Radiol Oncol 2003; 37(2): 115-26. Prostate IMRT fractionation strategies: two-phase treatment versus simultaneous integrated boost Pavel Stavrev and Dimitre Hristov Medical Physics Unit, Montreal General Hospital & McGill University, 1650 Cedar Ave., Montreal, H3G 1A4, Canada Background. The purpose of the study was to investigate the radiobiological effect of the number of frac-tions, position uncertainties and clonogen spread (microscopic disease) on two different inverse treatment planning alternatives: (a) 2-phase strategy; (b) simultaneous integrated boost (SIB). Material and methods. The tumour control probability (TCP) and normal tissue complication probability (NTCP) were calculated for the 2-phase strategy, which has well defined fractionation scheme and compared to the TCP and NTCP for the SIB strategy calculated as a function of the number of fractions. For a 7-beam IMRT prostate treatment, we have performed inverse treatment planning for the two different strategies fol-lowing the above method. Results. When the position uncertainties and clonogen spread were accounted for in the TCP calculation a drop as large as 10% was found. A drop of 5-7% in the TCP was obtained for the SIB strategy, if delivered in the same number of fractions as the 2-phased one. Conclusions. The potential of inverse planning to design tight conformal dose distributions is fully revealed in the SIB optimization process. The optimized SIB superior dose distributions require modification of the delivered dose per fraction and therefore careful selection of the fractionation regime. Hence physically op-timized SIB treatments may not always lead to better tumour control and tissue sparing. Key words: prostatic neoplasms - radiotherapy; radiotherapy, conformal; radiotherapy dosage; dose frac-tionation Received 1 April 2003 Accepted 6 May 2003 Correspondence to: Pavel Stavrev, Ph.D., (currently at) Department of Medical Physics, Cross Cancer Institute, 11560 University Ave, Edmonton, Alberta, T6G 1Z2, Canada; E-mail: pstavrev@phys.ualberta.ca This work is supported by an MRC grant MOP 36470. Introduction The availability of inverse planning and in-tensity modulated radiotherapy (IMRT) technology opened the possibility of designing new treatment strategies with superior dose distributions, namely tighter treatment mar-gins and therefore better organ sparing. Recently Mohan et al.,1 and Wu et al.,2 have suggested a »simultaneous integrated boost« (SIB) IMRT approach to head and neck 116 Stavrev P et al. / Prostate IMRT fractionation strategies cancer, leading to better conformity and su-perior dose distributions in the organs at risk compared to a standard way of radiation treatment planning. The SIB strategy was proposed as an alternative to the commonly used two-phase radiation therapy. The idea it-self, namely, - uniting the conventional 2-phase treatment strategy in one, is not new, it was considered by a number of authors be-fore.3-6 The application of IMRT to it is the important new development. In their study this approach was applied to head and neck cancer. In this paper we consider the SIB ap-proach applied to the case of prostate cancer taking the effect of position uncertainties and possible clonogen spread into account. Further development of the investigations of Mohan et al.,1 is conducted by more detailed radiobiological analyses. While, the main quantity under consideration in Wu et al.2 was the »normalized total dose« NTD (simi-larly to Lebesque and Keus),3 here we demon-strate the application of tumour control prob-ability (TCP) and normal tissues complication probability (NTCP) models to evaluate the SIB IMRT plans as a function of the number of fractions. We demonstrate with this work that the SIB IMRT physical optimization, al-though leading to superior dose distributions in physical terms - with respect to specified dose and dose-volume criteria - may result in lower tumour control or higher probability for organ damage depending on the fraction-ation strategy chosen. Material and methods Treatment strategies A patient who had recently undergone radiation treatment for the carcinoma of the prostate in our centre was re-planned with inverse planning for the purpose of this study (Figures 1a, b, c). The original treatment tech-nique employed a four-field box arrangement (Plan I) with 18 MV MLC-shaped conformal beams to deliver a uniform dose of 44 Gy to planning target volume I (PTV1) in 22 daily fractions. In the second phase of the treat-ment (Plan II), a three-field technique with one anterior (gantry angle 0°) and two poste-rior lateral fields (gantry angles 260° and 100°) was employed to deliver a boost of 26 Gy to planning target volume II (PTV2) in 13 daily fractions. PTV1 encompassed the gross tumour volume (GTV) with a uniform 1.5 cm margin to account for microscopic disease, set-up uncertainties, and organ motion. PTV2 encompassed the GTV with a uniform 0.5 cm margin to account for set-up uncertainties and organ motion. In both phases the patient was treated in supine position. A 7-beam treatment technique (Figures 1b, 1c) was optimized with the Helios inverse planning option of the CadPlan treatment planning system (Varian Medical Systems, Palo Alto, CA). For the two-phase strategy, Plan I and Plan II were optimized separately with the optimization parameters listed in Table 1. In terms of target coverage and blad-der/rectum sparing these parameters resulted in dose distributions superior to the ones de-livered by the original forward treatment Table 1. Inverse treatment planning dose and priority prescriptions for the different treatment strategies PTV1 PTV2 Bladder Rectum Dmin[Gy] Dmax[Gy] Priority D min[Gy] Dmax[Gy] Priority Dmax[Gy] Priority Dmax[Gy] Priority Plan I Plan II SIB44 SIB55 44 44 55 44 70 70 100 % 100 % 100 % 26 70 70 26 70 70 100 % 100 % 100 % 33.9 20.0 53.9 53.9 50 % 50 % 50 % 50 % 26.4 15.6 42.0 42.0 50 % 50 % 50 % 50 % Radiol Oncol 2003; 37(2): 115-26. Stavrev P et al. / Prostate IMRT fractionation strategies 117 technique. Note that, in relative terms, the dose and the priority prescriptions for Plan I and Plan II in Table 1 are identical. For the single phase, simultaneous integrated boost (SIB) strategy, both PTV1 and PTV2 were included in the optimization process and the prescription dose levels were combined to reflect the goal of the treatment in terms of total doses. Thus the SIB optimization prescribes 70 Gy to PTV2 and given the initial PTV1 objective of the 2-phase strategy - a minimum of 44 Gy to PTV1 (Table 1). However, after adding the two dose distributions optimized separately in the two-phase strategy, the minimal dose to PTV1 was found to be 55 Gy. Thus, two SIB plans with different minimum dose prescriptions to PTV1 were optimized (Table 1). Hereafter these are referred to as SIB44 and SIB55. Biological models In order to estimate the biological effect of a given dose distribution to the tumour or the organs at risk, the biologically equivalent dose was calculated. Based on it the TCP and NTCP were calculated using the model functions and the parameter estimates by.7-10 BED calculation For each point (voxel) ijk from a certain structure the BED was calculated as: [1] BEDm = L 1 + ßd. where cc/ß ratios of 10, 6 and 3.9 for the tumour, bladder and rectum respectively,11 were used. Following the recent suggestions of Brenner et al.12,13 initiating the discussion14-17 about the possible low cc/ß ratio for prostate, we have investigated the case of tumour cc/ß of 2 Gy as well. For the two-phased approach the BED is the sum of: [2] MD»-Dj*'flt^2!l [.Ä c" »r where the index PTV1 refers to the dose distribution for the treatment of the larger volume accounting for the clonogen spreads, PTV2 refers to the boost volume and mfr and kfrare the number of fractions for both con- secutive phases. Because of the higher dose uniformity in the tumour, Eq. [2] is identical to Eq. [1]: nfr=mfr+kfr; Dijk=DPijkTV1+DPijkTV2. However, this statement does not hold true when the normal tissue is considered due to the significant dose heterogeneity throughout volumes of normal tissues in the vicinity of the treated targets. In this case each normal tissue voxel has different dose per fraction, which changes from phase-1 to phase-2. It should be noted here that for the pur-poses of the biological index estimation in the 2-phase strategy, the DVHs are rather useless tool. This is why the TCP/NTCP estimation was done on the bases of the BED distribu-tions instead of BED DVHs. Some au-thors11,18 use NTD - the dose corresponding to a standard df = 2 Gy dose per fraction regime: [3] D , + d, + d . instead BED, for the NTCP calculations. TCP and NTCP estimation The TCP is calculated by the following formula: [4] ff TCP = 0.5 ^2exp 2y» ln2 An The values of the parameters for prostate tumours (T3 stage) are: g50=0.95, D50=46.3 , as estimated in the work of Okunieff et al..9 There are several models for NTCP estimation. Here, the Lyman phenomenological model19 and the Critical Volume (CV) population model10,20-25 are used. The Lyman phenomenological model is given by: [5] n TCP = * »Djo Radiol Oncol 2003; 37(2): 115-26. 118 Stavrev P et al. / Prostate IMRT fractionation strategies where, the effective dose corresponding to a given dose distribution is, [6] D,/; = — V y D ijk This formula was first derived in an explic-it form by Niemierko and Goitein26 and re-flects a histogram reduction algorithm pro-posed by Lyman and Wolbarst.27 It was shown by Niemierko and Goitein26 that this reduction scheme is consistent with the Critical Element model. It was also shown by Niemierko and Goitein26, that the Kutcher and Burman reduction algorithm28,29 is close-ly related to the Lyman and Wolbarst27 one. Formula [5] was recently proposed by Niemierko30 as a generalization of the equiv-alent uniform dose notion. In the above formulae Dijk denotes the dose to the ijk-th voxel, N is the total number of voxels in a structure. The values of the NTCP parameters are n=.5;m=.11;D50=80 Gy (bladder) and n=.12;m=.15;D50=80 Gy (rec-tum).8 Recently, several authors have consid-ered the dose delivered to the rectal wall on-ly,18,31-34 as a complication factor, introduc-ing the usage of dose wall or dose surface histograms (DWH and DSH). In those works no parameter estimates are given and as far as the Burman et al.8 parameter values were calculated having in mind the dose to the whole volume, rather than the wall volume, here the NTCP are estimated based on the whole rectal and bladder volumes. Interestingly enough,18,31 report negligible differences in the NTCPs estimated by Lymans model and Burman et al.8 parameters based on the wall and whole rectal volume. Same results, for rectum, are obtained by Ting et al.32 using the critical element model.26 On the other hand we consider incorrect the application of the parameters given by Burman et al.8 for estimations using the DWHs because those parameters have been obtained by fits to a »data set« that did not have such sophisticated tools to extract rec-tum dose wall distributions.7 It should be emphasized that among the parameters estimated by Burman et al.8 there are some sets, which are considerably unreli-able, like those for rectum. If one examines closely the dose-volume effects reported in the »Emami data«35 it becomes obvious that in this case there are only 2 points for rectum and determining 3 parameter values from 2 data points is quite a long shot! Nevertheless these parameter values are used by many au-thors11,18.,31-33 and are found to produce rea-sonable NTCP values. For a comparison, we have also estimated the NTCP for bladder using the critical volume (CV) population model10,25 given with the following formulae: [7] ntcp = ln(- In jT, (r;, ,D„" , Dm)) + ln(- In p„) „-^•(^FrÄ-in^ [8] The parameters for bladder, estimated based on the »Emami data«,35 are taken from Stavrev et al.10 and are |xcr =0.26±0.11, o cr = 0.07±0.03, DF5S0U = 108 ± 24 [Gy], fF5 S0 U = 0.8 ± 0.2. However, Stavrev et al.10 didn’t bring out the parameter estimates for rectum due to the lack of data for their determination. A claim for CV model parameter estimation for rectum is made in the work of Hartford et al.,36 based on 41 patients. Unfortunately, the parameter values are not given in this work. In the above-presented TCP and NTCP estimation models, the response of the tissues to the variable fraction size is accounted for by a substitution of the voxel doses Dik by the BED ijk biologically equivalent voxel doses Accounting for the position uncertainties and clonogen spread One of the reasons behind the two phase strategy is that the slightly enlarged (in re-spect to GTV) volume (PTV2) is to account for Radiol Oncol 2003; 37(2): 115-26. Stavrev P et al. / Prostate IMRT fractionation strategies 119 the position uncertainties, while the initial target volume PTV1 is to account for both position uncertainties and possible clonogen spread. The position uncertainties and the way to account for them have been widely discussed in the literature.37-41 Following the ideas described in the article of Stavrev et al.37 one can define a reduced cell density - a notion combining the initial cell density with the position uncertainties. We presume the initial cell density H(r)constant over the GTV and the position uncertainties being described by a 3D normal distribution G(r). Here H is the Heviside step function being 1 in the GTV and 0 outside. Then the relative reduced cell density is given as: [9] P (r> = j O (r ) H (r - o )d o [10] TCP ¦ I /¦,„> The parameters a, N could be calculated directly from y50, D50.25 The possible clonogen spread may be modelled in a similar way. One can presume that a clonogen could leave its position and relocate at another one with a given probability. If the probability is presumed normal, it could be shown that Eq. [9] describes the process of migration as well. Hence, both processes could be described as convolutions of GTV with normal distributions with different standard deviations, which is equivalent to one convolution but the variance of the normal distribution is the sum of the first ones. The clinical practice guidelines in our institution determine the PTV2 as GTV with 5 mm margin and PTV1 as GTV with 15 mm margin. Hence, having in mind the normality (the 99 % of the possible values of the stochastic variable lay in +-3SD interval) of the position uncertainties and clonogen spread, we deduce that the first process is described with normal distribution with SD of ~1.6mm and the second one SD=3.2mm. Figure 2 demonstrates the GTV (the solid body) and the calculated reduced cell density, for the case under consideration. Results Figure 1 demonstrates isodose distributions for the 2-phased, SIB44 and SIB55 plans in the axial plane containing the treatment isocenter. Figure 3 illustrates the DVHs for the GTV, PTV1, bladder and rectum, as ob-tained for the 2-phased (solid line), SIB44 95 % 80 % 50 % 30 % 95 % 80 % 50 % 30 % 95 % 80 % 50 % 30 % Figure 1. Set-up for 7-beam prostate treatment tech-nique and central slice isodoses for (a) two-phase strategy, (b) - SIB 44, (c) - SIB 55. The PTV1 is denoted as 7, PTV2 - 2, GTV - 3, rectum - 5. The bladder is not seen on this slice. The 95 % isodose line lies between the PTV2 and PTV1 contours. The isodose distribu-tions are normalized to 100 % at the treatment isocenter. Radiol Oncol 2003; 37(2): 115-26. 120 Stavrev P et al. / Prostate IMRT fractionation strategies Figure 2. Illustration of the reduced cell density, accounting for the clonogen spread and position uncertainties Eq. [8]. The solid body represents the GTV surface on Figure (a), the reduced cell density »hallo« is shown for two per-pendicular planes. On Figures (b), (c) and (d) cross-sections in three perpendicular planes (axial 2a, coronal 2b, sagital 2c) with the GTV (the white object) and the reduced cell density are shown. (doted line) and SIB55 (dashed line) strate-gies. Both SIB strategies resulted in better sparing of the critical organs while satisfying the prescriptions with respect to the target volumes. 2-phased strategy For the 2-phased strategy we have calculated the NTCPs for bladder and rectum using Eq. Radiol Oncol 2003; 37(2): 115-26. [2], [5], [6] and have obtained the following values NTCP = 5.2% and NTCP bladder rectum 45%. The last represent the Lyman model NTCP estimates. An estimate of bladder NTCP was also obtained based on the CV model yielding the value of 8.25%. The TCP -Eq. [4] - based on the GTV BED distribution for the cases of a/ß = 2 and 10 Gy respectively is 93.1% and 84.2%. If the possible clono- Stavrev P et al. / Prostate IMRT fractionation strategies 121 1 0.8 0.6 0.4 0.2 bladder 1 0.8 0.6 0.4 0.2 20 40 60 80 dose [Gy] PTV1 0 20 40 60 80 dose [Gy] 1 0.8 0.6 0.4 0.2 0 1 0.8 0.6 0.4 0.2 rectum 0 20 40 60 80 dose [Gy] GTV 0 20 40 60 80 dose [Gy] Figure 3. DVHs for the three different treatments and different structures: (a) bladder, (b) rectum, (c) PTV1, (d) GTV. The two-phase approach (solid line) prescribes 44 Gy to the first phase volume and additional 26 Gy to the boost one. The actual delivered minimal dose to the first phase volume was 55 Gy. These prompted us to investi-gate two SIB IMRT plans delivering minimal doses of 44 Gy (dotted line) and 55 Gy (dashed line) to the first phase volume respectively. gen spread and the position uncertainties are taken into account using Eq. [9] and [10] one gets TCP ,„ = 2= 86% and TCP ,„ = 10 = 74.4%. The TCP and NTCP values for the 2-phased strategy are shown as lines parallel to the x-axes on Figures 4 a, b, c and d. SIB strategy The NTCPs for bladder and rectum, calculat-ed again on the basis of Eq. [2], [5], [6], for SIB44 and SIB55 correspondingly, as a func-tion of number of fractions are presented on Radiol Oncol 2003; 37(2): 115-26. 0 0 122 Stavrev P et al. / Prostate IMRT fractionation strategies 1 0.8 0.6 0.4 0.2 0 bladder a \ x ¦ V \ ¦ \. \ • \ '¦ \ DPTV1 . \ ¦ \u . = 55Gy - \ ¦ mm J ¦¦ \ \\ ¦ \ 'X A A \ X \ N \ X \ ^ N. ^ ' U . = 44Gy\- •. \ ¦ ¦ • . Dmin J ^^ ^ — ^-^- 2l_- —¦ ~ 1 0.8 0.6 0.4 0.2 rectum 10 15 20 25 30 35 number of fractions 1 0.95 0.9 0.85 0.8 0.75 0.7 Minimal dose to PTV1 44 Gy 0.65 0.6 1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 10 15 20 25 30 35 number of fractions 0.6 b 10 15 20 25 30 35 number of fractions Minimal dose to PTV1 55 Gy d a/P = 2Gy ^^ a/P = 10Gy 10 15 20 25 30 35 number of fractions Figure 4. Figures (a) and (b) show the influence of the fractionation on the bladder and rectum NTCPs for the SIB treatment strategies. The horizontal line represents the NTCP for the two-phase treatment. Figures (c) and (d) demonstrate the dependence of the TCP, accounted for clonogen spreads and marginal uncertainties, on the number of fractions for the two different SIB treatment plans. Again the horizontal line represents the TCP for the two-phase treatment. The effect of a possible smaller ct/ß ratio (2 vs. 10 Gy) is demonstrated. Note the drop in the TCP for SIB55 fraction treatment compared to the two-phased method. Considering the SIB55, reducing the number of fractions to 25 (ct/ß =10 Gy) or 30 (ct/ß =2 Gy) in order to achieve the two-phase-equivalent-TCP will or will not reduce the bladder and rectum NTCPs below their values for the two-phase treatment (Figures 4a and 4b). Figures 4a and 4b. Similarly the TCP, ac-counting for the clonogen spread and position uncertainties, as a function of number of fractions, for SIB44 is shown on Figure 4c and Radiol Oncol 2003; 37(2): 115-26. for SIB55 on Figure 4d. The both different curves on those plots correspond to the two different cc/ß ratios. In the case when the position uncertainties Stavrev P et al. / Prostate IMRT fractionation strategies 123 and clonogen spread are disregarded the TCP change with the number of fractions become negligibly small ~ 1.5% / 10 fractions. Discussion and conclusions First it should be said, that the TCP and NTCP values and relationships calculated here must be regarded more as relative numbers illuminating the interrelation of the dose-volume effects and fractionation on one hand and the biological outcomes on the other. It is clear from the DVHs shown on Figures 3a and 3b that the SIB strategy results in smaller doses delivered to the organs at risk. The dose delivered to GTV is equally uniform for the 2-phase and SIB strategy. Hence, from a point of view concerning the physical dose delivery the SIB strategy results in superior dose distributions. On the other hand while the 2-phase strategy is strictly tied to a given fractionation scheme, these is not true for the SIB one. Because of the difference in the dose distributions in PTV1 the impact on the possible clonogen spread and position uncertainty would be different. As it is seen from Figures 4c and 4d there is considerable drop (up to 7%) in the TCP when the SIB strategy is applied in the same number of fractions as the 2-phased one - 35 in our case. The comparison between Figures 4c and 4d illustrates, as expected, that this difference is smaller for SIB55 compared to SIB44, and also for the cc/ß = 2 Gy over cc/ß = 10 Gy. Figures 4c and 4d also demonstrate the magnitude of the cc/ß ratio impact over the TCP. The difference between the TCPs calculated for 2 Gy and 10 Gy cc/ß ratios is about 15% for SIB44 and 11% for SIB55, almost independent of the number of fractions. The same goes for the 2-phased strategy. Thus the effect of the different cc/ß ratios is very significant and although more detailed studies may end up with different, than the one used here, model param- eters, this would only shift up or down the TCP values but the impact on the TCP difference will be negligible. Hence, this result (Figures 4c and 4d) may be used as a hint of support for Brener’s statement12,13 in the light of the findings of Logue et al.16 for relatively high local control. Let us presume all the model parameters correctly estimated and consider the implication of the results shown on Figure 3. For the case cc/ß = 10 Gy and minimum of 44 Gy to PTV1, Figure 4c shows that if the SIB IMRT dose is delivered in 15 fractions it will result in the same TCP as the conventional 2-phase strategy. For the normal tissue, we get 24 and 21 fractions for bladder and rectum respectively. Hence in this case, regardless of the fractionation regime, either the TCP would be lower than the 2-phased strategy TCP, or the NTCP would be higher than the 2-phased strategy NTCP. This is quite natural, because the minimum dose to PTV1 in the conventional therapy was 55 Gy, not 44 Gy. When the optimization is done with the requirement - 55 Gy to PTV1, then one gets 24, 30 and 27 fractions for the tumour, bladder and rectum, respectively in order to achieve the same effect, as in the 2-phase strategy. In the case cc/ß = 2 Gy the situation is much better! The SIB44 plan leads to equivalent TCP at 21 fractions, and SIB55 at 29 fractions. In both cases, a 23 (or 29 for SIB55) fraction regime would lead to almost similar TCP for the tumour and NTCP for the bladder, while the NTCP for rectum will diminish. Now we should return to the question which most probably the reader has already asked himself - Why the value of NTCP for the rectum is so high? The answer to this question is simple - the parameter values of the Lymans model8,35 were calculated based on the nominal dose and in this case the usage of BED is improper. The use of Eq. [3] is equally incorrect. The NTCP values for bladder and rectum calculated using the nominal dose are .02% and 4 % correspondingly - these num- Radiol Oncol 2003; 37(2): 115-26. 124 Stavrev P et al. / Prostate IMRT fractionation strategies bers are quite acceptable as expected NTCPs. If calculated on the bases of Eq. [3] the NTCP values are almost negligible. On the other hand the fractionation effect could be ac-counted for only if BED (or Eq. [3]) is used with Lyman’s model. For the CV model the use of BED is equivalent of directly applying the LQ model of cell damage, when assessing the PFSU,25 a feature intrinsic to this model. Figure 4a - NTCP for bladder as a function of number of fractions - illustrates eloquently the difference between the Lyman and the CV model. The parameters for both models were estimated from the »Emami data«, but for the small probabilities (high number of fractions) NTCPCV is slightly higher than NTCPLyman and vice-versa for higher proba-bilities (smaller number of fractions). The potential of inverse planning to design tight conformal distributions is fully revealed when all relevant organs and targets along with the corresponding dosimetric con-straints (in terms of total doses) are consid-ered in a single optimization process. However, the delivery of such plans may gen-erally require modifications of existing frac-tionation regimes in order to assure similar outcomes. For the case of SIB prostate IMRT, ac-counting for position uncertainties and possi-ble clonogen spreads, we have estimated the radiobiological effect of various fractionation schemes using existing TCP/NTCP models. 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