We present a new nonparametric mixture-of-experts model for multivariate regression problems, inspired by the probabilistic k-nearest neighbors algorithm. Using a conditionally specified model, predictions for out-of-sample inputs are based on similarities to each observed data point, yielding predictive distributions represented by Gaussian mixtures. Posterior inference is performed on the parameters of the mixture components as well as the distance metric using a mean-field variational Bayes algorithm accompanied with a stochastic gradient-based optimization procedure. The proposed method is especially advantageous in settings where inputs are of relatively high dimension in comparison to the data size, where input-output relationships are complex, and where predictive distributions may be skewed or multimodal. Computational studies on five datasets, of which two are synthetically generated, illustrate clear advantages of our mixture-of-experts method for high-dimensional inputs, outperforming competitor models both in terms of validation metrics and visual inspection.

Objective. We propose a semiautomatic pipeline for radiation therapy treatment planning, combining ideas from machine learning-automated planning and multicriteria optimization (MCO). Approach. Using knowledge extracted from historically delivered plans, prediction models for spatial dose and dose statistics are trained and furthermore systematically modified to simulate changes in tradeoff priorities, creating a set of differently biased predictions. Based on the predictions, an MCO problem is subsequently constructed using previously developed dose mimicking functions, designed in such a way that its Pareto surface spans the range of clinically acceptable yet realistically achievable plans as exactly as possible. The result is an algorithm outputting a set of Pareto optimal plans, either fluence-based or machine parameter-based, which the user can navigate between in real time to make adjustments before a final deliverable plan is created. Main results. Numerical experiments performed on a dataset of prostate cancer patients show that one may often navigate to a better plan than one produced by a single-plan-output algorithm. Significance. We demonstrate the potential of merging MCO and a data-driven workflow to automate labor-intensive parts of the treatment planning process while maintaining a certain extent of manual control for the user.

Purpose: We present a framework for robust automated treatment planning using machine learning, comprising scenario-specific dose prediction and robust dose mimicking. Methods: The scenario dose prediction pipeline is divided into the prediction of nominal dose from input image and the prediction of scenario dose from nominal dose, each using a deep learning model with U-net architecture. By using a specially developed dose–volume histogram–based loss function, the predicted scenario doses are ensured sufficient target coverage despite the possibility of the training data being non-robust. Deliverable plans may then be created by solving a robust dose mimicking problem with the predictions as scenario-specific reference doses. Results: Numerical experiments are performed using a data set of 52 intensity-modulated proton therapy plans for prostate patients. We show that the predicted scenario doses resemble their respective ground truth well, in particular while having target coverage comparable to that of the nominal scenario. The deliverable plans produced by the subsequent robust dose mimicking were showed to be robust against the same scenario set considered for prediction. Conclusions: We demonstrate the feasibility and merits of the proposed methodology for incorporating robustness into automated treatment planning algorithms. 

We demonstrate the application of mixture density networks (MDNs) in the context of automated radiation therapy treatment planning. It is shown that an MDN can produce good predictions of dose distributions as well as reflect uncertain decision making associated with inherently conflicting clinical tradeoffs, in contrast to deterministic methods previously investigated in the literature. A two-component Gaussian MDN is trained on a set of treatment plans for postoperative prostate patients with varying extents to which rectum dose sparing was prioritized over target coverage. Examination on a test set of patients shows that the predicted modes follow their respective ground truths well, both spatially and in terms of their dose-volume histograms. A special dose mimicking method based on the MDN output is used to produce deliverable plans and thereby showcase the usability of voxel-wise predictive densities. Thus, this type of MDN may serve to support clinicians in managing clinical tradeoffs and has the potential to improve the quality of plans produced by an automated treatment planning pipeline.

Purpose: We propose a general framework for quantifying predictive uncertainties of dose-related quantities and leveraging this information in a dose mimicking problem in the context of automated radiation therapy treatment planning.

Methods: A three-step pipeline, comprising feature extraction, dose statistic prediction and dose mimicking, is employed. In particular, the features are produced by a convolutional variational autoencoder and used as inputs in a previously developed nonparametric Bayesian statistical method, estimating the multivariate predictive distribution of a collection of predefined dose statistics. Specially developed objective functions are then used to construct a probabilistic dose mimicking problem based on the produced distributions, creating deliverable treatment plans. 

Results: The numerical experiments are performed using a dataset of $94$ retrospective treatment plans of prostate cancer patients. We show that the features extracted by the variational autoencoder capture geometric information of substantial relevance to the dose statistic prediction problem and are related to dose statistics in a more regularized fashion than hand-crafted features. The estimated predictive distributions are reasonable and outperforms a non-input-dependent benchmark method, and the deliverable plans produced by the probabilistic dose mimicking agree better with their clinical counterparts than for a non-probabilistic formulation.

Conclusions: We demonstrate that prediction of dose-related quantities may be extended to include uncertainty estimation and that such probabilistic information may be leveraged in a dose mimicking problem. The treatment plans produced by the proposed pipeline resemble their original counterparts well, illustrating the merits of a holistic approach to automated planning based on probabilistic modeling. 

In this thesis, different parts of an automated process for radiation therapy treatment planning are investigated from a mathematical and computational perspective. Whereas traditional inverse planning is labor-intensive, often comprising several reiterations between treatment planner and physician before a plan can be approved, much of recent research have been aimed at using a data-driven approach by learning from historically delivered plans. Such an automated planning pipeline is commonly divided into a first part of predicting achievable values of dose-related quantities, and a second part of finding instructions to the treatment machine mimicking as best as possible the predicted values. Challenges associated with this type of prediction–mimicking workflow exist, however—for example, in typical applications, patient data is high-dimensional, scarce and has relatively low signal-to-noise ratio due to inter-planner variations, and significant information may be lost in the transition between prediction and mimicking.

We propose to address these challenges through better probabilistic modeling of the predictive inferences of dose-related quantities and increased accuracy of the optimization functions used for dose mimicking. In particular, starting with the disconnect between conventional planning objectives and evaluation metrics, in the first paper, we establish a framework for handling dose statistics as optimization function constituents. Subsequently, in the second and fourth papers, we present ways of predicting spatial dose and dose statistics, respectively, in a probabilistically rigorous fashion, the latter application relying on the similarity-based mixture-of-experts model developed in the third paper. As a nonparametric Bayesian regression model, equipped with a mean-field and stochastic variational inference algorithm, this mixture-of-experts model is suitable for managing complex input–output relationships and skewed or multimodal distributions. The second and fourth papers also introduce dose mimicking objectives able to leverage predictive distributions of spatial dose and dose statistics. In the fifth paper, we further build upon the probabilistic paradigm, merging the fields of multicriteria optimization and automated planning to create a semiautomatic alternative workflow in which certain manual intervention is possible. Lastly, in the sixth paper, we present a means of incorporating robustness against geometric uncertainties into an automated planning pipeline.

I denna avhandling studeras olika delar av en automatiserad process för strålterapiplanering från ett matematiskt och beräkningsmässigt perspektiv. Medan traditionell inversplanering är arbetsintensiv och ofta kräver upprepade iterationer mellan planerare och läkare, har mycket forskning på senare tid fokuserat på utvecklandet av datadrivna tillvägagångssätt baserade på inlärning från historiskt levererade planer. En sådant automatiserat arbetsflöde delas ofta upp i en första del av att först predicera uppnåeliga värden av dosrelaterade storheter och i en andra del av att bestämma de instruktioner till behandlingsmaskinen som bäst rekonstruerar de predicerade värdena. Emellertid finns utmaningar kopplade till denna typ av prediktion–rekonstruktion-flöde – exempelvis är patientdata i typiska tillämpningar högdimensionell, sällsynt och har relativt lågt signal--brus-förhållande, och väsentlig information kan gå förlorad i övergången mellan prediktion och rekonstruktion.

Vi föreslår att hantera dessa utmaningar genom förbättrade probabilistiska prediktionsmodeller för dosrelaterade storheter och ökad noggrannhet hos de optimeringsfunktioner som används vid dosrekonstruktion. Med utgång i diskrepansen mellan konventionella planeringsmålfunktioner och evalueringsmått etablerar vi i den första artikeln ett ramverk för att hantera dosstatistikor som beståndsdelar i optimeringsfunktioner. Vi presenterar sedan i den andra och den fjärde artikeln sätt att predicera spatial dos respektive dosstatistikor på ett probabilistiskt rigoröst sätt, varav det senare genom den likhetsbaserade mixture-of-experts-modell som utvecklas i den tredje artikeln. Som en ickeparametrisk bayesiansk regressionsmodell, försedd med tillhörande medelfälts- och stokastisk variationsinferensalgoritm, är denna mixture-of-experts-modell väl lämpad för att hantera komplexa indata–utdata-relationer och skeva eller multimodala fördelningar. Den andra och den fjärde artikeln introducerar också dosrekonstruktionsmålfunktioner som kan dra nytta av prediktiva fördelningar av spatial dos och dosstatistikor. I den femte artikeln bygger vi vidare på den probabilistiska paradigmen och förenar flermålsoptimering med automatisk planering för att skapa ett semiautomatiskt alternativt arbetsflöde, där viss manuell interaktion är möjlig. Slutligen presenterar vi i den sjätte artikeln ett sätt att ta hänsyn till robusthet med avseende på geometriska osäkerheter i ett automatiskt planeringsflöde.

We present a method of directly optimizing on deviations in clinical goal values in radiation therapy treatment planning. Using a new mathematical framework in which metrics derived from the dose-volume histogram are regarded as functionals of an auxiliary random variable, we are able to obtain volume-at-dose and dose-at-volume as infinitely differentiable functions of the dose distribution with easily evaluable function values and gradients. Motivated by the connection to risk measures in finance, which is formalized in this framework, we also derive closed-form formulas for mean-tail-dose and demonstrate its capability of reducing extreme dose values in tail distributions. Numerical experiments performed on a prostate and a head-and-neck patient case show that the direct optimization of dose-volume histogram metrics produced marginally better results than or outperformed conventional planning objectives in terms of clinical goal fulfilment, control of low- and high-dose tails of target distributions and general plan quality defined by a pre-specified evaluation measure. The proposed framework eliminates the disconnect between optimization functions and evaluation metrics and may thus reduce the need for repetitive user interaction associated with conventional treatment planning. The method also has the potential of enhancing plan optimization in other settings such as multicriteria optimization and automated treatment planning.

We present a new nonparametric mixture-of-experts model for multivariate regression problems, inspired by the probabilistic k-nearest neighbors algorithm. Using a conditionally specified model, predictions for out-of-sample inputs are based on similarities to each observed data point, yielding predictive distributions represented by Gaussian mixtures. Posterior inference is performed on the parameters of the mixture components as well as the distance metric using a mean-field variational Bayes algorithm accompanied with a stochastic gradient-based optimization procedure. The proposed method is especially advantageous in settings where inputs are of relatively high dimension in comparison to the data size, where input-output relationships are complex, and where predictive distributions may be skewed or multimodal. Computational studies on two synthetic datasets and one dataset comprising dose statistics of radiation therapy treatment plans show that our mixture-of-experts method performs similarly or better than a conditional Dirichlet process mixture model both in terms of validation metrics and visual inspection.

Methods: The scenario dose prediction pipeline is divided into the prediction of nominal dose from input image and the prediction of scenario dose from nominal dose, each using a deep learning model with U-net architecture. By using a specially developed dose-volume histogram-based loss function, the predicted scenario doses are ensured sufficient target coverage despite the possibility of the training data being non-robust. Deliverable plans may then be created by solving a robust dose mimicking problem with the predictions as scenario-specific reference doses.

Results: Numerical experiments are performed using a dataset of 52 intensity-modulated proton therapy plans for prostate patients. We show that the predicted scenario doses resemble their respective ground truth well, in particular while having target coverage comparable to that of the nominal scenario. The deliverable plans produced by the subsequent robust dose mimicking were showed to be robust against the same scenario set considered for prediction.

Conclusions: We demonstrate the feasibility and merits of the proposed methodology for incorporating robustness into automated treatment planning algorithms.

We propose a semiautomatic pipeline for radiation therapy treatment planning, combining ideas from machine learning-automated planning and multicriteria optimization (MCO). Using knowledge extracted from historically delivered plans, prediction models for spatial dose and dose statistics are trained and furthermore systematically modified to simulate changes in tradeoff priorities, creating a set of differently biased predictions. Based on the predictions, an MCO problem is subsequently constructed using previously developed dose mimicking functions, designed in such a way that its Pareto surface spans the range of clinically acceptable yet realistically achievable plans as exactly as possible. The result is an algorithm outputting a set of Pareto optimal plans, either fluence-based or machine parameter-based, which the user can navigate between in real time to make adjustments before a final deliverable plan is created. Numerical experiments performed on a dataset of prostate cancer patients show that one may often navigate to a better plan than one produced by a single-plan-output algorithm. In particular, we demonstrate the potential of merging MCO and a data-driven workflow to automate labor-intensive parts of the treatment planning process while maintaining a certain extent of manual control for the user.