An equivalent square field formula for determining head scatter factors of rectangular fields

A simple formula is derived for the calculation of an equivalent square field that gives the same head scatter factor as a given rectangular field. This formula is based strictly on the configuration of a medical linear accelerator treatment head. The geometric parameters used are the distances between the target and the top of each field-defining aperture. The formula accounts for both the effect of field elongation and the collimator exchange effect. This method predicts the output to within 1% accuracy for both open and wedged fields and does not require any new measured data other than the field size dependence of head scatter for a range of square field sizes. Interestingly, the formula we derived has the same format as the formula that was empirically obtained by Vadash and Bj?rngard [Med. Phys. 20, 733-734 (1993)].     

Equivalent squares of irregular photon fields

The tables of equivalent fields published by the British Journal of Radiology (BJR) are intended for calculation of depth-dose functions in rectangular photon fields. We have investigated the validity of the equivalent-field concept for fields of arbitrary shape over a range of photon energies, field sizes and depths. We show that the empirical scatter-radius function (Day function) used to generate the equivalent-field tables is a good approximation to the average over energy of normalized scatter-air ratios extracted from BJR beam data for depths up to 10 cm. However, this function tends to diverge from the data as depth increases. Accuracy can be improved by making the Day function depend on depth. Equivalent squares, determined by sector integration of the original or modified Day functions, are suitable for megavoltage photon-beam dose calculations at central-axis and off-axis points in irregular as well as rectangular fields.     

Calculating dose and output factors for wedged photon radiotherapy fields using a convolution/superposition method

To account for clinical divergent and polychromatic photon beams, we have developed kernel tilting and kernel hardening correction methods for convolution dose calculation algorithms. The new correction methods were validated by Monte Carlo simulation. The accuracy and computation time of the our kernel tilting and kernel hardening correction methods were also compared to the existing approaches including terma divergence correction, dose divergence correction methods, and the effective mean kernel method with no kernel hardening correction. Treatment fields of 10 x 10-40 x 40 cm2 (field size at source to axis distance (SAD)) with source to source distances (SSDs) of 60, 80, and 100 cm, and photon energies of 6, 10, and 18 MV have been studied. Our results showed that based on the relative dose errors at a depth of 15 cm along the central axis, the terma divergence correction may be used for fields smaller than 10 x 10 cm2 with a SSD larger than 80 cm; the dose divergence correction with an additional kernel hardening correction can reduce dose error and may be more applicable than the terma divergence correction. For both these methods, the dose error increased linearly with the depth in the phantom; the 90% isodose lines at the depth of 15 cm were shifted by about 2%-5% of the field width due to significant underestimation of the penumbra dose. The kernel hardening effect was less prominent than the kernel tilting effect for clinical photon beams. The dose error by using nonhardening corrected kernel is less than 2.0% at a depth of 15 cm along the central axis, yet it increased with a smaller field size and lower photon energy. The kernel hardening correction could be more important to compute dose in the fields with beam modifiers such as wedges when beam hardening is more significant. The kernel tilting correction and kernel hardening correction increased computation time by about 3 times, and 0.5-1 times, respectively. This can be justified by more accurate dose calculations for the majority of clinical treatments.     

Theoretical and experimental determination of phantom scatter factors for photon fields with different radial energy variation

The output factor used for monitor unit determination in radiotherapy can be divided into two factors: the head scatter factor and the phantom scatter factor. Theoretical and experimental phantom scatter factors have been compared for different beam qualities between 4 MV and 50 MV and field sizes from 5 cm x 5 cm to 30 cm x 30 cm. The theoretical data were obtained through a convolution method based on Monte Carlo calculated energy spectra and dose kernels. The calculations have been performed both for accelerators with a rather large energy variation within the field and for accelerators with a constant energy distribution in the field. Deviations between theoretical and experimental data were found to be less than 1%.     

Build-up cap materials for measurement of photon head-scatter factors

The suitability of high-Z materials as build-up caps for head-scatter measurements has been investigated. Build-up caps are often used to enable characterization of fields too small for a mini-phantom. We have studied lead and brass build-up caps with sufficiently large wall thicknesses, as compared to the range of contaminating electrons originating in the accelerator head, and compared them with build-up caps made of ionization chamber equivalent materials, i.e. graphite. The results were also compared with measurements taken using square and cylindrical polystyrene mini-phantoms. Field sizes ranging from 3 cm x 3 cm up to 40 cm x 40 cm were studied for nominal photon energies of 4, 6, 10 and 18 MV. The results show that the use of lead and brass build-up caps produces normalized head-scatter data slightly different from graphite build-up caps for large fields at high photon energies. At lower energies, however, no significant differences were found. The intercomparison between the two different plastic mini-phantoms and graphite caps showed no differences.     

The effect of strong longitudinal magnetic fields on dose deposition from electron and photon beams

The use of strong, uniform, longitudinal magnetic fields for external electron and photon beam irradiation is considered. Using the EGS4 Monte Carlo code modified to account for the presence of magnetic fields, dramatic narrowing of penumbra for photon and electron irradiations is demonstrated. In the vicinity of heterogeneities, "hot" and "cold" spots due to multiple scattering in electron beams are reduced substantially. However, in the presence of strong magnetic fields, the effect of inhomogeneities can be observed far from the location of the inhomogeneity due to reduced "washout" caused by lateral multiple scattering. The enhanced "Bragg peak," proposed or calculated by other authors, is not observed on the central axis of broad beams, owing to lateral equilibrium. It is proven that for broad parallel beams, the central axis depth-dose curve is independent of the strength of the external longitudinal magnetic field, as long as it is uniform. However, strong longitudinal magnetic fields can induce enhancements by redirection of the electron fields coming from point sources. Strong uniform longitudinal magnetic fields provide a way of controlling the spreading of electron beams due to multiple scattering, making the electron beams more "geometrical" in character, simplifying dose-deposition patterns, possibly allowing electron beams to be used in new ways for radiotherapy. Photon therapy also benefits from strong uniform longitudinal magnetic fields since the penumbra or other lateral disequilibrium effects associated with lateral electron transport can be eliminated.     

Flow fields in electromagnetic stirring of rectangular strands with linear inductors: Part II. computation of flow fields in billets,blooms, and slabs of steel

The model presented in Part I of this series of papers is used to compute flow velocities in the longitudinal stirring of steel blooms and billets, and in the horizontal stirring of steel slabs. In longitudinal stirring of blooms and billets the reverse flow is on the side of the strand opposite to the inductor. The effects of penetration depth of the electromagnetic force, of the force itself, of the length of the stirrer, and of the width of the liquid core were determined. In horizontal stirring of slabs the reverse flow takes place outside of the stirrer region, forming the so-called butterfly stirring pattern. The characteristics of this flow field depend to a considerable extent on the width of the stirrer. The effects of stirrer width, of thickness of the liquid core, of force and of width of the slab were elucidated. The maximum velocities in both types of stirring are represented as simple formulae.     

Flow fields in electromagnetic stirring of rectangular strands with linear inductors: Part II. computation of flow fields in billets, blooms, and slabs of steel

The model presented in Part I of this series of papers is used to compute flow velocities in the longitudinal stirring of steel blooms and billets, and in the horizontal stirring of steel slabs. In longitudinal stirring of blooms and billets the reverse flow is on the side of the strand opposite to the inductor. The effects of penetration depth of the electromagnetic force, of the force itself, of the length of the stirrer, and of the width of the liquid core were determined. In horizontal stirring of slabs the reverse flow takes place outside of the stirrer region, forming the so-called butterfly stirring pattern. The characteristics of this flow field depend to a considerable extent on the width of the stirrer. The effects of stirrer width, of thickness of the liquid core, of force and of width of the slab were elucidated. The maximum velocities in both types of stirring are represented as simple formulae. Formerly with Institut für Allgemeine Metallurgie, Technische Universit?t Clausthal     

A new approach for the calculation of photon dose conversion factors in the PMMA slab phantom

A new simple method using the computer code MCNP is proposed for calculation of photon dose conversion factors in the PMMA slab phantom. Absorbed dose is calculated by multiplying fluence buildup in the PMMA slab phantom by virtual energy deposition in the ICRU tissue substance. This method does not need auxiliary calculations to determine the dose conversion factors, such as calculation of backscatter factors in the ICRU tissue cube and the PMMA slab phantoms. The discrepancies between the results of the direct method presented here and a more conventional indirect method is less than 2%, except for low energy photons (<100 keV) at large depths. As the direct method reduces the number of calculational steps, the results are more reliable than those of the indirect method.     

Flow fields in electromagnetic stirring of rectangular strands with linear inductors: Part I. theory and experiments with cold models

A model is presented to compute the electromagnetic force fields and fluid flow fields in electromagnetic stirring of continuously cast strands with rectangular cross-section. The model involves the solution of the Maxwell equations, the Navier-Stokes equations, and the transport equations for the turbulence characteristicsk and e. The procedure of depth-averaging is applied in the treatment of several three-dimensional flows. Experiments were performed to check the computations using mercury as fluid. The spatial distribution of the magnetic induction and of the force density was determined for the laboratory inductor used in the stirring experiments. The flow velocity was measured photographically or with a drag probe, respectively. The agreement between experimental and theoretical data was found to be within 25 pct. It is concluded that the theory is sufficiently reliable to predict the flow fields in electromagnetic stirring of steel strands. In Part II of this paper the model is applied to analyze stirring situations in continuous casting of steel. Formerly with Institut für Allgemeine Metallurgie, Technische Universit?t Clausthal     

Flow fields in electromagnetic stirring of rectangular strands with linear inductors: Part I. theory and experiments with cold models

A model is presented to compute the electromagnetic force fields and fluid flow fields in electromagnetic stirring of continuously cast strands with rectangular cross-section. The model involves the solution of the Maxwell equations, the Navier-Stokes equations, and the transport equations for the turbulence characteristicsk and e. The procedure of depth-averaging is applied in the treatment of several three-dimensional flows. Experiments were performed to check the computations using mercury as fluid. The spatial distribution of the magnetic induction and of the force density was determined for the laboratory inductor used in the stirring experiments. The flow velocity was measured photographically or with a drag probe, respectively. The agreement between experimental and theoretical data was found to be within 25 pct. It is concluded that the theory is sufficiently reliable to predict the flow fields in electromagnetic stirring of steel strands. In Part II of this paper the model is applied to analyze stirring situations in continuous casting of steel.     

Migration of human keratinocytes in electric fields requires growth factors and extracellular calcium

Currents that leak out of wounds generate electric fields lateral to the wound. These fields induce directional locomotion of human keratinocytes in vitro and may promote wound healing in vivo. We have examined the effects of growth factors and calcium, normally present in culture medium and the wound fluid, on the directional migration of human keratinocytes in culture. In electric fields of physiologic strength (100 mV per mm), keratinocytes migrated directionally towards the cathode at a rate of about 1 microm per min. This directional migration requires several growth factors. In the absence of these growth factors, the cell migration rate decreased but directionality was maintained. Epidermal growth factor alone restored cell migration rates at concentrations as low as 0.2 ng per ml. Insulin at 5-100 microg per ml or bovine pituitary extract at 0.2%-2% vol/vol also stimulated keratinocyte motility but was not sufficient to fully restore the migration rate. Keratinocyte migration in electric fields requires extracellular calcium. Changes in calcium concentrations from 3 microM to 3.3 mM did not significantly change keratinocyte migration rate nor directionality in electric fields; however, addition of the chelator ethyleneglycol-bis(beta-aminoethyl ether)-N,N,N',N'-tetraacetic acid to migration medium reduced, and eventually abolished, keratinocyte motility. Our results show that (i) growth factors and extracellular calcium are required for electric field-induced directional migration of human keratinocytes, and (ii) keratinocytes migrate equally well in low and high calcium media.