A mixed-encoding genetic algorithm with beam constraint for conformal radiotherapy treatment planning

Ultra-high-temperature sensing using fiber grating sensor and demodulation method based on support vector regression optimized by a genetic algorithm

We propose an ultra-high-temperature sensing method using a fiber Bragg grating (FBG) and demodulation technique based on support vector regression optimized by a genetic algorithm (GA-SVR). A type-I FBG inscribed by a femtosecond laser in a silica fiber was packaged with a tube and used as a temperature sensor. The external ambient temperature was retrieved from the transient FBG wavelength and its increase rate in reaching thermal equilibrium of the FBG with the external environment using GA-SVR. The temperature sensing in the range of 400 to 1000 °C was realized with an accuracy of 4.8 °C. The highest sensing temperature exceeded the FBG resisting temperature of 700 °C. The demodulation time was decreased to approximately 15 s, only 3.14% of the FBG sensor time constant. The proposed method could realize the external ambient temperature determination before the FBG temperature reached the thermal equilibrium state, which enables to attain a demodulation time shorter than the time constant of the FBG sensor and a sensing temperature higher than the FBG resisting temperature. This method could be potentially applied in temperature inspection of combustion and other fields.

Determination of optimal number of beams in direct machine parameter optimization-based intensity modulated radiotherapy for head and neck cases

This paper aims to introduce an algorithm called “sensitivity-based beam number selection (SBBNS)” for fully automated and case-specific determination of an optimal number of equispaced beams in intensity-modulated radiotherapy (IMRT). We tested the algorithm in five head and neck cases of varying complexity. We used direct machine parameter optimization method coupled with Auto Plan feature available in Pinnacle TPS (Version 9.10.0) for optimization. The Pearson correlation test shows a correlation of 0.88 between predicted and actual optimal number of beams, which indicates that SBBNS method is capable of predicting optimal number of beams for head and neck cases with reasonable accuracy. The major advantage of the algorithm is that it intrinsically takes into account various case- and machine-specific factors for the determination of optimal number. The study demonstrates that the algorithm can be effectively applied to IMRT scenarios to determine case specific and optimal number of beams for head and neck cases.

The Applications of Genetic Algorithms in Medicine

A great wealth of information is hidden amid medical research data that in some cases cannot be easily analyzed, if at all, using classical statistical methods. Inspired by nature, metaheuristic algorithms have been developed to offer optimal or near-optimal solutions to complex data analysis and decision-making tasks in a reasonable time. Due to their powerful features, metaheuristic algorithms have frequently been used in other fields of sciences. In medicine, however, the use of these algorithms are not known by physicians who may well benefit by applying them to solve complex medical problems. Therefore, in this paper, we introduce the genetic algorithm and its applications in medicine. The use of the genetic algorithm has promising implications in various medical specialties including radiology, radiotherapy, oncology, pediatrics, cardiology, endocrinology, surgery, obstetrics and gynecology, pulmonology, infectious diseases, orthopedics, rehabilitation medicine, neurology, pharmacotherapy, and health care management. This review introduces the applications of the genetic algorithm in disease screening, diagnosis, treatment planning, pharmacovigilance, prognosis, and health care management, and enables physicians to envision possible applications of this metaheuristic method in their medical career.].

Beam geometry selection using sequential beam addition

PURPOSE

The selection of optimal beam geometry has been of interest since the inception of conformal radiotherapy. The authors report on sequential beam addition, a simple beam geometry selection method, for intensity modulated radiation therapy.

METHODS

The sequential beam addition algorithm (SBA) requires definition of an objective function (score) and a set of candidate beam geometries (pool). In the first iteration, the optimal score is determined for each beam in the pool and the beam with the best score selected. In the next iteration, the optimal score is calculated for each beam remaining in the pool combined with the beam selected in the first iteration, and the best scoring beam is selected. The process is repeated until the desired number of beams is reached. The authors selected three treatment sites, breast, lung, and brain, and determined beam arrangements for up to 11 beams from a pool comprised of 25 equiangular transverse beams. For the brain, arrangements were additionally selected from a pool of 22 noncoplanar beams. Scores were determined for geometries comprised equiangular transverse beams (EQA), as well as two tangential beams for the breast case.

RESULTS

In all cases, SBA resulted in scores superior to EQA. The breast case had the strongest dependence on beam geometry, for which only the 7-beam EQA geometry had a score better than the two tangential beams, whereas all SBA geometries with more than two beams were superior. In the lung case, EQA and SBA scores monotonically improved with increasing number of beams; however, SBA required fewer beams to achieve scores equivalent to EQA. For the brain case, SBA with a coplanar pool was equivalent to EQA, while the noncoplanar pool resulted in slightly better scores; however, the dose-volume histograms demonstrated that the differences were not clinically significant.

CONCLUSIONS

For situations in which beam geometry has a significant effect on the objective function, SBA can identify arrangements equivalent to equiangular geometries but using fewer beams. Furthermore, SBA provides the value of the objective function as the number of beams is increased, allowing the planner to select the minimal beam number that achieves the clinical goals. The method is simple to implement and could readily be incorporated into an existing optimization system.

An experimental investigation on the effect of beam angle optimization on the reduction of beam numbers in IMRT of head and neck tumors

In static intensity-modulated radiation therapy (IMRT), the fundamental factors that determine the quality of a plan are the number of beams and their angles. The objective of this study is to investigate the effect of beam angle optimization (BAO) on the beam number in IMRT. We used six head and neck cases to carry out the study. Basically the methodology uses a parameter called "Beam Intensity Profile Perturbation Score" (BIPPS) to determine the suitable beam angles in IMRT. We used two set of plans in which one set contains plans with equispaced beam configuration starting from beam numbers 3 to 18, and another set contains plans with optimal beam angles chosen using the in-house BAO algorithm. We used quadratic dose-based single criteria objective function as a measure of the quality of a plan. The objective function scores obtained for equispaced beam plans and optimal beam angle plans for six head and neck cases were plotted against the beam numbers in a single graphical plot for effective comparison. It is observed that the optimization of beam angles reduces the beam numbers required to produce clini-cally acceptable dose distribution in IMRT of head and neck tumors. Especially N0.1 (represents the beam number at which the objective function reaches a value of 0.1) is considerably reduced by beam angle optimization in almost all the cases included in the study. We believe that the experimental findings of this study will be helpful in understanding the interplay between beam angle optimization and beam number selection process in IMRT which, in turn, can be used to improve the performance of BAO algorithms and beam number selection process in IMRT.

Optimization of beam angles for intensity modulated radiation therapy treatment planning using genetic algorithm on a distributed computing platform

Planning intensity modulated radiation therapy (IMRT) treatment involves selection of several angle parameters as well as specification of structures and constraints employed in the optimization process. Including these parameters in the combinatorial search space vastly increases the computational burden, and therefore the parameter selection is normally performed manually by a clinician, based on clinical experience. We have investigated the use of a genetic algorithm (GA) and distributed-computing platform to optimize the gantry angle parameters and provide insight into additional structures, which may be necessary, in the dose optimization process to produce optimal IMRT treatment plans. For an IMRT prostate patient, we produced the first generation of 40 samples, each of five gantry angles, by selecting from a uniform random distribution, subject to certain adjacency and opposition constraints. Dose optimization was performed by distributing the 40-plan workload over several machines running a commercial treatment planning system. A score was assigned to each resulting plan, based on how well it satisfied clinically-relevant constraints. The second generation of 40 samples was produced by combining the highest-scoring samples using techniques of crossover and mutation. The process was repeated until the sixth generation, and the results compared with a clinical (equally-spaced) gantry angle configuration. In the sixth generation, 34 of the 40 GA samples achieved better scores than the clinical plan, with the best plan showing an improvement of 84%. Moreover, the resulting configuration of beam angles tended to cluster toward the patient's sides, indicating where the inclusion of additional structures in the dose optimization process may avoid dose hot spots. Additional parameter selection in IMRT leads to a large-scale computational problem. We have demonstrated that the GA combined with a distributed-computing platform can be applied to optimize gantry angle selection within a reasonable amount of time.

An algorithm for fast beam angle selection in intensity modulated radiotherapy

PURPOSE

This article aims to introduce a novel algorithm for fast beam angle selection in intensity modulated radiotherapy (IMRT).

METHODS

The algorithm models the optimization problem as a beam angle ranking problem and chooses suitable beam angles according to their rank. A new parameter called "beam intensity profile perturbation score (BIPPS)" is used for ranking the beam angles. The BIPPS-based beam angle ranking implicitly accounts for the dose-volume effects of the involved structures. A simulated phantom case with obvious optimal beam angles is used to verify the validity of the presented technique. In addition, the efficiency of the algorithm was examined in three clinical cases (prostate, pancreas, and head and neck) in terms of DVH and dose distribution. In all cases, the judgment of the algorithm's efficiency was based on the comparison between plans with equidistant beams (equal-angle-plan) and plans with beams obtained using the algorithm (suitable-angle-plan).

RESULTS

It is observed from the study that the beam angle ranking function over BIPPS instantly picks up a suitable set of beam angles for a specific case. It takes only about 15 min for choosing the suitable beam angles even for the most complicated cases. The DVHs and dose distributions confirm that the proposed algorithm can efficiently reduce the mean or maximum dose to OARs, while guaranteeing the target coverage and dose uniformity. On the average, about 17% reduction in the mean dose to critical organs, such as rectum, bladder, kidneys and parotids, is observed. Also, about 12% (averaged) reduction in the maximum dose to critical organs (spinal cord) is observed in the clinical cases presented in this study.

CONCLUSIONS

This study demonstrates that the algorithm can be effectively applied to IMRT scenarios to get fast and case specific beam angle configurations.

Genetic algorithm based deliverable segments optimization for static intensity-modulated radiotherapy

The static delivery technique (also called step-and-shoot technique) has been widely used in intensity-modulated radiotherapy (IMRT) because of the simple delivery and easy quality assurance. Conventional static IMRT consists of two steps: first to calculate the intensity-modulated beam profiles using an inverse planning algorithm, and then to translate these profiles into a series of uniform segments using a leaf-sequencing tool. In order to simplify the procedure and shorten the treatment time of the static mode, an efficient technique, called genetic algorithm based deliverable segments optimization (GADSO), is developed in our work, which combines these two steps into one. Taking the pre-defined beams and the total number of segments per treatment as input, the number of segments for each beam, the segment shapes and weights are determined automatically. A group of interim modulated beam profiles quickly calculated using a conjugate gradient (CG) method are used to determine the segment number for each beam and to initialize segment shapes. A modified genetic algorithm based on a two-dimensional binary coding scheme is used to optimize the segment shapes, and a CG method is used to optimize the segment weights. The physical characters of a multileaf collimator, such as the leaves interdigitation limitation and leaves maximum over-travel distance, are incorporated into the optimization. The algorithm is applied to some examples and the results demonstrate that GADSO is able to produce highly conformal dose distributions using 20-30 deliverable segments per treatment within a clinically acceptable computation time.

Automatic beam angle selection in IMRT planning using genetic algorithm

The selection of suitable beam angles in external beam radiotherapy is at present generally based upon the experience of the human planner. The requirement to automatically select beam angles is particularly highlighted in intensity-modulated radiation therapy (IMRT), in which a smaller number of modulated beams is hoped to be used, in comparison with conformal radiotherapy. It has been proved by many researchers that the selection of suitable beam angles is most valuable for a plan with a small number of beams (< or = 5). In this paper an efficient method is presented to investigate how to improve the dose distributions by selecting suitable coplanar beam angles. In our automatic beam angle selection (ABAS) algorithm, the optimal coplanar beam angles correspond to the lowest objective function value of the dose distributions calculated using the intensity-modulated maps of this group of candidate beams. Due to the complexity of the problem and the large search space involved, the selection of beam angles and the optimization of intensity maps are treated as two separate processes and implemented iteratively. A genetic algorithm (GA) incorporated with an immunity operation is used to select suitable beam angles, and a conjugate gradient (CG) method is used to quickly optimize intensity maps for each selected beam combination based on a dose-based objective function. A pencil-beam-based three-dimensional (3D) full scatter convolution (FSC) algorithm is employed for the dose calculation. Two simulated cases with obvious optimal beam angles are used to verify the validity of the presented technique, and a more complicated case simulating a prostate tumour and two clinical cases are employed to test the efficiency of ABAS. The results show that ABAS is valid and efficient and can improve the dose distributions within a clinically acceptable computation time.

An algorithm for systematic selection of beam directions for IMRT

Selection of the number of beams and their directions can be an important problem in radiation therapy, especially when a tumor surrounds a critical organ or is surrounded by multiple critical organs. Beam directions, in this sense, are chosen to not only avoid critical organs, but also to achieve better target dose uniformity. In intensity-modulated radiation therapy (IMRT), optimization of beam directions is further complicated due to the dependence of one beam direction on its corresponding beamlet intensities and the beamlet intensities of all other beam directions. The result is an excessively enlarged search space, even when the number of beams is small (two to three). Until now, only a handful of publications exist regarding beam direction optimization in IMRT. Here, we report a new systematic approach that determines a suitable number of "more optimal" beam directions without optimizing a complicated objective function or resorting to brute force. We start by assuming that beam directions chosen for an N-beam plan are candidates for beam directions in the search for an (N + 1)-beam plan. Knowing that beam directions in an N-beam plan are not always the best choices for the (N + 1)-beam plan, we introduce into the beam direction selection process an analysis of the beamlet weights of every beam direction set sampled. If the relative weights of any particular beam compared to other beams are insignificant and hence have no significant effect on the quality of the treatment plan, then we eliminate this beam from the plan. The algorithm terminates basically when the relative weights of the last beam compared to other beams are insignificant or the replacement of an eliminated beam does not improve the plan. This concept was applied to three two-dimensional phantoms and each plan was compared to a standard equally spaced IMRT plan in terms of dose distributions, dose-volume histograms, and objective function values. The results show improvements in both target dose uniformity and critical organ sparing often with a fewer number of beams than standard equally spaced beam plans.

Segment-based dose optimization using a genetic algorithm

Intensity modulated radiation therapy (IMRT) inverse planning is conventionally done in two steps. Firstly, the intensity maps of the treatment beams are optimized using a dose optimization algorithm. Each of them is then decomposed into a number of segments using a leaf-sequencing algorithm for delivery. An alternative approach is to pre-assign a fixed number of field apertures and optimize directly the shapes and weights of the apertures. While the latter approach has the advantage of eliminating the leaf-sequencing step, the optimization of aperture shapes is less straightforward than that of beamlet-based optimization because of the complex dependence of the dose on the field shapes, and their weights. In this work we report a genetic algorithm for segment-based optimization. Different from a gradient iterative approach or simulated annealing, the algorithm finds the optimum solution from a population of candidate plans. In this technique, each solution is encoded using three chromosomes: one for the position of the left-bank leaves of each segment, the second for the position of the right-bank and the third for the weights of the segments defined by the first two chromosomes. The convergence towards the optimum is realized by crossover and mutation operators that ensure proper exchange of information between the three chromosomes of all the solutions in the population. The algorithm is applied to a phantom and a prostate case and the results are compared with those obtained using beamlet-based optimization. The main conclusion drawn from this study is that the genetic optimization of segment shapes and weights can produce highly conformal dose distribution. In addition, our study also confirms previous findings that fewer segments are generally needed to generate plans that are comparable with the plans obtained using beamlet-based optimization. Thus the technique may have useful applications in facilitating IMRT treatment planning.

Nontumor integral dose variation in conventional radiotherapy treatment planning

Treatment planning involves selecting delivery parameters that distribute the dose to nontumor tissue in such a way as to minimize the risk of complications. This work studied the relationship between nontumor integral dose (NTID), the fractional energy deposited in nontumor tissue, and a variety of delivery parameters for three clinical cases: nasopharynx, pancreas, and prostate. Integral dose for an organ of uniform density is simply the product of the organ density, volume, and mean dose. For each case, conventional plans were generated with 2, 4, 8, 12 and 36 equally spaced beams. All plans were normalized to the same tumor mean dose (< 3%), which is equivalent to the same tumor integral dose. For the pancreas and prostate cases, the patients were assumed to be uniform density. For the nasopharynx case, bones and air cavities were outlined and each assigned a uniform non-unit density. With four or more beams and clinical margin values, the variation in NTID was < 1% as a function of number of beams. With eight or more beams, the variation was < 0.2%. Reducing the beam margin decreased the NTID because less normal tissue was irradiated. However, the effect of the number of beams on NTID was independent of margin size. Higher energy beams reduced the NTID, as expected, and the effect was independent of the number of beams. With four or more beams, variation in beam direction changed NTID by less than 1.5%. Changing beam weights changed NTID by < 2% for plans with four to eight beams. For the body sites studied, the majority of energy was deposited in nontumor tissue, ranging from 72% in the nasopharynx case to 97% for the prostate case. The NTID decreased with increasing tumor size for similar anatomic sizes and increased with increasing size of anatomical region for similar tumor size. Finally, the effect of heterogeneity-corrected doses on the NTID was found to be < 3% for the nasopharynx case. These data support the hypothesis that the NTID is approximately independent of beam orientation or relative weighting when many beams are used. Optimization, therefore, can only find the best distribution of dose; it cannot reduce the energy imparted. NTID may be useful in establishing an upper bound on the quality of plan that can be achieved by optimization.