RESUMEN
PURPOSE: The goal was to provide a quantitative evaluation of the accuracy of three different fixation systems for stereotactic radiotherapy and to evaluate patients' acceptance for all fixations. METHODS: A total of 16 consecutive patients with brain tumours undergoing fractionated stereotactic radiotherapy (SCRT) were enrolled after informed consent (Clinical trials.gov: NCT00181350). Fixation systems evaluated were the BrainLAB® mask, with and without custom made bite-block (fixations S and A) and a homemade neck support with bite-block (fixation B) based on the BrainLAB® frame. The sequence of measurements was evaluated in a randomized manner with a cross-over design and patients' acceptance by a questionnaire. RESULTS: The mean three-dimensional (3D) displacement and standard deviations were 1.16 ± 0.68 mm for fixation S, 1.92 ± 1.28 and 1.70 ± 0.83 mm for fixations A and B, respectively. There was a significant improvement of the overall alignment (3D vector) when using the standard fixation instead of fixation A or B in the craniocaudal direction (p = 0.037). Rotational deviations were significantly less for the standard fixation S in relation to fixations A (p = 0.005) and B (p = 0.03). EPI imaging with off-line correction further improved reproducibility. Five out of 8 patients preferred the neck support with the bite-block. CONCLUSION: The mask fixation system in conjunction with a bite-block is the most accurate fixation for SCRT reducing craniocaudal and rotational movements. Patients favoured the more comfortable but less accurate neck support. To optimize the accuracy of SCRT, additional regular portal imaging is warranted.
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Adenoma/cirugía , Neoplasias Encefálicas/cirugía , Procesamiento de Imagen Asistido por Computador/instrumentación , Imagenología Tridimensional/instrumentación , Aceptación de la Atención de Salud , Posicionamiento del Paciente/instrumentación , Radiocirugia/instrumentación , Planificación de la Radioterapia Asistida por Computador/instrumentación , Tomografía Computarizada por Rayos X/instrumentación , Artefactos , Astrocitoma/cirugía , Humanos , Neoplasias Meníngeas/cirugía , Meningioma/cirugía , Países Bajos , Neuroma Acústico/cirugía , Neoplasias Hipofisarias/cirugía , Estudios Prospectivos , Encuestas y CuestionariosRESUMEN
Electronic portal imaging devices (EPIDs) are increasingly used for portal dosimetry applications. In our department, EPIDs are clinically used for two-dimensional (2D) transit dosimetry. Predicted and measured portal dose images are compared to detect dose delivery errors caused for instance by setup errors or organ motion. The aim of this work is to develop a model to predict dose-volume histogram (DVH) changes due to setup errors during breast cancer treatment using 2D transit dosimetry. First, correlations between DVH parameter changes and 2D gamma parameters are investigated for different simulated setup errors, which are described by a binomial logistic regression model. The model calculates the probability that a DVH parameter changes more than a specific tolerance level and uses several gamma evaluation parameters for the planning target volume (PTV) projection in the EPID plane as input. Second, the predictive model is applied to clinically measured portal images. Predicted DVH parameter changes are compared to calculated DVH parameter changes using the measured setup error resulting from a dosimetric registration procedure. Statistical accuracy is investigated by using receiver operating characteristic (ROC) curves and values for the area under the curve (AUC), sensitivity, specificity, positive and negative predictive values. Changes in the mean PTV dose larger than 5%, and changes in V90 and V95 larger than 10% are accurately predicted based on a set of 2D gamma parameters. Most pronounced changes in the three DVH parameters are found for setup errors in the lateral-medial direction. AUC, sensitivity, specificity, and negative predictive values were between 85% and 100% while the positive predictive values were lower but still higher than 54%. Clinical predictive value is decreased due to the occurrence of patient rotations or breast deformations during treatment, but the overall reliability of the predictive model remains high. Based on our predictive model, 2D transit dosimetry measurements can now directly be translated in clinically more relevant DVH parameter changes for the PTV during conventional breast treatment. In this way, the possibility to design decision protocols based on extracted DVH changes is created instead of undertaking elaborate actions such as repeated treatment planning or 3D dose reconstruction for a large group of patients.
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Algoritmos , Artefactos , Neoplasias de la Mama/radioterapia , Modelos Biológicos , Protección Radiológica/métodos , Radiometría/métodos , Planificación de la Radioterapia Asistida por Computador/métodos , Carga Corporal (Radioterapia) , Simulación por Computador , Humanos , Dosificación Radioterapéutica , Efectividad Biológica Relativa , Reproducibilidad de los Resultados , Sensibilidad y EspecificidadRESUMEN
Electronic portal imaging devices (EPIDs) are not only applied for patient setup verification and detection of organ motion but are also increasingly used for dosimetric verification. The aim of our work is to obtain accurate dose distributions from a commercially available amorphous silicon (a-Si) EPID for transit dosimetry applications. For that purpose, a global calibration model was developed, which includes a correction procedure for ghosting effects, field size dependence and energy dependence of the a-Si EPID response. In addition, the long-term stability and additional buildup material for this type of EPID were determined. Differences in EPID response due to photon energy spectrum changes have been measured for different absorber thicknesses and field sizes, yielding off-axis spectrum correction factors based on transmission measurements. Dose measurements performed with an ionization chamber in a water tank were used as reference data, and the accuracy of the dosimetric calibration model was determined for a large range of treatment conditions. Gamma values using 3% as dose-difference criterion and 3 mm as distance-to-agreement criterion were used for evaluation. The field size dependence of the response could be corrected by a single kernel, fulfilling the gamma evaluation criteria in case of virtual wedges and intensity modulated radiation therapy fields. Differences in energy spectrum response amounted up to 30%-40%, but could be reduced to less than 3% using our correction model. For different treatment fields and (in)homogeneous phantoms, transit dose distributions satisfied in almost all situations the gamma criteria. We have shown that a-Si EPIDs can be accurately calibrated for transit dosimetry purposes.
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Radiometría/instrumentación , Radiometría/métodos , Silicio , Calibración , Diseño de Equipo , Humanos , Procesamiento de Imagen Asistido por Computador , Modelos Estadísticos , Fantasmas de Imagen , Dosificación Radioterapéutica , Planificación de la Radioterapia Asistida por Computador , Reproducibilidad de los ResultadosRESUMEN
The motion of lung tumors with respiration causes difficulties in the imaging with computed tomography (CT) and positronemitted tomography (PET). Since an accurate knowledge of the position of the tumor and the surrounding tissues is needed for radiation treatment planning, it is important to improve CT/PET image acquisition. The purpose of this study was to evaluate the potential to improve image acquisition using phased attenuation correction in respiration correlated CT/PET, where data of both modalities were binned retrospectively. Respiration correlated scans were made on a Siemens Biograph Sensation 16 CT/PET scanner which was modified to make a low pitch CT scan and list mode PET scan possible. A lollipop phantom was used in the experiments. The sphere with a diameter of 3.1 cm was filled with approximately 20 MBq 18F-FDG. Three longitudinal movement amplitudes were tested: 2.5, 3.9, and 4.8 cm. After collection of the raw CT data, list mode PET data, and the respiratory signal CT/PET images were binned to ten phases with the help of in-house-built software. Each PET phase was corrected for attenuation with CT data of the corresponding phase. For comparison, the attenuation correction was also performed with nonrespiration correlated (non-RC) CT data. The volume and the amplitude of the movement were calculated for every phaseof both the CT and PET data (with phased attenuation correction). Maximum and average activity concentrations were compared between the phased and nonphased attenuation corrected PET. With a standard non-RC CT/PET scan, the volume was underestimated by as much as 46% in CT and the PET volume was overestimated to 370%. The volumes found with RC-CT/PET scanning had average deviations of 1.9% (+/- 4.8%) and 1.5% (+/- 3.4%) from the actual volume, for the CT and PET volumes, respectively. Evaluation of the maximum activity concentration showed a clear displacement in the images with non-RC attenuation correction, and activity values were on average14% (+/- 12%) lower than with phased attenuation correction. The standard deviation of the maximum activity values found in the different phases was a factor of 10 smaller when phased attenuation correction was applied. In this phantom study, we have shown that a combination of respiration correlated CT/PET scanning with application of phased attenuation correction can improve the imaging of moving objects and can lead to improved volume estimation and a more precise localization and quantification of the activity.
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Aumento de la Imagen/métodos , Pulmón/diagnóstico por imagen , Tomografía de Emisión de Positrones/métodos , Tomografía Computarizada de Emisión/métodos , Humanos , Procesamiento de Imagen Asistido por Computador , Pulmón/fisiología , Fantasmas de Imagen , Reproducibilidad de los Resultados , Mecánica Respiratoria , Sensibilidad y EspecificidadRESUMEN
Electronic portal imaging devices (EPIDs) can be used to measure a two-dimensional (2D) dose distribution behind a patient, thus allowing dosimetric treatment verification. For this purpose we experimentally assessed the accuracy of a 2D portal dose prediction model based on pencil beam scatter kernels. A straightforward derivation of these pencil beam scatter kernels for portal dose prediction models is presented based on phantom measurements. The model is able to predict the 2D portal dose image (PDI) behind a patient, based on a PDI without the patient in the beam in combination with the radiological thickness of the patient, which requires in addition a PDI with the patient in the beam. To assess the accuracy of portal dose and radiological thickness values obtained with our model, various types of homogeneous as well as inhomogeneous phantoms were irradiated with a 6 MV photon beam. With our model we are able to predict a PDI with an accuracy better than 2% (mean difference) if the radiological thickness of the object in the beam is symmetrically situated around the isocenter. For other situations deviations up to 3% are observed for a homogeneous phantom with a radiological thickness of 17 cm and a 9 cm shift of the midplane-to-detector distance. The model can extract the radiological thickness within 7 mm (maximum difference) of the actual radiological thickness if the object is symmetrically distributed around the isocenter plane. This difference in radiological thickness is related to a primary portal dose difference of 3%. It can be concluded that our model can be used as an easy and accurate tool for the 2D verification of patient treatments by comparing predicted and measured PDIs. The model is also able to extract the primary portal dose with a high accuracy, which can be used as the input for a 3D dose reconstruction method based on back-projection.
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Algoritmos , Modelos Teóricos , Fantasmas de Imagen , Planificación de la Radioterapia Asistida por Computador , Neoplasias de la Mama/radioterapia , Femenino , Humanos , Dosificación Radioterapéutica , Dispersión de RadiaciónRESUMEN
Electronic portal imaging devices (EPIDs) are mainly used for patient setup verification during treatment but other geometric properties like block shape and leaf positions are also determined. Electronic portal dosimetry allows dosimetric treatment verification. By combining geometric and dosimetric information, the data transfer between treatment planning system (TPS) and linear accelerator can be verified which in particular is important when this transfer is not carried out electronically. We have developed a pretreatment verification procedure of geometric and dosimetric treatment parameters of a 10 MV photon beam using an EPID. Measurements were performed with a CCD camera-based iView EPID, calibrated to convert a greyscale EPID image into a two-dimensional absolute dose distribution. Central field dose calculations, independent of the TPS, are made to predict dose values at a focus-EPID distance of 157.5 cm. In the same EPID image, the presence of a wedge, its direction, and the field size defined by the collimating jaws were determined. The accuracy of the procedure was determined for open and wedged fields for various field sizes. Ionization chamber measurements were performed to determine the accuracy of the dose values measured with the EPID and calculated by the central field dose calculation. The mean difference between ionization chamber and EPID dose at the center of the fields was 0.8 +/- 1.2% (1 s.d.). Deviations larger than 2.5% were found for half fields and fields with a jaw in overtravel. The mean difference between ionization chamber results and the independent dose calculation was -0.21 +/- 0.6% (1 s.d.). For all wedged fields, the presence of the wedge was detected and the mean difference in actual and measured wedge direction was 0 +/- 3 degrees (1 s.d.). The mean field size differences in X and Y directions were 0.1 +/- 0.1 cm and 0.0 +/- 0.1 cm (1 s.d.), respectively. Pretreatment monitor unit verification is possible with high accuracy and also geometric parameters can be verified using the same EPID image.
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Radiometría/métodos , Dosificación Radioterapéutica , Planificación de la Radioterapia Asistida por Computador/métodos , Algoritmos , Calibración , Iones , Modelos Teóricos , Aceleradores de Partículas , Fantasmas de Imagen , FotonesRESUMEN
In this study, we present an algorithm for three-dimensional (3-D) dose reconstruction using portal images obtained with an electronic portal imaging device (EPID). For this purpose an algorithm for 2-D dose reconstruction, which was previously developed in our institution, was adapted. The external contour of the patient was used to correct for absorption of primary photons, but the presence of inhomogeneities was not taken into account. The accuracy of the algorithm was determined by irradiating two anthropomorphic breast phantoms with 6 MV photons. The dose values derived from portal images were compared with results from 3-D dose calculations, which, in turn, were verified with data obtained with an ionization chamber and film dosimetry. It was found that the application of contour information significantly improves the accuracy of 2-D dose reconstruction. If the total dose at the isocenter plane resulting from all treatment beams is reconstructed, the average deviation from the planned dose is 0.1%+/-1.7% (1 SD). If contour information is not available, the differences increase up to +/-20% for the individual beams. In that case, the dose can only be reconstructed with reasonable accuracy when (nearly) opposing beams are used. The average deviation of the 3-D reconstructed dose from the planned dose in the irradiated volume is 1.4%+/-5.4% (1 SD). If the irradiated volume is enclosed by planes less than 5 cm distant from the isocenter plane, then the average deviation is only 0.5%+/-3.4% (1 SD). It can be concluded that the proposed algorithm for a 3-D dose reconstruction allows a determination of the dose at the isocenter plane and the dose-volume histogram with an accuracy acceptable for an independent verification of the treatment.
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Algoritmos , Neoplasias de la Mama/diagnóstico por imagen , Neoplasias de la Mama/radioterapia , Imagenología Tridimensional/métodos , Intensificación de Imagen Radiográfica/métodos , Radiometría/métodos , Planificación de la Radioterapia Asistida por Computador/métodos , Femenino , Humanos , Imagenología Tridimensional/instrumentación , Fantasmas de Imagen , Protección Radiológica/instrumentación , Protección Radiológica/métodos , Intensificación de Imagen Radiográfica/instrumentación , Radiometría/instrumentación , Dosificación Radioterapéutica , Planificación de la Radioterapia Asistida por Computador/instrumentación , Reproducibilidad de los Resultados , Medición de Riesgo/métodos , Sensibilidad y EspecificidadRESUMEN
PURPOSE: To guarantee an accurate dose delivery, within +/- 2.5%, in a Phase III randomized trial of prostate cancer irradiation (68 vs. 78 Gy) by means of a comprehensive in vivo dosimetry program. METHODS AND MATERIALS: Prostate patients are generally treated in our clinic with a 3-field isocentric technique: an 8-MV anteroposterior beam and 2 18-MV wedged laterals. All fields are shaped conformally to the PTV. Patients were randomized between two dose levels of 68 Gy and 78 Gy. During treatment, the entrance and exit dose were measured for each patient with diodes. Special 2.5-mm thick steel build-up caps were applied to make the diodes appropriate for measurements in 18-MV photon beams as well. Portal images were used to verify the correct position of the diodes and to detect and correct for gas filling in the rectum that may influence the exit dose reading. Entrance and exit dose measurements were converted to midplane dose, which was used in combination with a depth dose correction to obtain the dose at the specification point. An action level of 2.5% was applied. RESULTS: The added build-up for the diodes in the 18-MV beams resulted in correction factors that were only slightly sensitive to changes in beam setup and comparable to the corrections used in the 8-MV beams for diodes without extra build-up. The calibration factor increased almost linearly with cumulative dose: 0.7%/kGy for the 8-MV and 1.2%/kGy for the 18-MV photon beams. The introduction of average correction factors made the analysis easier, while keeping the accuracy within acceptable limits. In a period of 3 years, 225 patients were analyzed, from which 8 patients needed to be corrected. The average ratio of measured and prescribed dose was 1.009 (standard deviation [SD] 0.012) for the total group treated on two linear accelerators. When the results were analyzed per accelerator, the ratios were 1.002 (SD, 0.001) for Accelerator A and 1.015 (SD, 0.001) for Accelerator B. This difference could be attributed to the cumulative effect of three small imperfections in the performance of Accelerator B that were well within the limits of our quality assurance program. CONCLUSION: Diodes can be used for accurate in vivo dosimetry during prostate irradiation in high-energy photon beams. The dose delivery in this randomized trial is guaranteed within the 2.5% limits on an individual patient basis. This could not be achieved without the in vivo dosimetry program, despite our high-standard quality assurance program of treatment delivery.
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Neoplasias de la Próstata/radioterapia , Radioterapia Conformacional/métodos , Algoritmos , Calibración , Humanos , Masculino , Fenómenos Físicos , Física , Neoplasias de la Próstata/diagnóstico por imagen , Radiografía , Dosificación Radioterapéutica , Radioterapia Conformacional/instrumentación , Radioterapia Conformacional/normasRESUMEN
PURPOSE: Conformal radiotherapy requires accurate knowledge of the actual dose delivered to a patient. The impact of routine in vivo dosimetry, including its special requirements, clinical findings and resources, has been analysed for three conformal treatment techniques to evaluate its usefulness in daily clinical practice. MATERIALS AND METHODS: Based on pilot studies, routine in vivo dosimetry quality control (QC) protocols were implemented in the clinic. Entrance and exit diode dose measurements have been performed during two treatment sessions for 378 patients having prostate, bladder and parotid gland tumours. Dose calculations were performed with a CT-based three-dimensional treatment planning system. In our QC-protocol we applied action levels of 2.5% for the prostate and bladder tumour group and 4.0% for the parotid gland patients. When the difference between the measured dose at the dose specification point and the prescribed dose exceeded the action level the deviation was investigated and the number of monitor units (MUs) adjusted. Since an accurate dose measurement was necessary, some properties of the on-line high-precision diode measurement system and the long-term change in sensitivity of the diodes were investigated in detail. RESULTS: The sensitivity of all diodes decreased by approximately 7% after receiving an integrated dose of 10 kGy, for 4 and 8 MV beams. For 34 (9%) patients the difference between the measured and calculated dose was larger than the action level. Systematic errors in the use of a new software release of the monitor unit calculation program, limitations of the dose calculation algorithms, errors in the planning procedure and instability in the performance of the accelerator have been detected. CONCLUSIONS: Accurate in vivo dosimetry, using a diode measurement system, is a powerful tool to trace dosimetric errors during conformal radiotherapy in the range of 2.5-10%, provided that the system is carefully calibrated. The implementation of an intensive in vivo dosimetry programme requires additional staff for measurements and evaluation. The patient measurements add only a few minutes to the total treatment time per patient and guarantee an accurate dose delivery, which is a prerequisite for conformal radiotherapy.
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Radioterapia Conformacional , Humanos , Procesamiento de Imagen Asistido por Computador , Masculino , Modelos Estructurales , Neoplasias de la Parótida/diagnóstico por imagen , Neoplasias de la Parótida/radioterapia , Neoplasias de la Próstata/diagnóstico por imagen , Neoplasias de la Próstata/radioterapia , Control de Calidad , Radiometría/métodos , Radiometría/normas , Dosificación Radioterapéutica , Planificación de la Radioterapia Asistida por Computador , Radioterapia Conformacional/normas , Tomografía Computarizada por Rayos X , Neoplasias de la Vejiga Urinaria/diagnóstico por imagen , Neoplasias de la Vejiga Urinaria/radioterapiaRESUMEN
Recent investigations of the three-dimensional (3D) binocular eye positions in near vision have shown that a full characterization of vergence requires incorporation of its torsional component. The latter has a proportional relationship with horizontal vergence and elevation, causing the eyes to have intorsion in near upgaze but extorsion in near downgaze. In this study, we focus on the dynamical implementation of the torsional vergence component in both pure vergence and combined direction-depth binocular eye movements. We report on experiments in five subjects whose eye movements were recorded binocularly with the 3D magnetic search-coil technique. In pure vergence movements at a given elevation, torsional vergence increased with almost the same time course as horizontal vergence. In addition, the dynamic relationships among torsional vergence, horizontal vergence and elevation were close to static results in all subjects. In combined direction-depth movements a similar relationship held for the complete movements, but we could not firmly establish a straight-line relationship during the saccadic portion of the movement. Possible factors determining these responses are discussed. We computed the angular velocity profiles of pure vergence movements to see how tilting of the vergence angular velocity axis relative to Listing's plane generates torsional vergence. It is widely held that both saccadic and vergence movements are controlled by dedicated pulse generators specifying velocity signals. Little thought has been given to the question of how these controllers can be coordinated to yield realistic eye movements in 3D. Our finding that this tilt was close to full-angle, suggests a model in which version and vergence velocity signals are combined before the 3D neural integrator proposed by Tweed and Vilis. The implications of this scheme for the control of binocular eye movements in three dimensions are discussed, along with possible neural correlates.
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Movimientos Oculares/fisiología , Visión Binocular/fisiología , Adulto , Humanos , Masculino , Modelos BiológicosRESUMEN
In the context of Hering's equal-innervation law, this paper discusses the problem of how the three-dimensional positions of the two eyes, each expressed by a rotation vector, can be separated into contributions of the version and vergence system. As proposed by Van Rijn and Van den Berg [(1993) Vision Research, 33, 691-708], this can be done by taking the sum and difference of the position rotation vectors of each eye. In our alternative procedure the vergence signal is defined as the rotation which transforms the left eye position into the right eye position and the version signal is the common factor in both eye positions that remains after removing the vergence signal. The version and vergence contributions, defined in this way, can be interpreted straightforwardly as rotations. When Van Rijn and Van den Berg applied their definitions to their own data, they obtained the interesting result that the reconstructed version and vergence contributions were effectively limited to two dimensions (2D). The version signal was confined to Listing's plane (no torsion) whereas the vergence signal remained within a horizontal-torsional plane (no vertical vergence). They showed theoretically that a model based on 2D version/2D vergence control will indeed produce the torsional eye positions in near fixations found in their experiments. This model cannot account for a second set of data in the literature [Mok, Ro, Cadera, Crawford & Vilis (1992) Vision Research, 32, 2055-2064]. With our definitions, we found that the simple 2D version/2D vergence control strategy cannot account for the Van Rijn and Van den Berg (1993) data but is nicely compatible with the considerably smaller amount of cyclotorsion in the data collected by Mok et al. (1992). We also show that, in such a system, having 2D vergence control is compatible with minimization of torsional disparity and provides the cyclovergence signals suitable for stabilizing the eyes in the non-Listing positions caused by a vertical saccade in near vision.
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Convergencia Ocular/fisiología , Visión Binocular/fisiología , Fijación Ocular , Humanos , Matemática , Modelos Biológicos , Músculos Oculomotores/inervación , RotaciónRESUMEN
Earlier studies have shown that eye positions, recorded in subjects scanning a distant visual scene with the head in a stable position, have only two degrees of freedom (Listing's law). Due to cyclovergence, this law is modified in near-vision. Two previous quantitative studies have documented that the sign of the torsional vergence component depends systematically on elevation: when fixating a nearby target, the eyes show intorsion in up gaze, extorsion in down gaze and no cyclotorsion at some intermediate elevation level (to be denoted as the null elevation). Both studies found a linear cyclovergence/elevation relation, but disagreed on the amount of cyclotorsion. A further uncertainty is how this phenomenon develops dynamically when the binocular fixation point shifts from a far to a near position. Therefore, we have investigated the dynamic coupling between the horizontal and torsional components of vergence in human subjects who were instructed to refixate a light target after it stepped in depth. The target steps were presented at various vertical and horizontal directions relative to the straight-ahead axis of the cyclopean eye. We found that the quantitative relations among horizontal vergence, torsional vergence and elevation were intermediate between those found in the two earlier near-vision studies and that they correspond reasonably to the predictions of a model by Mok and co-workers. The cyclotorsion vergence component had about the same latency and dynamics as the horizontal component. When refixations were studied at different elevations, the torsional vergence component changed from incyclotorsion in up gaze to excyclotorsion in down gaze. In agreement with expectations derived from two quantitative models, the null elevation of cyclovergence was near the binocular primary position. Furthermore, we found no consistent additional dependence on the horizontal direction of the refixation trajectory relative to the midsaggital plane. Other experiments showed that the cyclotorsional changes accompanying convergence were not critically dependent upon the visual conditions. Quantitatively similar similar cyclotorsional components were found even in convergent refixations executed in full darkness towards the location of a remembered (flashed) target. We conclude that visual feedback is unlikely to be very important in controlling cyclovergence in these various conditions.
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Convergencia Ocular , Movimientos Oculares , Visión Binocular/fisiología , Adulto , Fijación Ocular , Humanos , Masculino , Modelos Biológicos , Variaciones Dependientes del Observador , Estimulación Luminosa , Reproducibilidad de los Resultados , Movimientos SacádicosRESUMEN
Earlier recordings of eye position in three dimensions have revealed that Listing's law is obeyed in reasonable approximation, both statically and dynamically. This implies that all eye positions are confined to a plane when using a rotation vector or quaternion representation. The orientation of the angular velocity axis is crucial in order to preserve the law. For a single-axis rotation, the eye's angular velocity axis has to tilt out of Listing's plane, otherwise the law cannot be preserved in eccentric saccades. Experimental work has confirmed that normal, visually-guided saccades resemble single-axis rotations whose angular velocity axis tilts by the right amount. We investigated how well the saccadic system implements Listing's law when the trajectory of the eyes is more complicated, as in a non-single-axis rotation where the angular velocity vector depends on instantaneous eye position. Eye position was measured in three dimensions using the magnetic scleral search coil method for five subjects. Non-single-axis rotations of the eye were evoked with a double-step paradigm. We found that Listing's law is obeyed equally well during fixations, single-axis saccades and in non-single-axis saccades. Some deviations from the law were found in both curved and single-axis eye movements, but we demonstrated that the net torsional component of eye position of these saccades is negligible compared to that expected if the angular velocity axis did not tilt at all. In addition, analysis of the angular velocity signals in the curved movements showed strong similarity to the computed signal required for implementing Listing's law. Our results show that the observed deviations from Listing's law reflect only minor failures in the mechanism underlying its dynamic implementation. We conclude that single-axis rotations are not a necessary condition for the implementation of Listing's law in saccades. Our results are compatible with the notion that the implementation of Listing's law relies upon internal feedback. Various suggestions of how models can be reconciled with recent data on the three-dimensional control of saccades are discussed.