Loss of radiobiological effect of imaging dose in image guided radiotherapy due to prolonged imaging‐to‐treatment times

Purpose: Increased use of cone beam CT guidance in image guided radiotherapy has prompted the inclusion of the imaging dose in treatment plans, thus using imaging beams to treat tumors. Sublethal radiation damage repair duringτ d , the time between imaging and treatment, could reduce the effectiveness of the imaging dose, resulting in tumor underdosage. The theoretical magnitude of this effect was quantified using radiobiological modeling. Methods: The therapeutic effective dose (TED), which, if delivered using only therapeutic beams, would result in the same tumor cell survival as for both the imaging and therapeutic beams, was derived using the generalized linear‐quadratic model. The correction factorP dby which therapeutic dose can be scaled to compensate for sublethal damage repair was also derived. TED andP dare dependent on α / β , sublethal damage repair half‐time( T r ) , imaging dose( D I )and dose rate(D ̇ I ) , therapeutic dose( D T )and dose rate(D ̇ T ) , andτ d . TED andP dwere calculated as a function ofτ d , and each parameter was varied independently while holding the remaining parameters at their reference values. The reference values were based on prostate cancer cells and wereD p = D I + D T = 1.8 Gy ,D I / D p = 5 % ,D ̇ I = 0.33 Gy / min ,D ̇ T = 1.0 Gy / min , α / β = 3.1 Gy ,T r = 16 min , andτ d = 0 min . Estimates of the expected values of TED andP d ,⟨ TED ⟩and⟨ P d ⟩ , were calculated usingτ dandD ̇ Tdistributions from a few thousand prostate treatment fractions. Results: For a typicalτ dvalue of 5.0 min and all other parameters set to their reference values, TED was 0.5% lower than the prescription doseD p . Forτ d = 20 min and all other parameters at reference conditions, TED dropped by 5% relative toD pwhenD I / D pwas 20% and by 2% relative toD pwhen α / β = 1 Gy orT r = 5 min . TED / D pvaried more withD ̇ TthanD ̇ Iwhenτ d ≤ 20 min , varying by up to 1% over 0.05 ≤ D ̇ T ≤ 10 Gy / min and by less than 0.1% over 0.05 ≤ D ̇ I ≤ 2.0 Gy / min . Under the reference conditions,⟨ TED ⟩was lower thanD pby 0.5%. For the extremeD I / D p = 20 % and all other parameters at their reference values, setting α / β = 1 Gy resulted in⟨ TED ⟩dropping belowD pby 2.5% and settingT r = 5 min resulted in⟨ TED ⟩dropping belowD pby 4%. For tumors with aT rof 16 min or greater and α / β of 11 Gy,⟨ TED ⟩dropped belowD pby 0.2% or less. Conclusions: For prostate tumors receiving a reasonable percentage of 5% of their total dose from imaging beams, the theoretical drop in⟨ TED ⟩relative toD pwas 0.5%. This loss could be accounted for during treatment planning by scaling the therapeutic dose by the expected sublethal damage repair factor⟨ P d ⟩ . For nonprostate tumors with α / β values of 11 Gy, the theoretical drop in⟨ TED ⟩relative to the reference TED was low at 0.2%.