Standard Collimator Research Articles

The Design and Manufacture of an Annular Variable-Focusing Collimator for Highsensitivity Brain SPECT

Sensitivity near the center of the brain is critical for some clinical applications of brain SPECT, especially for those applications which require dynamic imaging. We have designed and built a novel collimator for the CeraSPECT dedicated brain SPECT system which uses variable focusing to increase the sensitivity for central regions of its field of view. The sensitivity at the center of the field of view is increased by a factor of two compared to the standard three-segment parallel-hole collimator; this sensitivity gain is achieved without compromising spatial resolution.

Performance of a novel collimator for high‐sensitivity brain SPECT

We assessed improvements in performance in detection and estimation tasks due to a novel brain single photon computed tomography collimator. Data were acquired on the CeraSPECT scanner using both new and standard collimators. The new variable focusing collimator SensOgrade samples the projections unequally, with central regions more heavily represented, to compensate for attenuation of counts from central brain structures. Furthermore, it utilizes more of the cylindrical crystal surface. Two phantom studies were performed. The first phantom was a 21-cm-diameter cylindrical background containing nine spheres ranging from 0.5 to 5 cm3 in volume. 99mTc sphere to background activity ratio was 10:1. Twenty-nine 10-min datasets were acquired with each collimator. The second phantom was the Radiology Support Devices (Long Beach, CA) striatal phantom with striatal-background ratios of 10:1 on the left and 5:1 on the right. Twenty-nine 4-min datasets were acquired with each collimator. Perfusion imaging using 99mTc-HMPAO was also performed in three healthy volunteers using both collimators under identical simulations. Projections were reconstructed by filtered backprojection with an unwindowed ramp filter. The nonprewhitening matched filter signal-to-noise ratio (NPW-SNR) was computed as a surrogate for human performance in detecting spherical lesions. Sphere activity concentration, radius, and location coordinates were simultaneously estimated by fitting images to an assumed model using an iterative nonlinear algorithm. Resolution recovery was implicit in the estimation procedure, as the point spread function was incorporated into the model. NPW-SNR for sphere detection was 1.5 to 2 times greater with the new collimator; for the striatal phantom the improvement in SNR was 54%. The SNR for estimating sphere activity concentration improved by 46 to 89% for spheres located more than 5 cm from the phantom center. Images acquired with the standard collimator were too noisy in the central regions to allow estimation of sphere activity. In 99mTc-HMPAO human studies, SNR was improved by 21 to 41% in the cortex, 66% in the basal ganglia, and 74% in the thalamus. The new collimator leads to substantially improved detection and estimation performance throughout the brain. The higher sensitivity will be particularly important for dynamic imaging.

Phase-II study on stereotactic radiotherapy of locally advanced pancreatic carcinoma

Background and purposeThe majority of patients with pancreatic cancer have advanced disease at the time of diagnosis and are not amenable for surgery. Stereotactic radiotherapy (SRT) may be an alternative treatment for patients with locally advanced disease. The effect of SRT was investigated in the present phase-II trial. Patients and methodsTwenty-two patients with locally advanced and surgically non-resectable, histological proven pancreatic carcinoma were included into the trial. The patients were immobilized by the Elekta stereotactic body frame (SBF) or a custom made body frame. SRT was given on standard LINAC with standard multi-leaf collimator. Central dose was 15Gy×3 within 5–10 days. ResultsEvaluation of response was found to be very difficult due to radiation and tumour related tissue reaction. Only two patients (9%) were found to have a partial response (PR), the remaining had no change (NC) or progression (PD) after treatment. Six patients had local tumour progression, but only one patient had an isolated local failure without simultaneous distant metastasis. Median time to local or distant progression was 4.8 months. Median survival time was 5.7 months and only 5% were alive 1 year after treatment. Acute toxicity reported 14 days after treatment was pronounced. There was a significant deterioration of performance status (P=0.008), more nausea (P=0.001) and more pain (P=0.008) after 14 days compared with base-line. However, 8 of 12 patients (66%) improved in performance status, scored less nausea, pain, or needed less analgesic drugs at 3 months after treatment. Four patients suffered from severe mucositis or ulceration of the stomach or duodenum and one of the patients had a non-fatal ulcer perforation of the stomach. ConclusionsSRT was associated with poor outcome, unacceptable toxicity and questionable palliative effect and cannot be recommended for patients with advanced pancreatic carcinoma.

SU-FF-T-408: Regular Lesions Stereotactic Treatment: Physical and Dosimetrical Comparison Between Circular and Mini/micro Multileaf Collimators

Purpose: The comparison of stereotactic treatments for small spherical and ellipsoidal intracranial lesions using three different collimators with single isocenter: the standard circular collimators and two dynamic multileaf collimators (DMLC) with 3 mm and 5 mm leaf thickness, micro and mini DMLC respectively. Method and Materials: Spherical and ellipsoidal lesions of different sizes were designed to evaluate treatments with collimators under consideration. For spherical lesions with diameter from 15 mm up to 35 mm a treatment with 9 arcs of 140 degrees was performed. For ellipsoidal lesions treated with circular collimators, different combinations of treatment variables were studied to achieve 80% isodose surface conformation: number of arcs, gantry start/stop angles, couch angles and arc spacing. This treatment was matched up to 9 arcs with the two DMLCs. For the comparison geometrical (penumbra, difference between the target volume and 80% isodose volume and conformal indexes) and radiobiological (EUD, TCP and NTCP) parameters were used. Results: Circular collimators and micro DMLC behave similarly with spherical targets in terms of conformal indexes and TCP/NTCP, but EUD and 20% isodose volume are greater for micro DMLC. In the case of ellipsoidal target TCP/NTCP are comparable, EUD is greater for micro DMLC but conformal indexes are higher for circular collimators. The 20% isodose volume is less with micro DMLC; the difference, however, is entirely due to the wider penumbra along the deformation axis with circular collimators. The same considerations are valid for targets with diameters ⩾ 35 mm, where mini DMLC becomes competitive versus circular collimator. Conclusion: The analysis shows that micro and mini DMLC are more functional for non spherical lesions. Circular collimators however are widely used and yield sharper dose fall off along directions perpendicular to the deformation axis and thus are preferable in the case of neighbourhood of organs at risk.

Crystal collimation as an option for the large hadron colliders

We present a study in which we propose using a bent crystal and the channeling mechanism for halo collimation in hadron colliders. Experimental results carried out at IHEP with 70GeV protons and detailed Monte Carlo calculations highlight that a crystal may well resist the highly radioactive environment of a large hadron collider and can be profitably used to steer halo protons out of the main stream. A crystal, integrated in a collimation system may serve either as a diagnostic tool for precise alignment of a traditional massive collimator, made of amorphous dense material or directly as a primary scraper. In this second option, simulations performed specifically in the case of the CERN large hadron collider (LHC) show that the halo intensity would fall off by more than an order of magnitude with respect to a standard collimation system.

Stereotactic radiosurgery for brain AVMs: Role of interobserver variation in target definition on digital subtraction angiography

We evaluated the extent of interobserver variation in contouring arteriovenous malformations (AVMs) on digital subtraction angiography (DSA) with respect to volume, spatial localization, and dosimetry and correlated our findings with the clinical outcome. Thirty-one patients who had undergone radiosurgery for brain AVMs were studied. Six clinicians independently contoured the nidus on the original DSA. As a measure of variation, the ratio between the volumes of agreement and the corresponding encompassing volumes, as well as the absolute positional shift between the individual target volumes were derived. Using the original treatment plan, the dosimetric coverage of the individually contoured volumes with standard collimators was compared with a similar plan using dynamic conformal arcs. The mean contoured nidus volume was 3.6 +/- 5.6 cm3. The mean agreement ratio was 0.45 +/- 0.18 for all possible pairs of observers. The mean absolute positional shift between individually contoured volumes was 2.8 +/- 2.6 mm. These differences were more marked in previously treated groups and tended to be more pronounced in those with treatment failure. The mean coverage of the individual volumes by the 80% prescription isodose was 88.1% +/- 3.2% using conventional collimators and 78.9% +/- 4.4% using dynamic conformal arcs (p = 0.001). Substantial interobserver variations exist when contouring brain AVMs on DSA for the purpose of radiosurgical planning. Such variations may result in underdosage to the AVM and, thereby, contribute to treatment failure. The consequences of contouring variations may increase with the use of more conformal radiosurgical techniques.

Cardiac single-photon emission-computed tomography using combined cone-beam/fan-beam collimation

The objective of this work is to increase system sensitivity in cardiac single-photon emission-computed tomography (SPECT) studies without increasing patient imaging time. For imaging the heart, convergent collimation offers the potential of increased sensitivity over that of parallel-hole collimation. However, if a cone-beam collimated gamma camera is rotated in a planar orbit, the projection data obtained are not complete. Two cone-beam collimators and one fan-beam collimator are used with a three-detector SPECT system. The combined cone-beam/fan-beam collimation provides a complete set of data for image reconstruction. The imaging geometry is evaluated using data acquired from phantom and patient studies. For the Jaszazck cardiac torso phantom experiment, the combined cone-beam/fan-beam collimation provided 1.7 times greater sensitivity than standard parallel-hole collimation (low-energy high-resolution collimators). Also, phantom and patient comparison studies showed improved image quality. The combined cone-beam/fan-beam imaging geometry with appropriate weighting of the two data sets provides improved system sensitivity while measuring sufficient data for artifact free cardiac images.

Impact of interobserver variability in contouring of AVMs

Delineation of the nidus of brain AVMs on digital subtraction angiography (DSA) forms the basis of target definition for radiosurgery (RS). However, interclinician discrepancy in the assessment of nidus position and volume exists. In this study, the magnitude of the interobserver variability as well as its dosimetric and clinical impact are assessed. DSAs from 31 patients who underwent RS for a brain AVM were selected for nidus contouring by six experienced clinicians (2 neurosurgeons, 2 radiation oncologists, 2 neuroradiologists) using BrainScan v5.2 software (BrainLAB AG, Heimstetten, Germany). All patients had a minimum follow-up of 3 years or earlier complete obliteration. The interobserver variability was assessed by 1. the ratio between the volume of agreement (VOA6) of all observers and the corresponding encompassing volume (ECV); 2. the same ratio for all possible pairs of observers (VOA2/ECV2); 3. translation of the center of mass of all individual volumes. Dosimetric consequences were calculated for both the use of standard collimators and for dynamic conformal arcs. The original treatment plan was evaluated for dosimetric coverage of the VOA6. In one patient no VOA6 could be determined due to a large contouring variation. The mean ratio between VOA6 and ECV6 was 0.19 ± 0.14. For all possible pairs of clinicians, the VOA6/ECV6 was 0.45 ± 0.14. The mean translation between the center of mass of the individual volumes was 2.6 mm. The mean coverage of the individual volumes by the 80% ( = prescription isodose)and 75% isodoses was 88.1% and 90.2%, respectively, when standard round collimators were used. Using dynamic arc technique, this was significantly (p = 0.002) lower (78.9% and 82,6%, respectively). Complete obliteration was seen in 24/31 (77%) cases at a mean of 33 months. There was no significant relationship with nidus volume (p = 0.09) and marginal SRS dose (p = 0.09). The VOA6 was incompletely covered by the original treatment plan in 3/31 patients (10%); In 1/24 with complete obliteration (4%) and 2/7 with incomplete obliteration (29%). Failure to obliterate did not correlate with VOA6/ECV6 (p = 0.69), VOA2/ECV2 (p = 0.56), but was significantly correlated with the mean coverage of individual volumes by the 80% isodose (p = 0.004). There is a significant interobserver variability in the contouring of the nidus on DSA and a better definition is required. This variability may result in underdosage. The clinical impact of this will increase with the use of more conformal stereotactic techniques

Inherent smoothness of intensity patterns for intensity modulated radiation therapy generated by simultaneous projection algorithms

The efficient delivery of intensity modulated radiation therapy (IMRT) depends on finding optimized beam intensity patterns that produce dose distributions, which meet given constraints for the tumour as well as any critical organs to be spared. Many optimization algorithms that are used for beamlet-based inverse planning are susceptible to large variations of neighbouring intensities. Accurately delivering an intensity pattern with a large number of extrema can prove impossible given the mechanical limitations of standard multileaf collimator (MLC) delivery systems. In this study, we apply Cimmino's simultaneous projection algorithm to the beamlet-based inverse planning problem, modelled mathematically as a system of linear inequalities. We show that using this method allows us to arrive at a smoother intensity pattern. Including nonlinear terms in the simultaneous projection algorithm to deal with dose–volume histogram (DVH) constraints does not compromise this property from our experimental observation. The smoothness properties are compared with those from other optimization algorithms which include simulated annealing and the gradient descent method. The simultaneous property of these algorithms is ideally suited to parallel computing technologies.

Neutron fibres and possible applications to NCT

We summarize previous researches regarding neutron guides of small transverse cross-section (neutron fibres), smaller than those of the standard hollow guides and collimators employed currently. Those studies may not be widely known in the neutron capture therapy (NCT) community, but they may be interesting for it. Such neutron fibres could allow to deliver and concentrate neutron beams selectively in regions of size smaller than 1 mm. We present new estimates and point out and discuss some new possible specific applications of those neutron fibres, which would not replace standard NCT but could supplement it. Thus, we entertain the possibility that neutron fibres could be useful for additional therapies (in typical NCT durations) of: (i) rather small tumours, (ii) thin borders of tumours. The use of these neutron fibres could reduce the undesirable delivery of radiation to healthy tissue around regions with malignant tissue.

The effect of leaf width and sampling distance on the “stair-stepping” of field borders defined by multileaf collimators

Standard multileaf collimators (MLCs) are now available with 1.0 and 0.5 cm leaf widths. The aim of this work is to compare the dose-undulation and effective penumbra of field edges formed by these MLC leaf widths and to determine how reducing the sampling distance (centre-to-centre distance between adjacent MLC leaves) for the 1.0 cm leaf width compares to the smaller leaf width. The undulation of the 50% isodose line and the 80-20% and 80-30% effective penumbra were compared for a field edge angled at 45 degrees to the MLC leaf motion direction at 8 cm depth. The larger leaf width field was also segmented to form field edges with 0.5, 0.33 and 0.2 cm sampling distance. Random setup variation of 2 mm standard deviation was also incorporated. Dose undulation was 1.5 mm for the 0.5 cm MLC leaf width compared to 4.5 mm for the 1.0 cm width. The 80-20% effective penumbra was 2 mm less for the 0.5 cm leaf width and the 80-30% effective penumbra was approximately 3 mm less. When random setup variation was incorporated the 0.5 cm leaf width isodoses were straight compared with approximately 3 mm undulation for the larger MLC. Reducing the sampling distance for the 1.0 cm MLC leaf width to 0.33 cm resulted in penumbra only slightly greater than the 0.5 cm leaf width and removed the undulation. Effective penumbra and dose undulation are reduced for the 0.5 cm leaf width compared to a 1.0 cm leaf width. Reducing the sampling distance for the 1.0 cm MLC leaf can approximate the 0.5 cm leaf width, at the expense of longer treatment times, and increased quality assurance investment.

Gamma camera PET with low energy collimators: characterization and correction of scatter

Imaging of myocardial viability with fluorodeoxyglucose (FDG) is possible with positron emission tomography (PET) and with SPECT. The image resolution from SPECT is poor but the data is reported to provide clinical information comparable to PET. Studies have just begun to appear using gamma camera PET and either axial slat collimators or open frame graded absorbers to image myocardial viability. Alternatively, it may be possible to use standard low energy collimators en detecting coincidences. Although image quality may suffer, it may be possible to devise methods such that no clinical information is lost. Such an approach also paves the way for dual isotope sequential or simultaneous imaging of coincidence and single photons. Here, we characterize the scatter fraction and scatter distribution of gamma camera PET with low energy collimators, and investigate the improvements possible with a convolution-subtraction scatter correction scheme. Monte Carlo simulations, line sources, a realistic phantom, and a human study were used. The scatter fraction was found to be almost identical to that obtained with axial slat collimators on a triple head gamma camera hybrid PET scanner. Images acquired with low energy collimators were degraded but still of good quality compared to acquisitions using axial collimation. The scatter correction scheme showed a degree of improvement over reconstructions without scatter correction. This approach is useful not only toward making sequential or simultaneous dual isotope imaging possible, but may also be useful to save time in a busy clinic that does both SPECT scans and cardiac FDG studies, since collimators would not need to be changed.

Dynamic intensity modulated electron arc therapy using standard multi-leaf collimators

Dynamic intensity modulated electron arc therapy using standard multi-leaf collimators

Design, construction, and performance of an asymmetrical collimator for a cobalt unit

Purpose: Besides four linear accelerators, our institute has a 100-cm SAD cobalt unit which has some specific and useful features for radiotherapy. The unit is equipped with a electronic portal imaging device (EPID) and an asymmetrical collimator to perform similar treatment techniques as on the linear accelerators, using the same shielding and half-beam techniques. The design, construction, and performance of the asymmetrical collimator are described. Methods and Materials: The new design includes the doubling of the drive and read-outs for both X and Y jaws. Spare parts of the standard collimator provided by the manufacturer were used as much as possible. Special trimmers were designed to allow asymmetry to the center of the field. The trimmers are removable, but the design allows the use of trimmers, wedges, and shadow tray simultaneously. Results: Transmission through the trimmers is less than 5% of the dose at d max. The use of the trimmers extends the source to diaphragm distance to 53 cm, resulting in a smaller penumbra as compared to the standard collimator. Without the trimmers, the maximum field size remains unchanged, i.e., 40 × 40 cm 2; with the trimmers, it is 38 × 36 cm 2. Percentage depth doses and output factors were similar to the standard collimator. Conclusion: The modified collimator is compact and allows use of the same shielding blocks as the linear accelerators, providing the same treatment techniques and capabilities. This simplifies an exchange of patients between our treatment machines.

Tomographie par ouverture codée sous deux incidences orthogonales

Standard collimators have the disadvantage of providing limited resolution and sensitivity for gamma detection. Coded-aperture tomography is a method that can help to improve these characteristics: the standard LEUHR parallel collimator is replaced by a multi-pinhole mask that increases the spatial resolution and sensitivity and provides the possibility of obtaining dynamic and multi-spectral tomographic images. Reconstruction is obtained via a planar projection of a single object through the mask, thereby permitting contiguous sections parallel to the detector to be obtained. This reconstruction was based on an itérative Maximum Likelihood-Expectation Maximization (ML-EM) algorithm that takes into account this particular acquisition geometry. The acquisition sensitivity of this method was estimated to be ten times higher than that of a Low Energy-High Resolution (LEUHR) collimator, and allowed reconstruction of the following volume: 133.30 × 176.70 × 130.33 mm 3, (l × w × h) divided into nineteen sections of 19 × 25 pixels, corresponding to 7.0 voxels. Reconstructions of numerical and physical simulations of a single object were made. The resolution in the section and in depth was measured at 7 mm, i.e., the same size as one voxel. The uniformity was still not satisfactory. Scattering and attenuation correction still had to be carried out to obtain quantitative values.

The treatment planning of segmental, conformal stereotactic radiosurgery utilizing a standard multileaf collimator

Over a period of approximately 3 years, our institution has implemented and refined a system of Stereotactic Radiosurgery (SRS) which utilizes the standard multi leaf collimator (MLC) of the Scanditronix MM50 Racetrack Microtron and treats in an arrangement of segmental “pseudo-arcs.” This system employs a commercial BRW-based stereotactic frame which is mounted to the treatment table. With the exception of the table-mounted frame hardware there have been no modifications to the treatment machine to accommodate these treatments. By use of standard evaluation parameters (e.g., treatment time, planning time, dose conformance and dose heterogeneity ratios) this system compares quite favorably with reported data from institutions treating SRS with either a GammaKnife or a standard linear accelerator with tertiary collimators.

Dose characteristics of in-house-built collimators for stereotactic radiotherapy with a linear accelerator

Dose characteristics of a stereotactic radiotherapy unit based on a standard Varian Clinac 4/100 4 MV linear accelerator, in-house-built Lipowitz collimators and the SMART stereotactic radiotherapy treatment planning software have been determined. Beam collimation is constituted from the standard collimators of the linear accelerator and a tertiary collimation consisting of a replaceable divergent Lipowitz collimator. Four collimators with isocentre diameters of 15, 25, 35 and 45 mm, respectively, were constructed. Beam characteristics were measured in air, acrylic or water with ionization chamber, photon diode, electron diode, diamond detector and film. Monte Carlo simulation was also applied. The radiation leakage under the collimators was less than 1% at 50 mm depth in water. Specific beam characteristics for each collimator were imported to SMART and dose planning with five non-coplanar converging arcs separated by angles was performed for treatment of a RANDO phantom. Dose verification was made with TLD and radiochromic film. The in-house-built collimators were found to be suitable for stereotactic radiotherapy and patient treatments with this system are in progress.

Reconstruction of multiple line source attenuation maps

A simple configuration for a transmission source for single photon emission computed tomography (SPECT) is proposed, which utilizes a series of collimated line sources parallel to the axis of rotation of the camera. The detector is equipped with a standard parallel hole collimator. The authors have demonstrated that this type of source configuration can be used to generate sufficient data for the reconstruction of the attenuation map when using 8-10 line sources spaced by 3.5-4.5 cm for a 30/spl times/40 cm detector placed 65 cm from the sources. Transmission data for a nonuniform thorax phantom was simulated, then binned and reconstructed using filtered backprojection (FBP) and iterative methods. It was found that optimum maps were obtained with data binned into 2-3 bins and FBP reconstruction. The activity in the source was investigated for uniform and exponential activity distributions. The effect of gaps and overlaps of the neighboring fan beams was also studied. A prototype of the line source system has been built and the experimental verification of the simulation results has started.

The use of tertiary collimation for spinal irradiation with extended SSD electron fields

The spine can be treated with an electron beam when its maximum posterior depth is within the therapeutic range of electrons. Electron fields treated at extended source-to-surface distances (SSDs), however, have larger penumbras and narrower therapeutic isodose widths relative to those at the standard SSD of 100 cm. We investigated the use of tertiary collimation close to the patient surface for these fields to sharpen the penumbra, minimizing dose to normal tissue and maximizing target coverage. Using film dosimetry in a polystyrene phantom, we measured the dose distribution for electron fields at extended SSD under varying collimation conditions. Beam penumbra and therapeutic width as a function of depth, SSD, applicator insert size, and tertiary collimator opening were determined. We also measured the dose distributions in the junction region for various gaps between x-ray fields and an electron field as used for craniospinal irradiation. Measurements show that tertiary collimation close to the skin surface reduces penumbra width (lateral distance between the 90 and 20% isodose lines) by 56% and increases therapeutic isodose width (lateral width of the 90% isodose curve) by 25% at a depth of dmax relative to standard collimation. These numbers change to 23 and 13%, respectively, at an average depth of the spine. When lateral brain and posterior spine fields are used to irradiate the entire craniospinal axis, tertiary collimation aids in reducing the volume of the hot spot in the junction region by as much as 10% without compromising target coverage. Tertiary collimation for extended SSD electron fields is preferable to standard collimation in order to minimize dose to normal tissue and increase target coverage. This technique can be applied to both spinal and craniospinal irradiation. Support structures for the tertiary blocking are needed because the weight of the lead is usually too great for placement on the skin.

Planning and delivering high doses to targets surrounding the spinal cord at the lower neck and upper mediastinal levels: static beam-segmentation technique executed with a multileaf collimator

Background and purpose. It remains a technical challenge to limit the dose to the spinal cord below tolerance if, in head and neck or thyroid cancer, the planning target volume reaches to a level below the shoulders. In order to avoid these dose limitations, we developed a standard plan involving Beam Intensity Modulation (BIM) executed by a static technique of beam segmentation. In this standard plan, many machine parameters (gantry angles, couch position, relative beam and segment weights) as well as the beam segmentation rules were identical for all patients. Materials and methods. The standard plan involved: the use of static beams with a single isocenter; BIM by field segmentation executable with a standard Philips multileaf collimator; virtual simulation and dose computation on a general 3D-planning system (Sherouse's GRATIS®); heuristic computation of segment intensities and optimization (improving the dose distribution and reducing the execution time) by human intelligence. The standard plan used 20 segments spread over 8 gantry angles plus 2 non-segmented wedged beams (2 gantry angles). Results. The dose that could be achieved at the lowest target voxel, without exceeding tolerance of the spinal cord (50 Gy at highest voxel) was 70–80 Gy. The in-target 3D dose-inhomogeneity was ≈25%. The shortest time of execution of a treatment (22 segments) on a patient (unpublished) was 25 min. Conclusions. A heuristic model has been developed and investigated to obtain a 3D concave dose distribution applicable to irradiate targets in the lower neck and upper mediastinal regions. The technique spares efficiently the spinal cord and allows the delivery of higher target doses than with conventional techniques. It can be planned as a standard plan using conventional 3D-planning technology. The routine clinical implementation is performed with commercially available equipment, however, at the expense of extended execution times.