Chen Shou Chui

Use of fast Fourier transforms in calculating dose distributions for irregularly shaped fields for three dimensional treatment planning

In three-dimensional radiation treatment planning, essentially all fields are irregular and compensated. Consequently, it is important to predict accurately dose for such fields to ensure adequate coverage of the target region and sparing of healthy tissues. Traditional approaches, namely, those involving scatter integration and extended source and those utilizing negatively weighted fields, are inaccurate, especially near the boundaries defined by blocks and collimators. In the method presented in this paper, dose distributions for arbitrarily shaped beams are calculated by two-dimensional convolution of the relative primary photon fluence distributions and kernels representing the cross-sectional profiles of a pencil beam at a series of depths. The pencil beam dose distributions are computed, once and for all, with the Monte Carlo method for photon energy spectrum for each treatment machine. The finite size of the source, which is important for cobalt machines, is also taken into account using convolution of the source with the relative primary fluence distribution. Convolutions are performed using fast Fourier transforms on an array processor. Results of calculations are in excellent agreement with measured data. While no data are presented for fields modified by compensators, the method of calculation should apply at least as well for such fields since the variations in fluence distribution for compensated fields are not as sharp as for points near the block boundaries.

Radionuclide photon dose kernels for internal emitter dosimetry

Photon point dose kernels and absorbed fractions were generated in water for the full photon emission spectrum of each radionuclide of interest in nuclear medicine, by simulating the transport of particles using Monte Carlo. The kernels were then fitted to a mathematical expression. Absorbed fractions for point sources were obtained by integrating the kernels over spheres. Photon dose kernels and absorbed fractions were generated for the following radionuclides: I-123, I-124, I-125, I-131, In-111, Cu-64, Cu-67, Ga-67, Ga-68, Re-186, Re-188, Sm-153, Sn-117m, Tc-99m. The Monte Carlo simulation was verified by comparing the dose kernels to published monoenergetic photon kernels. Further validation was obtained by generating an I-125 brachytherapy seed kernel and comparing it with published data. Since Monte Carlo simulation was initialized by sampling from the complete photon spectra of these radionuclides, interpolation between monoenergetic kernels and absorbed fractions was not required. The absorbed-fraction due to uniform spherical distributions can be directly applied for use in internal dosimetry. In addition, the kernels can be used as input for three-dimensional internal dosimetry calculations.

Extraction of pencil beam kernels by the deconvolution method

A method has been developed to extract pencil beam kernels from measured broad beam profiles. In theory, the convolution of a symmetric kernel with a step function will yield a function that is symmetric about the inflection point. Conversely, by deconvolution, the kernel may be extracted from a measured distribution. In practice, however, due to the uncertainties and errors associated with the measurements and due to the singularities produced in the fast Fourier transforms employed in the deconvolution process, the kernels thus obtained and the dose distributions calculated therefrom, often exhibit erratic fluctuations. We propose a method that transforms measured profiles to new, modified distributions so that they satisfy the theoretical symmetry condition. The resultant kernel from the deconvolution is then free of fluctuations. We applied this method to compute photon and electron dose distributions at various depths in water and electron fluence distributions in air. The agreement between measured and computed profiles is within 1% in dose or 1 mm in distance in high dose gradient regions.

Interinstitutional experience in verification of external photon dose calculations

Under the auspices of NCI contracts, four institutions have collaborated to assess the accuracy of the pixel-based dose calculation methods they employ for external photon treatment planning. The approach relied on comparing calculations using each groups algorithm with measurements in phantoms of increasing complexity. The first set of measurements consisted of ionization chamber measurements in water phantoms in normally incident square fields, an elongated field, a wedged field, a blocked field, and an obliquely incident beam. The second group of measurements was carried out using thermoluminescent dosimeters in phantoms designed to investigate the effects of surface curvature, high density heterogeneities, and low density heterogeneities. The final study tested the entire treatment planning system, including CT data conversion, in an anthropomorphic phantom. Overall, good agreement between calculation and measurements was found for all algorithms. Regions in which discrepancies were observed are pointed out, areas for algorithm improvement are identified and the clinical import of algorithm accuracy is discussed.

Off-center ratios for three-dimensional dose calculations.

A new method is proposed for computing the off-center ratios (OCRs) in three-dimensional dose calculations. For an open field, the OCR at a point is computed as the product of the primary OCR (POCR) and the boundary factors (BFs). The POCR describes the beam profile for an infinite field, that is, without the effect of the collimators. It is defined as the ratio of the dose at a point off the central ray to the dose at the point on the central ray at the same depth for an infinite field. The POCR is a function of radial distance from the beam central ray and depth. The BF describes the shape of the beam in the neighborhood of the field boundary defined by the collimators. It is defined as the ratio of the OCR at a point for a finite field to the OCR at the same point for an infinite field. The BF is a function of distance from the field boundary, depth, and field size. For a wedged field, we assume that the boundary factors remain the same as for open fields but the POCRs are altered. The changes in beam profiles are described by a factor called the wedge profile factor (WPF), defined as the ratio of the dose at a point for the largest wedged field to the dose at the same point for an open field of the same field size. The WPF is a function of lateral distance from the beam central plane and depth. Calculated OCRs using this new method are in agreement with the measured data along both the transverse and the diagonal directions of the field.

Dose computations for asymmetric fields defined by independent jaws.

Asymmetric fields defined by independent jaws can be used to split a beam or to match adjacent fields. We have extended a method originally developed for symmetric fields to calculate the dose for asymmetric fields. The dose to a point is computed as the product of the tissue maximum ratio (TMR), the off center ratio (OCR), and the inverse square factor. The TMR is computed from the measured central axis depth doses for symmetric fields. The OCR is obtained by multiplying the primary OCR (POCR) and the boundary factors (BFs) for the four jaws. The POCRs and BFs were derived from measured beam profiles, which include the effect of off-axis beam quality variations. Using this method, the beam profiles and isodose distributions for asymmetric fields of a 6-MV accelerator were calculated and compared with the measured data. The agreement is within experimental errors both in the penumbra region and along the central ray of the asymmetric field.

The use of diode dosimetry in quality improvement of patient care in radiation therapy

The purpose of this work is to improve the quality of patient care in radiation therapy by implementing a comprehensive quality assurance (QA) program aiming to enhance patient in vivo dosimetry on a routine basis. The characteristics of two commercially available semi-conductor diode dosimetry systems were evaluated. The diodes were calibrated relative to an ionization chamber-electrometer system with calibrations traceable to the National Institute of Standards and Technology (NIST). Correction factors of clinical relevance were quantified to convert the diode readings into patient dose. The results of dose measurements on 6 patients undergoing external beam radiation therapy for carcinoma of the prostate on three different therapy units are presented. Field shaping during treatments was accomplished either by multileaf collimation or by cerrobend blocking. A deviation of less than +/-4% between the measured and prescribed patient doses was observed. The results indicate that the diodes exhibit excellent linearity, dose reproducibility, minimal anisotropy, and can be used with confidence for patient dose verification. Furthermore, diodes render real time verification of dose delivered to patients.

The effect of angular spread on the intensity distribution of arbitrarily shaped electron beams

Knowledge of the relative intensity distribution at the patients surface is essential for pencil beam calculations of three-dimensional dose distributions for arbitrarily shaped electron beams. To calculate the relative intensity distribution, the spatial spread resulting from angular spread is convolved with a two-dimensional step function whose shape corresponds to the applicator aperture. Two different approaches to obtain angular spread or the equivalent spatial spread are investigated. In the first method, the pencil beam angular spread is assumed to be Gaussian in shape. The angular spread constants (sigma theta) are then obtained from the slopes of measured intensity profiles. In the second method, the angular spread, in the form of an array of numerical values, is obtained by the deconvolution of measured intensity profiles. After obtaining the angular spread, the calculation for convolution is done in a number of parallel planes normal to the central axis at various distances from the electron collimator. Intensity at any arbitrary point in space is computed by interpolating between intensity distributions in adjacent planes on either side of the point. The effects of variations in angular spread as a function of field size for two treatment machines, one with a scanned electron beam and the other with a scattering foil, have been studied. The consequences of assuming angular spread to be of Gaussian shape are also examined. The electron intensity calculation techniques described in this paper apply primarily to methods of dose calculations that employ pencil beams generated using Monte Carlo simulations.