title: Three-parameter shear wave inversion in MR elastography of incompressible transverse isotropic media: Application to in vivo lower leg muscles.
abstract: OBJECTIVE
  To develop and demonstrate MR elastography (MRE) for the measurement of three independent viscoelastic constants of skeletal muscle according to the theory of linear elasticity of incompressible materials with transverse isotropy (TI).
  
  
  METHODS
  Three-dimensional multifrequency MRE was applied to soleus, gastrocnemius, and tibialis anterior muscles in 10 healthy volunteers. The rotational wave fields were solved for complex-valued viscoelastic parameters μ12, μ13, and E3 corresponding to two shear moduli (within the planes of isotropy and symmetry of TI materials) and Young's modulus (along the principal fiber axis).
  
  
  RESULTS
  Anisotropy was represented by the inequality μ12  < μ13  < 1/3E3 considering storage and loss properties of the soleus and gastrocnemius muscles, whereas storage shear moduli of tibialis were indistinguishable. Storage moduli were: 1.06 ± 0.12, 1.33 ± 0.10, 6.92 ± 0.95 kPa (soleus); 0.90 ± 0.11, 1.30 ± 0.15, 8.22 ± 1.37 kPa (gastrocnemius); 1.26 ± 0.16, 1.27 ± 0.11, 9.29 ± 1.42 kPa (tibialis), for μ12, μ13, and E3, respectively. The muscles were different in their μ12 and E3 values, whereas μ13 was less sensitive to the muscle type. Leg differences were observed in the soleus and gastrocnemius muscles.
  
  
  CONCLUSIONS
  Recovery of the full elasticity tensor in incompressible TI materials is feasible by three-dimensional inversion of the time-harmonic shear wave equation. The method is potentially useful for the clinical evaluation of skeletal muscle anisotropy.
authors.affiliation: Department of Radiology, Charité-Universitätsmedizin Berlin, Campus Charité Mitte, Berlin, Germany.
authors.forename: Jing
authors.initials: J
authors.lastname: Guo
authors.affiliation: Department of Radiology, Charité-Universitätsmedizin Berlin, Campus Charité Mitte, Berlin, Germany.
authors.forename: Sebastian
authors.initials: S
authors.lastname: Hirsch
authors.affiliation: Department of Radiology, Charité-Universitätsmedizin Berlin, Campus Charité Mitte, Berlin, Germany.
authors.forename: Michael
authors.initials: M
authors.lastname: Scheel
authors.affiliation: Institute of Medical Informatics, Charité-Universitätsmedizin Berlin, Campus Benjamin Franklin, Berlin, Germany.
authors.forename: Jürgen
authors.initials: J
authors.lastname: Braun
authors.affiliation: Department of Radiology, Charité-Universitätsmedizin Berlin, Campus Charité Mitte, Berlin, Germany.
authors.forename: Ingolf
authors.initials: I
authors.lastname: Sack
mesh_terms: D000328:Adult; D000465:Algorithms; D016880:Anisotropy; D055119:Elastic Modulus; D054459:Elasticity Imaging Techniques / Q000379:methods*; D005260:Female; D006801:Humans; D021621:Imaging, Three-Dimensional / Q000379:methods*; D007866:Leg / Q000000981:diagnostic imaging*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008297:Male; D008875:Middle Aged; D018482:Muscle, Skeletal / Q000000981:diagnostic imaging*
keywords: MRE; Young's modulus; anisotropic shear modulus; gastrocnemius; magnetic resonance elastography; soleus; tibialis; transverse isotropy