DUAL ENERGY COMPUTED TOMOGRAPHY FOR PROTON THERAPY TREATMENT PLANNING

Proton radiation therapy is gaining popularity because of the unique characteristics of its dose distribution, e.g., high dose-gradient at the distal end of the percentage-depth-dose curve (known as the Bragg peak). The high dose-gradient offers the possibility of delivering high dose to the target while still sparing critical organs distal to the target. However, the high dose-gradient is a double-edged sword: a small shift of the highly conformal high-dose area can cause the target to be substantially under-dosed or the critical organs to be substantially over-dosed. Because of that, large margins are required in treatment planning to ensure adequate dose coverage of the target, which prevents us from realizing the full potential of proton beams. Therefore, it is critical to reduce uncertainties in the proton radiation therapy. One major uncertainty in a proton treatment is the range uncertainty related to the estimation of proton stopping power ratio (SPR) distribution inside a patient. The SPR distribution inside a patient is required to account for tissue heterogeneities when calculating dose distribution inside the patient. In current clinical practice, the SPR distribution inside a patient is estimated from the patient’s treatment planning computed tomography (CT) images based on the CT number-to-SPR calibration curve. The SPR derived from a single CT number carries large uncertainties in the presence of human tissue composition variations, which is the major drawback of the current SPR estimation method. We propose to solve this problem by using dual energy CT (DECT) and hypothesize that the range uncertainty can be reduced by a factor of two from currently used value of 3.5%. A MATLAB program was developed to calculate the electron density ratio (EDR) and effective atomic number (EAN) from two CT measurements of the same object. An empirical relationship was discovered between mean excitation energies and EANs existing in human body tissues. With the MATLAB program and the empirical relationship, a DECT-based method was successfully developed to derive SPRs for human body tissues (the DECT method). The DECT method is more robust against the uncertainties in human tissues compositions than the current single-CT-based method, because the DECT method incorporated both density and elemental composition information in the SPR estimation. Furthermore, we studied practical limitations of the DECT method. We found that the accuracy of the DECT method using conventional kV-kV x-ray pair is susceptible to CT number variations, which compromises the theoretical advantage of the DECT method. Our solution to this problem is to use a different x-ray pair for the DECT. The accuracy of the DECT method using different combinations of x-ray energies, i.e., the kV-kV, kV-MV and MV-MV pair, was compared using the measured imaging uncertainties for each case. The kV-MV DECT was found to be the most robust against CT number variations. In addition, we studied how uncertainties propagate through the DECT calculation, and found general principles of selecting x-ray pairs for the DECT method to minimize its sensitivity to CT number variations. The uncertainties in SPRs estimated using the kV-MV DECT were analyzed further and compared to those using the stoichiometric method. The uncertainties in SPR estimation can be divided into five categories according to their origins: the inherent uncertainty, the DECT modeling uncertainty, the CT imaging uncertainty, the uncertainty in the mean excitation energy, and SPR variation with proton energy. Additionally, human body tissues were divided into three tissue groups – low density (lung) tissues, soft tissues and bone tissues. The uncertainties were estimated separately because their uncertainties were different under each condition. An estimate of the composite range uncertainty (2s) was determined for three tumor sites – prostate, lung, and head-and-neck, by combining the uncertainty estimates of all three tissue groups, weighted by their proportions along typical beam path for each treatment site. In conclusion, the DECT method holds theoretical advantages in estimating SPRs for human tissues over the current single-CT-based method. Using existing imaging techniques, the kV-MV DECT approach was capable of reducing the range uncertainty from the currently used value of 3.5% to 1.9%-2.3%, but it is short to reach our original goal of reducing the range uncertainty by a factor of two. The dominant source of uncertainties in the kV-MV DECT was the uncertainties in CT imaging, especially in MV CT imaging. Further reduction in beam hardening effect, the impact of scatter, out-of-field object etc. would reduce the Hounsfeld Unit variations in CT imaging. The kV-MV DECT still has the potential to reduce the range uncertainty further.

A LAPLACE TRANSFORM PAIR MODEL TO DETERMINE BREMSSTRAHLUNG SPECTRA FROM ATTENUATION DATA (RADIATION, X-RAY, SPECTRAL MODELING)

Every x-ray attenuation curve inherently contains all the information necessary to extract the complete energy spectrum of a beam. To date, attempts to obtain accurate spectral information from attenuation data have been inadequate.^ This investigation presents a mathematical pair model, grounded in physical reality by the Laplace Transformation, to describe the attenuation of a photon beam and the corresponding bremsstrahlung spectral distribution. In addition the Laplace model has been mathematically extended to include characteristic radiation in a physically meaningful way. A method to determine the fraction of characteristic radiation in any diagnostic x-ray beam was introduced for use with the extended model.^ This work has examined the reconstructive capability of the Laplace pair model for a photon beam range of from 50 kVp to 25 MV, using both theoretical and experimental methods.^ In the diagnostic region, excellent agreement between a wide variety of experimental spectra and those reconstructed with the Laplace model was obtained when the atomic composition of the attenuators was accurately known. The model successfully reproduced a 2 MV spectrum but demonstrated difficulty in accurately reconstructing orthovoltage and 6 MV spectra. The 25 MV spectrum was successfully reconstructed although poor agreement with the spectrum obtained by Levy was found.^ The analysis of errors, performed with diagnostic energy data, demonstrated the relative insensitivity of the model to typical experimental errors and confirmed that the model can be successfully used to theoretically derive accurate spectral information from experimental attenuation data. ^

Electron intensity modulation for mixed-beam radiation therapy with an x-ray multi-leaf collimator

The current standard treatment for head and neck cancer at our institution uses intensity-modulated x-ray therapy (IMRT), which improves target coverage and sparing of critical structures by delivering complex fluence patterns from a variety of beam directions to conform dose distributions to the shape of the target volume. The standard treatment for breast patients is field-in-field forward-planned IMRT, with initial tangential fields and additional reduced-weight tangents with blocking to minimize hot spots. For these treatment sites, the addition of electrons has the potential of improving target coverage and sparing of critical structures due to rapid dose falloff with depth and reduced exit dose. In this work, the use of mixed-beam therapy (MBT), i.e., combined intensity-modulated electron and x-ray beams using the x-ray multi-leaf collimator (MLC), was explored. The hypothesis of this study was that addition of intensity-modulated electron beams to existing clinical IMRT plans would produce MBT plans that were superior to the original IMRT plans for at least 50% of selected head and neck and 50% of breast cases. Dose calculations for electron beams collimated by the MLC were performed with Monte Carlo methods. An automation system was created to facilitate communication between the dose calculation engine and the treatment planning system. Energy and intensity modulation of the electron beams was accomplished by dividing the electron beams into 2x2-cm2 beamlets, which were then beam-weight optimized along with intensity-modulated x-ray beams. Treatment plans were optimized to obtain equivalent target dose coverage, and then compared with the original treatment plans. MBT treatment plans were evaluated by participating physicians with respect to target coverage, normal structure dose, and overall plan quality in comparison with original clinical plans. The physician evaluations did not support the hypothesis for either site, with MBT selected as superior in 1 out of the 15 head and neck cases (p=1) and 6 out of 18 breast cases (p=0.95). While MBT was not shown to be superior to IMRT, reductions were observed in doses to critical structures distal to the target along the electron beam direction and to non-target tissues, at the expense of target coverage and dose homogeneity. ^