British Journal of Radiology (2006) 79, 244-247
© 2006 British Institute of Radiology
doi: 10.1259/bjr/70202978
Margins between clinical target volume and planning target volume for electron beam therapy
S J Thomas, MA, MSc, PhD
Medical Physics, Addenbrooke's Hospital, Cambridge CB2 2QQ, UK
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Abstract
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When growing a clinical target volume (CTV) to a planning target volume (PTV), it is necessary to determine suitable margins, based on the systematic and random uncertainties. For electron therapy, where treatments are usually given with single fields, the factors affecting the margin are very different in the direction of the incident beam from those in the perpendicular directions, since set-up errors do not affect the depth of the 90% isodose. For a typical case, the perpendicular margins are three times the margin in the direction of the incident beam. This gives rise to problems with volume growing algorithms if the beam axis is not aligned with a cardinal axis.
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Introduction
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The International Commission of Radiation Units and Measurements (ICRU), in reports 50 and 62 [1, 2], defines the gross tumour volume (GTV), the clinical target volume (CTV) and the planning target volume (PTV). Both reports discuss factors contributing to the CTV-PTV margin, but do not give any recipes for its calculation. The British Institute of Radiology (BIR) has recently published a report on Geometric Uncertainties in Radiotherapy [3], which reviews sources of uncertainty and describes methods of calculating CTV-PTV margins. All the specific advice relates to photon beams rather than electron beams.
ICRU report 71 [4] extends the work of ICRU 62 to electron beam therapy. This report gives a recipe for calculating the CTV-PTV margin, based on work by Stroom et al [5]. A CTV-PTV margin which ensures at least 95% of the dose to 99% of the CTV is given by:
where 
is the standard deviation for the systematic (preparation) error, and 
is the standard deviation for the random (execution) error. However, this margin recipe is based on photon beam therapy, making a number of assumptions that do not hold for electron beams.
The aim of the work described below is to develop a method of calculating margins that is valid for the conditions applying in electron beam therapy.
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Theory
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The methods described by the BIR report on Geometric Uncertainties in Radiotherapy [3], for photon therapy with multiple beams give the following margin, to ensure a minimum dose to the CTV of 95% for 90% of patients:
where and are as in Equation (1), a and b are corrections for planning algorithm error and breathing, respectively, p is the unblurred beam penumbra width, and 
is a value that depends on the beam configuration, being always 1.64 in the superior–inferior (sup-inf) direction for coplanar beams, and taking lower values in transverse planes depending on the number and arrangement of beams. When = 1.64 and p = 3.2 mm, the last term of Equation (2) approximates to 0.7, as in Equation (1).
The derivation is based on the assumption of a CTV that is approximately spherical, with an arrangement of beams designed to conform the dose distribution to it in three dimensions. However, the more usual situation in electron therapy is as shown in Figure 1
. A single beam, shaped by a metal cut-out, is chosen with an energy appropriate to the depth required to ensure that the 90% isodose covers the PTV. It is apparent that the effect of geometrical uncertainties in the x and y directions in Figure 1 is very different from the effect of geometrical uncertainties in the z direction.
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Figure 1. A typical electron treatment. The planning target volume(PTV) is shown in dark grey, the collimator (cut-out) is shown in light grey. The 90% isodose conforms to the PTV in the xy plane, at the depth of maximum PTV width.
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Systematic errors
The BIR report [3] describes four gaussian sources of systematic error, the standard deviations of which may be combined in quadrature; the doctor's delineation error doctor, the organ position and shape (excluding breathing) error motion, the set up error setup and the phantom transfer error transfer.
doctor is the systematic error resulting from interclinician and intraclinician variation in volume delineation. The issue of whether doctor can be combined in quadrature with other errors is still a matter of debate; recent work by McKenzie [6] suggests that it cannot be handled in the same manner as the other gaussian errors, but requires an alternative theoretical basis. In the example below I have omitted it, and assumed that it has been included in the CTV.
motion is the systematic error in position and shape (excluding breathing). It will not be affected by modality, so can be treated in the same way as for photons. setup (the standard deviation of the systematic set-up error) can be treated in the same way as for photons in the x and y direction. However, in the z direction, most errors have no effect on the position of the isodoses. A systematic shift of a few millimetres in the z position of the patient relative to the end of the applicator may have a small effect on delivered dose (generally less than 1%), but will not affect the depth of the isodoses.
The phantom transfer error transfer, is the error accumulated in transferring image data through the treatment planning system to the linear accelerator, including errors in imaging, planning, and linear accelerator geometry. Since the component from accelerator geometry will have no effect on the depth of isodoses, transfer will be less in z than in x and y.
An additional systematic uncertainty, which affects only the z direction, is uncertainty in electron density derived from CT. For low atomic number materials, published data for eight CT scanners showed a maximum error in electron density of 2.5%, with a standard deviation below 1% [7]. Most electron treatments are given through soft tissue. The density, in the depth of the 90% depth dose, varies with energy from 0.2 mm at 6 MeV to 0.6 mm at 21 MeV. For bone, if a standard curve is used for all scanners, errors of up to 6% can be observed, with a standard deviation below 2.5%. If 10 mm of the depth is bone of density 1.5, density becomes 0.4 mm at 6 MeV, 0.8 mm at 21 MeV.
In all the clinical examples in the BIR report [3], the dominant systematic gaussian errors are setup and transfer. Since these are insensitive to systematic errors in the z direction, the problem will change from a 3D case to a 2D case. As shown by Van Herk et al [8], this reduces the systematic margin from 2.5 to 2.15.
Linear errors
Geometric Uncertainties in Radiotherapy [3] defines two linear errors, the "breathing positional error" b and the "treatment planning system photon-beam algorithm error" a.
The breathing error b can be treated in the same manner as for photons, since the derivation of the margin is not dependent on modality.
Electron treatment planning algorithms do not usually give as good agreement with measurement as do photon algorithms. The errors are very dependent on the shape of the patient surface, and the size and shape of inhomogeneities. For photon planning, simple measurements can determine whether the planning system over-corrects or under-corrects the field sizes, and corrections can be made. For electrons, this error is very plan dependent, and is probably best not included in the PTV margin. Hence a has been taken as zero.
Treatment execution errors
There are two random gaussian errors considered by the BIR report [3], the daily set-up error set-up and the organ position and shape execution error, motion. Both of these combine in quadrature to give the of Equation (2).
set-up can be treated in the same way as for photons in the x and y direction. However, in the z direction, most errors have no effect on the position of the isodoses, for the same reasons as given for systematic set-up errors.
motion will be unaffected by modality, so can be treated in the same way as for photons.
Unblurred penumbra width
The unblurred beam penumbra width p requires a very different treatment for electrons than for photons. In the x and y directions, although the penumbra of an electron field can still be defined by a gaussian, the width of the gaussian varies very rapidly with depth and energy. A penumbra can be described by an error function with a parameter p; an approximation for p (in mm) can be derived from the data of Lax et al [9]:
where Z is depth in mm, E is the electron energy at the surface in MeV, and R is the range in mm, which can itself be approximated by:
The depth to be used depends on the exact shape of the systematic target volume (STV), which is the volume resulting after a margin is added to the CTV to account for systematic errors [3]. The STV-PTV margin accounts for the random (execution) errors. Table 1 calculates the p for two different depths. In the first case, the STV is assumed to be ellipsoidal, and symmetrically situated between 10 mm deep and the depth of the 90% isodose (D90). In this case the widest point of the target volume will be depth D1 = (10 mm + D90)/2. In the second case, the calculation has been done at D90; this has been chosen to deal with the extreme cases where the target volumes are widest at their deepest position. All penumbral widths are within 1 mm of 5 mm at D1, and within 2 mm of 6 mm at D90.
The depth dose fall-off can also be approximated with a gaussian. Values of pdd can be chosen such that the shape of the measured percentage depth dose curve (centred on the depth of the 50%) is matched by values of
Figure 2 gives an example of this fit; the shape of the depth dose is well modelled from the depth of dose maximum to the depth of 5% dose. Table 1
shows values of pdd derived by this method, which vary from 7 mm at 6 MeV to 23 mm at 21 MeV. pdd is used in place of p in Equation (2).
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Figure 2. This illustrates the use of a gaussian to model the shape of the depth dose curve. The line is measured beam data for a 15 MeV beam, the points are calculated from Equation (5), using a pdd of 12 mm. A close fit is observed from the depth of maximum dose down to the depth of 5%.
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Fitting to a 90% dose level with a single beam gives a of 1.28, as derived in Van Herk et al [8]. If a simplified version of Equation (2) is required, to enable comparison with Equation (1), the final term of Equation (2) can be approximated to 0.3, for values of up to 5 mm, using the linear approximation of Van Herk et al [8], for x and y, if p = 5 mm,. For z, it approximates to 0.2 at 6 MeV, reducing to 0.1 at 18 MeV.
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Example
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Let us assume we are treating a target volume in the head or neck. We will assume an anterior beam, so that the z direction of Figure 1 corresponds to the posteroanterior (PA) direction. We will use values for the systematic and random errors based on those used in Chapter 7 of Geometric Uncertainties in Radiotherapy [3]. For the example chosen, where the patient is immobilized, breathing errors are taken to be negligible, so b is omitted.
Table 2 shows the resulting margins. For the values shown, the anteroposterior (AP) margin is about 3 mm, the superior-inferior (Sup-Inf) and lateral margins about 10 mm. This means that geometrical uncertainties will have a larger effect on the size of cut-out required than they do on the electron energy.
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Table 2. Example of typical clinical target volume-planning target volume (CTV-PTV) margins for electron therapy. The beam is assumed to be an anterior beam. All distances are in millimetres. Values of  p and pdd for 12 MeV have been used; changing the energy between 5 MeV and 21 MeV will change the margin by a maximum of 0.1 mm in anterior-posterior (AP), and a maximum of 0.2 mm right-left (R-L) and superior-inferior (S-I)
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Discussion
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For electron treatments, a much smaller CTV-PTV margin is required in the direction of the incident beam than perpendicular to it. With most volume growing software, this is only straightforward in cases where the beam direction is along one of the cardinal axes, e.g. an anterior, a posterior or a true lateral beam. In cases where the beam is being applied obliquely, the geometry is an expansion ellipsoid whose principal axes are not aligned with the cardinal axes. This cannot be dealt with by most planning systems. One method of dealing with this would be to avoid making a CTV-PTV expansion, but instead to use the values directly in the field shaping and choice of energy.
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Conclusions
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The methodology of the BIR report on geometrical uncertainties [3] can be followed for electrons in the direction perpendicular to the incident beam, but using a 2.15 multiplier for the systematic errors. In the direction of the incident beam, the effect of set up errors has no effect on the margin, so margins are smaller.
In the direction perpendicular to the incident electron beam, the margin required is approximately 2.15z+b+0.3, where and are the standard deviations for systematic (preparation) errors and random (execution) errors, respectively, and b is the linear breathing margin. In the direction of the incident beam, this reduces to 2.15z +b+0.15z, where z and z exclude any set-up errors.
Received for publication April 21, 2005.
Revision received June 23, 2005.
Accepted for publication July 4, 2005.
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References
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- International Commission on Radiation Units and Measurements. ICRU Report 50. Prescribing, recording and reporting photon beam therapy. Bethesda MD: ICRU, 1993
- International Commission on Radiation Units and Measurements. ICRU Report 62 (Supplement to ICRU report 50). Prescribing, recording and reporting photon beam therapy. Bethesda MD: ICRU, 1999
- British Institute of Radiology Working Party. Geometric uncertainties in radiotherapy. London, UK: British Institute of Radiology, 2003
- International Commission on Radiation Units and Measurements. ICRU Report 71. Prescribing, recording and reporting electron beam therapy. Oxford University Press, 2004
- Stroom JC, deBoer HC, Huizenga H, Visser AG. Inclusion of geometrical uncertainties in radiotherapy planning by means of coverage probability. Int J Radiat Oncol Biol Phys 1999;43:905–19.[CrossRef][Medline]
- McKenzie AL. A novel way to allow for uncertainties in delineation and changes in shape of target volumes in radiotherapy. In: Chambers LA, Chambers IR, editors. Proceedings of the 11th Annual Scientific Meeting; 2004 September 6–8; York, UK. York, UK: Institute of Physics in Engineering and Medicine, 2004
- Thomas SJ. Relative electron density calibration of CT scanners for radiotherapy treatment planning. Br J Radiol 1999;72:781–6.[Abstract]
- Van Herk M, Remeijer P, Rasch C, Lebesque JV. The probability of correct target dosage: dose-population histograms for deriving treatment margins in radiotherapy. Int J Radiat Oncol Biol Phys 2000;47:1121–35.[CrossRef][Medline]
- Lax I, Brahme A, Andreo P. Electron beam dose planning using Gaussian beams. Improved radial dose profiles. Acta Radiol Suppl 1983;364:49–59.[Medline]
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Abstract
Introduction
