Radiobiological Insights of Staged Brachytherapy Using Eye Plaque for Large Uveal Melanoma

Abstract

I-125 radioactive seeds embedded in an eye plaque is used to deliver the radiation dose of 85Gy to the apex of the tumor. However, it is challenging to treat a lesion in height (>10 mm) because of a high dose (> 500 Gy) to sclera. A staged radiotherapy (SRT) has been implemented successfully in stereotactic radiosurgery when a single dose is risky for a bigger sized lesion. The hypothesis of this work is that the SRT works for eye plaque brachytherapy of uveal melanoma to break the single fraction into two. To apply the concept of SRT, the following questions need to be answered: What are the two fraction doses? What is the time interval between the two fractions? In this work, the two split fraction doses and time interval are calculated using the "incomplete-repair' model. Equation (1) is the linear-quadratic (LQ) model. f(x) is the cell survival curve (SC). Equation (2) and (3) are radiobiological model developed dealing with the split doses by considering the incomplete repair. Ln(f(x)) = -αx - βx2 (1) Ln(fn(x, Ɵ)) = nLn(f(x))-nβx2hn(Ɵ) (2) hn(Ɵ) = (2/n)[ Ɵ/(1- Ɵ)][n-(1- Ɵn)/(1- Ɵ)] (3) Ɵ = exp(-µΔt) (4) x represents the fraction dose, Ɵx is the initial segment of the survival curve, Ɵ determines the rate at which repair proceeds. n is fraction number and µ represent repair constant which equals to ln2/T1/2. T1/2 is the half-life of I-125. For continuous dose vt delivered at dose rate v for time t, with repair constant µ, the LQ model is modified as Ln (f(vt, µ)) = -α(vt) -β(vt)2g(µt) (5) g(µt) = 2[µt-1+exp(-µt)]/(µt)2 (6) Assuming biological effective dose (BED) is the same for the single fraction and split two fractions, SC when n = 1 should be same as when n = 2. Therefore, the equation (7) is derived. Ɵ = [(α/β)x1 - 2(α/β)(x2)2 + (x1)2]/2(x2)2 - 1 (7) x1 is single fraction dose of 85Gy, x2 is the split dose to two fractions. α/β ratio of 10 Gy is used. By fitting the equation (7), the ranges of doses and time intervals were determined. The fraction doses and time interval to get the same BED as single fraction of 85 Gy are determined from 45 Gy to 50 Gy with time interval of 22 days to 76 days for staged brachytherapy eye plaque (SBEP). Our result is matched the treatment protocol for SBEP reported, e.g., 1st fraction dose of 40Gy and 50 Gy of 2nd fraction with 73 days of time interval are used. The max. dose of scleral dose is 328 Gy compared to the single fraction scleral dose of 543Gy. This work could provide guidelines in SBEP in dosage and time interval. The height of tumor matters the most in the SBEP since the taller the tumor, the higher dose to the sclera is. Reference.