title: Control algorithms for dynamic attenuators.
abstract: OBJECTIVE
  The authors describe algorithms to control dynamic attenuators in CT and compare their performance using simulated scans. Dynamic attenuators are prepatient beam shaping filters that modulate the distribution of x-ray fluence incident on the patient on a view-by-view basis. These attenuators can reduce dose while improving key image quality metrics such as peak or mean variance. In each view, the attenuator presents several degrees of freedom which may be individually adjusted. The total number of degrees of freedom across all views is very large, making many optimization techniques impractical. The authors develop a theory for optimally controlling these attenuators. Special attention is paid to a theoretically perfect attenuator which controls the fluence for each ray individually, but the authors also investigate and compare three other, practical attenuator designs which have been previously proposed: the piecewise-linear attenuator, the translating attenuator, and the double wedge attenuator.
  
  
  METHODS
  The authors pose and solve the optimization problems of minimizing the mean and peak variance subject to a fixed dose limit. For a perfect attenuator and mean variance minimization, this problem can be solved in simple, closed form. For other attenuator designs, the problem can be decomposed into separate problems for each view to greatly reduce the computational complexity. Peak variance minimization can be approximately solved using iterated, weighted mean variance (WMV) minimization. Also, the authors develop heuristics for the perfect and piecewise-linear attenuators which do not require a priori knowledge of the patient anatomy. The authors compare these control algorithms on different types of dynamic attenuators using simulated raw data from forward projected DICOM files of a thorax and an abdomen.
  
  
  RESULTS
  The translating and double wedge attenuators reduce dose by an average of 30% relative to current techniques (bowtie filter with tube current modulation) without increasing peak variance. The 15-element piecewise-linear dynamic attenuator reduces dose by an average of 42%, and the perfect attenuator reduces dose by an average of 50%. Improvements in peak variance are several times larger than improvements in mean variance. Heuristic control eliminates the need for a prescan. For the piecewise-linear attenuator, the cost of heuristic control is an increase in dose of 9%. The proposed iterated WMV minimization produces results that are within a few percent of the true solution.
  
  
  CONCLUSIONS
  Dynamic attenuators show potential for significant dose reduction. A wide class of dynamic attenuators can be accurately controlled using the described methods.
authors.affiliation: Department of Radiology, Stanford University, Stanford, California 94305 and Department of Electrical Engineering, Stanford University, Stanford, California 94305.
authors.forename: Scott S
authors.initials: SS
authors.lastname: Hsieh
authors.affiliation: Department of Radiology, Stanford University, Stanford California 94305 and Department of Bioengineering, Stanford University, Stanford, California 94305.
authors.forename: Norbert J
authors.initials: NJ
authors.lastname: Pelc
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004867:Equipment Design; D006801:Humans; D008962:Models, Theoretical; D011829:Radiation Dosage; D011860:Radiography, Abdominal / Q000295:instrumentation / Q000379:methods; D013902:Radiography, Thoracic / Q000295:instrumentation / Q000379:methods; D014057:Tomography, X-Ray Computed / Q000295:instrumentation* / Q000379:methods*