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Corresponding author at: Radiation Technologist in Department of Radiation Technology, Osaka Heavy Ion Therapy Center, 3-1-10 Otemae, Chuo-ku, Osaka City, Osaka 540-0008, Japan.
Osaka Heavy Ion Therapy Center, Osaka City, Osaka, JapanDepartment of Medical Physics and Engineering, Osaka University Graduate School of Medicine, Osaka City, Osaka, Japan
Osaka Heavy Ion Therapy Center, Osaka City, Osaka, JapanDepartment of Carbon Ion Radiotherapy, Osaka University Graduate School of Medicine, Osaka City, Osaka, Japan
Osaka Heavy Ion Therapy Center, Osaka City, Osaka, JapanDepartment of Medical Physics and Engineering, Osaka University Graduate School of Medicine, Osaka City, Osaka, Japan
Prostate cancer cells show different radiosensitivity than reference cells.
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Radiosensitivity differences affect the final clinical dose distribution.
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Prostate cancer cell-based clinical dose from one-directional irradiation is no longer flat.
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Opposed left–right irradiation used in clinic improves this lack of flatness.
Abstract
[Purpose] Treatment plans for carbon ion radiotherapy (CIRT) in Japan are designed to uniformly deliver the prescribed clinical dose based on the radiosensitivity of human salivary gland (HSG) cells to the planning target volume (PTV). However, sensitivity to carbon beams varies between cell lines, that is, it should be checked that the clinical dose distribution based on the cell radiosensitivity of the treatment site is uniform within the PTV.
[Methods] We modeled the linear energy transfer (LET) dependence of the linear-quadratic (LQ) coefficients specific to prostate cancer, which accounts for the majority of CIRT. This was achieved by irradiating prostate cancer cells (PC3) with X-rays from a 4 MV-Linac and carbon beams with different LETs of 11.1–214.3 keV/μm. By using the radiosensitivity of PC3 cells derived from cellular experiments, we reconstructed prostate-cancer-specific clinical dose distributions on patient computed tomography (CT).
[Results] The LQ coefficient, α, of PC3 cells was larger than that of HSG cells at low (<50 keV/μm) LET and smaller at high (>50 keV/μm) LET, which was validated by cellular experiments performed on rectangular SOBPs. The reconstructed dose distribution on patient CT was sloped when 1 fraction incident from the one side of the patient was considered, but remained uniform from the sum of 12 fractions of the left–right opposing beams (as is used in clinical practice).
[Conclusion] Our study reveals the inhomogeneity of clinical doses in single-field plans calculated using the PC3 radiosensitivity data. However, this inhomogeneity is compensated by using the combination of left–right opposing beams.
Carbon ion radiotherapy (CIRT) can create a spatially superior physical dose distribution with the Bragg peak and can have considerable biological effects on tumors because the relative biological effectiveness (RBE) is correlated with the linear energy transfer (LET), which increases toward the end of the range of carbon beams. However, appropriate evaluation of RBE is essential in order to achieve optimal results with CIRT.
Clinical application of CIRT was implemented at the National Institute of Radiological Sciences (NIRS) in Japan using the mixed beam model based on the experimental biological data established by Kanai et al [
] and calculated the biological dose by multiplying physical dose by RBE, assuming HSG to represent the radiosensitivity of all tumor cells. The clinical dose was defined by the biological dose multiplied by a clinical coefficient representing the difference between in vivo and in vitro biological effects, based on the experience of fast-neutron beam therapy performed at NIRS. A clinical coefficient was determined to be 1.46 to scale the RBE of a carbon beam in spread-out Bragg peak (SOBP) with a dose-averaged LET of 80 keV/μm, which is equivalent to a neutron beam in NIRS, to a clinical RBE = 3 for fast-neutron radiotherapy [
]. The microdosimetric kinetic model (MKM) was introduced for calculating the biological effects in clinical settings, taking into account the effects of various fragmentation nuclides [
The Gesellschaft für Schwerionenforschung (GSI) in Germany developed the Local Effect Model (LEM), which evaluates biological effects of charged particles by analyzing the response of cells or tissues to X-rays [
Krämer M, Jäkel O, Haberer T, Kraft G, Schardt D, Weber U. Treatment planning for heavy-ion radiotherapy: physical beam model and dose optimization. vol. 45. 2000.
]. Currently the Heidelberg Ion-Beam Therapy Center (HIT) is still using LEM I for clinical treatments, mostly with alpha / beta = 2 Gy, although a slightly higher value has been puplished for cordoma tissue [
The above information demonstrates that, although endpoints differ between countries, treatment planning in clinical practice is ultimately based on a reference biological response regardless of the type of cancer. However, the sensitivity to carbon ions has been found to vary among cancer tissues [
Relative biological effectiveness for cell-killing effect on various human cell lines irradiated with heavy-ion medical accelerator in Chiba (HIMAC) carbon-ion beams.
A Consistent protocol reveals a large heterogeneity in the biological effectiveness of proton and carbon-ion beams for various sarcoma and normal-tissue-derived cell lines.
]. It is particularly important to investigate the specific radiosensitivity of prostate cancer cells to carbon beams, because prostate cancer accounts for the majority of CIRT and has been reported to have a different radiosensitivity (specifically, a smaller alpha–beta ratio) to other cancers [
The physical dose used at the Osaka Heavy Ion Therapy Center (OHITC) is optimized so that the clinical dose based on the RBE of HSG cells is uniform within the tumor [
] regardless of the tumor site. However, it is unclear whether this can be applied directly to prostate cancer. Cellular experiments using prostate cancer cells rather than HSG would enable their biological parameters to be elucidated, and prostate-cancer-specific clinical doses could be calculated. The present study, therefore, aimed to evaluate the suitability of the current HSG-based treatment plan by reconstructing prostate-cancer-specific clinical dose distributions based on cellular experiments.
2. Methods
2.1 Dose calculation methods used in clinical practice
Physical and biological dose calculations are currently performed at the OHITC using the VQA Plan (Ver. 5.10, Hitachi ltd., Tokyo, Japan), a particle-treatment-planning software which implements the dose calculation method reported by references [
]. The physical dose at voxel is given by the following equation, based on the triple-Gaussian model:
(1)
(2)
where is the physical dose contribution of the th component of beam to voxel ; is the irradiation monitor unit (MU) of beam ; and and are the integral depth dose and Gaussian distribution of the th component at depth , respectively.
The biological dose in CIRT is defined as the dose of the reference radiation (i.e., X-rays) required to produce an equivalent biological effect based on the linear-quadratic (LQ) model. The radiosensitivity of HSG cells is used as the LQ coefficients α and β, which depend on the LET (Fig. 1).
Fig. 1Coefficients of the linear-quadratic model α (red line) and β (blue line) of human salivary glands for carbon (solid line) and helium (dashed line). Abbreviations: LET, linear energy transfer. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
The in equation (1) is divided into physical doses given by carbon isotopes and other fragment isotopes , where the LQ coefficients for carbon (, ) and helium (, ) are applied, respectively [
According to the LQ model, the biological effect of voxel can be calculated using:
(5)
The biological dose is expressed by equation (6) using the LQ coefficients of for X-rays of HSG cells. The clinical dose, , is expressed by equation (7), using the clinical coefficients 1.46 obtained from fast-neutron radiotherapy [
The dose calculation method currently used for treatment planning is based on the radiosensitivity of HSG cells. In the following sections, the specific radiosensitivity of prostate cancer cells will be used to calculate prostate-cancer-specific clinical doses.
] in Dulbecco’s Modified Eagle Medium (Thermo Fisher Scientific, Massachusetts, USA) containing 10 % fetal bovine serum (Thermo Fisher Scientific) and 1 % penicillin, streptomycin, and l-glutamine (NACALAI TESQUE, Inc. Kyoto, Japan) at 37 °C and 5 % CO2 under humidified conditions.
The survival rate of PC3 cells was estimated after exposure to X-ray and carbon ion beams by colony-formation assay. The PC3 cells were seeded at 6.0 × 105 cells in each 25 cm2 cell culture flasks 4 days before irradiation. Since cell doubling time was about 33 h, final density was around 2.5 × 106 cells (90 % confluency) just before irradiation. Cells grown in 25 cm2 plastic flasks were irradiated by X-ray and carbon ion beams (as described in the following sections), then washed with phosphate-buffered saline and treated with trypsin. The cells were seeded into three 60 mm diameter dishes. Fourteen days after seeding, the cells were fixed with formalin and stained with crystal violet solution. The number of colonies with >50 cells was recorded and the survival rate calculated. At least three independent experiments were performed for each irradiation.
2.3 Modeling of linear-quadratic coefficients for PC3 cells
Differences in radiosensitivity were evaluated by comparing LQ coefficients for the reference radiation (X-rays) in equation (6) and the LQ coefficients for carbon ion beam in equations ((3), (4)), which were derived from cell experiment data. PC3 cells were irradiated with X-rays at doses ranging from 0.5 to 8 Gy (with a non-irradiated control) using a 4 MV-Linac (Mitsubishi Electric, Tokyo, Japan), and the LQ coefficients for X-rays were determined from cell survival rates obtained in the colony-formation assay (Section 2.2). The LQ coefficients for carbon ion beam vary depending on the LET, so we also irradiated PC3 with several mono-energy carbon beams. Fig. 2(a) shows a schematic diagram of an experiment using a mono-energy carbon beam: PC3 cells were placed at a depth of 5.4 mm water equivalent length (WEL) with acrylic flask walls, and were irradiated with carbon beams of six different mono-energies. The cell survival rate was derived by colony-formation assay when the physical dose of carbon beam was 1–5 Gy (with a non-irradiated control) by adjusting the irradiated MU.
Fig. 2Irradiation conditions for the modeling of LQ coefficients for PC3 cells. (a) Experimental setup with the thickness of the acrylic plate adjusted to place PC3 cells at the depths indicated by the vertical dashed lines in (b) (5.4 mm water equivalent length) and (c) (155, 185, and 215 mm water equivalent length). (b) Depth profile of the physical dose (solid line) and dose-averaged linear energy transfer (dot-dashed line) from mono-energy carbon beams, and (c) from rectangular spread-out Bragg peak. The physical dose is divided into components of carbon isotopes (dotted line) and fragment isotopes (dashed line). Abbreviations: LET, linear energy transfer; RBE, relative biological effectiveness; WEL, water equivalent length.
The physical doses (components due to carbon isotopes and fragment isotopes) and dose-averaged LET in the depth direction given by a carbon beam of 0.1 MU/spot are shown in Fig. 2(b). The dose-averaged LET values at the cell surface (i.e., 5.4 mm WEL depth) for each energy carbon beam are summarized in Table 1.The dose-averaged LET was obtained using Monte Carlo calculations, taking into account fragment particles and energy spread, provided by Hitachi ltd. as data of VQA. Monte Carlo calculations were performed by GEANT4 simulation toolkit [
The survival rate of PC3 irradiated with X-rays of dose was calculated using equation (8). The carbon isotope component is dominant in the total physical dose with minor contribution (up to 3.5 %) from the fragment component at the depth of the cell-attachment surface [5.4 mm WEL; Fig. 2(b)]; thus, the cell response can be derived from the LQ coefficients and in equations ((3), (4)) for carbon isotopes, and the survival rate of PC3 can be expressed by equation (9).
(8)
(9)
First, we obtained the LQ coefficients of PC3 for X-rays, and , by fitting the cell survival rate given by X-rays from experimental data using equation (8). Assuming that β is independent on the value of LET as suggested by [
A model for the relative biological effectiveness of protons: The tissue specific parameter α/β of photons is a predictor for the sensitivity to LET changes.
Direct evaluation of radiobiological parameters from clinical data in the case of ion beam therapy: An alternative approach to the relative biological effectiveness.
]. Next, we derived for each LET by fitting the cell survival rate given by the carbon beam for each LET with equation (9). Since depends on LET, we formulated it in the following function for LET:
(10)
This is an empirical model represented by a sum of Gaussian functions on the logarithm of the LET and a constant b, where a, μ, and σ are the height of the curve's peak, the position of the center of the peak, and the standard deviation of the Gaussian functions, respectively.
2.4 Validation of linear-quadratic coefficients in spread-out Bragg peak
The biological effects in carbon SOBP are expressed using the dose-averaged α and dose-averaged β in equations ((3), (4)). The modeling of the LQ coefficients of PC3 for carbon radiation obtained in section 2.3 must be validated for SOBP by confirming that the cell experiments in SOBP reproduce the dose-averaged α and β calculated from it.
Fig. 2(c) shows the physical dose, dose-averaged LET, and clinical dose based on HSG from a rectangular SOBP with a center depth of 185 mm and a width of 70 mm, constructed assuming clinical treatment for prostate cancer. The SOBP was created using the VQA Plan so that the clinical dose based on HSG cells would be constant at 4.3 Gy (RBE).
The physical dose in the SOBP includes carbon isotope components as well as fragment-isotope components; thus, the LQ coefficients for the fragment isotopes should also be considered. We calculated the dose-averaged α and β of PC3 using the LQ coefficients and of PC3 for carbon isotopes modeled by equations ((9), (10)), and the LQ coefficients and of HSG for fragment isotopes (equations [
The biological effect of PC3 is calculated using the following equation:
(13)
and are obtained by fitting equation (8), the PC3 survival rate by X-rays was applied to equation (14) to obtain the biological dose based on the radiosensitivity of PC3 cells. The biological dose was converted to the clinical dose by multiplying by the clinical coefficient 1.46, as shown in equation (15).
(14)
(15)
Carbon SOBP was irradiated to PC3 cells positioned at the proximal (155 mm WEL depth), center (185 mm WEL depth), and distal (215 mm WEL depth) positions of the SOBP by placement of the acrylic plates [Fig. 2(a)]. The SOBPs were irradiated with MU scaled to achieve a physical dose at each depth of 1, 2, and 5 Gy. The cell survival rate under each condition was derived by colony-formation assay (Section 2.2). As shown in Fig. 2(c), the physical dose in the SOBP contains components from carbon and fragment isotopes, so the response of cells in the SOBP can be attributed to the dose-averaged LQ coefficients (, in equations [
]). By fitting the cell survival rate from the experiment in equation (16), we derived , at three depths in the SOBP and adapted these values to equations ((13), (14), (15)) to calculate the clinical dose based on cell experiments.
(16)
Clinical doses obtained from modeling the LQ coefficients of PC3 cells (Section 2.3) were compared with clinical doses based on experimental data to confirm that modeling of LQ coefficients of PC3 cells can be generalized to SOBP.
2.5 Clinical dose calculation for computed tomography (CT)
CT of the prostate and base of the seminal vesicle of one patient with prostate cancer was carried out as contoured clinical target volume. We added a margin of 8 mm in the left–right (LR) direction and 5 mm in the other direction to the clinical target volume to make the planning target volume (PTV). The treatment plan comprised right-left opposing beams (one beam per day) for the PTV, created using the VQA Plan with a dose-fractionation protocol of 51.6 Gy (RBE) in 12 fractions. The conditions of the plan were imported into in-house dose calculation software, which incorporated the LQ coefficients of both HSG and PC3 cells. The clinical dose was calculated using equations ((1), (2), (3), (4), (5), (6), (7)) based on the LQ coefficients of HSG cells (HSG-based clinical dose) and from equations (1), (2), and ((11), (12), (13), (14), (15)) based on the LQ coefficients of PC3 cells (PC3-based clinical dose). For the PC3-based clinical dose, the HSG-based clinical dose was applied outside the PTV.
3. Results
3.1 Linear energy transfer dependence of linear-quadratic coefficients for PC3 cells
The cell survival rates were found to be lower following carbon-beam irradiation than those with X-ray irradiation and to decrease with increasing LET (Fig. 3(a)). Each calculated rate was well fitted by the LQ model (equation [
] for X-ray irradiation, equation (9) for carbon beam irradiation), and increased LET was found to cause a more linear LQ curve. The derived LQ coefficients for each LET are summarized in Table 2.
Fig. 3Modeling results for LQ coefficients for PC3. (a) Experimental survival rates of PC3 cells (circles) and the fitted curves given by the linear-quadratic (LQ) model (solid lines) obtained by irradiation with X-rays or with mono-energetic carbon beams (as shown in Fig. 2[b]). (b) The linear energy transfer (LET) dependence of the LQ coefficient (α) of PC3 cells (open circles) and the fitted function according to equation (10) (red line). The α values of human salivary gland cells obtained using mono-LET carbon beam (dotted line) and mixed-LET carbon beam at the corresponding depth (dashed line) are shown for comparison. (c) Experimental survival rates of PC3 cells (circles) and their fitted curves (solid lines) at three positions in the spread-out Bragg peak from Fig. 2(c). The survival curve (dashed line) was calculated from modeling the LQ coefficients of PC3 cells using equations ((11), (12)), which reflected experimental values well. (d) Clinical doses (red line) calculated from dose-averaged LQ coefficients α (purple line) calculated using equation (11) and β (pink line) calculated using equation (12) based on modeled PC3 radiosensitivity and clinical dose (black dashed line) calculated using equation (16) based on experiments at the spread-out Bragg peak. All error bars represent ± standard deviation of the experimental values. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 2Linear-quadratic coefficients of PC3 cells for X-rays and for mono-energetic carbon beams with several LETs derived in fitting cell survival rates with linear-quadratic models.
X-rays
carbon beams
LET [keV/μ]
1.0
11.1
21.2
34.2
53.5
92.6
214.3
α [Gy−1]
0.302 ± 0.008
0.481 ± 0.036
0.610 ± 0.020
0.759 ± 0.028
1.069 ± 0.016
1.122 ± 0.024
1.199 ± 0.028
β [Gy−2]
0.0417 ± 0.0049
LQ coefficient α correspond to that of the LQ curves represented by the solid lines in Fig. 3(a), respectively. Abbreviations: LET, linear energy transfer.
The LQ coefficients, α, for PC3 cells as well as for HSG cells obtained from a mono-LET carbon beam increased with increasing LET, peaking at around 100–200 keV/µm (Fig. 3(b)). The biological effect of mixed-LET is expressed as a dose-averaged α, whereas an α corresponding to an element of the LET spectrum is weighted by dose [
]. The dose-averaged α of the peak of the mixed-LET spectrum is smaller than that of the mono-LET spectrum. The α values for PC3 cells created a less steeply sloping curve compared with those for HSG obtained using a mixed-LET carbon beam at the depth of the cell surface.
3.2 Validation of LQ coefficients for PC3 cells in the SOBP
The dose-averaged α and β values at the proximal (155 mm WEL depth), center (185 mm WEL depth), and distal (215 mm WEL depth) positions of the SOBP are summarized in Table 3. The survival rate curves drawn using these coefficients are shown as dashed lines in Fig. 3(c), the cell survival rate for cells placed at the same depth and irradiated with the same carbon beam are indicated with circles. Survival curves based on modeled LQ coefficients of PC3 cells (dashed lines) and experimental curves (solid lines) agreed well at the proximal and distal positions. At the center position, the calculated survival rate was slightly smaller than the experimental value, but it was within the error bars (±1 standard deviation).
Table 3Modeled linear-quadratic coefficients in the spread-out Bragg peak calculated from linear-quadratic coefficients of PC3 cells and experimental values derived in fitting cell survival rates in the same spread-out Bragg peak with linear-quadratic models.
proximal
center
distal
Modeled LQ coefficients
dose-averaged α [Gy−1]
0.675
0.752
0.902
dose-averaged β[Gy−2]
0.045
0.047
0.050
Experimental LQ coefficients
dose-averaged α [Gy−1]
0.581 ± 0.019
0.802 ± 0.046
0.871 ± 0.028
dose-averaged β[Gy−2]
0.070 ± 0.004
0.025 ± 0.010
0.056 ± 0.006
Modeled and experimental LQ coefficients correspond to that of the LQ curves represented by the dashed and solid lines in Fig. 3(c), respectively. Abbreviations: LQ, linear-quadratic.
The clinical dose of the SOBP based on PC3 radiosensitivity is shown as a solid red line in Fig. 3(d) and those calculated using the experimental dose-averaged α and β values are shown as white circles, and the curves show good agreement within ±1 standard deviation.
3.3 Clinical dose distribution in clinical cases
As shown in the upper row of Fig. 4(a), the HSG-based clinical dose for 1 fraction from the left side of the patient was flat at the prescribed dose, whereas the PC3-based clinical dose was higher, especially on the proximal side of PTV, which was not uniform. The profile of the PC3-based clinical dose in the LR direction across the isocenter showed that proximal side is about 10 % higher than distal side (Fig. 4 (b)). On the other hand, the sum of 12 fractions of the left and right opposing beams reduced this slope, resulting in a roughly flat PC3-based clinical dose (lower row of Fig. 4(a)). This was also confirmed by the dose profile in the LR direction shown in Fig. 4(c).
Fig. 4Comparison of human salivary gland (HSG)- and PC3-based clinical dose on patient computed tomography with prostate cancer. (a) HSG-based clinical dose (left column), PC3-based clinical dose (middle column), and the difference between them (right column) using 1 fraction of the incident beam from the left side of the patient (upper row) and the sum of 12 fractions of the left and right opposing beams (lower row). Color bars indicate the % dose relative to the prescribed dose (i.e., 4.3 and 51.6 Gy [relative biological equivalent] for 1 or 12 fraction, respectively). (b) HSG- and PC3-based clinical dose profiles (red and dashed lines, respectively) in the LR direction across the isocenter using 1 fraction, and (c) the sum of 12 fractions. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
We derived the radiosensitivity of PC3 cells and determined the clinical doses specific to prostate cancer via cell-based experiments, to compare with the radiosensitivity of HSG cells which is used in conventional calculations of clinical doses for carbon beam therapy. This is, to the best of our knowledge, the first study to reconstruct clinical doses using carbon radiosensitivity of cells other than reference cells that are used in treatment planning (i.e., HSG cells in Japan).
Placing PC3 cells at a very shallow depth enabled us to eliminate the dose contribution of fragment isotopes as much as possible (at most 3.5 %, see Fig. 2 (c)) to model the radiosensitivity of PC3 and to derive the LET dependence of the LQ coefficient due to carbon isotopes. However, when calculating the dose-averaged LQ coefficients for PC3 in SOBPs where fragment isotopes are not negligible, we substituted fragment-terms for HSG as shown in Equations (11, 12). Although fragment-terms should be derived by irradiating PC3 with fragment particles, such as helium, we substituted fragment-terms for HSG because the irradiation with ions other than 12C is not possible. Note that within SOBPs with a mixture of carbon isotopes and fragment isotopes, we verified that the effect of this substitution is negligible by confirming that the cell survival rates using the dose-averaged α and β given in Eqs. (11, 12) are consistent with the cell survival rates from cellular experiments (Fig. 3 (c)).
Recently, a treatment plan that takes into account the dose-dependence of RBE by using a carbon beam as the reference dose and estimating the biological effect of fragment particles by using MKM has been developed [
]. In this report, the final clinical dose from MKM was reported to be similar (within ±1.5 %) to that of the model used in this study within the target area. Therefore, the differences in radiosensitivity of the reference cells revealed by this study would have the same effect if they were adapted to MKM.
The α values of HSG cells derived from the survival rate of HSG when irradiated with mono-LET and that obtained from irradiation with mixed-LETs at the cell surface were calculated from the LET spectral components and dose fractions using Monte Carlo simulation [
]. The α corresponding to each LET element was then weighted by dose fraction. A carbon beam with mono-LET incident from the accelerator is mainly energy-dispersed by the ripple filter and the LET spectrum is broadened, which would have resulted in a small peak around 100–200 keV/μm that we observed. The ripple filter could not be removed due to mechanical constraints, so the α of PC3 cells for mixed-LET was derived directly. Assuming that the dose-averaged α in mixed-LET is representative of the α in its LET spectrum, the derived α of PC3 for mixed-LET can be directly compared with the dose-averaged α of HSG. The more moderate peak of the former indicates that PC3 cells have different carbon radiosensitivity to HSG cells. The LET spectrum may be further broadened with the use of SOBP for prostate cancer, and the dose-averaged α may vary as the carbon beam progresses through the body. However, our calculations and experimental results agreed well in the SOBP (Fig. 3(c, d)), suggesting that the effects of changes in the LET spectrum are small.
The value of α in the region above the LET that was used for the PC3 cell experiments (>300 keV/μm) is uncertain, but it does not affect the final clinical dose as such high LETs do not appear in clinical CIRT.
Calculation of the PC3-based clinical dose from the CT data of patients with prostate cancer revealed that the dose distribution in the target region was sloped when irradiated from one direction. The slope of the PC3-based clinical dose is attributable to the fact that the LET dependence of PC3 α is different from that of HSG. The α of PC3 was lower than that of HSG on the high-LET side. Given that the SOBP was designed to have a constant HSG-based clinical dose, the PC3-based clinical dose would have been sloped to be lower at the distal end, which contains more high-LET components, than at the proximal end, which contains more low-LET components. This slope of the clinical dose was more noticeable with irradiation from one direction and was compensated for by the opposing irradiation. Thus, irradiation from multiple directions may be advantageous in compensating for the heterogeneity of clinical doses in SOBP resulting from the diversity of cellular radiosensitivity.
The PC3-based clinical dose from the left–right opposed beam was uniform in the target area and approximately 10 % higher than the dose estimated using the radiosensitivity of HSG cell (Fig. 4 (c)), which corresponds to a total treatment dose of about 56.8 Gy (RBE). Since HSG-based 51.6 Gy (RBE) and PC3-based 56.8 Gy (RBE) are biologically equivalent, it may be practical to standardize on the HSG-based prescription dose when used in clinical practice. However, the prescription doses were originally determined in clinical trials and discussions of absolute overdose and underdose for clinical doses are not appropriate based on the results of this study. We have demonstrated that the shape of the clinical dose in the SOBP may change due to differences in the radiosensitivity of individual cells. Since the relative dose distribution is flat, we believe that there should be no problem in adjusting the depth dose of the currently used plan.
The α and β of PC3 cells and αβ ratio for 250 kVp X-rays have been reported to be 0.487, 0.055, and 8.855, respectively [
Leith JT, ’ L, Quaranto BA, ’ Giavanna Padpield BA, Michelson S, Hercbergs A. Radiobiological studies of PC-3 and DU-145 human prostate cancer cells: x-ray sensitivity in vitro and hypoxic fractions of xenografted tumors in vivo. Int J Radiat Oncol Biol Phys 1993;25:283–7.
], which our results support. In a summary of published LQ coefficients from six prostate cancer cell types including PC3, Nahum et al found the mean ± standard error of α and β to be 0.2603 ± 0.059 and 0.0315 ± 0.0064, respectively [
] may reduce the differences compared with in vivo αβ ratios. In addition, the hypoxic environment of cancer cells may cause radioresistance and reduce the αβ ratio due to changes in α and β.
Fig. 5LQ coefficients obtained in this study (red circles) and those for six prostate cancer cell types summarized by Nahum et al
(black symbols). Boxplots represent the median, 25th and 75th percentile, maximum, and minimum values of the latter. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
There have been no other reports on the LET dependence of LQ coefficients of prostate cancer cells for carbon beam irradiation, so we compared our results with LQ coefficients of other cancer cells in the particle irradiation data ensemble (PIDE) database provided by GSI [
]. Only data on cancer cells that were experimented with three or more mono-energetic (not SOBP) carbon beams were extracted from PIDE. Fig. 6 illustrates the LQ coefficients for PC3 cells, which exhibit average values compared with other cancer cell lines. However, the LET dependence of the LQ coefficient is specific to each cancer cell, and so the clinical dose must be reconstructed for each cancer tissue to evaluate the validity of the treatment, and optimization of the physical dose may be required.
Fig. 6Linear energy transfer dependence of linear-quadratic coefficients for human salivary gland (black dashed line), PC3 (red line), and various cancer cell lines extracted from the particle irradiation data ensemble [
]. Abbreviations: HSG, human salivary gland; LET, linear energy transfer. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
As also demonstrated by the comparison with the data by Nahum, large uncertainties affect the experimental determination of LQ parameters due to differences in experimenters or cell environments. However, since the colony formation assays with X-rays and carbon beams of various LETs were performed on the same day by the same experimenter, we believe that the relative relationship in cell survival rates is reliable. Since the clinical dose is calculated using the relative sensitivity of each LET to X-rays with carbon beams, we believe that these uncertainties have limited impacts on the final clinical dose. However, since the current study used only one cell (PC3), the sensitivity of different cells to X-rays and carbon rays was not determined. Since different cells may have different final clinical doses, we look forward to studies examining the carbon beam sensitivity of various other cell lines.
In addition, individual radiosensitivity to carbon radiation varies among the patient population, and by analyzing tumor control probability, the standard deviations of α and β for prostate cancer were reported to be 11.3 % and 12.9 %, respectively [
A validated tumor control probability model based on a meta-analysis of low, intermediate, and high-risk prostate cancer patients treated by photon, proton, or carbon-ion radiotherapy.
]. If this individual uncertainty is taken into account for α and β obtained in this study, PC3-based clinical dose shown in Fig. 4 can vary within the region shown in Fig. 7. The most probable shape of the clinical dose is preserved.
Fig. 7PC3-based Clinical doses considering the individual uncertainties in the LQ coefficients using 1 fraction of the incident beam from the left side of the patient (a) and the sum of 12 fractions of the left and right opposing beams (b). The red line represents the reference PC3-based clinical dose (same as in Fig. 4(b, c)), and the filled area represents the possible PC3-based clinical dose when α and β are increased (dashed line) or decreased (dotted line) by 11.3% and 12.9%, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
]. It is expected that future studies will allow dosimetry that takes hypoxia into account.
The present study focused on prostate cancer, which is the most significant application of CIRT, but different cancers—and even different healthy tissues—may have different carbon beam sensitivities. Calculating clinical doses that account for these differences will only be possible once experiments using various other cells have been carried out. Differences in radiosensitivity to carbon beams among cell lines may exert a considerable effect on the final clinical dose distribution. However, this study found that these differences can be compensated by using the combination of left–right opposing beams, as far as prostate cancer is concerned. Treatment planning with clinical doses specific to each cancer type—and even each healthy tissue—could make use of the LET-dependent biological effects of CIRT.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The authors acknowledge and thank the staff at Osaka Heavy Ion Administration Company for their help in operating the accelerator to conduct cell experiments. The authors would like to thank Enago (www.enago.jp) for the English language review.
Ethical statement
This study was approved by the institutional research ethics committee of our institution.
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