title: A robust empirical parametrization of proton stopping power using dual energy CT.
abstract: OBJECTIVE
  In this study the authors present a new method for estimation of proton stopping power ratios (SPRs) using dual energy CT (DECT), which is robust toward CT noise. The authors propose a parametrization for SPR based directly on the CT numbers in a DECT image set, whereby the intermediate steps of estimating the relative electron density, ρe, and mean excitation energy, I, are avoided.
  
  
  METHODS
  The SPR parametrization proposed in this study is a purely empirical fit based on the theoretical SPR values for a list of 34 reference human tissues. To investigate the SPR estimation made with this new method the authors performed a calibration and an evaluation with the method. The authors initially calculated CT numbers using CT energy spectrum characterization parameters obtained from calibration based on a Gammex 467 electron density calibration phantom. These CT numbers were fitted to the theoretical SPR for the reference human tissues using the new SPR parametrization presented in this study. The method was evaluated based on theoretical CT numbers for the reference human tissues. The root-mean-square error (RMSE) of the SPR and the proton range error from the continuous slowing down approximation were calculated for the reference human tissues. To test the stability of the parametrization the authors varied the density and elemental composition of the reference human tissues and calculated their new SPR estimates. Further, clinically realistic noise values were added to the theoretical CT numbers to investigate how CT noise affected the estimated water equivalent range through 10 cm of the reference human tissues. All results for the new SPR parametrization were compared to the results obtained using two previously published DECT methods for SPR estimation. Comparisons were also made to a single energy CT (SECT) SPR estimation method, the stoichiometric method, which is commonly used in clinical practise for proton therapy treatment planning.
  
  
  RESULTS
  The RMSE for the SPR of the 34 reference human tissues using the new SPR parametrization was 0.12%, compared to 0.19% and 0.28% for the two previously published DECT methods. The SPR parametrization was more stable toward variations of the calcium content in the reference human tissues, but less stable toward density variations and changes to the hydrogen content than the two other DECT methods. When adding noise to the theoretical CT numbers the SPR parametrization gave the lowest water equivalent range errors of all four tested SPR estimation methods (maximum error reduced to 0.4 mm). In all cases tested, the new SPR parametrization outperformed the SECT stoichiometric method.
  
  
  CONCLUSIONS
  The new SPR parametrization gave lower RMSEs than the two other published DECT methods, and was in particular more robust against added noise. The method has potential for reducing range uncertainty margins in treatment planning of proton therapy.
authors: Department of Medical Physics, Aarhus University Hospital, Aarhus 8000, Denmark.
authors: Vicki T
authors: VT
authors: Taasti
authors: Department of Medical Physics, Aarhus University Hospital, Aarhus 8000, Denmark.
authors: Jørgen B B
authors: JB
authors: Petersen
authors: Department of Medical Physics, Aarhus University Hospital, Aarhus 8000, Denmark.
authors: Ludvig P
authors: LP
authors: Muren
authors: Department of Clinical Engineering and Department of Radiology, Aarhus University Hospital, Aarhus 8000, Denmark.
authors: Jesper
authors: J
authors: Thygesen
authors: Department of Medical Physics, Aarhus University Hospital, Aarhus 8000, Denmark.
authors: David C
authors: DC
authors: Hansen
mesh_terms: D006801:Humans; D011522:Protons; D059629:Signal-To-Noise Ratio; D014057:Tomography, X-Ray Computed / Q000379:methods*
chemical_list: D011522:Protons