An on-lattice agent-based Monte Carlo model simulating the growth kinetics of multicellular tumor spheroids.

PURPOSE: To develop an on-lattice agent-based model describing the growth of multicellular tumor spheroids using simple Monte Carlo tools. METHODS: Cells are situated on the vertices of a cubic grid. Different cell states (proliferative, hypoxic or dead) and cell evolution rules, driven by 10 parameters, and the effects of the culture medium are included. About twenty spheroids of MCF-7 human breast cancer were cultivated and the experimental data were used for tuning the model parameters. RESULTS: Simulated spheroids showed adequate sizes of the necrotic nuclei and of the hypoxic and proliferative cell phases as a function of the growth time, mimicking the overall characteristics of the experimental spheroids. The relation between the radii of the necrotic nucleus and the whole spheroid obtained in the simulations was similar to the experimental one and the number of cells, as a function of the spheroid volume, was well reproduced. The statistical variability of the Monte Carlo model described the whole volume range observed for the experimental spheroids. Assuming that the model parameters vary within Gaussian distributions it was obtained a sample of spheroids that reproduced much better the experimental findings. CONCLUSIONS: The model developed allows describing the growth of in vitro multicellular spheroids and the experimental variability can be well reproduced. Its flexibility permits to vary both the agents involved and the rules that govern the spheroid growth. More general situations, such as, e. g., tumor vascularization, radiotherapy effects on solid tumors, or the validity of the tumor growth mathematical models can be studied.

Air density dependence of the response of the PTW SourceCheck 4pi ionization chamber for 125I brachytherapy seeds.

PURPOSE: To analyze the air density dependence of the response of the new SourceCheck 4pi ionization chamber, manufactured by PTW. METHODS: The air density dependence of three different SourceCheck 4pi chambers was studied by measuring 125I sources. Measurements were taken by varying the pressure from 746.6 to 986.6hPa in a pressure chamber. Three different HDR 1000 Plus ionization chambers were also analyzed under similar conditions. A linear and a potential-like function of the air density were fitted to experimental data and their achievement in describing them was analyzed. RESULTS: SourceCheck 4pi chamber response showed a residual dependence on the air density once the standard pressure and temperature factor was applied. The chamber response was overestimated when the air density was below that under normal atmospheric conditions. A similar dependence was found for the HDR 1000 Plus chambers analyzed. A linear function of the air density permitted a very good description of this residual dependence, better than with a potential function. No significant variability between the different specimens of the same chamber model studied was found. CONCLUSION: The effect of overestimation observed in the chamber responses once they are corrected for the standard pressure and temperature may represent a non-negligible ∼4% overestimation in high altitude cities as ours (700m AMSL). This overestimation behaves linearly with the air density in all cases analyzed.

A method to relate StarTrack(®) measurements to R50 variations in clinical linacs.

The relation between the data recorded with any device for the daily checking of the behavior of a clinical linac and the reference magnitudes to be monitored may be unknown. An experimental method relating the energy stability of the electron beam measured with StarTrack(®) to the R50 beam quality index is proposed. The bending magnet current is varied producing a change in the exit energy window and, therefore, a modification of the R50 value. For different values of this current, the output data of StarTrack(®) and the R50, obtained from depth doses measured in a water phantom are determined. A linear fit between both sets of data allows the identification of the StarTrack(®) output that provides the best way to obtain the quality index R50, for each beam nominal energy. Using these fits, an historical datum series is used to analyze the method proposed in the daily quality control. The ouput data of the StarTrack(®) and the R50 values show a good linear correlation. It is possible to establish a methodology that allows the monitoring of R50 by direct use of the daily quality control data measured with StarTrack(®). A method to monitor R50 in the daily quality control using the StarTrack(®) device has been developed. The method may be applied to similar devices in which the statistical control variable does not show a linear behavior with R50.

Monte Carlo study for designing a dedicated "D"-shaped collimator used in the external beam radiotherapy of retinoblastoma patients.

PURPOSE: Retinoblastoma is the most common intraocular malignancy in the early childhood. Patients treated with external beam radiotherapy respond very well to the treatment. However, owing to the genotype of children suffering hereditary retinoblastoma, the risk of secondary radio-induced malignancies is high. The University Hospital of Essen has successfully treated these patients on a daily basis during nearly 30 years using a dedicated "D"-shaped collimator. The use of this collimator that delivers a highly conformed small radiation field, gives very good results in the control of the primary tumor as well as in preserving visual function, while it avoids the devastating side effects of deformation of midface bones. The purpose of the present paper is to propose a modified version of the "D"-shaped collimator that reduces even further the irradiation field with the scope to reduce as well the risk of radio-induced secondary malignancies. Concurrently, the new dedicated "D"-shaped collimator must be easier to build and at the same time produces dose distributions that only differ on the field size with respect to the dose distributions obtained by the current collimator in use. The scope of the former requirement is to facilitate the employment of the authors' irradiation technique both at the authors' and at other hospitals. The fulfillment of the latter allows the authors to continue using the clinical experience gained in more than 30 years. METHODS: The Monte Carlo code PENELOPE was used to study the effect that the different structural elements of the dedicated "D"-shaped collimator have on the absorbed dose distribution. To perform this study, the radiation transport through a Varian Clinac 2100 C/D operating at 6 MV was simulated in order to tally phase-space files which were then used as radiation sources to simulate the considered collimators and the subsequent dose distributions. With the knowledge gained in that study, a new, simpler, "D"-shaped collimator is proposed. RESULTS: The proposed collimator delivers a dose distribution which is 2.4 cm wide along the inferior-superior direction of the eyeball. This width is 0.3 cm narrower than that of the dose distribution obtained with the collimator currently in clinical use. The other relevant characteristics of the dose distribution obtained with the new collimator, namely, depth doses at clinically relevant positions, penumbrae width, and shape of the lateral profiles, are statistically compatible with the results obtained for the collimator currently in use. CONCLUSIONS: The smaller field size delivered by the proposed collimator still fully covers the planning target volume with at least 95% of the maximum dose at a depth of 2 cm and provides a safety margin of 0.2 cm, so ensuring an adequate treatment while reducing the irradiated volume.

Retinoblastoma external beam photon irradiation with a special 'D'-shaped collimator: a comparison between measurements, Monte Carlo simulation and a treatment planning system calculation.

Retinoblastoma is the most common eye tumour in childhood. According to the available long-term data, the best outcome regarding tumour control and visual function has been reached by external beam radiotherapy. The benefits of the treatment are, however, jeopardized by a high incidence of radiation-induced secondary malignancies and the fact that irradiated bones grow asymmetrically. In order to better exploit the advantages of external beam radiotherapy, it is necessary to improve current techniques by reducing the irradiated volume and minimizing the dose to the facial bones. To this end, dose measurements and simulated data in a water phantom are essential. A Varian Clinac 2100 C/D operating at 6 MV is used in conjunction with a dedicated collimator for the retinoblastoma treatment. This collimator conforms a 'D'-shaped off-axis field whose irradiated area can be either 5.2 or 3.1 cm(2). Depth dose distributions and lateral profiles were experimentally measured. Experimental results were compared with Monte Carlo simulations' run with the penelope code and with calculations performed with the analytical anisotropic algorithm implemented in the Eclipse treatment planning system using the gamma test. penelope simulations agree reasonably well with the experimental data with discrepancies in the dose profiles less than 3 mm of distance to agreement and 3% of dose. Discrepancies between the results found with the analytical anisotropic algorithm and the experimental data reach 3 mm and 6%. Although the discrepancies between the results obtained with the analytical anisotropic algorithm and the experimental data are notable, it is possible to consider this algorithm for routine treatment planning of retinoblastoma patients, provided the limitations of the algorithm are known and taken into account by the medical physicist and the clinician. Monte Carlo simulation is essential for knowing these limitations. Monte Carlo simulation is required for optimizing the treatment technique and the dedicated collimator.

Low-dose radiation hyper-radiosensitivity in multicellular tumour spheroids.

OBJECTIVE: We propose and study a new model aimed at describing the low-dose hyper-radiosensitivity phenomenon appearing in the survival curves of different cell lines. METHODS: The model uses the induced repair assumption, considering that the critical dose at which this mechanism begins to act varies from cell to cell in a given population. The model proposed is compared with the linear-quadratic model and the modified linear-quadratic model, which is commonly used in literature and in which the induced repair is taken into account in a heuristic way. The survival curve for the MCF-7 line of human breast cancer is measured at low absorbed doses and the uncertainties in these doses are estimated using thermoluminiscent dosemeters. RESULTS: It is shown that these multicellular spheroids present low-dose hyper-radiosensitivity. The new model permits an accurate description of the data of two human cell lines (previously published) and of the multicellular spheroids of the MCF-7 line here measured. CONCLUSION: The model shows enough flexibility to account for data with very different characteristics and considers in a faithful way the hypothesis of the repair induction.

Neutron dosimetry in organs of an adult human phantom using linacs with multileaf collimator in radiotherapy treatments.

PURPOSE: To calculate absorbed doses due to neutrons in 87 organs/tissues for anthropomorphic phantoms, irradiated in position supine (head first into the gantry) with orientations anteroposterior (AP) and right-left (RLAT) with a 18 MV accelerator. Conversion factors from monitor units to µGy per neutron in organs, equivalent doses in organs/tissues, and effective doses, which permit to quantify stochastic risks, are estimated. METHODS: MAX06 and FAX06 phantoms were modeled with MCNPX and irradiated with a 18 MV Varian Clinac 2100C/D accelerator whose geometry included a multileaf collimator. Two actual fields of a pelvic treatment were simulated using electron-photon-neutron coupled transport. Absorbed doses due to neutrons were estimated from kerma. Equivalent doses were estimated using the radiation weighting factor corresponding to an average incident neutron energy 0.47 MeV. Statistical uncertainties associated to absorbed doses, as calculated by MCNPX, were also obtained. RESULTS: Largest doses were absorbed in shallowest (with respect to the neutron pathway) organs. In µGyMU(-1), values of 2.66 (for penis) and 2.33 (for testes) were found in MAX06, and 1.68 (for breasts), 1.05 (for lenses of eyes), and 0.94 (for sublingual salivary glands) in FAX06, in AP orientation. In RLAT, the largest doses were found for bone tissues (leg) just at the entrance of the beam in the body (right side in our case). Values, in µGyMU(-1), of 1.09 in upper leg bone right spongiosa, for MAX06, and 0.63 in mandible spongiosa, for FAX06, were found. Except for gonads, liver, and stomach wall, equivalent doses found for FAX06 were, in both orientations, higher than for MAX06. Equivalent doses in AP are higher than in RLAT for all organs/tissues other than brain and liver. Effective doses of 12.6 and 4.1 µSvMU(-1) were found for AP and RLAT, respectively. The organs/tissues with larger relative contributions to the effective dose were testes and breasts, in AP, and breasts and red marrow, in RLAT. Equivalent and effective doses obtained for MAX06/FAX06 were smaller (between 2 and 20 times) than those quoted for the mathematical phantoms ADAM/EVA in ICRP-74. CONCLUSIONS: The new calculations of conversion coefficients for neutron irradiation in AP and RLAT irradiation geometries show a reduction in the values of effective dose by factors 7 (AP) and 6 (RLAT) with respect to the old data obtained with mathematical phantoms. The existence of tissues or anatomical regions with maximum absorbed doses, such as penis, lens of eyes, fascia (part of connective tissue), etc., organs/tissues that classic mathematical phantoms did not include because they were not considered for the study of stochastic effects, has been revealed. Absorbed doses due to photons, obtained following the same simulation methodology, are larger than those due to neutrons, reaching values 100 times larger as the primary beam is approached. However, for organs far from the treated volume, absorbed photon doses can be up to three times smaller than neutron ones. Calculations using voxel phantoms permitted to know the organ dose conversion coefficients per MU due to secondary neutrons in the complete anatomy of a patient.

Specific absorbed fractions in thyroid diagnostics and treatment: Monte Carlo calculation with PENELOPE.

In nuclear medicine, diagnostic and therapy procedures in which a certain radiopharmaceutical is administered to a patient are performed. An important point is the determination of the dose absorbed by the important organs of the patient due to these procedures. This dose depends on the particular radionuclide used and the so-called specific absorbed fractions. In this work, by means of Monte Carlo (MC) simulation, the specific absorbed fractions in case the thyroid gland acts as a source organ and for photon energies between 30 keV and 2 MeV have been determined. The computer code PENELOPE has been used as well as the adult male mathematical phantom provided with the distribution of this code. Three different simulation types were carried out. In one of them, only photon transport was considered. In the other two, electron transport was included, doing a detailed and a mixed simulation. In general, the fractions were estimated with uncertainties <9 %, for the mixed and detailed simulations, and <3 %, for the simulation in which only photons are included. For some target organs and, especially for energies <100 keV, the uncertainties found were larger. The results obtained here have been compared with those obtained by other authors using other MC codes. A good agreement has been found in 80 % of the cases.

Ambient neutron dose equivalent outside concrete vault rooms for 15 and 18 MV radiotherapy accelerators.

In this work, the ambient dose equivalent, H*(10), due to neutrons outside three bunkers that house a 15- and a 18-MV Varian Clinac 2100C/D and a 15-MV Elekta Inor clinical linacs, has been calculated. The Monte Carlo code MCNPX (v. 2.5) has been used to simulate the neutron production and transport. The complete geometries including linacs and full installations have been built up according to the specifications of the manufacturers and the planes provided by the corresponding medical physical services of the hospitals where the three linacs operate. Two of these installations, those lodging the Varian linacs, have an entrance door to the bunker while the other one does not, although it has a maze with two bends. Various treatment orientations were simulated in order to establish plausible annual equivalent doses. Specifically anterior-posterior, posterior-anterior, left lateral, right lateral orientations and an additional one with the gantry rotated 30° have been studied. Significant dose rates have been found only behind the walls and the door of the bunker, near the entrance and the console, with a maximum of 12 µSv h(-1). Dose rates per year have been calculated assuming a conservative workload for the three facilities. The higher dose rates in the corresponding control areas were 799 µSv y(-1), in the case of the facility which operates the 15-MV Clinac, 159 µSv y(-1), for that with the 15-MV Elekta, and 21 µSv y(-1) for the facility housing the 18-MV Varian. A comparison with measurements performed in similar installations has been carried out and a reasonable agreement has been found. The results obtained indicate that the neutron contamination does not increase the doses above the legal limits and does not produce a significant enhancement of the dose equivalent calculated. When doses are below the detection limits provided by the measuring devices available today, MCNPX simulation provides an useful method to evaluate neutron dose equivalents based on a detailed description of linac, patient and bunker.

Thermal drift reduction with multiple bias current for MOSFET dosimeters.

New thermal compensation methods suitable for p-channel MOSFET (pMOS) dosimeters with the usual dose readout procedure based on a constant drain current are presented. Measuring the source-drain voltage shifts for two or three different drain currents and knowing the value of the zero-temperature coefficient drain current, I(ZTC), the thermal drift of source-drain or threshold voltages can be significantly reduced. Analytical expressions for the thermal compensation have been theoretically deduced on the basis of a linear dependence on temperature of the parameters involved. The proposed thermal modelling has been experimentally proven. These methods have been applied to a group of ten commercial pMOS transistors (3N163). The thermal coefficients of the source-drain voltage and the threshold voltage were reduced from -3.0 mV °C(-1), in the worst case, down to -70 µV °C(-1). This means a thermal drift of -2.4 mGy °C(-1) for the dosimeter. When analysing the thermal drifts of all the studied transistors, in the temperature range from 19 to 36 °C, uncertainty was obtained in the threshold voltage due to a thermal drift of ±9 mGy (2 SD), a commonly acceptable value in most radiotherapy treatments. The procedures described herein provide thermal drift reduction comparable to that of other technological or numerical strategies, but can be used in a very simple and low-cost dosimetry sensor.

Monte Carlo simulation of the dynamic micro-multileaf collimator of a LINAC Elekta Precise using PENELOPE.

Micro-multileaf collimators are devices that are added to LINAC heads for stereotactic radiosurgery. In this work, the performance of an Elekta Precise LINAC with a dynamic micro-multileaf collimator manufactured by 3D-line has been studied. Monte Carlo simulations based on PENELOPE code and measurements with three different detectors (PTW Semiflex 31010 chamber, PTW PinPoint 31016 chamber and PTW Diode 60008) have been carried out. Simulations were tuned by reproducing the experimental TPR(20, 10) quality index, providing a nice description of both the PDD curve and the transverse profiles at the two depths measured. The geometry of the micro-multileaf collimator was tested by calculating the transmission through it, and it was needed to significantly reduce the leaf separation indicated by the manufacturer to reproduce the experimental results. An approximate simulation in which the transport of the particles traversing the dynamic micro-multileaf collimator was described in a simplified way was analyzed, providing good agreement with the full simulations. With the MC model fixed, output factors for various field sizes were calculated and compared to the experimental ones, obtaining good agreement. Percentage depth doses (PDDs) and transverse profiles at two depths measured with the diode for small fields were well reproduced by the simulation, while the measurements performed with the PinPoint chamber showed differences in the PDDs, at large depths, and transverse profiles, at the penumbra. Monte Carlo simulations and Semiflex and diode measurements, performed for a 7.0 cm × 7.0 cm field, were in nice agreement, while those obtained with the PinPoint chamber showed differences that increased with the depth in water. At the phantom entrance, all measurements showed non-negligible differences that made Monte Carlo a good option to estimate the absorbed dose in this region.

Neutron dose equivalent and neutron spectra in tissue for clinical linacs operating at 15, 18 and 20 MV.

In this work, the dose equivalent due to photoneutrons and the neutron spectra in tissue was calculated for various linacs (Varian Clinac 2100C, Elekta Inor, Elekta SL25 and Siemens Mevatron KDS) operating at energies between 15 and 20 MV, using the Monte Carlo code MCNPX (v. 2.5). The dose equivalent in an ICRU tissue phantom has been calculated for anteroposterior treatments with a detailed simulation of the geometry of the linac head and the coupled electron-photon-neutron transport. Neutron spectra at the phantom entrance and at 1-cm depth in the phantom, depth distribution of the neutron fluence in the beam axis and dose distributions outside the beam axis at various depths have also been calculated and compared with previously published results. The differences between the neutron production of the various linacs considered has been analysed. Varian linacs show a larger neutron production than the Elekta and Siemens linacs at the same operating energy. The dose equivalent due to neutrons produced by medical linacs operating at energies >15 MeV is relevant and should not be neglected because of the additional doses that patients can receive.

Ant colony algorithm implementation in electron and photon Monte Carlo transport: application to the commissioning of radiosurgery photon beams.

PURPOSE: In this work, the authors describe an approach which has been developed to drive the application of different variance-reduction techniques to the Monte Carlo simulation of photon and electron transport in clinical accelerators. METHODS: The new approach considers the following techniques: Russian roulette, splitting, a modified version of the directional bremsstrahlung splitting, and the azimuthal particle redistribution. Their application is controlled by an ant colony algorithm based on an importance map. RESULTS: The procedure has been applied to radiosurgery beams. Specifically, the authors have calculated depth-dose profiles, off-axis ratios, and output factors, quantities usually considered in the commissioning of these beams. The agreement between Monte Carlo results and the corresponding measurements is within approximately 3%/0.3 mm for the central axis percentage depth dose and the dose profiles. The importance map generated in the calculation can be used to discuss simulation details in the different parts of the geometry in a simple way. The simulation CPU times are comparable to those needed within other approaches common in this field. CONCLUSIONS: The new approach is competitive with those previously used in this kind of problems (PSF generation or source models) and has some practical advantages that make it to be a good tool to simulate the radiation transport in problems where the quantities of interest are difficult to obtain because of low statistics.

A Monte Carlo tool to simulate breast cancer screening programmes.

A Monte Carlo tool which permits the simulation of screening mammography programmes is developed. Various statistical distributions describing different parameters involved in the problem are used: the characteristics of the population under study, a tumour growth model and a model for tumour detection based on parameters such as sensitivity and specificity which depends on the woman's age. We reproduce results of different actual programmes. The model enables us to find out the configuration (the age of the women who attend the screening trials and screening frequency) which produces maximum benefits with minimum risks. In addition, the model has permitted us to validate some of the assumed hypothesis, such as the probability distribution of the tumour detection as a function of the tumour size, the frequency of the histological types and the transition probability between different histological types.

Monte Carlo simulation using the PENELOPE code with an ant colony algorithm to study MOSFET detectors.

In this work we have developed a simulation tool, based on the PENELOPE code, to study the response of MOSFET devices to irradiation with high-energy photons. The energy deposited in the extremely thin silicon dioxide layer has been calculated. To reduce the statistical uncertainties, an ant colony algorithm has been implemented to drive the application of splitting and Russian roulette as variance reduction techniques. In this way, the uncertainty has been reduced by a factor of approximately 5, while the efficiency is increased by a factor of above 20. As an application, we have studied the dependence of the response of the pMOS transistor 3N163, used as a dosimeter, with the incidence angle of the radiation for three common photons sources used in radiotherapy: a (60)Co Theratron-780 and the 6 and 18 MV beams produced by a Mevatron KDS LINAC. Experimental and simulated results have been obtained for gantry angles of 0 degrees, 15 degrees, 30 degrees, 45 degrees, 60 degrees and 75 degrees. The agreement obtained has permitted validation of the simulation tool. We have studied how to reduce the angular dependence of the MOSFET response by using an additional encapsulation made of brass in the case of the two LINAC qualities considered.

Benchmark of penelope for low and medium energy X-rays.

The Monte Carlo code penelope is benchmarked for X-ray beams with energies between 30 and 300 keV. The results of different simulations performed with penelope are compared with those obtained with a semi-empirical computational model and with experimental measurements. Half-value layer indexes obtained from the attenuation curves for Al and Cu and depth dose curves in water have been considered for this comparison. A good agreement is reached on what guarantees the feasibility of the code.

Dose dependence of the growth rate of multicellular tumour spheroids after irradiation.

The present study investigated differences in the growth rate of multicellular tumour spheroids of the MCF-7 line of human breast cancer before and after their irradiation. Growth of the spheroids was analysed according to a model based on a Gompertz function. In this model, normalization to a common initial volume is achieved in a way that enables meaningful comparisons to be made between the results obtained for each spheroid. For irradiated spheroids the model includes an additional term to take account of sterilized cells. We found that the growth rate observed before irradiation is not fully recovered by irradiated spheroids and that growth recovery reduces with higher irradiation doses. Surviving fractions obtained at doses below 3 Gy are comparable with those found in clonogenic assays on spheroids of the same cellular line. At larger doses, discrepancies between the different studies are considerable.