Target Size Variation in Microdosimetric Distributions and its Impact on the Linear-Quadratic Parameterization of Cell Survival

Abstract

The linear-quadratic (LQ) parameterization of survival fraction [SF( D)] inherently assumes that all cells in a population receive the same dose ( D), albeit the distribution of specific energy z over the individual cells f( z, D) can be very wide. From these microdosimetric distributions, which are target size dependent, we estimate the size of the cellular sensitive volume by analyzing its influence on the LQ parameterization of cell survival. A Monte Carlo track structure code was used to simulate detailed tracks from a Co source as well as proton and carbon ions of various energies. From these tracks, f( z, D) distributions were calculated for spherical targets with diameters ranging from 10 nm to 12 μm. A cell survival function based on f( z, D) was fitted to experimental LQ α values, revealing an intrinsic limitation that target size imposes on the usage of f( z, D) to describe the linear term of the LQ parameterization. The results indicate that such threshold volume arises naturally from the relationship between the particle's probability of no-hit and the probability of cell survival. Further analysis led to the proposal of a radiobiological property [Formula: see text], defined as the mean lineal energy corresponding to the target size that allows equivalence between the mean inactivation dose (MID) and the mean specific energy [Formula: see text]. The fact that [Formula: see text] is an increasing continuous function of target size within the range of biological targets of interest in radiobiology, ensures the uniqueness of [Formula: see text] for any radiation quality, thus, its potential usefulness in modeling. In conclusion, an accurate estimation of such threshold volumes may be useful for improving modeling of cell survival curves.

Deep learning-based tumor segmentation on digital images of histopathology slides for microdosimetry applications

“…17 As the microdosimetric spread directly influences the doseresponse and affects the treatment outcome, there exists a need for the consideration of nuclei/cell size distributions in dosimetry investigation and radiobiological modeling of tissue response. 18,19 To study the effect of varying size distributions of cells and nuclei, we have previously developed a comprehensive software package to build morphologically realistic three-dimensional cellular geometry models. 20 These models produced by the software are used as input data to MC based dose calculations for patient-specific dosimetry, including microdosimetry and theranostics.…”

“…17 As the microdosimetric spread directly influences the dose-response and affects the treatment outcome, there exists a need for the consideration of nuclei/cell size distributions in dosimetry investigation and radiobiological modeling of tissue response. 18,19 To study the effect of varying size distributions of cells and nuclei, we have previously developed a comprehensive software package that derives cell and nuclei size distributions from digital images of 2D histopathological slides to build morphologically realistic 3D cellular geometry models. 20 The histopathology images were contoured manually by a pathologist in tumor vs non-tumor regions.…”

Systematic microdosimetric data for protons of therapeutic energies calculated with Geant4-DNA

“…These elements include a linear relationship between parameter α of the linear-quadratic model of cell survival and the dose average lineal energy y D , and a formula for saturation correction. Recently, models have emerged that, while relying on microdosimetric concepts, advance different from the TDRA approaches (Vassiliev 2012(Vassiliev , 2017a and (Villegas et al 2018). These studies suggest that the frequency average lineal energy, y F , could be a useful alternative to y D .…”

“…We considered spherical SVs, from 2 to 1000 nm in diameter. We chose spheres, because some of the standard models, the TDRA in its original formulation (Kellerer and Rossi 1972) and the MKM (Kase et al 2006), as well as more recent models (Vassiliev 2012, 2017a, Villegas et al 2018, use spherical SVs. Our data extends the previously reported Geant4-DNA results for protons and complements the existing data calculated using other software.…”