Impact of dose size in single fraction spatially fractionated (grid) radiotherapy for melanoma Hualin Zhang, Hualiang Zhong, Rolf F. Barth, Minsong Cao, and Indra J. Das Citation: Medical Physics 41, 021727 (2014); doi: 10.1118/1.4862837 View online: http://dx.doi.org/10.1118/1.4862837 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/41/2?ver=pdfcov Published by the American Association of Physicists in Medicine Articles you may be interested in Dosimetric and geometric evaluation of a novel stereotactic radiotherapy device for breast cancer: The GammaPod™ Med. Phys. 40, 041722 (2013); 10.1118/1.4794477 The dosimetric impact of inversely optimized arc radiotherapy plan modulation for real-time dynamic MLC tracking delivery Med. Phys. 39, 1588 (2012); 10.1118/1.3685583 Planning tools for modulated electron radiotherapy Med. Phys. 37, 2215 (2010); 10.1118/1.3395573 Dosimetric and radiobiological impact of dose fractionation on respiratory motion induced IMRT delivery errors: A volumetric dose measurement study Med. Phys. 33, 1380 (2006); 10.1118/1.2192908 Dose reconstruction in deforming lung anatomy: Dose grid size effects and clinical implications Med. Phys. 32, 2487 (2005); 10.1118/1.1949749
Impact of dose size in single fraction spatially fractionated (grid) radiotherapy for melanoma Hualin Zhanga) Department of Radiation Oncology, Northwestern University Feinberg School of Medicine, Chicago, Illinois 60611 and Department of Radiation Oncology, Indiana University School of Medicine, Indianapolis, Indiana 46202
Hualiang Zhong Department of Radiation Oncology, Henry Ford Health System, Detroit, Michigan 48202
Rolf F. Barth Department of Pathology, The Ohio State University, Columbus, Ohio 43210
Minsong Cao and Indra J. Das Department of Radiation Oncology, Indiana University School of Medicine, Indianapolis, Indiana 46202
(Received 22 May 2013; revised 28 December 2013; accepted for publication 8 January 2014; published 27 January 2014) Purpose: To evaluate the impact of dose size in single fraction, spatially fractionated (grid) radiotherapy for selectively killing infiltrated melanoma cancer cells of different tumor sizes, using different radiobiological models. Methods: A Monte Carlo technique was employed to calculate the 3D dose distribution of a commercially available megavoltage grid collimator in a 6 MV beam. The linear-quadratic (LQ) and modified linear quadratic (MLQ) models were used separately to evaluate the therapeutic outcome of a series of single fraction regimens that employed grid therapy to treat both acute and late responding melanomas of varying sizes. The dose prescription point was at the center of the tumor volume. Dose sizes ranging from 1 to 30 Gy at 100% dose line were modeled. Tumors were either touching the skin surface or having their centers at a depth of 3 cm. The equivalent uniform dose (EUD) to the melanoma cells and the therapeutic ratio (TR) were defined by comparing grid therapy with the traditional open debulking field. The clinical outcomes from recent reports were used to verify the authors’ model. Results: Dose profiles at different depths and 3D dose distributions in a series of 3D melanomas treated with grid therapy were obtained. The EUDs and TRs for all sizes of 3D tumors involved at different doses were derived through the LQ and MLQ models, and a practical equation was derived. The EUD was only one fifth of the prescribed dose. The TR was dependent on the prescribed dose and on the LQ parameters of both the interspersed cancer and normal tissue cells. The results from the LQ model were consistent with those of the MLQ model. At 20 Gy, the EUD and TR by the LQ model were 2.8% higher and 1% lower than by the MLQ, while at 10 Gy, the EUD and TR as defined by the LQ model were only 1.4% higher and 0.8% lower, respectively. The dose volume histograms of grid therapy for a 10 cm tumor showed different dosimetric characteristics from those of conventional radiotherapy. A significant portion of the tumor volume received a very large dose in grid therapy, which ensures significant tumor cell killing in these regions. Conversely, some areas received a relatively small dose, thereby sparing interspersed normal cells and increasing radiation tolerance. The radiobiology modeling results indicated that grid therapy could be useful for treating acutely responding melanomas infiltrating radiosensitive normal tissues. The theoretical model predictions were supported by the clinical outcomes. Conclusions: Grid therapy functions by selectively killing infiltrating tumor cells and concomitantly sparing interspersed normal cells. The TR depends on the radiosensitivity of the cell population, dose, tumor size, and location. Because the volumes of very high dose regions are small, the LQ model can be used safely to predict the clinical outcomes of grid therapy. When treating melanomas with a dose of 15 Gy or higher, single fraction grid therapy is clearly advantageous for sparing interspersed normal cells. The existence of a threshold fraction dose, which was found in the authors’ theoretical simulations, was confirmed by clinical observations. © 2014 American Association of Physicists in Medicine. [http://dx.doi.org/10.1118/1.4862837] Key words: spatially fractionated (grid) radiotherapy, equivalent uniform dose, therapeutic ratio, melanoma
021727-1
Med. Phys. 41 (2), February 2014
0094-2405/2014/41(2)/021727/9/$30.00
© 2014 Am. Assoc. Phys. Med.
021727-1
021727-2
Zhang et al.: Impact of dose size in grid radiotherapy
1. INTRODUCTION The usefulness of spatially fractionated (grid) radiotherapy for treating bulky tumors has been recognized for at least two decades.1–5 As reported by Zwicker et al.6 and Zhang et al.,7 grid therapy takes advantage of the fact that in general normal cells have better repair capabilities than tumor cells. When normal cells are spared in grid therapy, those underirradiated areas can serve as centers of regrowth of normal tissues. Ideally, the tumor cell kill rate would be maintained while the normal cell survival ratio would be increased, thereby providing a clinical advantage. The latest study by Zhang et al.8 demonstrated that grid therapy provided a pronounced therapeutic advantage in both hypofractionated- (fewer fractions and higher dose/fraction) and conventionally fractionated regimens compared to results seen with single fraction, open debulking field regimens. However, the true therapeutic advantage (excluding the fractionation benefit) exists only in hypofractionated grid therapy. In addition, both theoretical studies and clinical outcomes have revealed that a course of open field conventional radiotherapy is needed to fully control tumor growth after grid therapy.3, 5, 8 This is primarily because the effective dose delivered by single fraction grid therapy is not large enough to achieve full control of tumor growth, even though damage to normal cells is reduced, and/or selective killing of tumor cells has been achieved via the grid field. Although it has been demonstrated that hypofractionated grid therapy has certain advantages over conventionally fractionated grid therapy and open field therapy for debulking tumors,8 the following issues have remained unresolved: (1) the extent of therapeutic advantage for different dose sizes in selectively killing interspersed cancer cells has not been precisely defined. (2) it is unclear whether hypofractionated grid therapy provides similar therapeutic advantages for tumors of varying sizes located at different depths, since the dose distribution is different for different tumor volumes; (3) it is uncertain whether the LQ radiobiology response model is appropriate for evaluating single fraction large dose grid therapy which has large dose spots across the target volume. It is apparent that, unless these issues are resolved, grid therapy will remain as a trial-and-error process, and cannot be widely used as a standard clinical treatment regimen. In this study, we have re-evaluated grid therapy, using a commercially available grid collimator, and applying a previously validated and further improved-upon Monte Carlo (MC) technique to obtain 3D, rather than 2D dose distributions in water. Equivalent open field doses were derived for treating tumors of diverse sizes in nine fraction dose regimens (1, 2, 3, 5, 7.5, 10, 15, 20, and 30 Gy/fraction). In addition to the conventional linear quadratic (LQ) model, a modified linear quadratic (MLQ) model—which significantly increases the cell survival ratio in high dose (>12 Gy) irradiation—was used to evaluate the impact of both different fraction dose regimens and radiobiology models on grid therapy. Based on the resulting 3D dose distributions, normal tissue and melanoma cell survival statistics were estimated using both the LQ and MLQ models. The therapeutic advantage of grid therapy was Medical Physics, Vol. 41, No. 2, February 2014
021727-2
evaluated at different dose sizes for treating melanoma of varying sizes and depths. 2. METHODS AND MATERIALS 2.A. Grid collimator
The structure of the grid has been described in detail in Ref. 9. In brief, the High Dose Radiation Grid (Radiation Products Design, Albertville, MN) consists of a hexagonal pattern of circular divergent holes in a cerrobend block designed to be mounted in the standard linear accelerator (LINAC) accessory mount of the source (Varian 21 EX, Varian Oncology System, Palo Alto, CA). All holes in the grid were divergent, and the grid block was aligned with the tilt angle to accord with the beam divergence. The tilted cone-shaped holes were carefully modeled in the Monte Carlo simulation. The accuracy of dose profiles obtained from the Monte Carlo simulations was verified by our measurements.7 2.B. Monte-Carlo simulation
A MC N-particle Transport code (MCNPX, version 2.6) (Ref. 10) was used to calculate the doses in a water phantom at dmax (1.5 cm) and at other depths for a 6-MV photon beam from a Varian 21 EX LINAC. This code is an extension of MCNP (Ref. 11) for particle types and energy ranges. The photon interaction cross section file used in this study was the ENDF/B-VII library, distributed by the Radiation Shielding Information Computing Center (RSICC).11 The tally technique used in this study has been described in Ref. 8. An array of spherical, 1-mm-diameter tally cells, spaced at 2 mm center-to-center, was defined at depths ranging from 0.25 to 7 cm at 0.25 cm increments for simulating 2D dose at each layer. The dose distributions from all layers constituted a 3D dose distribution. For each simulation, the low energy cutoff was set at 10 keV and used a minimum of 5 × 108 histories. The statistical error of each tallied dose was found to be less than 4%. An energy spectrum of 6 MV (Ref. 12) passing after the monitor ionization chamber was used in our practical LINAC source model. It should be noted that in clinical treatments, a multileaf collimator may be used occasionally to achieve dose conformity of the grid field, depending on the tumor’s shape and dimension. We chose to ignore the secondary collimator for the grid field, because in the clinic where the authors worked, the secondary collimator was not used in most grid therapy cases. In this study, the dosimetric data for grid therapy were all derived from the grid field formed by a 10 × 10 cm2 field. 2.C. Dosimetric behavior of grid therapy
The intensity of the grid therapy field not only varies along the beam path as a function of depth but also in transverse and radial directions. In addition, as the depth increases, the degree of dose modulation will also vary (Fig. 1). Therefore, in order to better account for cell killing in grid therapy for
021727-3
Zhang et al.: Impact of dose size in grid radiotherapy
021727-3 TABLE I. α and β values for melanomas (Ref. 13) and normal tissues (Ref. 17). Tissue type Melanoma Melanoma Melanoma Melanoma Melanoma Melanoma Melanoma Melanoma Melanoma Normal tissue 1 Normal tissue 2 Normal tissue 3
F IG . 1. Monte Carlo simulated dose profiles for 6 MV grid therapy at the different depths in a water phantom. (a) In plane and (b) cross plane.
tumors, a three-dimensional (3D) dose distribution is preferable to a 2D distribution at one depth. In this study, the dose prescription point was at the center of the tumor. We chose spherical or ellipsoidal melanomas ranging in size from 2.0 to 10.0 cm in diameter, and located either at a depth of 3.0 cm or touching the skin surface. This was done because these sizes and locations are often seen in our clinic; however, some tumors were not bulky and, therefore, were not treated by grid therapy. Among all tumors investigated, only the 10 cm tumor was ellipsoidal, with a diameter of 10 cm at the axes perpendicular to the beam axis, and 6 cm along the beam. The dose prescription point was at the center of the tumor volume. Dose sizes ranging from 1 to 30 Gy at 100% dose line were modeled. The prescription dose of grid therapy is also called the nominal dose. 2.D. Biological effects of grid therapy
The biological model for calculating interspersed normal tissue and tumor cell survival used in this study has been previously described in the literature.6 The LQ model parameters (α and β) of radiobiological response for melanoma cells were those described by Brenner and Hall13 and were consistent with data reported by Thames,14 Wigg,15 and Malaise.16 For normal tissues, we used α/β = 3.1 Gy.17 As previously described,7 in the present study we also used three types of normal tissue cells to estimate the therapeutic outcome: Medical Physics, Vol. 41, No. 2, February 2014
Cell lines
A
β
α/β
Sk-mel 128 EE MF EF RPM17951 GE HX-34 VN HX-118 SF(2 Gy) = 0.3 SF(2 Gy) = 0.5 SF(2 Gy) = 0.7
0.13 0.21 0.28 0.35 0.27 0.61 0.27 0.53 0.33 0.366 0.211 0.108
0.113 0.1 0.0879 0.0701 0.0468 0.101 0.0421 0.0783 0.038 0.1180 0.0680 0.0350
1.15 2.1 3.19 4.99 5.77 6.04 6.41 6.77 8.68 3.1 3.1 3.1
radiosensitive [SF(2Gy) = 0.3]; moderately radiosensitive [SF(2Gy) = 0.5]; and radioresistant [SF(2Gy) = 0.7]. (See Table I.) In recent years, the suitability of the LQ model when describing cell killing at high doses (>12 Gy) has become the subject of debate.18–20 Brenner18 has made several assertions regarding applicability of the LQ model for high dose radiotherapy: (1) the LQ model is a mechanistic and biologically based model; (2) most other mechanistic models of cell killing predict the same fractionation dependencies as does the LQ; (3) the LQ model has well documented predictive properties for fractionation/dose-rate effects in the laboratory; (4) the LQ model has been repeatedly validated and it would be reasonable to use it for doses up to ∼18 Gy per fraction; (5) to date, there is no evidence of problems when LQ has been used clinically. However, in order to validate Brenner’s assertion and further validate the radiobiologic modeling results, a MLQ model—introduced by Guerrreo and Li21 —was used to estimate the surviving fractions of the same melanoma cell lines after grid therapy, in addition to the classical LQ model. The MLQ model has significantly increased the cell survival ratio in high dose (>12 Gy) regions compared to the classical LQ model. The MLQ model can be expressed as SF (x, y, z) = exp(−α · D(x, y.z) − β · g(δ · D(x, y, z)) ·D(x, y, z)2 ),
(1)
where D(x, y, z) was the MC simulated dose at the point (x, y, z), which was related to the prescription dose via the PDD of the central hole, and the MC-calculated 3D dose distribution at the layer z. g(t) = 2(t + e−t − 1)/t2 is the dose protraction factor/function which describes the reduction in the effect of lethal mis-repair induced by a protracted treatment regimen, t is a variable used in the function, t = δ*D(x,y,z), and δ is a histology-related parameter.21 Since our purpose for using the MLQ model was to test the impact of a radiobiological model in which the survival ratio of high dose irradiation is increased, we decided to use δ = 0.15 for all investigated melanoma cell lines, and interspersed three types of normal cells as well. As we see, if g(t) = 1.0, the MLQ model will become the classical LQ model.
021727-4
Zhang et al.: Impact of dose size in grid radiotherapy
The average survival fraction of uniformly interspersed tumor or normal tissue cells with uniform cell densities in grid therapy was GTV SF(D(x, y, z)) · dx · dy · dz SF(Grid) = GTV dx · dy · dz GTV SF(D(x, y, z)) · dx · dy · dz = . (2) VGTV
021727-4
It should be noted that in the clinic, other open field sizes could also be used for debulking tumors; we related the 10 × 10 cm2 open field to our single fraction grid therapy in order to explicate the relationship and clearly convey the underlying concept. The Open field dose also came from Monte Carlo simulations verified by a water tank scanning system.
3. RESULTS For calculations of the surviving fractions, the same dose distribution was used for both tumor cells and normal tissues. This was based on those cases in which the tumor and normal tissue or organ at risk could not be well delineated and, therefore, would receive a similar radiation dose, e.g., early stage bulky melanomas. The average tumor cell survival fraction in grid therapy SF(Grid) has the EUD,6 which is the equivalent uniform dose that would kill the same number of tumor cells across the tumor volume. The consequential difference between uniform dose and high gradient nonuniform dose has been debated among many researchers. Of note, it is difficult to reconcile the grid-therapy outcomes with conventional TCP models. Because EUD is different from TCP—which depends on the dose to individual cells—it is used to evaluate the overall performance of a 3D dose distribution. In this study we mainly use EUD, rather than TCP, to analyze different dose regimens. The accuracy of EUD could be compromised by large dose nonuniformities; nevertheless, it does provide a simple form to characterize complex dose distributions. The EUD could be obtained by solving the following equation: α • EUD2 + β • EUD + ln(SFc (Grid) = 0.
3.A. A Dose volume histogram (DVH) of grid therapy
In Fig. 2, the DVHs were calculated for a 10 cm tumor (6 cm in height and 10 cm in the major and minor axes) located at a depth of 3 cm and treated by either a 20 Gy nominal dose of grid therapy or 4.2 Gy of open field therapy. Theoretically, both regimens would kill the same number of tumor cells, but the grid therapy allows more normal cells to survive, as demonstrated in Secs. 3.D–3.E. Figure 2(a) depicts the differential dose volume histogram (d-DVH) showing the dose spectrum in the tumor; and Fig. 2(b) depicts the cumulative DVH that shows the dose coverage at the tumor. The dose spectrum in grid therapy has two peaks, but open field therapy has only one peak. In grid therapy, 60% of the tumor volume will receive at least 4 Gy, 40% will receive 10 Gy, and about 20% could receive up to 17 Gy. In open field therapy,
(3)
In the above equation α and β are for different melanoma cancer cell lines; (SFc (Grid) is the average survival fraction of the corresponding cancer cell line across the tumor volume in grid therapy, calculated by the Eq. (2). The definition of grid therapy therapeutic ratio (TR) is similar to that described in the literature:8 SFnormal (Grid) . (4) TR= SFnormal (EUD) A TR value greater than 1 would imply a survival advantage for normal cells in grid irradiation, because it shows that at the same tumor cell killing rate, more interspersed normal cells were spared by grid field than by open field. 2.E. Equivalent uniform dose in open field therapy
If a tumor is debulked by open fields instead of grid therapy, EUD can be calculated from a single portal open field or a set of multiple portal open fields. Traditionally, only a single portal open field with a large dose was used for debulking purposes. Therefore, we evaluated EUDs at prescription doses in a single portal 10 × 10 cm2 open field for various tumor sizes to establish the relationship between the EUD and prescription doses, and thereby equated grid therapy to open field therapy based on the same tumor cell killing or the same EUD. Medical Physics, Vol. 41, No. 2, February 2014
F IG . 2. Differential and cumulative dose volume histograms for a 10 cm tumor (6 cm in height and 10 cm in the major and minor axes) located 3 cm deep and treated with either a single fraction of 20 Gy prescription dose grid therapy or one fraction of 4.2 Gy open field. Both regimens have the same equivalent uniform dose of 4.1 Gy.
021727-5
Zhang et al.: Impact of dose size in grid radiotherapy
021727-5
the dose spectrum is much narrower than in grid therapy, with the delivered dose ranging only from 3.8 to 4.5 Gy. 3.B. Equivalent uniform dose (EUD)
Figure 3 depicts the EUDs of single fraction grid therapy regimens calculated by the LQ model. The values were averaged from all the melanoma cell lines. Figure 3 demonstrates that the EUD is different for different tumor sizes and locations at the same nominal dose. The average EUDs were found to be approximated by 3rd order polynomial functions: EUD = a3∗ DP3 + a2∗ DP2 + a1∗ DP + a0,
(5)
where DP was the prescription dose, and also called the nominal fraction dose; a3, a2, a1, and a0 are fitting coefficients, which were 2.3432 × 10−4 , −1.3463 × 10−2 , 3.6573 × 10−1 , and 1.8992 × 10−1 , for tumors located at a depth of 3 cm. These values were to be 2.2832 × 10−4 , −1.3227 × 10−2 , 3.4568 × 10−1 , and 1.7593 × 10−1 , respectively, for tumors touching the skin surface. 3.C. EUD of a single portal open field
Figure 4 depicts the EUDs of different prescription doses for a single portal 10 × 10 cm2 open field for different spherical tumor volumes and locations. The EUD was found to be weakly dependent upon tumor size and location and close to
F IG . 4. The equivalent uniform doses (EUD) of tumors of different sizes treated with single fraction open field radiotherapy at different prescription doses.
the prescription dose DPD . The average EUD of all tumor sizes for a single portal and single fraction open field could be linearly approximated by EUD = k ∗ DP ,
(6)
where k was a fitting coefficient, with a value of 0.978 for tumors at a depth of 3 cm and 0.901 for tumors at the skin surface. It indicated that in the open field therapy, if the tumor was at a depth of 3 cm, the EUD is close to the prescription dose DP . When tumors touched the skin and the center was shallower than 3 cm, the EUD was about 10% lower than the DP . 3.D. LQ vs MLQ model in grid therapy
We made a comparison between LQ and MLQ models for predicting TR and EUD at the different prescription doses for a 10 cm tumor (6 cm in height and 10 cm in the major and minor axes). Compared to results from the MLQ model, the LQ model-calculated EUD is 2.8% higher and the TR is 1% lower at the prescription dose of 20 Gy. At 10 Gy, the difference between two models is less than 1% for both the EUD and TR. 3.E. The TR of grid therapy F IG . 3. The equivalent uniform doses (EUD) of tumors of different sizes in single fraction grid therapy calculated by the LQ model. Medical Physics, Vol. 41, No. 2, February 2014
Figure 5 depicts the TRs of single fraction grid therapy in treating a 10-cm melanoma with different cell lines at
021727-6
Zhang et al.: Impact of dose size in grid radiotherapy
021727-6
F IG . 5. Therapeutic ratios (TR) of a 10-cm melanoma tumor irradiated with different doses of single fraction grid therapy calculated by the LQ and MLQ models. The different melanoma and normal tissue cell lines with experimentally determined radioresponse LQ parameters are listed in Table I. Medical Physics, Vol. 41, No. 2, February 2014
021727-7
Zhang et al.: Impact of dose size in grid radiotherapy
021727-7
4. DISCUSSION
F IG . 6. Therapeutic ratios (TR) of melanoma tumors with different diameters treated with different doses of single fraction grid therapy averaged by all melanoma and normal cell lines.
different doses. The left panel shows the results from the LQ model; the right is the MLQ model. The results from both models are similar, and only a small difference (less than 2%) is seen. Figure 5 also reveals that the acutely responding melanoma cells (α/β > 6, except for G.E.) surrounded by radiosensitive normal tissues (normal tissue 1 and 2) were more suitable in treatment with grid therapy, while the later responding tumor (α/β < 6)—or any tumor cells interspersed among radioresistant normal cells (normal tissue 3)—would not benefit from this highly nonuniform field. In addition, the fact that the TR of HX34 (α/β = 6.4) was greater than that of V.N. (α /β = 6.77) indicated that the TR depended not only on the single ratio of α /β but also on the individual α and β values. This relationship has been suggested by Malaise et al.,16 and also was confirmed in our previous study of 2D cervical cancers.8 Figure 6 illustrates the average TR for all tumor cell lines and the average TR for all types of normal tissues. The results indicate that grid therapy would not provide any additional therapeutic advantage in sparing interspersed normal tissue cells if the fraction dose were smaller than 15 Gy, because the TR is less than 1.0. This means the grid field killed more normal cells than the open field at the same tumor cell killing rate. Medical Physics, Vol. 41, No. 2, February 2014
In this study, we have provided an improved dosimetric simulation and assessed the radiobiological response of melanoma cells in the 3D dose distribution of single fraction grid therapy. The biological advantage of grid therapy at varying doses has been evaluated using the LQ and MLQ models for cell survival calculations, and the results have been described in terms of TRs and EUDs. The differential dose volume histogram [Fig. 2(a)] demonstrated that two well-separated groups of doses were actually delivered to the tumor in grid therapy at 20 Gy nominal fraction dose. One group peaked at ∼3 Gy, and the other at ∼18 Gy, unlike the dose in open field therapy, which had a single peak at 4.2 Gy. This indicates that a significant portion of the tumor volume would receive a very large dose, ensuring significant tumor cell killing in these regions; and that some areas would receive a relatively small dose. As reported by Mackonis et al.,22, 23 the coexistence of cold and hot dose regions most likely would enhance bystander killing effects, thereby further increasing the benefits of a highly modulated field through an increase in the EUD. The cumulative DVH of the 10 cm tumor provided evidence for the dose coverage achieved with grid therapy in a 3D target [Fig. 2(b)]. In contrast to the conventional open field treatment, in which the DVH curve has a single plateau and then drops rapidly at the prescription dose, grid therapy had a distinctive DVH curve with two plateaus. The first plateau was located at the low dose region (∼2.5 Gy) that covered 100% of the volume. The second occurred at a dose (∼6 Gy) that covered ∼50% of the tumor volume. Most importantly, the second plateau was long, and slowly declined until it reached the nominal dose. This ensured that grid therapy would deliver large doses to a significant part of the tumor volume. The radiobiological characteristics of melanoma cells seen in grid therapy for 3D tumors are consistent with those seen in previous studies of melanoma and cervical cancer cells as 2D targets.6–8 The more acutely responding tumor cells interspersed in radiosensitive normal tissues would be more effectively treated with grid therapy (Fig. 5). It was also found that the use of the MLQ model to increase cell survival fraction at high dose would not change the theoretical prediction and conclusions of grid therapy. This is because the very high dose volume is small, and the unique characteristics of grid therapy mainly rely on the dramatic dose variation across the tumor volume. Our results also demonstrated that bulky melanomas within radioresistant normal tissues would not be more effectively debulked by megavoltage grid therapy than by open field therapy. Therefore, determining the radiosensitivity of tumor and normal cells before treatment could help in selecting the most effective treatment regimens for grid therapy. Whether tumors touched the skin surface or were located at a depth of 3 cm, our results indicated that a minimum fraction dose was necessary if grid therapy was to achieve average TRs greater than 1 (Fig. 6). Moreover, although slightly different minimum doses were needed for tumors of different
021727-8
Zhang et al.: Impact of dose size in grid radiotherapy
sizes, the overall minimum dose was ∼15 Gy. As reported in the literature,13–17 almost all tumor cells have an overlapping α/β range; generally, they fall into an α/β ratio spectrum ranging from 1.1 to 20.9. This coincides with the α/β ratio range which includes melanoma and cervical cancer lines, both of which we have investigated. Thus, the clinical outcomes of diverse cancers treated with grid therapy could serve as a reference for examining the results of our current and previous studies,8 which assessed the average radiobiological effects of grid therapy in treating melanoma and cervical cancers. Mohiuddin et al.3 reported that an overall response of 94% was achieved with a nominal dose >15 Gy. When the grid therapy dose was
Impact of dose size in single fraction spatially fractionated (grid) radiotherapy for melanoma Hualin Zhanga) Department of Radiation Oncology, Northwestern University Feinberg School of Medicine, Chicago, Illinois 60611 and Department of Radiation Oncology, Indiana University School of Medicine, Indianapolis, Indiana 46202
Hualiang Zhong Department of Radiation Oncology, Henry Ford Health System, Detroit, Michigan 48202
Rolf F. Barth Department of Pathology, The Ohio State University, Columbus, Ohio 43210
Minsong Cao and Indra J. Das Department of Radiation Oncology, Indiana University School of Medicine, Indianapolis, Indiana 46202
(Received 22 May 2013; revised 28 December 2013; accepted for publication 8 January 2014; published 27 January 2014) Purpose: To evaluate the impact of dose size in single fraction, spatially fractionated (grid) radiotherapy for selectively killing infiltrated melanoma cancer cells of different tumor sizes, using different radiobiological models. Methods: A Monte Carlo technique was employed to calculate the 3D dose distribution of a commercially available megavoltage grid collimator in a 6 MV beam. The linear-quadratic (LQ) and modified linear quadratic (MLQ) models were used separately to evaluate the therapeutic outcome of a series of single fraction regimens that employed grid therapy to treat both acute and late responding melanomas of varying sizes. The dose prescription point was at the center of the tumor volume. Dose sizes ranging from 1 to 30 Gy at 100% dose line were modeled. Tumors were either touching the skin surface or having their centers at a depth of 3 cm. The equivalent uniform dose (EUD) to the melanoma cells and the therapeutic ratio (TR) were defined by comparing grid therapy with the traditional open debulking field. The clinical outcomes from recent reports were used to verify the authors’ model. Results: Dose profiles at different depths and 3D dose distributions in a series of 3D melanomas treated with grid therapy were obtained. The EUDs and TRs for all sizes of 3D tumors involved at different doses were derived through the LQ and MLQ models, and a practical equation was derived. The EUD was only one fifth of the prescribed dose. The TR was dependent on the prescribed dose and on the LQ parameters of both the interspersed cancer and normal tissue cells. The results from the LQ model were consistent with those of the MLQ model. At 20 Gy, the EUD and TR by the LQ model were 2.8% higher and 1% lower than by the MLQ, while at 10 Gy, the EUD and TR as defined by the LQ model were only 1.4% higher and 0.8% lower, respectively. The dose volume histograms of grid therapy for a 10 cm tumor showed different dosimetric characteristics from those of conventional radiotherapy. A significant portion of the tumor volume received a very large dose in grid therapy, which ensures significant tumor cell killing in these regions. Conversely, some areas received a relatively small dose, thereby sparing interspersed normal cells and increasing radiation tolerance. The radiobiology modeling results indicated that grid therapy could be useful for treating acutely responding melanomas infiltrating radiosensitive normal tissues. The theoretical model predictions were supported by the clinical outcomes. Conclusions: Grid therapy functions by selectively killing infiltrating tumor cells and concomitantly sparing interspersed normal cells. The TR depends on the radiosensitivity of the cell population, dose, tumor size, and location. Because the volumes of very high dose regions are small, the LQ model can be used safely to predict the clinical outcomes of grid therapy. When treating melanomas with a dose of 15 Gy or higher, single fraction grid therapy is clearly advantageous for sparing interspersed normal cells. The existence of a threshold fraction dose, which was found in the authors’ theoretical simulations, was confirmed by clinical observations. © 2014 American Association of Physicists in Medicine. [http://dx.doi.org/10.1118/1.4862837] Key words: spatially fractionated (grid) radiotherapy, equivalent uniform dose, therapeutic ratio, melanoma
021727-1
Med. Phys. 41 (2), February 2014
0094-2405/2014/41(2)/021727/9/$30.00
© 2014 Am. Assoc. Phys. Med.
021727-1
021727-2
Zhang et al.: Impact of dose size in grid radiotherapy
1. INTRODUCTION The usefulness of spatially fractionated (grid) radiotherapy for treating bulky tumors has been recognized for at least two decades.1–5 As reported by Zwicker et al.6 and Zhang et al.,7 grid therapy takes advantage of the fact that in general normal cells have better repair capabilities than tumor cells. When normal cells are spared in grid therapy, those underirradiated areas can serve as centers of regrowth of normal tissues. Ideally, the tumor cell kill rate would be maintained while the normal cell survival ratio would be increased, thereby providing a clinical advantage. The latest study by Zhang et al.8 demonstrated that grid therapy provided a pronounced therapeutic advantage in both hypofractionated- (fewer fractions and higher dose/fraction) and conventionally fractionated regimens compared to results seen with single fraction, open debulking field regimens. However, the true therapeutic advantage (excluding the fractionation benefit) exists only in hypofractionated grid therapy. In addition, both theoretical studies and clinical outcomes have revealed that a course of open field conventional radiotherapy is needed to fully control tumor growth after grid therapy.3, 5, 8 This is primarily because the effective dose delivered by single fraction grid therapy is not large enough to achieve full control of tumor growth, even though damage to normal cells is reduced, and/or selective killing of tumor cells has been achieved via the grid field. Although it has been demonstrated that hypofractionated grid therapy has certain advantages over conventionally fractionated grid therapy and open field therapy for debulking tumors,8 the following issues have remained unresolved: (1) the extent of therapeutic advantage for different dose sizes in selectively killing interspersed cancer cells has not been precisely defined. (2) it is unclear whether hypofractionated grid therapy provides similar therapeutic advantages for tumors of varying sizes located at different depths, since the dose distribution is different for different tumor volumes; (3) it is uncertain whether the LQ radiobiology response model is appropriate for evaluating single fraction large dose grid therapy which has large dose spots across the target volume. It is apparent that, unless these issues are resolved, grid therapy will remain as a trial-and-error process, and cannot be widely used as a standard clinical treatment regimen. In this study, we have re-evaluated grid therapy, using a commercially available grid collimator, and applying a previously validated and further improved-upon Monte Carlo (MC) technique to obtain 3D, rather than 2D dose distributions in water. Equivalent open field doses were derived for treating tumors of diverse sizes in nine fraction dose regimens (1, 2, 3, 5, 7.5, 10, 15, 20, and 30 Gy/fraction). In addition to the conventional linear quadratic (LQ) model, a modified linear quadratic (MLQ) model—which significantly increases the cell survival ratio in high dose (>12 Gy) irradiation—was used to evaluate the impact of both different fraction dose regimens and radiobiology models on grid therapy. Based on the resulting 3D dose distributions, normal tissue and melanoma cell survival statistics were estimated using both the LQ and MLQ models. The therapeutic advantage of grid therapy was Medical Physics, Vol. 41, No. 2, February 2014
021727-2
evaluated at different dose sizes for treating melanoma of varying sizes and depths. 2. METHODS AND MATERIALS 2.A. Grid collimator
The structure of the grid has been described in detail in Ref. 9. In brief, the High Dose Radiation Grid (Radiation Products Design, Albertville, MN) consists of a hexagonal pattern of circular divergent holes in a cerrobend block designed to be mounted in the standard linear accelerator (LINAC) accessory mount of the source (Varian 21 EX, Varian Oncology System, Palo Alto, CA). All holes in the grid were divergent, and the grid block was aligned with the tilt angle to accord with the beam divergence. The tilted cone-shaped holes were carefully modeled in the Monte Carlo simulation. The accuracy of dose profiles obtained from the Monte Carlo simulations was verified by our measurements.7 2.B. Monte-Carlo simulation
A MC N-particle Transport code (MCNPX, version 2.6) (Ref. 10) was used to calculate the doses in a water phantom at dmax (1.5 cm) and at other depths for a 6-MV photon beam from a Varian 21 EX LINAC. This code is an extension of MCNP (Ref. 11) for particle types and energy ranges. The photon interaction cross section file used in this study was the ENDF/B-VII library, distributed by the Radiation Shielding Information Computing Center (RSICC).11 The tally technique used in this study has been described in Ref. 8. An array of spherical, 1-mm-diameter tally cells, spaced at 2 mm center-to-center, was defined at depths ranging from 0.25 to 7 cm at 0.25 cm increments for simulating 2D dose at each layer. The dose distributions from all layers constituted a 3D dose distribution. For each simulation, the low energy cutoff was set at 10 keV and used a minimum of 5 × 108 histories. The statistical error of each tallied dose was found to be less than 4%. An energy spectrum of 6 MV (Ref. 12) passing after the monitor ionization chamber was used in our practical LINAC source model. It should be noted that in clinical treatments, a multileaf collimator may be used occasionally to achieve dose conformity of the grid field, depending on the tumor’s shape and dimension. We chose to ignore the secondary collimator for the grid field, because in the clinic where the authors worked, the secondary collimator was not used in most grid therapy cases. In this study, the dosimetric data for grid therapy were all derived from the grid field formed by a 10 × 10 cm2 field. 2.C. Dosimetric behavior of grid therapy
The intensity of the grid therapy field not only varies along the beam path as a function of depth but also in transverse and radial directions. In addition, as the depth increases, the degree of dose modulation will also vary (Fig. 1). Therefore, in order to better account for cell killing in grid therapy for
021727-3
Zhang et al.: Impact of dose size in grid radiotherapy
021727-3 TABLE I. α and β values for melanomas (Ref. 13) and normal tissues (Ref. 17). Tissue type Melanoma Melanoma Melanoma Melanoma Melanoma Melanoma Melanoma Melanoma Melanoma Normal tissue 1 Normal tissue 2 Normal tissue 3
F IG . 1. Monte Carlo simulated dose profiles for 6 MV grid therapy at the different depths in a water phantom. (a) In plane and (b) cross plane.
tumors, a three-dimensional (3D) dose distribution is preferable to a 2D distribution at one depth. In this study, the dose prescription point was at the center of the tumor. We chose spherical or ellipsoidal melanomas ranging in size from 2.0 to 10.0 cm in diameter, and located either at a depth of 3.0 cm or touching the skin surface. This was done because these sizes and locations are often seen in our clinic; however, some tumors were not bulky and, therefore, were not treated by grid therapy. Among all tumors investigated, only the 10 cm tumor was ellipsoidal, with a diameter of 10 cm at the axes perpendicular to the beam axis, and 6 cm along the beam. The dose prescription point was at the center of the tumor volume. Dose sizes ranging from 1 to 30 Gy at 100% dose line were modeled. The prescription dose of grid therapy is also called the nominal dose. 2.D. Biological effects of grid therapy
The biological model for calculating interspersed normal tissue and tumor cell survival used in this study has been previously described in the literature.6 The LQ model parameters (α and β) of radiobiological response for melanoma cells were those described by Brenner and Hall13 and were consistent with data reported by Thames,14 Wigg,15 and Malaise.16 For normal tissues, we used α/β = 3.1 Gy.17 As previously described,7 in the present study we also used three types of normal tissue cells to estimate the therapeutic outcome: Medical Physics, Vol. 41, No. 2, February 2014
Cell lines
A
β
α/β
Sk-mel 128 EE MF EF RPM17951 GE HX-34 VN HX-118 SF(2 Gy) = 0.3 SF(2 Gy) = 0.5 SF(2 Gy) = 0.7
0.13 0.21 0.28 0.35 0.27 0.61 0.27 0.53 0.33 0.366 0.211 0.108
0.113 0.1 0.0879 0.0701 0.0468 0.101 0.0421 0.0783 0.038 0.1180 0.0680 0.0350
1.15 2.1 3.19 4.99 5.77 6.04 6.41 6.77 8.68 3.1 3.1 3.1
radiosensitive [SF(2Gy) = 0.3]; moderately radiosensitive [SF(2Gy) = 0.5]; and radioresistant [SF(2Gy) = 0.7]. (See Table I.) In recent years, the suitability of the LQ model when describing cell killing at high doses (>12 Gy) has become the subject of debate.18–20 Brenner18 has made several assertions regarding applicability of the LQ model for high dose radiotherapy: (1) the LQ model is a mechanistic and biologically based model; (2) most other mechanistic models of cell killing predict the same fractionation dependencies as does the LQ; (3) the LQ model has well documented predictive properties for fractionation/dose-rate effects in the laboratory; (4) the LQ model has been repeatedly validated and it would be reasonable to use it for doses up to ∼18 Gy per fraction; (5) to date, there is no evidence of problems when LQ has been used clinically. However, in order to validate Brenner’s assertion and further validate the radiobiologic modeling results, a MLQ model—introduced by Guerrreo and Li21 —was used to estimate the surviving fractions of the same melanoma cell lines after grid therapy, in addition to the classical LQ model. The MLQ model has significantly increased the cell survival ratio in high dose (>12 Gy) regions compared to the classical LQ model. The MLQ model can be expressed as SF (x, y, z) = exp(−α · D(x, y.z) − β · g(δ · D(x, y, z)) ·D(x, y, z)2 ),
(1)
where D(x, y, z) was the MC simulated dose at the point (x, y, z), which was related to the prescription dose via the PDD of the central hole, and the MC-calculated 3D dose distribution at the layer z. g(t) = 2(t + e−t − 1)/t2 is the dose protraction factor/function which describes the reduction in the effect of lethal mis-repair induced by a protracted treatment regimen, t is a variable used in the function, t = δ*D(x,y,z), and δ is a histology-related parameter.21 Since our purpose for using the MLQ model was to test the impact of a radiobiological model in which the survival ratio of high dose irradiation is increased, we decided to use δ = 0.15 for all investigated melanoma cell lines, and interspersed three types of normal cells as well. As we see, if g(t) = 1.0, the MLQ model will become the classical LQ model.
021727-4
Zhang et al.: Impact of dose size in grid radiotherapy
The average survival fraction of uniformly interspersed tumor or normal tissue cells with uniform cell densities in grid therapy was GTV SF(D(x, y, z)) · dx · dy · dz SF(Grid) = GTV dx · dy · dz GTV SF(D(x, y, z)) · dx · dy · dz = . (2) VGTV
021727-4
It should be noted that in the clinic, other open field sizes could also be used for debulking tumors; we related the 10 × 10 cm2 open field to our single fraction grid therapy in order to explicate the relationship and clearly convey the underlying concept. The Open field dose also came from Monte Carlo simulations verified by a water tank scanning system.
3. RESULTS For calculations of the surviving fractions, the same dose distribution was used for both tumor cells and normal tissues. This was based on those cases in which the tumor and normal tissue or organ at risk could not be well delineated and, therefore, would receive a similar radiation dose, e.g., early stage bulky melanomas. The average tumor cell survival fraction in grid therapy SF(Grid) has the EUD,6 which is the equivalent uniform dose that would kill the same number of tumor cells across the tumor volume. The consequential difference between uniform dose and high gradient nonuniform dose has been debated among many researchers. Of note, it is difficult to reconcile the grid-therapy outcomes with conventional TCP models. Because EUD is different from TCP—which depends on the dose to individual cells—it is used to evaluate the overall performance of a 3D dose distribution. In this study we mainly use EUD, rather than TCP, to analyze different dose regimens. The accuracy of EUD could be compromised by large dose nonuniformities; nevertheless, it does provide a simple form to characterize complex dose distributions. The EUD could be obtained by solving the following equation: α • EUD2 + β • EUD + ln(SFc (Grid) = 0.
3.A. A Dose volume histogram (DVH) of grid therapy
In Fig. 2, the DVHs were calculated for a 10 cm tumor (6 cm in height and 10 cm in the major and minor axes) located at a depth of 3 cm and treated by either a 20 Gy nominal dose of grid therapy or 4.2 Gy of open field therapy. Theoretically, both regimens would kill the same number of tumor cells, but the grid therapy allows more normal cells to survive, as demonstrated in Secs. 3.D–3.E. Figure 2(a) depicts the differential dose volume histogram (d-DVH) showing the dose spectrum in the tumor; and Fig. 2(b) depicts the cumulative DVH that shows the dose coverage at the tumor. The dose spectrum in grid therapy has two peaks, but open field therapy has only one peak. In grid therapy, 60% of the tumor volume will receive at least 4 Gy, 40% will receive 10 Gy, and about 20% could receive up to 17 Gy. In open field therapy,
(3)
In the above equation α and β are for different melanoma cancer cell lines; (SFc (Grid) is the average survival fraction of the corresponding cancer cell line across the tumor volume in grid therapy, calculated by the Eq. (2). The definition of grid therapy therapeutic ratio (TR) is similar to that described in the literature:8 SFnormal (Grid) . (4) TR= SFnormal (EUD) A TR value greater than 1 would imply a survival advantage for normal cells in grid irradiation, because it shows that at the same tumor cell killing rate, more interspersed normal cells were spared by grid field than by open field. 2.E. Equivalent uniform dose in open field therapy
If a tumor is debulked by open fields instead of grid therapy, EUD can be calculated from a single portal open field or a set of multiple portal open fields. Traditionally, only a single portal open field with a large dose was used for debulking purposes. Therefore, we evaluated EUDs at prescription doses in a single portal 10 × 10 cm2 open field for various tumor sizes to establish the relationship between the EUD and prescription doses, and thereby equated grid therapy to open field therapy based on the same tumor cell killing or the same EUD. Medical Physics, Vol. 41, No. 2, February 2014
F IG . 2. Differential and cumulative dose volume histograms for a 10 cm tumor (6 cm in height and 10 cm in the major and minor axes) located 3 cm deep and treated with either a single fraction of 20 Gy prescription dose grid therapy or one fraction of 4.2 Gy open field. Both regimens have the same equivalent uniform dose of 4.1 Gy.
021727-5
Zhang et al.: Impact of dose size in grid radiotherapy
021727-5
the dose spectrum is much narrower than in grid therapy, with the delivered dose ranging only from 3.8 to 4.5 Gy. 3.B. Equivalent uniform dose (EUD)
Figure 3 depicts the EUDs of single fraction grid therapy regimens calculated by the LQ model. The values were averaged from all the melanoma cell lines. Figure 3 demonstrates that the EUD is different for different tumor sizes and locations at the same nominal dose. The average EUDs were found to be approximated by 3rd order polynomial functions: EUD = a3∗ DP3 + a2∗ DP2 + a1∗ DP + a0,
(5)
where DP was the prescription dose, and also called the nominal fraction dose; a3, a2, a1, and a0 are fitting coefficients, which were 2.3432 × 10−4 , −1.3463 × 10−2 , 3.6573 × 10−1 , and 1.8992 × 10−1 , for tumors located at a depth of 3 cm. These values were to be 2.2832 × 10−4 , −1.3227 × 10−2 , 3.4568 × 10−1 , and 1.7593 × 10−1 , respectively, for tumors touching the skin surface. 3.C. EUD of a single portal open field
Figure 4 depicts the EUDs of different prescription doses for a single portal 10 × 10 cm2 open field for different spherical tumor volumes and locations. The EUD was found to be weakly dependent upon tumor size and location and close to
F IG . 4. The equivalent uniform doses (EUD) of tumors of different sizes treated with single fraction open field radiotherapy at different prescription doses.
the prescription dose DPD . The average EUD of all tumor sizes for a single portal and single fraction open field could be linearly approximated by EUD = k ∗ DP ,
(6)
where k was a fitting coefficient, with a value of 0.978 for tumors at a depth of 3 cm and 0.901 for tumors at the skin surface. It indicated that in the open field therapy, if the tumor was at a depth of 3 cm, the EUD is close to the prescription dose DP . When tumors touched the skin and the center was shallower than 3 cm, the EUD was about 10% lower than the DP . 3.D. LQ vs MLQ model in grid therapy
We made a comparison between LQ and MLQ models for predicting TR and EUD at the different prescription doses for a 10 cm tumor (6 cm in height and 10 cm in the major and minor axes). Compared to results from the MLQ model, the LQ model-calculated EUD is 2.8% higher and the TR is 1% lower at the prescription dose of 20 Gy. At 10 Gy, the difference between two models is less than 1% for both the EUD and TR. 3.E. The TR of grid therapy F IG . 3. The equivalent uniform doses (EUD) of tumors of different sizes in single fraction grid therapy calculated by the LQ model. Medical Physics, Vol. 41, No. 2, February 2014
Figure 5 depicts the TRs of single fraction grid therapy in treating a 10-cm melanoma with different cell lines at
021727-6
Zhang et al.: Impact of dose size in grid radiotherapy
021727-6
F IG . 5. Therapeutic ratios (TR) of a 10-cm melanoma tumor irradiated with different doses of single fraction grid therapy calculated by the LQ and MLQ models. The different melanoma and normal tissue cell lines with experimentally determined radioresponse LQ parameters are listed in Table I. Medical Physics, Vol. 41, No. 2, February 2014
021727-7
Zhang et al.: Impact of dose size in grid radiotherapy
021727-7
4. DISCUSSION
F IG . 6. Therapeutic ratios (TR) of melanoma tumors with different diameters treated with different doses of single fraction grid therapy averaged by all melanoma and normal cell lines.
different doses. The left panel shows the results from the LQ model; the right is the MLQ model. The results from both models are similar, and only a small difference (less than 2%) is seen. Figure 5 also reveals that the acutely responding melanoma cells (α/β > 6, except for G.E.) surrounded by radiosensitive normal tissues (normal tissue 1 and 2) were more suitable in treatment with grid therapy, while the later responding tumor (α/β < 6)—or any tumor cells interspersed among radioresistant normal cells (normal tissue 3)—would not benefit from this highly nonuniform field. In addition, the fact that the TR of HX34 (α/β = 6.4) was greater than that of V.N. (α /β = 6.77) indicated that the TR depended not only on the single ratio of α /β but also on the individual α and β values. This relationship has been suggested by Malaise et al.,16 and also was confirmed in our previous study of 2D cervical cancers.8 Figure 6 illustrates the average TR for all tumor cell lines and the average TR for all types of normal tissues. The results indicate that grid therapy would not provide any additional therapeutic advantage in sparing interspersed normal tissue cells if the fraction dose were smaller than 15 Gy, because the TR is less than 1.0. This means the grid field killed more normal cells than the open field at the same tumor cell killing rate. Medical Physics, Vol. 41, No. 2, February 2014
In this study, we have provided an improved dosimetric simulation and assessed the radiobiological response of melanoma cells in the 3D dose distribution of single fraction grid therapy. The biological advantage of grid therapy at varying doses has been evaluated using the LQ and MLQ models for cell survival calculations, and the results have been described in terms of TRs and EUDs. The differential dose volume histogram [Fig. 2(a)] demonstrated that two well-separated groups of doses were actually delivered to the tumor in grid therapy at 20 Gy nominal fraction dose. One group peaked at ∼3 Gy, and the other at ∼18 Gy, unlike the dose in open field therapy, which had a single peak at 4.2 Gy. This indicates that a significant portion of the tumor volume would receive a very large dose, ensuring significant tumor cell killing in these regions; and that some areas would receive a relatively small dose. As reported by Mackonis et al.,22, 23 the coexistence of cold and hot dose regions most likely would enhance bystander killing effects, thereby further increasing the benefits of a highly modulated field through an increase in the EUD. The cumulative DVH of the 10 cm tumor provided evidence for the dose coverage achieved with grid therapy in a 3D target [Fig. 2(b)]. In contrast to the conventional open field treatment, in which the DVH curve has a single plateau and then drops rapidly at the prescription dose, grid therapy had a distinctive DVH curve with two plateaus. The first plateau was located at the low dose region (∼2.5 Gy) that covered 100% of the volume. The second occurred at a dose (∼6 Gy) that covered ∼50% of the tumor volume. Most importantly, the second plateau was long, and slowly declined until it reached the nominal dose. This ensured that grid therapy would deliver large doses to a significant part of the tumor volume. The radiobiological characteristics of melanoma cells seen in grid therapy for 3D tumors are consistent with those seen in previous studies of melanoma and cervical cancer cells as 2D targets.6–8 The more acutely responding tumor cells interspersed in radiosensitive normal tissues would be more effectively treated with grid therapy (Fig. 5). It was also found that the use of the MLQ model to increase cell survival fraction at high dose would not change the theoretical prediction and conclusions of grid therapy. This is because the very high dose volume is small, and the unique characteristics of grid therapy mainly rely on the dramatic dose variation across the tumor volume. Our results also demonstrated that bulky melanomas within radioresistant normal tissues would not be more effectively debulked by megavoltage grid therapy than by open field therapy. Therefore, determining the radiosensitivity of tumor and normal cells before treatment could help in selecting the most effective treatment regimens for grid therapy. Whether tumors touched the skin surface or were located at a depth of 3 cm, our results indicated that a minimum fraction dose was necessary if grid therapy was to achieve average TRs greater than 1 (Fig. 6). Moreover, although slightly different minimum doses were needed for tumors of different
021727-8
Zhang et al.: Impact of dose size in grid radiotherapy
sizes, the overall minimum dose was ∼15 Gy. As reported in the literature,13–17 almost all tumor cells have an overlapping α/β range; generally, they fall into an α/β ratio spectrum ranging from 1.1 to 20.9. This coincides with the α/β ratio range which includes melanoma and cervical cancer lines, both of which we have investigated. Thus, the clinical outcomes of diverse cancers treated with grid therapy could serve as a reference for examining the results of our current and previous studies,8 which assessed the average radiobiological effects of grid therapy in treating melanoma and cervical cancers. Mohiuddin et al.3 reported that an overall response of 94% was achieved with a nominal dose >15 Gy. When the grid therapy dose was
