Accelerated Multi-Criterial Optimization in Radiation Therapy using Voxel-Wise Dose Prediction


Wu, Q. Jackie

Jensen, Patrick James





Medical Physics


In external beam radiation therapy (EBRT) for cancer patients, it is highly desirable to completely eradicate the cancerous cells for the purpose of improving the patient’s quality of life and increasing the patient’s likelihood of survival. However, there can be significant side effects when large regions of healthy cells are irradiated during EBRT, particularly for organs-at-risk (OARs). Due to the juxtaposition of the cancerous and non-cancerous tissue, trade-offs need to be made between target coverage and OAR sparing during treatment planning. For this reason, the treatment planning process can be posed as a multi-criterial optimization (MCO) problem, which has previously been studied extensively with several exact solutions existing specifically for radiation therapy. Typical MCO implementations for EBRT involve creating, optimizing, and calculating many treatment plans to infer the set of feasible best radiation doses, or the Pareto surface. However, each optimization and calculation can take 10-30 minutes per plan. As a result, generating enough plans to attain an accurate representation of the Pareto surface can be very time-consuming, particularly in higher-dimensions with many possible trade-offs.

The purpose of this study is to streamline the MCO workflow by using a machine-learning model to quickly predict the Pareto surface plan doses, rather than exactly computing them. The primary focus of this study focuses on the development and analysis of the dose prediction model. The secondary focus of this study is to develop new metrics for analyzing the similarity between different Pareto surface interpolations. The tertiary focus of this study is to investigate the feasibility of deliberately irradiating the epidural space in spine stereotactic radiosurgery (SRS), as well as estimate its potential effect on preventing tumor recurrence.

For the primary focus of this study, the model’s architecture proceeds as follows. The model begins by creating an initial dose distribution via an inverse fit of inter-slice and intra-slice PTV distance maps on a voxel-wise basis. The model proceeds by extracting three sets of transverse patches from all structure maps and the initialized dose map at each voxel. The model then uses the patch vectors as inputs for a neural network which updates and refines the dose initialization to achieve a final dose prediction. The primary motivation behind our model is to use our understanding of the general shape of dose distributions to remove much of the nonlinearity of the dose prediction problem, decreasing the difficulty of subsequent network predictions. Our model is able to take the optimization priorities into account during dose prediction and infer feasible dose distributions across a range of optimization priority combinations, allowing for indirect Pareto surface inference.

The model’s performance was analyzed on conventional prostate volumetric modulated arc therapy (VMAT), pancreas stereotactic body radiation therapy (SBRT), and spine stereotactic radiosurgery (SRS) with epidural space irradiation. For each of these treatment paradigms, the Pareto surfaces of many patients were thoroughly sampled to train and test the model. On all of these cases, our model achieved good performance in terms of speed and accuracy. Overfitting was shown to be minimal in all cases, and dose distribution slices and dose-volume histograms (DVHs) were shown for comparison, confirming the proficiency of our model. This model is relatively fast (0.05-0.20 seconds per plan), and it is capable of sampling the entire Pareto surface much faster than commercial dose optimization and calculation engines.

While these results were generally promising, the model achieved lower error on the prostate VMAT treatment plans compared to the pancreas SBRT and spine SRS treatment plans. This is likely due to the existence of heavier beam streaks in the stereotactic treatment plans which are generated by a sharper control of the delivered dose distribution. However, the Pareto surface errors were similar across all three cases, so these dose distribution errors did not propagate to the Pareto objective space.

The secondary focus of this study is the development and analysis of Pareto surface similarity metrics. The dose prediction model can be used to rapidly estimate many Pareto-optimal plans for quick Pareto surface inference. This could allow for a potentially significant increase in the speed at which Pareto surfaces are inferenced to provide treatment planning assistance and acceleration. However, previous investigations into Pareto surface analysis typically do not compare a ground truth Pareto surface with a Pareto surface prediction. Therefore, there is a need to develop a Pareto surface metric in order to evaluate the ability of the model to generate accurate Pareto surfaces in addition to accurate dose distributions.

To address these needs, we developed four Pareto surface similarity metrics, emphasizing the ability to represent distances between the interpolations rather than the sampled points. The most straightforward metric is the root-mean-square error (RMSE) evaluated between matched, sampled points on the Pareto surfaces, augmented by intra-simplex upsampling of the barycentric dimensions of each simplex. The second metric is the Hausdorff distance, which evaluates the maximum closest distance between the sets of sampled points. The third metric is the average projected distance (APD), which evaluates the displacements between the sampled points and evaluates their projections along the mean displacement. The fourth metric is the average nearest-point distance (ANPD), which numerically integrates point-to-simplex distances over the upsampled simplices of the Pareto surfaces. These metrics are compared by their convergence rates as a function of intra-simplex upsampling, the calculation times required to achieve convergence, and their qualitative meaningfulness in representing the underlying interpolated surfaces. For testing, several simplex pairs were constructed abstractly, and Pareto surfaces were constructed using inverse optimization and our dose prediction model applied to conventional prostate VMAT, pancreas SBRT, and spine SRS with epidural irradiation.

For the abstract simplex pairs, convergence within 1% was typically achieved at approximately 50 and 100 samples per barycentric dimension for the ANPD and the RMSE, respectively. The RMSE and the ANPD required approximately 50 milliseconds and 3 seconds to calculate to these sampling rates, respectively, while the APD and HD required much less than 1 millisecond. Additionally, the APD values closely resembled the ANPD limits, while the RMSE limits and HD tended to be more different. The ANPD is likely more meaningful than the RMSE and APD, as the ANPD’s point-to-simplex distance functions more closely represent the dissimilarity between the underlying interpolated surfaces rather than the sampling points on the surfaces. However, in situations requiring high-speed evaluations, the APD may be more desirable due to its speed, lack of subjective specification of intra-simplex upsampling rates, and similarity to the ANPD limits.

The tertiary focus of this study is the analysis of the feasibility of epidural space irradiation in spine SRS. The epidural space is a frequent site of cancer recurrence after spine SRS. This may be due to microscopic disease in the epidural space which is under-dosed to obey strict spinal cord dose constraints. We hypothesized that the epidural space could be purposefully irradiated to prescription dose levels, potentially reducing the risk of recurrence in the epidural space without increasing toxicity. To address this, we sought to analyze the feasibility of irradiating the epidural space in spine SRS. Analyzing the data associated with this study is synergistic to our MCO acceleration study, since the range of trade-offs between epidural space irradiation and spinal cord sparing represents an MCO problem which our dose prediction model may quickly solve.

Spine SRS clinical treatment plans with associated spinal PTV (PTVspine) and spinal cord contours, and prior delivered dose distributions were identified retrospectively. An epidural space PTV (PTVepidural) was contoured to avoid the spinal cord and focus on regions near the PTVspine. Clinical plan constraints included PTVspine constraints (D95% = 1800 cGy, D5% < 1950 cGy) and spinal cord constraints (Dmax < 1300 cGy, D10% < 1000 cGy). Prior clinical plan doses were mapped onto the new PTVepidural contour for analysis. Plans were copied and revised to additionally target the PTVepidural, optimizing PTVepidural D95% after meeting clinical plan constraints. Tumor control probabilities (TCPs) were estimated for the PTVepidural using a radiobiological linear-quadratic model of cell survival for both clinical and revised plans. Clinical and revised plans were compared according to their PTVepidural DVH distributions, D95% distributions, and TCPs.

Seventeen SSRS plans were identified and included in this study. Revised plan DVHs demonstrated higher doses to the epidural low-dose regions, with D95% improving from 10.96 Gy ± 1.76 Gy to 16.84 Gy ± 0.87 Gy (p < 10-5). Our TCP modeling set the clinical plan TCP average to 85%, while revised plan TCPs were all greater than 99.99%. Therefore, irradiating the epidural space in spine SRS is likely feasible, and purposefully targeting the epidural space in SSRS should increase control in the epidural space without significantly increasing the risk of spinal cord toxicity.



Nuclear physics and radiation


Artificial Intelligence


Multi-Criterial Optimization


Radiation Therapy


Stereotactic Radiosurgery


Volumetric Modulated Arc Therapy


Accelerated Multi-Criterial Optimization in Radiation Therapy using Voxel-Wise Dose Prediction






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