Regular PaperInvestigations of a GPU-based levy-firefly algorithm for constrained optimization of radiation therapy treatment planning
Introduction
Intensity Modulated Radiation therapy (IMRT) is an advanced means of treatment modality delivering highly modulated external megavoltage radiation beams utilizing linear accelerators. For many types of cancer, such as prostate and nasopharyngeal cancer the use of IMRT allows a highly intensive treatment of the tumor volume while limiting the radiation dose to adjacent healthy tissues [1], [2]. In contrast to the traditionally 3D conformal radiotherapy (3DCRT) where the treatment is delivered with large uniform beams, in IMRT the intensity of each beam varies within the treatment field. This is achieved by dividing the radiation field into a collection of pencil beams (beamlets) [3], [4]. When planning a radiation therapy case, the dose constraints are assigned to both the target and surrounding normal structures. These dose constraints need not to be given in terms of the dose assigned to each point in the body, but rather are usually phrased in terms of aggregate functions such as maximum or minimum dose, and dose limit for a given volume (dose-volume constraints). Then, according to the prescribed dose objectives, numerical inverse optimization is performed in order to determine the individual intensities of the beamlets [5], [6]. The optimized intensity maps are then decomposed into a series of deliverable multi-leaf collimator (MLC) patterns in the sequencing step. It is worth note that alternative optimization methods, such as the direct aperture optimization (DAO), have been proposed in the past where the aperture shapes and beamlet intensities are optimized simultaneously. In that way all of the MLC delivery constraints of the leaf sequencing algorithm are included in the optimization [7], [8], [9]. Traditionally, the optimization model contains a single objective function subject to a set of hard constraints on the treatment plan.
A number of increasingly sophisticated mathematical programming models have been proposed for the inverse treatment planning and deconvolution process (see, e.g. Ref. [10] for a recent overview of this topic). For instance, the well-known Newton–Raphson algorithm is gradient-based and it works well for smooth unimodal problems. Gradient-based algorithms have been proposed in the past for optimizing single-objective problems in radiation therapy treatment planning under volume-dose constraints [11], [12], [13], [14]. However for optimization problems with discontinuity, a derivative-free non-gradient algorithm (i.e. Nelder–Mead downhill simplex) is preferred. Zhu and Xing recently proposed a total-variation based compressed sensing technique to better balance the tradeoff between fluence modulation complexity and deliverability [15]. Kalantzis et al. [16] have introduced an accelerated reduced order prioritized optimization method where the IMRT optimization is performed in a presampled eigen mode space of the beamlets intensities. Romeijn et al. [17] have followed a linear programming approach for fluence-based IMRT optimization by approximating any convex objective function by a piecewise linear convex function [17]. Wang et al. [18] have employed mixed integer linear programming (MILP) to optimize beam orientations and beam weights, whereas Xing et al. [19] have used a nonlinear programming model, the weighted least squares for IMRT optimization.
An alternative approach to the aforementioned deterministic methods is the Metaheuristic Algorithms (MAs) which form an important part of contemporary global optimization algorithms. MAs are often nature-inspired and they are now among the most widely used algorithms for optimization problems [20]. These algorithms have been developed by mimicking the most successful processes in nature, including biological systems as well as physical and chemical processes. Convergence analysis of a few algorithms such as the particle swarm optimization (PSO) show some insight, but in general mathematical analysis of MAs remains unsolved and still an ongoing active research topic [21]. The main components of any metaheuristic algorithm are: intensification and diversification, or exploitation and exploration. Diversification aims to generate diverse solutions so as to explore the search space on the global scale, while intensification focus on the search in a local region by exploiting the information that a current solution is found in this region [22]. MAs have been proposed in the past for dosimetric optimization of LINAC-based IMRT treatment [23], [24], [25] and robotic radiosurgery [26]. Simulated annealing [27], PSO [28] and a hybridized genetic algorithm with an ant colony [29] have been also applied to beam angle optimization (BAO). Finally, other metaheuristics, such as the Bat Algorithm [30] and Memetics [31], [32] have also found applications in optimization of IMRT and Gamma Knife treatment planning.
A global optimization stochastic algorithm which has attracted interest from researchers is the Firelfy algorithm (FA). As a novel literature, the FA is a metaheuristic, nature inspired optimization algorithm developed by X. Yang [33], it is based on the idealized behavior of the emitted light from the fireflies, in the summer sky in the tropical temperature regions. Although the FA has many similarities with other swarm intelligence algorithms, such as Artificial Bee Colony (ABC), Bacterial Foraging (BFA) and Particle Swarm Optimization (PSO), it is indeed much simpler both in concept and implementation [34], [35], [36]. Additionally, recent developments have demonstrated the superiority of the FA in performance compared to other metaheuristic algorithms for solving various optimization tasks [37], [38], [39], [40]. One of the key advantages of the FA is the global communication among the swarming particles (i.e. fireflies), which can provide a quick convergence by switching from exploration to exploitation. However, if we allow the algorithm to switch to exploitation stage too quickly, it may lead to stagnation soon after the initial stage.
Due to the high dimensionality of the search space, IMRT optimization is a computationally demanding task. One way to ameliorate that issue is the parallelization of the optimization algorithm. Previous studies have signified promising results towards that direction for various computational platforms. Ziegenhein et al. [41] have demonstrated a parallelized quasi-Newton method on a multi-core CPU with the usage of pre-calculated dose influence data sets. Na et al. [42] suggested a web-based radiation therapy planning system at the Amazon Elastic Compute Cloud (EC2). Men et al. [43] proposed a gradient projection method for GPU-based quadratic optimization model for IMRT treatment planning. Although all metaheuristic algorithms are simple in terms of complexity and easy to implement, they require extensive computational resources. That is due to the extensive iterative calculations and random number generators required for their execution. That issue becomes more apparent for large scale optimization problems with thousands variables, such as the IMRT optimization. Efforts have been made towards the parallelization of MAs for radiation planning optimization. Nazareth et al. [44], describes the use of a genetic algorithm that is run on a distributed computing platform for BAO. Fiege et al. [25], describe the application of a parallel Matlab-based multiobjective genetic algorithm (Ferret) for IMRT optimization.
This paper suggests, for the first time to our best knowledge, an immerging GPU-based Levy Firefly algorithm for constraint optimization in radiation therapy treatment planning. The applicability of the proposed method is demonstrated through two cases of IMRT treatment planning: an early stage prostate cancer and a head and neck (H&N) cancer case. Performance tests were conducted for both cases in comparison to a sequential version of the algorithm executed on a CPU.
Section snippets
Treatment planning preparation
The treatment planning system we have used in this investigation is the computational environment for radiotherapy research (CERR) [45], a MATLAB®-based implementation of a treatment planning suite for radiation therapy (Fig. 1).
The main advantages of CERR is the user-friendly graphical user interface (GUI), access to dose deposition matrices, implementation of programming modules from the user and availability of the toolboxes of MATLAB®. Based on the defined target and structures of the
Speedup of parallelized LFA
The computational time required to perform the dose calculations and consequently the evaluation of the objective function for the optimization problem, on a given case, generally scales with the system size. This is determined principally by the product of the total number of beamlet intensities (or pencil beams) that need to be optimized and the total number of voxels for which dose need to be computed during the optimization. For testing purposes, Fig. 4 illustrates profiling results of the
Conclusion
In the current study a GPU-based levy-firefly algorithm was presented. The method was applied for the first time, to our best knowledge, for constrained optimization of IMRT treatment planning. The applicability of our method was demonstrated for two treatment plans: IMRT plan for a prostate cancer and IMRT for a H&N cancer case.
The studies indicated a maximum speedup of ~11-fold for the GPU code compared to the sequential for 1060 beamlets, which agrees with previous studies [63], [64]. We
References (90)
Evidence behind use of intensity-modulated radiotherapy: a systematic review of comparative clinical studies
Lancet Oncol.
(2008)A treatment planning analysis of inverse-planned and forward-planned intensity-modulated radiation therapy in nasopharyngeal carcinoma
Int. J. Radiat. Oncol. Biol. Phys.
(2007)Optimized planning using physical objectives and constraints
Semin. Radiat. Oncol.
(1999)IMRT treatment planning for prostate cancer using prioritized prescription optimization and mean-tail-dose functions
Linear Algebra Appl.
(2008)- et al.
Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm
Inf. Process. Lett.
(2007) Levy flight random searches in biological phenomena
Physica A
(2002)- et al.
Parameter tuning for configuring and analyzing evolutionary algorithms
Swarm Evolut. Comput.
(2011) - et al.
The Mahalanobis distance
Chemometr. Intell. Lab. Syst.
(2000) - et al.
Feature selection using tabu search method
Pattern Recognit.
(2002) Image segmentation using PSO and PCM with Mahalanobis distance
Exp. Syst. Appl.
(2011)
An efficient constraint handling method for genetic algorithms
Comput. Methods Appl. Mech. Eng.
Comparison of IMRT optimization based on a pencil beam and a superposition algorithm
Med. Phys.
A finite size pencil beam for IMRT dose optimization
Phys. Med. Biol.
Intensity Modulated Radiation Therapy: The State of the Art
Direct aperture optimization: a turnkey solution for step-and-shoot IMRT
Med. Phys.
An exact approach to direct aperture optimization in IMRT treatment planning
Phys. Med. Biol.
Direct aperture optimization for IMRT using Monte Carlo generated beamlets
Med. Phys.
Handbook of Optimization in Medicine
A gradient inverse planning algorithm with dose-volume constraints
Med. Phys.
Speed and convergence properties of gradient algorithms for optimization of IMRT
Med. Phys.
Multiobjective inverse planning for intensity modulated radiotherapy with constraint-free gradient-based optimization algorithms
Phys. Med. Biol.
Search for IMRT inverse plans with piecewise constant fluence maps using compressed sensing techniques
Med. Phys.
A novel reduced-order prioritized optimization method for radiation therapy treatment planning
IEEE Trans. Biomed. Eng.
A novel linear programming approach to fluence map optimization for intensity modulated radiation therapy treatment planning
Phys. Med. Biol.
Optimization of beam orientations and beam weights for conformal radiotherapy using mixed integer programming
Phys. Med. Biol.
Fast iterative algorithms for three-dimensional inverse treatment planning
Med. Phys.
Review of metaheuristics and generalized evolutionary walk algorithms
Int. J. Bio-Inspired Comput.
Metaheuristics in combinatorial optimisation: Overview and conceptural comparison
ACM Comput. Surv.
A hierarchical evolutionary algorithm for multiobjective optimization in IMRT
Med. Phys.
Segment-based dose optimization using a genetic algoirthm
Phys. Med. Biol.
PARETO: a novel evolutionary optimization approach to multiobjective IMRT planning
Med. Phys.
Dosimetric optimization method for cyberknife robotic radiosurgery system using a memetic algorithm
Optimization of beam orientations in radiation therapy: some theoretical considerations
Phys. Med. Biol.
A particle swarm optimization algorithm for beam angle selection in intensity-modulated radiotherapy planning
Phys. Med. Biol.
Accelerating the radiotherapy planning with a hybrid method of genetic algorithm and ant colony system
Adv. Nat. Comput.
Optimization of Gamma knife treatment planning via guided evolutionary simulated annealing
Med. Phys.
Nature-Inpsired Metaheuristic Algorithms
Firefly algorithm, stochastic test functions and design optimization
Int. J. Bio-inspired Comput.
Comparative study of firefly algorithm and particle swarm optimization for noisy non-linear optimization problems
Int. J. Intell. Syst. Appl.
Cited by (27)
A systematic review on the potency of swarm intelligent nanorobots in the medical field
2024, Swarm and Evolutionary ComputationA reinforcement learning based artificial bee colony algorithm with application in robot path planning
2022, Expert Systems with ApplicationsAn efficient multilevel thresholding segmentation method for thermography breast cancer imaging based on improved chimp optimization algorithm
2021, Expert Systems with ApplicationsCitation Excerpt :For example, the Gray wolf optimizer (Heidari & Pahlavani, 2017), the Ant lion optimizer for optimization problems (Dinkar & Deep, 2018), the Bat algorithm (Li et al., 2019), and the WOA (Ling et al., 2017). Also, the Jaya optimization algorithm (Iacca et al., 2021), the basic PSO (Jensi & Jiji, 2016) and FA (Kalantzis et al., 2016) have been enhanced using LF. These methods confirm that LF can significantly boost the efficiency of the optimization algorithms.
Red fox optimization algorithm
2021, Expert Systems with Applications