Marco Carlone

Patient dosimetry for hybrid MRI-radiotherapy systems

A novel geometry has been proposed for a hybrid magnetic resonance imaging (MRI)-linac system in which a 6 MV linac is mounted on the open end of a biplanar, low field (0.2 T) MRI magnet on a single gantry that is free to rotate around the patient. This geometry creates a scenario in which the magnetic field vector remains fixed with respect to the incident photon beam, but moves with respect to the patient as the gantry rotates. Other proposed geometries are characterized by a radiation source rotating about a fixed cylindrical magnet where the magnetic field vector remains fixed with respect to the patient. In this investigation we simulate the inherent dose distribution patterns within the two MRI-radiation source geometries using PENELOPE and EGSnrc Monte Carlo radiation transport codes with algorithms implemented to account for the magnetic field deflection of charged particles. Simulations are performed in phantoms and for clinically realistic situations. The novel geometry results in a net Lorentz force that remains fixed with respect to the patient (in the cranial-caudal direction) and results in a cumulative influence on dose distribution for a multiple beam treatment scenario. For a case where patient anatomy is reasonably homogeneous (brain plan), differences in dose compared to a conventional (no magnetic field) case are minimal for the novel geometry. In the case of a lung plan where the inhomogeneous patient anatomy allows for the magnetic field to have significant influence on charged particle transport, larger differences occur in a predictable manner. For a system using a fixed cylindrical geometry and higher magnetic field (1.5 T), differences from the case without a magnetic field are significantly greater.

TU‐C‐M100F‐01: Development of a Linac‐MRI System for Real‐Time ART

Purpose: To describe the novel design of the coupling an of MRI to a medical linac to provide real‐time tracking of the tumor and healthy tissues during irradiation by the treatment beam Method and Materials: Various embodiments are defined in our patents (Fallone, Carlone, Murray) to avoid mutual interference between the MR and the linac. Our method allows rotation of a linac with respect to the subject to allow irradiation of the subject from any angle without disturbing the magnet homogeneity. Magnetic shielding of the linac prevents disturbance from the MRI. RF signal shielding, modifications the RF‐signal triggering and pulse shaping are used to minimize linac interference of MRI RF read sequences. Various Monte Carlo calculations (EGS4 NRC and Penelope) and finite‐element analyses (Comsol) are performed in all design stages. Results: The initial design for the human system involves a bi‐planar MRI with 65 cm opening to allow rotation of the shoulders within the bore. A short 6 MV waveguide is coupled to one open end of the MR, and a beam‐stop and a projection imaging device (eg, flatpanel) is coupled to the other end. Rotation is provide by two concentric rings, and the permanent‐magnet design is preferred in the initial stage to provide stability and lack of electric wiring in the rotation process. Low fields allows very small fringe fields to minimize linac interference yet with adequate image quality of soft tissue for lungs, prostate, GBM, etc. Mutual interference issues and other issues arising externally are calculated and resolved. Conclusion: We have shown the design to be a practical, viable and realizable within a reasonable time frame. Our other presentations detail resolutions to mutual MRI‐linac interferences.

Mechanistic formulation of a lineal‐quadratic‐linear (LQL) model: Split‐dose experiments and exponentially decaying sources

PURPOSE In recent years, several models were proposed that modify the standard linear-quadratic (LQ) model to make the predicted survival curve linear at high doses. Most of these models are purely phenomenological and can only be applied in the particular case of acute doses per fraction. The authors consider a mechanistic formulation of a linear-quadratic-linear (LQL) model in the case of split-dose experiments and exponentially decaying sources. This model provides a comprehensive description of radiation response for arbitrary dose rate and fractionation with only one additional parameter. METHODS The authors use a compartmental formulation of the LQL model from the literature. They analytically solve the models differential equations for the case of a split-dose experiment and for an exponentially decaying source. They compare the solutions of the survival fraction with the standard LQ equations and with the lethal-potentially lethal (LPL) model. RESULTS In the case of the split-dose experiment, the LQL model predicts a recovery ratio as a function of dose per fraction that deviates from the square law of the standard LQ. The survival fraction as a function of time between fractions follows a similar exponential law as the LQ but adds a multiplicative factor to the LQ parameter beta. The LQL solution for the split-dose experiment is very close to the LPL prediction. For the decaying source, the differences between the LQL and the LQ solutions are negligible when the half-life of the source is much larger than the characteristic repair time, which is the clinically relevant case. CONCLUSIONS The compartmental formulation of the LQL model can be used for arbitrary dose rates and provides a comprehensive description of dose response. When the survival fraction for acute doses is linear for high dose, a deviation of the square law formula of the recovery ratio for split doses is also predicted.

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.

Transit dose contributions to intracavitary and interstitial PDR brachytherapy treatments.

The objective of this study was to determine the magnitude of transit dose contributions to the planned dose in common intracavitary and interstitial brachytherapy treatments delivered using a pulsed dose rate (PDR) remote afterloader. The total transit dose arises from the travel of the radiation source into (entry) and out of (exit) the applicator, and between the dwell positions (inter-dwell). In this paper, we used a well-type ionization chamber to measure the transit dose component for a PDR afterloader and compared the results against measurements for a high dose rate (HDR) afterloader. Our results show that for typical intracavitary and interstitial treatments, the major contribution to transit dose is from the entry+exit source travel, as the inter-dwell component is effectively compensated for (<0.5%) by the afterloader. The transit dose was generally found to be larger for PDR treatments than for HDR treatments, as it is influenced by the source activity, dwell times and number of radiation pulses. The overall increase in the planned dose contributed by the transit dose in a typical intracavitary PDR treatment was estimated to be <2%, but much higher for interstitial treatments. This study shows that the effect of the transit dose on common clinical intracavitary PDR brachytherapy treatments is practically negligible, but requires attention in highly fractionated large volume interstitial treatments.

Functional form comparison between the population and the individual Poisson based TCP models

Functional form comparison between the population and the individual Poisson based TCP models In this work, the functional form similarity between the individual and fundamental population TCP models is investigated. Using the fact that both models can be expressed in terms of the geometric parameters γ50 and D50, we show that they have almost identical functional form for values of γ50 ≥ 1. The conceptual inadequacy of applying an individual model to clinical data is also discussed. A general individual response TCP expression is given, parameterized by Df and γf - the dose corresponding to a control level of f, and the normalized slope at that point. It is shown that the dose-response may be interpreted as an individual response only if γ50 is sufficiently high. Based on the functional form equivalency between the individual and the population TCP models, we discuss the possibility of applying the individual TCP model for the case of heterogeneous irradiations. Due to the fact that the fundamental population TCP model is derived for homogeneous irradiations only, we propose the use of the EUD, given by the generalized mean dose, when the fundamental population TCP model is used to fit clinical data.

Population TCP estimators in case of heterogeneous irradiation: a new discussion of an old problem.

Abstract Purpose. To investigate the capacity of two phenomenological expressions to describe the population tumor response in case of a heterogeneous irradiation of the tumor. The generalization of the individual tumor control probability (TCP) models to include the case of a heterogeneous irradiation is a trivial problem. However, an analytical solution that results in a closed form population TCP formula for the heterogeneous case is, unfortunately, a very complex mathematical problem. Therefore we applied a numerical approach to the problem. Method. Pseudo-experimental data sets are constructed through the generation of dose distributions and population TCP data obtained by a numerical solution of a multi-dimensional integral over an individual TCP model. The capacity of the following two phenomenological – Poisson and equivalent uniform dose (EUD) based – TCP expressions: to describe the population tumor response in case of heterogeneous irradiation is investigated through their fitting to the psuedo-experimental data sets. Results and conclusions. While both expressions produce statistically acceptable fits to the pseudo-experimental data within 2% TCP error band, the use of the second expression is preferable since it produces considerably better fits to the data sets.

Sci‐Fri PM: Planning‐02: MRI‐based radiation treatment planning for an MRI‐linac system

At Cross Cancer Institute, we are investigating a novel MRI-linac system consisting of a bi-planar 0.2 T permanent magnet coupled with a 6 MV Linac. The system can freely revolve axially around the patient to deliver dose from any desired angle. For such a system, the radiation treatment planning procedure is expected to rely on the MR images only, i.e. MRI Simulation. Replacing the current CT/CT+MRI-based RTP procedure with MRI Simulation will eliminate the need for the planning CT scanning sessions (no additional x-ray exposure) and consequently the image fusion between MRI and planning CT. In this work, we propose a comprehensive MRI-based RTP procedure for an MRI-Linac system. Specifically, the method consists of a) data acquisition, b) analysis and correction of image artifacts caused by the scanner-related and patient-induced distortions, c) segmentation of organ structures relevant to dosimetric calculations (e.g. soft tissue, bone, air), d) conversion of MR images into CT-like images by assigning bulk electron density values to organ contours defined at step c), e) dose calculations in external magnetic field, and f) plan evaluation. Monte Carlo simulations were performed to determine the linac-MRI scanners magnetic field induced effects on the dose deposited patterns using patient data. Specifically, we investigated the dosimetric differences between the corresponding MRI-based RT plans simulated at zero and 0.2 T. We found that the maximum percent differences for brain studies were within 4%. Most of these differences occurred at the inferior field edge and superficially at beam exits.

SU‐FF‐T‐344: On the Equivalency of the Population and Individual TCP Models

Purpose: To demonstrate that the functional form of the population tumor control probability (TCP) model is well approximated by the individual TCP model. Method and Materials: Due to inter‐parameter relations, the parameters of the population based Poisson TCP model in the limit of large heterogeneity reduce to the geometric parameters D 50 and γ50:1 TCP pop =0.5erfc[π 0.5 γ 50 (D 50 /D − 1)] . On the other hand the individual TCP model can also be written in the terms of the geometrical characteristics of the dose‐response relationship — D 50 and γ50: TCP ind =0.5 exp [2γ 50 /( ln 2)(1‐D/D 50 )] = exp [− N o exp (−α D )] . For typical clinical values2 of the parameters D 50 and γ50, we evaluate and compare the individual and population‐based TCP models. Results: The two models are approximately equivalent for different values of D 50 and γ50. When plotted, the individual and population‐based TCP models almost overlap over a wide range of doses for all D 50 values and γ50 higher than 1. When γ50 is less than 1 both functions start to differ from one another. Conclusion: The equivalency between the individual and population TCP models is demonstrated. The individual TCP model has been observed to fit clinical datasets reasonably well, and this phenomenon may be attributed to the similarity of the models. When fitted to clinical data, the individual TCP model will produce parameter estimates completely emptied from their biological meaning and become purely phenomenological.

SU-FF-T-372: Evaluation of the Limits of Accuracy of the High Heterogeneity TCP Model

Purpose: To determine the limits of accuracy of a TCP model that assumes high heterogeneity, such as the Roberts and Hendry (IJROBP 41 689–699 1998) model.Method and Materials: A TCP model that incorporates heterogeneity in radiosensitivity, clonogen number and growth rate is reduced to a two parameter model by grouping variables using a method previously introduced by Carlone et al (Carlone et al Med Phys 30 2832–2848 2003). The model is then approximated in the high heterogeneity limit by approximating the TCP function as a Heaviside step function with a step at 0.577. The high heterogeneity approximation, when plotted in the reduced parameter space has iso‐TCP lines that are linear, and cross at a common point. This suggests a further variable reduction such that TCP depends on a single variable, δ: TCP = ½erfc(δ/sqrt(2)). A similar variable substitution can be inserted into the exact TCP model; the result is a function of two variables, however the TCP function depends much more strongly on the variable δ than on the second variable. The limits of accuracy of the approximation are determined by calculating the difference between the two solutions. Results: When only heterogeneity in a is considered, the high heterogeneity TCP approximation is accurate (< 5%) when σα D is larger than 1.6. When σα D is large as compared to 0.577, the TCP function can be accurately evaluated using only parameter ratios (Roberts and Hendry closed formula), however it does depend on the value of sa when σα when σα D ≈ 0.577. When σα is small, maximum errors on the order of 30% to 50% can occur. Conclusion: When the quantity σα D is significantly larger than 1, the heterogeneous TCP function can be accurately modeled using only parameter ratios, and the high heterogeneity approximation.