A mathematical model for the shrinkage of acoustic neurinoma following gamma-knife treatment and some relationships between parameters of the formula and dose-volume histogram

Initial swelling followed by gradual shrinkage is regarded as usual in the Gamma Knife treatment of acoustic neurinomas. We developed a mathematical model representing these changes with 3 independent variables, and a relationship was revealed between these variables and a dose-volume histogram. One hundred and fifty-one patients were treated for acoustic neurinomas between 1992 and 1997 at our facility. Of these, 84 cases could be evaluated with our mathematical model because they were followed by MRI for more than 12 months and at least 5 studies were performed. Peripheral, average and maximum doses were 13.9±3.1, 18.6±4.2 and 28.6±7.5 Gy, respectively. Pretreatment volumes were 5.5±9.3 cm3. There were 3 groups, stable (16 cases), rapidly swelling and shrinking (41 cases) and slow-growing and reducible (27 cases). The second group had a small mean time constant of 0.3 months for the initial growing and -23 months for the contiguous shrinkage. The values for the third group were 1 and -43 months, respectively. The degree of swelling in the third group was 3 times higher than that in the second group. The low frequency of the dose distribution over 26 Gy discriminated the members of the second group from the others (p<0.0426), witch indicated that significantly higher doses may not produce good results. (author)