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_{d}), α/β and radiosensitivity α, were estimated. Other radiobiological models: EUD, BED, TCP, _{d} are α/β = 8.1 ± 4.1 Gy, α = 0.22 ± 0.08 Gy^{−1}, T_{d} = 4.0 ± 1.8 day, respectively. The prolonged IMRT dose delivery for entire HNC treatment course could possibly result in the loss of biological effectiveness,

Intensity modulated radiation therapy (IMRT) is becoming the standard technique to treat head-and-neck cancer (HNC) in radiation treatment, since IMRT is capable of delivering highly conformal doses to the target volume while sparing normal structures. However, because of the increasing complexity of the IMRT plan, it generally takes longer time to deliver the same amount of dose as compared to 3D conformal radiotherapy (3DCRT). It is known that the extended IMRT delivery time may reduce treatment effectiveness for cancer cells, specifically for the cancer cells with short repair halftime.

The prolonged IMRT dose delivery for HNC treatment could possibly result in the loss of biological effectiveness. Nowadays, there are various IMRT dose delivery techniques available, such as step-and-shot IMRT, dynamic IMRT, helical Tomotherapy (HT) and recently available volumetric modulated arc therapy (VMAT),

The linear quadratic (LQ) formalism is widely used to analyze both

In this paper, _{d} and α/β ratios for HNC cell lines. Two cell lines were irradiated by a series of single/split dose regimens using a 6 MV photon beam. The obtained survival data were then analyzed and fitted to the LQ model. A plausible set of radiobiological parameters for HNC, such as sublethal damage repair halftime (T_{r}), α and α/β _{r}, the tumor doubling time (T_{d}) and the variation of lag-off time (T_{k}) were also studied.

A specially-designed split-dose _{2} and 95% air with a complete DMEM growth medium, supplemented with 10% FBS (GIBCO-Invitrogen, Carlsbad, CA, USA). KB cells were derived from a primary epidermal carcinoma of the mouth, and obtained from the American Type Culture Collection (Manassas, VA, USA). UMSCC-1 cells were derived from a primary squamous cell carcinoma of the retromolar trigone, and kindly provided by Thomas Carey (University of Michigan, Ann Arbor, MI, USA). The cells were irradiated with 8 Gy fractions, split in different intervals from 0 to 6 h using a 6 MV photon beam generated by a Siemens Primus accelerator at our department.

UMSCC-1 and KB cells from a stock culture were prepared into a single cell suspension by trypsinization to count cell density. In 100-mm Petri dishes, three thousand cells were seeded and allowed to grow for 24 h. Cells were then irradiated with 8 Gy fractions, split in different intervals: 0, 15 min, 30 min, 45 min, 1 h, 2 h, 4 h and 6 h at our department. A water-equivalent plate of 5 cm thick solid water was placed on the bottom of the flask to ensure the full backscatter condition. Another 1.5 cm thick solid water was placed on the top of the flask to serve as a built-up material for the 6 MV beam. The attached cells were in the bottom of P100 flask at a water-equivalent depth of 5 mm, since they were covered by a 15-mL medium. Therefore, the attached cells were at the depth of dose maximum for the 6-MV (1.6 cm). Four 100 mm Petri dishes were irradiated each time using a 20 × 20 cm radiation field.

UMSCC-1 and KB cells from an 80% confluency culture were typsinized, and viable cells were counted through trypan blue staining. 3 × 10^{4} cells per well were plated in a 12-well plate and cultured for 72 h (less than 80% confluency at 72 h). The cells were typsinized, counted, re-plated at a density of 3 × 10^{4} cells per well in a 12-well plate and sub-cultured for another 72 h. The total numbers of cells were recorded to calculate the population doubling time (PDT). The experiment was performed in triplicates each time and was repeated three times. The PDT was calculated using the following equation [

where _{i}_{i}, N_{0} is the initial number of cells. The average value of the PDT for each measurement was quoted as the PDT of UMSCC-1 or KB cells, respectively.

The surviving fraction S of cells irradiated to a total dose D within an effective treatment time T is given by Linear-Quadratic formalism (LQ). According to [

and:

where the quantity _{d}_{d}_{K} is “kick-off” time of accelerated proliferation, meaning the time from the beginning of treatment to the starting of accelerated proliferation. T_{k} for head and neck tumors as revealed by [

The general Lea-Catcheside dose protraction factor

here, _{γ}_{γ}

where, T_{i} is the time interval between the two split fractions, T_{f} is the dose delivery time.

The radiobiological models, such as biological equivalent dose, equivalent uniform dose, and tumor control probability, were used to measure the treatment effectiveness of different IMRT techniques using the newly derived parameter set.

Biologically effective dose (BED) is the concept used to compare different treatment modalities or fractionation schedules:

For conventional EBRT, when the dose-delivering time is much shorter than the repairtime _{r}_{d} is the effective tumor cell repopulation rate, T_{d} is the potential doubling time. The treatment time

The dose inhomogeneities are considered by using the concept of equivalent uniform dose (EUD), which is defined as the dose that, if distributed uniformly, will lead to the same biological effect as the actual non-uniform dose distribution [

To account for dose heterogeneity, the survival fraction is calculated based on the dose volume histogram (DVH) by:

where V_{0} is the tumor volume, V_{i} is the sub volume corresponding to dose bin D_{i} on the DVH. A representative DVH for a H&N case was used to calculate the EUDs.

The numerical value of EUD is relative to the value delivered by a standard reference regimen, e.g., 2 Gy fraction. By definition, surviving fraction

Thus, the corresponding EUD that results in the surviving fraction

For a given plan, the surviving fraction

The tumor control probability (TCP) with clonogen proliferation is also calculated from the cell surviving fraction S shown in Equation (1) using the Poisson hypothesis [

where, S is the cell surviving fraction shown in Equations (2) and (3), K is the number of tumor clonogens, and is assume to be an arbitrary number (^{5}) in the calculation. We also assumed the density of tumor clonogens throughout the tumor was constant.

In our study, the least χ^{2} (chi-square) method is used to fit the survival rate from _{r} are independent variables. The basic idea of this fitting method is that the best-fit curve for a given data set has the minimal sum of the squares of the offsets (the least chi-square error). The sum of the squares of the offsets is defined as:

where ^{Meas}(D_{j}) is the j-th observed survival rate, ^{Calc}(D_{j}) is the calculated survival rate for the given dose D_{j}; σ^{2}(D_{j}) is the corresponding statistical error for the j-th data point.

^{−1} with repair halftime T_{r} = 18 ± 21 min; while the fitting results for UMSCC-1 cell line (shown as ^{−1} with repairtime T_{r} = 16 ± 25 min. The derived potential doubling times for UMSCC-1 cell line and KB cell line are T_{d} = 3.6 ± 2.2 days, T_{d} = 4.5 ± 2.8 days, respectively. Similar results were obtained for both cell lines. Combined the results from these two cell lines, we have: α/β = 8.1 ± 4.3 Gy, α = 0.22 ± 0.08 Gy^{−1}, the repair halftime T_{r} = 17 ± 21 min and the potential doubling time T_{d} = 4.0 ± 1.8 days. Unless otherwise stated, the parameter set was used in the calculation throughout the paper. Our finding is consistent with previous publications [

Impacts of repair halftime on the IMRT treatment effectiveness measured by BED and TCP were computed as a function of delivery times.

Fitted cell sublethal repair curves using split-doses exposure of 8 Gy. (^{−1} with repairtime T_{r} = 18 ± 21 min; (^{−1} with repair halftime T_{r} = 16 ± 25 min. Both cell lines are from HNC cells.

The calculated BED and TCP as a function of repair halftime for H&N tumor. The combined parameter based on the studies of two cell lines from this analysis: α/β = 8.3 ± 4.1 Gy, α = 0.22 ± 0.08 Gy^{−1} and repair halftime T_{r} = 17 ± 21 min, T_{d} = 4.0 ± 1.8 days were used in the calculation. The fraction dose delivery time of 2, 10, 17 and 30 min were calculated and shown.

Influences of dose delivery time on (^{−1} and repair halftime T_{r} = 16 ± 21 min, the potential doubling time T_{d} = 4.0 ± 1.8 days were used in the calculation.

_{r}, where the dose fraction delivery times T_{f} were assumed to be 5 min (solid) and 30 min (dashed), respectively. _{f} results in reduced tumor EUD.

The variation of EUD as a function of repair halftime T_{r}. The fraction dose delivery time of 5 min (dashed) and 30 min (solid) were shown. The standard fraction scheme was considered in the calculation: 70 Gy in 2 Gy/fraction.

Given a repair halftime of 17 min determined from this analysis, for the fraction dose delivery time T_{f} = 5 min, EUD is calculated to be 71.2 Gy; EUD dropped to 63.5 Gy if T_{f} = 30 min was assumed (12% drop compared to that of 5 min dose delivery fraction).

Comparison of EUD changes assuming different fraction dose delivery time (same DVHs were used). The derived results from this analysis: α/β = 8.3 ± 4.1 Gy, α = 0.22 ± 0.08 Gy^{−1}, T_{r }= 17 ± 21 min and T_{d} = 4.0 ± 1.8 day were used in the EUD calculation.

EUD (Gy) | EUD (Gy) | EUD change (%) | |
---|---|---|---|

T_{f} = 5 min |
T_{f} = 30 min |
||

T_{r} = 17 min |
71.2 | 63.5 | −12.1 |

T_{r} = 38 min |
71.6 | 67.8 | −5.6 |

It is generally known that the α/β ratio for H&N carcinomas is great and varies over a large range: 9–20 Gy from the literatures [_{f} =30 min) due to the variations of α/β ratios in the range of 8.3–20.0 Gy.

Influence of α/β ratio on EUD for H&N tumor. The result from this analysis α/β = 8.3 Gy was used. The standard fraction scheme was considered in the calculation: 70 Gy in 2 Gy/fraction.

_{d} = 2, 4, 5 and 40 days. The kick-off time T_{k} = 28 days (range 21–35 days) according to [_{d} = 4 days for HNC, given a standard fraction scheme, a prescription dose of 70 Gy in 2 Gy/fx delivered in 7 weeks, BED was calculated to be 71 Gy; if the overall treatment time was shortened to be within 6 weeks, the BED is 76 Gy, the biological dose gain was then 76–71 = 5 Gy (~6.6% BED increase); the BED gain by shortening overall treatment time from 7 weeks to 6 weeks can go even higher if the doubling time T_{d} is <4 days (larger slope lines shown in _{d} = 40 (or longer) days. The corresponding TCP changes due to the variation of the overall treatment time (T_{t}) were shown in _{t}, the TCP drops significantly for HNC when T_{r} < 5 days. Thereby, additional dosing was required to counteract the cell proliferation in the prolonged radiation treatment to maintain the same tumor control rate.

(_{d} = 2, 4, 5 and 40 days. The kick-off time T_{k} = 28 day according to [

The

Large number of monitor units (MUs) and/or large number of segments,

For fast repopulation cancer cells, it is known that there is a potential decrease in tumor control due to prolonged overall treatment time for radiotherapy of HNC [_{d} estimated to be around 2–4 days, the overall treatment time is an important factor governing tumor control. The optimal fractionation scheme for H&N radiotherapy remains to be determined. As a matter of fact, altered fractionation schedules are being developed and examined to optimize treatment results under various clinical circumstances [

The effectiveness of the linear-quadratic (LQ) model has been demonstrated in both clinical and

Plausible radiobiological parameter sets using two head-and-neck carcinoma cell lines were derived from the present ^{−1}, the repair halftime T_{r} = 17 ± 21 min and the potential doubling time T_{d} = 4.0 ± 1.8 day. The estimated α/β ratio from our

The authors declare no conflict of interest.