Photon Depth - Dose Data Formats

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The absorbed dose distribution in a radiation therapy field is the result of a statistical aggregate of energy deposition events which are each well understood, at least in terms of probability functions for their various outcomes. The best calculations have been done with Monte Carlo type computer programs that follow many thousands of event histories which are created by using random numbers to choose among the various possibilities at each step. The program tallies the energy depositions into an array of memory locations which represent the spatial distribution of absorbed dose. However the time necessary to achieve clinically useful accuracy and resolution is prohibitive except for research applications to test theoretical assumptions.

For routine clinical use it is customary to use lookup tables of relative-dose factors that are derived from measurements in a phantom of tissue-equivalent material such as water, for spot calculations of dose to a point on the collimator axis. These tables contain "normalized" data, which means that the values are given relative to one of the data points which is given the value of one. That is, all the measured values are divided by the value at the "reference point"; when the relative values are used they are multiplied by appropriate "calibration factors" which are probably measured with a different instrument that is specialized for absolute measurements. However the measurements are of total absorbed dose for different phantom and detector locations and the terms "scatter factor" and "output factor" are misleading because they come from conventions of normalization and not from separating primary and scattered radiation contributions to the total dose.
 

 
 

Percent Depth Dose

The depth-dose tabulation which seems simplest, the Percent Depth Dose table, is physically the most complicated. For a given SSD, or source to surface distance, for a series of depths, measured doses on the central ray of a therapy field are listed as percent of that at the depth of maximum dose for each field size. The scatter factor, listed for each field size, dates from the 1950's and before when therapy fields were measured in roentgens with an air-wall ion chamber and the exposure at the surface of a patient or phantom was affected by backscatter from the mass of absorber. 

With today's absorbed dose calibration of therapy fields the same Percent Depth Dose format is used, but two factors are listed for each field size. The Output Factor is measured "in air", that is with an ion chamber surrounded by a minimum of absorbing material to provide buildup and to exclude electron contamination. The dependence on collimator setting of this measurement is not properly part of the scatter factor because the entire "mini-phantom" surrounding the detector is included in the smallest field size. It is due to forward-scattered photons from primary collimator and source or target assembly which constitute an extended source that is partly occluded by the field collimator depending on its setting, and in a linac which is controlled by a transmission ion chamber the output is affected also by back-scattered electrons which depend mainly on the upper jaw setting. 

The Output Factors are listed relative to that for the standard geometry chosen for machine calibration, for example at depth of maximum dose in a field that is 10x10 cm at 100 cm SSD. 

The Scatter Factor is measured for a series of field sizes at the depth of maximum dose in a phantom set at the given SSD and presented as a ratio to that in the standard calibration field, after factoring out the dependence of machine output on collimator setting. Thus the product of Output Factor and Scatter Factor is in fact the "normalizing factor" that was taken out of the tabulated depth-dose data for each field size to get values relative to one at the depth of maximum dose. They must be listed separately, however, because the effective field size for table lookup might differ from the collimator setting because of blocked fields or extended distance. 

The physical effects which determine the relative dose values in the Percent Depth Dose table include the inverse-square factor of dependence on area of a diverging beam of radiation from a point source. Because of this geometrical effect a Percent Depth Dose table applies to only one SSD. A ratio of inverse square factors called the "Mayneord Factor" is sometimes used for an approximate correction to apply PDD data to a different SSD. 

In addition the contribution to total absorbed dose due to scatter from surrounding irradiated material depends on depth and on the projected field size which shows a geometric divergence from that at the reference distance for which the collimator scales are calibrated. The Scatter Factor which was taken out only represents the difference in scatter contribution at d(max), in each field size, from that in the calibration field. 
 
 

 
 

Tissue - Air  Ratio

Tissue - Output  Ratio

In modern radiotherapy practice most multiple-port treatment plans are isocentric, with a different SSD for each field, and even single-field treatments are often at non-standard SSD due to patient positioning or field size constraints. In the early 1960's another format for relative depth-dose data was developed, called Tissue-Air Ratio or TAR. It is conceptually based on measurements in a phantom by a detector fixed at the isocenter of the gantry-mounted therapy machine, for various depths and field sizes. By moving the phantom to measure the effect of overlying absorber we achieve the equivalent of a depth-dose scan along the axis of a field at infinite SSD where rays are parallel and field size is independent of distance. It is common to use data from a detector that scans in depth, multiplied by a factor proportional to the square of distance from the source, to simulate measurements at isocenter; however each point characterizes a different projected field size. The TAR table values, for given depths and field sizes at isocenter, are then derived by interpolating between measurements for different collimator settings. 

When originally proposed the TAR values were intended to be ratios of "exposure" in the patient to "exposure" measured in air with a suitable buildup cap or "mini-phantom" on the ion chamber. With the advent of absorbed dose calibration (See From Roentgens to CentiGrays) it was customary to use "relative TAR" tables, with values relative to the absorbed dose at the field size and depth at isocenter for which the dose integrator was calibrated, a format now called "Tissue-Output Ratio" or TOR. In either case the dependence of absorbed dose on scatter from surrounding tissue is included in the tabulated values for every depth and field size, not "normalized" with separate Scatter Factors for each field size. 

The dependence of machine output on collimator setting, relative to the calibrated field size, is measured with a "mini-phantom" smaller than any field size of interest, factored out of the depth-dose data, and tabulated as a separate Output Factor since the collimator setting may not correspond to irradiated field size. 

Contemporary recommendations for therapy machine output calibrations specify measurement of absorbed dose in a tissue- or water- equivalent phantom at a depth well beyond the buildup layer, at least 5 cm, with a representative field size, typically 10x10 cm. Although these recommendations are the result of ion chamber calibration considerations, they are also a representative field size and depth for clinical use; for isocentric treatment plans such a calibration at isocenter is directly applicable to the prescription point. 
 

 
 
 
 

Tissue - Phantom  Ratio

Tissue - Maximum  Ratio

If a Tissue-Air Ratio or Tissue-Output Ratio table is "normalized", by factoring out the values at calibration depth, for each field size, the result is called a Tissue-Phantom Ratio table. The factors that are removed to get values of one at calibration depth are called Scatter Factors and are listed for each field size with the Output Factors. The special case with calibration at depth of maximum dose is called Tissue-Maximum Ratio. 

As with the Percent Depth Dose table, these Scatter Factors only tell the difference in total dose from that in a standard 10x10 field, at calibration depth, due to the dependence of scatter on field size. The bulk of the scatter contribution, with its dependence on depth and field size, is still included in the tabulated values. 

Nevertheless Tissue-Phantom and Tissue-Maximum Ratio tables are the most common, probably from the use of depth-dose scanning systems that do not offer absolute calibration but give data that is "normalized" or scaled relative to some value in the data set, either digitally or by analog adjustment of the equipment. Then the separate measurement of Output Factor and Scatter Factor, relative to the calibration field geometry, is regarded as more accurate. With such data a Tissue-Output Ratio table would be derived by multiplying relative depth-dose values by the Scatter Factor for each field size. 

These data tables are accurate only for spot dosimetry on the beam axis with perpendicular incidence in a homogeneous medium. They are applicable at distances other than that of the isocenter by doing the lookup for the projected field size at the distance of interest and by including an inverse square factor which is simple to calculate. 

These tables are also used for spot dosimetry along the axis of rectangular fields, with a lookup table of equivalent square fields or an approximate formula using area/perimeter. 

Another common practice is to combine Output Factor and Scatter Factor into a single Relative Dose Factor that is measured in a phantom for a series of field sizes. This would be sufficient if the clinical field size always corresponded to the collimator setting, but with blocks or extended distances the lookups of Output Factor and Scatter Factor are for different equivalent field sizes. The errors from this practice, up to a few percent, are small compared with commonly-accepted errors from ignoring inhomogeneities in the patient. 
 
 

 
 

Scatter - Air  Ratio

Scatter - Output  Ratio

A realistic allowance for the difference between a standard field in a homogeneous phantom and actual patient geometry must account for two components of absorbed dose. One is locally absorbed and proportional to the primary radiation incident on the point of interest, allowing for buildup and attenuation by overlying tissue. The other depends on scatter from surrounding irradiated tissue. 

Clarkson (1941) and Gupta and Cunningham (1966,1970) showed that the primary component of total absorbed dose could be represented by the idealization of zero-area Tissue-Air Ratio. Subtracting these values from TAR or TOR values measured for non-zero field sizes yields a table called Scatter-Air Ratio or Scatter-Output Ratio. These zero-area TAR values cannot be measured because ion chambers do not have zero area and because penumbra effects that intrude in small fields are spurious to the concept. Instead they are modeled with plausible assumptions. 

One model is a mathematical function of exponentials that are measured with narrow-beam geometry; another is produced by extrapolating TAR or TOR values, measured for small field sizes, to zero field size for each depth. In their use they are added back to adjusted SAR values to calculate an effective TAR or TOR for a specific field geometry, so the result is not sensitive to what model was used, provided the same one is used to derive SAR. 

IRREG was the name of the historic program developed by Cunningham's group in Toronto and widely circulated, to do spot dosimetry with irregular field boundaries by Clarkson integration using a Scatter-Air Ratio lookup table based on central-axis depth dose data. Off-axis point doses can also be calculated to good approximation by entering the appropriate SSD and depth, with allowance for off-axis output profile and oblique penetration in determining the primary dose contribution. 

Most treatment planning computer systems include the IRREG program or equivalant, and SAR data tables, for spot dosimetry at points of interest with measured SSD and depth; they assume unit density, homogeneous patient anatomy with not-too-steep surface contours. This function is usually separate from calculations that show a dose distribution in a cross section of the patient. 
 

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GS23DEC90:\RTTEACH\DDDATA.DOC Rev. 26 Apr 94  => dddata.htm Sep 97 
Posted 8 August 1998 by  [Glen Sandberg]