In order to improve the understanding of the mechanisms involved in the generation of early DNA damage, a new calculation chain based on the Geant4-DNA toolkit was developed. This work presents for the first time the simulation of the physical, physicochemical and chemical stages of early radiation damage at the scale of an entire human genome  and using Geant4-DNA models. The DnaFabric software was extended to generate and export this nucleus model to a text file with a specific format that can be read by Geant4 user applications. This calculation chain was used to simulate the irradiation of the nucleus by primary protons of different energies  and the results, in terms of DNA double strand breaks, agree with experimental data found in the literature (pulsed field electrophoresis technique). These results show that the simulation is consistent and that its parameters are well balanced. Among the different parameters that can be adjusted, our results demonstrate that the criterion used to select direct strand break appears to have a very significant role on the final number of simulated double strand breaks. Improvements might have applications in many fields including medicine, radiation protection and space exploration. Better predictive capabilities would improve the accuracy of radiotherapy and hadron therapy as well as of estimates of their risks. One way of addressing this prediction uses a mechanistic approach to study the chain of physical and chemical events triggered by irradiation within a cell and leading to very early radiation induced effects. Many such studies focus on damage to the DNA molecule, considered highly sensitive to radiation8, must be used to adapt the study of the initial energy deposition of ionising radiation to the DNA scale (only a few nanometers). Geant4-DNA12 processes are an extension of the Geant413 Monte Carlo code that makes possible the track structure simulations used in this work. Moreover, the simulation must be performed within a geometrical model of the DNA target to be able to compute relevant values, such as DNA double strand breaks (DSBs). This model should be accurate enough to discriminate between the physical and chemical interactions that occur within the sensitive volumes of the DNA.In this work, we use a mechanistic approach with Monte Carlo simulations and we focus on the damage to DNA induced by radiation. Specifically designed Monte Carlo codes, known as track structure codes15 to highly complex, advanced and promising depictions describing the DNA components atomistically16. Their complexity generally makes it hard to adapt them to the different biological conditions that may influence DNA topology, although the lack of complete knowledge of the organisation of the DNA within a cell nucleus may require this adaptation. That is, although the double helix structure of the DNA has been well described, not yet the case for the higher levels of DNA organisation such as chromatin distribution within the chromosome territories. Furthermore, the organisation of the DNA within a nucleus is also dynamic and changes with the cell cycle and the cell type. DnaFabric software17 was therefore developed to facilitate the generation of complex DNA models that can go from a few pairs of nucleotides to whole-genome representations. This software makes it possible to generate, modify, and visualise complex DNA geometries which can also be exported for use in Geant4-DNA calculations.The DNA geometrical models currently used in this research field range from very simple representations based on cylindersThis work presents for the first time the simulation of the physical, physicochemical and chemical stages of early radiation damage at the scale of an entire human genome  and using Geant4-DNA models. This simulation takes the form of a calculation chain that is based on several Geant4-DNA user applications and several analysis programs. In the end, the simulation determines the DNA damage produced by the irradiation. This paper presents the first results obtained with this calculation chain for proton irradiation at different energies and compares them with available experimental data. This comparison makes it possible to set some relevant parameters for the calculation and analysis hypothesis.17 described an early version of the software and presented a first set of DNA geometrical models. That first version, however, was unable to deal with geometries composed of more than 105 elements; in practice, it could only generate and manipulate a DNA fibre of roughly 18 kbp. Recent improvements enable it to work with a cell nucleus filled with an entire human genome of 6 Gbp (36 ⋅ 109 distinct volumes). The geometry generated can then be exported to a text file (extension “.fab2g4dna”) with a specific format that can be read by Geant4 user applications.DnaFabric is a C++ program to generate, edit, display and export complex DNA geometrical models from the nucleotide scale to the entire DNA content of a cell-nucleus. A previous paper18 management system was implemented to define several 3D representations for each geometrical object. Thus, an object far from the viewpoint can be displayed as a low-detail representation, while an object close to the view point is, on the contrary, fully detailed.Among the various improvements to DnaFabric is a new module (“Engines”), which allows users to implement a simulation to modify a predefined DNA geometrical model. This module includes tools that can work with the hierarchical organisation of the DnaFabric geometrical models and perform multi-threaded simulations while updating the geometry rendered on the visualisation screen. Furthermore, the hierarchical organisation of the DNA models is now based on a graph structure that can define several memory-light placeholder objects used as references to a single memory-heavy object. This refinement of the hierarchical organisation allows DnaFabric to deal with billions of heavy object instances. The visualisation module was also modified to enable it to render such a huge number of objects. In practice, a level of detail (LOD)17.The DNA model used in this work was built with DnaFabric and its elementary pre-implemented geometrical models: a nucleotide pair, histone protein, nucleosome, linker and 5 voxels filled with hetero-chromatin fibres. This section describes these built-in DNA models only briefly, since most have previously been described19 to model the inner hydration shell of the DNA. Indeed, it is believed that the inner hydration shell that can transfer an ionisation from itself to the DNA19. The position and volume of each constituent within the nucleotide pair was calculated from PDB file data provided by the Glactone project20. The use of 6 spheres in the nucleotide pair model was chosen instead of an atomistic representation because it speeds-up the computations while not impacting the final outcome since an atomistic level of details is not required in our work.Six different spherical volumes were implemented in DnaFabric to represent the DNA constituents used as base units in our model: phosphate, deoxyribose, adenine, guanine, thymine and cytosine. They were used to build nucleotide pairs (the base unit of DNA) such as that presented in Fig. 21 was built with pairs of nucleotides, by stacking several of them along the z axis as described in a previous publication17. This produced a B-DNA double helix similar to that depicted in Fig. The B-DNA double helix, which is the most common type of DNA double helix found in living cells17. In this work, pieces of the fibre (23 nucleosomes) were shaped and oriented to form a set of five different voxel configurations: “straight”, “right”, “left”, “up” and “down” voxels. They are represented in Fig. Several nucleosomes were helically placed and linked together to create a continuous chromatin fibreμm), and the genome modelled in a hierarchical form: the 5 voxels described above are used to fill chromatin domains. Each domain is represented by a sphere with a radius of 500 nm that contains several hundreds voxels (~106 pairs of nucleotides). Each domain belongs to a human chromosome, which is attributed to a spatial region of the cell nucleus: the chromosome territory. The number of domains to be placed in each chromosome territory is specified in Table Finally, a model of a fibroblast cell nucleus was built and filled with the DNA content of the human male genome. The external shape of the nucleus is ellipsoidal  during the simulation. The aim of the calculation chain is to compute the yields of DSBs generated per primary particle from both the direct  and indirect  effects. Nevertheless, the user can also access intermediate results to, for example, separate the direct from the indirect DNA strand breaks (SBs) or determine the base damage and its location.The simulation of the physical, physicochemical and chemical stages in this chain uses a slightly modified version of the Geant4.10.1 source code. The user applications contained in the chain can handle the files exported by DnaFabric (“.fab2g4dna”) that enable it to consider the full content of the human genome .A Geant4-DNA user application to simulate the physico-chemical and chemical stages (“chem_geo”).A clustering algorithm to reveal DNA cluster damage with a user-specified distance parameter (“DBScan”).Several analysis routines and scripts to synchronise the elements of the calculation chain and to process the results it generates.The main hypotheses, assumptions and parameters associated with each of these parts are detailed in the sections below.12. The DNA volumes described in section title:dna_models were filled with liquid water, which constitutes an approximation for biological medium, to simulate the physical interactions because the Geant4-DNA models available in version 10.1 use interaction cross sections in liquid water only.The physical interactions between the incident protons (including secondary electrons) and the DNA target were simulated with the physical models present by default in Geant4-DNA (version 10.1) and already detailed in the literatureThe geometrical description of the DNA used in this user application (“phys_geo”) comes from six “.fab2g4dna” files. The first file describes the cell nucleus and contains the position and type of each of the voxels within it. The other files detail the DNA content of the five voxels introduced in section title:dna_models. The voxels and nucleus in the user application are imported by a parser that generates the corresponding Geant4 geometry. A cutting algorithm is also used to deal with the geometrical overlaps that can appear after conversion into Geant4 geometry. This algorithm is executed once for each of the 5 voxels included in the simulation.9 pairs of nucleotides.The introduction of a cell nucleus model and its DNA content into the “phys_geo” user application requires the use of specific features. Specifically, the inclusion of several million voxels into the Geant4 simulation necessitates a parametrisation process to keep the amount of memory required by the simulation at a reasonable level (<10 GB). Parameterisation in Geant4.10.1 allows the user to define a volume in memory only once and then to use this definition to represent a large number of identical volumes in the simulation, which reduces the amount of required memory. This method cannot be used, however, if different types of volumes are parameterised in the same area and if the multithreading mode is enabled, as it is in our case to speed up the simulation. We therefore modify Geant4 to enable us to parameterise the 5 different types of voxels and resolve this issue; principally; some variables were made thread-local to avoid data race issues when the multithreading mode is activated. This modification finally allowed the simulation of the physical stage in a cell nucleus filled with around 6.4 ⋅ 1023 during this simulation. The first set is used to calculate the DNA damage induced by the physical interactions (direct effects) and the second to generate the input data for the chemical stage (indirect effects). The simulations can thus be separated so that those for the different stages can be run independently when necessary. The first dataset corresponds to the physical interactions located in the DNA volumes: 2-deoxyribose, phosphate, adenine, guanine, thymine, cytosine and their hydration shells. Specifically, the information recorded there concerns the type of interaction , the particles (type and energy) and the DNA molecules involved . The second set of data includes the water molecules that have been ionised or excited and the solvated electrons . Water molecules and solvated electrons are saved only if they are located within a voxel to limit the size of the output file.Two datasets are stored in an ntuple generated by the ROOT-CERN library24 to make this possible are summarized below:A number was associated with each DNA molecule to indicate its DNA strand (1 or 2).The capability to deal with coefficients of diffusion equal to zero was introduced to specify that each DNA molecule should be treated as a “static” object.A new type of reaction was added to prevent one of the reactants from disappearing. It implements the absorption capacity of the histone proteins, which will remain in the simulation regardless of the molecules they may have absorbed.Like the physical stage, the physicochemical and chemical stages are simulated with a Geant4 user-application (“chem_geo”) built especially to take the geometrical description of the DNA exported from DnaFabric into account. This time, however, the general idea is to consider the DNA model not as a group of Geant4 physical volumes but as a set of spatially ordered molecules that should not diffuse over time. The modifications introduced in the Geant4-DNA chemistry module (version 10.1)• radical was considered able to react with the DNA molecules26. The latter is an acceptable approximation in this work because the reactions between 2-deoxyribose and eaq or H• are associated with reaction rates that are much lower27 than the one associated with the reaction involving 2-deoxyribose and OH•.The DNA molecules presented in Table 9 individual molecules, which exceeds the limitations of not only the chemistry module (Geant4-DNA version 10.1) but also current hardware. Fragmentation of the simulation to isolated voxels allowed us to reduce the amount of memory required drastically. In such a configuration, each voxel contains no more than 10000 individual molecules, which is easily manageable. The drawback of this separation is the need to run numerous different simulations (one simulation per event/voxel pair). On the other hand, it facilitates the distribution of the chemical stage simulations on multiple threads through the use of pseudo-parallelism (one simulation per thread).The physicochemical and chemical stages are not simulated in the cell nucleus as a whole; instead, reactions are limited to particular voxels. Moreover, reactants can react with one another only if they are produced by the same track (independent track approximation). The separation of the chemical stage simulation within the different voxels is due to the need to minimise memory use and simulation time. Considering the entire nucleus with its human genome simultaneously during the chemical stage would have required loading about 36 ⋅ 1011. The dissociation channels describe how an unstable water molecule that has been ionised or excited during the physical stage will decay into chemical species. These chemical species are then randomly placed in a sphere of 1 nm centered on the position of the former unstable water molecule. The resulting chemical species then diffuse and react with each other and with solvated electrons or DNA molecules during the chemical stage. The simulation of the chemical stage takes place in several time steps during which all the molecules move according to their diffusion coefficients11. Two potentially reactant molecules can trigger a reaction alongside this movement, initiated either through spatial proximity determined at the end of each time step or during a time step, through the so-called “Brownian Bridge” technique. Scavenging reactions that decrease the number of OH• radicals available to damage the DNA were not specifically modelled in this calculation. A simplification of these scavenging reactions was taken into account by different methods: histone reactions, voxel spatial limitation and, most importantly, by limiting the chemical stage simulation time to 2.5 ns30. Other similar simulation codes31 use a 10 ns duration but they take into account the scavenging of the chemical species through random absorption of the radicals at each time step.The physicochemical stage is simulated with the default “dissociation channels” given in the chemistry moduledirect) to the DNA molecule. Determinations of which interactions leads to an SB or to base damage and of whether the damage occurs in the atom in which the energy was deposited or if a charge transfer occurs, are still the subject of active research. In general, ionisation and excitation occurring within the DNA are considered able to induce DNA damage under some conditions1. It is also commonly accepted that ionisation taking place within the DNA hydration shell can lead to direct DNA damage through a charge transfer process32 and that a dissociative attachment34 can create a resonance effect able to alter the DNA structure36. The latter finding implies that electrons with energies inferior to those required to ionise or excite DNA molecules can still lead to DNA damage. Precise and complete data about the process by which physical interactions causes direct DNA damage remain sparse. Modelling thus requires making assumptions, and in mechanistic simulations, it usually assumes selection based on the amount of energy deposited in sensitive parts of the DNA. The amount of energy and the sensitive volumes change with each simulation code37.The data generated during the simulation of the physical stage does not allow direct DNA damage to be identified immediately. More specifically, the cartography of all the interactions that take place within the DNA is available but does not necessarily correspond to direct damage  constituents of a nucleotide pair, the region generally known as the “backbone” of the DNA double helix. Nevertheless, a linear probability was also tested to estimate the influence of this selection process on the amount of DNA damage. This probability increases linearly from 0 for a deposited energy less than 5 eV, to 1 when the deposited energy exceeds 37.5 eV31.In this work, the criterion chosen to calculate the number of SBIt should be noted that energy depositions are computed within DNA but with data about liquid water which constitutes an approximation.• and 2-deoxyribose can generate an indirect SB (SBindirect). Those reactions, however, are not all necessarily considered indirect SBs. Instead, when such a reaction is detected, a uniform probability of ~40% •42. It also implies that an average of 11% of all the chemical reactions between OH• and DNA will lead to an indirect SB.During the simulation of the chemical stage, every chemical reaction defined in the code is saved in an output file for later analysis. In the current implementation of the analysis, used for this work, only reactions between OHdirect and SBindirect are identified and localized within the DNA geometrical model, a clustering algorithm is used to calculate the number of DSBs. In this work, a DSB is defined as a cluster containing at least two SBs separated by less than 10 bp and with at least one SB per strand. This clustering takes place in a merging process that starts by forming initial clusters of SBs separated by less than 10 bp. The clusters are then merged if they share one of their points . At the end of the merging procedure, the clusters obtained are composed of at least two SBs. This works describes the final number of SBs contained in each cluster as the cluster (or DSB) complexity. It should be noted that this definition of DSB complexity does not include base damage, as the clustering algorithm considers only the SBs. Similarly, clusters formed of two or more SBs that are all located on the same strand are identified as complex single-strand breaks (SSBs) here. Like for the DSBs, their complexity indicates the number of SBs in the cluster. Any isolated SB not belonging to any cluster is considered a simple SSB.After the SBdirect.A 17.5 eV threshold for the energy deposited in the backbone of a nucleotide to determine an SBOH• and a sugar (2-deoxyribose and phosphate) give rise to an SBindirect.40% of the chemical reactions between A chemical stage duration of 2.5 ns.A cluster defines a DSB if it comprises at least two SBs located on opposite strands and separated by less than 10 bp.Finally the calculation chain presented here computes the number of DSBs by applying a set of default parameters that can be easily changed by the user. These are:46. In this case, our simulated results require further processing to take experimental constraints into account:DSBs are detected indirectly since experimental data are basically numbers of DNA fragments resulting from DSBs generated during the irradiation. Knowing that two DSBs are required to create a DNA fragment, it is possible to deduce a number of DSBs from the number of detected fragments. However, the technique has low resolution and some of the smaller fragments are not detected; this artificially decreases the number of experimental DSBs.Experimental results are not given as DSBs per primary particle (proton) but as DSB per Gy and per Gbp (DSB/Gy/Gbp). Furthermore, it should be noted that several Gy are delivered to the cell nucleus in each experimental irradiation and that extrapolation is used to obtain the number of DSB/Gy/Gbp.The simulation performed with the calculation chain provides a set of DSBs and SSBs with their associated complexity per simulated primary particle (pp). However, further steps are required to compare the yield of DSB/pp to experimental data obtained with a technique known as pulsed field gel electrophoresisDSBdistant/pp). It is, then, multiplied by the yield of primary particles required to deposit 1 Gy in the cell nucleus and divided by the number of Gbp included in the human genome (diploid cell: ~6.4 Gbp).To take these two points into account, an additional analysis routine was added to the calculation chain. In this analysis, the position of each simulated DSB in the human genome is used to calculate the fragment size. If the fragment size is lower than the detection threshold of the experimental data (10000 bp), it is removed. A final number of fragments per primary particle (pp) is therefore obtained, which takes into account the resolution constraints of pulsed field gel electrophoresis experiments. This number of fragments corresponds to a number of distant DSBs per primary particle  and are shown in Table d,∞ to simulate the electronic equilibrium caused by the broad beam irraditions reported in the literature46. The primary proton source is represented by a square surface (16 × 12 μm) placed above the cell nucleus. The direction of the particles is parallel to the Z axis. Figure This work simulated the irradiation of a fibroblast cell nucleus. The geometrical model used to represent the fibroblast nucleus was generated as explained in section title:models_cell_nucleus and filled with the DNA content of a human male genome. The primary particles used in these simulations were mono-energetic protons of 0.5 MeV, 0.7 MeV, 0.8 MeV, 1 MeV, 1.5 MeV, 2 MeV, 3 MeV, 4 MeV, 5 MeV, 10 MeV and 20 MeV. LETNDSB/Gy/Gbp(sbp) the number of DSB computed per Gy and Gbp, NDSB/event the number of DSB per track simulated, EGy1 the amount of deposited energy (eV) required to get one Gy in the nucleus volume, LETd,∞(Ep) the LET of the primary with an energy of Ep, n the number of Gbp in the nucleus and F a factor to take into account that only 92% of the nucleus volume and 97% of the DNA is irradiated. Specific computations were done to determine the parameters of this equation and the results are:The outpout of the simulation is a mean number of DSBs per track that is converted to a DSB yield per Gy and per Gbp using the following normalization:The statistical relevancy of the simulation results is controled by a dedicated module that starts new batches of 1000 primaries until the statistical uncertainty on the DSB yields is lower than a user specified value. In this work, this value was set to 2% which means that around 5000 primaries were simulated for each energy. Simulations were performed in parallel on a computer cluster which each node was in charge of computing results for one LET value. There were 24 threads per node and the simulations lasted around 3 weeks (depending on the particle energy).46 and simulated data40 from the literature. A minimum fragment size of 10000 bp was used to compute the number of DSB/pp for all the results of section title:dna_damages.Initially, the default parameters of the calculation chain were used to compute the number of DSBs in the DNA and compare them with both experimentaldirect (17.5 eV threshold) was modified in a sensitivity analysis to estimate its influence on the final number of DSBs. The threshold was changed to 12.5 and 30 eV and replaced by the linear probability presented above.In a second simulation, the criterion used to determine the SBet al.43, Campa et al.44 and Belli et al.46. Our simulation reproduced the experimental conditions of Frankenberg et al.43. The results of Campa et al.44 and Belli et al.46 came from V-79 Chinese hamster cells, and the lowest fragment size was higher than reported by Frankenberg et al.43: 23000 bp in the work of Belli et al.46 Despite these differences, the results are included in Fig. et al.43 start at 8.16 DSB/Gy/Gbp for 7.9 keV/μm and end at 12.22 DSB/Gy/Gbp for 35 keV/μm. The scattering of the data from Belli et al.46 and Campa et al.44 around those of Frankenberg et al.43 illustrates the weight of the uncertainties associated with this kind of experimental measurement and the influence of biological factors such as cell type. The results obtained in this work also increase with the LET starting at 5 DSB/Gy/Gbp for 2.6 keV/μm and up to 11.3 DSB/Gy/Gbp for 47.9 keV/μm. Overall, the agreement between our results here and the experimental data is good. This is especially true for the data of Frankenberg et al.43 around a LET of 20 keV/μm. Interestingly, our results are slightly lower than the experiment for LET lower than 15 keV/μm and higher than 30 keV/μm.Figure et al.31 and Nikjoo et al.40 simulated respectively with the PARTRAC and KURBUC codes. As previously, our results are based on the default parameters of the calculation chain. It should be noted that some hypotheses differ from those used in PARTRAC or KURBUC. One example is the SBdirect selection criterion in PARTRAC31, which uses the linear acceptation probability previously described (between 5 and 37.5 eV). The duration of the chemical stage also differs: it is of 10−9 s in KURBUC40 and 2.5 ⋅ 10−9 s in our work. Despite these differences, the results with PARTRAC and KURBUC are comparable to the ones obtained in this work because all of them use similar methodology and the same experimental measurements as references . On the other hand, our results are lower than those with PARTRAC for all LET lower than 35 keV/μm. For example, our results are 35% lower than those with PARTRAC for a LET of 4.6 keV/μm. The results with KURBUC are higher than both those with PARTRAC and our findings. Indeed, the difference between the yields of DSBs computed with KURBUC and in this work varies between 5 and 10 DSB/Gy/Gbp for all LET considered.Figure tot) at the origin of the DSBs and SSBs . We can also discriminate between the SBs from the physical stage  and from the chemical stage (the SBindirect). Figure tot, SBdirect and SBindirect simulated in this work as a function of the LET of the protons used as primary particle. As previously, the results are presented per Gy and per Gbp. The total number of SBs obtained in the simulation (SBtot) is almost constant at around 220 for LET values below 20 keV/μm. Nonetheless, for LET values higher than 20 keV/μm, the number of SBtot decreases to 185 for a LET of 47.9 keV/μm. The number of SBdirect is quite stable until LET values of 20 keV/μm but substantially lower than those for either SBtot or SBindirect. Specifically, there are around 40 SBdirect for LET values below 2.6 to 20 keV/μm, equivalent to only 20% of the SBtot and 24% of the SBindirect. For LET values higher than 20 keV/μm, the number of SBdirect progressively increases to 52 at 47.9 keV/μm.The results shown in Figs direct generated during the physical stage of our simulation, as explained in section title:configs. Figure μm with an increase factor of roughly 1.7, and then remains almost constant from 20 to 47.9 keV/μm. The use of a threshold of 12.5 eV for the energy deposited in the backbone of a nucleotide yields to the highest number of DSB/Gy/Gbp. The yield of DSB/Gy/Gbp starts at 12 for a LET of 2.6 keV/μm and increases to 18 for a LET of 47.9 keV/μm. The threshold of 17.5 eV (default) reduces the number of DSB/Gy/Gbp by half, it starts at 6 for a LET of 2.6 keV/μm and increases to 11 at a LET of 47.9 keV/μm. A further increase of the deposited energy threshold to 30 eV decreases the simulated numbers of DSB/Gy/Gbp to 3.5 at a LET of 2.6 keV/μm and 7 at 47.9 keV/μm. These three sets of results clearly demonstrate the increasing of the deposited energy threshold  decreases the total number of simulated DSB/Gy/Gbp  for all the LET considered in this work. Finally, the use of the linear acceptance probability (see the end of section title:configs) produces a higher number of DSB/Gy/Gbp than the results obtained with the default criterion of our calculation chain (threshold of 17.5 eV) but a lower number than computed with an energy threshold of 12.5 eV.Figure et al.43 whose experimental conditions were reproduced in our simulations. Nonetheless, we note the shortage of experimental data available in the literature for proton projectiles with energies between 0 and 20 MeV; moreover, the values for those that do exist are quite scattered. This scattering may be due to the different experimental conditions, in particular the use of different type of cells or different minimum fragment size thresholds, but also from the numerous uncertainties associated with the pulsed field gel electrophoresis technique43. Nevertheless, one important consideration is that the general agreement of our simulated results with the experimental data does not mean that the simulation reproduced accurately all the processes involved in the creation of early DNA damage. The default configuration in the calculation chain must use some parameters that are adjusted to keep the simulation balanced in terms of the number of DSBs calculated. In the end, the agreement observed in Fig. The comparison between our simulated results, computed in our calculation chain in its default configuration, and the experimental data from the literature see Fig.  shows go31 while KURBUC and our calculation chain use a threshold of 17.5 eV40. Other elements specific to our simulation may also influence the discrepancies: the use of the physical models of the version 10.1 of Geant4, our DNA geometry  and the chemical reactions considered in the simulation.The numbers of DSB/Gy/Gbp calculated in this work are similar to those calculated with other simulation codes, as illustrated in Fig. 31. The slight increase of the yield of direct SB with the LET was also not reported previously. As for the DSB yields, the parameters and hypothesis specific to our simulation are likely to explain these discrepancies, especially the use of a 17.5 eV threshold. The fact that 80% of the simulated SB were created during the chemical stage raises questions about the real influence of the SBdirect selection criterion on the final calculation of the number DSB/Gy/Gbp in our work. That is, the SBdirect selection criterion influences only the output of the physical stage, whereas the final number of DSB/Gy/Gbp considers the outputs of both the physical and chemical stages. Figure direct) can result in very substantial differences in the final number of DSB/Gy/Gbp computed through the simulation of the physical, physicochemical and chemical stages.Figure direct on the number of DSB/Gy/Gbp is explained by the DSB determination process , which is conditioned in turn by the creation of a specific type of SB cluster (see section title:ssb_dsb), one that contains at least one SB on each of the two strands of the DNA. Therefore, it is possible for a cluster identified as a DSB to become an SSB if the SB of an opposite strand disappears  in order to compute the resulting yields of DSB/Gy/Gbp. The results were then compared with data from experiments that used pulsed field gel electrophoresiseaq, hydrogen chemical species and DNA in the simulation. The addition of these reactions together with the use of the data related to the reaction between OH• and DNA bases will enable us to introduce base damage in the simulation. Consideration of base damage is required to extend the simulation from the computation of DSBs to the calculation of chromosome aberrations. Furthermore, the addition of recently published DNA cross sections50 in the simulation is ongoing work. Their introduction in the simulation will allow to fill the DNA geometry with a composite material which physical properties are closer to DNA than liquid water in terms of interaction probability and amount of energy deposited. The use of these DNA cross sections together with the latest Geant4 physical models for liquid water51 will improve the simulation of the physical stage.We are currently working at including the reactions of the The calculation chain created in this work was developed as part of the Geant4 and Geant4-DNA collaborations; the code will be made publicly available in a suitable form for the user community.Supplementeray Figure 1


We also investigate the effect of non-zero temperature by looking at a two-spin system and find similar behavior, with temperature dampening the coherence. The characteristic behavior of coherence resembles that of entanglement and is opposite to that of discord. The distribution of the coherence on the spins is investigated and found that it arises entirely due to the correlations between the spins.We study quantum coherence in a spin chain with both symmetric exchange and antisymmetric Dzyaloshinsky-Moriya couplings. Quantum coherence is quantified using the recently introduced quantum Jensen-Shannon divergence, which has the property that it is easily calculable and has several desirable mathematical properties. We calculate exactly the coherence for arbitrary number of spins at zero temperature in various limiting cases. The  While this gives some insight into the nature of coherence, these techniques do not quantify coherence in a rigorous sense. Recently a scheme for measuring coherence was developed by Baumgratz and co-workers in ref.4 based on the framework of quantum information theory. Fundamental quantities such as incoherent states, maximally coherent states and incoherent operations which are needed for the development of the procedure were introduced and analyzed. Rapid developments have been made in understanding the theory of quantum coherence through numerous works16 and in using it as a resource in quantum information theory23. Investigations on the role of quantum coherence in thermodynamic processes26, assisted subspace discrimination27, quantum state merging28 and in the generation of gaussian entanglement29 have been carried out. Currently there is a lot of interest in applying the procedure of quantifying coherence and relating them to experimental quantities in feasible systems like Bose-Einstein condensates31, cavity optomechanical system33 and spin systems39.Quantum coherence is one of the central concepts in quantum physics, and hence its detection and quantification is a fundamental task. Traditionally, the distinction between quantum and classical coherence is made using phase space distributions4 the set of properties a functional should satisfy in order to be considered as a coherence measure were proposed. Based on these developments several functions were introduced to serve as measures of coherence47. All these measures of coherence can be broadly classified into either the entropic or the geometric class of measures. This depends on whether the measure is based on the entropy functional or has a metric nature which can give rise to a geometric structure. A mathematical functional is deemed to be a metric if it obeys the axioms of distance and satisfies the triangle inequality. In ref.47 we introduced a new measure based on the quantum version of the Jensen-Shannon divergence. It was found previously that this measure has many desirable mathematical properties as it combines the features of both the entropic and geometric class. For example, the quantum Jensen-Shannon divergence is a distance measure, is symmetric in its input states, its square root obeys the triangle inequality, and is easily calculable. These properties allowed us to decompose the total coherence in a system into various contributions. Coherence can originate from individual subsystems  or may be distributed across several subsystems (intrinsic coherence). Intrinsic coherence has the property that local basis transformations, which in general change the amount of coherence (coherence is a basis dependent quantity), leave the coherence unaffected. Several models were examined in ref.47, but to date utilizing the quantum Jensen-Shannon divergence for quantifying coherence has not been explored any further.In ref.52. This is natural since quantum correlations underlies both entanglement and quantum phase transitions. But entanglement accounts only for non-local quantum correlations and does not consider other kinds of correlations and quantum features54. To have a complete understanding of the role played by quantumness of an object in physical phenomena it is important to consider the role played by other features like quantum coherence. Studies have been carried out with a view to understand the role of quantum coherence in spin chain models. Most of these works were focussed on anisotropic XY model34 with a view to understand the role of quantum coherence in investigating quantum phase transitions. Such a deep understanding of coherence is applicable to not only naturally occurring systems in condensed matter, but also artificially created metamaterials such as those being routinely produced with cold atom, ion trap, and superconducting systems58. Of particular interest are materials with spin-orbit coupling as this is one of the basic ingredients of topological quantum states, which are fundamental to many fascinating effects such as the quantum Hall effect, topological insulators, and anyonic statistics.In the context of quantum many-body systems, it was found in numerous works that entanglement can be used to detect quantum phase transitions in condensed matter systemsJx,y,z are the symmetric exchange spin-spin interactions, i. When 60. Despite its simplicity the model describes the magnetic properties of a wide range of compounds and also has a very rich mathematical structure based on group theory62. Though the Heisenberg model was successful in describing the magnetism of several systems like KCuF3, CsNiCl3 and CsCuCl3 it could not explain the weak ferromagnetic behaviour of certain compounds like α-Fe2O3, MnCO3 and CoCO3 in their antiferromagnetic state. A detailed investigation of this problem was carried out by Dyzaloshinskii63 and Moriya64. As described in63 weak ferromagnetic behavior arises due to the relativistic spin-lattice and dipole interactions. This DM interaction causes spin canting, a behavior in which the spins are tilted by a small angle instead of being exactly parallel to each other. This characteristic feature is the source of the small amount of magnetism in the above mentioned materials. Based on crystal symmetry64 it was found that spin-canting can be described by the DM antisymmetric exchange interaction term.In this paper, we study the behavior of quantum coherence in the XYZ spin chain with Dyzaloshinskii-Moriya (DM) interactions. The Hamiltonian that we consider is67 and quantum discord69. From the studies on quantum entanglement67 and discord69, it was found that the critical temperature below which these correlations start decreasing can be altered by varying the DM interaction. Further, the direction of the DM interaction has a direct bearing on the extent to which this change happens. In particular, it was found that as the DM interaction increases, the entanglement increases whereas the quantum discord decreases.Generally, the magnitude of the DM interaction is small compared to the spin-spin interaction in naturally occurring materials, but is important to include it as it changes the nature of the system greatly. These changes have been studied from the perspective of quantum information theory particularly in the measurement of quantum correlations like entanglementThis paper is organized as follows. First we examine the coherence of certain limiting cases of the model which allow for an exact solution. Later we characterize the quantum coherence of a two qubit spin models with added DM coupling interaction. Finally the basis dependence of quantum coherence and its effect in spin chain models is presented. A summary of our conclusions is presented in the Section of Discussion.In this section we consider some of the limiting cases of the Hamiltonian (1) where it is possible to obtain an exact expression for the coherence at zero temperature.Jz = 0, Jx = Jy = J, and The first limiting case we consider is where Being a one-dimensional system, this can be explicitly solved using a Jordan-Wigner transformation to map between spins and fermions:Under this transformation, the Hamiltonian (2) can be recast asFor periodic boundary conditions this can be diagonalized by Fourier transform where N/2 fermions.The ground state of the Hamiltonian (2) is in the total spin n =  and q =  are the sets of momentum satisfying Λq < 0. Reverting to the spin formulation, the ground state isσ1, …, σN) is a phase factor which originates from (9) and the phases picked up by the Jordan-Wigner transformation.The ground state can then be written asWe now evaluate the coherence using the square root of the quantum Jensen-Shannon divergence, defined as47 as a measure of coherence. Here ρ and ρd denote the density matrix of the state and the closest incoherent state under the distance measure and S(ρ) is the von Neumann entropy. We take the closest incoherent state to be the density matrix where all the off-diagonal elements of ρ are set to zero4. For pure states this measure satisfies all the axioms of a distance and also obeys the triangle inequality and hence is a metric. Thus this measure has both entropic nature and geometric properties. In the limit where N is sufficiently large, the quantum coherence of the system as measured using the Jensen-Shannon divergence (11) attains the value C = 1 as shown below. To evaluate the measure we need to find the entropy of the density matrix of the state, its closest incoherent state ρd and also the entropy of the symmetric sum of these density matrices.This was introduced in ref.ρ is zero. For the state (10) the precise knowledge of Ω is in fact not necessary, as it is invariant under the particular phases of the state. We may thus take the phases to be zero, and we evaluate the eigenvalues of the incoherent density matrix and the (ρ + ρd)/2 to beρ + ρd)/2 to beN, which is the maximum value of the the Jensen-Shannon divergence. The large amount of coherence of this state originates from the superposition of Firstly, since the state is pure, the entropy of the density matrix he state  the precJx,y = D = 0, with HamiltonianThe opposite limit is in the ferromagnetic limit with J < 0 for ferromagnetism, the ground state configuration of the system is eitherσ = ±1. For J > 0 we have antiferromagnetism, and the ground state is a Neel state with every second spin flipped in (17). In either case, we take the condensed matter physics point of view that the ground state is spontaneously broken to one of these states. In all these cases the states are already in the decohered basis, henceFor If we choose to preserve the spin-flip symmetry the ferromagnetic ground state isJz the zero temperature ground state has a large amount of coherence, as given by (15). As the Jz term is increased, this diminishes, and for the spontaneously broken case of (18) it reduces to zero. Thus the Jz parameter can be seen as the crucial control for the amount of coherence.In either case the coherence is considerably lower than the opposite regime as given in (15). We thus see the general behavior that for zero The previous section revealed the general behavior that is expected in the XYZ model with DM interactions. We now examine what occurs at intermediate values of the parameters, and also include non-zero temperature effects. An exact solution for the thermodynamic limit is not available for the general case. We therefore consider a two-site system which should show the general dependence of the coherence on various parameters. The Hamiltonian of a two qubit Heisenberg model with Dzyaloshinsky Moriya interaction isThe DM interaction can be oriented in an arbitrary direction in general. We examine the effect of the DM interaction in various directions in the following sections.XYZ model with DM interaction oriented along the z-direction Jx,y,z < 0 and antiferromagnetic when Jx,y,z > 0. Diagonalizing the Hamiltonian in (22) the eigenvalues areThe Hamiltonian of a two qubit anisotropic ρ(T) of the model. The thermal density matrix ρ(T) = exp(−βH)/Z describes the state of a spin chain at thermal equilibrium, where Z = Tr[exp(−βH)] is the partition function of the system and β = 1/kBT with kB and T being the Boltzmann constant and the temperature respectively. Throughout our discussion we assume kB = 1 for the sake of convenience. In the computational basis (i.e. σz eigenstates) the thermal density matrix of the two qubit XYZ model with DM interaction isHere we are interested in investigating the temperature dependence of the quantum coherence in the two qubit Heisenberg model. This can be accomplished from the knowledge of the thermal density matrix XYZ model including the DM interaction in the z direction. We first observe that coherence decreases with temperature as expected due to an increase in thermal fluctuations, which has the effect of decreasing quantum coherence  and the DM interaction is in the z-direction. Here again we find that the coherence saturates at a finite value. This value varies with temperature when Jz is varied, but when Dz is changed the saturation value is always C = 0.56. These conclusions can be observed from the fact that the results displayed in plots (a) and (b) of Fig. This behaviour is also observed in the case of an XXZ model, where the spin-spin exchange coefficients in two directions coincide whereas in the third direction it is different  respectively. This has the Hamiltoniansx-direction andy-direction. These have rather similar properties hence we will discuss (29) primarily and simply show the results for (28).We now turn to the two qubit Heisenberg model with DM coupling in the ρ(T) of the system can then be calculated to bey-direction using (11) as before and is displayed in Fig. The eigenvalues of (29) arex-direction we verify that identical results are obtained as that shown in Fig. Jx → Jy, Jy → Jx, Jz → Jz for the same temperature. This is as expected as in terms of coherence the Hamiltonians (28) and (29) only differ according to a replacement of σx ↔ σy in the DM interaction. Both are coherence generating terms and since the coherence is generally unaffected by phase information, similar effects should result from either.For coherence in the Jx = Jy ≠ Jz) and the completely isotropic XXX model (Jx = Jy = Jz) with DM interaction in the x-direction are also analyzed. The behaviour of quantum coherence with respect to spin-spin and DM interaction parameters are given in Fig. Dy given in Fig. σx term is a coherence generating term and has similar effects on both the XYZ Hamiltonian as well as the XXZ model and isotropic XXX model.The quantum coherence of the XXZ model (4 and Jensen-Shannon divergence47 requires a characterization of incoherent states (states with zero coherence). To define the incoherent states in a d-dimensional Hilbert space b1 may become coherent when it is transformed to a different basis b2 via a unitary transformation. So in the new basis b2 this state need not belong to the set of incoherent state and hence it cannot be used to measure the coherence. Alternatively a state in the basis b1 which has a finite amount of coherence will become diagonal and hence incoherent in the b2 basis. The set of incoherent states thus completely depend upon the choice of the basis used and so the coherence is a basis dependent quantity. Throughout our study on the XYZ model discussed in this work we have computed the coherence in the z-basis. In this section we investigate whether there is any change in the behavior if the coherence in the x and y bases are measured, and contrast them with the results obtained through the computational basis.Measurement of coherence in quantum systems via measures like relative entropy, x or the y basis, the thermal density matrix ρ is rotated into its respective basis. After this, the incoherent state ρd and the state (ρ + ρd)/2 corresponding to the rotated density matrix are found, and the quantum Jensen-Shannon divergence is calculated in the same way. The entropy S(ρ) is invariant under basis transformation, but on changing the basis the incoherent density matrix ρd changes and hence S(ρd) and S((ρ + ρd)/2) depend on the basis.To compute the coherence in the x and y basis are shown in Figs The coherence in the z and x-basis for a XYZ-Dz model. From the plots we notice that for a fixed Jz, quantum coherence decreases with temperature, irrespective of the measurement basis. But when Jz is higher, the rate of fall of quantum coherence with temperature is lower when the measurement basis is orthogonal to the direction of the DM interaction. This is because the coherence which is distributed between all the elements can be classified into two classes. One class contains the diagonal and the antidiagonal elements and the other class contains the remaining terms. These classes have a different dependence on Jz and temperature which causes this behavior. When the measurement basis and orientation of the DM coupling are the same the density matrix contains only the diagonal and the antidiagonal terms (i.e. an X-state) and thus have the same Jz and temperature dependence and the fall is more uniform.In Fig. Dz and Jz in the x-basis and as a function of Dx and Jx in the z-basis is given in Fig. y-basis for a XYZ-Dz model, showing a qualitatively similar behaviour to Fig. 47 and the value always interpolates between that of the completely ferromagnetic state and the antiferromagnetic state.A comparison of the quantum coherence of the XYZ model as a function of Jx,y symmetric exchange promoting coherence in the system, while the Jz interaction suppressing it. The physical picture of this is simple, as the DM interaction in any direction always contains off-diagonal terms in Pauli operators, which tend to create coherence, which is likewise true for the Jx,y interactions. The Jz term favors states which are eigenstates in the z-basis, which naturally do not have coherence. This can be seen to be true for any number of spins, and the coherence smoothly interpolates between these two limits. When including temperature effects, we find that quantum coherence decreases with temperature. This can be attributed to a decoherence effect where any superposition instead becomes a mixture. These are all expected effects and shows that the quantum Jensen-Shannon divergence intuitively captures the nature of coherence, even when extended to a interacting many-body system as the one considered here.The coherence of the XYZ Heisenberg model with Dzyaloshinsky-Moriya interactions was investigated at both zero temperature and non-zero temperatures. Two main analysis were performed, one at zero temperature but for an arbitrary number of spins, where an exact solution is possible in limiting cases. The non-zero temperature case was examined for a minimal two-spin system, under various limits and directions of the DM interaction. For the zero temperature case, a clear picture of the role of coherence emerged, with the DM antisymmetric exchange and 47 was zero and the entire coherence was due to the interaction between the spins. Thus the non-local nature of coherence gives rise to a behavior which is similar to the one observed for the quantum entanglement. We also examined the quantum coherence of the models in different bases and found that there is a quantitative and qualitative change in the coherence depending on the choice of the basis. The coherence is relatively maximum when the direction of DM interaction is orthogonal to the direction of the measurement basis.In general, when interaction parameters associated with coherence are increased, the quantum coherence increases. However, the qualitative behavior depends on the type of the interaction parameter. When the spin-spin interaction which is aligned along the direction of the DM interaction is varied, the saturation value of coherence depends strongly upon the temperature. If the spin-spin interaction being varied is orthogonal to the direction of the DM coupling, then the coherence saturates to almost the same value. Finally, when the anti-symmetric DM coupling strength is changed the coherence tends to change more rapidly than with the symmetric version. This indicates that the DM interaction influences the quantum coherence in a manner which is stronger than the spin-spin coupling. Another observation is that the temperature at which the coherence falls from its maximum value tends to increases with the interaction parameter. This agrees with the observations for entanglement, but is the opposite to that found for quantum discord. The reason for this is that the entanglement accounts only for the non-local quantum correlations of the system, whereas quantum discord takes into consideration the total amount of quantum correlations in the system. The local quantum correlations which are not accounted in the entanglement studies may fall much faster than the rise in non-local quantum correlations. We note that in all the spin models considered in this paper, the local coherence as defined in ref.71. Further research in this direction will involve the study of distribution and shareability of coherence in spin models. Earlier studies on a finite sized XXZ model47 have indicated that the anisotropy acts as a switch changing the nature of the system from polygamy to monogamy. A comparison of this work with these earlier studies will help us to understand the role played by DM coupling in the shareability of coherence. Some other future possibilities include the study of spin models with staggered DM interactions72 as well as spin chain models with random exchange interactions73 to understand the role of coherence in condensed matter systems.In addition to revealing some of the coherence properties of a many-body system, our work shows that the quantum Jensen-Shannon divergence is a useful quantity in terms of quantifying the coherence in quantum systems. As discussed in the introduction one of the main advantages of the coherence measure is that it is formally a distance measure, and thus can be used to distinguish the distribution of coherence in multipartite systems. It can be potentially applied to a variety of different systems, from naturally occuring many-body systems to synthetic metamaterials


Monte Carlo simulations were performed using MCNP4C code, for a single pellet source in water medium and Plexiglas, and measurements were performed in Plexiglas phantom material using LiF TLD chips. Absolute dose rate distribution and the dosimetric parameters, such as dose rate constant, radial dose functions, and anisotropy functions, were obtained for a single pellet source. In order to investigate the effect of the applicator and surrounding pellets on dosimetric parameters of the source, the simulations were repeated for six different arrangements with a single active source and five non‐active pellets inside central metallic tubing of a vaginal cylindrical applicator. In commercial treatment planning systems (TPS), the attenuation effects of the applicator and inactive spacers on total dose are neglected. The results indicate that this effect could lead to overestimation of the calculated F, by up to 7% along the longitudinal axis of the applicator, especially beyond the applicator tip. According to the results obtained in this study, in a real situation in treatment of patients using cylindrical vaginal applicator and using several active pellets, there will be a large discrepancy between the result of superposition and Monte Carlo simulations.In this study, dose rate distribution around a spherical PACS number: 87.53.Jw The Selectron low‐dose‐rate (LDR) remote afterloading system distributed by Nucletron  is mainly used in gynecological brachytherapy to deliver the prescribed dose via different combinations of active spherical Cs‐137 pellet sources  and inactive (dummy) pellets into applicator sets. In this study, the radial dose functions and anisotropy functions of a single pellet source in different positions inside the applicator were measured and calculated for different distances and angles in presence of the central metallic tubing of a vaginal applicator and inactive pellets. Having the TG‐43 parameters of the single pellet in different positions inside the applicator, we can determine the dose distributions around every configuration of active and inactive pellets by adding the dose from each pellet; there is no need to do a separate Monte Carlo simulation for every configurations used to treat the patients with vaginal cancer. These parameters will be utilized to update the data in the treatment planning systems in order to determine accurate radiation delivery for treatment of patients using such LDR units.The purpose of this research is to investigate the dosimetry parameters of an individual low‐dose‐rate Cs‐137 Selectron pellet source within the 0.6 cm diameter central metallic tubing of a vaginal cylindrical applicator using Monte Carlo simulation and experimental techniques, following the recommendations of Task Group #43 (TG‐43) of the American Association of Physicists in Medicine (AAPM).,8 InThe Selectron remote afterloading sources consist of spherical Cs‐137 pellets, composed of 1.5 mm active source core of ceramic, encapsulated in 0.5 mm steel, with an overall diameter of 2.5 mm.In 1995, AAPM Task Group 43 (TG‐43) introduced a protocol for dosimetric evaluation of low‐energy brachytherapy sources used for interstitial brachytherapy.D· is the dose rate at the point of interest at some distance r from the center of the source and polar angle θ relative to the longitudinal axis of the source, Sk is the air kerma strength, Λ is the dose rate constant in water, Gx is the geometry function at the point of interest, Gx  is the geometry function at the reference point 1 cm from the source and at 90° from the longitudinal axis of the source, gX(r) is the radial dose function, and F is the 2D anisotropy function. The subscript X in the geometry and radial dose functions indicates the point and line source approximation in the geometry function. For a detailed description of the above parameters see the updated AAPM TG‐43 U1 protocol.In this protocol, the general 2D dose rate distribution around a brachytherapy source is defined as used in this study for determination of dosimetry parameters of Selectron Cs‐137 source is a general purpose Monte‐Carlo radiation transport code which is able to consider photoelectric, coherent, Compton and pair production interaction processes.The MCNP4C code,11 uIn the simulation geometry used to score dose rate constant and radial dose function of a single active pellet without the presence of applicator and other inactive pellets, the source was located at the center of a spherical water phantom with dimensions big enough (60 cm diameter) to provide the full scattering conditions. Because of the spherical symmetry of the source, there is no anisotropy around the source, so concentric spherical shells with 0.05 cm thickness were simulated around the source in order to calculate dose around the source at different distances from the source center. In order to investigate the effect of the applicator and inactive pellets on dosimetry parameters of the source, the simulations were done in a spherical water phantom with a single pellet source inside central metallic tubing of a vaginal applicator while other pellets are inactive. Tally cells used in this investigation were small spherical cells of 0.5 mm radius whose center is located at the calculation point and, in order to investigate the effect of the position of the single active pellet inside the applicator on dosimetry parameters, the simulations were done for an active pellet in six different positions inside the applicator.TG‐43 dosimetric parameters of the source, such as dose rate constant, radial dose functions and anisotropy functions, were calculated with and without the applicator and dummy pellets in each arrangement. The geometry of the simulations is shown in h–1U–1 by using the tally multiplier (FMn) card. In order to score the air kerma strength, Sk, as a measure of brachytherapy source strength, the air kerma rate was calculated at distances ranging from 0.5 to 150 cm by placing the tally cells in a 4 m diameter air volume, and by using the product of free‐space air kerma rate, and the distance d squared. The energy cutoff δ=10 keV was considered in this calculation. The densities and chemical composition of the applicator, and active and inactive pellets used in these simulations were obtained from the work of Pérez et al.;There are many different tally types available in MCNP4C for scoring diverse physical characteristics. Tally type F6 (energy deposition averaged over a volume Mev per gram per photon) was used to calculate dose rate distribution around the source, but as F6 is a kerma estimator, it is only valid when electronic equilibrium exists. Comparison of results of tally F6 with the results of tally *F8 (energy deposited in a cell) indicates that for 662 keV photon of Cs‐137 sources, the electronic equilibrium exists at distances greater than 2 mm from the source; so collision kerma closely approximates the absorbed dose and tally F6 can be used to score absorbed dose. Furthermore, we converted dose units of MeV/g per photon to Gy 1.6×102×10The simulations for dose rate constant, radial dose function, and 2D anisotropy function were performed for up to From these simulations, the total errors at radial distances of 1.0 cm and 5.0 cm were found to be 0.3% and 1.5%, respectively.3×3×1 mmD· is the initial absorbed dose rate at the start of the experiment at a point , R is the TLD response corrected for background and the physical differences between the TLD chips using the predetermined chip factors,T is the exposure time. In these measurements, the exposure time was selected such that the absorbed doses ranged from 10 to 100 cGy for which TLD responses were linear. Sk is the initial source air‐kerma strength at the start of the measurement. This parameter had been determined two months before the time of this investigation. We used this result by considering radioactive decay of the source. ∊ is the calibration factor for the TLD response (nC/cGy) measured with a Cs‐137 radiotherapy source with 250 Ci activity at the time of calibration. The Cs‐137 source was an old radiotherapy unit which is used for research and calibrations, not for treatment of patients. Two TLD chips were put on a 2 mm thick Plexiglas slab, and were exposed to a known amount of radiation. We used an ionization chamber detector to measure the total dose received by each set of chips. E(r) is a correction factor for the energy dependence of the TLD between the calibration beam and the Cs‐137 photon, which equals unity in this case. d (T) is a correction factor used to account for the decay of the source during irradiation. d (T) is assumed to be unity for Cs‐137 source with 30 y half‐life. Flin is the nonlinearity correction of the TLD response for the given dose. Flin was assumed 1.0 for the dose range of 10 to 100 cGy.Dose rate distributions around the Cs‐137 pellet source were measured in homemade Plexiglas phantoms using Li‐F thermoluminescence dosimeter, TLD100 chips of dimensions 3×3×1 mm,,, were machined to accommodate TLD chips and the source holder. The experimental setup for measurement of radial dose function and anisotropy function is shown in Two D· is the dose rate at the reference point (r0=1 cm and θ0=90°), which was measured using LiF TLD in Plexiglas phantom and Monte Carlo calculations in water.The dose rate constant value of a single spherical source in the first position inside the applicator was calculated as:gx(r) describes the attenuation in tissue of the photons emitted from the brachytherapy source. The radial dose function is defined as:D· and  and D· are the dose rates measured at distances of r and ro, respectively, along the transverse axis of the source. Gx is known as the geometry function which takes into account the effect of the interior geometry of source on the dose distribution at a given point. The geometry function is defined by the AAPM TG‐43 as:The radial dose function, Two‐dimensional anisotropy function, F, is defined as:1.093±0.08 cGyh−1U−1. The Monte Carlo calculated dose rate constant for a single pellet source in water phantom without the applicator was found to be 1.102±0.06 cGyh−1U−1, and in presence of the applicator and non‐active pellets while the pellet in first position was active, was 1.095±0.05 cGyh−1U−1. Pérez et al.The measured dose rate constant of the Cs‐137 pellet source in position 1 inside the applicator, in Plexiglas phantom, was found to be gp(r) for the single pellet source without the applicator and in positions 1 to 6 inside the applicator are shown in (gp1(r)) when the first pellet is active. These results indicate up to 3.3% smaller radial dose function of the source at 10 cm depth due to the presence of the applicator and non‐active pellets.The radial dose function for the pellet source for point source approximation can be obtained by Eq. The Monte Carlo calculation of 2D anisotropy function for a single pellet source in different positions inside the applicator is shown in In addition, the real target can be a point located along the longitudinal axis of the source; therefore, the attenuation affects the target point more than the prescription point. Hence, the attenuation due to the applicator and pellets has more effect on target point than prescription point. Such reduction in dose around the vaginal applicator is expected to be observed in cases where tandem and ovoids are used in gynecological brachytherapy. The larger number of active pellets used in tandem‐ovoid sets and the more complicated geometry of such cases would cause even more errors in TPS dose calculation than the cases that use vaginal applicator. Williamson et al. According to Task Group #59 of AAPM (TG‐59), normal tissue toxicity is expected to be more in HDR treatment than LDR.The high‐tech environment of HDR brachytherapy makes it an acceptable alternative to LDR, which is why LDR remote afterloading units are not commonly used in US. The main reasons that HDR brachytherapy has become more popular in clinical practices are its ability to treat on an outpatient basis and the fact that it takes less time to treat patients.,19 Aand unit operators. Such disadvantages of HDR brachytherapy ensures that the clinical use of LDR will still be used in gynecological brachytherapy. It should be noted that presently in North America, the majority of brachytherapy remote afterloading units are HDR units (325 out of 500 units sold are HDR units).The TG‐43 dosimetric parameters of the model Selectron Cs‐137 LDR pellet source were studied using standard methods employing thermoluminescent dosimeters in water‐equivalent phantoms, and MCNP4C Monte Carlo code. According to the results, dose rate constant of the Cs‐137 model Selectron source is comparable to those of commercially available sources. Moreover, the anisotropy functions of this source, in position 1 are in excellent agreement with Monte Carlo calculated data. According to this study, the position of the single active source inside the applicator doesn't have any significant effect on radial dose function of the source. The effect of the position of the active source has a more significant effect on F along the applicator tip; this effect is due to the geometry of the applicator tip. Using the anisotropy functions in the presence of the applicator and inactive pellets, the dose distribution around different compositions of active and inactive pellets used in treatment of vaginal cancer can be assessed more precisely than commercial treatment planning systems.In summary, the attenuation of the applicator wall and adjacent active and inactive pellets in the source reduces the dose distribution of the Cs‐137. This effect is larger at smaller angles relative to the longitudinal axis of the applicator.The authors wish to acknowledge the personnel in the Radiotherapy Department of Namazi Hospital. We would also like to thank the Radiation Research Center of Shiraz University.