Thomas G. Stinchcomb

Analysis of survival of C-18 cells after irradiation in suspension with chelated and ionic bismuth-212 using microdosimetry.

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 average number of alpha-particle hits to the cell nucleus required to eradicate a tumour cell population

Alpha-particle emitters are currently being considered for the treatment of micrometastatic disease. Based on in vitro studies, it has been speculated that only a few alpha-particle hits to the cell nucleus are considered lethal. However, such estimates do not consider the stochastic variations in the number of alpha-particle hits, energy deposited, or in the cell survival process itself. Using a tumour control probability (TCP) model for alpha-particle emitters, we derive an estimate of the average number of hits to the cell nucleus required to provide a high probability of eradicating a tumour cell population. In simulation studies, our results demonstrate that the average number of hits required to achieve a 90% TCP for 10(4) clonogenic cells ranges from 18 to 108. Those cells that have large cell nuclei, high radiosensitivities and alpha-particle emissions occurring primarily in the nuclei tended to require more hits. As the clinical implementation of alpha-particle emitters is considered, this type of analysis may be useful in interpreting clinical results and in designing treatment strategies to achieve a favourable therapeutic outcome.

The use of microdosimetric moments in evaluating cell survival for therapeutic alpha-particle emitters

In evaluating the efficacy of alpha-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, D0, is a function of the source-target configuration, it is important to determine the individual cell survival parameter, z0, which is more fundamental. Unlike D0, z0 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 z0 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 z0 from D0 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.

Values of “S,” and for dosimetry using alpha‐particle emitters

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.

Image processing tools for alpha-particle track-etch dosimetry.

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.

Characterization of an alpha-particle irradiator for individual cell dosimetry measurements.

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.

Tumor Control Probability Model for Alpha-Particle-Emitting Radionuclides

Abstract Roeske, J.C. and Stinchcomb, T.G. Tumor Control Probability Model for Alpha-Particle-Emitting Radionuclides. Alpha-particle emitters are currently being evaluated for the treatment of metastatic disease. The dosimetry of α-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 α-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 z0. (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 α-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 α-particle energy.

Relationships between Cell Survival and Specific Energy Spectra for Therapeutic Alpha-Particle Emitters

Cell survival studies are a means of quantifying the biological effects of radiation. However, for alpha-particle sources, the dose-response relationship is complicated by the dominance of microdosimetric effects. In this work, we relate observed cell survival to the microdosimetric energy deposition spectra. The chord length distributions through spherical cell nuclei for sources distributed inside of, on the surface of and outside of the critical target are used as approximate analytical representations of the single-event specific energy spectra. Mathematical relationships are derived which relate cell survival to the Laplace transform of the single-event specific energy spectrum. The result is an analytical relationship between D0 (the observed slope of the cell survival curve) and Z0 (the specific energy required to reduce the survival probability of a single cell to 1/e). These studies indicate that for small energy deposition events, Z0 is approximately equal to D0. However, as the maximum energy deposited by a single event is increased, there are marked deviations between Z0 and D0. These differences between Z0 and D0 are also related to the shape of the single-event spectrum. This technique provides a powerful tool for relating observed cell survival to microdosimetric quantities for therapeutic alpha-particle emitters.

Correlation of microdosimetric measurements with relative biological effectiveness from clinical experience for two neutron therapy beams

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 60Co 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.

Binary methods for the microdosimetric analysis of cell survival data from alpha-particle irradiation.

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.