Tumour control probability: a formulation applicable to any temporal protocol of dose delivery.

An analytic expression for the tumour control probability (TCP), valid for any temporal distribution of dose, is discussed. The TCP model, derived using the theory of birth-and-death stochastic processes, generalizes several results previously obtained. The TCP equation is [equation: see text] where S(t) is the survival probability at time t of the n clonogenic tumour cells initially present (at t = 0), and b and d are, respectively, the birth and death rates of these cells. Equivalently, b = 0.693/Tpot and d/b is the cell loss factor of the tumour. In this expression t refers to any time during or after the treatment; typically, one would take for t the end of the treatment period or the expected remaining life span of the patient. This model, which provides a comprehensive framework for predicting TCP, can be used predictively, or--when clinical data are available for one particular treatment modality (e.g. fractionated radiotherapy)--to obtain TCP-equivalent regimens for other modalities (e.g. low dose-rate treatments).

The combined effects of sublethal damage repair, cellular repopulation and redistribution in the mitotic cycle. I. Survival probabilities after exposure to radiation.

An analytical model is presented that describes radiation-induced cellular inactivation in the presence of sublethal damage repair, cellular repopulation and redistribution in the mitotic cycle (the 3 Rs). The parameters of the model are measurable experimentally. Also taken into account are the initial age distribution of the cell population, the fact that subgroups of cells progress through the cycle at different speeds, the effects of a dose of radiation on the duration of the four phases of the cycle (G1, S, G2, M), the possibility that a certain fraction of the cells are quiescent, and cell loss and/or cell removal from the proliferating population. Survival probabilities are expressed as linear-quadratic functions of dose where the coefficient alpha and beta as well as the recovery constant (t0) are taken to depend on the position of the cell in the mitotic cycle. Explicit analytical expressions for inactivation probability are given for clonogenic cells exposed to continuous or fractionated radiation. Two model calculations are used to illustrate the formalism: in one, the redistribution of cells during fractionated therapy is examined. In the other calculation, it is shown that it is sufficient to take into account differences in proliferation rates and the change in the ratio alpha/beta within the generation cycle for cells that may have otherwise equal response to acute exposures to explain that in a fractionated treatment protocol late-responding cells are more sensitive to the dose per fraction than early-responding cells. It is not necessary to invoke differences in radiosensitivity between these two classes of cells.

A mathematical model for cell cycle progression under continuous low-dose-rate irradiation.

A mathematical model of the progression of cells through the mitotic cycle under continuous low-dose-rate irradiation is described. The model considers explicitly two special cases: (a) when a fraction of cells disintegrate and disappear after mitosis and (b) when a fraction of cells which have reached mitosis do not progress further but do not disintegrate either. We have established a relationship between the parameters of the model and dose and/or the age of the cell at exposure. This formalism is applied to studies of the effects of dose rate on HeLa cells (Mitchell, Bedford, and Bailey, Radiat. Res. 79, 520-536, 1979; 80, 186-197, 1979). Detailed information on the fraction of cells of a certain biological age at a given chronological time is needed because of the variation in the radioresponse of the cells as a function of age.

On the possibility of obtaining non-diffused proximity functions from cloud-chamber data: I. Fourier deconvolution.

A mathematical procedure, using Fourier deconvolution, is described whereby diffusion-free proximity functions can be obtained from cloud-chamber data. Such non-diffused distributions can be used to obtain further microdosimetric and nanodosimetric quantities hitherto not available from experiments, thus making the cloud chamber an almost ideal nanodosimeter.

On the possibility of obtaining non-diffused proximity functions from cloud-chamber data: II. Maximum entropy and Bayesian methods.

Maximum entropy and Bayesian methods are applied to an inversion problem which consists of unfolding diffusion from proximity functions calculated from cloud-chamber data. The solution appears to be relatively insensitive to statistical errors in the data (an important feature) given the limited number of tracks normally available from cloud-chamber measurements. It is the first time, to our knowledge, that such methods are applied to microdosimetry.

Three-dimensional reconstruction of the x-ray emission in laser imploded targets.

To investigate the uniformity of compression of spherical targets irradiated with high-energy CO(2) lasers, an array of pinhole cameras has been set up to obtain 2-D views from four different directions. To reconstruct the 3-D source we have devised a computer code based on a maximum entropy algorithm. With synthetic input data the code gives acceptable reconstructions provided the source is smooth and has a simple shape. We present a set of serial slices through the reconstructed x-ray emission distribution in a glass microsphere imploded with the LASL two-beam CO(2) laser.