Biologically effective dose distribution based on the linear quadratic model and its clinical relevance

Radiotherapy plans based on physical dose distributions do not necessarily entirely reflect the biological effects under various fractionation schemes. Over the past decade, the linear-quadratic (LQ) model has emerged as a convenient tool to quantify biological effects for radiotherapy. In this work, we set out to construct a mechanism to display biologically oriented dose distribution based on the LQ model.

A computer program that converts a physical dose distribution calculated by a commercially available treatment planning system to a biologically effective dose (BED) distribution has been developed and verified against theoretical calculations. This software accepts a user's input of biological parameters for each structure of interest (linear and quadratic dose-response and repopulation kinetic parameters), as well as treatment scheme factors (number of fractions, fractional dose, and treatment time). It then presents a two-dimensional BED display in conjunction with anatomical structures. Furthermore, to facilitate clinicians' intuitive comparison with conventional fractionation regimen, a conversion of BED to normalized isoeffective dose (NID) is also allowed.

Two sample cases serve to illustrate the application of our tool in clinical practice. (a) For an orthogonal wedged pair of x-ray beams treating a maxillary sinus tumor, the biological effect at the ipsilateral mandible can be quantified, thus illustrates the so-called "double-trouble" effects very well. (b) For a typical four-field, evenly weighted prostate treatment using 10 MV x-rays, physical dosimetry predicts a comparable dose at the femoral necks between an alternate two-fields/day and four-fields/day setups. However, our BED display reveals an approximate 21% higher BED for the two-fields/day scheme. This excessive dose to the femoral necks can be eliminated if the treatment is delivered with a 3:2 (anterio-posterior/posterio-anterior (AP/PA): bilaterally opposed (BLO)) dose weighting. With Co-60 beams, the increase of BED with alternate two-fields/day, 1:1 setup was even more pronounced (26%).

We have demonstrated the feasibility of constructing a biologically oriented dose distribution for clinical practice of radiotherapy. The discordance between physical dose distributions and the biological counterparts based on the given treatment schemes was quantified. The computerized display of BED at nonprescription points greatly enhanced the versatility of this tool. Although the routine use of this implementation in clinical radiotherapy should be cautiously done, depending largely on the accuracy of the published biological parameters, it may, nevertheless, help the clinicians derive an optimal treatment plan with a particular fractionation scheme or use it as a quantitative tool for outcome analysis in clinical research.