Paul S. Nizin

Electronic equilibrium and primary dose in collimated photon beams.

Electronic equilibrium conditions are studied in a homogeneous medium irradiated by monoenergetic photons with Compton scattering as a predominant process. Based on the concept of straight charged particle tracks, a geometrical model for spatial distribution of Compton electrons is developed in the limit of primary photon interactions. The model is applied to examine conditions of electronic equilibrium in collimated photon beams and to define equilibrium phase diagrams which establish correlation between various degrees of electronic equilibrium and primary dose. The diagrams predict that in a single direction (longitudinal or lateral) partial electronic equilibrium can be observed in radiation fields of dimensions smaller than the maximum range of secondary electrons. Associated macroscopic effects appear as a variation of the primary dose build-up rate with beam radius and depth in phantom. These effects are observed in the case of both primary and total absorbed dose as judged by the Monte Carlo generated data in waterlike material (1-8 MeV photons).

Tissue-air ratios for narrow 60Co gamma-ray beams.

This study introduces a table of tissue-air ratios (TAR) for narrow 60Co gamma-ray beams. The table is consistent with recently published TAR data for broad 60Co gamma-ray beams [Table 4.1, Br. J. Radiol. Suppl. 25 (1996)]. Narrow-beam TARs are derived analytically from broad-beam data of Table 4.1 and are tabulated for circular fields ranging from 0.2 to 2.2 cm in radius--an approximate equivalent of a 0.4 cm x 0.4 cm to 4 cm x 4 cm square-field range. The extent of depth is from 0.5 to 30 cm in water.

An approximation of central-axis absorbed dose in narrow photon beams.

In narrow photon beams of therapeutic energy range, the absorbed dose derived from experimental measurements is subject to a significant error. The error stems from high dose gradients characteristic to small radiation fields and from finite probe dimensions. In this study, a simple model for the narrow-beam absorbed dose is described. It is shown that broad-beam dose data are sufficient to predict a narrow-beam dose. The dose is calculated as a sum of primary and scatter components given in the form of respective analytical functions. For both functions, numerical coefficients are determined in broad-beam geometry. The model is evaluated by comparing calculated dose values with the Monte Carlo simulated narrow-beam dose data for 6 and 15 MV x rays.

INDEPENDENT DOSE CALCULATIONS FOR THE CORVUS MLC IMRT

Two independent dose calculation methods have been explored to validate MLC-based IMRT plans from the NOMOS CORVUS system. After the plan is generated on the CORVUS planning system, the beam parameters are imported into an independent workstation. The beam parameters consist of intensity maps at each gantry angle. In addition, CT scans of the patient are imported into the independent workstation to obtain the external contour of the patient. The coordinate system is defined relative to the alignment point chosen in the CORVUS plan. The 2 independent calculation methods are based on a pencil beam kernel convolution and a Clarkson-type differential scatter summation, respectively. The pencil beam data for a 1 x 1-cm beam, as formed by the multileaf collimator, were measured for the 6-MV photon beam from a Siemens PRIMUS linear accelerator using film dosimetry. In the pencil beam method, the dose at a point is calculated using the depth and off-axis distance from a given pencil beam, corrected for beam intensity. The scatter summation method used the conversion of measured depth dose data into scatter maximum ratios. In this method, the differential scatter from each pencil beam is corrected for the beam intensity. Isodose distributions were generated using the independent dose calculations and compared to the CORVUS plans. Although isodose distributions from both methods show good agreement with the CORVUS plan, our implementation of the differential scatter summation approach seems more favorable. The 2 independent dose calculation algorithms are described in this paper.

Independent dose calculations for the PEACOCK System.

An independent dose calculation method has been developed to validate intensity-modulated radiation therapy (IMRT) plans from the NOMOS PEACOCK System. After the plan is generated on the CORVUS planning system, the beam parameters are imported into an independent workstation. The beam parameters consist of intensity maps at each gantry angle and each arc position. In addition, CT scans of the patient are imported into the independent workstation to obtain the external contour of the patient. The coordinate system is defined relative to the alignment point chosen in the CORVUS plan. The independent calculation uses the pencil beam data viz tissue maximum ratio (TMR) and beam profiles for a single 1 x 0.8-cm beamlet formed by the NOMOS multileaf intensity-modulating collimator (MIMiC) leaf. The pencil beam data were measured for the 6-MV photon beam from Siemens PRIMUS linear accelerator using film dosimetry. The dose at a point is calculated using the depth and off-axis distance from a given pencil beam, corrected for its beam intensity. Isodose distributions are generated using the independent dose calculations and compared to the CORVUS plans. Isodose distributions show good agreement with the CORVUS plans for a number of clinical cases. The independent dose calculation algorithm is described in this paper.

On absorbed dose in narrow 60Co gamma-ray beams and dosimetry of the Gamma Knife

Using separate analytical functions describing primary dose, P0(dm,r), collimator scatter, Sc(r), and phantom scatter, TAR(d,r), an expression for absorbed dose in narrow 60Co gamma-ray beams is developed and each function is quantified: D(d,r) = P0(dm,r) Sc(r) TAR(d,r). The absorbed dose is calculated in beams as narrow as 0.2 cm in radius. Analytical and experimental results are compared using measured dose data for the Gamma Knife. Close agreement with experimental data is observed.

Phenomenological dose model for therapeutic photon beams: Basic concepts and definitions

A model for central-axis absorbed dose in therapeutic photon beams is developed. An expression for absorbed dose in a unit density material, including that in the regions of longitudinal and lateral electronic disequilibrium, is derived. The model is based on the concept of primary and scatter. Primary and scatter dose components are approximated using two identical analytical functions. Monte Carlo simulated dose data for 60Co gamma rays and 15 MV x rays in water are used to test the model. The accuracy of the model is demonstrated.

The elements of tissue-air ratio and systematic error.

The definition of tissue-air ratio (TAR) is based on the concept of primary dose. To determine TAR, both in-phantom and in-air ionization measurements are utilized. To convert ionization in the phantom into dose and that in air into primary dose, correction factors must be applied to chamber readings in both geometries. Due to difficulties in selecting proper correction factors, TAR is subject to systematic error. The error comes from two sources of uncertainty: (1) Primary dose cannot be measured. Therefore approximate methods, such as in-air ionization measurements, are used. (2) Detectors of ionization are of finite dimensions and they are inhomogeneous. In this study, analytical expression for a systematic error is derived. Because in this derivation systematic error is an accumulative error, it is no longer necessary to convert ionization, both in air and in phantom, into a dose when calculating TARs. A method of determining systematic error is described. This method is based on the ability to produce accurate zero-field data in photon beams by means of a linear extrapolation technique. Using 60Co gamma radiation in water as an example, it is shown how to generate TAR data free of systematic error. A possibility of determining TARs for therapeutic x rays is discussed.

Dosimetric study of the narrow beams of 60Co teletherapy unit for stereotactic radiosurgery.

This study explores the possibility of using a telecobalt unit for radiosurgery. A dosimetric study was performed for the narrow beam of Cobalt 60 (60Co) unit with circular radiation fields in diameters of 11, 17, 20, 27, 32, 35, 40, and 44 mm. Percentage depth dose and off-axis ratio were measured with ion chamber and radiographic film. The tissue air ratio values derived from measurements agreed well with the calculated values for all cone sizes and depths, ranging from the depth of maximum ionization of 24 cm in water. A quantitative evaluation of treatment plans with 60Co and 6-MV photon beams was carried out. The penumbra of the narrow beam of 60Co was larger than that of the 6-MV beam by 1.3 mm on average. This difference in penumbra can be attributed to the large source size of 60Co units. The feasibility of using narrow-beam 60Co for stereotactic radiosurgery/radiotherapy is discussed.

TH‐D‐ValA‐06: A Novel, Heterogeneity Inclusive, Pencil‐Beam Based Algorithm to Improve Lung IMRT Using the Corvus Planning System

Purpose: We investigate a new finite‐size pencil‐beam algorithm for calculating absorbed photondose in heterogeneous media of arbitrarily varying density for inverse planning in CORVUS treatment planning system and evaluate its performance modeling heterogeneous systems and in optimization of an IMRTlung plan. Method and Materials: A new FSPB is developed by extending a phenomenological model (Med. Phys 26:1893–1990, 1999) for the central‐axis absorbed dose in therapeuticphoton beams for heterogeneous media. The models parameters are rescaled based on the density of the medium. A differential equation is introduced to model the interface build‐up processes of CAX primary and scatter dose. Primary dose profiles are calculated using density‐dependent kernel integration, interpolated in the FSPB axis direction and evaluated depending on the density at the point of interest. Scatter dose profiles are computed using scatter integration and evaluated locally. Results: The new heterogeneity inclusive FSPB was implemented in a development version of CORVUS. Original and new FSPB dose calculations were compared with Monte Carlo calculations performed using PEREGRINE. For a heterogeneous semi‐slab phantom and for an IMRTlung plan, the dose distribution generated by the new FSPB agrees well with MC results, while the original one shows substantial discrepancies. IMRT plan optimizations were carried out using both original and new FSPB, and then a final dose calculation was performed using PEREGRINE. The plan calculated using the new FSPB shows better target conformality than the one computed using the original FSPB. Conclusion: The new FSPB possesses greatly improved accuracy as demonstrated in a variety of phantom and patient cases, both for dose calculation and IMRT optimization. FSPB best features were preserved with little extra computational overhead promising accurate and fast inverse planning and real‐time dose sculpting and dose volume histogram manipulation. Research sponsored by North American Scientific, NOMOS Radiation Oncology Division.