A bio-mathematical model for parallel organs and its use in ranking radiation treatment plans

To develop a new bio-mathematical model, named LQ-based parallel-organ model, that can overcome the limitation of interpreting the simple dose-volume information so as to rank the radio- toxicity of parallel organs in the same patient. A parallel organ consists of Function Subunits (FSUs), with each FSU being equal and representative in functional status. Based on the Linear-Quadratic model (LQ model), we had derived a bio-mathematical model to calculate the survival cell number for radiation dose response. We then compared the cell survival number for the ranking of treatment plans for the same patient. Ninety 3D plans from forty-five randomly selected lung cancer patients were generated using the ELEKTA precise 2.12 treatment planning system. The LQ-based parallel-organ model was tested against the widely used Lyman-Kutcher-Burman model (LKB model). There was no distinct statistical difference in plan ranking between using the LQ-based parallel-organ model and the LKB model (P = 0.475). Ranking plans by the V(x), Mean Lung Dose (MLD) and the LQ-based parallel-organ model shows that there was no distinct statistical difference between V(5), V(10), V(20), MLD and the LQ-based parallel-organ model, respectively (all Ps > 0.05). The proposed LQ-based parallel-organ model was found to be efficient and reliable for ranking treatment plans for the same patient.