Optimization of equivalent uniform dose using the L-curve criterion

Equivalent uniform aerobic dose in radiotherapy for hypoxic tumors

Objective.Equivalent uniform aerobic dose (EUAD) is proposed for comparison of integrated cell survival in tumors with different distributions of hypoxia and radiation dose.Approach.The EUAD assumes that for any non-uniform distributions of radiation dose and oxygen enhancement ratio (OER) within a tumor, there is a uniform distribution of radiation dose under hypothetical aerobic conditions with OER = 1 that produces equal integrated survival of clonogenic cells. This definition of EUAD has several advantages. First, the EUAD allows one to compare survival of clonogenic cells in tumors with intra-tumor and inter-tumor variation of radio sensitivity due to hypoxia because the cell survival is recomputed under the same benchmark oxygen level (OER = 1). Second, the EUAD for homogeneously oxygenated tumors is equal to the concept of equivalent uniform dose.Main results. We computed the EUAD using radiotherapy dose and the OER derived from the18F-Fluoromisonidazole PET (18F-FMISO PET) images of hypoxia in patients with glioblastoma, the most common and aggressive type of primary malignant brain tumor. The18F-FMISO PET images include a distribution of SUV (Standardized Uptake Value); therefore, the SUV is converted to partial oxygen pressure (pO2) and then to the OER. The prognostic value of EUAD in radiotherapy for hypoxic tumors is demonstrated using correlation between EUAD and overall survival (OS) in radiotherapy for glioblastoma. The correction to the EUAD for the absolute hypoxic volume that traceable to the tumor control probability improves the correlation with OS.Significance. While the analysis proposed in this research is based on the18F-FMISO PET images for glioblastoma, the EUAD is a universal radiobiological concept and is not associated with any specific cancer or any specific PET or MRI biomarker of hypoxia. Therefore, this research can be generalized to other cancers, for example stage III lung cancer, and to other hypoxia biomarkers.

Search for IMRT inverse plans with piecewise constant fluence maps using compressed sensing techniques

An intensity-modulated radiation therapy (IMRT) field is composed of a series of segmented beams. It is practically important to reduce the number of segments while maintaining the conformality of the final dose distribution. In this article, the authors quantify the complexity of an IMRT fluence map by introducing the concept of sparsity of fluence maps and formulate the inverse planning problem into a framework of compressing sensing. In this approach, the treatment planning is modeled as a multiobjective optimization problem, with one objective on the dose performance and the other on the sparsity of the resultant fluence maps. A Pareto frontier is calculated, and the achieved dose distributions associated with the Pareto efficient points are evaluated using clinical acceptance criteria. The clinically acceptable dose distribution with the smallest number of segments is chosen as the final solution. The method is demonstrated in the application of fixed-gantry IMRT on a prostate patient. The result shows that the total number of segments is greatly reduced while a satisfactory dose distribution is still achieved. With the focus on the sparsity of the optimal solution, the proposed method is distinct from the existing beamlet- or segment-based optimization algorithms.

Interpretation of the dosimetric results of three uniformity regularization methods in terms of expected treatment outcome

In IMRT treatment plan optimization there are various methods that try to regularize the variation of dose nonuniformity using purely dosimetric measures. However, although these methods can help in finding a good dose distribution, they do not provide any information regarding the expected treatment outcome. When a treatment plan optimization is performed using biological measures, the final goal should be some indication about the expected tumor control or normal tissue complications, which is the primary goal of treatment planning (the association of treatment configurations and dose prescription with the treatment outcome). In this study, this issue is analyzed distinguishing the dose-oriented treatment plan optimization from the response-oriented optimization. Three different dose distributions were obtained by using a dose-based optimization technique, an EUD-based optimization without applying any technique for regularizing the nonuniformity of the dose distribution, and an EUD-based optimization using a variational regularization technique, which controls dose nonuniformity. The clinical effectiveness of the three dose distributions was investigated by calculating the response probabilities of the tumors and organs-at-risk (OARs) involved in two head and neck and prostate cancer cases. The radiobiological models used are the linear-quadratic-Poisson and the Relative Seriality models. Furthermore, the complication-free tumor control probability and the biologically effective uniform dose (D) were used for treatment plan evaluation and comparison. The radiobiological comparison shows that the EUD-based optimization using L-curve regularization gives better results than the EUD-based optimization without regularization and dose-based optimization in both clinical cases. Concluding, it appears that the applied dose nonuniformity regularization technique is expected to improve the effectiveness of the optimized IMRT dose distributions. However, more patient cases are needed to validate the statistical significance of the results and conclusions presented in this paper.

Time-dependent cell disintegration kinetics in lung tumors after irradiation

We study the time-dependent disintegration kinetics of tumor cells that did not survive radiotherapy treatment. To evaluate the cell disintegration rate after irradiation, we studied the volume changes of solitary lung tumors after stereotactic radiotherapy. The analysis is performed using two approximations: (1) tumor volume is a linear function of the total cell number in the tumor and (2) the cell disintegration rate is governed by the exponential decay with constant risk, which is defined by the initial cell number and a half-life T(1/2). The half-life T(1/2) is determined using the least-squares fit to the clinical data on lung tumor size variation with time after stereotactic radiotherapy. We show that the tumor volume variation after stereotactic radiotherapy of solitary lung tumors can be approximated by an exponential function. A small constant component in the volume variation does not change with time; however, this component may be the residual irregular density due to radiation fibrosis and was, therefore, subtracted from the total volume variation in our computations. Using computerized fitting of the exponent function to the clinical data for selected patients, we have determined that the average half-life T(1/2) of cell disintegration is 28.2 days for squamous cell carcinoma and 72.4 days for adenocarcinoma. This model is needed for simulating the tumor volume variation during radiotherapy, which may be important for time-dependent treatment planning of proton therapy that is sensitive to density variations.