DOS 543  Discussion 1
Writing Prompt
Post: Time Dose Fractionation
The effect of radition on a cell population varies according to a variety of factors, including tissue type, tissue function, metabolic activity, and mitotic activity.^{1 } While it is difficult to isolate these factors individually, it is useful to be able to characterize a tissue's reaction to radiation based on its sensitivity or insensitivity to changes in dose fraction size. This sensitivity appears to have two components, one of which is linear with dose, and one of which is quadratic with dose. These components are labeled as alpha (α) and beta (β) for convenience. As dose changes, the relative contributions of α and β to the total cell kill varies.^{2} As a shorthand, the dose at which the contibution from α and from β is equal can be used to express a population's overall sensitivity to changes in fraction size. This particular sweetspot in the curve is called the α/β ratio, because when αD = βD^{2}, it can be rewritten as D = α/β.
Generally speaking, fastgrowing cells have high α/β ratios.^{1} Speaking metaphorically, they can be easily knocked around, so a light touch many times over can still hit them while slower growing normal tissues can tolerate the light touch more easily.
Slow growing cells like prostate cancer may have very low α/β ratios. They are hit harder by bigger doses. By increasing the fraction size, fewer fractions are needed, and an overall lower dose is delivered to surrounding tissue that have a relatively higher α/β ratio.
Borrowing a specific example from Werts, one can use the linearquadratic model to calculate a biologically equivalent dose (BED) for a single fraction of size D with the equation:
$BED=D\left(1+\frac{D}{\alpha /\beta}\right)$
When multiplying this by the number of fractions in a treatment, a total BED can be computed. If the fraction size changes, the BED of the single dose changes, and a different number of fractions may be needed to accomplish the same BED. It is worth noting that the BED is different for every tissue and needs to be calculated for each tissue according to its α/β ratio. In the example of prostate cancer, a typical treatment regime is 1.8 Gy per fraction times 44 fractions for a total absolute dose of 79.2 Gy. If we calculate the BED for prostate cancer, which may have a α/β ratio as low as 1.52 Gy (we will use 2 Gy for this example), then the BED to the tumor would be:
$BED=44fx\times 1.8\frac{Gy}{fx}\left(1+\frac{1.8Gy}{2Gy}\right)=150.48Gy$
If the fractionation scheme were changed to 4 Gy per fraction, the number of fractions required to achieve 150 Gy_{BED} would be:
$150Gy=Nfx\times 4\frac{Gy}{fx}\left(1+\frac{4}{2}\right)\phantom{\rule{0ex}{0ex}}N=\frac{150}{12}\approx 13$
The rectum is thought to have a α/β ratio of around 45 Gy. The BED to the rectum under both schemes would be:
$BE{D}_{4Gy\left(conventional\right)}=44fx\times 1.8\frac{Gy}{fx}\left(1+\frac{1.8Gy}{4Gy}\right)=114.84Gy\phantom{\rule{0ex}{0ex}}BE{D}_{4Gy\left(hypofrac\right)}=13fx\times 4\frac{Gy}{fx}\left(1+\frac{4Gy}{4Gy}\right)=104Gy$
This is certainly an improvement, but if other normal tissues with higher α/β ratios such as 10 Gy are considered, we see a much larger improvement:
$BE{D}_{10Gy\left(conventional\right)}=44fx\times 1.8\frac{Gy}{fx}\left(1+\frac{1.8Gy}{10Gy}\right)=93.5Gy\phantom{\rule{0ex}{0ex}}BE{D}_{10Gy\left(hypofrac\right)}=13fx\times 4\frac{Gy}{fx}\left(1+\frac{4Gy}{10Gy}\right)=72.8Gy$
The jury is still out on whether or not these hypofractionated schemes actually provide a therapeutic benefit for prostate cancer, because the true α/β ratios of the involved tissue may not actually be what were used in this example, and there may be other confounding factors influencing tumor response that are not considered in this model. In the mean time, long conventional fractionation schedules are still used in most prostate cancer cases.
Grayden
 Werts ED. The Radiation Biology of Dose Fractionation: Determinants of Effect. [PowerPoint]. Pittsburgh, PA: Allegheny General Hospital.
 Hall EJ. Radiobiology for the Radiologist. 3rd ed. Philadelphia, PA: Lippincott Williams & Wilkins; 1988: 2223.
Academic Courses > DOS 543 > Time Dose Fractionation

Written October 25, 2015
Fourth Semester, 10 Months into Internship 