accurate and robust correlation with expert‐traced results with 90% of acceptable percentage in terms of volume overlap. Conclusion We have implemented a novel single surface detection method that minimizes the intra‐class variance and provided a framework for tumor segmentation. Experiments on liver lesions and lungtumors show good applicability with sub‐voxel accuracy achieved for both cases.

MO‐EE‐A1‐04: A Comparison Study of a New Optimal Field Splitting Algorithm in IMRT

Introduction In IMRTtreatment planning, multi‐leaf collimator(MLC) with a maximum leaf spread constraint is used to deliver the prescribed intensity maps (IMs). However, the maximum leaf spread of an MLC may require splitting a large IM into several overlapping sub‐IMs that are each delivered separately. Existing approaches usually require fixed sizes of sub‐IMs. We developed a method producing sub‐IMs of flexible sizes subject to the maximum leaf spread, which may improve the delivery efficiency. In this work, we propose to optimally split an IM into sub‐IMs while minimizing the total complexity of the sub‐IMs. Method and Material The complexity measure of an intensity map we use is the total sum of positive gradients of all rows. We solve the optimal field splitting problem using dynamic programming. Our algorithm also balances minimum beam‐on times of the resulting sub‐IMs. We evaluated the performance of our algorithm by implementing it on clinical IMs obtained from the Department of Radiation Oncology, University of Iowa and comparing it to ommercial software derived solutions. 14 IMs from pelvic treatment plans on 2 patients were used for splitting resulting in 3 sub‐IMs (3‐splitting) algorithm experiments and 20 IMs from head & neck treatment plans from 3 patients were used for 2‐splitting algorithm experiments. We replaced the field splitting method in Pinnacle with our method and the results were compared. Results For 3‐splitting cases, the number of segments was reduced by 12.5%, and the number of MUs was improved by 30.0%, along with 144‐sec reduction of beam delivery time per fraction. For 2‐splitting, the number of segments was reduced by 5.3%, and the number of MUs was improved by 27.6%. The performance for 3‐splitting cases was better than for 2‐splitting. Conclusion We have developed an optimal field splitting method which appears to outperform the commercial software Pinnacle.

SU‐GG‐I‐94: Analysis of Breathing Pattern for Radiotherapy by Studying Diaphragm Trajectory

Purpose: Understanding breathing patterns would help in designing a patient‐specific treatment plan. This work pursues a robust means finding individual breathing patterns by studying diaphragm motion. To our best knowledge, no previous work utilized an automated 4‐D image segmentation technique for analyzing diaphragm motion. Method and Materials: In this study we intend to accurately segment the diaphragm from 4‐D image datasets to analyze breathing patterns. The core of the problem is to develop an effective 4‐D surface segmentation method for diaphragm. We developed a novel 4‐D optimal surface detection method capable of simultaneously detecting diaphragm over the entire respiration cycle. The optimality is controlled by cost functions designed for surfaces and by several geometric constraints defining the surface smoothness and position changes between phases. The problem is solved by transforming it into computing a minimum s‐t cut in a derived arc‐weighted directed graph. Gradient Vector Flow (GVF) is incorporated into cost function design to allow flexible initialization of the diaphragm surface and to encourage convergence to boundary concavities. A pre‐segmentation of the diaphragm in one phase is used as initial surfaces for all other phases. We implemented our algorithm and experimented on 7 sets of 4‐D chest/abdomen CTimages. Dome point of the diaphragm in the first phase is found and those in the remaining phases within a neighborhood are detected to generate the diaphragm trajectory. Results: Our method converges quickly and yields highly accurate contouring results by visual examination. The diaphragm trajectory over the breathing cycle can then be computed from the segmentation result. Conclusion: We developed a novel 4‐D surface segmentation method for accurate detection of diaphragm over the entire respiration cycle from 4‐D CTimage data. The breathing pattern can then be analyzed from the motion of diaphragm. The method helps in developing patient‐specific treatment plan.

SU‐GG‐T‐100: Optimal Field Splitting in IMRT

Purpose: Today one of the most advanced tools for delivering intensity maps in IMRT is the multileaf collimator(MLC), which is subject to a maximum leaf spread. Due to this constraint, a large field needs to be split into several sub‐fields each being delivered separately. Different from previous approaches in which the size of the sub‐fields is fixed, our method produces sub‐fields of flexible sizes subject to the maximum leaf spread constraint, which may potentially improve the delivery efficiency. In this work, we propose to optimally split an intensity map into sub‐fields while minimizing the total complexity of the sub‐fields. Method and Materials: The optimal field splitting problem is solved efficiently by using dynamic programming with an observation that the problem expresses the optimal substructure. To evaluate the performance of our method, we implemented our algorithm and experimented on 2000 randomly generated intensity maps with various field sizes and maximum intensity levels, and 21 sets of clinical intensity maps obtained from the Department of Radiation Oncology of the University of Iowa. Our results are compared with theoretical optimal lower bounds and those from the Pinnacle system. Results: Phantom experiment results showed that for all tested cases with various field sizes and intensity levels, our method yielded results close to the optimal bounds. For the clinical data, out of 21 intensity maps, both our method and Pinnacle system got optimal results in 14. For the 7 with room for improvement, our method outperformed Pinnacle in 3 cases and equally performed on the remaining 4 cases. Conclusion: We developed an optimal field splitting method literally with no constraint on the sub‐fields, which is proved to outperform current commercial software.