Two-dimensional waveform analysis in MR elastography of skeletal muscles. Papazoglou, S., Braun, J.R., Hamhaber, U., & Sack, I. Phys Med Biol, 50(6):1313--1325, Mar, 2005.
Two-dimensional waveform analysis in MR elastography of skeletal muscles. [link]Paper  doi  abstract   bibtex   
A method for direct determination of anisotropic elastic coefficients using two-dimensional shear wave patterns is introduced. Thereby, the symmetry of the wave patterns is approximated by a squared elliptic equation yielding an explicit relation between waveform and elasticity. The method is used to analyse MR elastography wave images of the biceps acquired by a continuous harmonic excitation at the distal tendon of the muscle. Typically V-shaped wave patterns were observed in this type of tissue, which could be well reproduced by the proposed elliptic approximation of the waveform assuming incompressibility and a transverse isotropic model of elasticity. Without additional experiments, the analysis of straightness, slope and interferences of the wave fronts enabled us to deduce two Young's moduli and one shear modulus, which fully describe the anisotropy of the elasticity of muscles. The results suggest strong anisotropy of the living human biceps causing a shear wave speed parallel to the muscle fibres that is approximately four times faster than the perpendicular shear wave speed.
@article{ Papazoglou2005,
  author = {Papazoglou, Sebastian and Braun, J�rgen and Hamhaber, Uwe and Sack,
	Ingolf},
  title = {Two-dimensional waveform analysis in MR elastography of skeletal
	muscles.},
  journal = {Phys Med Biol},
  year = {2005},
  volume = {50},
  pages = {1313--1325},
  number = {6},
  month = {Mar},
  abstract = {A method for direct determination of anisotropic elastic coefficients
	using two-dimensional shear wave patterns is introduced. Thereby,
	the symmetry of the wave patterns is approximated by a squared elliptic
	equation yielding an explicit relation between waveform and elasticity.
	The method is used to analyse MR elastography wave images of the
	biceps acquired by a continuous harmonic excitation at the distal
	tendon of the muscle. Typically V-shaped wave patterns were observed
	in this type of tissue, which could be well reproduced by the proposed
	elliptic approximation of the waveform assuming incompressibility
	and a transverse isotropic model of elasticity. Without additional
	experiments, the analysis of straightness, slope and interferences
	of the wave fronts enabled us to deduce two Young's moduli and one
	shear modulus, which fully describe the anisotropy of the elasticity
	of muscles. The results suggest strong anisotropy of the living human
	biceps causing a shear wave speed parallel to the muscle fibres that
	is approximately four times faster than the perpendicular shear wave
	speed.},
  doi = {10.1088/0031-9155/50/6/018},
  institution = {Institute of Radiology, Charit�-University Medicine Berlin, Humboldt
	University Berlin, Berlin, Germany.},
  keywords = {Algorithms; Elasticity; Humans; Image Interpretation, Computer-Assisted,
	methods; Magnetic Resonance Imaging, instrumentation/methods; Muscle,
	Skeletal, cytology/physiology; Phantoms, Imaging; Physical Stimulation,
	methods; Reproducibility of Results; Sensitivity and Specificity;
	Stress, Mechanical},
  language = {eng},
  medline-pst = {ppublish},
  owner = {Heiko},
  pii = {S0031-9155(05)85040-7},
  pmid = {15798324},
  timestamp = {2013.07.26},
  url = {http://dx.doi.org/10.1088/0031-9155/50/6/018}
}

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