The physical effects that contribute to the empirical values include the geometrical dependence (inverse square) of radiation intensity on distance from a point source, the buildup from the surface to an equilibrium between primary photons and locally-absorbed secondary electrons, the attenuation (exponential) of the primary photons with depth of overlying material, and the scattered radiation contributed from surrounding irradiated material. It has been shown that the long-range scattered dose contribution to off-axis points can be well approximated by central axis values in an equivalent square field, so the standard tables are measured values on the beam axis for a series of square field sizes.

There are several standard formats for these tables which are chosen for convenience in particular applications, although the same data can be represented in all the forms. Factors can be devised to convert data from one tabulation for use in another context, with considerable sacrifice of conceptual clarity and human-factor reliability.
 

For therapy fields that are planned with a fixed source-surface distance the standard format is called Percent Depth Dose, where values are tabulated for a particular SSD, relative to that measured at the depth of dose maximum for various field sizes. This table is used with a list of relative scatter factors for each field size to put back what was taken out to get values of 100% at d(max), but the difference in scatter contribution with depth for projected field sizes is incorporated into the tabulated values. It also needs an output calibration factor for each field size to take account of the difference between the standard geometry chosen for absolute calibration of the therapy machine and the 100% point chosen for each column of the data.
 

Thus for a specified SSD and beam quality, the dose rate at any depth on the beam axis is:  R(s,d) = PDD(s,d) x SF(s) x OF(s) x T x W  where  R(s,d)   is the dose rate, cGy/count or cGy/minute.  PDD(s,d)   is the tabulated value for field size s and depth d.   SF(s)   is the scatter factor for field size s.  OF(s)   is the output calibration factor for field size s.  T   is the transmission factor for a block tray if used.  W   is the wedge factor if one is in use.  So the absorbed dose at depth d on the beam axis is:  D(s,d,N) = R(s,d) x N  where  N is the number of dose integrator counts or minutes.  Therefore the dose setting or time to deliver the prescribed dose D is:  N = D(s,d,N) / R(s,d)       = D(s,d,N) / PDD(s,d) x SF(s) x OF(s) x T x W.     For isocentric treatment planning the region of interest is at a depth in the patient rather than near the surface, and the depth-dose data format is chosen for convenience of use near the isocenter where multiple beams combine to give a prescribed total dose. The Tissue-Air Ratio table is the historic antecedent of formats which give values measured at isocenter as a function of depth of overlying tissue or phantom material and of field size where originally the measured values were tabulated relative to an ionization chamber calibration of Roentgens exposure in air at the isocenter.  Although the definition of exposure has been extended to higher energies the "mini-phantom" or buildup cap which is required for secondary particle equilibrium is so large that it is impractical above the cobalt-60 energy range. Therefore modern calibration protocols rely on measurements at a depth in phantom material such as water or polystyrene, with a typical therapy field size, and they determine the absorbed dose in the phantom. We might call the table of data relative to such a calibration a "Relative Tissue-Air Ratio" or "Tissue-Calibration Ratio" but these are not standard names. The best we can do with standard terminology is "Tissue-Phantom Ratio Times Scatter Factor", or recently, "Tissue-Output Ratio".

 

In the Tissue-Phantom Ratio format the measured dose values at isocenter for each depth are presented as decimal fractions of that measured for calibration depth in each field size, and the Scatter Factor is listed relative to that measured for the standard calibration field size and depth, typically 10x10 cm at 5 cm depth for beams in the 4- to 10-MV energy range. The relative Output Factor is listed for each field size as well. If the irradiated field size differs from the collimator setting, because of extended distance, blocked fields, or off-axis calculation points, the appropriate equivalent square field s is used in the table lookup and for the Scatter Factor, while the Output Factor is found from the collimator equivalent square, c.  Then the dose rate at isocenter, with any depth d of overlying tissue, is:   R(c,s,d) = TPR(s,d) x SF(s) x OF(c) x T x W  relative to that measured at the isocenter distance q from the radiation source. For a calculation point at any other distance p from the source an inverse square factor is needed to determine the dose rate:  R(c,s,d,p,q) = TPR(s,d) x SF(s) x OF(c) x T x W x (q/p)2,  where the distance of the calculation point from the isocenter is (p-q), a positive number for points below or negative for points above, independent of the depth d of the point from the phantom surface.  If the absolute calibration of the machine was done at depth in a phantom, at isocenter, the relative Output Factor for the calibration field size is 1.000; otherwise it incorporates a factor to account for the difference in calibration geometry.  Now the dose setting or time to deliver the prescribed dose D is:   N = D(c,s,d,p,q,N) / R(c,s,d,p,q)       = D(c,s,d,p,q,N) / TPR(s,d) x SF(s) x OF(c) x T x W x (q/p)2  The Tissue-Maximum Ratio format presents the measured dose values at isocenter, as a decimal fraction of the dose measured at isocenter in each field size at the depth of maximum in a standard field, for each field size and depth below the phantom surface. The Scatter Factor that is taken out to get values relative to one at depth of maximum dose is listed for each field size, as well as the Output Factor that might also take account of differences from the absolute calibration geometry.  Then the dose rate at any point at a distance p from the source, at a depth d in the phantom, on the beam axis in a projected equivalent-square field size s, is given by:  R(c,s,d,p,q) = TMR(s,d) x SF(s) x OF(c) x T x W x (q/p)2  Thus the dose setting or time to deliver the prescribed dose D is:  N = D(c,s,d,p,q,N) / R(c,s,d,p,q)       = D(c,s,d,p,q,N) / TMR(s,d) x SF(s) x OF(c) x T x W x (q/p)2

 

For many years the best method of acquiring depth-dose data was with an analog plotting system that moved a radiation detector along the beam axis in a water phantom with an arbitrary dose rate factor that was adjusted to represent 100% at the depth of maximum dose in each field. Even if a ratio recording system was used to reduce the effect of fluctuations in accelerator output it had a reference detector at an arbitrary location in the beam and made no claim to be an absolute calibration. These depth-dose values were scaled with an inverse-square factor to the isocenter distance and interpolated from the projected field sizes to the nominal field size at each depth. Then separate measurements were made at reference depth, at isocenter, of the relative Scatter Factor and Output Factor for each field size.  The terminology and format of Tissue-Phantom Ratio and Tissue-Maximum Ratio tables were formalized in the context of the measurement methods that were prevalent in the 1970's, although conceptually they were based on ideas and laboratory measurements that date from the 1960's development of isocentric treatment planning with Cobalt-60 sources and Tissue-Air Ratio measurements. In the 1980's new technology has simplified the direct acquisition of data for the classical format which includes scatter data in the tabulated values at every depth.  Today a digital electrometer and motorized controls on collimator and table lift make the ideal measurement much easier, with the radiation detector permanently mounted at isocenter and the depth adjusted by moving the phantom. By measuring the charge accumulated during an accelerator run that is terminated at a given dose integrator setting we get the effect of a ratio measurement that is independent of dose rate and subject to end effects that are identical and typical of an actual therapy dose. We must only factor out the relative effect of collimator setting on accelerator output, due to variation of backscattered electrons which affect the dose integrator ion chamber, and the variation of forward-scattered photons from the primary collimator and flattening filter due to the occultation of this extended source by the field collimator jaws. This must be measured in the absence of nearby scattering material except for a mini-phantom that duplicates the calibration depth and excludes scattered electron contamination, with lateral dimensions less than the smallest field size to be calibrated.  Since the lookup of Scatter Factor and Tissue-Phantom Ratio is always for the same equivalent square field size, and the Scatter Factor was abstracted from the measured data to make the Tissue-Phantom ratio equal one at calibration depth, the chances for error are decreased and the data are conceptually simplified if the two factors are left together in a single number for each depth and field size, hence Tissue-Phantom Ratio times Scatter Factor, now called Tissue-Output Ratio.  With this format the dose rate at any point at a distance p from a source, at a depth d in the phantom, with equivalent-square collimator setting c, on the beam axis in an equivalent-square field of size s, is given by:  R(c,s,d,p,q) = TOR(s,d) x OF(c) x T x W x (q/p)2 Then the dose setting or time to deliver the prescribed dose D is:  N = D(c,s,d,p,q,N) / R(c,s,d,p,q)       = D(c,s,d,p,q,N) / TOR(s,d) x OF(c) x T x W x (q/p)2

The above formats are standardized ways to tabulate absorbed-dose data measured in a homogeneous tissue-equivalent phantom along the symmetry axis of a square field, to facilitate manual machine-setting calculations to deliver a prescribed dose to such an axial point in a uniform medium. For off-axis points and inhomo-geneous media the data must be extended and used in ways that have become practical with electronic computers.

G_S_23DEC90\RTTEACH\RELDD.DOC v.894 ==>Reldd.htm
Posted 8 August 1998 by  [Glen Sandberg]