Fractal network dimension and viscoelastic powerlaw behavior: I. A modeling approach based on a coarse-graining procedure combined with shear oscillatory rheometry

Physics in Medicine and Biology

Volumn 57, Issue 12, 2012, Pages 4023-4040

  Posnansky, Oleg ^a   Guo, Jing ^a   Hirsch, Sebastian ^a   Papazoglou, Sebastian ^a   Braun, Jürgen ^a   Sack, Ingolf ^a  

^a CHARITÉ UNIVERSITÄTSMEDIZIN BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

AGAROSE GEL; BIOLOGICAL SOFT TISSUE; BIOLOGICAL TISSUES; BIORHEOLOGY; COARSE GRAINING; COMPLEX SHEAR MODULUS; CONSTITUTIVE LAW; ELASTOGRAPHY; FRACTAL MODEL; FRACTAL NETWORK; FREQUENCY-DEPENDENT; IN-VIVO; MECHANICAL NETWORK; MODEL NETWORKS; MODELING APPROACH; MULTISCALES; POWER LAW EXPONENT; POWER-LAW; POWER-LAW BEHAVIOR; RHEOMETRY; RIGID ENVIRONMENT; SPATIAL VARIATIONS;

BIOMECHANICS; ELASTIC MODULI; ENVIRONMENTAL REGULATIONS; FRACTAL DIMENSION; MEDICAL IMAGING; RHEOMETERS;

TISSUE;

ARTICLE; ELASTICITY; ELASTOGRAPHY; FLOW KINETICS; FRACTAL ANALYSIS; THEORETICAL MODEL; VISCOSITY;

ELASTICITY; ELASTICITY IMAGING TECHNIQUES; FRACTALS; MODELS, THEORETICAL; RHEOLOGY; VISCOSITY;

EID: 84862013834     PISSN: 00319155     EISSN: 13616560     Source Type: Journal    
DOI: 10.1088/0031-9155/57/12/4023     Document Type: Article

References (35)

1. Carcione J 2007 Wave Fields in Real Media: Wave Propagation in Anisotropic, Anelastic, Porous and Electromagnetic Media (Amsterdam: Elsevier)
2. 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
3. Deffieux T, Montaldo G, Tanter M and Fink M 2009 Shear wave spectroscopy for in vivo quantification of human soft tissues visco-elasticity IEEE Trans. Med. Imaging 28 31322
4. Domb C and Lebowitz J L 2001 Phase Transitions and Critical Phenomena (London: Academic)
5. Feller W 1968 An Introduction to Probability Theory and Its Applications (New York: Wiley)
6. Geerligs M, Peters G W, Ackermans P A, Oomens C W and Baaijens F P 2008 Linear viscoelastic behavior of subcutaneous adipose tissue Biorheology 45 67788
7. 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
8. Guo J, Posnansky O, Hirsch S, Scheel M, Braun J and Sack I 2012 Fractal network dimension and viscoelastic powerlaw behavior: II. An experimental study of structure-mimicking phantoms by magnetic resonance elastography Phys. Med. Biol. 57 4041
9. Gurtovenko A A and Blumen A 2005 Polymer Analysis, Polymer Theory (Berlin: Springer) pp 171282
10. 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
11. Jeong H, Tombor B, Albert R, Oltvai Z N and Barabasi A-L 2000 The large-scale organization of metabolic networks Nature 407 6514
12. Klatt D, Friedrich C, Korth Y, Vogt R, Braun J and Sack I 2010a Viscoelastic properties of liver measured by oscillatory rheometry and multifrequency magnetic resonance elastography Biorheology 47 13341
13. Klatt D, Hamhaber U, Asbach P, Braun J and Sack I 2007 Noninvasive assessment of the rheological behavior of human internal organs using multifrequency MR elastography: a study of brain and liver viscoelasticity Phys. Med. Biol. 52 728194 (Pubitemid 350242840)
14. Klatt D, Papazoglou S, Braun J and Sack I 2010b Viscoelasticity-based Magnetic resonance elastography of skeletal muscle Phys. Med. Biol. 55 644559
15. Landau L D, Lifshitz E M and Pitaevskii L P 1980 Statistical Physics (Amsterdam: Elsevier)
16. 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
17. Mandelbrot B B 1983 The Fractal Geometry of Nature (New York: Freeman)
18. Milton G M 2002 Theory of Composites (Cambridge: Cambridge University Press)
19. Muthupillai R and Ehman R L 1996 Magnetic resonance elastography Nature Med. 2 6013 (Pubitemid 26150690)
20. 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
21. Papazoglou S, Hirsch S, Braun J and Sack I 2012 Multifrequency inversion in magnetic resonance elastography Phys. Med. Biol. 57 232946
22. 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)
23. Plewes D B, Betty I, Urchuk S N and Soutar I 1995 Visualizing tissue compliance with MR imaging J. Magn. Reson. Imaging 5 7338
24. Reynolds P J, Klein W and Stanley H E 1977 A real-space renormalization group for site and bond percolation J. Phys. C: Solid State Phys. 10 L16772
25. 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
26. Sack I, Streitberger K J, Krefting D, Paul F and Braun J 2011 The influence of physiological aging and atrophy on brain viscoelastic properties in humans Plos One 6 e23451
27. Schiessel H and Blumen A 1995 Mesoscopic pictures of the solgel transition - ladder models and fractal networks Macromolecules 28 40139
28. 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)
29. Stanley H E 1978 Introductions to Phase Transitions and Critical Phenomena (Oxford: Oxford University Press)
30. Streitberger K J et al 2011 In vivo viscoelastic properties of the brain in normal pressure hydrocephalus NMR Biomed. 24 38592
31. 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
32. Xu H, Rao M, Varghese T, Sommer A, Baker S, Hall T J, Sisney G A and Burnside E S 2010 Axial-shear strain imaging for differentiating benign and malignant breast masses Ultrasound Med. Biol. 36 181324
33. Yin M, Talwalkar J A, Glaser K J, Manduca A, Grimm R C, Rossman P J, Fidler J L and Ehman R L 2007 Assessment of hepatic fibrosis with magnetic resonance elastography Clin. Gastroenterol. Hepatol. 5 120713 (Pubitemid 47488968)
34. Zhang M, Nigwekar P, Castaneda B, Hoyt K, Joseph J V, di SantAgnese 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)
35. Ziol M et al 2005 Noninvasive assessment of liver fibrosis by measurement of stiffness in patients with chronic hepatitis C Hepatology 41 4854 (Pubitemid 40066382)