Critical volume model analysis of lung complication data from different strains of mice

The critical volume (CV) normal tissue complication probability (NTCP) model was used to fit experimental data on radiation pneumonitis in mice to test the model and determine the values of the model parameters characterizing the lung structure: relative critical volume and cell radiosensitivity. The entire lungs of mice from ten different strains were irradiated acutely and homogeneously to different doses. The experimental animals from the different strains expressed different radiation sensitivities, forming ten well-defined dose – response curves. The most widely accepted biological NTCP model (the individual CV NTCP) readily applicable to cases of acute uniform irradiation was used to fit all the individual dose – response curves simultaneously. To account for the apparent difference in the response of the different strains, it was assumed that the strains differed in their (cell) radiosensitivity. The maximum likelihood method of fitting was used. The obtained fit was statistically highly acceptable. The best-fit value of the relative critical volume, μ, was 78%, which is extremely close to the histologically observed value of around 72%. The values of radiosensitivity, α, ranged between 0.26 and 0.37 Gy – 1 for the different strains. The best-fit numbers of functional subunits (FSU) constituting the lung, N, and the number of cells in an FSU, No, were implausibly low: N = 9 and No = 23, respectively. The best-fit value of NoN was a very small number that was unlikely to correspond to the total number of cells comprising the lung, suggesting that a different interpretation of N and No was required. The individual CV model provided a simultaneous description of the individual responses of different mouse strains through assumed interindividual variability in α only. A new interpretation is given to the entities corresponding to No and N. NoN is interpreted as the number of certain elementary structures. These structures are considered to be equivalent to the classical functional subunit, which is much larger than a cell and plays a fundamental role in determining the radiation response of the organ. N is identified as the number of the few large subdivisions of the lungs, M = μN is the number that have to be damaged for the lung to fail. No is interpreted as the mean number of elementary structures (FSU) per large subdivision. This imposes a picture of damage to large, contiguous subdivisions containing many FSU, which is consistent with the histological appearance of the lungs of mice in respiratory distress. This picture is in marked contrast to the random distribution of small areas of damage expected for the small size of an FSU. This random distribution is characteristic of earlier stages of the development of radiation pneumonitis, suggesting that some additional process spreads injury from damaged FSU to adjacent, undamaged FSU during the terminal phase.