Fractional order viscoelasticity in characterization for atrial tissue

Jing Jin Shen; Cheng Gang Li; Hong Tao Wu; Masoud Kalantari

Korea-Australia Rheology Journal, Vol.25, No.2, 87-93, May, 2013

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Fractional order viscoelasticity in characterization for atrial tissue

Jing Jin Shen^{1, 2, †}, Cheng Gang Li¹, Hong Tao Wu¹, and Masoud Kalantari³

¹College of Mechanical Engineering, Nanjing University of Aeronautics and Astronautics, China
²Centre for Intelligent Machines (CIM), McGill University, Canada
³National Oilwell Varco, Canada

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Atrial tissue due to its solid-like and fluid-like constituents shows highly viscoelastic properties. Up to now, the distribution pattern of muscle fiber in heart is not well established, and it is hard to establish the constitutive model for atrial tissue completely based on the microstructure level. Consider the equivalence between the fractional viscoelasticity and the fractal spring-dashpot model, a generalized fractional order Maxwell model is proposed to model the porcine atrial tissue in the phenomenological sense. This model has a simple expression and intuitively physical meanings. The constitutive parameters in the model are estimated in the complex domain by a genetic algorithm. Final results illustrate the proposed model gets a well agreement with the experimental data.

Keywords:fractional order;atrial tissue;viscoelasticity;DMA test;genetic algorithm

[References]

Abramowitch S, Savio L, Journal of Biomechanical Engineering., 126, 92 (2004)
Abramowitch S, Zhang X, Curran M, Kilger R, Clinical Biomechanics., 25(4), 325 (2010)
Boldt A, Wetzel U, Lauschke J, Weigl J, Gummert J, Hindricks G, Kottkamp H, Dhein S, Heart., 90(4), 400 (2004)
Brinson H, Brinson L, Polymer engineering science and viscoelasticity: an introduction, Springer Verlag. (2008)
Carew E, Barber J, Vesely I, Annals of Biomedical Engineering., 28(9), 1093 (2000)
Cho KS, Korea-Aust. Rheol. J., 24(4), 323 (2012)
Craiem D, Magin R, Physics Biology., 013001-3, 7 (2010)
Craiem D, Rojo F, Atienza J, Armentano R, Guinea G, Physics in Medicine and Biology., 53, 4543 (2008)
Degeeter N, Ionescu C, Dekeyser R, A mechanical model of soft biological tissue; an application to lung parenchyma. In: Engineering in Medicine and Biology Society,2009, EMBC 2009, Annual International Conference of the IEEE. (2009)
Diethelm K, Ford N, Freed A, Luchko Y, Computer Methods in Applied Mechanics and Engineering., 194(6-8), 743 (2005)
Doehring T, Freed A, Carew E, Vesely I, Journal of Biomechanical Engineering., 127, 700 (2005)
Fung Y, Biomechanics: mechanical properties of living tissues, Springer. (1993)
Groth K, Granata K, Journal of Biomechanical Engineering., 0310051, 130 (2008)
Horowitz A, Lanir Y, Yin F, Perl M, Sheinman I, Strumpf R, Journal of Biomechanical Engineering., 110, 200 (1988)
Ionescu C, Fractional order models of the human respiratory system, Ph.D. thesis, Ghent University (2009)
Kiss M, Varghese T, Hall T, Physics in Medicine and Biology., 49, 4207 (2004)
Kumar A, Stickland AD, Scales PJ, Korea-Aust. Rheol. J., 24(2), 105 (2012)
Lakes R, Viscoelastic materials, Cambridge University Press, Cambridge, UK. (2009)
Mainardi F, Fractional calculus and waves in linear viscoelasticity: an introduction to mathematical models, Imperial College Press (2009)
Menard K, Dynamic Mechanical Analysis: a Practical Introduction, CRC, New York. (1999)
Meral F, Royston T, Magin R, Communications in Nonlinear Science and Numerical Simulation., 15(4), 939 (2010)
Orosz M, Molnarka G, Monos E, Medical Science Monitor., 3(4), 599 (1997)
Park S, Schapery R, International Journal of Solids and Structures., 36(11), 1653 (1999)
Sasaki N, Nakayama Y, Yoshikawa M, Enyo A, Journal of Biomechanics., 26(12), 1369 (1993)
Schiessel H, Blumen A, Journal of Physics A: Mathematical and General., 26, 5057 (1993)
Shen JJ, Masou K, Joszef K, Jorge A, Javid D, Measuring the properties of heart tissue with dynamic mechanical analysis method. In: 2011 CCToMM Symposium on Mechanisms, Machines, and Mechatronics (2011)
Shen JJ, Kalantari M, Kovecses J, Angeles J, Dargahi J, IEEE Transactions on Biomedical Engineering., 59(6), 1727 (2012)
Suki B, Barabasi A, Lutchen K, Journal of Applied Physiology., 76(6), 2749 (1994)
Tripathy S, Berger EJ, Computer Methods in Biomechanics and Biomedical Engineering., 1, 1 (2011)
Troyer KL, Estep DJ, Puttlitz CM, Acta Biomaterialia., 8(1), 234 (2012)
Yang W, Fung T, Chian K, Chong C, Journal of Biomechanical Engineering., 128, 909 (2006)

[Referenced By]

[1] Abramowitch S, Savio L, Journal of Biomechanical Engineering., 126, 92 (2004)

[2] Abramowitch S, Zhang X, Curran M, Kilger R, Clinical Biomechanics., 25(4), 325 (2010)

[3] Boldt A, Wetzel U, Lauschke J, Weigl J, Gummert J, Hindricks G, Kottkamp H, Dhein S, Heart., 90(4), 400 (2004)

[4] Brinson H, Brinson L, Polymer engineering science and viscoelasticity: an introduction, Springer Verlag. (2008)

[5] Carew E, Barber J, Vesely I, Annals of Biomedical Engineering., 28(9), 1093 (2000)

[6] Cho KS, Korea-Aust. Rheol. J., 24(4), 323 (2012)

[7] Craiem D, Magin R, Physics Biology., 013001-3, 7 (2010)

[8] Craiem D, Rojo F, Atienza J, Armentano R, Guinea G, Physics in Medicine and Biology., 53, 4543 (2008)

[9] Degeeter N, Ionescu C, Dekeyser R, A mechanical model of soft biological tissue; an application to lung parenchyma. In: Engineering in Medicine and Biology Society,2009, EMBC 2009, Annual International Conference of the IEEE. (2009)

[10] Diethelm K, Ford N, Freed A, Luchko Y, Computer Methods in Applied Mechanics and Engineering., 194(6-8), 743 (2005)

[11] Doehring T, Freed A, Carew E, Vesely I, Journal of Biomechanical Engineering., 127, 700 (2005)

[12] Fung Y, Biomechanics: mechanical properties of living tissues, Springer. (1993)

[13] Groth K, Granata K, Journal of Biomechanical Engineering., 0310051, 130 (2008)

[14] Horowitz A, Lanir Y, Yin F, Perl M, Sheinman I, Strumpf R, Journal of Biomechanical Engineering., 110, 200 (1988)

[15] Ionescu C, Fractional order models of the human respiratory system, Ph.D. thesis, Ghent University (2009)

[16] Kiss M, Varghese T, Hall T, Physics in Medicine and Biology., 49, 4207 (2004)

[17] Kumar A, Stickland AD, Scales PJ, Korea-Aust. Rheol. J., 24(2), 105 (2012)

[18] Lakes R, Viscoelastic materials, Cambridge University Press, Cambridge, UK. (2009)

[19] Mainardi F, Fractional calculus and waves in linear viscoelasticity: an introduction to mathematical models, Imperial College Press (2009)

[20] Menard K, Dynamic Mechanical Analysis: a Practical Introduction, CRC, New York. (1999)

[21] Meral F, Royston T, Magin R, Communications in Nonlinear Science and Numerical Simulation., 15(4), 939 (2010)

[22] Orosz M, Molnarka G, Monos E, Medical Science Monitor., 3(4), 599 (1997)

[23] Park S, Schapery R, International Journal of Solids and Structures., 36(11), 1653 (1999)

[24] Sasaki N, Nakayama Y, Yoshikawa M, Enyo A, Journal of Biomechanics., 26(12), 1369 (1993)

[25] Schiessel H, Blumen A, Journal of Physics A: Mathematical and General., 26, 5057 (1993)

[26] Shen JJ, Masou K, Joszef K, Jorge A, Javid D, Measuring the properties of heart tissue with dynamic mechanical analysis method. In: 2011 CCToMM Symposium on Mechanisms, Machines, and Mechatronics (2011)

[27] Shen JJ, Kalantari M, Kovecses J, Angeles J, Dargahi J, IEEE Transactions on Biomedical Engineering., 59(6), 1727 (2012)

[28] Suki B, Barabasi A, Lutchen K, Journal of Applied Physiology., 76(6), 2749 (1994)

[29] Tripathy S, Berger EJ, Computer Methods in Biomechanics and Biomedical Engineering., 1, 1 (2011)

[30] Troyer KL, Estep DJ, Puttlitz CM, Acta Biomaterialia., 8(1), 234 (2012)

[31] Yang W, Fung T, Chian K, Chong C, Journal of Biomechanical Engineering., 128, 909 (2006)