Optimization model applied to radiotherapy planning problem with dose intensity and beam choice

Abstract

Optimization applied to radiotherapy planning is a complex scientific issue seeking to deliver both possible highest dose into tumor tissue and lowest one into adjacent tissues. It is composed of one or more of the following main problems: beam choice, dose intensity and blades opening. In this paper, a mixed integer nonlinear optimization model is developed for radiation treatment planned by intensity modulated radiotherapy treatment involving both dose intensity and beam choice optimization problems. Moreover, metaheuristics proposed to solve the beam optimization problem are coupled with exact methods, which in turn solve the dose intensity problem. The proposed model is applied to two real computerized tomography images of prostate cases, where it has been shown to be highly efficient.

Introduction

Cancer is the denomination of more than 100 diseases characterized by cell growth disorder. It is a genetic mutation that can be developed and have the process accelerated by some external causes such as food habits, heredity, occupational factors, solar exposure and others. According to World Health Organization, in 2015 8.8 millions of people died of cancer and this statistic is expected to increase around the world by 70% in the next two decades [1].

Prostate cancer is the tumor kind approached in this paper and is the second most frequent case in men, and also is the fifth in death cases ranking by this disease [2]. Prostate tumor can be treated by surgery, chemotherapy, hormonal therapy and radiotherapy. The last one is the treatment method focused in this paper because it is a non invasive technique that aims to achieve the target area. Planning radiotherapy process requires extensive and complex steps. Firstly, a set of images of the tumor area is required as computerized tomography. Through the images a physician identifies body tissues dividing them into tumoral, healthy and organs at risk (OAR), then setting the dose limits for each one. OAR are more sensitive to radiation than the others, needing a specific dose limitation in order to prevent from future cell mutation and complications. After the tissue identification a medical physicist chooses the best beam set for treatment, usually by using trial and error methods based on previous knowledge, focusing the radiation into tumor area and avoiding adjacent tissues. The planning treatment is approved by the physician and the treatment actually begins [3], [4].

The major issue is to deliver high ionized radiation dose in tumor tissue preventing other tissues to receive high dose amount [5]. A manner to produce and deliver radiation to the patient is using a Linear Accelerator (AL) machine, which is shown in Fig. 1. This machine consists in three main parts: stand, gantry and collimator. Stand produces high energy beam in order of Megavolt (MV) achieving the patient body. The radiation absorbed from a beam is called absorbed dose (Gray - Gy). AL rotates around the patient by gantry movement and the beam is delivered by the collimator to reach tumor cells avoiding surrounding cells from receiving high dose, preventing future damage. Most of all AL machines are capable of rotating the gantry 360^∘ around patient table. However, not all possible angles are always used, on account of treatment time and cost. Routinely, an angle set is chosen in order to plan an efficient treatment. Thereby, in order to automatize the plan process and eliminate trial and error methods, implementing optimization models has been widely explored.

Optimization models in radiotherapy planning allow to calculate the adequate dosage to be delivered by each possible beam and choosing the best beam set for the treatment. The first research in this area was performed in 1968 by Bahr [6] and since then even more surveys have been made involving the planning problems [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18].

Our new mixed integer nonlinear optimization model initially determines the best beam set. Next, the best beam choice is supplied to a model in charge of optimizing the dose intensity delivering. Nonlinear methods can be solved by classic Newton’s methods [19] or even using fuzzy logic systems [20], [21]. However, based on [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18] we employ matheuristics methods to solve the new model, in which the metaheuristics Variable Neighbourhood Search (VNS) and Tabu Search (TS) solve the beam choice problem and convert the model into a mixed integer linear. From then on, one uses exact methods Primal Simplex (PS), Dual Simplex (DS) and Interior Point Method (IPM) for the dose intensity problem and final solution.

The proposed model is defined and presented in Section 2, followed by resolution method in Section 3. Metaheuristics are explained in details because they are one of the highlights developed in this paper coupled with the proposed model, and the exact methods used from a CPLEX® software were briefly explained. In Section 4 the analyses from the applied resolution methods are presented, and Section 5 points out the obtained conclusions.