Investigating energy deposition within cell populations using Monte Carlo simulations

A comparative study on the dose-effect of low-dose radiation based on microdosimetric analysis and single-cell sequencing technology

The biological mechanisms triggered by low-dose exposure still need to be explored in depth. In this study, the potential mechanisms of low-dose radiation when irradiating the BEAS-2B cell lines with a Cs-137 gamma-ray source were investigated through simulations and experiments. Monolayer cell population models were constructed for simulating and analyzing distributions of nucleus-specific energy within cell populations combined with the Monte Carlo method and microdosimetric analysis. Furthermore, the 10 × Genomics single-cell sequencing technology was employed to capture the heterogeneity of individual cell responses to low-dose radiation in the same irradiated sample. The numerical uncertainties can be found both in the specific energy distribution in microdosimetry and in differential gene expressions in radiation cytogenetics. Subsequently, the distribution of nucleus-specific energy was compared with the distribution of differential gene expressions to guide the selection of differential genes bioinformatics analysis. Dose inhomogeneity is pronounced at low doses, where an increase in dose corresponds to a decrease in the dispersion of cellular-specific energy distribution. Multiple screening of differential genes by microdosimetric features and statistical analysis indicate a number of potential pathways induced by low-dose exposure. It also provides a novel perspective on the selection of sensitive biomarkers that respond to low-dose radiation.

Multiscale Monte Carlo simulations for dosimetry in x-ray breast imaging: Part II - Microscopic scales

BACKGROUND

Although the benefits of breast screening and early diagnosis are known for reducing breast cancer mortality rates, the effects and risks of low radiation doses to the cells in the breast are still ongoing topics of study.

PURPOSE

To study specific energy distributions (f ( z , D g ) $f(z,D_{g})$ ) in cytoplasm and nuclei of cells corresponding to glandular tissue for different x-ray breast imaging modalities.

METHODS

A cubic lattice (500 μm length side) containing 4064 spherical cells was irradiated with photons loaded from phase space files with varying glandular voxel doses (D g $D_{g}$ ). Specific energy distributions were scored for nucleus and cytoplasm compartments using the PENELOPE (v. 2018) + penEasy (v. 2020) Monte Carlo (MC) code. The phase space files, generated in part I of this work, were obtained from MC simulations in a voxelized anthropomorphic phantom corresponding to glandular voxels for different breast imaging modalities, including digital mammography (DM), digital breast tomosynthesis (DBT), contrast enhanced digital mammography (CEDM) and breast CT (BCT).

RESULTS

In general, the average specific energy in nuclei is higher than the respective glandular dose scored in the same region, by up to 10%. The specific energy distributions for nucleus and cytoplasm are directly related to the magnitude of the glandular dose in the voxel (D g $D_{g}$ ), with little dependence on the spatial location. For similarD g $D_{g}$ values,f ( z , D g ) $f(z,D_{g})$ for nuclei is different between DM/DBT and CEDM/BCT, indicating that distinct x-ray spectra play significant roles inf ( z , D g ) $f(z,D_{g})$ . In addition, this behavior is also present when the specific energy distribution (F g ( z ) $F_{g}(z)$ ) is considered taking into account the GDD in the breast.

CONCLUSIONS

Microdosimetry studies are complementary to the traditional macroscopic breast dosimetry based on the mean glandular dose (MGD). For the same MGD, the specific energy distribution in glandular tissue varies between breast imaging modalities, indicating that this effect could be considered for studying the risks of exposing the breast to ionizing radiation.

Haralick texture analysis for microdosimetry: characterization of Monte Carlo generated 3D specific energy distributions

Objective.Explore the application of Haralick textural analysis to 3D distributions of specific energy (energy imparted per unit mass) scored in cell-scale targets considering varying mean specific energy (absorbed dose), target volume, and incident spectrum.Approach.Monte Carlo simulations are used to generate specific energy distributions in cell-scale water voxels ((1μm)3-(15μm)3) irradiated by photon sources (mean energies: 0.02-2 MeV) to varying mean specific energies (10-400 mGy). Five Haralick features (homogeneity, contrast, entropy, correlation, local homogeneity) are calculated using an implementation of Haralick analysis designed to reduce sensitivity to grey level quantization and are interpreted using fundamental radiation physics.Main results.Haralick measures quantify differences in 3D specific energy distributions observed with varying voxel volume, absorbed dose magnitude, and source spectrum. For example, specific energy distributions in small (1-3μm) voxels with low magnitudes of absorbed dose (10 mGy) have relatively high measures of homogeneity and local homogeneity and relatively low measures of contrast and entropy (all relative to measures for larger voxels), reflecting the many voxels with zero specific energy in an otherwise sporadic distribution. With increasing target size, energy is shared across more target voxels, and trends in Haralick measures, such as decreasing homogeneity and increasing contrast and entropy, reflect characteristics of each 3D specific energy distribution. Specific energy distributions for sources of differing mean energy are characterized by Haralick measures, e.g. contrast generally decreases with increasing source energy, correlation and homogeneity are often (not always) higher for higher energy sources.Significance.Haralick texture analysis successfully quantifies spatial trends in 3D specific energy distributions characteristic of radiation source, target size, and absorbed dose magnitude, thus offering new avenues to quantify microdosimetric data beyond first order histogram features. Promising future directions include investigations of multiscale tissue models, targeted radiation therapy techniques, and biological response to radiation.

Microdosimetric assessment about proton spread-out Bragg peak at different depths based on the normal human mesh-type cell population model

Objective.In clinical proton therapy, the spread-out Bragg peak (SOBP) is commonly used to fit the target shape. Dose depositions at microscopic sites vary, even with a consistent absorbed dose (D) in SOBP. In the present study, monolayer mesh-type cell population models were developed for microdosimetric assessment at different SOBP depths.Approach.Normal human bronchial epithelial (BEAS-2B) and hepatocytes (L-O2) mesh-type cell models were constructed based on fluorescence tomography images of normal human cells. Particle transport simulation in cell populations was performed coupled with Monte Carlo software PHITS. The relationship between microdosimetry and macrodosimetry of SOBP at different depths was described by analyzing the microdosimetric indicators such as specific energyz,specific energy distributionfz,D,and relative standard deviationσz/z¯within cells. Additionally, the microdosimetric distributions characteristics and their contributing factors were also discussed.Main results.The microscopic dose distribution is strongly influenced by cellular size, shape, and material. The mean specific energyz¯of nucleus and cytoplasm in the cell population is greater than the overall absorbed dose of the cell population model (Dp), with a maximumz¯/Dpof 1.1. The cellular dose distribution is different between the BEAS-2B mesh-type model and its concentric ellipsoid geometry-type model, which difference inz¯is about 10.3% for the nucleus and about 7.5% for the cytoplasm with the SOBP depth of 15 cm. WhenD= 2 Gy, the maximumzof L-O2 nucleus reaches 2.8 Gy andσz/z¯is 5.1% at the mid-depth SOBP (16-18 cm); while the maximumzof the BEAS-2B nucleus reaches 2.2 Gy with only 2.7% ofσz/z¯.Significance.The significant variation of microdosimetric distributions of SOBP different depths indicates the necessity to use mesh-type cell population models, which have the potential to be compared with biological results and build the bio-physical model.

Multiple Mesh-type Real Human Cell Models for Dosimetric Application Coupled with Monte Carlo Simulations

The mesh-type models are superior to voxel models in cellular dose assessment coupled with Monte Carlo codes. The aim of this study was to expand the micron-scale mesh-type models based on the fluorescence tomography of real human cells, and to investigate the feasibility of these models in the application of various irradiation scenarios and Monte Carlo codes. Six different human cell lines, including pulmonary epithelial BEAS-2B, embryonic kidney 293T, hepatocyte L-02, B-lymphoblastoid HMy2.CIR, Gastric mucosal GES-1, and intestine epithelial FHs74Int, were adopted for single mesh-type models reconstruction and optimization based on laser confocal tomography images. Mesh-type models were transformed into the format of polygon mesh and tetrahedral mesh for the GATE and PHITS Monte Carlo codes, respectively. The effect of model reduction was analyzed by dose assessment and geometry consideration. The cytoplasm and nucleus doses were obtained by designating monoenergetic electrons and protons as external irradiation, and S values with different "target-source" combinations were calculated by assigning radioisotopes as internal exposure. Four kinds of Monte Carlo codes were employed, i.e., GATE with "Livermore," "Standard" and "Standard and Geant4-DNA mixed" models for electrons and protons, as well as PHITS with "EGS" mode for electrons and radioisotopes. Multiple mesh-type real human cellular models can be applied to Monte Carlo codes directly without voxelization when combined with certain necessary surface reduction. Relative deviations between different cell types were observed among various irradiation scenarios. The relative deviation of nucleus S value reaches up to 85.65% between L-02 and GES-1 cells by 3H for the "nucleus-nucleus" combination, while that of 293T and FHs74Int nucleus dose for external beams at a 5.12 cm depth of water is 106.99%. Nucleus with smaller volume is far more affected by physical codes. There is a considerable deviation for dose within BEAS-2B at the nanoscale. The multiple mesh-type real cell models were more versatile than voxel models and mathematical models. The present study provided several models which can easily be extended to other cell types and irradiation scenarios for RBE estimations and biological effect predictions, including radiation biological experiments, radiotherapy and radiation protection.

Haralick texture feature analysis for characterization of specific energy and absorbed dose distributions across cellular to patient length scales

Objective.To investigate an approach for quantitative characterization of the spatial distribution of dosimetric data by introducing Haralick texture feature analysis in this context.Approach.Monte Carlo simulations are used to generate 3D arrays of dosimetric data for 2 scenarios: (1) cell-scale microdosimetry: specific energy (energy imparted per unit mass) in cell-scale targets irradiated by photon spectra (¹²⁵I,¹⁹²Ir, 6 MV); (2) tumour-scale dosimetry: absorbed dose in voxels for idealized models of¹²⁵I permanent implant prostate brachytherapy, considering 'TG186' (realistic tissues including 0% to 5% intraprostatic calcifications; interseed attenuation) and 'TG43' (water model, no interseed attenuation) conditions. Five prominent Haralick features (homogeneity, contrast, correlation, local homogeneity, entropy) are computed and trends are interpreted using fundamental radiation physics.Main results.In the cell-scale scenario, the Haralick measures quantify differences in 3D specific energy distributions due to source spectra. For example, contrast and entropy are highest for¹²⁵I reflecting the large variations in specific energy in adjacent voxels (photoelectric interactions; relatively short range of electrons), while 6 MV has the highest homogeneity with smaller variations in specific energy between voxels (Compton scattering dominates; longer range of electrons). For the tumour-scale scenario, the Haralick measures quantify differences due to TG186/TG43 simulation conditions and the presence of calcifications. For example, as calcifications increase from 0% to 5%, contrast increases while correlation decreases, reflecting the large differences in absorbed dose in adjacent voxels (higher absorbed dose in voxels with calcification due to photoelectric interactions).Significance.Haralick texture analysis provides a quantitative method for the characterization of 3D dosimetric distributions across cellular to tumour length scales, with promising future applications including analyses of multiscale tissue models, patient-specific data, and comparison of treatment approaches.

Patient-specific microdosimetry: a proof of concept

Microscopic energy deposition distributions from ionizing radiation are used to predict the biological effects of an irradiation and vary depending on biological target size. Ionizing radiation is thought to kill cells or inhibit cell cycling mainly by damaging DNA in the cell nucleus. The size of cells and nuclei depends on tissue type, cell cycle, and malignancy, all of which vary between patients. The aim of this study was to develop methods to perform patient-specific microdosimetry, that being, determining microdosimetric quantities in volumes that correspond to the sizes of cells and nuclei observed in a patient's tissue. A histopathological sample extracted from a stage I lung adenocarcinoma patient was analyzed. A pouring simulation was used to generate a three-dimensional tissue model from cell and nucleus size information determined from the histopathological sample. Microdosimetric distributions including f(y) and d(y) were determined for Co-60,Ir-192,Yb-169 and I-125 in a patient-specific model containing a distribution of cell and nucleus sizes. Fixed radius models and a summation method (where f(y) from many fixed radii models are summed) were compared to the full patient-specific model to evaluate their suitability for fast determination of patient-specific microdosimetric parameters. Fixed radius models do not provide a close approximation of the full patient-specific model y ̅_f or y ̅_d for the lower energy sources investigated, Yb-169 and I-125. The higher energy sources investigated, Co-60 and Ir-192 are less sensitive to target size variation than Yb-169 and I-125. A summation method yields the most accurate approximation of the full model d(y) for all radioisotopes investigated. A summation method allows for the computation of patient-specific microdosimetric distributions with the computing power of a personal computer. With appropriate biological inputs the microdosimetric distributions computed using these methods can yield a patient-specific relative biological effectiveness as part of a multiscale treatment planning approach.

Microdosimetry modeling with auger emitters in generalized cell geometry

A microdosimetry model was developed for the prediction of cell viability for irregular non-spherical cells that were irradiated by low energy, short range auger electrons. Measured cell survival rates for LNCaP prostate cancer were compared to the computational results for the radioisotopes¹⁷⁷Lu and¹⁶¹Tb (conjugated to PSMA). The cell geometries used for the computations were derived directly from the cell culture images. A general computational approach was developed to handle arbitrary cell geometries, based on distance probability distribution functions (PDFs) derived from basic image processing. The radiation calculations were done per coarse grained PDF bin to reduce computation time, rather than on a pixel/voxel basis. The radiation dose point kernels over the full electron spectrum were derived using Monte Carlo simulations for energies below 50 eV to account for the propagation of auger electrons over length scales at and below a cellular radius. The relative importance of short range auger electrons were evaluated between the two nuclide types. The microdosimetry results were consistent with the cell viability measurements, and it was found that¹⁶¹Tb was more efficient than¹⁷⁷Lu primarily due to the short range auger electrons. We foresee that imaging based microdosimetry can be used to evaluate the relative therapeutic effect between various nuclide candidates.

Development of patient-specific 3D models from histopathological samples for applications in radiation therapy

The biological effects of ionizing radiation depend on the tissue, tumor type, radiation quality, and patient-specific factors. Inter-patient variation in cell/nucleus size may influence patient-specific dose response. However, this variability in dose response is not well investigated due to lack of available cell/nucleus size data. The aim of this study was to develop methods to derive cell/nucleus size distributions from digital images of 2D histopathological samples and use them to build digital 3D models for use in cellular dosimetry. Nineteen of sixty hematoxylin and eosin stained lung adenocarcinoma samples investigated passed exclusion criterion to be analyzed in the study. A difference of gaussians blob detection algorithm was used to identify nucleus centers and quantify cell spacing. Hematoxylin content was measured to determine nucleus radius. Pouring simulations were conducted to generate one-hundred 3D models containing volumes of equivalent cell spacing and nuclei radius to those in histopathological samples. The nuclei radius distributions of non-tumoral and cancerous regions appearing in the same slide were significantly different (p < 0.01) in all samples analyzed. The median nuclear-cytoplasmic ratio was 0.36 for non-tumoral cells and 0.50 for cancerous cells. The average cellular and nucleus packing densities in the 3D models generated were 65.9% (SD: 1.5%) and 13.3% (SD: 0.3%) respectively. Software to determine cell spacing and nuclei radius from histopathological samples was developed. 3D digital tissue models containing volumes with equivalent cell spacing, nucleus radius, and packing density to cancerous tissues were generated.

Technical Note: Taking EGSnrc to new lows: Development of egs++ lattice geometry and testing with microscopic geometries

PURPOSE

This work introduces a new lattice geometry library, egs_lattice, into the EGSnrc Monte Carlo code, which can be used for both modeling very large (previously unfeasible) quantities of geometries (e.g., cells or gold nanoparticles (GNPs)) and establishing recursive boundary conditions. The reliability of egs_lattice, as well as EGSnrc in general, is cross-validated and tested at short length scales and low energies.

METHODS

New Bravais, cubic, and hexagonal lattice geometries are defined in egs_lattice and their transport algorithms are described. Simulations of cells and GNP-containing cavities are implemented to compare to independent, published Geant4-DNA and PENELOPE results. Recursive boundary conditions, implemented through a cubic lattice, are used to perform electron Fano cavity tests. The Fano test is performed on three different-sized cells containing GNPs in the region around the nucleus for three source energies.

RESULTS

Lattices are successfully implemented in EGSnrc, and are used for validation. EGSnrc calculated the dose to cell cytoplasm and nucleus when irradiated by an internal electron source with a median difference of 0.6% compared to published Geant4-DNA results. EGSnrc calculated the ratio of dose to a microscopic cavity containing GNPs over dose to a cavity containing a homogeneous mixture of gold, and results generally agree (within 1%) with published PENELOPE results. The electron Fano cavity test is passed for all energies and cells considered, with sub-0.1% discrepancies between EGSnrc-calculated and expected values. Additionally, the recursive boundary conditions used for the Fano test provided a factor of over a million increase in efficiency in some cases.

CONCLUSIONS

The egs_lattice geometry library, currently available as a pull request on the EGSnrc GitHub "develop" branch, is now freely accessible as open-source code. Lattice geometry implementations cross-validated with independent simulations in other MC codes and verified with the electron Fano cavity test demonstrate not only the reliability of egs_lattice, but also, by extension, EGSnrc's ability to simulate transport in nanometer geometries and score in microscopic cavities.

Investigating energy deposition in glandular tissues for mammography using multiscale Monte Carlo simulations

PURPOSE

To investigate energy deposition in glandular tissues of the breast on macro- and microscopic length scales in the context of mammography.

METHODS

Multiscale mammography models of breasts are developed, which include segmented, voxelized macroscopic tissue structure as well as nine regions of interest (ROIs) embedded throughout the breast tissue containing explicitly-modelled cells. Using a 30 kVp Mo/Mo spectrum, Monte Carlo (MC) techniques are used to calculate dose to ∼mm voxels containing glandular and/or adipose tissues, as well as energy deposition on cellular length scales. ROIs consist of at least 1000 mammary epithelial cells and ∼200 adipocytes; specific energy (energy imparted per unit mass; stochastic analogue of the absorbed dose) is calculated within mammary epithelial cell nuclei.

RESULTS

Macroscopic dose distributions within segmented breast tissue demonstrate considerable variation in energy deposition depending on depth and tissue structure. Doses to voxels containing glandular tissue vary between ∼0.1 and ∼4 times the mean glandular dose (MGD, averaged over the entire breast). Considering microscopic length scales, mean specific energies for mammary epithelial cell nuclei are ∼30% higher than the corresponding glandular voxel dose. Additionally, due to the stochastic nature of radiation, there is considerable variation in energy deposition throughout a cell population within a ROI: for a typical glandular voxel dose of 4 mGy, the standard deviation of the specific energy for mammary epithelial cell nuclei is 85% relative to the mean. Thus, for a glandular voxel dose of 4 mGy at the centre of the breast, corresponding mammary epithelial cell nuclei will receive specific energies up to ∼9 mGy (considering the upper end of the 1σ standard deviation of the specific energy), while a ROI located 2 cm closer to the radiation source will receive specific energies up to ∼40 mGy. Energy deposition within mammary epithelial cell nuclei is sensitive to cell model details including cellular elemental compositions and nucleus size, underlining the importance of realistic cellular models.

CONCLUSIONS

There is considerable variation in energy deposition on both macro- and microscopic length scales for mammography, with glandular voxel doses and corresponding cell nuclei specific energies many times higher than the MGD in parts of the breast. These results should be considered for radiation-induced cancer risk evaluation in mammography which has traditionally focused on a single metric such as the MGD.