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The effective dose (Deff) for electron beams
Radiotherapy and Oncology 74 (2005) 211–215 www.elsevier.com/locate/radonline
The effective dose (Deff) for electron beams Pawel Franciszek Kukolowicza,*, Malgorzata Gil-Ulkowskab, Wojciech Bulskib b
a Medical Physics Department, Holycross Cancer Centre, Artwinskiego 3, 25-734 Kielce, Poland Medical Physics Department, Cancer Centre-Institute Memorial M. Sklodowska-Curie, Roentgena 5, Warsaw, Poland
Received 27 October 2003; received in revised form 26 August 2004; accepted 28 September 2004 Available online 22 October 2004
Abstract Background and purpose: Calculation of the effective dose and proposal of a dose specification method for the electron beams. Patients and methods: In a homogenous water phantom the 3D dose distributions for electron beams of energy 6, 9, 12, 15, 18 and 21 MeV and beam size 10!10 cm were calculated. For a volume encompassed with 80, 85 and 90% isodose, the mean dose and the SD were calculated for each energy. Using the Brahme’s formulae, the effective dose was calculated. Results: The larger the minimum dose (value of the encompassing isodose), the larger the mean dose and the smaller the SD. The mean doses and SD to the volume encompassed with 80, 85 and 90% are in the range of 91–94%, and 5.1–6.2%, 93–96% and 4.2–4.6%, 94–96% and 3.0–3.2%, respectively. Thus the effective dose for the volume encompassed with 80, 85 and 90% are about 90, 93 and 95%, respectively. Conclusion: Taking into account the requirements regarding dose uniformity within the PTV and the sparing effect for normal tissue situated under the PTV, we propose to keep the 85% isodose as a minimum one and to prescribe the dose to the 90% isodose. The present method may be applied for single electron beams and typical cases. q 2004 Elsevier Ireland Ltd. All rights reserved. Keywords: Equivalent uniform dose; Dose prescription; Electrons
1. Introduction In the last decade, much effort has been devoted to working out recommendations on how to prescribe, record and report a treatment in external beam therapy. Following a long period of discussions, two separate documents were published, one by the International Commission on Radiation Units and Measurements and the second by the Nordic Association of Clinical Physics [1,5]. In 1999, the ICRU Report 62 was published as a Supplement to the ICRU Report 50 [6]. Both these documents describe, how to delineate the target to be irradiated for the radiotherapy to be successful, how to prescribe and how to report the dose in order to give a clear and unambiguous account of the treatment. The ICRU recommends that the dose be expressed at the ICRU Reference Point. From a geometrical point of view, the ICRU Reference Point is located at the centre (or in the central part) of the Planning Target Volume
* Corresponding author. 0167-8140/$ - see front matter q 2004 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.radonc.2004.09.012
(PTV), and when possible, at the intersection of the beam axes. Furthermore, the maximum dose and the minimum dose to the PTV should be reported. In ICRU Report 71, published in the year 2004, the general principles for reporting an electron beam therapy follows the recommendations for reporting photon therapy, i.e. as in the ICRU Report 50 and ICRU Report 62 [7]. It is emphasised that the prescription of a treatment is the responsibility of each radiation oncology team. The reporting of treatment must be done in a unique way. The dose that is to be reported is the dose at the ICRU Reference Point, which defined as in the ICRU Report 50. The NACP recommends the arithmetic mean value of the target dose distribution and its SD to be used for dose prescription and reporting. After publication of the Supplement to the ICRU Report 50, there is general agreement between both organizations on how to delineate the target volumes. In several papers published recently, the advantages and disadvantages of the recommendations have been evaluated from a theoretical as well as practical point of view. In 1997, Niemierko formulated the concept of the Equivalent
212
P. Franciszek Kukolowicz et al. / Radiotherapy and Oncology 74 (2005) 211–215
Uniform Dose (EUD) [9]. According to his research, any two dose distributions are equivalent if they lead to the same treatment outcome. Using the linear-quadratic model, he calculated the tissue complication probability for several theoretical dose distribution in the PTV and he concluded that if the dose distribution is quite homogenous, the EUD may be approximated by the mean dose to the PTV. Many years previously, in 1984, Brahme showed in a theoretical way that for a relatively small dose, the non-uniformity in the target volume (the SD smaller than 3%), the tumour control probability can be approximated by formula [3]: TCPðfDijk gÞ Z TCPðDMEAN Þ K
g2 s2 2 2TCPðDMEAN Þ DMEAN (1)
where, TCP({Dijk}) is the TCP for actual dose distribution in the target, the g37 is the slope of the dose–response curve at dose for which TCPZ0.37, TCP(DMEAN ) is the probability of the local control at the dose DMEAN, s is the SD of the dose in the target. He concludes that if the SD of the dose distribution in the target is less than 3–5% the treatment outcome for actual dose distribution would be the same as for the homogenous dose distribution for a dose equal to the mean dose to the target. Based on this result he proposed formulae to calculate the so called effective dose Deff [4]: 2 g50 s Deff Z DMEAN 1 K (2) 2TCPðDMEAN Þ DMEAN In this formula the same symbols are used as in formula (1). The only difference is that instead of g37, g50 is used. g50 is the slope of the dose–response curve at a dose for which TCPZ0.50. The quantitative difference between the g37 and the g50 is negligible. Detailed analysis of formula (2) reveal that the Deff plays the same role as the EUD proposed by Niemierko. The formula accounts for the heterogeneity of the dose distribution in the target volume for an equivalent uniform dose calculation. Kukołowicz and Mijnheer pointed out that for a variety of treatment techniques the mean dose to the PTV is correctly estimated by the ICRU Reference Dose [8]. Kukołowicz’s results are based on clinical data for photon dose distributions. There is no similar analysis for dose distributions of electron beams. Both the ICRU and NACP recommendations are applicable to electron beams. However, the agreement in dose specification between the two documents is not as obvious for electron beams as it is for photon beams, at least for clinical situations when the patient is irradiated with a single electron beam. In such cases, the ICRU Reference Dose is almost the same as the maximum dose; it must therefore be considerably larger than the EUD. From this point of view the NACP proposition seems to be better suited, as it makes use of the idea of the mean dose. However, the dose distribution in the PTV is usually less homogenous than it is for photon
beams resulting in a larger difference between the mean dose and the EUD. The idea of the NACP, for prescribing the dose to the mean dose, or the effective dose to the target volume, can be used for electron beams. The problem is that in many cases, the dose distribution for electron treatment plan is not calculated or the dose distribution is, at best, calculated in only one plane, so the mean dose is not known. In practice, the dose for electron plans is prescribed to an arbitrary chosen isodose value. As concerns the electron beams, the second decision which is made before the treatment is what minimum dose is to be delivered to the target volume. Both values, the isodose value and the minimum dose, are usually correlated with each other. Depending on the approach adopted in the radiotherapy department, the isodose values used for prescription purposes are 80, 85, 90 or 95%. For the two larger values the minimum dose values are usually 5–10% smaller. If the dose is prescribed to 80 or 85%, (these two are often treated as encompassing isodoses) the dose is prescribed to the minimum dose. The proper choice of both values should be such that the isodose value used for prescription is very near to the EUD and that the dose distribution is uniform enough; e.g. the uniformity conforms to the requirements of the ICRU 50 Report. In this paper, calculations will be presented for the mean dose and the SD of dose distribution in the region encompassed by a given isodose for electron beams. Based on the results, some rules of dose prescription for electron beams are proposed.
2. Materials and methods In the homogenous water phantom, the dose distributions for electron beams of energy 6, 9, 12, 15, 18 and 21 MeV and beam size 10!10 cm were calculated. The calculations were performed with a 3D treatment planning system: the TMS, Ver. 4.0B for beams generated by Mevatron 77 accelerator from Siemens. The water phantom was created by 21 parallel squares with sides equal to 20 cm placed 1 cm apart. The calculations were performed with a calculation grid spacing of 0.5 cm. The dose distributions were normalized to a maximum on the central axis. After the dose distribution calculation, in each slice where the maximum dose on the central axis was larger than 90%, the outlines of the regions V80, V85 and V90% encompassed by 80, 85 and 90% isodose were drawn. These regions were treated as the PTVs. In each slice, the outer contour of VX% was identical to the X% isodose line. The dose distribution was calculated again and both the mean dose and SD of dose distribution to the VX% were calculated. The effective dose was estimated according to Brahme’s formulae (2). The Deff was calculated assuming that g50 was 2 or 6, and TCP(DMEAN) was 0.5. In order to check to what extent the results depend on the type of accelerator, the calculations
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Table 1 The mean dose, the SD and the Deff calculated according to the Brahme’s formulae for electron beams of energy 6, 9, 12, 15, 18 and 21 MeV and for V80, V85 and V90%
V80 Mean dosea (%) SD (%) EUDgZ2 (%) EUDgZ6 (%) V85 Mean dose (%) SD (%) EUDgZ2 (%) EUDgZ6 (%) V90 Mean dose (%) SD (%) EUDgZ2 (%) EUDgZ6 (%)
6 MeV
9 MeV
12 MeV
15 MeV
18 MeV
21 MeV
92.4 5.6 92 90
91.5 5.9 91 89
92.1 5.1 92 90
94.1 5.7 93 92
94.5 6.2 94 92
94.4 6.2 94 92
93.9 4.6 93 93
93.1 4.6 93 92
92.9 4.2 93 92
95 4.4 95 94
95.7 4.5 95 94
95.7 4.5 95 94
96.3 3 96 96
95.1 3.1 95 94
94.6 3.1 94 94
95.9 3.1 96 95
96.6 3.2 96 96
96.7 3.2 96 96
The electron beam was generated with Mevatron 77 accelerator. For each case the ICRU Reference Dose is very close to 100%. a 100% is the maximum dose on the central axis.
were also performed for the 10!10 cm 12 MeV beam generated by Clinac 2300CD, for V80, V85 and V90%. The clinical data for 10 randomly chosen post-mastectomy patients were used in order to evaluate the influence of the skin surface and inhomogeneities on the dose distribution. Patients in our department are irradiated with a single field directed perpendicularly to the chest wall, with individually designed wax boluses in order to stick to the 80% as a minimum dose. It is the similar technique to the one applied in Aarhus [2]. The CT based calculation were performed with 3D treatment planning system TMS, Ver. 4.0B. The dose distribution was normalized to the mean dose to the PTV. There were 4 and 6 patients treated with the electron beams of energy 9 and 12 MeV, respectively. The calculations were performed with grid size of 0.5 cm.
3. Results In Table 1, the results of the calculation of the mean dose and the SD in the PTV for electron beams generated by a Mevatron 77 accelerator are shown. The Deff values calculated according to Brahme’s formula are also given. In Table 2, the results of the calculation of the mean dose and the SD to the V80, V85 and V90% for 12 MeV electron beam generated from Clinac 2300 C/D are shown.
4. Discussion In external radiotherapy, the application of electron beams is limited to superficial lesions. Limited range of electrons enables the irradiation of superficial malignant tissue and at the same time spares all tissues and organs lying under the irradiated region. If the 3D dose distribution
is not calculated before the treatment, which is very common practice for electron beams, the essential decision, which has to be made is the selection of the energy appropriate for the purpose of the treatment. Usually, the smallest available energy of the electron beam is chosen, which makes the dose given at the deepest point, in which the malignant cells are likely to be found, larger than a given value. This is a decision every radiotherapy department makes independently. The smaller the value of the minimum dose delivered to the PTV, the smaller the dose absorbed by the normal structures lying under the target. On the other hand, the smaller the prescription isodose, the less homogenous the dose distribution within the target volume. A compromise has to be reached. As shown in Table 1, the smaller the minimum dose, the larger the SD in the PTV. For minimum doses of 80, 85 and 90%, the SD is about 5.5, 4.5 and 3.0%, respectively. According to ICRU 50 recommendations, the minimum dose should not be less than the ICRU Reference Dose of more than 7%, and the maximum dose to the PTV should not be larger than the ICRU Reference Dose of more than 5%. For electron beams these requirements can be fulfilled in a precise manner if the minimum dose is equal to the 90% isodose, which makes the treatment range of electron beams smaller. In Table 3, the R80, R85 and R90 for all the energies of electron beams are compared. The larger the energy of the electron beam, the greater the difference between the R80 and R90. Table 2 The mean dose and the SD for electron beam of energy 12 MeV and for V80, V85 and V90% 12 MeV
V80%
V85%
V90%
Mean dose SD
92.0 5.2
92.7 4.4
94.3 3.2
The electron beam was generated with Clinac 2300CD accelerator.
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Table 3 The 80, 85 and 90% range for electron beams in centimetres
90% 85% 80%
6 MeV
9 MeV
12 MeV
15 MeV
18 MeV
21 MeV
1.7 1.8 1.9
2.6 2.8 2.9
3.6 3.8 4.0
4.6 4.9 5.1
5.5 6.0 6.3
6.0 6.5 7.0
For the smallest energy the difference is of 2 mm, for the largest one is of 1 cm which decreases the therapeutic volume by about 17%. The question which come to our attention is whether the requirements concerning the uniformity of dose distribution in the target volume for electron beams have to be as strict as for photon beams. If the electron beam is one of several beams used for the irradiation of the target volume with radical intent, the requirements are likely to be fulfilled. However, if a single electron beam is used on its own, we are of the opinion that less strict requirements regarding uniformity of dose distribution may be accepted. Similar opinion is formulated by the ICRU Report 71: “In electron beam therapy, it is not possible in general to enclose the whole PTV in the 95% isodose envelope. Lower isodoses have to be selected sometimes to encompass the PTV.” [7]. Usually, electron beams are used for lymph node irradiation, in order not to exceed the dose, which is safe when delivered to the spinal cord. The total dose delivered to a patient is usually relatively small, and even larger dose non-uniformity of electron dose distribution only slightly influences the uniformity of the total dose distribution. Individual electron beams are applied for irradiation of the chest wall for post-mastectomy patients. The main advantage of the application of electron beams for chest wall irradiation is sparing the lungs and the heart. It is better for both these organs if the minimum dose is small. In this case, a minimum dose of 80% makes the mean dose delivered to the lungs and heart as small as possible, but then the difference between the maximum and minimum dose to the PTV is of at least 20%. Considering the analysis of the application of electron beams, using 85% as a minimum dose and the R85 as the treatment range is a reasonable compromise. The calculations performed for electron beams generated by Clinac 2300CD show very close concordance with the results obtained for Mevatron 77 beams. The difference between the mean doses and SD for the same PTVX and the beams of the same nominal energy is smaller than 0.5%. The mean dose and SD to the PTV depend on the minimum dose. The larger the minimum dose (value of the encompassing isodose), the larger the mean dose and the smaller the SD. The mean doses to the VX% for 80, 85 and 90% minimum dose are in the range of 91–94%, 93–96% and 94–96%, respectively. For a single VX%, it is observed that the smallest values of the mean dose are for 9 and 12 MeV beams. For other energies, the mean doses are larger by about 2%. The SD for the VX% of 80, 85 and 90% are of about 6.0,
4.5 and 3%, respectively. For one VX% and different energies, only minor differences of SD are observed. The Deff calculated from Eq. (2) are for V80, V85 and V90% and gZ2 in the range 91–94%, 93–95% and 94–96%, respectively. The Deff calculated from Eq. (2) are for V80, V85 and V90% and gZ6 in the range 89–92%, 92–94% and 94–96%, respectively. The influence of dose non-uniformity on the Deff is very small. Only for the largest SD, that is 6%, and gZ 6, the Deff is smaller than the mean dose of about 2%. The Deff was calculated from the formulae proposed by the NACP protocol. Quantitatively similar results were obtained by Niemierko [9]. For values of SD typical for electron dose distributions, the differences between Niemierko’s results and those obtained from Eq. (2) are smaller than 2%. All the calculations were performed in idealized geometry. In all real situations, SD of dose distribution in the PTV is larger due to tissue heterogeneities. We compared the SD of dose distribution obtained for 10 randomly chosen post-mastectomy patients treated with electron beams of energy 9 or 12 MeV with results shown in Table 1. For post-mastectomy patients the SD of dose distribution in the PTV were in the range of 8–10%, depending on the shape of the chest wall and tissue heterogeneities. Thus, according to our expectations, clinically observed values of SD were several percent larger than those obtained in idealized conditions. As a result, the value of the Deff is also somewhat lower than shown in Table 1, for 80, 85 and 90% minimum isodoses the Deff can be estimated as 88, 90 and 92%, respectively. Taking into account two of the aspects of electron treatment, dose homogeneity and the dose administered to the normal structures, we proposed 85% as a minimum isodose. If this proposition has to be accepted, we suggest the prescription of the dose to the 90% isodose. Then the minimum dose is less than 7% smaller than the maximum dose, which is of less than 10% larger than the prescribed dose. It should be emphasized that the present method is useful for dose specification for single electron beams, for typical cases. If there is a risk of the dose distribution being influenced by heterogeneities, CT planning should be performed and another proposal of the NACP dose prescription might be considered.
5. Conclusion For electron beams, the effective dose (Deff) depends on the choice of the therapeutic range. The larger the minimum dose the larger the Deff. The effective dose for the volume encompassed with 80, 85 and 90% are about 90, 93 and 95%, respectively. Taking into account the requirements regarding dose uniformity within the PTV and the sparing effect for normal tissue situated under the PTV, we propose to keep the 85% isodose as a minimum one and to prescribe the dose to the 90% isodose. The present method may be applied for single electron beams and typical cases.
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References [1] Aaltonen P, Brahme A, Lax I, et al. Specification of dose delivery in radiation therapy. Recommendation by the Nordic Association of Clinical Physics (NACP). Acta Oncol 1997;36. [2] Bentzen SM, Christensen JJ, Overgaard J, Overgaard M. Some methodological problems in estimating radiobiological parameters from clinical data. Acta Oncol 1987;27:105–16. [3] Brahme A. Dosimetric precision requirements in radiation therapy. Acta Radiol 1984;23:379–91. [4] Brahme A. Which parameters of the dose distribution are best related to the radiation response of tumours and normal tissues. Proceedings of the International Seminar for Europe, the Middle East and Africa. Vienna: IAEA Publications; 1994 pp. 37–58, IAEA-TECDOC-734.
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[5] International Commission on Radiation Units and Measurements. ICRU Report 50. Prescribing, Recording, and Reporting Photon Beam Therapy. Report 50. Bethesda, MD: ICRU; 1993. [6] International Commission on Radiation Units and Measurements. ICRU Report 62. Prescribing, Recording, and Reporting Photon Beam Therapy (Supplement to ICRU Report 50). Bethesda, MD: ICRU; 1999. [7] International Commission on Radiation Units and Measurements. ICRU Report 71. General Recommendations for Prescribing, Recording, and Reporting External-Beam Therapy. Report 71. Bethesda, MD: ICRU; 2004. [8] Kukołowicz PF, Mijnheer BJ. Comparison between dose values specified at the ICRU reference point and the mean dose to the planning target volume. Radiother Oncol 1995;29:287–93. [9] Niemierko A. Reporting and analyzing dose distribution: a concept of equivalent uniform dose. Med Phys 1997;24:103–10.
The effective dose (Deff) for electron beams Pawel Franciszek Kukolowicza,*, Malgorzata Gil-Ulkowskab, Wojciech Bulskib b
a Medical Physics Department, Holycross Cancer Centre, Artwinskiego 3, 25-734 Kielce, Poland Medical Physics Department, Cancer Centre-Institute Memorial M. Sklodowska-Curie, Roentgena 5, Warsaw, Poland
Received 27 October 2003; received in revised form 26 August 2004; accepted 28 September 2004 Available online 22 October 2004
Abstract Background and purpose: Calculation of the effective dose and proposal of a dose specification method for the electron beams. Patients and methods: In a homogenous water phantom the 3D dose distributions for electron beams of energy 6, 9, 12, 15, 18 and 21 MeV and beam size 10!10 cm were calculated. For a volume encompassed with 80, 85 and 90% isodose, the mean dose and the SD were calculated for each energy. Using the Brahme’s formulae, the effective dose was calculated. Results: The larger the minimum dose (value of the encompassing isodose), the larger the mean dose and the smaller the SD. The mean doses and SD to the volume encompassed with 80, 85 and 90% are in the range of 91–94%, and 5.1–6.2%, 93–96% and 4.2–4.6%, 94–96% and 3.0–3.2%, respectively. Thus the effective dose for the volume encompassed with 80, 85 and 90% are about 90, 93 and 95%, respectively. Conclusion: Taking into account the requirements regarding dose uniformity within the PTV and the sparing effect for normal tissue situated under the PTV, we propose to keep the 85% isodose as a minimum one and to prescribe the dose to the 90% isodose. The present method may be applied for single electron beams and typical cases. q 2004 Elsevier Ireland Ltd. All rights reserved. Keywords: Equivalent uniform dose; Dose prescription; Electrons
1. Introduction In the last decade, much effort has been devoted to working out recommendations on how to prescribe, record and report a treatment in external beam therapy. Following a long period of discussions, two separate documents were published, one by the International Commission on Radiation Units and Measurements and the second by the Nordic Association of Clinical Physics [1,5]. In 1999, the ICRU Report 62 was published as a Supplement to the ICRU Report 50 [6]. Both these documents describe, how to delineate the target to be irradiated for the radiotherapy to be successful, how to prescribe and how to report the dose in order to give a clear and unambiguous account of the treatment. The ICRU recommends that the dose be expressed at the ICRU Reference Point. From a geometrical point of view, the ICRU Reference Point is located at the centre (or in the central part) of the Planning Target Volume
* Corresponding author. 0167-8140/$ - see front matter q 2004 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.radonc.2004.09.012
(PTV), and when possible, at the intersection of the beam axes. Furthermore, the maximum dose and the minimum dose to the PTV should be reported. In ICRU Report 71, published in the year 2004, the general principles for reporting an electron beam therapy follows the recommendations for reporting photon therapy, i.e. as in the ICRU Report 50 and ICRU Report 62 [7]. It is emphasised that the prescription of a treatment is the responsibility of each radiation oncology team. The reporting of treatment must be done in a unique way. The dose that is to be reported is the dose at the ICRU Reference Point, which defined as in the ICRU Report 50. The NACP recommends the arithmetic mean value of the target dose distribution and its SD to be used for dose prescription and reporting. After publication of the Supplement to the ICRU Report 50, there is general agreement between both organizations on how to delineate the target volumes. In several papers published recently, the advantages and disadvantages of the recommendations have been evaluated from a theoretical as well as practical point of view. In 1997, Niemierko formulated the concept of the Equivalent
212
P. Franciszek Kukolowicz et al. / Radiotherapy and Oncology 74 (2005) 211–215
Uniform Dose (EUD) [9]. According to his research, any two dose distributions are equivalent if they lead to the same treatment outcome. Using the linear-quadratic model, he calculated the tissue complication probability for several theoretical dose distribution in the PTV and he concluded that if the dose distribution is quite homogenous, the EUD may be approximated by the mean dose to the PTV. Many years previously, in 1984, Brahme showed in a theoretical way that for a relatively small dose, the non-uniformity in the target volume (the SD smaller than 3%), the tumour control probability can be approximated by formula [3]: TCPðfDijk gÞ Z TCPðDMEAN Þ K
g2 s2 2 2TCPðDMEAN Þ DMEAN (1)
where, TCP({Dijk}) is the TCP for actual dose distribution in the target, the g37 is the slope of the dose–response curve at dose for which TCPZ0.37, TCP(DMEAN ) is the probability of the local control at the dose DMEAN, s is the SD of the dose in the target. He concludes that if the SD of the dose distribution in the target is less than 3–5% the treatment outcome for actual dose distribution would be the same as for the homogenous dose distribution for a dose equal to the mean dose to the target. Based on this result he proposed formulae to calculate the so called effective dose Deff [4]: 2 g50 s Deff Z DMEAN 1 K (2) 2TCPðDMEAN Þ DMEAN In this formula the same symbols are used as in formula (1). The only difference is that instead of g37, g50 is used. g50 is the slope of the dose–response curve at a dose for which TCPZ0.50. The quantitative difference between the g37 and the g50 is negligible. Detailed analysis of formula (2) reveal that the Deff plays the same role as the EUD proposed by Niemierko. The formula accounts for the heterogeneity of the dose distribution in the target volume for an equivalent uniform dose calculation. Kukołowicz and Mijnheer pointed out that for a variety of treatment techniques the mean dose to the PTV is correctly estimated by the ICRU Reference Dose [8]. Kukołowicz’s results are based on clinical data for photon dose distributions. There is no similar analysis for dose distributions of electron beams. Both the ICRU and NACP recommendations are applicable to electron beams. However, the agreement in dose specification between the two documents is not as obvious for electron beams as it is for photon beams, at least for clinical situations when the patient is irradiated with a single electron beam. In such cases, the ICRU Reference Dose is almost the same as the maximum dose; it must therefore be considerably larger than the EUD. From this point of view the NACP proposition seems to be better suited, as it makes use of the idea of the mean dose. However, the dose distribution in the PTV is usually less homogenous than it is for photon
beams resulting in a larger difference between the mean dose and the EUD. The idea of the NACP, for prescribing the dose to the mean dose, or the effective dose to the target volume, can be used for electron beams. The problem is that in many cases, the dose distribution for electron treatment plan is not calculated or the dose distribution is, at best, calculated in only one plane, so the mean dose is not known. In practice, the dose for electron plans is prescribed to an arbitrary chosen isodose value. As concerns the electron beams, the second decision which is made before the treatment is what minimum dose is to be delivered to the target volume. Both values, the isodose value and the minimum dose, are usually correlated with each other. Depending on the approach adopted in the radiotherapy department, the isodose values used for prescription purposes are 80, 85, 90 or 95%. For the two larger values the minimum dose values are usually 5–10% smaller. If the dose is prescribed to 80 or 85%, (these two are often treated as encompassing isodoses) the dose is prescribed to the minimum dose. The proper choice of both values should be such that the isodose value used for prescription is very near to the EUD and that the dose distribution is uniform enough; e.g. the uniformity conforms to the requirements of the ICRU 50 Report. In this paper, calculations will be presented for the mean dose and the SD of dose distribution in the region encompassed by a given isodose for electron beams. Based on the results, some rules of dose prescription for electron beams are proposed.
2. Materials and methods In the homogenous water phantom, the dose distributions for electron beams of energy 6, 9, 12, 15, 18 and 21 MeV and beam size 10!10 cm were calculated. The calculations were performed with a 3D treatment planning system: the TMS, Ver. 4.0B for beams generated by Mevatron 77 accelerator from Siemens. The water phantom was created by 21 parallel squares with sides equal to 20 cm placed 1 cm apart. The calculations were performed with a calculation grid spacing of 0.5 cm. The dose distributions were normalized to a maximum on the central axis. After the dose distribution calculation, in each slice where the maximum dose on the central axis was larger than 90%, the outlines of the regions V80, V85 and V90% encompassed by 80, 85 and 90% isodose were drawn. These regions were treated as the PTVs. In each slice, the outer contour of VX% was identical to the X% isodose line. The dose distribution was calculated again and both the mean dose and SD of dose distribution to the VX% were calculated. The effective dose was estimated according to Brahme’s formulae (2). The Deff was calculated assuming that g50 was 2 or 6, and TCP(DMEAN) was 0.5. In order to check to what extent the results depend on the type of accelerator, the calculations
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Table 1 The mean dose, the SD and the Deff calculated according to the Brahme’s formulae for electron beams of energy 6, 9, 12, 15, 18 and 21 MeV and for V80, V85 and V90%
V80 Mean dosea (%) SD (%) EUDgZ2 (%) EUDgZ6 (%) V85 Mean dose (%) SD (%) EUDgZ2 (%) EUDgZ6 (%) V90 Mean dose (%) SD (%) EUDgZ2 (%) EUDgZ6 (%)
6 MeV
9 MeV
12 MeV
15 MeV
18 MeV
21 MeV
92.4 5.6 92 90
91.5 5.9 91 89
92.1 5.1 92 90
94.1 5.7 93 92
94.5 6.2 94 92
94.4 6.2 94 92
93.9 4.6 93 93
93.1 4.6 93 92
92.9 4.2 93 92
95 4.4 95 94
95.7 4.5 95 94
95.7 4.5 95 94
96.3 3 96 96
95.1 3.1 95 94
94.6 3.1 94 94
95.9 3.1 96 95
96.6 3.2 96 96
96.7 3.2 96 96
The electron beam was generated with Mevatron 77 accelerator. For each case the ICRU Reference Dose is very close to 100%. a 100% is the maximum dose on the central axis.
were also performed for the 10!10 cm 12 MeV beam generated by Clinac 2300CD, for V80, V85 and V90%. The clinical data for 10 randomly chosen post-mastectomy patients were used in order to evaluate the influence of the skin surface and inhomogeneities on the dose distribution. Patients in our department are irradiated with a single field directed perpendicularly to the chest wall, with individually designed wax boluses in order to stick to the 80% as a minimum dose. It is the similar technique to the one applied in Aarhus [2]. The CT based calculation were performed with 3D treatment planning system TMS, Ver. 4.0B. The dose distribution was normalized to the mean dose to the PTV. There were 4 and 6 patients treated with the electron beams of energy 9 and 12 MeV, respectively. The calculations were performed with grid size of 0.5 cm.
3. Results In Table 1, the results of the calculation of the mean dose and the SD in the PTV for electron beams generated by a Mevatron 77 accelerator are shown. The Deff values calculated according to Brahme’s formula are also given. In Table 2, the results of the calculation of the mean dose and the SD to the V80, V85 and V90% for 12 MeV electron beam generated from Clinac 2300 C/D are shown.
4. Discussion In external radiotherapy, the application of electron beams is limited to superficial lesions. Limited range of electrons enables the irradiation of superficial malignant tissue and at the same time spares all tissues and organs lying under the irradiated region. If the 3D dose distribution
is not calculated before the treatment, which is very common practice for electron beams, the essential decision, which has to be made is the selection of the energy appropriate for the purpose of the treatment. Usually, the smallest available energy of the electron beam is chosen, which makes the dose given at the deepest point, in which the malignant cells are likely to be found, larger than a given value. This is a decision every radiotherapy department makes independently. The smaller the value of the minimum dose delivered to the PTV, the smaller the dose absorbed by the normal structures lying under the target. On the other hand, the smaller the prescription isodose, the less homogenous the dose distribution within the target volume. A compromise has to be reached. As shown in Table 1, the smaller the minimum dose, the larger the SD in the PTV. For minimum doses of 80, 85 and 90%, the SD is about 5.5, 4.5 and 3.0%, respectively. According to ICRU 50 recommendations, the minimum dose should not be less than the ICRU Reference Dose of more than 7%, and the maximum dose to the PTV should not be larger than the ICRU Reference Dose of more than 5%. For electron beams these requirements can be fulfilled in a precise manner if the minimum dose is equal to the 90% isodose, which makes the treatment range of electron beams smaller. In Table 3, the R80, R85 and R90 for all the energies of electron beams are compared. The larger the energy of the electron beam, the greater the difference between the R80 and R90. Table 2 The mean dose and the SD for electron beam of energy 12 MeV and for V80, V85 and V90% 12 MeV
V80%
V85%
V90%
Mean dose SD
92.0 5.2
92.7 4.4
94.3 3.2
The electron beam was generated with Clinac 2300CD accelerator.
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Table 3 The 80, 85 and 90% range for electron beams in centimetres
90% 85% 80%
6 MeV
9 MeV
12 MeV
15 MeV
18 MeV
21 MeV
1.7 1.8 1.9
2.6 2.8 2.9
3.6 3.8 4.0
4.6 4.9 5.1
5.5 6.0 6.3
6.0 6.5 7.0
For the smallest energy the difference is of 2 mm, for the largest one is of 1 cm which decreases the therapeutic volume by about 17%. The question which come to our attention is whether the requirements concerning the uniformity of dose distribution in the target volume for electron beams have to be as strict as for photon beams. If the electron beam is one of several beams used for the irradiation of the target volume with radical intent, the requirements are likely to be fulfilled. However, if a single electron beam is used on its own, we are of the opinion that less strict requirements regarding uniformity of dose distribution may be accepted. Similar opinion is formulated by the ICRU Report 71: “In electron beam therapy, it is not possible in general to enclose the whole PTV in the 95% isodose envelope. Lower isodoses have to be selected sometimes to encompass the PTV.” [7]. Usually, electron beams are used for lymph node irradiation, in order not to exceed the dose, which is safe when delivered to the spinal cord. The total dose delivered to a patient is usually relatively small, and even larger dose non-uniformity of electron dose distribution only slightly influences the uniformity of the total dose distribution. Individual electron beams are applied for irradiation of the chest wall for post-mastectomy patients. The main advantage of the application of electron beams for chest wall irradiation is sparing the lungs and the heart. It is better for both these organs if the minimum dose is small. In this case, a minimum dose of 80% makes the mean dose delivered to the lungs and heart as small as possible, but then the difference between the maximum and minimum dose to the PTV is of at least 20%. Considering the analysis of the application of electron beams, using 85% as a minimum dose and the R85 as the treatment range is a reasonable compromise. The calculations performed for electron beams generated by Clinac 2300CD show very close concordance with the results obtained for Mevatron 77 beams. The difference between the mean doses and SD for the same PTVX and the beams of the same nominal energy is smaller than 0.5%. The mean dose and SD to the PTV depend on the minimum dose. The larger the minimum dose (value of the encompassing isodose), the larger the mean dose and the smaller the SD. The mean doses to the VX% for 80, 85 and 90% minimum dose are in the range of 91–94%, 93–96% and 94–96%, respectively. For a single VX%, it is observed that the smallest values of the mean dose are for 9 and 12 MeV beams. For other energies, the mean doses are larger by about 2%. The SD for the VX% of 80, 85 and 90% are of about 6.0,
4.5 and 3%, respectively. For one VX% and different energies, only minor differences of SD are observed. The Deff calculated from Eq. (2) are for V80, V85 and V90% and gZ2 in the range 91–94%, 93–95% and 94–96%, respectively. The Deff calculated from Eq. (2) are for V80, V85 and V90% and gZ6 in the range 89–92%, 92–94% and 94–96%, respectively. The influence of dose non-uniformity on the Deff is very small. Only for the largest SD, that is 6%, and gZ 6, the Deff is smaller than the mean dose of about 2%. The Deff was calculated from the formulae proposed by the NACP protocol. Quantitatively similar results were obtained by Niemierko [9]. For values of SD typical for electron dose distributions, the differences between Niemierko’s results and those obtained from Eq. (2) are smaller than 2%. All the calculations were performed in idealized geometry. In all real situations, SD of dose distribution in the PTV is larger due to tissue heterogeneities. We compared the SD of dose distribution obtained for 10 randomly chosen post-mastectomy patients treated with electron beams of energy 9 or 12 MeV with results shown in Table 1. For post-mastectomy patients the SD of dose distribution in the PTV were in the range of 8–10%, depending on the shape of the chest wall and tissue heterogeneities. Thus, according to our expectations, clinically observed values of SD were several percent larger than those obtained in idealized conditions. As a result, the value of the Deff is also somewhat lower than shown in Table 1, for 80, 85 and 90% minimum isodoses the Deff can be estimated as 88, 90 and 92%, respectively. Taking into account two of the aspects of electron treatment, dose homogeneity and the dose administered to the normal structures, we proposed 85% as a minimum isodose. If this proposition has to be accepted, we suggest the prescription of the dose to the 90% isodose. Then the minimum dose is less than 7% smaller than the maximum dose, which is of less than 10% larger than the prescribed dose. It should be emphasized that the present method is useful for dose specification for single electron beams, for typical cases. If there is a risk of the dose distribution being influenced by heterogeneities, CT planning should be performed and another proposal of the NACP dose prescription might be considered.
5. Conclusion For electron beams, the effective dose (Deff) depends on the choice of the therapeutic range. The larger the minimum dose the larger the Deff. The effective dose for the volume encompassed with 80, 85 and 90% are about 90, 93 and 95%, respectively. Taking into account the requirements regarding dose uniformity within the PTV and the sparing effect for normal tissue situated under the PTV, we propose to keep the 85% isodose as a minimum one and to prescribe the dose to the 90% isodose. The present method may be applied for single electron beams and typical cases.
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