The principles of Katz's cellular track structure radiobiological model

The cellular track structure theory (TST), introduced by Katz in 1968, applies the concept of action cross section as the probability of targets in the radiation detector being activated to elicit the observed endpoint (e.g. cell killing). The ion beam radiation field is specified by the charge Z, speed β (or energy), fluence and linear energy transfer (LET) of the ion, rather than by its total absorbed dose or dose-averaged LET. The detector is represented by radiosensitive elements of size a0 and radiosensitivity D0, its gamma-ray response being represented by c-hit or multi-target expressions rather than by the linear-quadratic formula. Key to TST is the Dδ(r) formula describing the radial distribution of delta-ray dose (RDD) around the ion path. This formula, when folded with the dose response of the detector and radially integrated, yields the 'point target' action cross section value, σPT. The averaged value of the cross section, σ, is obtained by radially integrating the a0-averaged RDD. In the 'track width' regime which may occur at the distal end of the ion's path, the value of σ may considerably exceed its geometrical value, [Formula: see text]. Several scaling principles are applied in TST, resulting in its simple analytic formulation. Multi-target detectors, such as cells, are represented in TST by m, D0, σ0 (the 'saturation value' of the cross section which replaces a0) and κ (a 'detector saturation index'), as the fourth model parameter. With increasing LET of the ion, the two-component formulation of TST allows for successive transition from shouldered survival curves at low LET values to exponential ones at radiobiological effectiveness (RBE) maximum, followed by 'thindown' at the end of the ion track. For a given cell line, having best-fitted the four model parameters (m, D0, σ0 and κ) to an available data set of measured survival curves, TST is able to quantitatively predict cell survival and RBE for this cell line after any other ion irradiation.

A TPS kernel for calculating survival vs. depth: distributions in a carbon radiotherapy beam, based on Katz's cellular Track Structure Theory

An algorithm was developed of a treatment planning system (TPS) kernel for carbon radiotherapy in which Katz's Track Structure Theory of cellular survival (TST) is applied as its radiobiology component. The physical beam model is based on available tabularised data, prepared by Monte Carlo simulations of a set of pristine carbon beams of different input energies. An optimisation tool developed for this purpose is used to find the composition of pristine carbon beams of input energies and fluences which delivers a pre-selected depth-dose distribution profile over the spread-out Bragg peak (SOBP) region. Using an extrapolation algorithm, energy-fluence spectra of the primary carbon ions and of all their secondary fragments are obtained over regular steps of beam depths. To obtain survival vs. depth distributions, the TST calculation is applied to the energy-fluence spectra of the mixed field of primary ions and of their secondary products at the given beam depths. Katz's TST offers a unique analytical and quantitative prediction of cell survival in such mixed ion fields. By optimising the pristine beam composition to a published depth-dose profile over the SOBP region of a carbon beam and using TST model parameters representing the survival of CHO (Chinese Hamster Ovary) cells in vitro, it was possible to satisfactorily reproduce a published data set of CHO cell survival vs. depth measurements after carbon ion irradiation. The authors also show by a TST calculation that 'biological dose' is neither linear nor additive.

A TL-based anthropomorphic benchmark for verifying 3-D dose distributions from external electron beams calculated by radiotherapy treatment planning systems

Initial results are reported of a Polish-Finnish project to verify electron dose distributions calculated by treatment planning systems (TPSs), CadPlan v.6.3.2 and Theraplan v.3.5, which use different electron beam dose distribution algorithms. Treatment of gross tumour volumes representing lung and parotid cancer was simulated in an Alderson anthropomorphic phantom with thermoluminescent detectors (TLDs) (Li(2)B(4)O(7):Mn,Si) placed at selected measurement points inside its volume. The observed discrepancy between relative values of dose calculated and measured by TLDs at each of the measurement points and those calculated by the different TPSs at the same points is discussed.

Two-dimensional thermoluminescence dosimetry using planar detectors and a TL reader with CCD camera readout

A novel method of determining two-dimensional (2-D) dose distributions is presented, using in-house developed, large-area (a few cm(2)) thermoluminescent (TL) detectors based on LiF powder plated on Al foil. An in-house developed planar large-area TL reader equipped with a coupled charge device (CCD) camera is used for readout, providing digital images of 2-D dose distributions on the surface of these large-area TL detectors. The capability of the newly developed system is demonstrated by mapping 2-D dose distributions around a brachytherapy source, at dose ranges and source geometries relevant for clinical radiotherapy. Examples of local and dynamic evaluation of TL output from conventional TL detectors are also shown.

On the relationship between dose-, energy- and LET-response of thermoluminescent detectors

Measurements of the response of thermoluminescent (TL) detectors after gamma ray doses high enough to observe signal saturation provide input to microdosimetric models which relate this gamma-ray response with the energy response after low doses of photons (gamma rays and low-energy X rays) and after high-LET irradiation. To measure their gamma ray response up to saturation, LiF:Mg,Ti (MTS-7 and MTT), LiF:Mg,Cu,P (MCP-7), CaSO4:Dy (KCD) and Al2O3:C detectors were irradiated with 60Co gamma rays over the range 1-5000 Gy. The X-ray photon energy response and TL efficiency (relative to gamma rays) after doses of beta rays and alpha particles, were also measured, for CaSO4:Dy and for Al2O3:C. Microdosimetric and track structure modelling was then applied to the experimental data. In a manner similar to LiF:Mg,Cu,P, the experimentally observed under response of alpha-Al2O3:C to X rays <100 keV, compared with cross-section calculations, is explained as a microdosimetric effect caused by the saturation of response of this detector without prior supralinearity (saturation of traps along the tracks). The enhanced X-ray photon energy response of CaSO4:Dy is related to the supralinearity observed in this material after high gamma ray doses, similarly to that in LiF:Mg,Ti. The discussed model approaches support the general rule relating dose-, energy- and ionisation density-responses in TL detectors: if their gamma ray response is sublinear prior to saturation, the measured photon energy response is lower, and if it is supralinear, it may be higher than that expected from the calculation of the interaction cross sections alone. Since similar rules have been found to apply to other solid-state detector systems, microdosimetry may offer a valuable contribution to solid-state dosimetry even prior to mechanistic explanations of physical phenomena in different TL detectors.

A simple track structure model of ion beam radiotherapy

A simple radiotherapy ion beam calculation based on the cellular track structure model, using in vitro cell survival parameters fitted from recent experimental data, is presented. The calculation represents a single-fraction ion exposure (roughly corresponding to a 2 Gy fraction of megavolt X rays) and exploits concepts used in clinical radiotherapy, such as entrance, or 'skin' ion dose. The depth distribution of cells surviving their irradiation by a beam of 385 MeV amu(-1) carbon ions is calculated over the range of the stopping ions, as a sequence of track-segments, in the continuous slowing-down approximation. An interpretation of the 'clinical relative biological effectiveness' concept is suggested.

New 2-D dosimetric technique for radiotherapy based on planar thermoluminescent detectors

At the Institute of Nuclear Physics of the Polish Academy of Sciences (IFJ) in Kraków, a two-dimensional (2-D) thermoluminescence (TL) dosimetry system was developed within the MAESTRO (Methods and Advanced Equipment for Simulation and Treatment in Radio-Oncology) 6 Framework Programme and tested by evaluating 2-D dose distributions around radioactive sources. A thermoluminescent detector (TLD) foil was developed, of thickness 0.3 mm and diameter 60 mm, containing a mixture of highly sensitive LiF:Mg,Cu,P powder and Ethylene TetraFluoroEthylene (ETFE) polymer. Foil detectors were irradiated with (226)Ra brachytherapy sources and a (90)Sr/(90)Y source. 2-D dose distributions were evaluated using a prototype planar (diameter 60 mm) reader, equipped with a 12 bit Charge Coupled Devices (CCD) PCO AG camera, with a resolution of 640 x 480 pixels. The new detectors, showing a spatial resolution better than 0.5 mm and a measurable dose range typical for radiotherapy, can find many applications in clinical dosimetry. Another technology applicable to clinical dosimetry, also developed at IFJ, is the Si microstrip detector of size 95 x 95 mm(2), which may be used to evaluate the dose distribution with a spatial resolution of 120 microm along one direction, in real-time mode. The microstrip and TLD technology will be further improved, especially to develop detectors of larger area, and to make them applicable to some advanced radiotherapy modalities, such as intensity modulated radiotherapy (IMRT) or proton radiotherapy.

Cellular parameters for track structure modeling of radiation hazard in space

Based on irradiation with 45 MeV/u N and B ions and with Co-60 gamma rays, cellular parameters of Katz's track structure model have been fitted for the survival of V79-379A Chinese hamster lung fibroblasts. Cellular parameters representing neoplastic transformations in C3H10T/1/2 cells after their irradiation with heavy ion beams, taken from earlier work, were also used to model the radiation hazard in deep space, following the system for evaluating, summing and reporting occupational exposures proposed in 1967 by a subcommittee of NCRP. We have performed model calculations of the number of transformations in surviving cells, after a given fluence of heavy charged particles of initial energy 500 MeV/u, penetrating thick layers of cells. We take the product of cell transformation and survival probabilities, calculated along the path lengths of charged particles using cellular survival and transformation parameters, to represent a quantity proportional to the "radiation risk factor" discussed in the NCRP document. The "synergistic" effect of simultaneous charged particle transfers is accounted for by the "track overlap" mode inherent in the model of Katz.

Microdosimetric one hit detector model for calculation of dose and energy response of some solid state detectors

A microdosimetric one hit detector model has been applied to calculate dose response, energy response and relative efficiency of thermoluminescent LiF:Mg,Cu,P (MCP-N), CaF2:Tm (TLD-300) and ESR alanine detectors on radiation of different qualities. For each detector type two model parameters, the target size and the saturation parameter, alpha, have been derived. Using those parameters and the microdosimetric distributions in nanometre size targets calculated using Monte Carlo track structure codes TRION and MOCA-14 it was possible to predict a great variety of experimental data for photons, X rays, beta electrons, protons, alpha particles and heavy ions. Due to a good reproducibility of experimental data some solid state detectors might be useful to test biophysical models of radiation action. Furthermore, these models can give some insight into the physics of radiation action in solid state detectors such as the range of charge interaction, energy levels etc.

On a model-based approach to radiation protection

There is a preoccupation with linearity and absorbed dose as the basic quantifiers of radiation hazard. An alternative is the fluence approach, whereby radiation hazard may be evaluated, at least in principle, via an appropriate action cross section. In order to compare these approaches, it may be useful to discuss them as quantitative descriptors of survival and transformation-like endpoints in cell cultures in vitro--a system thought to be relevant to modelling radiation hazard. If absorbed dose is used to quantify these biological endpoints, then non-linear dose-effect relations have to be described, and, e.g. after doses of densely ionising radiation, dose-correction factors as high as 20 are required. In the fluence approach only exponential effect-fluence relationships can be readily described. Neither approach alone exhausts the scope of experimentally observed dependences of effect on dose or fluence. Two-component models, incorporating a suitable mixture of the two approaches, are required. An example of such a model is the cellular track structure theory developed by Katz over thirty years ago. The practical consequences of modelling radiation hazard using this mixed two-component approach are discussed.

Validation of a radiotherapy treatment planning system using an anthropomorphic phantom and MTS-N thermoluminescent detectors

A treatment planning system (TPS) was validated in conditions of simulated radiotherapy (RT) of an anthropomorphic tissue-equivalent phantom. Individually calibrated solid MTS-N (LiF:Mg,Ti) detectors were placed within the treatment volume in this phantom which was then repeatedly irradiated by external 60Co or 6 MV X ray beams. On the basis of TLD-measured depth-dose curves for the two beams, the relative accuracy of determining dose (of the order of 1 Gy) at live depths in a water phantom is about 0.4-0.6%. In the volume of interest representing the target volume, the relative standard difference between the calculated and measured dose values ranged between 1.3% and 2.2% for the 60Co and 6 MV X ray beams, respectively. The TPS-calculated uniformity of irradiation of that volume is within 1%. While fraction-to-fraction repeatability was within 1-2%, systematic underexposure around the reference point, by 2-3%, was found in two consecutive exposures by sets of both beams.

CVD diamonds as thermoluminescent detectors for medical applications

Diamond is believed to be a promising material for medical dosimetry due to its tissue equivalence, mechanical and radiation hardness, and lack of solubility in water or in disinfecting agents. A number of diamond samples, obtained under different growth conditions at Limburg University, using the chemical vapour deposition (CVD) technique, was tested as thermoluminescence dosemeters. Their TL glow curve, TL response after doses of gamma rays, fading, and so on were studied at dose levels and for radiation modalities typical for radiotherapy. The investigated CVD diamonds displayed sensitivity comparable with that of MTS-N (Li:Mg,Ti) detectors, signal stability (reproducibility after several readouts) below 10% (1 SD) and no fading was found four days after irradiation. A dedicated CVD diamond plate was grown, cut into 20 detector chips (3 x 3 x 0.5 mm) and used for measuring the dose-depth distribution at different depths in a water phantom, for 60Co and six MV X ray radiotherapy beams. Due to the sensitivity of diamond to ambient light, it was difficult to achieve reproducibility comparable with that of standard LiF detectors.

Miniature thermoluminescent detectors for dosimetry in radiotherapy

At the Institute of Nuclear Physics in Kraków (INP), in collaboration with the Centre of Oncology in Kraków, several types of miniature thermoluminescent LiF:Mg,Ti and LiF:Mg,Cu,P detectors specially designed for clinical dosimetry in radiotherapy have been developed. The detectors are manufactured in the form of solid pellets of diameter down to 1 mm and typical thickness 0.5 mm, in the form of rods with a diameter of 0.5 mm and a length of a few mm, and as two-layer detectors with a thin (in the range of 0.065 mm) active layer of high-sensitive LiF:Mg,Cu,P. All three types of newly developed detectors have already been applied in proton beam dosimetry, surface dosimetry of eye-plaque brachytherapy applicators, phantom dosimetry for vascular brachytherapy and in vivo dosimetry in interstitial brachytherapy. These detectors were found to be very useful for dose measurements in high dose gradients, where spatial resolution better than 1 mm is required.