Damped sinusoidal function to model acute irradiation in radiotherapy patients.

In the paper, we suggest a damped sinusoidal function be used to model a regenerative response of mucosa in time after the radiotherapy treatment. The medical history of 389 RT patients irradiated within the years 1994-2000 at the Radiotherapy Department, Cancer Center, Maria Skłodowska-Curie Memorial Institute of Oncology, Gliwice, Poland, was taken into account. In the analyzed group of patients, the number of observations of a single patient ranged from 2 to 25 (mean = 8.3, median = 8) with severity determined by use of Dische's scores from 0 to 24 (mean = 7.4, median = 7). Statistical modeling of radiation-induced mucositis was performed for five groups of patients irradiated within the following radiotherapy schedules: CAIR, CB, Manchester, CHA-CHA, and Conventional. All of the regression parameters of the assumed model, i.e. amplitude, damping coefficient, angular frequency, phase of component, and offset, estimated in the analysis were statistically significant (p-value < 0.05) for the radiotherapy schedules. The model was validated using a non-oscillatory function. Following goodness-of-fit statistics, the damped sinusoidal function fits the data better than the non-oscillatory damped function. Model curves for harmonic characteristics with confidence intervals were plotted separately for each of the RT schedules and together in a combined design. The suggested model might be helpful in the numeric evaluation of the RT toxicity in the groups of patients under analysis as it allows for practical comparisons and treatment optimization. A statistical approach is also briefly described in the paper.