B Warkentin

Dosimetric IMRT verification with a flat-panel EPID

A convolution-based calibration procedure has been developed to use an amorphous silicon flat-panel electronic portal imaging device (EPID) for accurate dosimetric verification of intensity-modulated radiotherapy (IMRT) treatments. Raw EPID images were deconvolved to accurate, high-resolution 2-D distributions of primary fluence using a scatter kernel composed of two elements: a Monte Carlo generated kernel describing dose deposition in the EPID phosphor, and an empirically derived kernel describing optical photon spreading. Relative fluence profiles measured with the EPID are in very good agreement with those measured with a diamond detector, and exhibit excellent spatial resolution required for IMRT verification. For dosimetric verification, the EPID-measured primary fluences are convolved with a Monte Carlo kernel describing dose deposition in a solid water phantom, and cross-calibrated with ion chamber measurements. Dose distributions measured using the EPID agree to within 2.1% with those measured with film for open fields of 2 x 2 cm2 and 10 x 10 cm2. Predictions of the EPID phantom scattering factors (SPE) based on our scatter kernels are within 1% of the SPE measured for open field sizes of up to 16 x 16 cm2. Pretreatment verifications of step-and-shoot IMRT treatments using the EPID are in good agreement with those performed with film, with a mean percent difference of 0.2 +/- 1.0% for three IMRT treatments (24 fields).

Three‐dimensional IMRT verification with a flat‐panel EPID

A three-dimensional (3D) intensity-modulated radiotherapy (IMRT) pretreatment verification procedure has been developed based on the measurement of two-dimensional (2D) primary fluence profiles using an amorphous silicon flat-panel electronic portal imaging device (EPID). As described in our previous work, fluence profiles are extracted from EPID images by deconvolution with kernels that represent signal spread in the EPID due to radiation and optical scattering. The deconvolution kernels are derived using Monte Carlo simulations of dose deposition in the EPID and empirical fitting methods, for both 6 and 15 MV photon energies. In our new 3D verification technique, 2D fluence modulation profiles for each IMRT field in a treatment are used as input to a treatment planning system (TPS), which then generates 3D doses. Verification is accomplished by comparing this new EPID-based 3D dose distribution to the planned dose distribution calculated by the TPS. Thermoluminescent dosimeter (TLD) point dose measurements for an IMRT treatment of an anthropomorphic phantom were in good agreement with the EPID-based 3D doses; in contrast, the planned dose under-predicts the TLD measurement in a high-gradient region by approximately 16%. Similarly, large discrepancies between EPID-based and TPS doses were also evident in dose profiles of small fields incident on a water phantom. These results suggest that our 3D EPID-based method is effective in quantifying relevant uncertainties in the dose calculations of our TPS for IMRT treatments. For three clinical head and neck cancer IMRT treatment plans, our TPS was found to underestimate the mean EPID-based doses in the critical structures of the spinal cord and the parotids by approximately 4 Gy (11%-14%). According to radiobiological modeling calculations that were performed, such underestimates can potentially lead to clinically significant underpredictions of normal tissue complication rates.

A TCP-NTCP estimation module using DVHs and known radiobiological models and parameter sets

Radiotherapy treatment plan evaluation relies on an implicit estimation of the tumor control probability (TCP) and normal tissue complication probability (NTCP) arising from a given dose distribution. A potential application of radiobiological modeling to radiotherapy is the ranking of treatment plans via a more explicit determination of TCP and NTCP values. Although the limited predictive capabilities of current radiobiological models prevent their use as a primary evaluative tool, radiobiological modeling predictions may still be a valuable complement to clinical experience. A convenient computational module has been developed for estimating the TCP and the NTCP arising from a dose distribution calculated by a treatment planning system, and characterized by differential (frequency) dose‐volume histograms (DDVHs). The radiobiological models included in the module are sigmoidal dose response and Critical Volume NTCP models, a Poisson TCP model, and a TCP model incorporating radiobiological parameters describing linear‐quadratic cell kill and repopulation. A number of sets of parameter values for the different models have been gathered in databases. The estimated parameters characterize the radiation response of several different normal tissues and tumor types. The system also allows input and storage of parameters by the user, which is particularly useful because of the rapidly increasing number of parameter estimates available in the literature. Potential applications of the system include the following: comparing radiobiological predictions of outcome for different treatment plans or types of treatment; comparing the number of observed outcomes for a cohort of patient DVHs to the predicted number of outcomes based on different models/parameter sets; and testing of the sensitivity of model predictions to uncertainties in the parameter values. The module thus helps to amalgamate and make more accessible current radiobiological modeling knowledge, and may serve as a useful aid in the prospective and retrospective analysis of radiotherapy treatment plans. PACS number: 87.53.Tf

Skin dose in longitudinal and transverse linac‐MRIs using Monte Carlo and realistic 3D MRI field models

PURPOSE The magnetic fields of linac-MR systems modify the path of contaminant electrons in photon beams, which alters patient skin dose. To accurately quantify the magnitude of changes in skin dose, the authors use Monte Carlo calculations that incorporate realistic 3D magnetic field models of longitudinal and transverse linac-MR systems. METHODS Finite element method (FEM) is used to generate complete 3D magnetic field maps for 0.56 T longitudinal and transverse linac-MR magnet assemblies, as well as for representative 0.5 and 1.0 T Helmholtz MRI systems. EGSnrc simulations implementing these 3D magnetic fields are performed. The geometry for the BEAMnrc simulations incorporates the Varian 600C 6 MV linac, magnet poles, the yoke, and the magnetic shields of the linac-MRIs. Resulting phase-space files are used to calculate the central axis percent depth-doses in a water phantom and 2D skin dose distributions for 70 μm entrance and exit layers using DOSXYZnrc. For comparison, skin doses are also calculated in the absence of magnetic field, and using a 1D magnetic field with an unrealistically large fringe field. The effects of photon field size, air gap (longitudinal configuration), and angle of obliquity (transverse configuration) are also investigated. RESULTS Realistic modeling of the 3D magnetic fields shows that fringe fields decay rapidly and have a very small magnitude at the linac head. As a result, longitudinal linac-MR systems mostly confine contaminant electrons that are generated in the air gap and have an insignificant effect on electrons produced further upstream. The increase in the skin dose for the longitudinal configuration compared to the zero B-field case varies from ∼1% to ∼14% for air gaps of 5-31 cm, respectively. (All dose changes are reported as a % of D(max).) The increase is also field-size dependent, ranging from ∼3% at 20 × 20 cm(2) to ∼11% at 5 × 5 cm(2). The small changes in skin dose are in contrast to significant increases that are calculated for the unrealistic 1D magnetic field. For the transverse configuration, the entrance skin dose is equal or smaller than that of the zero B-field case for perpendicular beams. For a 10 × 10 cm(2) oblique beam the transverse magnetic field decreases the entry skin dose for oblique angles less than ±20° and increases it by no more than 10% for larger angles up to ±45°. The exit skin dose is increased by 42% for a 10 × 10 cm(2) perpendicular beam, but appreciably drops and approaches the zero B-field case for large oblique angles of incidence. CONCLUSIONS For longitudinal linac-MR systems only a small increase in the entrance skin dose is predicted, due to the rapid decay of the realistic magnetic fringe fields. For transverse linac-MR systems, changes to the entrance skin dose are small for most scenarios. For the same geometry, on the exit side a fairly large increase is observed for perpendicular beams, but significantly drops for large oblique angles of incidence. The observed effects on skin dose are not expected to limit the application of linac-MR systems in either the longitudinal or transverse configuration.

Inverse treatment planning by physically constrained minimization of a biological objective function.

In the current state-of-the art of clinical inverse planning, the design of clinically acceptable IMRT plans is predominantly based on the optimization of physical rather than biological objective functions. A major impetus for this trend is the unproven predictive power of radiobiological models, which is largely due to the scarcity of data sets for an accurate evaluation of the model parameters. On the other hand, these models do capture the currently known dose-volume effects in tissue dose-response, which should be accounted for in the process of optimization. In order to incorporate radiobiological information in clinical treatment planning optimization, we propose a hybrid physico-biological approach to inverse treatment planning based on the application of a continuous penalty function method to the constrained minimization of a biological objective. The objective is defined as the weighted sum of normal tissue complication probabilities evaluated with the Lyman normal-tissue complication probability model. Physical constraints specify the admissible minimum and maximum target dose. The continuous penalty function method is then used to find an approximate solution of the resulting large-scale constrained minimization problem. Plans generated by our approach are compared to ones produced by a commercial planning system incorporating physical optimization. The comparisons show clinically negligible differences, with the advantage that the hybrid technique does not require specifications of any dose-volume constraints to the normal tissues. This indicates that the proposed hybrid physico-biological method can be used for the generation of clinically acceptable plans.

Investigating the effect of cell repopulation on the tumor response to fractionated external radiotherapy

In this work we study the descriptive power of the main tumor control probability (TCP) models based on the linear quadratic (LQ) mechanism of cell damage with cell recovery. The Poisson, binomial, and a dynamic TCP model, developed recently by Zaider and Minerbo are considered. The Zaider-Minerbo model takes cell repopulation into account. It is shown that the Poisson approximation incorporating cell repopulation is conceptually incorrect. Based on the Zaider-Minerbo model, an expression for the TCP for fractionated treatments with varying intervals between two consecutive fractions and with cell survival probability that changes from fraction to fraction is derived. The models are fitted to an experimental data set consisting of dose response curves that correspond to different fractionation regimes. The binomial TCP model based on the LQ mechanism of cell damage solely was unable to fit the fractionated response data. It was found that the Zaider-Minerbo model, which takes tumor cell repopulation into account, best fits the data.

Fundamental form of a population TCP model in the limit of large heterogeneity.

A population tumor control probability (TCP) model for fractionated external beam radiotherapy, based on Poisson statistics and in the limit of large parameter heterogeneity, is studied. A reduction of a general eight-parameter TCP equation, which incorporates heterogeneity in parameters characterizing linear-quadratic radiosensitivity, repopulation, and clonogen number, to an equation with four parameters is obtained. The four parameters represent the mean and standard deviation for both clonogen number and a generalized radiosensitivity that includes linear-quadratic and repopulation descriptors. Further, owing to parameter inter-relationship, it is possible to express these four parameters as three ratios of parameters in the large heterogeneity limit. These ratios can be directly linked to two defining features of the TCP dose response: D50 and gamma50. In the general case, the TCP model can be written in terms of D50, gamma50 and a third parameter indicating the ratio of the levels of heterogeneity in clonogen number and generalized radiosensitivity; however, the third parameter is unnecessary when either of these two sources of heterogeneity is dominant. It is shown that heterogeneity in clonogen number will have little impact on the TCP formula for clinical scenarios, and thus it will generally be the case that the fundamental form of the Poisson-based population TCP model can be specified completely in terms of D50 and gamma50: TCP= 1/2 erfc[square root of pi(gamma50)(D50/D-1)]. This implies that limited radiobiological information can be determined by the analysis of dose response data: information about parameter ratios can be ascertained, but knowledge of absolute values for the fundamental radiobiological parameters will require independent auxiliary measurements.

Minimal skin dose increase in longitudinal rotating biplanar linac-MR systems: examination of radiation energy and flattening filter design.

The magnetic fields of linac-MR systems modify the path of contaminant electrons in photon beams, which alters patient entrance skin dose. Also, the increased SSD of linac-MR systems reduces the maximum achievable dose rate. To accurately quantify the changes in entrance skin dose, the authors use EGSnrc Monte Carlo calculations that incorporate 3D magnetic field of the Alberta 0.5 T longitudinal linac-MR system. The Varian 600C linac head geometry assembled on the MRI components is used in the BEAMnrc simulations for 6 MV and 10 MV beam models and skin doses are calculated at an average depth of 70 μm using DOSXYZnrc. 3D modeling shows that magnetic fringe fields decay rapidly and are small at the linac head. SSDs between 100 and 120 cm result in skin-dose increases of between ~6%-19% and ~1%-9% for the 6 and 10 MV beams, respectively. For 6 MV, skin dose increases from ~10.5% to ~1.5% for field-size increases of 5  ×  5 cm(2) to 20  ×  20 cm(2). For 10 MV, skin dose increases by ~6% for a 5  ×  5 cm(2) field, and decreases by ~1.5% for a 20  ×  20 cm(2) field. Furthermore, the proposed reshaped flattening filter increases the dose rate from the current 355 MU min(-1) to 529 MU min(-1) (6 MV) or 604 MU min(-1) (10 MV), while the skin-dose increases by only an additional ~2.6% (all percent increases in skin dose are relative to D max). This study suggests that there is minimal increase in the entrance skin dose and minimal/no decrease in the dose rate of the Alberta longitudinal linac-MR system. The even lower skin dose increase at 10 MV offers further advantages in future designs of linac-MR prototypes.

Derivation of the expressions for γ50 and D50 for different individual TCP and NTCP models

This paper presents a complete set of formulae for the position (D50) and the normalized slope (gamma50) of the dose-response relationship based on the most commonly used radiobiological models for tumours as well as for normal tissues. The functional subunit response models (critical element and critical volume) are used in the derivation of the formulae for the normal tissue. Binomial statistics are used to describe the tumour control probability, the functional subunit response as well as the normal tissue complication probability. The formulae are derived for the single hit and linear quadratic models of cell kill in terms of the number of fractions and dose per fraction. It is shown that the functional subunit models predict very steep, almost step-like, normal tissue individual dose-response relationships. Furthermore, the formulae for the normalized gradient depend on the cellular parameters alpha and beta when written in terms of number of fractions, but not when written in terms of dose per fraction.

Radiation damage, repopulation and cell recovery analysis of in vitro tumour cell megacolony culture data using a non-Poissonian cell repopulation TCP model

The effects of radiation damage, tumour repopulation and cell sublethal damage repair and the possibility of extracting information about the model parameters describing them are investigated in this work. Previously published data on two different cultured cell lines were analysed with the help of a tumour control probability (TCP) model that describes tumour cell dynamics properly. Different versions of a TCP model representing the cases of full or partial cell recovery between fractions of radiation, accompanied by repopulation or no repopulation were used to fit the data and were ranked according to statistical criteria. The data analysis shows the importance of the linear-quadratic mechanism of cell damage for the description of the in vitro cell dynamics. In a previous work where in vivo data were analysed, the employment of the single hit model of cell kill and cell repopulation produced the best fit, while ignoring the quadratic term of cell damage in the current analysis leads to poor fits. It is also concluded that more experiments using different fractionation regimes producing diverse data are needed to help model analysis and better ranking of the models.