A new inverse planning formalism with explicit DVH constraints and kurtosis-based dosimetric criteria

Conic formulation of fluence map optimization problems

The convexity of objectives and constraints in fluence map optimization (FMO) for radiation therapy has been extensively studied. Next to convexity, there is another important characteristic of optimization functions and problems, which has thus far not been considered in FMO literature: conic representation. Optimization problems that are conically representable using quadratic, exponential and power cones are solvable with advanced primal-dual interior-point algorithms. These algorithms guarantee an optimal solution in polynomial time and have good performance in practice. In this paper, we construct conic representations for most FMO objectives and constraints. This paper is the first that shows that FMO problems containing multiple biological evaluation criteria can be solved in polynomial time. For fractionation-corrected functions for which no exact conic reformulation is found, we provide an accurate approximation that is conically representable. We present numerical results on the TROTS data set, which demonstrate very stable numerical performance for solving FMO problems in conic form. With ongoing research in the optimization community, improvements in speed can be expected, which makes conic optimization a promising alternative for solving FMO problems.

Optimization in treatment planning of high dose-rate brachytherapy - Review and analysis of mathematical models

Treatment planning in high dose-rate brachytherapy has traditionally been conducted with manual forward planning, but inverse planning is today increasingly used in clinical practice. There is a large variety of proposed optimization models and algorithms to model and solve the treatment planning problem. Two major parts of inverse treatment planning for which mathematical optimization can be used are the decisions about catheter placement and dwell time distributions. Both these problems as well as integrated approaches are included in this review. The proposed models include linear penalty models, dose-volume models, mean-tail dose models, quadratic penalty models, radiobiological models, and multiobjective models. The aim of this survey is twofold: (i) to give a broad overview over mathematical optimization models used for treatment planning of brachytherapy and (ii) to provide mathematical analyses and comparisons between models. New technologies for brachytherapy treatments and methods for treatment planning are also discussed. Of particular interest for future research is a thorough comparison between optimization models and algorithms on the same dataset, and clinical validation of proposed optimization approaches with respect to patient outcome.

Intelligent IoT-based large-scale inverse planning system considering postmodulation factors

The model and algorithm of intensity-modulated radiotherapy (IMRT) are updated increasingly quickly, but the hardware upgrade of primary hospitals often lags behind. The new generation of intelligent precise radiotherapy platforms provides users with intelligent medical consortium services using big data, artificial intelligence and industrial Internet of Things technology. This technology can ensure that under the real-time guidance of a professional medical consortium, primary hospitals can realize rapid large-scale reverse planning design and can more accurately consider many factors of postprocessing. Although large-scale healthcare systems, such as volumetric-modulated arc therapy and other accurate radiotherapy technologies, have developed rapidly, the development of step-and-shoot-mode IMRT technology is still very important for developing countries. For software, in addition to the conformity of the dose distribution, the modulation speed, convenience and stability of the later dose delivery should also be considered in inverse planning. Therefore, this paper analyzes the main problems in conventional IMRT inverse planning, including the smoothing of the fluence map, the selection of the gantry angle and the dose leakage of tongue–groove effects. To address these issues, a novel Intelligent IoT-based large-scale inverse planning strategy with the key factors of the postmodulation is developed, and a detailed flow chart is also provided. The scheme consists of two steps. The first step is to obtain a relatively optimal combination of gantry angles by considering the dose distribution requirements and constraints and the modulation requirements and constraints. The second step is to optimize the intensity map, to smooth the map based on prior knowledge according to the determined angles, and to obtain the final modulation scheme according to the relevant objectives and constraints of the map decomposition (leaf sequencing). In an experiment, we calculate and validate the clinical head and neck case. Because of the special gantry angle selection, the angle combination is optimized from the initial equivalent distribution to adapt to the target area and protect the nontarget area. The value of the objective function varies greatly after the optimization, especially in the target area, and the target value decreases by approximately 10%. On this basis, we smooth the fluence map by a partial differential equation with prior knowledge and a minimization of the total number of monitor units. It is also shown from the objective function value that the target value is essentially unchanged for the target area, while for the nontarget area, the value decreases by 16%, which is very impressive.

Direct optimization of dose-volume histogram metrics in radiation therapy treatment planning

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.