Fractal network dimension and viscoelastic powerlaw behavior: II. An experimental study of structure-mimicking phantoms by magnetic resonance elastography

Physics in Medicine and Biology

Volumn 57, Issue 12, 2012, Pages 4041-4053

  Guo, Jing ^a   Posnansky, Oleg ^a   Hirsch, Sebastian ^a   Scheel, Michael ^a   Taupitz, Matthias ^a   Braun, Juergen ^a   Sack, Ingolf ^a  

^a CHARITÉ UNIVERSITÄTSMEDIZIN BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

AGAROSE GEL; COMPLEX SHEAR MODULUS; DYNAMIC RANGE; EFFECTIVE MEDIA; ELASTICITY MODULI; ELASTOGRAPHY; EXPERIMENTAL STUDIES; FRACTAL NETWORK; FREQUENCY DEPENDENCE; GEL PHANTOM; IMAGINARY PARTS; IN-VIVO; LOSS MODULI; MAGNETIC RESONANCE ELASTOGRAPHY; MECHANICAL NETWORK; MULTI FREQUENCY; MULTIPLE SCALE; MULTISCALES; NETWORK STRUCTURES; NETWORK TOPOLOGY; POWER LAW EXPONENT; POWER-LAW; POWER-LAW BEHAVIOR; REAL PART; SOFT BIOLOGICAL TISSUE; SOFT TISSUE; SPRING-POT; STRUCTURAL SENSITIVITY; STRUCTURE-SENSITIVE; VISCO-ELASTIC PARAMETERS; VISCOELASTIC PROPERTIES; WATER DIFFUSION; WATER MOBILITY;

DIFFUSION TENSOR IMAGING; ELASTIC MODULI; ELECTRIC NETWORK TOPOLOGY; MAGNETIC RESONANCE; MAGNETIC RESONANCE IMAGING; MEDICAL IMAGING; TENSORS; TISSUE; VISCOELASTICITY;

FRACTAL DIMENSION;

ARTICLE; ELASTICITY; ELASTOGRAPHY; FRACTAL ANALYSIS; IMAGE QUALITY; INSTRUMENTATION; VISCOSITY;

ELASTICITY; ELASTICITY IMAGING TECHNIQUES; FRACTALS; PHANTOMS, IMAGING; VISCOSITY;

EID: 84862017885     PISSN: 00319155     EISSN: 13616560     Source Type: Journal    
DOI: 10.1088/0031-9155/57/12/4041     Document Type: Article

References (47)

1. Asbach P et al 2010 Viscoelasticity-based staging of hepatic fibrosis with multifrequency MR elastography Radiology 257 806
2. Baghani A, Brant A, Salcudean S and Rohling R 2010 A high-frame-rate ultrasound system for the study of tissue motions IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57 153547
3. Bausch A R and Kroy K 2006 A bottom-up approach to cell mechanics Nature Phys. 2 2318 (Pubitemid 43553642)
4. Besicovitch A S 1929 On linear sets of points of fractional dimension Math. Ann. 101 16393
5. Bishop J, Poole G, Leitch M and Plewes D B 1998 Magnetic resonance imaging of shear wave propagation in excised tissue J. Magn. Reson. Imaging 8 125765 (Pubitemid 28533670)
6. Chen Q, Suki B and An K N 2004 Dynamic mechanical properties of agarose gels modeled by a fractional derivative model J. Biomech. Eng. 126 66671 (Pubitemid 40019153)
7. Clayton E H, Garbow J R and Bayly P V 2011 Frequency-dependent viscoelastic parameters of mouse brain tissue estimated by MR elastography Phys. Med. Biol. 56 2391406
8. Feder J 1988 Fractals (New York: Plenum)
9. Freimann F B, Streitberger K J, Klatt D, Lin K, McLaughlin J, Braun J, Sprung C and Sack I 2012 Alteration of brain viscoelasticity after shunt treatment in normal pressure hydrocephalus Neuroradiology 54 18996
10. Gennisson J L, Deffieux T, Mace E, Montaldo G, Fink M and Tanter M 2010 Viscoelastic and anisotropic mechanical properties of in vivo muscle tissue assessed by supersonic shear imaging Ultrasound Med. Biol. 36 789801
11. Gurtovenko A A and Blumen A 2005 Polymer Analysis, Polymer Theory (Berlin: Springer) pp 171282
12. Hausdorff F 1919 Dimension and äueres Ma Math. Ann. 79 15779
13. Holzapfel G A 2004 Nonlinear Solid Mechanics (West Sussex: Wiley)
14. Hoyt K, Kneezel T, Castaneda B and Parker K J 2008 Quantitative sonoelastography for the in vivo assessment of skeletal muscle viscoelasticity Phys. Med. Biol. 53 406380
15. Jurjiu A, Friedrich C and Blumen A 2002 Strange kinetics of polymeric networks modelled by finite fractals Chem. Phys. 284 22131
16. Klatt D, Papazoglou S, Braun J and Sack I 2010 Viscoelasticity-based magnetic resonance elastography of skeletal muscle Phys. Med. Biol. 55 644559
17. Kolmogorov A N and Tikhomirov V M 1959 ε-entropy and ε-capacity of sets in a function space Usp. Mat. Nauk 14 386
18. Kruse S A, Smith J A, Lawrence A J, Dresner M A, Manduca A, Greenleaf J F and Ehman R L 2000 Tissue characterization using magnetic resonance elastography: preliminary results Phys. Med. Biol. 45 157990 (Pubitemid 30408920)
19. Lorenz R, Bellemann M E, Hennig J and Il'yasov K A 2008 Anisotropic phantoms for quantitative diffusion tensor imaging and fiber-tracking validation Appl. Magn. Reson. 33 41929
20. Magin R L and Royston T J 2010 Fractional-order elastic models of cartilage: a multi-scale approach Commun. Nonlinear Sci. Numer. Simul. 15 65764
21. Meyers M A, Chen P Y, Lin A Y M and Seki Y 2008 Biological materials: structure and mechanical properties Prog. Mater. Sci. 53 1206 (Pubitemid 350017839)
22. Muthupillai R and Ehman R L 1996 Magnetic resonance elastography Nature Med. 2 6013 (Pubitemid 26150690)
23. Okamoto R J, Clayton E H and Bayly P V 2011 Viscoelastic properties of soft gels: comparison of magnetic resonance elastography and dynamic shear testing in the shear wave regime Phys. Med. Biol. 56 6379400
24. Oliphant T E, Manduca A, Ehman R L and Greenleaf J F 2001 Complex-valued stiffness reconstruction for magnetic resonance elastography by algebraic inversion of the differential equation Magn. Reson. Med. 45 299310 (Pubitemid 32119014)
25. Ophir J, Cespedes I, Ponnekanti H, Yazdi Y and Li X 1991 Elastography: a quantitative method for imaging the elasticity of biological tissues Ultrason. Imaging 13 11134
26. Papazoglou S, Braun J, Klatt D and Sack I 2012 New Developments in the Visualization and Processing of Tensor Fields ed D H Laidlaw and A Vilanova (Berlin: Springer) p 410
27. Papazoglou S, Hamhaber U, Braun J and Sack I 2008 Algebraic Helmholtz inversion in planar magnetic resonance elastography Phys. Med. Biol. 53 314758 (Pubitemid 351892392)
28. Parker K J, Huang S R, Musulin R A and Lerner R M 1990 Tissue response to mechanical vibrations for sonoelasticity imaging Ultrasound Med. Biol. 16 2416 (Pubitemid 20247313)
29. Posnansky O, Guo J, Hirsch S, Braun J and Sack I 2012 Fractal network dimension and viscoelastic powerlaw behavior: I. A modeling approach based on a coarse-graining procedure combined with shear oscillatory rheometry Phys. Med. Biol. 57 4023
30. Riek K, Klatt D, Nuzha H, Mueller S, Neumann U, Sack I and Braun J 2011 Wide-range dynamic magnetic resonance elastography J. Biomech. 44 13806
31. Romano A, Scheel M, Hirsch S, Braun J and Sack I 2012 In vivo waveguide elastography of white matter tracts in the human brain Magn. Reson. Med. doi: 10.1002/mrm.24141. [Epub ahead of print]
32. Sack I, Beierbach B, Hamhaber U, Klatt D and Braun J 2008 Non-invasive measurement of brain viscoelasticity using magnetic resonance elastography NMR Biomed. 21 26571 (Pubitemid 351513674)
33. Sack I, Beierbach B, Wuerfel J, Klatt D, Hamhaber U, Papazoglou S, Martus P and Braun J 2009 The impact of aging and gender on brain viscoelasticity Neuroimage 46 6527
34. Sack I, Gedat E, Bernarding J, Buntkowsky G and Braun J 2004 Magnetic resonance elastography and diffusion-weighted imaging of the sol/gel phase transition in agarose J. Magn. Reson. 166 25261
35. Sandrin L, Tanter M, Catheline S and Fink M 2002 Shear modulus imaging with 2-D transient elastography IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49 42635 (Pubitemid 34555340)
36. Schiessel H and Blumen A 1995 Mesoscopic pictures of the solgel transition - ladder models and fractal networks Macromolecules 28 40139
37. Sen P N and Basser P J 2005 A model for diffusion in white matter in the brain Biophys. J. 89 292738 (Pubitemid 41636050)
38. Sinkus R, Lorenzen J, Schrader D, Lorenzen M, Dargatz M and Holz D 2000 High-resolution tensor MR elastography for breast tumour detection Phys. Med. Biol. 45 164964 (Pubitemid 30408924)
39. Sinkus R, Siegmann K, Xydeas T, Tanter M, Claussen C and Fink M 2007 MR elastography of breast lesions: understanding the solid/liquid duality can improve the specificity of contrast-enhanced MR mammography Magn. Reson. Med. 58 113544 (Pubitemid 350234200)
40. Smith S M et al 2004 Advances in functional and structural MR image analysis and implementation as FSL Neuroimage 23 S20819 (Pubitemid 39421720)
41. Suki B, Barabasi A L and Lutchen K R 1994 Lung tissue viscoelasticity: a mathematical framework and its molecular basis J. Appl. Physiol. 76 274959 (Pubitemid 24184805)
42. Szafer A, Zhong J, Anderson A W and Gore J C 1995 Diffusion-weighted imaging in tissues: theoretical models NMR Biomed. 8 28996
43. Van Houten E E, Doyley M M, Kennedy F E, Weaver J B and Paulsen K D 2003 Initial in vivo experience with steady-state subzone-based MR elastography of the human breast J. Magn. Reson. Imaging 17 7285 (Pubitemid 36034137)
44. Vappou J, Breton E, Choquet P, Goetz C, Willinger R and Constantinesco A 2007 Magnetic resonance elastography compared with rotational rheometry for in vitro brain tissue viscoelasticity measurement Magma 20 2738
45. Wuerfel J, Paul F, Beierbach B, Hamhaber U, Klatt D, Papazoglou S, Zipp F, Martus P, Braun J and Sack I 2010 MR-elastography reveals degradation of tissue integrity in multiple sclerosis Neuroimage 49 25205
46. Young L S 1984 Dimension, entropy and lyapunov exponents in differentiable dynamical-systems Physica A 124 63945
47. Zhang M, Nigwekar P, Castaneda B, Hoyt K, Joseph J V, di Sant'Agnese A, Messing E M, Strang J G, Rubens D J and Parker K J 2008 Quantitative characterization of viscoelastic properties of human prostate correlated with histology Ultrasound Med. Biol. 34 103342 (Pubitemid 351893146)