Microdosimetric Kinetic Model Research Articles

Biophysical calculation of cell survival probabilities using amorphous track structure models for heavy-ion irradiation

Both the microdosimetric kinetic model (MKM) and the local effect model (LEM) can be used to calculate the surviving fraction of cells irradiated by high-energy ion beams. In this study, amorphous track structure models instead of the stochastic energy deposition are used for the MKM calculation, and it is found that the MKM calculation is useful for predicting the survival curves of the mammalian cells in vitro for 3He-, 12C- and 20Ne-ion beams. The survival curves are also calculated by two different implementations of the LEM, which inherently used an amorphous track structure model. The results calculated in this manner show good agreement with the experimental results especially for the modified LEM. These results are compared to those calculated by the MKM. Comparison of the two models reveals that both models require three basic constituents: target geometry, photon survival curve and track structure, although the implementation of each model is significantly different. In the context of the amorphous track structure model, the difference between the MKM and LEM is primarily the result of different approaches calculating the biological effects of the extremely high local dose in the center of the ion track.

Mammalian Cell Killing by Ultrasoft X Rays and High-Energy Radiation: An Extension of the MK Model

An alternate formulation of the microdosimetric-kinetic (MK) model is presented that applies to irradiation of mammalian cells with ultrasoft X rays as well as high-energy radiations of variable linear energy transfer (LET). Survival and DNA double-strand break measurements for V79 cells from the literature are examined to illustrate application of the model. It is demonstrated that the linear component of the linear-quadratic survival relationship (alpha) is enhanced because repairable potentially lethal lesions formed from a single ultrasoft X-ray energy deposition event, when closer on average than for a single high-energy radiation event, are more likely to combine to form a lethal lesion. The quadratic component (beta) of the linear-quadratic survival relationship is increased because the potentially lethal lesions formed by ultrasoft X rays are created with greater efficiency than those of high-energy radiation. In addition, potentially lethal lesions from very low-energy carbon K-shell X rays may be enriched in structural forms that favor combination to form lethal lesions instead of repair. These features account for the increased effectiveness of killing of V79 cells by ultrasoft X rays compared to cobalt-60 gamma radiation. The importance of pairwise combination of potentially lethal lesions to form exchange chromosome aberrations that become lethal lesions is discussed. The extended MK model explains and reconciles differences between the MK model and the theory of dual radiation action on the one hand, and on the other, the view that variation in the RBE with radiation quality is explained by differences in energy deposition in nanometer- rather than micrometer-size volumes.

The influence of concentration of DNA on the radiosensitivity of mammalian cells

To develop relations that explicitly show the dependence of the linear-quadratic survival parameters alpha and beta on the nuclear volume, average DNA concentration, and degree to which the chromatin is condensed in zones of the nucleus. The microdosimetric-kinetic model of mammalian cell killing is used. The relations indicate an increased tendency for lethal lesions to form by pairwise combination of potentially lethal lesions in regions of relatively greater local DNA concentration. In particular, the value of beta is proportional to the average nuclear concentration of DNA and to a parameter that reflects the condensation of DNA into a relatively concentrated phase, such as occurs in mitotic chromosomes and heterochromatin. These relations indicate local DNA concentration in the nucleus is a significant determinant of three magnitude of beta. Because alpha is composed of a term that is proportional to beta, it is also affected by DNA concentration, generally to equal or less degree. It may be possible to establish a correlation between nuclear size and morphology, as determined from microscope slides prepared from biopsy specimens, with radiation sensitivity and the alpha/beta ratio that could be useful in radiation treatment planning.

A microdosimetric-kinetic model for the effect of non-Poisson distribution of lethal lesions on the variation of RBE with LET.

The microdosimetric-kinetic (MK) model for cell killing by ionizing radiation is summarized. An equation based on the MK model is presented which gives the dependence of the relative biological effectiveness in the limit of zero dose (RBE1) on the linear energy transfer (LET). The relationship coincides with the linear relationship of RBE1 and LET observed for low LET, which is characteristic of a Poisson distribution of lethal lesions among the irradiated cells. It incorporates the effect of deviation from the Poisson distribution at higher LET. This causes RBE1 to be less than indicated by extrapolation of the linear relationship to higher LET, and to pass through a maximum in the range of LET of 50 to 200 keV per micrometer. The relationship is compared with several experimental studies from the literature. It is shown to approximately fit their results with a reasonable choice for the value of a cross-sectional area related to the morphology and ultrastructure of the cell nucleus. The model and the experiments examined indicate that the more sensitive cells are to radiation at low LET, the lower will be the maximum in RBE they attain as LET increases. An equation that portrays the ratio of the sensitivity of a pair of cell types as a function of LET is presented. Implications for radiotherapy with high-LET radiation are discussed.

A Microdosimetric-Kinetic Model for the Sensitization of V79 Cells to Radiation by Incorporation of Bromodeoxyuridine

Hawkins, R. B. A Microdosimetric-Kinetic Model for the Sensitization of V79 Cells to Radiation by Incorporation of Bromodeoxyuridine. Radiat. Res. 155, 698-702 (2001). The sensitization of G(1)-phase V79 cells to killing by ionizing radiation through incorporation of bromodeoxyuridine (BrdU) in their DNA has been reported to occur exclusively through an increase in the value of the quadratic parameter of the linear-quadratic survival relationship (beta) with no change in the linear parameter (alpha). The consequence of this, as understood through the microdosimetric-kinetic model of cell survival, is discussed. It is shown that the invariance of alpha implies that sensitization is due solely to a decrease in the rate of repair of the initial (potentially lethal) lesions in DNA containing BrdU. Further, for alpha to be unchanged, the average size of the compartments into which the nucleus is partitioned (domains), as postulated in the microdosimetric-kinetic model, must vary in proportion to the reciprocal of the square root of the rate constant for repair of the DNA lesions. This implies that the domain is not a structural subunit of the nucleus. It is a surrogate representation of the consequence of lesions in DNA being restricted to a region in the vicinity of the location in the nucleus at which they are created. A lesion is confined because the distance it can diffuse by random flight to react with another lesion to form a lethal lesion is restricted because a lesion's lifetime is limited by the repair process.

A microdosimetric-kinetic theory of the dependence of the RBE for cell death on LET.

Experiments with cultured mammalian cells exposed to ionizing radiation of varying LET are examined in the context of a microdosimetric-kinetic (MK) model of radiation induced mammalian. cell killing similar to the site model of the theory of dual radiation action. The experimentally measured RBE, in the limit of zero dose, increases linearly with LET for LET less than a value that lies in the range of about 40-90 keV per micron. It is shown that the tendency of the RBE to increase linearly with LET can be explained as a result of the random variation of specific energy among microscopic sized domains (sites), into which the nucleus may be partitioned, and the effect of this variation on the formation of lethal lesions by pairwise combination of repairable primary lesions in DNA. the microscopic subunits corresponding to a site have diameter in the range of 0.56-0.75 microns. The linearity of RBE with increasing LET implies that value of the quadratic parameter of the linear-quadratic survival relation (beta) is constant, at least for LET low enough to be in the linear range, and this in turn implies the production of primary DNA lesion, likely double strand breaks, does not increase with LET. the experiments, interpreted with MK model, also imply that the repairability and potential for lethality of the primary DNA lesion does not change with variation of LET within the linear range. The failure of RBE to maintain its linear increase for higher values of LET, and the resulting RBE maximum at about 100 keV per micron, are likely primarily due to the departure of the distribution of lethal lesions among cells from the Poisson distribution. Some implications concerning the use of radiation to treat cancer are noted.

A microdosimetric-kinetic model of cell death from exposure to ionizing radiation of any LET, with experimental and clinical applications.

A model of mammalian cell death and survival following exposure to ionizing radiation that combines a kinetic description of repair and injury processes with a microdosimetric description of radiation energy deposition is presented. With reduction of one of the defining kinetic equations from quadratic to linear form, relations are obtained that describe the results of commonly performed variations of the cell survival experiment. These include single-dose survival of linear-quadratic form, survival after split-dose treatment and after post-irradiation change ill culture conditions and survival after exposure to continuously administered irradiation at low constant dose-rate. The effect of the inhomogeneous deposition of radiation energy inherent in exposure to radiation of significantly non-zero LET is included in these relations which apply to radiation of any LET. The values of the kinetic rate and time constants for repair and the processes that lead to cell death postulated in the model, which compose the alpha and beta parameters of the linear-quadratic survival relation, are estimated from cell survival experiments and DNA double-strand break measurements from the literature. A relation for estimating the daily fractional dose equivalent to continuous irradiation as employed in low dose-rate brachytherapy cancer treatment is presented.