shows oxygen partial pressure as a function of radial distance from the center of a capillary as predicted by Eq. (1)
. The solid line represents the assumed oxygen diffusion parameters (p0
= 60 mmHg, Rmax
= 150 μm) that are most consistent with those expected in human tumors (25
). This set of parameters results in an average oxygen partial pressure of 6.9 mmHg assuming that 20% of the tumor cells are maximally resistant (p
< 0.5 mmHg) and 80% of the tumor cells are either well-oxygenated (p
> 20 mmHg) or at intermediate oxygen levels (p
= 0.5–20 mmHg). The value of p
= 6.9 mmHg is consistent with typical median oxygen partial pressures of 3–5 mmHg and 10–15 mmHg reported for prostate (17
) and H&N (16
) cancers, respectively.
Oxygen partial pressure as a function of radial distance from the center of a capillary. The solid line represents the assumed oxygen diffusion parameters that result in an average oxygen partial pressure of ~ 6.9 mmHg.
shows the expected decrease in cellular radiosensitivity as a function of oxygen partial pressure. HRF
values derived from data reported by Ling et al.
), Koch et al.
), Whillans and Hunt (27
), and Carlson et al.
) are denoted by white triangles, black circles, white circles, and gray circles, respectively. Reported OER
) were transformed into HRF
values by dividing the maximum OER
by the OER
for each level of oxygenation. The HRF
is at its maximum for anoxic conditions with a value of 2.8 and decreases to unity as the cells approach normoxic conditions. The dotted line shows the oxygen partial pressure (p
= 0.5 mmHg) below which cells are assumed to be maximally resistant, i.e., radiobiologically hypoxic (9
). Eq. (4)
with best fit parameters m
= 2.8 and K
= 1.5 is used to convert the probability density function of the partial pressure of oxygen into a continuous distribution of HRF
Figure 2 Hypoxia reduction factor (HRF) values derived from published cell survival data (11, 15, 26, 27). Solid line shows a fit to the values using Eq. (4) with m = 2.8 and K = 1.5.
shows surviving fraction of tumor clonogens as a function of radial distance from the capillary center for conventional H&N and prostate cancer treatments. Predictions are calculated using Eq. (3)
, neglecting intrafraction DSB repair (G
= 1), and the total number of fractions, i.e., S
. Our simulations predict that tumor cell killing decreases by a factor of ~ 105
over a radial distance of 130 μm assuming an oxygen partial pressure of 60 mmHg at the capillary wall. The surviving fraction increases from 4.7×10−9
for H&N cancer and from 1.0×10−8
for prostate cancer. This predicted trend is consistent with experimental data from mouse tumors that shows a loss in radiosensitivity with distance from blood vessels (28
Surviving fraction of tumor clonogens as a function of radial distance from the capillary center for conventional radiotherapy fractionations.
shows surviving fraction of H&N and prostate tumor clonogens for an entire course of radiotherapy as a function of number of fractions, neglecting intrafraction DSB repair (G
= 1) and clonogen repopulation (γ = 0). The equivalence of each fractionation schedule is demonstrated by the isoeffect achieved under normoxic conditions (i.e., HRF
= 1). Solid symbols show model predictions for hypoxic fractions of 10%, 20%, and 30%. Tumor hypoxia increases cell survival by a factor of ~ 103
for conventionally fractioned radiotherapy as shown in earlier modeling studies (9
). Tumor cell survival increases by additional factors of ~ 6×102
and ~ 4×102
as the dose per fraction is increased from 1.7 Gy (n
= 40) to 24 Gy (n
= 1) and from 2.0 Gy (n
= 40) to 18 Gy (n
= 1) for H&N and prostate cancer, respectively. shows the individual and combined effects of tumor hypoxia, tumor cell repopulation, and intrafraction DSB repair on total surviving fraction. Clonogen repopulation is most significant for hyperfractionated H&N cancer and strongly depends on the assumed lag time. For Tk
= 21 days, cell killing decreases by a factor of ~ 6×102
as the dose per fraction is decreased from 3.7 to 1.7 Gy. For single fraction treatments, cell killing may be overpredicted by up to a factor of 24 if intrafraction DSB repair is neglected.
Total surviving fraction of tumor clonogens as a function of dose per fraction assuming daily fractionation and full reoxygenation between fractions. Dependence of model predictions on the assumed value of the hypoxic fraction of cells is shown.
Total surviving fraction of tumor clonogens as a function of dose per fraction assuming daily fractionation and full reoxygenation between fractions. Dependence of model predictions on intrafraction DSB repair and clonogen repopulation is shown.
shows the distribution of SER
values for the hypoxic cell radiosensitizer misonidazole derived from published in vitro
). White triangles and gray circles represent estimates for misonidazole concentrations of 1.2 mM and 5.0 mM, respectively. The SER
is maximum for anoxic conditions with values of 1.4 and 2.0 for 1.2 mM and 5.0 mM concentrations, respectively, and decreases to unity as the cells approach normoxic conditions. shows the surviving fraction of tumor clonogens for different combinations of misonidazole and radiation. Values are shown for the characteristic 1–5 fractions of SBRT treatments. The addition of a hypoxic cell radiosensitizer at high doses per fraction is shown to be a potential strategy to obtain similar or greater levels of cell killing than achieved with conventional fractionation. Misonidazole has a greater sensitizing effect for large doses per fraction because of the increased importance of the hypoxic fraction of cells.
Figure 6 Sensitizer enhancements ratio (SER) values derived from published cell survival data (15). Solid lines shows a fit to the values using Eq. (10) with x = 1.4 and y = 0.4 for the 1.2 mM concentration and x = 2.0 and y = 0.9 for the 5.0 mM concentration. (more ...)
Figure 7 Effect of misonidazole and radiation on surviving fraction of tumor clonogens assuming a realistic distribution of tumor hypoxia, intrafraction DSB repair, and clonogen repopulation. Dotted lines show predictions neglecting corrections for hypoxia, repair, (more ...)