RESUMO
BACKGROUND AND PURPOSE: The FLASH effect has been validated in different preclinical experiments with electrons (eFLASH) and protons (pFLASH) operating at an average dose rate above 40 Gy/s. However, no systematic intercomparison of the FLASH effect produced by eFLASHvs. pFLASH has yet been performed and constitutes the aim of the present study. MATERIALS AND METHODS: The electron eRT6/Oriatron/CHUV/5.5 MeV and proton Gantry1/PSI/170 MeV were used to deliver conventional (0.1 Gy/s eCONV and pCONV) and FLASH (≥110 Gy/s eFLASH and pFLASH) dose rates. Protons were delivered in transmission. Dosimetric and biologic intercomparisons were performed using previously validated dosimetric approaches and experimental murine models. RESULTS: The difference between the average absorbed dose measured at Gantry 1 with PSI reference dosimeters and with CHUV/IRA dosimeters was -1.9 % (0.1 Gy/s) and + 2.5 % (110 Gy/s). The neurocognitive capacity of eFLASH and pFLASH irradiated mice was indistinguishable from the control, while both eCONV and pCONV irradiated cohorts showed cognitive decrements. Complete tumor response was obtained after an ablative dose of 20 Gy delivered with the two beams at CONV and FLASH dose rates. Tumor rejection upon rechallenge indicates that anti-tumor immunity was activated independently of the beam-type and the dose-rate. CONCLUSION: Despite major differences in the temporal microstructure of proton and electron beams, this study shows that dosimetric standards can be established. Normal brain protection and tumor control were produced by the two beams. More specifically, normal brain protection was achieved when a single dose of 10 Gy was delivered in 90 ms or less, suggesting that the most important physical parameter driving the FLASH sparing effect might be the mean dose rate. In addition, a systemic anti-tumor immunological memory response was observed in mice exposed to high ablative dose of electron and proton delivered at CONV and FLASH dose rate.
Assuntos
Produtos Biológicos , Neoplasias , Terapia com Prótons , Humanos , Animais , Camundongos , Prótons , Elétrons , Dosagem Radioterapêutica , RadiometriaRESUMO
Objective.4D dose reconstruction in proton therapy with pencil beam scanning (PBS) typically relies on a single pre-treatment 4DCT (p4DCT). However, breathing motion during the fractionated treatment can vary considerably in both amplitude and frequency. We present a novel 4D dose reconstruction method combining delivery log files with patient-specific motion models, to account for the dosimetric effect of intra- and inter-fractional breathing variability.Approach.Correlation between an external breathing surrogate and anatomical deformations of the p4DCT is established using principal component analysis. Using motion trajectories of a surface marker acquired during the dose delivery by an optical tracking system, deformable motion fields are retrospectively reconstructed and used to generate time-resolved synthetic 4DCTs ('5DCTs') by warping a reference CT. For three abdominal/thoracic patients, treated with respiratory gating and rescanning, example fraction doses were reconstructed using the resulting 5DCTs and delivery log files. The motion model was validated beforehand using leave-one-out cross-validation (LOOCV) with subsequent 4D dose evaluations. Moreover, besides fractional motion, fractional anatomical changes were incorporated as proof of concept.Main results.For motion model validation, the comparison of 4D dose distributions for the original 4DCT and predicted LOOCV resulted in 3%/3 mm gamma pass rates above 96.2%. Prospective gating simulations on the p4DCT can overestimate the target dose coverage V95%by up to 2.1% compared to 4D dose reconstruction based on observed surrogate trajectories. Nevertheless, for the studied clinical cases treated with respiratory-gating and rescanning, an acceptable target coverage was maintained with V95%remaining above 98.8% for all studied fractions. For these gated treatments, larger dosimetric differences occurred due to CT changes than due to breathing variations.Significance.To gain a better estimate of the delivered dose, a retrospective 4D dose reconstruction workflow based on motion data acquired during PBS proton treatments was implemented and validated, thus considering both intra- and inter-fractional motion and anatomy changes.
Assuntos
Neoplasias Pulmonares , Terapia com Prótons , Humanos , Terapia com Prótons/métodos , Estudos Retrospectivos , Estudos Prospectivos , Tomografia Computadorizada Quadridimensional/métodos , Movimento (Física) , Carmustina , Planejamento da Radioterapia Assistida por Computador/métodosRESUMO
Background and purpose: The FLASH effect has been validated in different preclinical experiments with electrons (eFLASH) and protons (pFLASH) operating at a mean dose rate above 40 Gy/s. However, no systematic intercomparison of the FLASH effect produced by e vs. pFLASH has yet been performed and constitutes the aim of the present study. Materials and methods: The electron eRT6/Oriatron/CHUV/5.5 MeV and proton Gantry1/PSI/170 MeV were used to deliver conventional (0.1 Gy/s eCONV and pCONV) and FLASH (≥100 Gy/s eFLASH and pFLASH) irradiation. Protons were delivered in transmission. Dosimetric and biologic intercomparisons were performed with previously validated models. Results: Doses measured at Gantry1 were in agreement (± 2.5%) with reference dosimeters calibrated at CHUV/IRA. The neurocognitive capacity of e and pFLASH irradiated mice was indistinguishable from the control while both e and pCONV irradiated cohorts showed cognitive decrements. Complete tumor response was obtained with the two beams and was similar between e and pFLASH vs. e and pCONV. Tumor rejection was similar indicating that T-cell memory response is beam-type and dose-rate independent. Conclusion: Despite major differences in the temporal microstructure, this study shows that dosimetric standards can be established. The sparing of brain function and tumor control produced by the two beams were similar, suggesting that the most important physical parameter driving the FLASH effect is the overall time of exposure which should be in the range of hundreds of milliseconds for WBI in mice. In addition, we observed that immunological memory response is similar between electron and proton beams and is independent off the dose rate.
RESUMO
Objective.4D dose calculation (4DDC) for pencil beam scanned (PBS) proton therapy is typically based on phase-sorting of individual pencil beams onto phases of a single breathing cycle 4DCT. Understanding the dosimetric limitations and uncertainties of this approach is essential, especially for the realistic treatment scenario with irregular free breathing motion.Approach.For three liver and three lung cancer patient CTs, the deformable multi-cycle motion from 4DMRIs was used to generate six synthetic 4DCT(MRI)s, providing irregular motion (11/15 cycles for liver/lung; tumor amplitudes â¼4-18 mm). 4DDCs for two-field plans were performed, with the temporal resolution of the pencil beam delivery (4-200 ms) or with 8 phases per breathing cycle (500-1000 ms). For the phase-sorting approach, the tumor center motion was used to determine the phase assignment of each spot. The dose was calculated either using the full free breathing motion or individually repeating each single cycle. Additionally, the use of an irregular surrogate signal prior to 4DDC on a repeated cycle was simulated. The CTV volume with absolute dose differences >5% (Vdosediff>5%) and differences in CTVV95%andD5%-D95%compared to the free breathing scenario were evaluated.Main results.Compared to 4DDC considering the full free breathing motion with finer spot-wise temporal resolution, 4DDC based on a repeated single 4DCT resulted inVdosediff>5%of on average 34%, which resulted in an overestimation ofV95%up to 24%. However, surrogate based phase-sorting prior to 4DDC on a single cycle 4DCT, reduced the averageVdosediff>5%to 16% (overestimationV95%up to 19%). The 4DDC results were greatly influenced by the choice of reference cycle (Vdosediff>5%up to 55%) and differences due to temporal resolution were much smaller (Vdosediff>5%up to 10%).Significance.It is important to properly consider motion irregularity in 4D dosimetric evaluations of PBS proton treatments, as 4DDC based on a single 4DCT can lead to an underestimation of motion effects.
Assuntos
Neoplasias Pulmonares , Terapia com Prótons , Humanos , Prótons , Planejamento da Radioterapia Assistida por Computador/métodos , Tomografia Computadorizada Quadridimensional/métodos , Movimento (Física) , Terapia com Prótons/métodos , Respiração , Neoplasias Pulmonares/diagnóstico por imagem , Neoplasias Pulmonares/radioterapiaRESUMO
Recently, proton therapy treatments delivered with ultra-high dose rates have been of high scientific interest, and the Faraday cup (FC) is a promising dosimetry tool for such experiments. Different institutes use different FC designs, and either a high voltage guard ring, or the combination of an electric and a magnetic field is employed to minimize the effect of secondary electrons. The authors first investigate these different approaches for beam energies of 70, 150, 230 and 250 MeV, magnetic fields between 0 and 24 mT and voltages between -1000 and 1000 V. When applying a magnetic field, the measured signal is independent of the guard ring voltage, indicating that this setting minimizes the effect of secondary electrons on the reading of the FC. Without magnetic field, applying the negative voltage however decreases the signal by an energy dependent factor up to 1.3% for the lowest energy tested and 0.4% for the highest energy, showing an energy dependent response. Next, the study demonstrates the application of the FC up to ultra-high dose rates. FC measurements with cyclotron currents up to 800 nA (dose rates of up to approximately 1000 Gy s-1) show that the FC is indeed dose rate independent. Then, the FC is applied to commission the primary gantry monitor for high dose rates. Finally, short-term reproducibility of the monitor calibration is quantified within single days, showing a standard deviation of 0.1% (one sigma). In conclusion, the FC is a promising, dose rate independent tool for dosimetry up to ultra-high dose rates. Caution is however necessary when using a FC without magnetic field, as a guard ring with high voltage alone can introduce an energy dependent signal offset.
Assuntos
Terapia com Prótons , Calibragem , Prótons , Radiometria , Reprodutibilidade dos TestesRESUMO
A deeper understanding of biological mechanisms to promote more efficient treatment strategies in proton therapy demands advances in preclinical radiation research. However this is often limited by insufficient availability of adequate infrastructures for precision image guided small animal proton irradiation. The project SIRMIO aims at filling this gap by developing a portable image-guided research platform for small animal irradiation, to be used at clinical facilities and allowing for a precision similar to a clinical treatment, when scaled down to the small animal size. This work investigates the achievable dosimetric properties of different lowest energy clinical proton therapy beams, manipulated by a dedicated portable beamline including active focusing after initial beam energy degradation and collimation. By measuring the lateral beam size in air close to the beam nozzle exit and the laterally integrated depth dose in water, an analytical beam model based on the beam parameters of the clinical beam at the Rinecker Proton Therapy Center was created for the lowest available clinical beam energy. The same approach was then applied to estimate the lowest energy beam model of different proton therapy facilities, Paul Scherrer Institute, Centre Antoine Lacassagne, Trento Proton Therapy Centre and the Danish Centre for Particle Therapy, based on their available beam commissioning data. This comparison indicated similar beam properties for all investigated sites, with emittance values of a few tens of mm·mrad. Finally, starting from these beam models, we simulated propagation through a novel beamline designed to manipulate the beam energy and size for precise small animal irradiation, and evaluated the resulting dosimetric properties in water. For all investigated initial clinical beams, similar dosimetric results suitable for small animal irradiation were found. This work supports the feasibility of the proposed SIRMIO beamline, promising suitable beam characteristics to allow for precise preclinical irradiation at clinical treatment facilities.
Assuntos
Terapia com Prótons/instrumentação , Animais , Estudos de Viabilidade , Radiometria , Dosagem Radioterapêutica , Planejamento da Radioterapia Assistida por Computador , Radioterapia Guiada por Imagem , SíncrotronsRESUMO
The literature is controversial about the scan direction dependency of interplay effects in pencil beam scanning (PBS) treatment of moving targets. A directional effect is supported by many simulation studies, whereas the experimental data are mostly limited to simple geometries, not reflecting realistically clinical treatment plans. We have compared increasingly complex treatment fields, from a homogeneous single energy layer to a more modulated lung plan, under identical experimental settings, seeking evidence for differences in motion mitigation due to the selection of primary scanning direction. In total, 120 experimental samples were taken, combining two primary scan directions and three rescanning regimes with different motion scenarios. 4D dose distributions were measured in water with a moving ionisation chamber array and compared to those of a stationary delivery using 2D gamma analysis. Each plan has been verified twice for the same rescanning regime and motion scenario, changing the meandering direction in between to scan perpendicularly to, or along, the target motion. Additionally, machine log files of the lung plan, together with 4DCT data, were used to calculate the dose distribution that such deliveries would have produced in the patient. The primary meandering direction has a clear influence on measured dose distributions when considering a single energy layer. Introducing spot weight modulation and multiple energy layers however, makes the dynamic of interplay more complex and difficult to predict. Overall, gamma (3%/3 mm) differences between scanning along or orthogonal to the target motion follow a normal distribution [Formula: see text] when considering multiple motion scenarios and rescanning regimes. Nevertheless, data spread [Formula: see text] is significant enough such that, for individual experiments and set-ups, a dependency may be observed even if this is not a general result. Patient reconstructed doses follow the same trend, the two primary scan directions producing statistically insignificant differences in dose distributions in terms of conformity or homogeneity. Except for extremely simplified cases of mono-energetic and homogeneous treatment fields, the interplay effect has been found to be only marginally influenced by the choice of the primary scanning direction.
Assuntos
Terapia com Prótons/métodos , Planejamento da Radioterapia Assistida por Computador/métodos , Tomografia Computadorizada Quadridimensional , Humanos , Neoplasias Hepáticas/diagnóstico por imagem , Neoplasias Hepáticas/fisiopatologia , Neoplasias Hepáticas/radioterapia , Movimento , Dosagem RadioterapêuticaRESUMO
For radiotherapy, it is crucial to guarantee that the delivered dose matches the planned dose. Therefore, patient specific quality assurance (QA) of absolute dose distributions is necessary. Here, we investigate the potential of replacing patient specific QA for pencil beam scanned proton therapy with Monte Carlo simulations. First, the set-up of the automated Monte Carlo model is presented with an emphasis on the absolute dose validation. Second, the absolute dose results obtained from the Monte Carlo simulation for a comprehensive set of patient fields are compared to patient specific QA measurements. Absolute doses measured with the Farmer chamber are shown to be 1.4% higher than the doses measured with the Semiflex chamber. For single energy layers, Monte Carlo simulated doses are 2.1% ± 0.4% lower than the ones measured with the ionization chamber and 1.1% ± 1.0% lower than measurements compared to patient field verification measurements. After rescaling to account for this 1.1% discrepancy, 98 fields (94.2%) agree within 2% to measurements, the maximum difference being 2.3%. In conclusion, an automated, easy-to-use Monte Carlo calculation system has been set up. This system reproduced patient specific QA results over a wide range of cases, showing that the time consuming measurements could be reduced or even replaced using Monte Carlo simulations without jeopardizing treatment quality.
Assuntos
Simulação por Computador/normas , Terapia com Prótons/métodos , Planejamento da Radioterapia Assistida por Computador/métodos , Humanos , Método de Monte Carlo , Terapia com Prótons/normas , Dosagem Radioterapêutica , Planejamento da Radioterapia Assistida por Computador/normasRESUMO
The lateral fall-off is crucial for sparing organs at risk in proton therapy. It is therefore of high importance to minimize the penumbra for pencil beam scanning (PBS). Three optimisation approaches are investigated: edge-collimated uniformly weighted spots (collimation), pencil beam optimisation of uncollimated pencil beams (edge-enhancement) and the optimisation of edge collimated pencil beams (collimated edge-enhancement). To deliver energies below 70 MeV, these strategies are evaluated in combination with the following pre-absorber methods: field specific fixed thickness pre-absorption (fixed), range specific, fixed thickness pre-absorption (automatic) and range specific, variable thickness pre-absorption (variable). All techniques are evaluated by Monte Carlo simulated square fields in a water tank. For a typical air gap of 10 cm, without pre-absorber collimation reduces the penumbra only for water equivalent ranges between 4-11 cm by up to 2.2 mm. The sharpest lateral fall-off is achieved through collimated edge-enhancement, which lowers the penumbra down to 2.8 mm. When using a pre-absorber, the sharpest fall-offs are obtained when combining collimated edge-enhancement with a variable pre-absorber. For edge-enhancement and large air gaps, it is crucial to minimize the amount of material in the beam. For small air gaps however, the superior phase space of higher energetic beams can be employed when more material is used. In conclusion, collimated edge-enhancement combined with the variable pre-absorber is the recommended setting to minimize the lateral penumbra for PBS. Without collimator, it would be favourable to use a variable pre-absorber for large air gaps and an automatic pre-absorber for small air gaps.
Assuntos
Imagens de Fantasmas , Terapia com Prótons/instrumentação , Terapia com Prótons/métodos , Planejamento da Radioterapia Assistida por Computador/normas , Humanos , Método de Monte Carlo , Dosagem Radioterapêutica , Planejamento da Radioterapia Assistida por Computador/métodosRESUMO
Motion-induced range changes and incorrectly placed dose spots strongly affect the quality of pencil-beam-scanned (PBS) proton therapy, especially in thoracic tumour sites, where density changes are large. Thus motion-mitigation techniques are necessary, which must be validated in a realistic patient-like geometry. We report on the development and characterisation of a dynamic, anthropomorphic, thorax phantom that can realistically mimic thoracic motions and anatomical features for verifications of proton and photon 4D treatments. The presented phantom is of an average thorax size, and consists of inflatable, deformable lungs surrounded by a skeleton and skin. A mobile 'tumour' is embedded in the lungs in which dosimetry devices (such as radiochromic films) can be inserted. Motion of the tumour and deformation of the thorax is controlled via a custom made pump system driving air into and out of the lungs. Comprehensive commissioning tests have been performed to evaluate the mechanical performance of the phantom, its visibility on CT and MR imaging and its feasibility for dosimetric validation of 4D proton treatments. The phantom performed well on both regular and irregular pre-programmed breathing curves, reaching peak-to-peak amplitudes in the tumour of <20 mm. Some hysteresis in the inflation versus deflation phases was seen. All materials were clearly visualised in CT scans, and all, except the bone and lung components, were MRI visible. Radiochromic film measurements in the phantom showed that imaging for repositioning was required (as for a patient treatment). Dosimetry was feasible with Gamma Index agreements (4%/4 mm) between film dose and planned dose >90% in the central planes of the target. The results of this study demonstrate that this anthropomorphic thorax phantom is suitable for imaging and dosimetric studies in a thoracic geometry closely-matched to lung cancer patients under realistic motion conditions.
Assuntos
Imagens de Fantasmas , Terapia com Prótons/métodos , Respiração , Técnicas de Imagem de Sincronização Respiratória/métodos , Humanos , Imageamento por Ressonância Magnética/métodos , Movimento (Física) , Fótons , Radiometria/métodos , Tórax/diagnóstico por imagem , Tomografia Computadorizada por Raios X/métodosRESUMO
Proton therapy, especially in the form of pencil beam scanning (PBS), allows for the delivery of highly conformal dose distributions for complex tumor geometries. However, due to scattering of protons inside the patient, lateral dose gradients cannot be arbitrarily steep, which is of importance in cases with organs at risk (OARs) in close proximity to, or overlapping with, planning target volumes (PTVs). In the PBS approach, physical pencil beams are planned using a regular grid orthogonal to the beam direction. In this work, we propose an alternative to this commonly used approach where pencil beams are placed on an irregular grid along concentric paths based on the target contour. Contour driven pencil beam placement is expected to improve dose confirmation by allowing the optimizer to best enhance the penumbra of irregularly shaped targets using edge enhancement. Its effectiveness has been shown to improve dose confirmation to the target volume and reduce doses to OARs in head-and-neck planning studies. Furthermore, the deliverability of such plans, as well as the dosimetric improvements over conventional grid-based plans, have been confirmed in first phantom based verifications.
Assuntos
Terapia com Prótons/métodos , Planejamento da Radioterapia Assistida por Computador/métodos , Radioterapia de Intensidade Modulada/métodos , Humanos , Órgãos em Risco , Imagens de Fantasmas , Terapia com Prótons/normas , Doses de Radiação , Dosagem Radioterapêutica , Planejamento da Radioterapia Assistida por Computador/normas , Radioterapia de Intensidade Modulada/normasRESUMO
Pencil beam scanning proton therapy allows the delivery of highly conformal dose distributions by delivering several thousand pencil beams. These beams have to be individually optimised and accurately delivered requiring a significant quality assurance workload. In this work we describe a toolkit for independent dose calculations developed at Paul Scherrer Institut which allows for dose reconstructions at several points in the treatment workflow. Quality assurance based on reconstructed dose distributions was shown to be favourable to pencil beam by pencil beam comparisons for the detection of delivery uncertainties and estimation of their effects. Furthermore the dose reconstructions were shown to have a sensitivity of the order of or higher than the measurements currently employed in the clinical verification procedures. The design of the independent dose calculation tool allows for a high modifiability of the dose calculation parameters (e.g. depth dose profiles, angular spatial distributions) allowing for a safe environment outside of the clinical treatment planning system for investigating the effect of such parameters on the resulting dose distributions and thus distinguishing between different contributions to measured dose deviations. The presented system could potentially reduce the amount of patient-specific quality assurance measurements which currently constitute a bottleneck in the clinical workflow.
Assuntos
Neoplasias de Cabeça e Pescoço/radioterapia , Processamento de Imagem Assistida por Computador/métodos , Terapia com Prótons/métodos , Algoritmos , Encéfalo/patologia , Humanos , Modelos Teóricos , Método de Monte Carlo , Garantia da Qualidade dos Cuidados de Saúde , Planejamento da Radioterapia Assistida por ComputadorRESUMO
The first goal of this paper is to clarify the reference conditions for the reference dosimetry of clinical proton beams. A clear distinction is made between proton beam delivery systems which should be calibrated with a spread-out Bragg peak field and those that should be calibrated with a (pseudo-)monoenergetic proton beam. For the latter, this paper also compares two independent dosimetry techniques to calibrate the beam monitor chambers: absolute dosimetry (of the number of protons exiting the nozzle) with a Faraday cup and reference dosimetry (i.e. determination of the absorbed dose to water under IAEA TRS-398 reference conditions) with an ionization chamber. To compare the two techniques, Monte Carlo simulations were performed to convert dose-to-water to proton fluence. A good agreement was found between the Faraday cup technique and the reference dosimetry with a plane-parallel ionization chamber. The differences-of the order of 3%-were found to be within the uncertainty of the comparison. For cylindrical ionization chambers, however, the agreement was only possible when positioning the effective point of measurement of the chamber at the reference measurement depth-i.e. not complying with IAEA TRS-398 recommendations. In conclusion, for cylindrical ionization chambers, IAEA TRS-398 reference conditions for monoenergetic proton beams led to a systematic error in the determination of the absorbed dose to water, especially relevant for low-energy proton beams. To overcome this problem, the effective point of measurement of cylindrical ionization chambers should be taken into account when positioning the reference point of the chamber. Within the current IAEA TRS-398 recommendations, it seems advisable to use plane-parallel ionization chambers-rather than cylindrical chambers-for the reference dosimetry of pseudo-monoenergetic proton beams.
Assuntos
Terapia com Prótons/normas , Radiometria/normas , Radioterapia de Alta Energia/normas , Calibragem , Humanos , Terapia com Prótons/instrumentação , Radiometria/instrumentação , Dosagem Radioterapêutica/normas , Radioterapia de Alta Energia/instrumentaçãoRESUMO
Intensity-modulated proton therapy (IMPT) delivered with beam scanning is currently available at a limited number of proton centers. However, a simplified form of IMPT, the technique of field 'patching', has long been a standard practice in proton therapy centers. In field patching, different parts of the target volume are treated from different directions, i.e., a part of the tumor gets either full dose from a radiation field, or almost no dose. Thus, patching represents a form of binary intensity modulation. This study explores the limitations of the standard binary field patching technique, and evaluates possible dosimetric advantages of continuous dose modulations in IMPT. Specifics of the beam delivery technology, i.e., pencil beam scanning versus passive scattering and modulation, are not investigated. We have identified two geometries of target volumes and organs at risk (OAR) in which the use of field patching is severely challenged. We focused our investigations on two patient cases that exhibit these geometries: a paraspinal tumor case and a skull-base case. For those cases we performed treatment planning comparisons of three-dimensional conformal proton therapy (3DCPT) with field patching versus IMPT, using commercial and in-house software, respectively. We also analyzed the robustness of the resulting plans with respect to systematic setup errors of ±1 mm and range errors of ±2.5 mm. IMPT is able to better spare OAR while providing superior dose coverage for the challenging cases identified above. Both 3DCPT and IMPT are sensitive to setup errors and range uncertainties, with IMPT showing the largest effect. Nevertheless, when delivery uncertainties are taken into account IMPT plans remain superior regarding target coverage and OAR sparing. On the other hand, some clinical goals, such as the maximum dose to OAR, are more likely to be unmet with IMPT under large range errors. IMPT can potentially improve target coverage and OAR sparing in challenging cases, even when compared with the relatively complicated and time consuming field patching technique. While IMPT plans tend to be more sensitive to delivery uncertainties, their dosimetric advantage generally holds. Robust treatment planning techniques may further reduce the sensitivity of IMPT plans.