A comparison of Monte Carlo dropout and bootstrap aggregation on the performance and uncertainty estimation in radiation therapy dose prediction with deep learning neural networks.

Recently, artificial intelligence technologies and algorithms have become a major focus for advancements in treatment planning for radiation therapy. As these are starting to become incorporated into the clinical workflow, a major concern from clinicians is not whether the model is accurate, but whether the model can express to a human operator when it does not know if its answer is correct. We propose to use Monte Carlo Dropout (MCDO) and the bootstrap aggregation (bagging) technique on deep learning (DL) models to produce uncertainty estimations for radiation therapy dose prediction. We show that both models are capable of generating a reasonable uncertainty map, and, with our proposed scaling technique, creating interpretable uncertainties and bounds on the prediction and any relevant metrics. Performance-wise, bagging provides statistically significant reduced loss value and errors in most of the metrics investigated in this study. The addition of bagging was able to further reduce errors by another 0.34% for [Formula: see text] and 0.19% for [Formula: see text] on average, when compared to the baseline model. Overall, the bagging framework provided significantly lower mean absolute error (MAE) of 2.62, as opposed to the baseline model's MAE of 2.87. The usefulness of bagging, from solely a performance standpoint, does highly depend on the problem and the acceptable predictive error, and its high upfront computational cost during training should be factored in to deciding whether it is advantageous to use it. In terms of deployment with uncertainty estimations turned on, both methods offer the same performance time of about 12 s. As an ensemble-based metaheuristic, bagging can be used with existing machine learning architectures to improve stability and performance, and MCDO can be applied to any DL models that have dropout as part of their architecture.

A reinforcement learning application of a guided Monte Carlo Tree Search algorithm for beam orientation selection in radiation therapy.

Current beam orientation optimization algorithms for radiotherapy, such as column generation (CG), are typically heuristic or greedy in nature because of the size of the combinatorial problem, which leads to suboptimal solutions. We propose a reinforcement learning strategy using Monte Carlo Tree Search that can find a better beam orientation set in less time than CG. We utilize a reinforcement learning structure involving a supervised learning network to guide the Monte Carlo Tree Search and to explore the decision space of beam orientation selection problems. We previously trained a deep neural network (DNN) that takes in the patient anatomy, organ weights, and current beams, then approximates beam fitness values to indicate the next best beam to add. Here, we use this DNN to probabilistically guide the traversal of the branches of the Monte Carlo decision tree to add a new beam to the plan. To assess the feasibility of the algorithm, we used a test set of 13 prostate cancer patients, distinct from the 57 patients originally used to train and validate the DNN, to solve for 5-beam plans. To show the strength of the guided Monte Carlo tree search (GTS) compared to other search methods, we also provided the performances of guided search, uniform tree search and random search algorithms. On average, GTS outperformed all other methods. It found a better solution than CG in 237 seconds on average, compared to 360 seconds for CG, and outperformed all other methods in finding a solution with a lower objective function value in less than 1000 seconds. Using our guided tree search (GTS) method, we could maintain planning target volume (PTV) coverage within 1% error similar to CG, while reducing the organ-at-risk (OAR) mean dose for body, rectum, left and right femoral heads; mean dose to bladder was 1% higher with GTS than with CG.

Using deep learning to predict beam-tunable Pareto optimal dose distribution for intensity-modulated radiation therapy.

PURPOSE: Many researchers have developed deep learning models for predicting clinical dose distributions and Pareto optimal dose distributions. Models for predicting Pareto optimal dose distributions have generated optimal plans in real time using anatomical structures and static beam orientations. However, Pareto optimal dose prediction for intensity-modulated radiation therapy (IMRT) prostate planning with variable beam numbers and orientations has not yet been investigated. We propose to develop a deep learning model that can predict Pareto optimal dose distributions by using any given set of beam angles, along with patient anatomy, as input to train the deep neural networks. We implement and compare two deep learning networks that predict with two different beam configuration modalities. METHODS: We generated Pareto optimal plans for 70 patients with prostate cancer. We used fluence map optimization to generate 500 IMRT plans that sampled the Pareto surface for each patient, for a total of 35 000 plans. We studied and compared two different models, Models I and II. Although they both used the same anatomical structures - including the planning target volume (PTV), organs at risk (OARs), and body - these models were designed with two different methods for representing beam angles. Model I directly uses beam angles as a second input to the network as a binary vector. Model II converts the beam angles into beam doses that are conformal to the PTV. We divided the 70 patients into 54 training, 6 validation, and 10 testing patients, thus yielding 27 000 training, 3000 validation, and 5000 testing plans. Mean square loss (MSE) was taken as the loss function. We used the Adam optimizer with a default learning rate of 0.01 to optimize the network's performance. We evaluated the models' performance by comparing their predicted dose distributions with the ground truth (Pareto optimal) dose distribution, in terms of dose volume histogram (DVH) plots and evaluation metrics such as PTV D98 , D95 , D50 , D2 , Dmax , Dmean , Paddick Conformation Number, R50, and Homogeneity index. RESULTS: Our deep learning models predicted voxel-level dose distributions that precisely matched the ground truth dose distributions. The DVHs generated also precisely matched the ground truth. Evaluation metrics such as PTV statistics, dose conformity, dose spillage (R50), and homogeneity index also confirmed the accuracy of PTV curves on the DVH. Quantitatively, Model I's prediction error of 0.043 (confirmation), 0.043 (homogeneity), 0.327 (R50), 2.80% (D95), 3.90% (D98), 0.6% (D50), and 1.10% (D2) was lower than that of Model II, which obtained 0.076 (confirmation), 0.058 (homogeneity), 0.626 (R50), 7.10% (D95), 6.50% (D98), 8.40% (D50), and 6.30% (D2). Model I also outperformed Model II in terms of the mean dose error and the max dose error on the PTV, bladder, rectum, left femoral head, and right femoral head. CONCLUSIONS: Treatment planners who use our models will be able to use deep learning to control the trade-offs between the PTV and OAR weights, as well as the beam number and configurations in real time. Our dose prediction methods provide a stepping stone to building automatic IMRT treatment planning.

Diffusion Entropy vs. Multiscale and Rényi Entropy to Detect Progression of Autonomic Neuropathy.

We review the literature to argue the importance of the occurrence of crucial events in the dynamics of physiological processes. Crucial events are interpreted as short time intervals of turbulence, and the time distance between two consecutive crucial events is a waiting time distribution density with an inverse power law (IPL) index µ, with µ < 3 generating non-stationary behavior. The non-stationary condition is characterized by two regimes of the IPL index: (a) perennial non-stationarity, with 1 < µ < 2 and (b) slow evolution toward the stationary regime, with 2 < µ < 3. Human heartbeats and brain dynamics belong to the latter regime, with healthy physiological processes tending to be closer to the border with the perennial non-stationary regime with µ = 2. The complexity of cognitive tasks is associated with the mental effort required to address a difficult task, which leads to an increase of µ with increasing task difficulty. On this basis we explore the conjecture that disease evolution leads the IPL index µ moving from the healthy condition µ = 2 toward the border with Gaussian statistics with µ = 3, as the disease progresses. Examining heart rate time series of patients affected by diabetes-induced autonomic neuropathy of varying severity, we find that the progression of cardiac autonomic neuropathy (CAN) indeed shifts µ from the border with perennial variability, µ = 2, to the border with Gaussian statistics, µ = 3 and provides a novel, sensitive index for assessing disease progression. We find that at the Gaussian border, the dynamical complexity of crucial events is replaced by Gaussian fluctuation with long-time memory.

Incorporating human and learned domain knowledge into training deep neural networks: A differentiable dose-volume histogram and adversarial inspired framework for generating Pareto optimal dose distributions in radiation therapy.

PURPOSE: We propose a novel domain-specific loss, which is a differentiable loss function based on the dose-volume histogram (DVH), and combine it with an adversarial loss for the training of deep neural networks. In this study, we trained a neural network for generating Pareto optimal dose distributions, and evaluate the effects of the domain-specific loss on the model performance. METHODS: In this study, three loss functions - mean squared error (MSE) loss, DVH loss, and adversarial (ADV) loss - were used to train and compare four instances of the neural network model: (a) MSE, (b) MSE + ADV, (c) MSE + DVH, and (d) MSE + DVH+ADV. The data for 70 prostate patients, including the planning target volume (PTV), and the organs at risk (OAR) were acquired as 96 × 96 × 24 dimension arrays at 5 mm3 voxel size. The dose influence arrays were calculated for 70 prostate patients, using a 7 equidistant coplanar beam setup. Using a scalarized multicriteria optimization for intensity-modulated radiation therapy, 1200 Pareto surface plans per patient were generated by pseudo-randomizing the PTV and OAR tradeoff weights. With 70 patients, the total number of plans generated was 84 000 plans. We divided the data into 54 training, 6 validation, and 10 testing patients. Each model was trained for a total of 100,000 iterations, with a batch size of 2. All models used the Adam optimizer, with a learning rate of 1 × 10-3 . RESULTS: Training for 100 000 iterations took 1.5 days (MSE), 3.5 days (MSE+ADV), 2.3 days (MSE+DVH), and 3.8 days (MSE+DVH+ADV). After training, the prediction time of each model is 0.052 s. Quantitatively, the MSE+DVH+ADV model had the lowest prediction error of 0.038 (conformation), 0.026 (homogeneity), 0.298 (R50), 1.65% (D95), 2.14% (D98), and 2.43% (D99). The MSE model had the worst prediction error of 0.134 (conformation), 0.041 (homogeneity), 0.520 (R50), 3.91% (D95), 4.33% (D98), and 4.60% (D99). For both the mean dose PTV error and the max dose PTV, Body, Bladder and rectum error, the MSE+DVH+ADV outperformed all other models. Regardless of model, all predictions have an average mean and max dose error <2.8% and 4.2%, respectively. CONCLUSION: The MSE+DVH+ADV model performed the best in these categories, illustrating the importance of both human and learned domain knowledge. Expert human domain-specific knowledge can be the largest driver in the performance improvement, and adversarial learning can be used to further capture nuanced attributes in the data. The real-time prediction capabilities allow for a physician to quickly navigate the tradeoff space for a patient, and produce a dose distribution as a tangible endpoint for the dosimetrist to use for planning. This is expected to considerably reduce the treatment planning time, allowing for clinicians to focus their efforts on the difficult and demanding cases.

Bridging Waves and Crucial Events in the Dynamics of the Brain.

Earlier research work on the dynamics of the brain, disclosing the existence of crucial events, is revisited for the purpose of making the action of crucial events, responsible for the 1/f -noise in the brain, compatible with the wave-like nature of the brain processes. We review the relevant neurophysiological literature to make clear that crucial events are generated by criticality. We also show that although criticality generates a strong deviation from the regular wave-like behavior, under the form of Rapid Transition Processes, the brain dynamics also host crucial events in regions of nearly coherent oscillations, thereby making many crucial events virtually invisible. Furthermore, the anomalous scaling generated by the crucial events can be established with high accuracy by means of direct analysis of raw data, suggested by a theoretical perspective not requiring the crucial events to yield a visible physical effect. The latter follows from the fact that periodicity, waves and crucial events are the consequences of a spontaneous process of self-organization. We obtain three main results: (a) the important role of crucial events is confirmed and established with greater accuracy than previously; (b) we demonstrate the theoretical tools necessary to understand the joint action of crucial events and periodicity; (c) we argue that the results of this paper can be used to shed light on the nature of this important process of self-organization, thereby contributing to the understanding of cognition.

Meditation-Induced Coherence and Crucial Events.

In this paper we emphasize that 1/f noise has two different origins, one compatible with Laplace determinism and one determined by unpredictable crucial events. The dynamics of heartbeats, manifest as heart rate variability (HRV) time series, are determined by the joint action of these different memory sources with meditation turning the Laplace memory into a strongly coherent process while exerting an action on the crucial events favoring the transition from the condition of ideal 1/f noise to the Gaussian basin of attraction. This theoretical development affords a method of statistical analysis that establishes a quantitative approach to the evaluation of the stress reduction realized by the practice of Chi meditation and Kundalini Yoga.

Crucial events, randomness, and multifractality in heartbeats.

We study the connection between multifractality and crucial events. Multifractality is frequently used as a measure of physiological variability, where crucial events are known to play a fundamental role in the transport of information between complex networks. To establish the connection of interest we focus on the special case of heartbeat time series and on the search for a diagnostic prescription to distinguish healthy from pathologic subjects. Over the past 20 years two apparently different diagnostic techniques have been established: the first is based on the observation that the multifractal spectrum of healthy patients is broader than the multifractal spectrum of pathologic subjects; the second is based on the observation that heartbeat dynamics are a superposition of crucial and uncorrelated Poisson-like events, with pathologic patients hosting uncorrelated Poisson-like events with larger probability than the healthy patients. In this paper, we prove that increasing the percentage of uncorrelated Poisson-like events hosted by heartbeats has the effect of making their multifractal spectrum narrower, thereby establishing that the two different diagnostic techniques are compatible with one another and, at the same time, establishing a dynamic interpretation of multifractal processes that had been previously overlooked.