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PubMed2001

Verification of dynamic intensity-modulated beam deliveries in canine subjects.

Our objective in this work was to assess the precision and degree of accuracy with which intensity modulated radiation therapy (IMRT) can deliver highly localized dose distributions to tumors near critical structures using the dynamic sliding window technique. Measurements of dose distribution were performed both in vivo and in vitro using a combination of dosimeters [thermoluminescent dosimeters (TLD's), films, and diodes]. In vivo measurements were performed in two groups of purpose-bred dogs: one receiving four-field three-dimensional (3D) conformal treatment and the other receiving IMRT. The algorithms used in the inverse planning process included the Macro Pencil Beam (MPB) model and Projections onto Convex Sets (POCS). Single beam measurements were performed in phantoms to verify the accuracy of monitor unit settings required for delivering the desired doses. The composite doses from the delivery of the seven beam intensity modulated plans were measured in phantoms and cadavers, Biological end points (spinal cord toxicity and neurologic deficits due to irradiation) were evaluated at the end of one year to determine the spatial accuracy of the IMRT treatments over a fractionated course in live subjects. Results in single beam measurements were used at first to improve the dose calculation and translation algorithms. Results of the measurements for the delivery of all seven beams in phantoms confirmed that the system was capable of accurate spatial and dosimetric IMRT delivery. The in vivo results showed dramatic differences between control and IMRT-treated dogs, with the IMRT group showing no adverse effects and the control animals showing severe spinal cord injuries due to irradiation. The measurements presented in this paper have helped to verify the successful and accurate delivery of IMRT in a clinically related model using the University of Washington Medical Center (UWMC) system.

Algorithms↗
PubMed2001

Delivery of intensity-modulated radiation therapy with a conventional multileaf collimator: comparison of dynamic and segmental methods.

Intensity-modulated radiation therapy (IMRT) can be delivered with a conventional multileaf collimator (MLC), either in dynamic mode (DMLC) or in segmental mode (SMLC, also known as "step-and-shoot"). The advantage of DMLC is its ability to deliver the desired intensity profile produced by inverse planning with a high degree of fidelity. The SMLC method, on the other hand, resembles treatment with multiple static fields, and can be more easily verified. However, the use of SMLC requires that the desired profile be approximated by discrete levels of intensity, which may lead to degradation in the delivered dose distribution. Clearly, the results of SMLC delivery depend on the number of levels and the spatial resolution of the intensity distribution. In this work, we compare the DMLC method and the SMLC method employing different numbers of levels and different spatial resolutions. Three disease sites were studied: prostate, nasopharynx, and breast, with three cases for each. In general, a 5- to 10-level SMLC plan produced results comparable to that from a DMLC plan. The target coverage is improved by increasing the number of levels while critical organs are better protected with finer spatial resolutions. The beam-on-time (MUs) requirement for SMLC was approximately 20% less than DMLC, but the delivery time (in minutes) was about twice as long. Thus, the choice depends on many factors including machine capability, quality assurance, target coverage, critical organ protection, beam-on-time, delivery time, and other clinical considerations.

Breast Neoplasms↗
PubMed2002

Incorporation of realistic delivery limitations into dynamic MLC treatment delivery.

The clinical implementation of IMRT involves the use of a number of complex software-based systems, typically including an inverse planning system, a leaf sequencer, and a computer-controlled treatment delivery system. The inverse planning system determines the desired fluence patterns, the leaf sequencer translates those fluence maps into leaf trajectories, and the control system delivers those trajectories. While verification of intensity-modulated treatment fields has focused primarily on the dosimetric aspects of delivery, accurate delivery of the intended fluence distribution is dependent upon both the leaf sequencer and delivery control systems. Leaf sequencing algorithms typically do not incorporate many control system limitations, and this can lead to discrepancies between planned and delivered sequences. In this work, simple and complex fields were sequenced for the dynamic sliding window technique using different leaf speeds and tolerance settings to identify various limitations of the accelerator control system. This work was conducted on a Varian 2100 EX equipped with a Millennium 120 leaf MLC. The identified limitations were then incorporated into the sequencing algorithm using a limiting leaf velocity (less than the maximum leaf velocity), the leaf position tolerance, and the communications delay in the control system. Collision avoidance in leaf pairs was found to depend on a control system-enforced minimum gap between leaves and led to acceleration effects. By incorporating these effects into the leaf sequencing algorithm, dynamic sliding-window leaf sequences were produced which did not require beam interruptions or dose rate modulations for the parameter values used in calculating the sequence (dose rate, tolerance, leaf speed, and total monitor units). Incorporation of control system limitations into the leaf sequencing algorithm results in IMRT fields that are delivered with the prescribed constant dose rate, require less time to deliver, and have well-defined, calculable transmission dose characteristics.

Acceleration↗
PubMed2002

Multiple local minima in IMRT optimization based on dose-volume criteria.

Multiple local minima traps are known to exist in dose-volume and dose-response objective functions. Nevertheless, their presence and consequences are not considered impediments in finding satisfactory solutions in routine optimization of IMRT plans using gradient methods. However, there is often a concern that a significantly superior solution may exist unbeknownst to the planner and that the optimization process may not be able to reach it. We have investigated the soundness of the assumption that the presence of multiple minima traps can be ignored. To find local minima, we start the optimization process a large number of times with random initial intensities. We investigated whether the occurrence of local minima depends upon the choice of the objective function parameters and the number of variables and whether their existence is an impediment in finding a satisfactory solution. To learn about the behavior of multiple minima, we first used a symmetric cubic phantom containing a cubic target and an organ-at-risk surrounding it to optimize the beam weights of two pairs of parallel-opposed beams using a gradient technique. The phantom studies also served to test our software. Objective function parameters were chosen to ensure that multiple minima would exist. Data for 500 plans, optimized with random initial beam weights, were analyzed. The search process did succeed in finding the local minima and showed that the number of minima depends on the parameters of the objective functions. It was also found that the consequences of local minima depended on the number of beams. We further searched for the multiple minima in intensity-modulated treatment plans for a head-and-neck case and a lung case. In addition to the treatment plan scores and the dose-volume histograms, we examined the dose distributions and intensity patterns. We did not find any evidence that multiple local minima affect the outcome of optimization using gradient techniques in any clinically significant way. Our study supports the notion that multiple minima should not be an impediment to finding a good solution when gradient-based optimization techniques are employed. Changing the parameters for the objective function had no observable effect on our findings.

Dose-Response Relationship, Radiation↗
PubMed2002

Dosimetric performance of an enhanced dose range radiographic film for intensity-modulated radiation therapy quality assurance.

Film-based quality assurance (QA) is an important element of any intensity modulated radiation therapy (IMRT) program. XV2 film is often used for IMRT QA, however, it has saturation and energy response limitations which hinder accurate film dosimetry. A new commercially released ready-pack film has been introduced that has an extended dose range (EDR2), reportedly allowing measured doses above 600 cGy without saturation. Also, this film may have less energy dependence due to its composition. The purpose of this paper is to study and compare the two types of film with respect to absolute dose accuracy for IMRT plans, percent depth dose accuracy for square fields between 2 and 20 cm, ability to measure composite plan isodoses and single beam fluence maps for IMRT cases, and sensitivity to processor variations over time. In 19 IMRT patient QA tests, the EDR2 film was able to achieve an absolute dose accuracy of better than 2% vs over 4% for XV2 film. The EDR2 film was able to reproduce ionization chamber and diode-measured percent depth doses to 20 cm depth generally to within 1% over the range of field sizes tested compared to about 10% for the XV2 film. When compared to calculations, EDR2 film agreed better than XV2 film for both composite plan isodoses and single beam fluence intensity maps. The EDR2 film was somewhat more resistant to processor changes over time than the XV2 film, with a standard deviation of dose reproducibility of less than 2% compared to 6%, respectively.

Equipment Failure Analysis↗
PubMed2002

Smoothing intensity-modulated treatment delivery under hardware constraints.

A method is developed to smooth intensity-modulated beam delivery while considering hardware constraints. The method uses matrix algebra to model MLC leaf motion and hardware constraints such as interleaf digitization, synchronization requirements, and intersegment field abutment to deliver intensity modulated beam sequences. It was implemented and demonstrated for simulated and clinical intensity modulated cases. The simulated cases included intensity distributions from 3 x 3 to 30 x 30 in dimension with 1,000 intensity levels. The clinical examples included four treatments sites: prostate, head and neck, lung, and esophagus cancers. In particular, we studied the relationships between the intensity levels, segment numbers and their influence on the dose-volume histograms of the inversely optimized IMRT treatment plans. It was found that a significant reduction in the leaf segment numbers was achieved by applying the smoothing approach. The effects were found to be more significant for the unconstrained delivery than for the constrained delivery. The effects were also found to be more sensitive for the complex intensity distributions such as the head-and-neck cases than for the less complex ones such as the prostate cases. These results demonstrated the feasibility of maintaining inversely optimized treatment plans under acceptable tolerance levels while smoothing IMRT treatments with hardware constraints.

Algorithms↗
PubMed2003

Validation of dynamic MLC-controller log files using a two-dimensional diode array.

Intensity-modulated radiation therapy (IMRT) delivered with multi-leaf collimator (MLC) in the step-and-shoot mode uses multiple static MLC segments to achieve intensity modulation. For typical IMRT treatment plans, significant numbers of segments are delivered with monitor units (MUs) of much less than 10. Verification of the ability of the linear accelerator (linac) to deliver small MU segments accurately is an important step in the IMRT commissioning and quality assurance (QA) process. Recent studies have reported large discrepancies between the intended and delivered segment MUs. These discrepancies could potentially cause large errors in the delivered patient dose. We have undertaken a systematic study to evaluate the accuracy of the dynamic MLC log files, which are created automatically by our commercial MLC workstation after each delivery, in recording the fractional MU delivered in the step-and-shoot mode. Two linac models were evaluated with simple-geometry leaf sequences and delivered with different total MUs and different nominal dose rates. A commercial two-dimensional diode array was used for the measurement. Large discrepancies between the intended and delivered segment MUs were found. The discrepancies were larger for small MU segments at higher dose rate, with some small MU segments completely undelivered. The recorded fractional MUs in the log files were found to agree with what was delivered within the limits of our experimental uncertainty. Our results indicate that it is important to verify the delivery accuracy of small MU segments that could potentially occur in a patient treatment and that the log files are useful in checking the integrity of the linac delivery once validated. Thus validated log files can be used as a QA tool for general IMRT delivery and patient-specific plan verification.

Documentation↗
PubMed2003

MAGIC-type polymer gel for three-dimensional dosimetry: intensity-modulated radiation therapy verification.

A new type of polymer gel dosimeter, which responds well to absorbed dose even when manufactured in the presence of normal levels of oxygen, was recently described by Fong et al. [Phys. Med. Biol. 46, 3105-3113 (2001)] and referred to by the acronym MAGIC. The aim of this study was to investigate the feasibility of using this new type of gel for intensity-modulated radiation therapy (IMRT) verification. Gel manufacturing was carried out in room atmosphere under normal levels of oxygen. IMRT inverse treatment planning was performed using the Helios software. The gel was irradiated using a linear accelerator equipped with a dynamic multileaf collimator, and intensity modulation was achieved using sliding window technique. The response to absorbed dose was evaluated using magnetic resonance imaging. Measured and calculated dose distributions were compared with regard to in-plane isodoses and dose volume histograms. In addition, the spatial and dosimetric accuracy was evaluated using the gamma formalism. Good agreement between calculated and measured data was obtained. In the isocenter plane, the 70% and 90% isodoses acquired using the different methods are mostly within 2 mm, with up to 3 mm disagreement at isolated points. For the planning target volume (PTV), the calculated mean relative dose was 96.8 +/- 2.5% (1 SD) and the measured relative mean dose was 98.6 +/- 2.2%. Corresponding data for an organ at risk was 34.4 +/- 0.9% and 32.7 +/- 0.7%, respectively. The gamma criterion (3 mm spatial/3% dose deviation) was fulfilled for 94% of the pixels in the target region. Discrepancies were found in hot spots the upper and lower parts of the PTV, where the measured dose was up to 11% higher than calculated. This was attributed to sub optimal scatter kernels used in the treatment planning system dose calculations. Our results indicate great potential for IMRT verification using MAGIC-type polymer gel.

Ascorbic Acid↗
PubMed2003

Guidance document on delivery, treatment planning, and clinical implementation of IMRT: report of the IMRT Subcommittee of the AAPM Radiation Therapy Committee.

Intensity-modulated radiation therapy (IMRT) represents one of the most significant technical advances in radiation therapy since the advent of the medical linear accelerator. It allows the clinical implementation of highly conformal nonconvex dose distributions. This complex but promising treatment modality is rapidly proliferating in both academic and community practice settings. However, these advances do not come without a risk. IMRT is not just an add-on to the current radiation therapy process; it represents a new paradigm that requires the knowledge of multimodality imaging, setup uncertainties and internal organ motion, tumor control probabilities, normal tissue complication probabilities, three-dimensional (3-D) dose calculation and optimization, and dynamic beam delivery of nonuniform beam intensities. Therefore, the purpose of this report is to guide and assist the clinical medical physicist in developing and implementing a viable and safe IMRT program. The scope of the IMRT program is quite broad, encompassing multileaf-collimator-based IMRT delivery systems, goal-based inverse treatment planning, and clinical implementation of IMRT with patient-specific quality assurance. This report, while not prescribing specific procedures, provides the framework and guidance to allow clinical radiation oncology physicists to make judicious decisions in implementing a safe and efficient IMRT program in their clinics.

Algorithms↗
PubMed2003

Fuzzy logic guided inverse treatment planning.

A fuzzy logic technique was applied to optimize the weighting factors in the objective function of an inverse treatment planning system for intensity-modulated radiation therapy (IMRT). Based on this technique, the optimization of weighting factors is guided by the fuzzy rules while the intensity spectrum is optimized by a fast-monotonic-descent method. The resultant fuzzy logic guided inverse planning system is capable of finding the optimal combination of weighting factors for different anatomical structures involved in treatment planning. This system was tested using one simulated (but clinically relevant) case and one clinical case. The results indicate that the optimal balance between the target dose and the critical organ dose is achieved by a refined combination of weighting factors. With the help of fuzzy inference, the efficiency and effectiveness of inverse planning for IMRT are substantially improved.

Algorithms↗
PubMed2003

Beam orientation optimization for IMRT by a hybrid method of the genetic algorithm and the simulated dynamics.

We have developed a new method for beam orientation optimization in intensity-modulated radiation therapy (IMRT). The problem of beam orientation optimization in IMRT is solved by a decoupled two-step iterative process: (1) optimization of the intensity profiles for given beam configurations; (2) selection of optimal beam configurations based on the ranking by an objective function score for the results of the intensity profile optimization. The simulated dynamics algorithm is used for the intensity profile optimization. This algorithm enforces both the hard constraints and dose-volume constraints. A genetic algorithm is used to select beam orientation configurations. The method has been tested for both a simulated and clinical case, and the results show that beam orientation optimization significantly improved IMRT plans within a time period that is clinically acceptable. The results also show the dependence of the optimal orientation configurations on the prescribed constraints. In addition, beam orientation optimization by the method described here can provide multiple plans with similar dose distributions. This degeneracy characteristic can be exploited to our advantage in introducing additional planning objectives, e.g., the smoothness of intensity profiles, for the selection of the optimal plan among the degenerate configurations for treatment delivery.

Algorithms↗
PubMed2003

A dose delivery verification method for conventional and intensity-modulated radiation therapy using measured field fluence distributions.

Treatment verification has been a weak link in external beam radiation therapy. As new and more complicated treatment techniques, such as intensity-modulated radiation therapy (IMRT), are implemented into clinical practice, verifying the accuracy of treatment delivery becomes increasingly important. Existing methods for treatment verification are highly labor intensive. We have developed a method for verifying the delivery of external beam radiotherapy and implemented the methodology into a system consisting of both hardware and software components. The system uses grayscale images acquired on the treatment machine from the planned treatment beams. From these images, the photon fluence distribution of each beam is derived. These measured photon fluence maps are then used as input to a separate dose calculation engine to compute the delivered absolute dose and the dose distribution in the same patient, assuming that the patient is set up as required by the treatment plan. The dose distribution generated from the measured fluence maps can then be compared to that of the treatment plan. Software tools, such as overlaying isodose curves generated with this method on those imported from the plan, dose difference maps, dose difference volume histograms, and three-dimensional perspective views of the dose differences, have also been developed. The system thus provides a means to verify the dose, the dose prescription, and the monitor units applied. The potential exists with a suitable electronic portal imaging system to reduce the quality assurance efforts, especially for IMRT.

Algorithms↗
PubMed2004

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.

Algorithms↗
PubMed2004

Clinical implementation of intensity-modulated tangential beam irradiation for breast cancer.

A Monte Carlo based intensity-modulated radiation therapy (IMRT) treatment planning system has been developed and used for breast treatment. An iterative method was used for optimization to generate IMRT plans and a step-and-shoot technique was used for beam delivery. The patient setup and incident beam directions were the same as those for conventional tangential photon treatment. The weights for the opposed beamlets in the two tangential beams were determined first by the doses at the depths of the maximum dose at both sides to minimize hot spots. The intensity of an individual beamlet pair was then optimized based on the dose at the midplane. Fine tuning was made to achieve optimal target dose uniformity and to reduce the dose to the heart when necessary. The final dose calculations were performed using the Monte Carlo method and the plans were verified by phantom measurements. The dose distributions and dose-volume-histograms of IMRT plans were compared with those of conventional plans that were generated using a commercial treatment planning system and recalculated using an in-house Monte Carlo system for the first 25 patients. The dose comparisons showed that the percentage volume receiving more than 95% of the prescription dose (V95) and the percentage volume receiving more than 100% of the prescription dose (V100) for the clinical target volume (CTV) of IMRT plans were about the same as those of conventional plans. The percentage volume receiving more than 105% of the prescription dose (V105) for the CTV was reduced from 23.1% to 7.9% on average. The percentage volume of the lung receiving more than 20 Gy dose (V20 Gy) during the entire treatment was reduced by about 10%. The percentage volume of the heart receiving more than 30 Gy dose (V30 Gy) is reduced from 3.3% to 0.3%. Further studies revealed that a less than 5 degrees change in couch angle and collimator angle at patient setup had no significant effect on the dose coverage of CTV but had significant effect on the dose to the lung and heart. The study on the effect of beam spoiler showed that it increased the dose at the buildup region by 0- 13% that varies with location. The machine output linearity and stability for small monitor unit delivery of Siemens accelerators used for this study was checked and found to be suitable for breast IMRT. The total effect of variations was calculated to be less than 1% for typical breast treatments. The beam delivery time was increased by about 2 min compared with conventional tangential treatments. The whole treatment including patient setup and beam delivery can be completed in a 15 min slot. The IMRT technique has been proven practical for breast treatment clinically. The results showed that tangential IMRT improved the dose homogeneity in the breast and reduced the dose to the lung and heart.

Algorithms↗
PubMed2004

A new smoothing procedure to reduce delivery segments for static MLC-based IMRT planning.

In the application of pixel-based intensity-modulated radiation therapy (IMRT) using the step-and-shoot delivery method, one major difficulty is the prolonged delivery time. In this study, we present an integrated IMRT planning system that involves a simple smoothing method to reduce the complexity of the beam profiles. The system consists of three main steps: (a) an inverse planning process based on a least-square dose-based cost function; (b) smoothing of the intensity maps; (c) reoptimization of the segment weights. Step (a) obtains the best plan with the lowest cost value using a simulated annealing optimization algorithm with discrete intensity levels. Step (b) takes the intensity maps obtained from (a) and reduces the complexity of the maps by smoothing the adjacent beamlet intensities. During this process each beamlet is assigned a structure index based on anatomical information. A smoothing update is applied to average adjacent beamlets with the same index. To control the quality of the plan, a predefined clinical protocol is used as an acceptance criterion. The smoothing updates that violate the criterion are rejected. After the smoothing process, the segment weights are reoptimized in step (c) to further improve the plan quality. Three clinical cases were studied using this system: a medulloblastoma, a prostate cancer, and an oropharyngeal carcinoma. While the final plans demonstrate a degradation of the original plan quality, they still meet the plan acceptance criterion. On the other hand, the segment numbers or delivery times are reduced by 40%, 20%, and 20% for the three cases, respectively.

Algorithms↗
PubMed1997

The optimum intensities for multiple static multileaf collimator field compensation.

A method of determining the optimum beam intensities for compensation using multiple static multileaf collimator fields is presented. In this method a histogram of the number of beam pixels against beam intensity is generated for the intensity-modulated beam (IMB). The intensity of each beam to be used is chosen to minimize the mean square deviation between each bin in the histogram and the closest beam intensity. This method has been applied to sample IMBs possessing one maximum and two maxima. For both cases, the use of uniform beam intensity increments is shown to be close to optimal. In the case with two maxima, the efficacy of irradiating both peaks simultaneously, rather than separately, has been studied and shown to be of potential benefit. The optimum intensities for an IMB for breast radiotherapy are also presented.

Humans↗
PubMed2000

Beam orientation optimization in intensity-modulated radiation treatment planning.

Beam direction optimization is an important problem in radiation therapy. In intensity modulated radiation therapy (IMRT), the difficulty for computer optimization of the beam directions arises from the fact that they are coupled with the intensity profiles of the incident beams. In order to obtain the optimal incident beam directions using iterative or stochastic methods, the beam profiles ought to be optimized after every change of beam configuration. In this paper we report an effective algorithm to optimize gantry angles for IMRT. In our calculation the gantry angles and the beam profiles (beamlet weights) were treated as two separate groups of variables. The gantry angles were sampled according to a simulated annealing algorithm. For each sampled beam configuration, beam profile calculation was done using a fast filtered backprojection (FBP) method. Simulated annealing was also used for beam profile optimization to examine the performance of the FBP for beam orientation optimization. Relative importance factors were incorporated into the objective function to control the relative importance of the target and the sensitive structures. Minimization of the objective function resulted in the best possible beam orientations and beam profiles judged by the given objective function. The algorithm was applied to several model problems and the results showed that the approach has potential for IMRT applications.

Algorithms↗
PubMed2003

Use of intensity modulation for missing tissue compensation of pediatric spinal fields.

Irradiation of the cranio-spinal axis is often one of the treatment modalities of certain childhood cancers, e.g., medulloblastoma. In order to achieve a uniform dose to the spinal cord, missing tissue compensators are required. In the past, our practice was to fabricate compensators out of strips of lead. We report on the use of intensity modulated fields to achieve the desired compensation. Seven cases of pediatric cancer whose treatment involved irradiation of the cranio-spinal axis had compensators designed using a beam intensity modulation method rather than making mechanical compensators. The compensators only adjusted for missing tissue along the spinal axis. Comparisons between calculated and measured doses were made at depth in phantoms and on the surface of the patient. The intensity modulated fields were delivered using a step-and-shoot delivery on an Elekta SL20 accelerator equipped with multileaf collimator. The intensity-modulated compensators provided more flexibility in design than the physical compensator method. Finer intensity steps were achievable, more accurate dose distributions were able to be calculated, and adjustments during treatment, e.g., junction changes, were more easily implemented. Convolution/superposition dose calculations were within +/-3% of measurements. Intensity modulated fields are a practical and more efficient method of delivering uniform doses to the spine in pediatric cancer treatments. They provide many advantages over mechanical compensators with regard to time and flexibility.

Algorithms↗