Primary Dose Component Research Articles

"Zero-field" dose data for 60Co and other high-energy photon beams in water.

A procedure of separating the primary- and scatter-dose components in therapeutic photon beams is examined. It is based on the observation that the scatter-dose component is proportional to the variable z = rd/(r+d), where r and d are beam radius and depth in phantom, respectively. It is, therefore, possible to express an absorbed dose in the form of a linear equation D(r) = P+Nz, where at a fixed depth d, both primary dose P and coefficient N are constant. A method of linear extrapolation of an absorbed dose D(r) to "zero-field" size, i.e., r = 0, is utilized. Since Monte Carlo technique is capable of scoring separately the primary- and scatter-dose components, it is used to evaluate the accuracy of the linear extrapolation method within the range of 60Co-15-MV nominal photon energies. The results demonstrate that this method is sufficiently accurate to obtain the primary dose component in photon beams. For 60Co gamma radiation in water, tabulated sets of measured depth-dose data are analyzed by the linear extrapolation method to review "zero-field" dose values [percentage depth dose (PDD) and tissue-air ratio (TAR) tables of the British Journal of Radiology, Suppl. 17]. The "zero-field" PDD data are found to be accurate within limits of experimental uncertainties. Inconsistencies in the TAR table are illustrated and discussed. 60Co tables of relative doses, D(r,d)/P(dmax), including "zero-field" values for both fixed SSD and isocentric geometries, are generated. Dose calculation in irregular fields is considered. The linear extrapolation method is recommended as a standard procedure for separating primary dose from depth-dose data in high-energy photon beams.

Monte Carlo calculations of scatter to primary ratios for normalisation of primary and scatter dose

The separation of total absorbed dose into primary and scatter components is a commonly used technique in photon dose calculations. The primary dose component can be characterised by a measured narrow beam attenuation coefficient and a single normalisation value which establishes the relative proportion of the primary to the total dose at some reference depth and field size. The determination of this normalisation value from measured data requires an extrapolation of measured values for finite field sizes to obtain a zero field size value. The authors have used Monte Carlo simulations to score primary and scatter dose for photon beams of 4, 6, 10, 15 and 24 MV and report values of the scatter to primary ratio at the depth of dose maximum for the circular equivalent of a 10 cm*10 cm field. These values have an uncertainty of less than 1% and can be used in lieu of extrapolation of measured data to establish the relative magnitude of the primary dose for a wide range of photon beam energies.

X-ray dose computations in heterogeneous media using 3-dimensional FFT convolution

Dose distributions of nominal 6 and 18 MV X-ray beams and cobalt-60 photon beams were modelled in three dimensions in heterogeneous phantoms using convolutions that employ the fast Fourier transform. Doses were computed at 65536 calculation points (i.e. a 64*64*16 matrix) for five spectral components. Primary fluence was calculated by ray-tracing through the inhomogeneous medium. Dose was obtained by convolution with the primary fluence. The primary dose component, mediated by electrons, was calculated separately from the scatter component, mediated by scattered X-rays. The calculation time was approximately 3 minutes per spectral component on a Digital Equipment Corporation VAXstation 3500. Comparisons of FFT convolution calculations with measurements showed that an FFT convolution algorithm can predict most of the characteristics of an X-ray beam passing through a heterogeneous phantom.

10‐MV x‐ray primary and scatter dose calculation using convolutions

Three-dimensional (3-D) forward and backward primary dose spread functions in water were developed for 10-MV x rays. Three-dimensional forward and backward primary dose spread functions in a heterogeneous medium were constructed from the ones in water using the density scaling theorem. Each of the forward and backward primary dose components were calculated using a method of convolving the primary water collision kerma distribution with the forward or backward primary dose spread function. Scatter dose was separated into forward and backward components. Each scatter dose component was calculated using a differential scatter method, a kind of convolution method, where the primary water collision kerma distribution was convolved with a differential scatter-maximum ratio or differential backscatter factor equation. From the dose calculation and measurement results obtained for water phantoms containing a cork or aluminum slab, it was found that the 3-D forward and backward primary dose functions were effective especially in regions where there was a loss of longitudinal and/or lateral electronic equilibrium.

A method of measuring the primary dose component in high-energy photon beams.

We present an approach for deriving the primary component of dose from measurements in a megavoltage gamma or x-ray beam. The theoretical development of the approach is discussed showing that primary dose can be obtained from four measurements of ionization in narrow beam geometry and two measurements of ionization in a large beam in a phantom. The uncertainty in the final result is analyzed and is about an order of magnitude greater than the uncertainty in an individual measurement.

Monte Carlo calculations of scatter dose for small field sizes in a 60Co beam.

Photon dose calculations are frequently based on the separation of primary and scatter dose components. For small field sizes it is difficult to make this separation from measured data. Such problems lend themselves to solution by calculational methods, which permit rigorous definition of primary and scatter dose. Using Monte Carlo methods, we verify an equation derived from O'Connor's scaling theorem relating scatter-primary ratios at small depths and field sizes to those at larger depths and fields. This equation may prove to be useful when separating primary and scatter dose components, and consequently in dose calculations involving irregular fields or inhomogeneities.

Calculated buildup curves for photons with energies up to 60Co.

This report investigates the buildup region of the depth-dose curve for broad parallel beams of 60Co and lower energy photons incident on slabs of tissue as defined by the International Commission on Radiation Units and Measurements (ICRU) and other materials. The EGS Monte Carlo system was used to simulate the transport of photons and electrons in the materials. Calculated buildup regions of the depth-dose curves are presented for photons incident on ICRU tissue. For 60Co beams, the primary and scatter dose components are presented, both for the buildup region and at depth in the phantom. Effects of beam radius were investigated and found to have only a small effect in the buildup region of the central axis depth-dose curve. The calculated effects of beam radius are larger at depth and in good agreement with experiment. Effects of scatter and attenuation in a small miniphantom of water were investigated as a function of photon energy and were found to cancel within 0.8%. The mean distance of electron transport was calculated for 60Co beams incident on carbon, water, polystyrene, aluminum, and lead.

The effect of off-axis quality changes on zero area TAR for megavoltage beams

An analytical technique was employed to extract the primary component of dose at off-axis points from broad-beam water phantom data for a Clinac-18 Clinac-6 (100), Clinac-4 (Pb filter) and Philip's cobalt unit. The methodology presented here does not require separate off-axis HVL measurements and guarantees the accurate description of the data within the radiation field. It is shown that the off-axis reduction in the primary dose component for linacs does lead to significant (5-10%) errors in dose calculations if it is not taken into account in extended field external beam calculations. A method is described in which the off-axis variation in zero field TAR can be easily extracted from broad-beam scan data using the framework established by Cundiff et al (1973) as modified by Hanson and Berkeley (1980) for the dosimetry of large irregular fields. The technique is self-consistent and leads to parameters which have simple physical interpretations and which guarantee an accurate description of the beam.

A photon dose distribution model employing convolution calculations

A three-dimensional photon beam calculation is described which models the primary, first-scatter, and multiple-scatter dose components from first principles. Three key features of the model are (1) a multiple-scatter calculation based on diffusion theory, (2) the demonstration of the modulation transfer function of the radiation dose transport process, and (3) the use of the finite fast Fourier transform to perform the required convolutions. The results of calculations for cobalt-60 in a homogeneous phantom are used to verify the accuracy of the model.