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About the non-consistency of PTV-based prescription in lung
Physica Medica xxx (2017) xxx–xxx
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Original paper
About the non-consistency of PTV-based prescription in lung S. Lebredonchel, T. Lacornerie, E. Rault, A. Wagner, N. Reynaert, F. Crop ⇑ Centre Oscar Lambret, 3, rue Frédéric Combemale, 59000 Lille, France
a r t i c l e
i n f o
Article history: Received 14 December 2016 Received in Revised form 16 March 2017 Accepted 18 March 2017 Available online xxxx Keywords: Monte Carlo PTV Lung DVH DMH
a b s t r a c t Purpose: The goal of this study is to show that the PTV concept is inconsistent for prescribing lung treatments when using type B algorithms, which take into account lateral electron transport. It is well known that type A dose calculation algorithms are not capable of calculating dose in lung correctly. Dose calculations should be based on type B algorithms. However, the combination of a type B algorithm with the PTV concept leads to prescription inconsistencies. Methods: A spherical isocentric setup has been simulated, using multiple realistic values for lung density, tumor density and collimator size. Different prescription methods are investigated using DoseVolume-Histograms (DVH), Dose-Mass-Histograms (DMH), generalized Equivalent Uniform Dose (gEUD) and surrounding isodose percentage. Results: Isodose percentages on the PTV drop down to 50% for small tumors and low lung density. When applying the same PTV prescription to different patients with different lung characteristics, the effective mean dose to the GTV is very different, with factors up to 1.4. The most consistent prescription method seems to be the DDMH 50% (PTV) DMH point, but is also limited to tumors with size over 1 cm. Conclusions: Even when using the different prescription methods, the prescription to the PTV is not consistent for type B-algorithm based dose calculations if clinical studies should produce coherent data. This combination leads to patients’ GTV with low lung density possibly receiving very high dose compared to patients with higher lung density. The only solution seems to remove the classical PTV concept for type B dose calculations in lung. Ó 2017 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
1. Introduction Lung treatments are characterized by a high density tumor region surrounded with low density lung tissue. Type A algorithms, which do not take into account secondary electron transport in heterogeneities, lead to large errors in these low density regions [1–4]. Type B algorithms on the other hand take into account lateral electron transport in an approximate or exact manner. Details on the different dose calculation algorithms in the case of stereotactic treatments of lung lesions can be found in a recent review paper by Fogliata et al. [5]. Here we investigate in detail the consequences of using a PTV in combination with type B algorithms. The PTV concept [6] is based on an uncertainty margin around the CTV in order to compensate for random and systematic uncertainties. The PTV is thus a fictitious volume including low lung density volume. In the case of type A algorithms, this poses no problem Abbreviations: MC, Monte Carlo; PTV, Planning Target Volume; DVH, DoseVolume Histogram; DMH, Dose-Mass Histogram; gEUD, generalized Equivalent Uniform Dose; FFF, Flattening Filter Free. ⇑ Corresponding author. E-mail address: [email protected] (F. Crop).
for prescribing to the PTV: the dose is (incorrectly) homogeneous, allowing conventional prescriptions. There is an issue however in the case of type B algorithms combined with the PTV concept: dose is correctly calculated, but the current prescription methods lead to inconsistencies and no consensus has been reached [7]. The conventional practice of prescribing to DDVH 95% (PTV) is also commonly applied when type B algorithms are used for dose calculation (for example RTOG 0813 or LungTech EORTC). These type B algorithms calculate the dose correctly to both the tumor region and the surrounding lung [8]. A simple comparison with breast treatments can explain the issue at hand: when using a PTV in air for the flash region around breast in air (Fig. 1), the dose in air will be very low. This leads to a PTV DVH as shown in Fig. 1. In clinical practice, no one will prescribe or optimize on this type of volume for the breast. Neither will anyone use this kind of PTV volume to perform analysis of mean dose, median dose. . . In lung is the situation similar: less severe but more heterogeneous. This could lead to dose escalation to the GTV, depending on tumor size and lung density. Furthermore, by optimizing the fluence to the PTV, an excessive fluence will be optimized in order to obtain high doses in low density regions. The comparison with
http://dx.doi.org/10.1016/j.ejmp.2017.03.009 1120-1797/Ó 2017 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: Lebredonchel S et al. About the non-consistency of PTV-based prescription in lung. Phys. Med. (2017), http://dx.doi.org/ 10.1016/j.ejmp.2017.03.009
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Fig. 1. Breast treatment with PTV in air, calculated with a Collapsed Cone algorithm. The DVH shows a skewed behavior.
breast treatments holds again: in water, this will play less of a role. In lungs, higher dose to the GTV is not really an issue, but inconsistencies in the results of clinical studies and evidence-based medicine are a real issue. Coherent dose prescriptions and dose reporting are required in order to apply correctly the dose prescriptions [7,9]. In lung, this issue is further complicated due to the large variety of lung and tumor densities and tumor sizes amongst patients: are these factors taken into account in ‘‘conventional” prescriptions? Lacornerie et al. [10] demonstrated in a clinical setting (Novalis, Clinac and Cyberknife) that prescribing to the PTV using a type B algorithm leads to an under-estimation of the dose to the GTV, due to important differences between lung and target density. They demonstrated that prescribing directly to D50% of the GTV reduces the dose variability. However, the PTV is used during optimization with a type A algorithm in order to obtain sufficient fluence around the GTV and to provide robustness against positioning uncertainties. Van der Voort et al. [4] show that different dose levels according to the size of the lesion should be used when using MC based dose calculations (CyberKnife). They encountered the issue of the dose coverage of the PTV depending on several parameters. They optimized the MC volume to the PTV in order to respect the classical 95% PTV or isodose coverage and propose different dose prescription levels as the usage of PTV is very variable for MC calculated dose distributions. In the current paper, we investigate in detail the issues related to combination of the PTV prescription with type B calculated dose distributions for lung treatments focusing on the impact of lung density, target density and target size. We also investigate whether these issues can be resolved by using the Dose-Mass Histogram (DMH) concept [11,12] or the generalized Equivalent Uniform Dose (gEUD) concept [13,14]. 2. Methods 2.1. Monte Carlo calculations Monte Carlo calculations simulate particle transport by taking into account secondary electron transport in heterogeneities. The
EGS++ [15] and BEAMnrc packages [16–18] were used for Monte Carlo dose calculations. A custom user code was programmed in order to speed up calculations by taking into account the correlations between the particle histories for different setups. Electron and photon cut-off energies were defined as 0.521 MeV and 0.01 MeV respectively. The number of histories was chosen in order to obtain an uncertainty level below 0.7%. The BEAMnrc model of the 6 MV Cyberknife from Wagner et al. was used [19]. The theoretical setup consists of a spherical isocentric irradiation of a central GTV inside a 10 cm radius low density lung sphere (Fig. 2), corresponding to a central lung tumor. This is comparable to the setup of [3], but here we investigate the consequences of prescribing to a PTV with type B algorithms. The CyberKnife uses a 6 MV Flattening Filter-Free (FFF) accelerator, thus results should be comparable to any other 6 MV-FFF based linac attaining a 5 mm PTV margin. 2.2. Influencing factors Using the theoretical setup as defined in Fig. 2, there are several influencing factors for lung treatments. The factors investigated are: a) lung density, b) tumor density and c) tumor size. Realistic lung and tumor density values were taken from measurements of 30 patients: lung density was between 0.1 g/cm3 and 0.5 g/cm3, tumor density was found between 0.8 g/cm3 and 1.1 g/cm3. Even though 0.1 g/cm3 lung density might seem very low, this is actually a common value encountered in our patient population. Tumor size varied between 5 mm and 5 cm diameter. A PTV margin of 5 mm was applied. For each tumor size, the collimator size was chosen to correspond to the PTV size in water for a single field. The difference between the isodose percentage for a single beam and an isocentric irradiation is shown in Fig. 3: an isocentric setup leads naturally to a broader penumbra. This figure also shows the underlying reason for the use of 80% isodose line surrounding the tumor in the past (type A algorithms). A single beam has its sharpest penumbra at the 50–60% isodose line. The combination of multiple beams then leads to the 80% isodose line surrounding the tumor at the specific collimator size: this is not the point of the sharpest gradient for the combination of beams. This % isodose line varies slightly in water around the 80% value
Please cite this article in press as: Lebredonchel S et al. About the non-consistency of PTV-based prescription in lung. Phys. Med. (2017), http://dx.doi.org/ 10.1016/j.ejmp.2017.03.009
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All calculations are thus based on a tracking or gating method for the tumor: we do not consider the Internal Target Volume (ITV) delineating all possible positions of the GTV during respiration. The consequences of an even larger low density air volume for a free-breathing treatment with ITV are further considered in the discussion. 2.3. Prescribing in clinical practice: DVH, DMH, gEUD and isodose Standard practice uses Dose-Volume-Histograms (DVH): this histogram corresponds to the percentage of volume receiving a certain dose. The Dose-Mass-Histogram (DMH) uses the percentage of mass instead, and includes explicitly the tissue densities: this leads to a lower influence of low density areas [2]. The effect of different prescription methods in clinical practice is investigated here. Typical clinical practice in SBRT is to prescribe a) to the DDVH 95% (PTV), or b) to the 80% isodose line surrounding PTV [20]. In the current paper, this will be extended towards the use of DVH DMH DMH a) DDVH 95% (PTV), b) D50% (PTV) [21], c) D95% (PTV), d) D50% (PTV) and e) gEUD(PTV). The gEUD is calculated according to the following formula, with a factor of a = 10 [13,14,22]:
Fig. 2. Spherical isocentric irradiation setup (figure not to scale).
depending on the collimator size (see Table 7, last line). The tumor size also has a direct geometric effect: when the GTV is small, the relative volume or relative mass of the surrounding PTV becomes more and more important.
gEUD ¼
X
!1=a
v i Dai
i
These different prescription methods, and the influence of the lung and tumor densities, are compared by evaluating the effective delivered dose to 50% of the GTV, compared to the prescription GTV point: ðDD50% Þ. However, there is always a difference, even in 95% PTV
water, between D50% GTV and D95% PTV, depending on multiple fac-
Fig. 3. Dose profile difference between single beam and isocentric irradiation in water.
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Table 1 Scaling factors for the evaluation of the different prescription methods.
95% PTV prescription
DVH D50% GTV D95% PTV
50% PTV prescription
D50% GTV D95% PTV
D50% GTV D50% PTV
DVH;lung
D50% GTV D50% PTV
DMH
H2 O
DVH;lung H2 O
D50% GTV D95% PTV
D50% GTV D50% PTV
DMH;lung
D50% GTV D95% PTV
50% gEUDPTV
H2 O
H2 O
D50% GTV D50% PTV
gEUD D GTV 50% DgEUDPTV lung GTV
DMH;lung
H2 O
tors. Therefore, in order to be able to compare the different prescription methods, each of these scaling factors should be normalized by a factor calculated in homogeneous water (case of DDVH 95% (PTV)):
GTV ðDD50% Þ . 95% PTV H2 O
This calculation in homogeneous water replaces
all densities, lung and tumor, by water with density 1 g/cm3. By dividing by this factor, the influence of the different factors and prescription method become apparent, removing the inherent difference between GTV and PTV already present in water. The same holds true for the comparison of DVH with DMH: the latter norGTV malization factor ðDD50% Þ 95% PTV
H2 O
is equal for DVH and DMH, permitting
the comparison between DVH and DMH prescription methods. If this factor is around 1, the dose to the GTV remains coherent in different patient-per-patient based conditions, compared to the prescribed histogram point for the PTV. The consistency of the different prescription methods (Table 1), DVH DMH DMH DDVH 95% (PTV), D50% (PTV), D95% (PTV), D50% (PTV) and gEUD(PTV) can thus be summarized in five tables. A high scaling factor indicates that the actual dose to the GTV will largely surpass standard practice due to the PTV prescription.
2.4. Influence of random position of GTV inside the PTV As the PTV concept is created in order to take into account the uncertainty on the position of the GTV, the random variation of the position of the GTV inside the PTV is evaluated (respiration is contained in the ITV concept). The current study is thus based on a tracking or gating method. However, we go further into detail of the consequences of a free-breathing treatment in the discussion. We applied a uniform random position of the GTV inside the PTV: this can be considered as an intermediate between a single fraction with the GTV on an extreme position and multiple frac-
tions where the GTV is in a Gaussian-probability distributed position inside the PTV. In this study, two collimator sizes are used: the first collimator size is equal to the PTV size and the second corresponds to the GTV. This latter approach mimics the suggested method by Disher et al. [23]: they propose to use the lateral electron disequilibrium of smaller field sizes by having higher maximum dose in the GTV which could lead to better lung sparing (but at 20 MV beam quality). 3. Results 3.1. Influencing factors DVH, DMH, gEUD and peripheral isodose results were calculated by varying lung and tumor density and tumor with collimator size (Table 2–7; Figs. 45a,b, and 6). These tables indicate the dose scaling to the GTV when prescribing to the PTV, due to the influence of the lung and tumor density and also the tumor/collimator size, excluding the differences already present in homogeneous water. The resulting dose distributions are most impacted by the density of the surrounding lung tissue. When the surrounding lung tissue has a low density, the density of the tumor volume starts to influence the dose distribution. When the volume of the GTV is lower, there is a more important effect of the volume ratio of the GTV to the PTV. The PTV, without the GTV, starts to have a larger volume than the GTV itself. 3.2. Prescribing in clinical practice: DVH, DMH, gEUD and peripheral isodose The results for all scaling factors are represented in Tables 2–6. Differences between DVH and DMH and the lung density influence are represented in Figs. 4, 5a, 5b and 6. We see very high factors for DVH prescriptions. These factors seem best when using DDMH 50% (PTV). The results for gEUD(PTV) are represented in Table 6, and lie in DVH between the DDVH 95% (PTV) and D50% (PTV) prescription methods. The resulting peripheral isodose lines in lung or in water are represented in Table 7. We see that the use of peripheral isodoses is always valid in water (1 g/cm3) up to the small lesions. But in lung, depending on the lung density, these peripheral isodose percentages drop drastically.
Table 2 DDVH 95% (PTV) prescription method, differences between 5 and 10% are shown in yellow, differences of larger than 10% are shown in red.
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Table 3 DDVH 50% (PTV) prescription method, differences between 5 and 10% are shown in yellow, differences of larger than 10% are shown in red.
Table 4 DDMH 95% (PTV) prescription method, differences between 5 and 10% are shown in yellow, differences of larger than 10% are shown in red.
Table 5 DDMH 50% (PTV) prescription method, differences between 5 and 10% are shown in yellow, differences of larger than 10% are shown in red.
Please cite this article in press as: Lebredonchel S et al. About the non-consistency of PTV-based prescription in lung. Phys. Med. (2017), http://dx.doi.org/ 10.1016/j.ejmp.2017.03.009
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S. Lebredonchel et al. / Physica Medica xxx (2017) xxx–xxx Table 6 50% gEUD PTV prescription method, differences between 5 and 10% are shown in yellow, differences of larger than 10% are shown in red.
Table 7 Isodose percentage on the periphery of the PTV, corresponding to the collimator size, corresponding to an isocentric irradiation. The last line corresponds to the isodose line of an isocentric irradiation in water.
3.3. Influence of random position of GTV inside the PTV The results of the random position inside the PTV are shown in Fig. 7. By adding the positioning uncertainty, the impact of tumor movement and uncertainty of GTV position becomes clear: the GTV is severely under dosed in the latter case where collimator size equals GTV.
4. Discussion 4.1. Influencing factors
gap between PTV and GTV. This leads to a ‘‘leg” in the DVH. When the prescription point is inside this ‘‘leg”, this will result in very large dose scaling to the GTV. We see that the use of DMH largely reduces this ‘‘leg” influence. The size of this ‘‘leg” is also dependent on the volume of the PTV compared to the GTV: this becomes more and more important for small GTV volumes as the PTV volume becomes relatively more important. The dose homogeneity of the GTV is also influenced by the surrounding lung density: the dose is more heterogeneous with low density lung surrounding the GTV. This is due to the lack of electronic equilibrium in the build-up direction.
4.1.1. Lung density influence Lung density appears to be the most important factor (Tables 2–5 and Figs. 4, 5 and 6). Prescribing conventionally to 95% of the PTV DVH results in a high dose to the GTV, with factors over 1.4. This means that patients with low lung density will receive in the GTV up to 1.4 times the prescribed dose when the prescrip-
4.1.2. Tumor density influence Whatever prescription method is applied, we see that tumor density has almost no influence when surrounding lung density is high (0.5 g/cm3). However, when lung density is low (<0.26 g/ cm3), the influence becomes slightly more important, especially for small GTV sizes. The underlying reason is twofold (Fig. 6): a)
tion is made to the DDVH 95% (PTV). The underlying reason is the deposited dose in the lung: as lung density lowers, the deposited dose in lung will also be lower. The result is shown in Fig. 4: lung density will dictate the lower region of the PTV DVH and leads to a bigger
DVH the PTV DVH prescription points (DDVH 95% (PTV) and D50% (PTV)) are actually no longer considering the GTV volume, only the PTV volume, and are equal for all GTV densities. This is thus due to the relative PTV volume compared to the GTV volume. b) The lack of
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Fig. 4. Lung density influence, for a GTV with 3 cm diameter, on both DVH and DMH.
electronic equilibrium due to the low density surrounding tissue: the buildup can only be obtained inside the GTV. If the water equivalent distance towards the center of the GTV becomes smaller than the buildup, scaling becomes more important. This can be shown for the case of a GTV size of 30 mm in low lung density (0.1 g/ 3
DDVH 95% (PTV)
cm ) for the prescription method: scaling varies between 1.37 and 1.41 and becomes more important for smaller sizes. DDMH 50% (PTV)
prescriptions do not exhibit this issue for non-small tumors as the 50% PTV point still contains GTV (see Fig. 6 lower right). One has to note that the theoretical case of a well delineated tumor was evaluated. In reality, the GTV can also contain low density tissue, which complicates this discussion even further. 4.1.3. Tumor size Tumor size has minimal influence in the presence of high density surrounding lung tissue (Tables 2–5 and Fig. 5a and b). With low lung density, tumor size quickly has an important influence, generating very large scaling factors. The same underlying reason of the lung ‘‘leg” can be seen in Fig. 5b. This is a combination of the lower volume ratio of GTV to PTV, combined with the specific lower dose in the low density PTV volume. When using a DMH, the volumetric lung influence is reduced, but the same effect starts to appear for very small tumor sizes. 4.2. Different prescription methods It is already clear, from a pure volumetric point of view, that the prescription methods based on the PTV cannot be coherent: the PTV, excluding GTV, contains more than double the volume of the GTV for tumors smaller than 3 cm diameter. The DMH concept lowers this volumetric influence by applying the mass percentage.
However, the mass percentage of the PTV is above 50% for tumors of 1 cm and below (0.26 g/cm3 lung density). This purely geometric effect is translated by the fact that the ratios Mass(GTV)/Mass (PTV) > Vol(GTV)/Vol(PTV). The application of the DDVH 95% (PTV) prescription point does not appear to be consistent: large scaling factors are present (Table 2). When switching to the DDVH 50% (PTV) prescription method instead, large scaling factors appear for fewer situations (Table 3). This is shown in Fig. 4 (leftmost graphs): the 50% PTV point is actually just on the break point between lung and GTV resulting in the 1.06 scaling factor for a 5 cm tumor with surrounding lung density of 0.1 g/cm3. When this ‘‘leg”, or thus lung influence, becomes more important for smaller tumor sizes, the DDVH 50% (PTV) prescription is no longer coherent. When using the DDMH 95% (PTV) instead, we see a small reduction of this effect (Table 4). The reason is represented in Figs. 4 and 5, second row (DMH): the ‘‘leg” due to the lung tissue is present even for the DMH beyond the 95% PTV point. Finally, the use of the DDMH 50% (PTV) prescription seems the most robust towards all variations in lung treatments (Table 5). However, it remains inaccurate for tumor sizes below 1 cm for normal to low density lung tissue: this is a mixture between the relative volume of the GTV compared to the PTV and the low density. There seems to be an inconsistency in the scaling factors between the 1 cm tumor volume and the 5 mm tumor volume. The underlying reason is that for the 5 mm tumor volume, the buildup is not even obtained while the GTV volume is insignificant compared to the PTV volume (3.7% volume). This leads to a factor slightly lower than for 1 cm tumor volume. The use of even lower DMH prescription points (D40%, D30%) could possibly resolve the issue, but the question is: isn’t it better to prescribe
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Fig. 5. (a and b): Lung density influence on DVH and DMH, for different tumor size a): 5 cm diameter and b) 1 cm diameter.
to the GTV after all? This issue is also closely related to dose optimization [10]. When considering the prescription to the gEUD of the PTV, the results are in between the results of prescribing to DDVH 95% (PTV) and
DDVH 50% (PTV) (see table 6). We can note that the use of gEUD(GTV) instead of D50% (GTV) does improve scaling factors by about a couple of % (results not shown here). It can be noted thus that the gEUD(GTV) could be slightly better than the use of the D50%
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Fig. 6. Tumor size and tumor density influence.
Fig. 7. Influence of random position of the GTV inside the PTV on the GTV DVH, with lung density of 0.26 g/cm3 and tumor density of 1 g/cm3. The dashed lines represent the resulting DVH for the GTV when a random position inside the PTV is applied.
(GTV) point, but further research is required in order to evaluate this in real conditions with density heterogeneities present. However, an issue remains with the use of the gEUD for the PTV prescription: how do we consider the ‘‘a” factor for the PTV volume excluding the GTV? Is it considered as tumor volume, healthy volume or in between [8]? Considering the use of the peripheral isodose, we see in Table 7 (last line) that the isocentric irradiation corresponds to the 80% isodose line in water. However, the use of this isodose percentage is not warranted in lung as the isodose percentage to prescribe on
depends heavily on the influencing factors (Table 7). Consequently, isocentric irradiations are not consistent either with the peripheral dose concept for PTV in lung, even when using Monte Carlo calculated dose. This also suggests that if one would optimize to obtain the 80% isodose line in low density lung on the PTV, it would require excess fluence in the ring surrounding the GTV. Even a minor displacement of the tumor region will lead to very high doses to high density tissues, leading to a non-robust plan: the dose actually delivered will not be the planned/reported dose. When excluding these low density voxels from optimization, the
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fluence will no longer be optimized for positioning uncertainties, so this does not provide a solution either. This influence would most likely be lower when applying the DMH concept: the surrounding low density lung would then have a lower weight. Another possible solution could be to attribute higher density to the PTV region and then recalculate afterwards. However, this does not change the final prescription issue to the PTV.
GTV in clinical situations with the presence of low density voxels inside the GTV. Further research is required in order to evaluate the best prescription method on the GTV itself in clinical conditions (D50% ; gEUDðGTVÞ . . .Þ, however, this does not invalidate the conclusions in the current study. Here we removed this factor and proved that even in homogeneous density GTV, the PTV prescription is not consistent.
The DDVH 50% (GTV) was evaluated throughout the analysis. The combination of a possible electronic disequilibrium in the GTV and the presence of low density voxels inside the GTV, giving rise to low MC calculated dose, could result in clinical practice in inco-
The use of the DDMH 50% (PTV) prescription seems the most consistent, but is still not valid for tumors with a diameter equal to or below 1 cm in medium to low density lung. Eventually, the DMH concept only minimizes the volumetric effect of the PTV but does not fundamentally change the dose distribution or prescription. Further research is required on the application of the DMH concept in lung during optimization. The current study is centered on a CyberKnife FFF 6 MV beam model with tracking (or gating), but when applying the same concepts to free breathing tumors, one can expect even larger discrepancies due to the relative small GTV volume compared to the ITV and PTV. The same applies in a real clinical setting: several other factors will add in as there are the GTV contouring, does GTV contain low density voxels, ribs. . . We showed that, even when not considering these, the PTV prescription is inherently inconsistent in lung. In practice, one will see a mix of different densities inside the PTV, leading to a mix of the current results. In the light of Ricardi et al. [9], we could suggest: a solution to consistency seems abandoning the PTV concept and relying on other methods for dose prescription, reporting and optimization as robust planning, fluence propagation, or optimizing using a type A algorithm.
herent DDVH 95% (GTV) results. The same can be mentioned about the gEUD(GTV): low density voxels inside the GTV could skew the results as the gEUD is sensitive towards low dose regions for tumoral tissue, but further research is required. Finally, there is still ongoing issue for the medical definition of CTV vs GTV in SBRT [24]. As this is a theoretical study, the GTV is well defined whereas in reality the GTV consists of heterogeneous density and has a nonwell defined border. Up to now, we have considered tracking or gated treatments. When considering free-breathing treatments, one can expect even larger variations, as the percentage ‘‘low density” lung volume becomes considerably larger: the ITV around the GTV would already contain low density lung volume. When adding a PTV to an already larger ITV volume, all factors would increase even further. The application of a different coverage probability, machine or technique leading to a different PTV size will also influence the obtained conversion factors: our results are specifically for a 5 mm PTV.
Acknowledgements 4.3. Influence of random position of GTV inside the PTV Not applicable. The results of randomly varying the GTV position uniformly inside the PTV volume are represented in Fig. 7. It is clear that a flash region is required when introducing position uncertainty. This shows that the D50% (GTV) point remains constant in the presence of uncertainty when applying a correctly sized field larger than the GTV. However, the GTV will no longer be correctly irradiated when applying a field size that equals the size of the GTV in the case of 6 MV photons. Thus restricting the field size to the GTV for 6 MV beam quality is not a good idea, even when it seems to spare lung tissue. Therefore, the use of lateral electron disequilibrium by applying higher max GTV dose as proposed by Disher et al. [23] applied for 20 MV photons, should require robust calculation in order to be sure that the presented dose is also the delivered dose in reality. 5. Conclusions Prescribing to the PTV using Monte Carlo calculated dose distributions is not consistent in lung. This conclusion can be extended towards general type B dose calculations as all studies show very good agreement between algorithms taking into account lateral electron disequilibrium. The most important factor leading to large inconsistencies is the lung density and its subsequent low dose and lack of buildup. The other factors, such as tumor density and tumor size become more important in the presence of low surrounding lung density, but all factors also influence each other. We showed that, due to the combination of MC calculated dose with the PTV concept, patients with very low lung density could receive up to 1.4 times the dose to the GTV even when prescribing exactly the same dose to the PTV. The D50% (GTV) GTV point was used as reference in this study: the use of a high % DVH/DMH(GTV) point, or the use of gEUD (GTV) could possibly over-evaluate low density voxels inside the
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Original paper
About the non-consistency of PTV-based prescription in lung S. Lebredonchel, T. Lacornerie, E. Rault, A. Wagner, N. Reynaert, F. Crop ⇑ Centre Oscar Lambret, 3, rue Frédéric Combemale, 59000 Lille, France
a r t i c l e
i n f o
Article history: Received 14 December 2016 Received in Revised form 16 March 2017 Accepted 18 March 2017 Available online xxxx Keywords: Monte Carlo PTV Lung DVH DMH
a b s t r a c t Purpose: The goal of this study is to show that the PTV concept is inconsistent for prescribing lung treatments when using type B algorithms, which take into account lateral electron transport. It is well known that type A dose calculation algorithms are not capable of calculating dose in lung correctly. Dose calculations should be based on type B algorithms. However, the combination of a type B algorithm with the PTV concept leads to prescription inconsistencies. Methods: A spherical isocentric setup has been simulated, using multiple realistic values for lung density, tumor density and collimator size. Different prescription methods are investigated using DoseVolume-Histograms (DVH), Dose-Mass-Histograms (DMH), generalized Equivalent Uniform Dose (gEUD) and surrounding isodose percentage. Results: Isodose percentages on the PTV drop down to 50% for small tumors and low lung density. When applying the same PTV prescription to different patients with different lung characteristics, the effective mean dose to the GTV is very different, with factors up to 1.4. The most consistent prescription method seems to be the DDMH 50% (PTV) DMH point, but is also limited to tumors with size over 1 cm. Conclusions: Even when using the different prescription methods, the prescription to the PTV is not consistent for type B-algorithm based dose calculations if clinical studies should produce coherent data. This combination leads to patients’ GTV with low lung density possibly receiving very high dose compared to patients with higher lung density. The only solution seems to remove the classical PTV concept for type B dose calculations in lung. Ó 2017 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
1. Introduction Lung treatments are characterized by a high density tumor region surrounded with low density lung tissue. Type A algorithms, which do not take into account secondary electron transport in heterogeneities, lead to large errors in these low density regions [1–4]. Type B algorithms on the other hand take into account lateral electron transport in an approximate or exact manner. Details on the different dose calculation algorithms in the case of stereotactic treatments of lung lesions can be found in a recent review paper by Fogliata et al. [5]. Here we investigate in detail the consequences of using a PTV in combination with type B algorithms. The PTV concept [6] is based on an uncertainty margin around the CTV in order to compensate for random and systematic uncertainties. The PTV is thus a fictitious volume including low lung density volume. In the case of type A algorithms, this poses no problem Abbreviations: MC, Monte Carlo; PTV, Planning Target Volume; DVH, DoseVolume Histogram; DMH, Dose-Mass Histogram; gEUD, generalized Equivalent Uniform Dose; FFF, Flattening Filter Free. ⇑ Corresponding author. E-mail address: [email protected] (F. Crop).
for prescribing to the PTV: the dose is (incorrectly) homogeneous, allowing conventional prescriptions. There is an issue however in the case of type B algorithms combined with the PTV concept: dose is correctly calculated, but the current prescription methods lead to inconsistencies and no consensus has been reached [7]. The conventional practice of prescribing to DDVH 95% (PTV) is also commonly applied when type B algorithms are used for dose calculation (for example RTOG 0813 or LungTech EORTC). These type B algorithms calculate the dose correctly to both the tumor region and the surrounding lung [8]. A simple comparison with breast treatments can explain the issue at hand: when using a PTV in air for the flash region around breast in air (Fig. 1), the dose in air will be very low. This leads to a PTV DVH as shown in Fig. 1. In clinical practice, no one will prescribe or optimize on this type of volume for the breast. Neither will anyone use this kind of PTV volume to perform analysis of mean dose, median dose. . . In lung is the situation similar: less severe but more heterogeneous. This could lead to dose escalation to the GTV, depending on tumor size and lung density. Furthermore, by optimizing the fluence to the PTV, an excessive fluence will be optimized in order to obtain high doses in low density regions. The comparison with
http://dx.doi.org/10.1016/j.ejmp.2017.03.009 1120-1797/Ó 2017 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
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Fig. 1. Breast treatment with PTV in air, calculated with a Collapsed Cone algorithm. The DVH shows a skewed behavior.
breast treatments holds again: in water, this will play less of a role. In lungs, higher dose to the GTV is not really an issue, but inconsistencies in the results of clinical studies and evidence-based medicine are a real issue. Coherent dose prescriptions and dose reporting are required in order to apply correctly the dose prescriptions [7,9]. In lung, this issue is further complicated due to the large variety of lung and tumor densities and tumor sizes amongst patients: are these factors taken into account in ‘‘conventional” prescriptions? Lacornerie et al. [10] demonstrated in a clinical setting (Novalis, Clinac and Cyberknife) that prescribing to the PTV using a type B algorithm leads to an under-estimation of the dose to the GTV, due to important differences between lung and target density. They demonstrated that prescribing directly to D50% of the GTV reduces the dose variability. However, the PTV is used during optimization with a type A algorithm in order to obtain sufficient fluence around the GTV and to provide robustness against positioning uncertainties. Van der Voort et al. [4] show that different dose levels according to the size of the lesion should be used when using MC based dose calculations (CyberKnife). They encountered the issue of the dose coverage of the PTV depending on several parameters. They optimized the MC volume to the PTV in order to respect the classical 95% PTV or isodose coverage and propose different dose prescription levels as the usage of PTV is very variable for MC calculated dose distributions. In the current paper, we investigate in detail the issues related to combination of the PTV prescription with type B calculated dose distributions for lung treatments focusing on the impact of lung density, target density and target size. We also investigate whether these issues can be resolved by using the Dose-Mass Histogram (DMH) concept [11,12] or the generalized Equivalent Uniform Dose (gEUD) concept [13,14]. 2. Methods 2.1. Monte Carlo calculations Monte Carlo calculations simulate particle transport by taking into account secondary electron transport in heterogeneities. The
EGS++ [15] and BEAMnrc packages [16–18] were used for Monte Carlo dose calculations. A custom user code was programmed in order to speed up calculations by taking into account the correlations between the particle histories for different setups. Electron and photon cut-off energies were defined as 0.521 MeV and 0.01 MeV respectively. The number of histories was chosen in order to obtain an uncertainty level below 0.7%. The BEAMnrc model of the 6 MV Cyberknife from Wagner et al. was used [19]. The theoretical setup consists of a spherical isocentric irradiation of a central GTV inside a 10 cm radius low density lung sphere (Fig. 2), corresponding to a central lung tumor. This is comparable to the setup of [3], but here we investigate the consequences of prescribing to a PTV with type B algorithms. The CyberKnife uses a 6 MV Flattening Filter-Free (FFF) accelerator, thus results should be comparable to any other 6 MV-FFF based linac attaining a 5 mm PTV margin. 2.2. Influencing factors Using the theoretical setup as defined in Fig. 2, there are several influencing factors for lung treatments. The factors investigated are: a) lung density, b) tumor density and c) tumor size. Realistic lung and tumor density values were taken from measurements of 30 patients: lung density was between 0.1 g/cm3 and 0.5 g/cm3, tumor density was found between 0.8 g/cm3 and 1.1 g/cm3. Even though 0.1 g/cm3 lung density might seem very low, this is actually a common value encountered in our patient population. Tumor size varied between 5 mm and 5 cm diameter. A PTV margin of 5 mm was applied. For each tumor size, the collimator size was chosen to correspond to the PTV size in water for a single field. The difference between the isodose percentage for a single beam and an isocentric irradiation is shown in Fig. 3: an isocentric setup leads naturally to a broader penumbra. This figure also shows the underlying reason for the use of 80% isodose line surrounding the tumor in the past (type A algorithms). A single beam has its sharpest penumbra at the 50–60% isodose line. The combination of multiple beams then leads to the 80% isodose line surrounding the tumor at the specific collimator size: this is not the point of the sharpest gradient for the combination of beams. This % isodose line varies slightly in water around the 80% value
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All calculations are thus based on a tracking or gating method for the tumor: we do not consider the Internal Target Volume (ITV) delineating all possible positions of the GTV during respiration. The consequences of an even larger low density air volume for a free-breathing treatment with ITV are further considered in the discussion. 2.3. Prescribing in clinical practice: DVH, DMH, gEUD and isodose Standard practice uses Dose-Volume-Histograms (DVH): this histogram corresponds to the percentage of volume receiving a certain dose. The Dose-Mass-Histogram (DMH) uses the percentage of mass instead, and includes explicitly the tissue densities: this leads to a lower influence of low density areas [2]. The effect of different prescription methods in clinical practice is investigated here. Typical clinical practice in SBRT is to prescribe a) to the DDVH 95% (PTV), or b) to the 80% isodose line surrounding PTV [20]. In the current paper, this will be extended towards the use of DVH DMH DMH a) DDVH 95% (PTV), b) D50% (PTV) [21], c) D95% (PTV), d) D50% (PTV) and e) gEUD(PTV). The gEUD is calculated according to the following formula, with a factor of a = 10 [13,14,22]:
Fig. 2. Spherical isocentric irradiation setup (figure not to scale).
depending on the collimator size (see Table 7, last line). The tumor size also has a direct geometric effect: when the GTV is small, the relative volume or relative mass of the surrounding PTV becomes more and more important.
gEUD ¼
X
!1=a
v i Dai
i
These different prescription methods, and the influence of the lung and tumor densities, are compared by evaluating the effective delivered dose to 50% of the GTV, compared to the prescription GTV point: ðDD50% Þ. However, there is always a difference, even in 95% PTV
water, between D50% GTV and D95% PTV, depending on multiple fac-
Fig. 3. Dose profile difference between single beam and isocentric irradiation in water.
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Table 1 Scaling factors for the evaluation of the different prescription methods.
95% PTV prescription
DVH D50% GTV D95% PTV
50% PTV prescription
D50% GTV D95% PTV
D50% GTV D50% PTV
DVH;lung
D50% GTV D50% PTV
DMH
H2 O
DVH;lung H2 O
D50% GTV D95% PTV
D50% GTV D50% PTV
DMH;lung
D50% GTV D95% PTV
50% gEUDPTV
H2 O
H2 O
D50% GTV D50% PTV
gEUD D GTV 50% DgEUDPTV lung GTV
DMH;lung
H2 O
tors. Therefore, in order to be able to compare the different prescription methods, each of these scaling factors should be normalized by a factor calculated in homogeneous water (case of DDVH 95% (PTV)):
GTV ðDD50% Þ . 95% PTV H2 O
This calculation in homogeneous water replaces
all densities, lung and tumor, by water with density 1 g/cm3. By dividing by this factor, the influence of the different factors and prescription method become apparent, removing the inherent difference between GTV and PTV already present in water. The same holds true for the comparison of DVH with DMH: the latter norGTV malization factor ðDD50% Þ 95% PTV
H2 O
is equal for DVH and DMH, permitting
the comparison between DVH and DMH prescription methods. If this factor is around 1, the dose to the GTV remains coherent in different patient-per-patient based conditions, compared to the prescribed histogram point for the PTV. The consistency of the different prescription methods (Table 1), DVH DMH DMH DDVH 95% (PTV), D50% (PTV), D95% (PTV), D50% (PTV) and gEUD(PTV) can thus be summarized in five tables. A high scaling factor indicates that the actual dose to the GTV will largely surpass standard practice due to the PTV prescription.
2.4. Influence of random position of GTV inside the PTV As the PTV concept is created in order to take into account the uncertainty on the position of the GTV, the random variation of the position of the GTV inside the PTV is evaluated (respiration is contained in the ITV concept). The current study is thus based on a tracking or gating method. However, we go further into detail of the consequences of a free-breathing treatment in the discussion. We applied a uniform random position of the GTV inside the PTV: this can be considered as an intermediate between a single fraction with the GTV on an extreme position and multiple frac-
tions where the GTV is in a Gaussian-probability distributed position inside the PTV. In this study, two collimator sizes are used: the first collimator size is equal to the PTV size and the second corresponds to the GTV. This latter approach mimics the suggested method by Disher et al. [23]: they propose to use the lateral electron disequilibrium of smaller field sizes by having higher maximum dose in the GTV which could lead to better lung sparing (but at 20 MV beam quality). 3. Results 3.1. Influencing factors DVH, DMH, gEUD and peripheral isodose results were calculated by varying lung and tumor density and tumor with collimator size (Table 2–7; Figs. 45a,b, and 6). These tables indicate the dose scaling to the GTV when prescribing to the PTV, due to the influence of the lung and tumor density and also the tumor/collimator size, excluding the differences already present in homogeneous water. The resulting dose distributions are most impacted by the density of the surrounding lung tissue. When the surrounding lung tissue has a low density, the density of the tumor volume starts to influence the dose distribution. When the volume of the GTV is lower, there is a more important effect of the volume ratio of the GTV to the PTV. The PTV, without the GTV, starts to have a larger volume than the GTV itself. 3.2. Prescribing in clinical practice: DVH, DMH, gEUD and peripheral isodose The results for all scaling factors are represented in Tables 2–6. Differences between DVH and DMH and the lung density influence are represented in Figs. 4, 5a, 5b and 6. We see very high factors for DVH prescriptions. These factors seem best when using DDMH 50% (PTV). The results for gEUD(PTV) are represented in Table 6, and lie in DVH between the DDVH 95% (PTV) and D50% (PTV) prescription methods. The resulting peripheral isodose lines in lung or in water are represented in Table 7. We see that the use of peripheral isodoses is always valid in water (1 g/cm3) up to the small lesions. But in lung, depending on the lung density, these peripheral isodose percentages drop drastically.
Table 2 DDVH 95% (PTV) prescription method, differences between 5 and 10% are shown in yellow, differences of larger than 10% are shown in red.
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Table 3 DDVH 50% (PTV) prescription method, differences between 5 and 10% are shown in yellow, differences of larger than 10% are shown in red.
Table 4 DDMH 95% (PTV) prescription method, differences between 5 and 10% are shown in yellow, differences of larger than 10% are shown in red.
Table 5 DDMH 50% (PTV) prescription method, differences between 5 and 10% are shown in yellow, differences of larger than 10% are shown in red.
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S. Lebredonchel et al. / Physica Medica xxx (2017) xxx–xxx Table 6 50% gEUD PTV prescription method, differences between 5 and 10% are shown in yellow, differences of larger than 10% are shown in red.
Table 7 Isodose percentage on the periphery of the PTV, corresponding to the collimator size, corresponding to an isocentric irradiation. The last line corresponds to the isodose line of an isocentric irradiation in water.
3.3. Influence of random position of GTV inside the PTV The results of the random position inside the PTV are shown in Fig. 7. By adding the positioning uncertainty, the impact of tumor movement and uncertainty of GTV position becomes clear: the GTV is severely under dosed in the latter case where collimator size equals GTV.
4. Discussion 4.1. Influencing factors
gap between PTV and GTV. This leads to a ‘‘leg” in the DVH. When the prescription point is inside this ‘‘leg”, this will result in very large dose scaling to the GTV. We see that the use of DMH largely reduces this ‘‘leg” influence. The size of this ‘‘leg” is also dependent on the volume of the PTV compared to the GTV: this becomes more and more important for small GTV volumes as the PTV volume becomes relatively more important. The dose homogeneity of the GTV is also influenced by the surrounding lung density: the dose is more heterogeneous with low density lung surrounding the GTV. This is due to the lack of electronic equilibrium in the build-up direction.
4.1.1. Lung density influence Lung density appears to be the most important factor (Tables 2–5 and Figs. 4, 5 and 6). Prescribing conventionally to 95% of the PTV DVH results in a high dose to the GTV, with factors over 1.4. This means that patients with low lung density will receive in the GTV up to 1.4 times the prescribed dose when the prescrip-
4.1.2. Tumor density influence Whatever prescription method is applied, we see that tumor density has almost no influence when surrounding lung density is high (0.5 g/cm3). However, when lung density is low (<0.26 g/ cm3), the influence becomes slightly more important, especially for small GTV sizes. The underlying reason is twofold (Fig. 6): a)
tion is made to the DDVH 95% (PTV). The underlying reason is the deposited dose in the lung: as lung density lowers, the deposited dose in lung will also be lower. The result is shown in Fig. 4: lung density will dictate the lower region of the PTV DVH and leads to a bigger
DVH the PTV DVH prescription points (DDVH 95% (PTV) and D50% (PTV)) are actually no longer considering the GTV volume, only the PTV volume, and are equal for all GTV densities. This is thus due to the relative PTV volume compared to the GTV volume. b) The lack of
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Fig. 4. Lung density influence, for a GTV with 3 cm diameter, on both DVH and DMH.
electronic equilibrium due to the low density surrounding tissue: the buildup can only be obtained inside the GTV. If the water equivalent distance towards the center of the GTV becomes smaller than the buildup, scaling becomes more important. This can be shown for the case of a GTV size of 30 mm in low lung density (0.1 g/ 3
DDVH 95% (PTV)
cm ) for the prescription method: scaling varies between 1.37 and 1.41 and becomes more important for smaller sizes. DDMH 50% (PTV)
prescriptions do not exhibit this issue for non-small tumors as the 50% PTV point still contains GTV (see Fig. 6 lower right). One has to note that the theoretical case of a well delineated tumor was evaluated. In reality, the GTV can also contain low density tissue, which complicates this discussion even further. 4.1.3. Tumor size Tumor size has minimal influence in the presence of high density surrounding lung tissue (Tables 2–5 and Fig. 5a and b). With low lung density, tumor size quickly has an important influence, generating very large scaling factors. The same underlying reason of the lung ‘‘leg” can be seen in Fig. 5b. This is a combination of the lower volume ratio of GTV to PTV, combined with the specific lower dose in the low density PTV volume. When using a DMH, the volumetric lung influence is reduced, but the same effect starts to appear for very small tumor sizes. 4.2. Different prescription methods It is already clear, from a pure volumetric point of view, that the prescription methods based on the PTV cannot be coherent: the PTV, excluding GTV, contains more than double the volume of the GTV for tumors smaller than 3 cm diameter. The DMH concept lowers this volumetric influence by applying the mass percentage.
However, the mass percentage of the PTV is above 50% for tumors of 1 cm and below (0.26 g/cm3 lung density). This purely geometric effect is translated by the fact that the ratios Mass(GTV)/Mass (PTV) > Vol(GTV)/Vol(PTV). The application of the DDVH 95% (PTV) prescription point does not appear to be consistent: large scaling factors are present (Table 2). When switching to the DDVH 50% (PTV) prescription method instead, large scaling factors appear for fewer situations (Table 3). This is shown in Fig. 4 (leftmost graphs): the 50% PTV point is actually just on the break point between lung and GTV resulting in the 1.06 scaling factor for a 5 cm tumor with surrounding lung density of 0.1 g/cm3. When this ‘‘leg”, or thus lung influence, becomes more important for smaller tumor sizes, the DDVH 50% (PTV) prescription is no longer coherent. When using the DDMH 95% (PTV) instead, we see a small reduction of this effect (Table 4). The reason is represented in Figs. 4 and 5, second row (DMH): the ‘‘leg” due to the lung tissue is present even for the DMH beyond the 95% PTV point. Finally, the use of the DDMH 50% (PTV) prescription seems the most robust towards all variations in lung treatments (Table 5). However, it remains inaccurate for tumor sizes below 1 cm for normal to low density lung tissue: this is a mixture between the relative volume of the GTV compared to the PTV and the low density. There seems to be an inconsistency in the scaling factors between the 1 cm tumor volume and the 5 mm tumor volume. The underlying reason is that for the 5 mm tumor volume, the buildup is not even obtained while the GTV volume is insignificant compared to the PTV volume (3.7% volume). This leads to a factor slightly lower than for 1 cm tumor volume. The use of even lower DMH prescription points (D40%, D30%) could possibly resolve the issue, but the question is: isn’t it better to prescribe
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Fig. 5. (a and b): Lung density influence on DVH and DMH, for different tumor size a): 5 cm diameter and b) 1 cm diameter.
to the GTV after all? This issue is also closely related to dose optimization [10]. When considering the prescription to the gEUD of the PTV, the results are in between the results of prescribing to DDVH 95% (PTV) and
DDVH 50% (PTV) (see table 6). We can note that the use of gEUD(GTV) instead of D50% (GTV) does improve scaling factors by about a couple of % (results not shown here). It can be noted thus that the gEUD(GTV) could be slightly better than the use of the D50%
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Fig. 6. Tumor size and tumor density influence.
Fig. 7. Influence of random position of the GTV inside the PTV on the GTV DVH, with lung density of 0.26 g/cm3 and tumor density of 1 g/cm3. The dashed lines represent the resulting DVH for the GTV when a random position inside the PTV is applied.
(GTV) point, but further research is required in order to evaluate this in real conditions with density heterogeneities present. However, an issue remains with the use of the gEUD for the PTV prescription: how do we consider the ‘‘a” factor for the PTV volume excluding the GTV? Is it considered as tumor volume, healthy volume or in between [8]? Considering the use of the peripheral isodose, we see in Table 7 (last line) that the isocentric irradiation corresponds to the 80% isodose line in water. However, the use of this isodose percentage is not warranted in lung as the isodose percentage to prescribe on
depends heavily on the influencing factors (Table 7). Consequently, isocentric irradiations are not consistent either with the peripheral dose concept for PTV in lung, even when using Monte Carlo calculated dose. This also suggests that if one would optimize to obtain the 80% isodose line in low density lung on the PTV, it would require excess fluence in the ring surrounding the GTV. Even a minor displacement of the tumor region will lead to very high doses to high density tissues, leading to a non-robust plan: the dose actually delivered will not be the planned/reported dose. When excluding these low density voxels from optimization, the
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fluence will no longer be optimized for positioning uncertainties, so this does not provide a solution either. This influence would most likely be lower when applying the DMH concept: the surrounding low density lung would then have a lower weight. Another possible solution could be to attribute higher density to the PTV region and then recalculate afterwards. However, this does not change the final prescription issue to the PTV.
GTV in clinical situations with the presence of low density voxels inside the GTV. Further research is required in order to evaluate the best prescription method on the GTV itself in clinical conditions (D50% ; gEUDðGTVÞ . . .Þ, however, this does not invalidate the conclusions in the current study. Here we removed this factor and proved that even in homogeneous density GTV, the PTV prescription is not consistent.
The DDVH 50% (GTV) was evaluated throughout the analysis. The combination of a possible electronic disequilibrium in the GTV and the presence of low density voxels inside the GTV, giving rise to low MC calculated dose, could result in clinical practice in inco-
The use of the DDMH 50% (PTV) prescription seems the most consistent, but is still not valid for tumors with a diameter equal to or below 1 cm in medium to low density lung. Eventually, the DMH concept only minimizes the volumetric effect of the PTV but does not fundamentally change the dose distribution or prescription. Further research is required on the application of the DMH concept in lung during optimization. The current study is centered on a CyberKnife FFF 6 MV beam model with tracking (or gating), but when applying the same concepts to free breathing tumors, one can expect even larger discrepancies due to the relative small GTV volume compared to the ITV and PTV. The same applies in a real clinical setting: several other factors will add in as there are the GTV contouring, does GTV contain low density voxels, ribs. . . We showed that, even when not considering these, the PTV prescription is inherently inconsistent in lung. In practice, one will see a mix of different densities inside the PTV, leading to a mix of the current results. In the light of Ricardi et al. [9], we could suggest: a solution to consistency seems abandoning the PTV concept and relying on other methods for dose prescription, reporting and optimization as robust planning, fluence propagation, or optimizing using a type A algorithm.
herent DDVH 95% (GTV) results. The same can be mentioned about the gEUD(GTV): low density voxels inside the GTV could skew the results as the gEUD is sensitive towards low dose regions for tumoral tissue, but further research is required. Finally, there is still ongoing issue for the medical definition of CTV vs GTV in SBRT [24]. As this is a theoretical study, the GTV is well defined whereas in reality the GTV consists of heterogeneous density and has a nonwell defined border. Up to now, we have considered tracking or gated treatments. When considering free-breathing treatments, one can expect even larger variations, as the percentage ‘‘low density” lung volume becomes considerably larger: the ITV around the GTV would already contain low density lung volume. When adding a PTV to an already larger ITV volume, all factors would increase even further. The application of a different coverage probability, machine or technique leading to a different PTV size will also influence the obtained conversion factors: our results are specifically for a 5 mm PTV.
Acknowledgements 4.3. Influence of random position of GTV inside the PTV Not applicable. The results of randomly varying the GTV position uniformly inside the PTV volume are represented in Fig. 7. It is clear that a flash region is required when introducing position uncertainty. This shows that the D50% (GTV) point remains constant in the presence of uncertainty when applying a correctly sized field larger than the GTV. However, the GTV will no longer be correctly irradiated when applying a field size that equals the size of the GTV in the case of 6 MV photons. Thus restricting the field size to the GTV for 6 MV beam quality is not a good idea, even when it seems to spare lung tissue. Therefore, the use of lateral electron disequilibrium by applying higher max GTV dose as proposed by Disher et al. [23] applied for 20 MV photons, should require robust calculation in order to be sure that the presented dose is also the delivered dose in reality. 5. Conclusions Prescribing to the PTV using Monte Carlo calculated dose distributions is not consistent in lung. This conclusion can be extended towards general type B dose calculations as all studies show very good agreement between algorithms taking into account lateral electron disequilibrium. The most important factor leading to large inconsistencies is the lung density and its subsequent low dose and lack of buildup. The other factors, such as tumor density and tumor size become more important in the presence of low surrounding lung density, but all factors also influence each other. We showed that, due to the combination of MC calculated dose with the PTV concept, patients with very low lung density could receive up to 1.4 times the dose to the GTV even when prescribing exactly the same dose to the PTV. The D50% (GTV) GTV point was used as reference in this study: the use of a high % DVH/DMH(GTV) point, or the use of gEUD (GTV) could possibly over-evaluate low density voxels inside the
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Please cite this article in press as: Lebredonchel S et al. About the non-consistency of PTV-based prescription in lung. Phys. Med. (2017), http://dx.doi.org/ 10.1016/j.ejmp.2017.03.009