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A new type of alpha-particle irradiator allows survival of each cell to be observed individually along with the size and shape of its nucleus and the positions of the hits it receives. This paper discusses methods of data analysis that can utilize these additional data. Using idealizations of the cell nucleus geometry (i.e., spheres, ellipsoids), the path length (l), energy deposited (e), and specific energy (z) has been determined on a cell-by-cell basis for 772 cells all subjected to the same fluence. Each cell is regarded as a Bernoulli trial with a different probability for success (colony formation). For the survival expectation, A exp(-z/z(o)), the values of A and z(o) are chosen to maximize the likelihood for the observed outcome. Similar results are presented using the alternate functional forms A exp(-e/e(o)) and A exp(-l/l(o)). With these parameter values, the goodness of fit is also evaluated using a chi-square method with variances given by the binary (Bernoulli) methods. A further purpose of the paper is to assess the validity of the microdosimetric computations that would have had to be made if these individual cell-by-cell experimental measurements were not available or were incomplete.

In cases where both the source and cell geometry are well known, track-etch dosimetry allows the potential for individual cell dosimetry. However, analysis of track-etch images is both tedious and time-consuming. We describe here several image processing tools that we are using in conjunction with a track-etch based irradiator. Briefly, cells grown on LR 115 (a track-etch material) are irradiated from below by a collimated, planar alpha-particle source. Prior to irradiation, images of the cells are obtained. A computer program reads each image and automatically determines the location of individual cells. Next, the algorithm automatically identifies the cellular and nuclear boundaries. Following irradiation, and after the cells have reached their biological endpoint (e.g., cell survival), the cell dish is etched and images are obtained of alpha-particle tracks. Using the characteristic background pattern in the LR 115, the etched images are spatially registered to the original images. These two sets of images are then superimposed to create a composite image of the cells and associated alpha-particle tracks. Incorporating this tool into our irradiation scheme will enable more efficient analysis of the large amounts of data that are essential in assessing biological endpoints.

Alpha-particle emitters are currently being evaluated for the treatment of metastatic disease. The dosimetry of alpha-particle emitters is a challenge, however, because the stochastic patterns of energy deposition within cellular targets must be taken into account. We propose a model for the tumor control probability of alpha-particle emitters which takes into account these stochastic effects. An expression for cell survival, which is a function of the microdosimetric single-event specific-energy distribution, is multiplied by the number of cells within the tumor cluster. Poisson statistics is used to model the probability of zero surviving cells within the cluster. Based on this analysis, a number of observations have been made: (1) The dose required to eradicate a tumor is nearly a linear function of the cell survival parameter z(0). (2) Cells with smaller nuclei will require more dose to achieve the same level of tumor control probability, relative to cells with larger nuclei, for an identical source-target configuration and cell sensitivity. (3) As the targeting of alpha-particle emitters becomes more specific, the dose required to achieve a given level of tumor control decreases. (4) Additional secondary effects include cell shape and the initial alpha-particle energy.

In a recent paper [J. Nucl. Med. 38, 1923–1929 (1997)], the authors presented a dosimetry system which combines the computational ease of the MIRD schema with additional information provided by microdosimetry for use with alpha-particle emitters. In addition to the absorbed dose (average specific energy) to the targets (cell nuclei), this system gives the spread (standard deviation) in values of this specific energy received by individual targets. It also gives the fraction of targets receiving zero (or any number of) hits. In this paper, input quantities are presented for alpha-particle energies and cell and nuclear sizes appropriate for the radionuclides being investigated. The quantities include S values for the usual determination of the absorbed dose along with the microdosimetric quantities, 〈z 1 〉 and 〈z 1 2 〉, the average and average square, respectively, of the single-hit specific energy. Using analytical procedures described previously [Med. Phys. 19, 1385–1393 (1992)], the single-hit distributions of specific energy are determined for the given alpha-particle energies, source locations, and target sizes. From these distributions, the values for the input quantities are calculated. Sources considered are (1) those located inside and on the surface of the target cell and an unbounded source in the medium external to the cell; (2) those distributed uniformly on either side of a plane boundary or on the surface of the plane with a spherical target at various distances from the plane; and (3) those located either inside or on the surface of a spherical boundary centered externally to the target. Examples show how the input quantities are used to provide the spread in specific-energy values and the probability of any number of hits for nuclei of cells exposed to these sources. Thus a complete micro-dosimetric analysis involving the calculation of multi-hit specific energy distributions is not necessary to provide this information. Such information may be useful in interpreting the biological response due to alpha-particle emitters.

Microdosimetry is the study of the stochastic variation of energy deposited within sub-cellular targets. As such, the size and shape of the critical target (i.e. cell nucleus) are essential when considering microdosimetric quantities. In this work, a microdosimetric analysis examines the expected cell survival as a function of the size and shape of the cell nucleus under conditions of irradiation by radionuclides emitting alpha particles. The results indicate that, in general, cell survival is relatively insensitive to changes in the shape of the cell nucleus when the volume is held constant. However, cell survival is a strong function of the variation in the size of the target. These results are useful when analysing the results of cell survival experiments for alpha particle emitters.

Analytic microdosimetry using Fourier transform techniques has been applied to internal alpha emitters. These techniques need revision and simplification for use with short‐lived radionuclides such as those which may be useful for radioimmunotherapy. Analytic methods may have advantages over Monte Carlo methods in some cases (e.g., where time is important). Applications to eight different source geometries show the usefulness of these techniques. Comparisons of some of the results to Monte Carlo calculations prove its accuracy. For a uniform source of 5.867‐MeV alphas spread throughout the volume outside a cell surface, the two methods agree well. Results are within 1% both for the average specific energy and for the number of hits. Analytic microdosimetry provides an alternate method to use for the critical evaluation of models that seek to predict the relation between alpha energy deposition and cell survival data. Similarly, it may be helpful to point the way toward the rational interpretation of general biological results for antibodies labeled with alpha emitters.

Analysis of cell survival after alpha-particle irradiation must account for the distribution in the amounts of energy deposited in each cell nucleus. Microdosimetric computations are usually used to determine these distributions. Irradiation with microbeams and other modern techniques has made these computations unnecessary for certain cell geometries. These techniques allow the survival of individual cells to be correlated with the amount of radiation delivered to individual cell nuclei. However, to maintain the individuality of data generated for each cell, new methods of analysis are required. In this study, we propose the use of binary methods. Each cell is regarded as a Bernoulli trial with a different probability for success (colony formation). Parameter values of the survival model are chosen to maximize the likelihood of the observed outcome. To evaluate this method, simulated data for 500, 5000 and 50,000 cells irradiated by alpha particles are analyzed along with the associated outcome for four different cell survival models. Each survival model has a different dependence on the radius of the cell nucleus. These results indicate that the model that was simulated has the highest likelihood value in all cases. However, the ability to distinguish between competing models is present only for a larger numbers of cells.

A computer-controlled, alpha-particle irradiator is described that allows for the measurement of the number and location of alpha-particle hits to individual cell nuclei, and subsequent scoring of cell survival. Cells are grown on a track-etch material (LR 115) and images are obtained of the cells prior to irradiation. The cells are then irradiated from below by a planar, collimated Am-241 source. The exposure time is varied so that the average number of hits to cell nuclei ranges from 0 to 3. After cell survival has been scored, images of the etched material are obtained and spatially registered to the original cell images. The etched images and cellular images are superimposed allowing for the determination of the number and position of hits to individual cell nuclei. This paper characterizes the irradiator including the energy and fluence of the incident alpha particles. Additionally, we describe the sources of uncertainty associated with this experiment, including the cell dish repositioning and cell migration during scanning and irradiation.

A method is described for obtaining S values between a tumor and its host organ for use with the MIRD formalism. It applies the point‐source specific absorbed fractions for an infinite water medium, tabulated by Berger, to a rectangular solid of arbitrary dimensions which contains a rectangular tumor of arbitrary dimensions. Contributions from pairs of source and target volume elements are summed for the S values between the tumor and itself, between the remaining healthy host organ and itself, and between the tumor and the remaining healthy host organ, with the reciprocity theorem assumed for the last. This method labeled MTUMOR, is interfaced with the widely used MIRDOSE program which incorporates the MIRD formalism. An example is calculated.

In evaluating the efficacy of α-particle emitters, a cell survival curve is often determined for a particular source-target configuration. Investigators often wish to use this information about survival for a different source-target configuration which might be more appropriate for a therapeutic application. Since the population cell survival parameter, D 0 , is a function of the source-target configuration, it is important to determine the individual cell survival parameter, Z 0 , which is more fundamental. Unlike D 0 , Z 0 does not depend upon the microdosimetric variations in the specific energy distribution resulting from changes in the source-target configuration. Instead it is determined by the cell sensitivity and the radiation quality. However, the calculation of Z 0 from the data on survival involves computing the microdosimetric specific energy distributions of the radiation. This paper describes an approximate but sufficiently accurate method for determining Z 0 from D 0 if the first and second moments of the single-hit specific energy distributions are known or can be estimated. Examples of applications are given. This may alleviate the need for multihit microdosimetric calculations.

This study examined the effect of internal exposure to α-particle radiation on subsequent fertility among women employed in the radium dial industry prior to 1930, when appreciable amounts of radium were often ingested through the practice of pointing the paint brush with the lips. The analysis was limited to women for whom a radium body burden measurement had been obtained and who were married prior to age 45 (n = 603). Internal radiation dose to the ovary was calculated based on initial intakes of radium-226 and radium-228, average ovarian mass, number and energy of α particles emitted, fraction of energy absorbed within the ovary, effective retention integrals and estimated photon irradiation. Time between marriage and pregnancy, number of pregnancies and number of live births served as surrogates for fertility. Radiation appeared to have no effect on fertility at estimated cumulative ovarian dose equivalents below 5 Sv; above this dose, however, statistically significant declines in both number of pre...

A previous analysis of non-stochastic dose (Jostes et al., Radiat. Res. 127, 211-219, 1991; Schwartz et al., Health Phys. 62, 458-461, 1992) based on data obtained during irradiations of C-18 cells in suspension by alpha particles emitted from two forms (chelated and ionic) of 212Bi was made using survival curves. No appreciable difference in slope (1/D0) was found between the two forms. Such non-stochastic analyses do not account for the large differences in specific energies deposited in the individual cell nuclei. This microdosimetric (stochastic) analysis aims to determine the survival sensitivity (1/z0) of the individual C-18 cells using the distribution of specific energies deposited in the individual cell nuclei. The resulting sensitivity is greater for the alpha particles emitted from the chelated 212Bi than from the ionic 212Bi. An attempt to account for this greater sensitivity in terms of greater LET of alpha particles passing through the cell nuclei from the chelated 212Bi is unsuccessful. Instead the greater sensitivity disappears if the microdosimetric analysis uses average values for the radii of the cell and of its nucleus rather than the values (from the peak in the cell size distribution) used by the non-stochastic dose analysis.

The use of a spherical tissue-equivalent proportional counter for measurements of the lineal energy (y) and derivations of the linear energy transfer (LET) for fast neutrons has the advantage of giving distributions of dose and dose equivalent as functions of either LET or y. A measurement next to the target shielding of the neutron therapy facility at the University of Chicago Hospitals and Clinics (UCHC) is described, and the data processing is outlined. The distributions are presented and compared to those from measurements in the neutron beam. The average quality factors are presented.

Microdosimetric measurements were made for the neutron therapy beams at the University of Chicago and at the Cleveland Clinic with the same geometry and phantom material using the same tissue-equivalent spherical proportional counter and standard techniques. The energy deposition spectra (dose distributions in lineal energy) are compared for these beams and for their scattered components (direct beam blocked). The model of dual radiation action (DRA) of Kellerer and Rossi is employed to interpret these data in terms of biological effectiveness over this limited range of radiation qualities. The site-diameter parameter of the DRA theory is determined for the Cleveland beam by setting the biological effectiveness (relative to /sup 60/Co gamma radiation) equal to the relative biological effectiveness value deduced from radiobiology experiments and clinical experience. The resulting value of this site-diameter parameter is then used to predict the biological effectiveness of the Chicago beam. The prediction agrees with the value deduced from radiobiology and clinical experience. The biological effectiveness of the scattered components of both beams is also estimated using the model.

Using a Carnegie Model "C" ionization chamber together with Geiger-Mueller tube coincidence circuits, the nature of the radiation which produces large bursts (greater than 200 particles) of cosmic rays under thick absorbers at 11,500-feet elevation has been investigated at Climax, Colorado. The percentage of this radiation which was accompanied by air showers was determined and found to be dependent upon the burst size. The absorption mean free paths for the burst-producing radiation (excluding bursts produced by $\ensuremath{\mu}$-mesons and by air showers) were measured in lead and iron and found to be 350\ifmmode\pm\else\textpm\fi{}40 g/${\mathrm{cm}}^{2}$ in lead and 240\ifmmode\pm\else\textpm\fi{}20 g/${\mathrm{cm}}^{2}$ in iron. The barometric effect on this radiation yielded an absorption mean free path of 65\ifmmode\pm\else\textpm\fi{}14 g/${\mathrm{cm}}^{2}$ in the atmosphere, and the zenith angle distribution was found to be that due to an absorption mean free path of 75\ifmmode\pm\else\textpm\fi{}14 g/${\mathrm{cm}}^{2}$. These results are shown to indicate that the radiation responsible for these large bursts consists largely of protons and $\ensuremath{\pi}$-mesons of energy greater than 60 Bev.