The elimination of an artifact in the FLURZnrc-derived electron-fluence spectrum close to the Spencer-Attix-Nahum cut-offΔ.

Objective. An artifact in the electron fluence, differential in energy,ΦE, computed by the EGSnrc Monte-Carlo user-code FLURZnrc, was identified and a methodology has been developed to eliminate it. This artifact manifests itself as an 'unphysical' increase inΦEat energies close to the production threshold for knock-on electrons,AE; this in turn causes an over-estimation of the Spencer-Attix-Nahum (SAN) 'track-end' dose by a factor ∼1.5, thereby inflating the dose derived from the SAN cavity integral. For SAN cut-offΔSAN =1 keV for 1 MeV and 10 MeV photons in water, aluminium and copper, withmaximum fractional energy loss per step ESTEPE= 0.25 (default value), this anomalous increase in the SAN cavity-integral dose is of the order of 0.5%-0.7%.Approach. The dependence ofΦEon the value ofAE(the maximum energy loss involved in the restricted electronic stopping power (dE/ds)AE) at or close toΔSANwas investigated; this was done for different values ofESTEPE.Main results.The error in the electron-fluence spectrum occurs whenΔSANis setclose toorequal to AE; this error disappears (at the 0.1% level or better) ifAEis set ≤ 0.5 ×ΔSAN. However, ifESTEPE≤ 0.04 the error in the electron-fluence spectrum is negligible even whenΔSAN=AE.Significance. An artifact in the FLURZnrc-derived electron fluence, differential in energy, at or close to electron energyAEhas been identified. It is shown how this artifact can be avoided, thereby ensuring the accurate evaluation of the SAN cavity integral.

Analysis of tumour dose-response data from animal experiments via two TCP models accounting for tumor hypoxia and resensitization.

To treat animal dose-response data exhibiting inverse dose-response behavior with two tumor control probability (TCP) models accounting for tumor hypoxia and re-oxygenation leading to resensitization of the tumor. One of the tested TCP models uses a modified linear-quadratic (LQ) model of cell survival where both α and ß radiosensitivities increase in time during the treatment due to re-oxygenation of the hypoxic tumor sub-population. The other TCP model deals with two types of hypoxia-chronic and acute-and accounts for tumor re-sensitization via oxygenation of the chronically hypoxic and fluctuating oxygenation of the acutely hypoxic sub-populations. The two models are fit using the maximum likelihood method to the data of Fowler et al. on mice mammary tumors irradiated to different doses using different fractionated schedules. These data are chosen since as many as five of the dose-response curves show an inverse dose behavior, which is interpreted as due to re-sensitization. The p-values of the fits of both models to the data render them statistically acceptable. A performed comparison test shows that both models describe the data equally well. It is also demonstrated that the most sensitive (oxic) tumor component has no impact on the treatment outcome. The ability of the tested models to predict and describe the impact of re-sensitization on the treatment outcome is thus proven. It is also demonstrated that prolonged treatment schedules can be more beneficial than shorter ones. However, this may be true only for schedules with small number of fractions, i.e. for hypo-fractionated treatments only.

The Impact of Different Timing Schedules on Prostate HDR-Mono-Brachytherapy. A TCP Modeling Investigation.

BACKGROUND: Mechanistic TCP (tumor control probability) models exist that account for possible re-sensitization of an initially hypoxic tumor during treatment. This phenomenon potentially explains the better outcome of a 28-day vs 14-day treatment schedule of HDR (high dose rate) brachytherapy of low- to intermediate-risk prostate cancer as recently reported. METHODS: A TCP model accounting for tumor re-sensitization developed earlier is used to analyze the reported clinical data. In order to analyze clinical data using individual TCP model, TCP distributions are constructed assuming inter-individual spread in radio-sensitivity. RESULTS: Population radio-sensitivity parameter values are found that result in TCP population values which are close to the reported ones. Using the estimated population parameters, two hypothetical regimens are investigated that are shorter than the ones used clinically. The impact of the re-sensitization rate on the calculated treatment outcome is also investigated as is the anti-hypothesis that there is no re-sensitization during treatment. CONCLUSIONS: The carried out investigation shows that the observed clinical data cannot be described without assuming an initially hypoxic state of the tumor followed by re-oxygenation and, hence, re-sensitization. This phenomenon explains the better outcome of the prolonged treatment schedule compared to shorter regimens based on the fact that prostate cancer is a slowly repopulating tumor.

Theoretical investigation of the impact of different timing schemes in hypofractionated radiotherapy.

PURPOSE: This study compares the effectiveness of three fractionation schemes of equal fraction size, comprising five fractions of SBRT over 5 days, 10 days, or 15 days, respectively. METHOD: This comparative study is based on two tumor-control-probability (TCP) models that take into account tumor cell re-sensitization and repopulation during treatment; the Zaider-Minerbo-Stavreva (ZMS) and the Ruggieri-Nahum (RN) models. The ZMS model is further modified to include also re-sensitization according to the ß mechanism of the linear-quadratic (LQ) model of cell killing. The modified version of the ZMS model is verified through fitting to the experimental data set of Fisher and Moulder. The study applies an idea used in a plan ranking methodology developed for the case when the specific values of the model parameters are not known. RESULTS: The TCPs of the compared regimens are calculated for various values of the model parameters and for two different values of the dose per fraction. The TCPs are presented as 2-D functions of two of the model parameters for each model correspondingly. The differences between the TCPs of each of the prolonged regimens and the TCP of the every week day regimen are also calculated for each model. CONCLUSIONS: Both models predict that the prolonged regimens are superior in terms of TCP to the every week-day one for most of the studied cases; however this is shown to exist to a different degree by the two models. It is shown again to a different degree that reversed situations where the every week day schedule is better than the prolonged regimens are also possible. It is concluded that a 30% TCP difference observed in a clinical study in favor of the fifteen-day regimen is theoretically possible. However, the fifteen-day regimen is outperformed in terms of TCP by the every week day regimen in more cases than the regimen lasting ten days. Therefore the choice of a prolongation in time must be made with care.

Analysis of a cohort of prostate patients treated with HDR mono-brachytherapy.

The aim of this study is to perform volumetric and basic radiobiological analyses using the database on prostate patients treated by HDR brachytherapy in our institution during the period 2011-2016. Real-time ultrasound based technique was used, with Oncentra Prostate planning software. The whole period was divided into two sub-periods, according to the 100% dose per fraction, which was 10.5 Gy during the first period (2011-2012), and 11 Gy during the second period (2013-2016), for each of the three fractions. The follow up time varied from 19 to 81 months, with a median of 45 months and a mean of 47 months. The uniformity of the treatment technique for both periods is investigated. Tumour Control Probability (TCP) values for the expected local control are calculated according to a population phenomenological TCP model for different values of the α/ß ratio. The calculations are based on the obtained averaged Dose Volume Histograms for the two investigated sub-periods. 74 patients were treated in total. Local control failure is observed in 5 cases, which corresponds to an observed TCP = 93.2%. The comparison of the calculated population average DVH with the DVHs of the cases with local control failure shows that in 4 of them, doses higher than average were delivered to the prostate. It is shown that the uniformity of the treatment was improved during the second sub-period. A possible explanation of the observed failures may be that these cases exhibit inherent tumour cell radio-resistance higher than average. Our radiobiological analysis indicates a α/ß ratio value somewhat higher than the one currently accepted. The value of the prostate α/ß ratio is estimated to be in the range of [3.5-6] Gy.

Tumor Control Probability Modeling and Systematic Review of the Literature of Stereotactic Body Radiation Therapy for Prostate Cancer.

PURPOSE: Dose escalation improves localized prostate cancer disease control, and moderately hypofractionated external beam radiation is noninferior to conventional fractionation. The evolving treatment approach of ultrahypofractionation with stereotactic body radiation therapy (SBRT) allows possible further biological dose escalation (biologically equivalent dose [BED]) and shortened treatment time. METHODS AND MATERIALS: The American Association of Physicists in Medicine Working Group on Biological Effects of Hypofractionated Radiation Therapy/SBRT included a subgroup to study the prostate tumor control probability (TCP) with SBRT. We performed a systematic review of the available literature and created a dose-response TCP model for the endpoint of freedom from biochemical relapse. Results were stratified by prostate cancer risk group. RESULTS: Twenty-five published cohorts were identified for inclusion, with a total of 4821 patients (2235 with low-risk, 1894 with intermediate-risk, and 446 with high-risk disease, when reported) treated with a variety of dose/fractionation schemes, permitting dose-response modeling. Five studies had a median follow-up of more than 5 years. Dosing regimens ranged from 32 to 50 Gy in 4 to 5 fractions, with total BED (α/ß = 1.5 Gy) between 183.1 and 383.3 Gy. At 5 years, we found that in patients with low-intermediate risk disease, an equivalent doses of 2 Gy per fraction (EQD2) of 71 Gy (31.7 Gy in 5 fractions) achieved a TCP of 90% and an EQD2 of 90 Gy (36.1 Gy in 5 fractions) achieved a TCP of 95%. In patients with high-risk disease, an EQD2 of 97 Gy (37.6 Gy in 5 fractions) can achieve a TCP of 90% and an EQD2 of 102 Gy (38.7 Gy in 5 fractions) can achieve a TCP of 95%. CONCLUSIONS: We found significant variation in the published literature on target delineation, margins used, dose/fractionation, and treatment schedule. Despite this variation, TCP was excellent. Most prescription doses range from 35 to 40 Gy, delivered in 4 to 5 fractions. The literature did not provide detailed dose-volume data, and our dosimetric analysis was constrained to prescription doses. There are many areas in need of continued research as SBRT continues to evolve as a treatment modality for prostate cancer, including the durability of local control with longer follow-up across risk groups, the efficacy and safety of SBRT as a boost to intensity modulated radiation therapy (IMRT), and the impact of incorporating novel imaging techniques into treatment planning.

Monte-Carlo-computed dose, kerma and fluence distributions in heterogeneous slab geometries irradiated by small megavoltage photon fields.

Small-field dosimetry is central to the planning and delivery of radiotherapy to patients with cancer. Small-field dosimetry is beset by complex issues, such as loss of charged-particle equilibrium (CPE), source occlusion and electron-scattering effects in low-density tissues. The purpose of the present research is the elucidation of the fundamental physics of small fields through the computation of absorbed dose, kerma and fluence distributions in heterogeneous media using the Monte-Carlo (MC) method. Absorbed dose and kerma were computed using the DOSRZnrc MC user-code for beams with square field sizes ranging from 0.25 × 0.25 to 7 × 7 cm2 (for 6 MV 'full linac' geometry) and 0.25 × 0.25 to 16 × 16 cm2 (for 15 MV 'full linac' geometry). In the bone inhomogeneity the dose increases (vs. homogeneous water) for field sizes <1 × 1 cm2 at 6 MV and ⩽3 × 3 cm2 at 15 MV and decreases (vs. homogeneous water) for field sizes ⩾3 × 3 cm2 at 6 MV and ⩾5 × 5 cm2 at 15 MV. In the lung inhomogeneity there is negligible decrease in dose compared to in uniform water for field sizes >5 × 5 cm2 at 6 MV and ⩾16 × 16 cm2 at 15 MV, consistent with the Fano theorem. The near-unity value of the absorbed-dose to collision-kerma ratio, D/K col, at the centre of the bone and lung slabs in the heterogeneous phantom demonstrates that CPE is achieved in bone for field sizes >1 × 1 cm2 at 6 MV and ⩾5 × 5 cm2 at 15 MV; CPE is achieved in lung at field sizes >5 × 5 cm2 at 6 MV and ⩾16 × 16 cm2 at 15 MV. Electron-fluence perturbation factors for the 0.25 × 0.25 cm2 field were 1.231 and 1.403 for bone-to-water and 0.454 and 0.333 for lung-to-water at 6 and 15 MV, respectively. For field sizes large enough for quasi-CPE, the MC-derived dose-perturbation factors, lung-to-water, [Formula: see text] were close to unity; electron-fluence perturbation factors, lung-to-water, [Formula: see text] were ∼1.0, consistent with the Fano theorem. At 15 MV in the lung inhomogeneity the magnitude and also the 'shape' of the primary electron-fluence spectrum differ significantly from that in water. Beam penumbrae relative to water are narrower in the bone inhomogeneity and broader in the lung inhomogeneity for all field sizes.

Modelling the effect of spread in radiosensitivity parameters and repopulation rate on the probability of tumour control.

PURPOSE: To investigate the impact of a variable inter-individual spread in the tumour cell radiosensitivity and repopulation rate on the tumour control probability (TCP). METHODS: The radiosensitivity parameters and the repopulation rate are presumed to be log-normally distributed among the population. Corresponding distributions of TCP across the population are built using a Monte-Carlo simulation algorithm. An analytical formula for the TCP distribution is derived for the case of variability in radiosensitivity only and found to be in excellent agreement with the corresponding Monte-Carlo simulations. RESULTS AND CONCLUSIONS: It is found that a large variation in individual-patient radiosensitivity results in a dichotomous TCP distribution over the population. In general, the form and width of the TCP distribution depend on the variation in the radiosensitivity. Accounting for tumour repopulation and its variability leads to lower TCP values as expected. It is shown that for a standard fractionation regimen resulting in a population TCP of almost zero, a simple change of the regimen to a hypofractionated one (i.e. typical of SBRT), a decrease in the physical dose is possible such that a beneficial tumour treatment outcome can be still achieved. The reduction in dose will in turn reduce eventual adverse effects caused in the surrounding healthy tissues. This theoretical finding is supported by the increasing amount of clinical evidence for the efficacy of SBRT. The desirability of a pre-clinical independent estimation of the individual radiosensitivity is emphasised.

Investigation of the effect of natural tumor cell death on radiotherapy outcomes.

The aim of the work is to investigate the impact of radiation-independent (natural or spontaneous) tumor cell death on tumor control probability (TCP) during and following fractionated external-beam radiotherapy employing both analytical and numerical methods. The analytical method solves a TCP model accounting for tumor repopulation and non-radiation tumor cell death during fractionated external-beam radiotherapy. The numerical method is based on a Monte Carlo simulation of the processes of radiation-induced cell kill, as well as cell division and natural cell death randomly taking place in the time interval between fractions. Distributions of the number of surviving cells are constructed using the Monte Carlo method for cases with and without natural cell death. The analytically and numerically calculated values of TCP were found to be in excellent agreement (as shown in the Method and materials section), thereby validating both methods. The TCP model is then fitted to two different experimental data sets with the aim of determining the model parameter values, primarily the natural death rate. Two versions of the linear-quadratic model of cell damage-with and without assumed re-sensitization of the tumor cells during treatment-are used. In two of the fits a strong correlation between the repopulation and spontaneous cell death rates is observed. It was possible to determine separately the values of the two rates only in the fit of the model with resensitization to the most diversified data set consisting of seven different fractionation regimes. The observed correlation together with a theoretical consideration leads to the conclusion that in most cases it is the net effect of the two processes of birth and death rather than the processes separately that determines treatment outcome. However, depending on the values of the rates of the two processes and the duration of the treatment, the treatment outcome may be more accurately determined by the absolute values of the two rates rather than just by their difference.

Origins of the changing detector response in small megavoltage photon radiation fields.

Differences in detector response between measured small fields, f clin, and wider reference fields, f msr , can be overcome by using correction factors [Formula: see text] or by designing detectors with field-size invariant responses. The changing response in small fields is caused by perturbations of the electron fluence within the detector sensitive volume. For solid-state detectors, it has recently been suggested that these perturbations might be caused by the non-water-equivalent effective atomic numbers Z of detector materials, rather than by their non-water-like densities. Using the EGSnrc Monte Carlo code we have analyzed the response of a PTW 60017 diode detector in a 6 MV beam, calculating the [Formula: see text] correction factor from computed doses absorbed by water and by the detector sensitive volume in 0.5 × 0.5 and 4 × 4 cm2 fields. In addition to the 'real' detector, fully modelled according to the manufacturer's blue-prints, we calculated doses and [Formula: see text] factors for a 'Z → water' detector variant in which mass stopping-powers and microscopic interaction coefficients were set to those of water while preserving real material densities, and for a 'density → 1' variant in which densities were set to 1 g cm-3, leaving mass stopping-powers and interaction coefficients at real levels. [Formula: see text] equalled 0.910 ± 0.005 (2 standard deviations) for the real detector, was insignificantly different at 0.912 ± 0.005 for the 'Z → H2O' variant, but equalled 1.012 ± 0.006 for the 'density → 1' variant. For the 60017 diode in a 6 MV beam, then, [Formula: see text] was determined primarily by the detector's density rather than its atomic composition. Further calculations showed this remained the case in a 15 MV beam. Interestingly, the sensitive volume electron fluence was perturbed more by detector atomic composition than by density; however, the density-dependent perturbation varied with field-size, whereas the Z-dependent perturbation was relatively constant, little affecting [Formula: see text].

Optimal dose and fraction number in SBRT of lung tumours: A radiobiological analysis.

The efficacy of Stereotactic Body Radiation Therapy (SBRT) in early-stage non-small cell lung cancer for severely hypofractionated schedules is clinically proven. Tumour control probability (TCP) modelling might further optimize prescription dose and number of treatment fractions (n). To this end, we will discuss the following controversial questions. Which is the most plausible cell-survival model at doses per fraction (d) as high as 20Gy? Do clinical data support a dose-response relationship with saturation over some threshold-dose? Given the reduced re-oxygenation for severe hypofractionation, is the inclusion of tumour hypoxia in TCP modelling relevant? Can iso-effective schedules be derived by assuming a homogeneous tumour-cell population with α/ß≈10Gy, or should distinct cell subpopulations, with different α/ß values, be taken into account? Is there scope for patient-specific individualization of n? Despite the difficulty of providing definite answers to the above questions, reasonable suggestions for lung SBRT can be derived from the literature. The LQ model appears to be the best-fitting model of cell-survival even at such large d, and is therefore the preferred choice for TCP modelling. TCP increases with dose, reaching saturation above 90% local control, but there is still uncertainty on the threshold-dose. In silico simulations accounting for variations in tumour oxygenation are consistent with an improved therapeutic ratio at 5-8 fractions instead of the current 3-fraction reference schedules. Tumour hypoxia modelling might also explain how α/ß changes with n, identifying the clonogen subpopulation which determines tumour response. Finally, an optimal patient-specific n can be derived from the planned lung dose distribution.

Fast and high temperature hyperthermia coupled with radiotherapy as a possible new treatment for glioblastoma.

BACKGROUND: A new transcranial focused ultrasound device has been developed that can induce hyperthermia in a large tissue volume. The purpose of this work is to investigate theoretically how glioblastoma multiforme (GBM) can be effectively treated by combining the fast hyperthermia generated by this focused ultrasound device with external beam radiotherapy. METHODS/DESIGN: To investigate the effect of tumor growth, we have developed a mathematical description of GBM proliferation and diffusion in the context of reaction-diffusion theory. In addition, we have formulated equations describing the impact of radiotherapy and heat on GBM in the reaction-diffusion equation, including tumor regrowth by stem cells. This formulation has been used to predict the effectiveness of the combination treatment for a realistic focused ultrasound heating scenario. Our results show that patient survival could be significantly improved by this combined treatment modality. DISCUSSION: High priority should be given to experiments to validate the therapeutic benefit predicted by our model.

Modelling the radiotherapy effect in the reaction-diffusion equation.

PURPOSE: In recent years, the reaction-diffusion (Fisher-Kolmogorov) equation has received much attention from the oncology research community due to its ability to describe the infiltrating nature of glioblastoma multiforme and its extraordinary resistance to any type of therapy. However, in a number of previous papers in the literature on applications of this equation, the term (R) expressing the 'External Radiotherapy effect' was incorrectly derived. In this note we derive an analytical expression for this term in the correct form to be included in the reaction-diffusion equation. METHODS: The R term has been derived starting from the Linear-Quadratic theory of cell killing by ionizing radiation. The correct definition of R was adopted and the basic principles of differential calculus applied. RESULTS: The compatibility of the R term derived here with the reaction-diffusion equation was demonstrated. Referring to a typical glioblastoma tumour, we have compared the results obtained using our expression for the R term with the 'incorrect' expression proposed by other authors.

Impact of microscopic disease extension, extra-CTV tumour islets, incidental dose and dose conformity on tumour control probability.

The impact of microscopic disease extension (MDE), extra-CTV tumour islets (TIs), incidental dose and dose conformity on tumour control probability (TCP) is analyzed using insilico simulations in this study. MDE in the region in between GTV and CTV is simulated inclusive of geometric uncertainties (GE) using spherical targets and spherical dose distribution. To study the effect of incidental dose on TIs and the effect of dose-response curve (DRC) on tumour control, islets were randomly distributed and TCP was calculated for various dose levels by rescaling the dose. Further, the impact of dose conformity on required PTV margins is also studied. The required PTV margins are ~2 mm lesser than assuming a uniform clonogen density if an exponential clonogen density fall off in the GTV-CTV is assumed. However, margins are almost equal if GE is higher in both cases. This shows that GE has a profound impact on margins. The effect of TIs showed a bi-phasic relation with increasing dose, indicating that patients with islets not in the beam paths do not benefit from dose escalation. Increasing dose conformity is also found to have considerable effect on TCP loss especially for larger GE. Further, smaller margins in IGRT should be used with caution where uncertainty in CTV definition is of concern.

Dosimetric response of variable-size cavities in photon-irradiated media and the behaviour of the Spencer-Attix cavity integral with increasing Δ.

Cavity theory is fundamental to understanding and predicting dosimeter response. Conventional cavity theories have been shown to be consistent with one another by deriving the electron (+positron) and photon fluence spectra with the FLURZnrc user-code (EGSnrc Monte-Carlo system) in large volumes under quasi-CPE for photon beams of 1 MeV and 10 MeV in three materials (water, aluminium and copper) and then using these fluence spectra to evaluate and then inter-compare the Bragg-Gray, Spencer-Attix and 'large photon' 'cavity integrals'. The behaviour of the 'Spencer-Attix dose' (aka restricted cema), D S-A(▵), in a 1-MeV photon field in water has been investigated for a wide range of values of the cavity-size parameter ▵: D S-A(▵) decreases far below the Monte-Carlo dose (D MC) for ▵ greater than ≈ 30 keV due to secondary electrons with starting energies below ▵ not being 'counted'. We show that for a quasi-scatter-free geometry (D S-A(▵)/D MC) is closely equal to the proportion of energy transferred to Compton electrons with initial (kinetic) energies above ▵, derived from the Klein-Nishina (K-N) differential cross section. (D S-A(▵)/D MC) can be used to estimate the maximum size of a detector behaving as a Bragg-Gray cavity in a photon-irradiated medium as a function of photon-beam quality (under quasi CPE) e.g. a typical air-filled ion chamber is 'Bragg-Gray' at (monoenergetic) beam energies ⩾260 keV. Finally, by varying the density of a silicon cavity (of 2.26 mm diameter and 2.0 mm thickness) in water, the response of different cavity 'sizes' was simulated; the Monte-Carlo-derived ratio D w/D Si for 6 MV and 15 MV photons varied from very close to the Spencer-Attix value at 'gas' densities, agreed well with Burlin cavity theory as ρ increased, and approached large photon behaviour for ρ ≈ 10 g cm(-3). The estimate of ▵ for the Si cavity was improved by incorporating a Monte-Carlo-derived correction for electron 'detours'. Excellent agreement was obtained between the Burlin 'd' factor for the Si cavity and D S-A(▵)/D MC at different (detour-corrected) ▵, thereby suggesting a further application for the D S-A(▵)/D MC ratio.

Secondary bremsstrahlung and the energy-conservation aspects of kerma in photon-irradiated media.

Kerma, collision kerma and absorbed dose in media irradiated by megavoltage photons are analysed with respect to energy conservation. The user-code DOSRZnrc was employed to compute absorbed dose D, kerma K and a special form of kerma, K ncpt, obtained by setting the charged-particle transport energy cut-off very high, thereby preventing the generation of 'secondary bremsstrahlung' along the charged-particle paths. The user-code FLURZnrc was employed to compute photon fluence, differential in energy, from which collision kerma, K col and K were derived. The ratios K/D, K ncpt/D and K col/D have thereby been determined over a very large volumes of water, aluminium and copper irradiated by broad, parallel beams of 0.1 to 25 MeV monoenergetic photons, and 6, 10 and 15 MV 'clinical' radiotherapy qualities. Concerning depth-dependence, the 'area under the kerma, K, curve' exceeded that under the dose curve, demonstrating that kerma does not conserve energy when computed over a large volume. This is due to the 'double counting' of the energy of the secondary bremsstrahlung photons, this energy being (implicitly) included in the kerma 'liberated' in the irradiated medium, at the same time as this secondary bremsstrahlung is included in the photon fluence which gives rise to kerma elsewhere in the medium. For 25 MeV photons this 'violation' amounts to 8.6%, 14.2% and 25.5% in large volumes of water, aluminium and copper respectively but only 0.6% for a 'clinical' 6 MV beam in water. By contrast, K col/D and K ncpt/D, also computed over very large phantoms of the same three media, for the same beam qualities, are equal to unity within (very low) statistical uncertainties, demonstrating that collision kerma and the special type of kerma, K ncpt, do conserve energy over a large volume. A comparison of photon fluence spectra for the 25 MeV beam at a depth of ≈51 g cm−2 for both very high and very low charged-particle transport cut-offs reveals the considerable contribution to the total photon fluence by secondary bremsstrahlung in the latter case. Finally, a correction to the 'kerma integral' has been formulated to account for the energy transferred to charged particles by photons with initial energies below the Monte-Carlo photon transport cut-off PCUT; for 25 MeV photons this 'photon track end' correction is negligible for all PCUT below 10 keV.

Breakdown of Bragg-Gray behaviour for low-density detectors under electronic disequilibrium conditions in small megavoltage photon fields.

In small photon fields ionisation chambers can exhibit large deviations from Bragg-Gray behaviour; the EGSnrc Monte Carlo (MC) code system has been employed to investigate this 'Bragg-Gray breakdown'. The total electron (+positron) fluence in small water and air cavities in a water phantom has been computed for a full linac beam model as well as for a point source spectrum for 6 MV and 15 MV qualities for field sizes from 0.25 × 0.25 cm(2) to 10 × 10 cm(2). A water-to-air perturbation factor has been derived as the ratio of total electron (+positron) fluence, integrated over all energies, in a tiny water volume to that in a 'PinPoint 3D-chamber-like' air cavity; for the 0.25 × 0.25 cm(2) field size the perturbation factors are 1.323 and 2.139 for 6 MV and 15 MV full linac geometries respectively. For the 15 MV full linac geometry for field sizes of 1 × 1 cm(2) and smaller not only the absolute magnitude but also the 'shape' of the total electron fluence spectrum in the air cavity is significantly different to that in the water 'cavity'. The physics of this 'Bragg-Gray breakdown' is fully explained, making reference to the Fano theorem. For the 15 MV full linac geometry in the 0.25 × 0.25 cm(2) field the directly computed MC dose ratio, water-to-air, differs by 5% from the product of the Spencer-Attix stopping-power ratio (SPR) and the perturbation factor; this 'difference' is explained by the difference in the shapes of the fluence spectra and is also formulated theoretically. We show that the dimensions of an air-cavity with a perturbation factor within 5% of unity would have to be impractically small in these highly non-equilibrium photon fields. In contrast the dose to water in a 0.25 × 0.25 cm(2) field derived by multiplying the dose in the single-crystal diamond dosimeter (SCDDo) by the Spencer-Attix ratio is within 2.9% of the dose computed directly in the water voxel for full linac geometry at both 6 and 15 MV, thereby demonstrating that this detector exhibits quasi Bragg-Gray behaviour over a wide range of field sizes and beam qualities.

On differences in radiosensitivity estimation: TCP experiments versus survival curves. A theoretical study.

We have compared two methods of estimating the cellular radiosensitivity of a heterogeneous tumour, namely, via cell-survival and via tumour control probability (TCP) pseudo-experiments. It is assumed that there exists intra-tumour variability in radiosensitivity and that the tumour consists predominantly of radiosensitive cells and a small number of radio-resistant cells.Using a multi-component, linear-quadratic (LQ) model of cell kill, a pseudo-experimental cell-survival versus dose curve is derived. This curve is then fitted with a mono-component LQ model describing the response of a homogeneous cell population. For the assumed variation in radiosensitivity it is shown that the composite pseudo-experimental survival curve is well approximated by the survival curve of cells with uniform radiosensitivity.For the same initial cell radiosensitivity distribution several pseudo-experimental TCP curves are simulated corresponding to different fractionation regimes. The TCP model used accounts for clonogen proliferation during a fractionated treatment. The set of simulated TCP curves is then fitted with a mono-component TCP model. As in the cell survival experiment the fit with a mono-component model assuming uniform radiosensitivity is shown to be highly acceptable.However, the best-fit values of cellular radiosensitivity produced via the two methods are very different. The cell-survival pseudo-experiment yields a high radiosensitivity value, while the TCP pseudo-experiment shows that the dose-response is dominated by the most resistant sub-population in the tumour, even when this is just a small fraction of the total.

The performance of normal-tissue complication probability models in the presence of confounding factors.

PURPOSE: This work explores different methods for accounting for patient-specific factors in normal-tissue complication probability (NTCP) modeling, and compares the performance of models using pseudoclinical datasets for "lung" and "rectum" complications. METHODS: Datasets consisting of dose distributions and resulting normal-tissue complications were simulated, letting varying levels of confounding factors (i.e., nondosimetric factors) influence the outcome. The simulated confounding factors were patient radiosensitivity and health status. Seven empirical NTCP models were fitted to each dataset; this is analogous to fitting alternative models to datasets from different populations, treated with the same technique. The performance of these models was compared using the area under the ROC curve (AUC) and the impact of confounding factors on the model performance was studied. The patient-specific factors were then accounted for by (1) stratification and (2) two ways of modifying the traditional NTCP models to include these factors. RESULTS: Confounding factors had a greater impact on model performance than the choice of model. All models performed similarly well on the rectum datasets (except the maximum dose model), while critical-volume type models were slightly better than the mean dose-, the Lyman-Kutcher-Burman-, and the relative seriality models for lung. This difference was more apparent without confounding factors in the dataset. The two alternative functions including patient-specific factors used in this work (one logistic and one cumulative normal function) were found to be equivalent, and more efficient than stratifying datasets according to patient-specific factors and fitting models to subgroups individually. For datasets including confounding factors, the performance improved greatly when using models accounting for these; AUC increased from around 0.7 to close to unity. CONCLUSIONS: This work shows that identifying confounding factors, and developing methods to quantify them, is more important than the choice of NTCP model. Most dose-volume histogram (DVH)-based NTCP models can be generalized to include confounding factors.