title: A simulation technique for 3D MR-guided acoustic radiation force imaging.
abstract: OBJECTIVE
  In magnetic resonance-guided focused ultrasound (MRgFUS) therapies, the in situ characterization of the focal spot location and quality is critical. MR acoustic radiation force imaging (MR-ARFI) is a technique that measures the tissue displacement caused by the radiation force exerted by the ultrasound beam. This work presents a new technique to model the displacements caused by the radiation force of an ultrasound beam in a homogeneous tissue model.
  
  
  METHODS
  When a steady-state point-source force acts internally in an infinite homogeneous medium, the displacement of the material in all directions is given by the Somigliana elastostatic tensor. The radiation force field, which is caused by absorption and reflection of the incident ultrasound intensity pattern, will be spatially distributed, and the tensor formulation takes the form of a convolution of a 3D Green's function with the force field. The dynamic accumulation of MR phase during the ultrasound pulse can be theoretically accounted for through a time-of-arrival weighting of the Green's function. This theoretical model was evaluated experimentally in gelatin phantoms of varied stiffness (125-, 175-, and 250-bloom). The acoustic and mechanical properties of the phantoms used as parameters of the model were measured using independent techniques. Displacements at focal depths of 30- and 45-mm in the phantoms were measured by a 3D spin echo MR-ARFI segmented-EPI sequence.
  
  
  RESULTS
  The simulated displacements agreed with the MR-ARFI measured displacements for all bloom values and focal depths with a normalized RMS difference of 0.055 (range 0.028-0.12). The displacement magnitude decreased and the displacement pattern broadened with increased bloom value for both focal depths, as predicted by the theory.
  
  
  CONCLUSIONS
  A new technique that models the displacements caused by the radiation force of an ultrasound beam in a homogeneous tissue model theory has been rigorously validated through comparison with experimentally obtained 3D displacement data in homogeneous gelatin phantoms using a 3D MR-ARFI sequence. The agreement of the experimentally measured and simulated results demonstrates the potential to use MR-ARFI displacement data in MRgFUS therapies.
authors: Utah Center for Advanced Imaging Research, University of Utah, Salt Lake City, Utah 84112.
authors: Allison
authors: A
authors: Payne
authors: Department of Computer Science, University of Utah, Salt Lake City, Utah 84112.
authors: Josh
authors: J
authors: de Bever
authors: Department of Bioengineering, University of Utah, Salt Lake City, Utah 84112.
authors: Alexis
authors: A
authors: Farrer
authors: Department of Mechanical Engineering, University of Utah, Salt Lake City, Utah 84112.
authors: Brittany
authors: B
authors: Coats
authors: Utah Center for Advanced Imaging Research, University of Utah, Salt Lake City, Utah 84108.
authors: Dennis L
authors: DL
authors: Parker
authors: Department of Bioengineering, University of Utah, Salt Lake City, Utah 84112 and Department of Electrical and Computer Engineering, University of Utah, Salt Lake City, Utah 84112.
authors: Douglas A
authors: DA
authors: Christensen
mesh_terms: D000162:Acoustics; D021621:Imaging, Three-Dimensional / Q000379:methods*; D060328:Magnetic Phenomena; D008962:Models, Theoretical; D019047:Phantoms, Imaging
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