SUPRALINEARITY AND LET DISCRIMINATION IN RADIATION MEASUREMENTS

According to track theory, detectors whose response to gamma rays is supralinear will inherently discriminate against low LET in favour of high LET radiations, especially at low dose, while detectors whose response is linear or exponential exhibit the reverse discrimination. The detailed characteristics of these discriminations can be calculated once the radiosensitivity parameters of the detector are known. If both one hit (exponential) and c-hit (supralinear) detectors are exposed to the same radiation field, the complimentary discriminations can be used to sort out the low and high LET components of the radiation field. An even more interesting discrimination may be possible. For if the detector parameters are appropriately chosen, they may be able to reflect the discriminations made by biological tissue, for inactivation in the gamma kill mode (the low LET response) and in the ion kill mode (the high LET response). With nuclear emulsions it has been possible to choose emulsions and develop them so as to obtain characteristically different response. Some emulsions can be altered from 1-hit to 2-hit detectors by varying the composition of the developer and the developing time. To achieve a detector whose response parallels biological cells we have sought a 2-hit response to X-rays of such a sensitivity that single electrons do not make visible tracks, while single particles do. With Ilford K-1 emulsion we have achieved clean 2-hit response at such sensitivity that a 5.5 MeV alpha particle makes 7–8 grains developable. At slightly higher sensitivity the alpha particle track consists of 11–13 grains, but there is a small component of 1-hit response, similar to that found in biological cells whose survival curve displays an initial negative slope after gamma irradiation. Using computer simulations, we have estimated the radiosensitivity parameters of these emulsions - developer combinations, have simulated the predicted track appearance of other particles, and have calculated “survival curves” and “RBE's” of these materials after irradiation with beams of ions of different composition. Detectors have different discriminating properties for high and low LET radiation, depending on the values of their radiosensitivity parameters Eo and C. These are (1) the dose of gamma rays at which there is an average of 1-hit per sensitive element and (2) the hitedness, nominally the number of electrons which must pass through the sensitive target in order to activate it. When absorbed dose is the basis of comparison, as in radiobiology or in other integrating detectors, the 1-hit detector must always yield a higher response to randomly deposited than to concentrated energy depositions. Thus the 1-hit detector always discriminates against high LET in favour of low LET radiations. Its response is more nearly uniform to particles of all LET for the highest values of Eo, for then, even close to the path of a heavy ion, there is an insufficient local dose to saturate sensitive element response. If the detecting elements are small molecules where Eo is often quite high the response to gamma rays and high LET radiations, say neutrons, is most nearly uniform. These considerations have stimulated studies of the response of alanine (measured by esr) to X-rays, neutrons, and helium ions, made with F. Bermann, with results consistent with these perspectives. The response of 1-hit detectors to X-rays is a saturating exponential, linear at low dose and sublinear at high dose. With such detectors the only discrimination that can be achieved is by variation of Eo. We now know that the variation of Eo in 1-hit nuclear emulsions ranges over a factor approaching 1080. When translated into the structure of particle tracks (and ignoring problems of background, fading, and the kinematic limitation on delta ray energy) track segments of identical appearance can be produced in different emulsions, (Zeff/B)2 for these particles differs by a factor approaching 1000, as between K-5 and K-1 emulsions, differently developed. In the grain count regime, measurements of grain count can be made with reasonable comfort over a range of factor 10, say, from 15 to 150 grains/100 microns. This means that in a single emulsion only a factor of 10 in (Z/B)2 can be accommodated by this technique, but that the useable range of this parameter over which grain count measurements can be made can be extended by several hundred times, by suitable choice of emulsion-development regimes, designed for the particular experimental problems. The situation is quite different from many hit detectors. Here the transition from dispersed grains to a solid track takes place in a narrower interval of (Z/B)2, for the grain density varies nominally as (Z2/B2)c where c is the hittedness. Thus if a sharp discrimination is desired, but with a narrow window, one can go to c-hit emulsions. Our efforts in these researches have been directed toward the production of 2-hit response at the lowest possible value of Eo. We ask the question as to what is the transition region such that an emulsion passes from a 2-hit to a 1-hit detector. In part this depends on the homogeneity of grain size distribution, and on grain size itself. We have worked with Ilford K-1 emulsion using blackness-exposure curves after X-rays to determine the hittedness, and alpha particle tracks, in conjunction with track theory and hittedness to determine Eo. In this emulsion different developments produce (A) 1-hit detection with Eo=1.2 × 107 erg/cm3, (B) a supralinear response fitted by no obvious model, (C) a supralinear response well fitted by the radiobiological alpha-beta model, and (D) a 2-hit response with Eo=1.7 × 107 erg/cm3. Tracks of alpha particles in these emulsions coded by the letters A, B, C, and D are shown in Fig. 1. In Figs. 2 and 3 we show computer simulations of sections of tracks of Z=1, 2, 3, 5, and 10 ions in 1- and 2-hit emulsions for which Eo=1.5 × 107, erg/cm3, for comparison with the alpha particle tracks. These computer generated tracks are shown for particles coming from the right and stopping at left. Shown are 100 micron sections from 900 – 1000 microns and from 400 – 500 microns of residual range, and that left the stopping 200 microns of the track. There is a large difference between the response of a 1-hit and 2-hit detector in the rate of increase of grain density as a function of range. For comparison we show in Figs. 4 and 5 for an emulsion 10 times more sensitive, for Which Eo=1.5 × 106 erg/cm3. To compare the response of emulsion detectors to radiobiology, it is useful to display calculated curves of the logarithm of the probability K for killing cells or for making grains developable as a function of the fluence of beam of different particles. In Fig. 6 we display as top and bottom panels the calculated curves for 2-hit emulsion of different sensitivity, as in Figs. 3 and 5, and in the central, panel calculated curve for T-1 human kidney cells. The bombardments are for (Z, B)=(18, 0.12), (7, 0.12), (2, 0.12), (2, 0.25), (2, 0.50) and (1, 0.99), which are characteristic of a range from high to low LET, used in radiobiology. There is a transition in the shape of these curves, from supralinear at right, low LET, to linear at left, at high LET. At intermediate values of LET, the curves are linear at low dose and supralinear at high dose. These changes are associated with the increase of the importance of the ion kill mode of inactivation with an increase in LET. We must remember that these emulsions curves are calculated rather than measured and are presently part of an experiment design for subsequent test. If we are to have an emulsion useful in dosimetry, which has the same sort of discrimination against low LET radiations that we find in mammalian cells, it appears that we must have an emulsion of somewhat lower Eo than we have presently achieved, perhaps by factor 3. From Figs. 3 and 5 such an emulsion should give grains at the very end of a proton track as well as a stronger signal from an alpha particle than we have presently obtained. This should give a response to neutron secondaries rather like the response of biological cells while discriminating against gamma rays. The goal seems achievable. We can imagine, at least, that 2 sheets of K-1 emulsion exposed to the same neutron field can be differently developed so that one of these sheets is a 1-hit detector which discriminates in favour of gamma rays, while the other is a 2-hit detector which discriminates in favour of neutrons. We would be able to measure directly the gamma ray component and the neutron component of a neutron field by measuring emulsion blackness alone. Additionally the discriminatinns available by varying Eo and c in the measurement of particle tracks can be expected to open new applications of emulsions in the field of heavy ion research. No recipes are available for the best design of such detectors. We know nothing about fading or about the control that must be exercised to achieve consistent results. We know only that a new class of emulsion response is possible.