Erno Sajo

A stochastic model of cell survival for high‐Z nanoparticle radiotherapy

PURPOSE The authors present a stochastic framework for the assessment of cell survival in gold nanoparticle radiotherapy. METHODS The authors derive the equations for the effective macroscopic dose enhancement for a population of cells with nonideal distribution of gold nanoparticles (GNP), allowing different number of GNP per cell and different distances with respect to the cellular target. They use the mixed Poisson distribution formalism to model the impact of the aforementioned physical factors on the effective dose enhancement. RESULTS The authors show relatively large differences in the estimation of cell survival arising from using approximated formulae. They predict degeneration of the cell killing capacity due to different number of GNP per cell and different distances with respect to the cellular target. CONCLUSIONS The presented stochastic framework can be used in interpretation of experimental cell survival or tumor control probability studies.

Nanoscale radiation transport and clinical beam modeling for gold nanoparticle dose enhanced radiotherapy (GNPT) using X-rays

We review radiation transport and clinical beam modelling for gold nanoparticle dose-enhanced radiotherapy using X-rays. We focus on the nanoscale radiation transport and its relation to macroscopic dosimetry for monoenergetic and clinical beams. Among other aspects, we discuss Monte Carlo and deterministic methods and their applications to predicting dose enhancement using various metrics.

Deterministic photon transport calculations in general geometry for external beam radiation therapy.

A deterministic method is described for performing three-dimensional (3D) photon transport calculations of a LINAC head and phantom/patient geometry to obtain dose distributions for therapy planning. The space, energy, and directional-dependent photon flux density is obtained by numerically solving the Boltzmann equation in general 3D geometry using the method of characteristics. The deterministic transport calculations use similar ray tracing routines as found in Monte Carlo (MC) codes. A special treatment is developed to better represent the impact of scattering from accelerator head components. Equations are presented for computing the water kerma distribution due to the uncollided and collided photon flux density field in the patient region. Kerma results obtained from the deterministic computation are compared to Monte Carlo values for a variety of source spectra and field sizes. The agreement for kerma values in the beam is usually within the MC uncertainties. It is concluded that the deterministic method is a rigorous, first-principles approach that could provide a superior alternative to Monte Carlo calculations for some types of problems. However additional development is needed to provide capability for 3D electron transport calculations.

Targeted radiotherapy enhancement during electronic brachytherapy of accelerated partial breast irradiation (APBI) using controlled release of gold nanoparticles

Several studies have demonstrated low rates of local recurrence with brachytherapy-based accelerated partial breast irradiation (APBI). However, long-term outcomes on toxicity (e.g. telangiectasia) and cosmesis remain a major concern. The purpose of this study is to investigate the dosimetric feasibility of using targeted non-toxic radiosensitizing gold nanoparticles (GNPs) for localized dose enhancement to the planning target volume (PTV) during electronic brachytherapy APBI while reducing normal tissue toxicity. We propose to incorporate GNPs into a micrometer-thick polymer film on the surface of routinely used lumpectomy balloon applicators and provide subsequent treatment using a 50 kVp Xoft device. An experimentally determined diffusion coefficient was used to determine space-time customizable distribution of GNPs for feasible in-vivo concentrations of 7 mg/g and 43 mg/g. An analytical approach from previously published work was employed to estimate the dose enhancement due to GNPs as a function of distance up to 1 cm from the lumpectomy cavity surface. Clinically significant dose enhancement values of at least 1.2, due to 2 nm GNPs, were found at 1 cm away from the lumpectomy cavity wall when using electronic brachytherapy APBI. Higher customizable dose enhancement was also achieved at other distances as a function of nanoparticle size. Our preliminary results suggest that significant dose enhancement can be achieved to residual tumor cells targeted with GNPs during APBI with electronic brachytherapy.

Deterministic calculations of photon spectra for clinical accelerator targets

A method is proposed to compute photon energy spectra produced in clinical electron accelerator targets, based on the deterministic solution of the Boltzmann equation for coupled electron-photon transport in one-dimensional (1-D) slab geometry. It is shown that the deterministic method gives similar results as Monte Carlo calculations over the angular range of interest for therapy applications. Relative energy spectra computed by deterministic and 3-D Monte Carlo methods, respectively, are compared for several realistic target materials and different electron beams, and are found to give similar photon energy distributions and mean energies. The deterministic calculations typically require 1-2 mins of execution time on a Sun Workstation, compared to 2-36 h for the Monte Carlo runs.

Dosimetry intercomparison using a 35-keV x-ray synchrotron beam

The purpose of this study was to compare dose measurements using ion chamber and radiochromic film dosimetry for a 35-keV synchrotron beam useful for Auger electron therapy. A 1.3-GeV electron beam, transported through a 3-pole superconducting wiggler magnet, produced a polychromatic photon beam from which a 35-keV beam (3.3 mm Al HVL) was selected using a monochromator. A 2.8 cm x 2.5 cm field was produced by vertically oscillating a polymethylmethacrylate phantom in which dose to water was measured as a function of depth. Charge, measured using a 0.23-cm(3) cylindrical, air-equivalent ionization chamber, was converted to dose using American Association of Physicists in Medicine TG-61 protocol for 40-300 kV X-ray beam dosimetry with minor assumptions. Optical density of radiochromic film (Gafchromic EBT) was converted to dose using a 125 kVp X-ray beam (2.9 mm Al HVL) calibration curve. Fractional depth-dose curves measured using ion chamber and film agreed well with each other, the maximum difference being 4.5% at 8.85 cm. Both agreed well with that predicted by MCNP5 Monte Carlo calculations. At 2.0-cm depth, film doses from five independent measurements predicted 0.952+/-0.022 of dose measured using the ion chamber. Dose measurements using two independent methods, ionization chamber and radiochromic film dosimetry, showed good agreement and should be suitable for future dosimetry necessary for cell and small animal irradiations. Improving agreement will require additional investigations of methods for converting ionization and film optical density to dose.

Comparison of measured and calculated neutron transmission through steel for a 252Cf source

Abstract The ENDF/B-VI evaluated nuclear data file, recently released by the U.S. National Nuclear Data Center, contains several improvements over earlier ENDF/B-IV and ENDF/B-V evaluations which are known to overestimate the iron inelastic cross sections in the energy interval above 1.0 MeV. In order to benchmark the ENDF/B-VI iron data, in this paper a comparison is made of calculated vs measured neutron leakage spectra obtained for a 252 Cf fission source located at the center of an iron sphere. In addition, various response parameters that are sensitive to high-energy neutrons are examined. It is found that although the ENDF/B-VI cross sections substantially improve the computed neutron transmission relative to ENDF/B-V results, the differential energy spectrum obtained using ENDF/B-VI above 1.0 MeV is generally lower than that of the measurements. However, the integrated flux above the 1 MeV threshold is within the experimental uncertainty. The results appear to indicate that the ENDF/B-VI cross sections will not entirely resolve the spectrum discrepancies observed at high neutron energies.

Potential of using cerium oxide nanoparticles for protecting healthy tissue during accelerated partial breast irradiation (APBI)

The purpose of this study is to investigate the feasibility of using cerium oxide nanoparticles (CONPs) as radical scavengers during accelerated partial breast irradiation (APBI) to protect normal tissue. We hypothesize that CONPs can be slowly released from the routinely used APBI balloon applicators-via a degradable coating-and protect the normal tissue on the border of the lumpectomy cavity over the duration of APBI. To assess the feasibility of this approach, we analytically calculated the initial concentration of CONPs required to protect normal breast tissue from reactive oxygen species (ROS) and the time required for the particles to diffuse to various distances from the lumpectomy wall. Given that cerium has a high atomic number, we took into account the possible inadvertent dose enhancement that could occur due to the photoelectric interactions with radiotherapy photons. To protect against a typical MammoSite treatment fraction of 3.4Gy, 5ng·g(-1) of CONPs is required to scavenge hydroxyl radicals and hydrogen peroxide. Using 2nm sized NPs, with an initial concentration of 1mg·g(-1), we found that 2-10days of diffusion is required to obtain desired concentrations of CONPs in regions 1-2cm away from the lumpectomy wall. The resultant dose enhancement factor (DEF) is less than 1.01 under such conditions. Our results predict that CONPs can be employed for radioprotection during APBI using a new design in which balloon applicators are coated with the NPs for sustained/controlled in-situ release from within the lumpectomy cavity.

Kilovoltage radiosurgery with gold nanoparticles for neovascular age-related macular degeneration (AMD): a Monte Carlo evaluation.

This work uses Monte Carlo radiation transport simulation to assess the potential benefits of gold nanoparticles (AuNP) in the treatment of neovascular age-related macular degeneration with stereotactic radiosurgery. Clinically, a 100 kVp x-ray beam of 4 mm diameter is aimed at the macula to deliver an ablative dose in a single fraction. In the transport model, AuNP accumulated at the bottom of the macula are targeted with a source representative of the clinical beam in order to provide enhanced dose to the diseased macular endothelial cells. It is observed that, because of the AuNP, the dose to the endothelial cells can be significantly enhanced, allowing for greater sparing of optic nerve, retina and other neighboring healthy tissue. For 20 nm diameter AuNP concentration of 32 mg g(-1), which has been shown to be achievable in vivo, a dose enhancement ratio (DER) of 1.97 was found to be possible, which could potentially be increased through appropriate optimization of beam quality and/or AuNP targeting. A significant enhancement in dose is seen in the vicinity of the AuNP layer within 30 μm, peaked at the AuNP-tissue interface. Different angular tilting of the 4 mm beam results in a similar enhancement. The DER inside and in the penumbra of the 4 mm irradiation-field are almost the same while the actual delivered dose is more than one order of magnitude lower outside the field leading to normal tissue sparing. The prescribed dose to macular endothelial cells can be delivered using almost half of the radiation allowing reduction of dose to the neighboring organs such as retina/optic nerve by 49% when compared to a treatment without AuNP.

Angular dose anisotropy around gold nanoparticles exposed to X-rays

Gold nanoparticle (GNP) radiotherapy has recently emerged as a promising modality in cancer treatment. The use of high atomic number nanoparticles can lead to enhanced radiation dose in tumors due to low-energy leakage electrons depositing in the vicinity of the GNP. A single metric, the dose enhancement ratio has been used in the literature, often in substantial disagreement, to quantify the GNPs capacity to increase local energy deposition. This 1D approach neglects known sources of dose anisotropy and assumes that one average value is representative of the dose enhancement. Whether this assumption is correct and within what accuracy limits it could be trusted, have not been studied due to computational difficulties at the nanoscale. Using a next-generation deterministic computational method, we show that significant dose anisotropy exists which may have radiobiological consequences, and can impact the treatment outcome as well as the development of treatment planning computational methods.