title: Transconvolution and the virtual positron emission tomograph--a new method for cross calibration in quantitative PET∕CT imaging.
abstract: OBJECTIVE
  Positron emission tomography (PET)∕computed tomography (CT) measurements on small lesions are impaired by the partial volume effect, which is intrinsically tied to the point spread function of the actual imaging system, including the reconstruction algorithms. The variability resulting from different point spread functions hinders the assessment of quantitative measurements in clinical routine and especially degrades comparability within multicenter trials. To improve quantitative comparability there is a need for methods to match different PET∕CT systems through elimination of this systemic variability. Consequently, a new method was developed and tested that transforms the image of an object as produced by one tomograph to another image of the same object as it would have been seen by a different tomograph. The proposed new method, termed Transconvolution, compensates for differing imaging properties of different tomographs and particularly aims at quantitative comparability of PET∕CT in the context of multicenter trials.
  
  
  METHODS
  To solve the problem of image normalization, the theory of Transconvolution was mathematically established together with new methods to handle point spread functions of different PET∕CT systems. Knowing the point spread functions of two different imaging systems allows determining a Transconvolution function to convert one image into the other. This function is calculated by convolving one point spread function with the inverse of the other point spread function which, when adhering to certain boundary conditions such as the use of linear acquisition and image reconstruction methods, is a numerically accessible operation. For reliable measurement of such point spread functions characterizing different PET∕CT systems, a dedicated solid-state phantom incorporating (68)Ge∕(68)Ga filled spheres was developed. To iteratively determine and represent such point spread functions, exponential density functions in combination with a Gaussian distribution were introduced. Furthermore, simulation of a virtual PET system provided a standard imaging system with clearly defined properties to which the real PET systems were to be matched. A Hann window served as the modulation transfer function for the virtual PET. The Hann's apodization properties suppressed high spatial frequencies above a certain critical frequency, thereby fulfilling the above-mentioned boundary conditions. The determined point spread functions were subsequently used by the novel Transconvolution algorithm to match different PET∕CT systems onto the virtual PET system. Finally, the theoretically elaborated Transconvolution method was validated transforming phantom images acquired on two different PET systems to nearly identical data sets, as they would be imaged by the virtual PET system.
  
  
  RESULTS
  The proposed Transconvolution method matched different PET∕CT-systems for an improved and reproducible determination of a normalized activity concentration. The highest difference in measured activity concentration between the two different PET systems of 18.2% was found in spheres of 2 ml volume. Transconvolution reduced this difference down to 1.6%. In addition to reestablishing comparability the new method with its parameterization of point spread functions allowed a full characterization of imaging properties of the examined tomographs.
  
  
  CONCLUSIONS
  By matching different tomographs to a virtual standardized imaging system, Transconvolution opens a new comprehensive method for cross calibration in quantitative PET imaging. The use of a virtual PET system restores comparability between data sets from different PET systems by exerting a common, reproducible, and defined partial volume effect.
authors.affiliation: Department of Nuclear Medicine, Inselspital, Bern University Hospital and University of Bern, 3010 Bern, Switzerland.
authors.forename: George A
authors.initials: GA
authors.lastname: Prenosil
authors.forename: Thilo
authors.initials: T
authors.lastname: Weitzel
authors.forename: Michael
authors.initials: M
authors.lastname: Hentschel
authors.forename: Bernd
authors.initials: B
authors.lastname: Klaeser
authors.forename: Thomas
authors.initials: T
authors.lastname: Krause
mesh_terms: D002138:Calibration; D006801:Humans; D007089:Image Enhancement / Q000379:methods* / Q000592:standards; D007090:Image Interpretation, Computer-Assisted / Q000379:methods* / Q000592:standards; D064847:Multimodal Imaging / Q000379:methods* / Q000592:standards; D049268:Positron-Emission Tomography / Q000379:methods* / Q000592:standards; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013382:Subtraction Technique; D014057:Tomography, X-Ray Computed / Q000379:methods* / Q000592:standards