**Acknowledgement**

This manuscript recapitulates some information from original works that have previously been published in *Analytical Chemistry* (Chen et al., 2011) and *Experimental Cell Research*  (Yang et al., 2012). This work was supported in part by NSF Grants IIS-0713346 and DMI-0500372, ONR Grants N00014-04-1-0799 and N00014-07-1-0935, and NIH Grant R43 GM084520. We also appreciate the financial support from Drexel University.

### **4. References**

Addae-Mensah, K. A. & Wikswo, J. P. (2008). Measurement techniques for cellular biomechanics in vitro. *Exp. Biol. Med.,* Vol.233, No.7, pp. 792-809,

Dynamic Mechanical Response of Epithelial Cells to Epidermal Growth Factor 183

Fredriksson, C., Kihlman, S., Rodahl, M. & Kasemo, B. (1998). The piezoelectric quartz crystal mass and dissipation sensor: A means of studying cell adhesion. *Langmuir,* 

Fung, Y. C. (1984). Structure and stress-strain relationship of soft tissues. *American Zoologist,* 

Furtado, L. M. & Thompson, M. (1998). Hybridization of complementary strand and singlebase mutated oligonucleotides detected with an on-line acoustic wave sensor. *Analyst,* 

Galbraith, C. G. & Sheetz, M. P. (1997). A micromachined device provides a new bend on fibroblast traction forces. *Proceedings of the National Academy of Sciences of the United* 

Galli Marxer, C., Collaud Coen, M., Greber, T., Greber, U. & Schlapbach, L. (2003). Cell spreading on quartz crystal microbalance elicits positive frequency shifts indicative of

Heitmann, V., Reiss, B. & Wegener, J. (2007). The quartz crystal microbalance in cell biology: Basics and applications. *Springer Ser. Chem. Sens. Biosens.,* Vol.5, No.Piezoelectric

Heitmann, V. & Wegener, J. (2007). Monitoring cell adhesion by piezoresonators: Impact of increasing oscillation amplitudes. *Analytical Chemistry,* Vol.79, No.9, pp. 3392-3400,

Hoffman, B. D. & Crocker, J. C. (2009). Cell mechanics: Dissecting the physical responses of cells to force. *Annual Review of Biomedical Engineering,* Vol.11, No.1, pp. 259-288, Hook, F., Rodahl, M., Brzezinski, P. & Kasemo, B. (1998). Energy dissipation kinetics for protein and antibody-antigen adsorption under shear oscillation on a quartz crystal

Hook, F., Kasemo, B., Nylander, T., Fant, C., Sott, K. & Elwing, H. (2001). Variations in coupled water, viscoelastic properties, and film thickness of a mefp-1 protein film during adsorption and cross-linking: A quartz crystal microbalance with dissipation monitoring, ellipsometry, and surface plasmon resonance study. *Analytical Chemistry,* 

Janmey, P. A. (1998). The cytoskeleton and cell signaling: Component localization and

Janmey, P. A., Georges, P. C., Hvidt, S., YuLi, W. & Dennis, E. D. (2007). Basic rheology for biologists, In: *Methods in cell biology*, pp. 1, 3-27, Academic Press, ISBN 0091-679X, Janshoff, A., Wegener, J., Sieber, M. & Galla, H. J. (1996). Double-mode impedance analysis of epithelial cell monolayers cultured on shear wave resonators. *European Biophysics* 

Janshoff, A., Steinem, C., Sieber, M., el Bayâ, A., Schmidt, M. A. & Galla, H. J. (1997). Quartz crystal microbalance investigation of the interaction of bacterial toxins with ganglioside containing solid supported membranes. *European Biophysics Journal,* Vol.26, No.3, pp.

Kasza, K. E., Rowat, A. C., Liu, J., Angelini, T. E., Brangwynne, C. P., Koenderink, G. H. & Weitz, D. A. (2007). The cell as a material. *Curr. Opin. Cell Biol.,* Vol.19, No.1, pp. 101-

viscosity changes. *Anal. Bioanal. Chem.,* Vol.377, No.3, pp. 578-586,

microbalance. *Langmuir,* Vol.14, No.4, pp. 729-734, ISSN 0743-7463

mechanical coupling. *Physiol. Rev.,* Vol.78, No.3, pp. 763-781,

Vol.14, No.2, pp. 248-251, ISSN 0743-7463

*States of America,* Vol.94, No.17, pp. 9114-9118,

Vol.73, No.24, pp. 5796-5804, ISSN 0003-2700

*Journal,* Vol.25, No.2, pp. 93-103,

261-270,

107, ISSN 0955-0674

Vol.24, No.1, pp. 13-22,

Sensors, pp. 303-338,

ISSN 0003-2700

Vol.123 No.10, pp. 1937 - 1945,


Fredriksson, C., Kihlman, S., Rodahl, M. & Kasemo, B. (1998). The piezoelectric quartz crystal mass and dissipation sensor: A means of studying cell adhesion. *Langmuir,*  Vol.14, No.2, pp. 248-251, ISSN 0743-7463

182 Viscoelasticity – From Theory to Biological Applications

127-132, ISSN 0928-4931

Addae-Mensah, K. A. & Wikswo, J. P. (2008). Measurement techniques for cellular

Aizawa, H., et al. (2001). Conventional diagnosis of treponema pallidum in serum using latex piezoelectric immunoassay. *Materials Science and Engineering: C,* Vol.17, No.1-2, pp.

Alcaraz, J., Buscemi, L., Grabulosa, M., Trepat, X., Fabry, B., Farr, R. & Navajas, D. (2003). Microrheology of human lung epithelial cells measured by atomic force microscopy.

Alessandrini, A., Croce, M. A., Tiozzo, R. & Facci, P. (2006). Monitoring cell-cycle-related viscoelasticity by a quartz crystal microbalance. *Appl. Phys. Lett.,* Vol.88, No.8, pp.

Alexopoulos, L. G., Haider, M. A., Vail, T. P. & Guilak, F. (2003). Alterations in the mechanical properties of the human chondrocyte pericellular matrix with osteoarthritis.

Bao, G. & Suresh, S. (2003). Cell and molecular mechanics of biological materials. *Nat Mater,* 

Bretscher, A. (1989). Rapid phosphorylation and reorganization of ezrin and spectrin accompany morphological changes induced in a-431 cells by epidermal growth factor.

Chen, J. Y., Li, M., Penn, L. S. & Xi, J. (2011). Real-time and label-free detection of cellular response to signaling mediated by distinct subclasses of epidermal growth factor

Chinkers, M., McKanna, J. A. & Cohen, S. (1979). Rapid induction of morphological changes in human carcinoma cells a-431 by epidermal growth factors. *J. Cell Biol.,* Vol.83, No.1,

Chinkers, M., McKanna, J. A. & Cohen, S. (1981). Rapid rounding of human epidermoid carcinoma cells a-431 induced by epidermal growth factor. *J. Cell Biol.,* Vol.88, No.2, pp.

Collinsworth, A. M., Zhang, S., Kraus, W. E. & Truskey, G. A. (2002). Apparent elastic modulus and hysteresis of skeletal muscle cells throughout differentiation. *American* 

Dei Tos, A. P. & Ellis, I. (2005). Assessing epidermal growth factor receptor expression in tumours: What is the value of current test methods. *Eur. J. Cancer,* Vol.41, No.10, pp.

Dixon, M. C. (2008). Quartz crystal microbalance with dissipation monitoring: Enabling realtime characterization of biological materials and their interactions. *J. Biomol. Tech.,* 

Fabry, B., Maksym, G. N., Butler, J. P., Glogauer, M., Navajas, D. & Fredberg, J. J. (2001). Scaling the microrheology of living cells. *Physical Review Letters,* Vol.87, No.14, pp. 148102, Fletcher, D. A. & Mullins, R. D. (2010). Cell mechanics and the cytoskeleton. *Nature,* Vol.463,

Fredberg, J. J. & Stamenovic, D. (1989). On the imperfect elasticity of lung tissue. *Journal of* 

receptors. *Analytical Chemistry,* Vol.83, No.8, pp. 3141-3146, ISSN 0003-2700

*Journal of Physiology - Cell Physiology,* Vol.283, No.4, pp. C1219-C1227,

biomechanics in vitro. *Exp. Biol. Med.,* Vol.233, No.7, pp. 792-809,

*Biophysical Journal,* Vol.84, No.3, pp. 2071-2079, ISSN 0006-3495

*Journal of Biomechanical Engineering,* Vol.125, No.3, pp. 323-333,

083905/083901-083905/083903, ISSN 0003-6951

Vol.2, No.11, pp. 715-725, ISSN 1476-1122

*The Journal of Cell Biology,* Vol.108, No.3, pp. 921-930,

Vol.19, No.3, pp. 151-158, ISSN 1943-4731 (Electronic)

**4. References** 

pp. 260-265,

1383-1392, ISSN 0959-8049

No.7280, pp. 485-492, ISSN 0028-0836

*Applied Physiology,* Vol.67, No.6, pp. 2408-2419,

422-429,


Kuznetsova, T. G., Starodubtseva, M. N., Yegorenkov, N. I., Chizhik, S. A. & Zhdanov, R. I. (2007). Atomic force microscopy probing of cell elasticity. *Micron,* Vol.38, No.8, pp. 824- 833, ISSN 0968-4328

Dynamic Mechanical Response of Epithelial Cells to Epidermal Growth Factor 185

Pax, M., Rieger, J., Eibl, R. H., Thielemann, C. & Johannsmann, D. (2005). Measurements of fast fluctuations of viscoelastic properties with the quartz crystal microbalance. *The* 

Radmacher, M. (1997). Measuring the elastic properties of biological samples with the afm.

Radmacher, M. (2007). Studying the mechanics of cellular processes by atomic force microscopy, In: *Methods in cell biology*, YuLi W. & Dennis E. D., pp. 347-372, Academic

Redepenning, J., Schlesinger, T. K., Mechalke, E. J., Puleo, D. A. & Bizios, R. (1993). Osteoblast attachment monitored with a quartz crystal microbalance. *Analytical* 

Reipa, V., Almeida, J. & Cole, K. D. (2006). Long-term monitoring of biofilm growth and disinfection using a quartz crystal microbalance and reflectance measurements. *Journal* 

Rewcastle, G. W., Palmer, B. D., Thompson, A. M., Bridges, A. J., Cody, D. R., Zhou, H., Fry, D. W., McMichael, A. & Denny, W. A. (1996). Tyrosine kinase inhibitors. 10. Isomeric 4- [(3-bromophenyl)amino]pyrido[d]- pyrimidines are potent atp binding site inhibitors of the tyrosine kinase function of the epidermal growth factor receptor. *J. Med. Chem.,* 

Ridley, A. J. (1994). Membrane ruffling and signal transduction. *BioEssays,* Vol.16, No.5, pp.

Rijken, P. J., Hage, W. J., van Bergen en Henegouwen, P. M., Verkleij, A. J. & Boonstra, J. (1991). Epidermal growth factor induces rapid reorganization of the actin microfilament

Rijken, P. J., Post, S. M., Hage, W. J., van Bergen en Henegouwen, P. M. P., Verkleij, A. J. & Boonstra, J. (1995). Actin polymerization localizes to the activated epidermal growth factor receptor in the plasma membrane, independent of the cytosolic free calcium

Rodahl, M., Hook, F. & Kasemo, B. (1996). Qcm operation in liquids: An explanation of measured variations in frequency and q factor with liquid conductivity. *Analytical* 

Rodahl, M. & Kasemo, B. (1996). A simple setup to simultaneously measure the resonant frequency and the absolute dissipation factor of a quartz crystal microbalance. *Rev. Sci.* 

Rodahl, M., Hook, F., Fredriksson, C., Keller, C. A., Krozer, A., Brzezinski, P., Voinova, M. & Kasemo, B. (1997). Simultaneous frequency and dissipation factor qcm measurements of biomolecular adsorption and cell adhesion. *Faraday Discuss*, No.107, pp. 229-246, ISSN

Satcher Jr, R. L. & Dewey Jr, C. F. (1996). Theoretical estimates of mechanical properties of the endothelial cell cytoskeleton. *Biophysical Journal,* Vol.71, No.1, pp. 109-118, ISSN 0006-3495

transient. *Experimental Cell Research,* Vol.218, No.1, pp. 223-232, ISSN 0014-4827 Rijken, P. J., van Hal, G. J., van der Heyden, M. A. G., Verkleij, A. J. & Boonstra, J. (1998). Actin polymerization is required for negative feedback regulation of epidermal growth factor-induced signal transduction. *Experimental Cell Research,* Vol.243, No.2, pp. 254-

*IEEE Engineering in Medicine and Biology Magazine,* Vol.16, No.2, pp. 47,

*of Microbiological Methods,* Vol.66, No.3, pp. 449-459, ISSN 0167-7012

system in human a431 cells. *J. Cell Sci.,* Vol.100, No.3, pp. 491-499,

*Chemistry,* Vol.68, No.13, pp. 2219-2227, ISSN 0003-2700

*Instrum.,* Vol.67, No.9, pp. 3238-3241, ISSN 0034-6748

*Chemistry,* Vol.65, No.23, pp. 3378-3381, ISSN 0003-2700

Vol.39, No.9, pp. 1823-1835, ISSN 0022-2623

*Analyst,* Vol.130, No.11, pp. 1474-1477,

Press, ISBN 0091-679X,

321-327, ISSN 1521-1878

262, ISSN 0014-4827

1359-6640 (Print)


Pax, M., Rieger, J., Eibl, R. H., Thielemann, C. & Johannsmann, D. (2005). Measurements of fast fluctuations of viscoelastic properties with the quartz crystal microbalance. *The Analyst,* Vol.130, No.11, pp. 1474-1477,

184 Viscoelasticity – From Theory to Biological Applications

Vol.396, No.3, pp. 1143-1152, ISSN 1618-2642

No.1, pp. 23-34, ISSN 0003-2697

Vol.275, No.45, pp. 35328-35334,

ISSN 0927-7765

No.3, pp. M171-M173, ISSN 1058-2916

*Research,* Vol.12, No.24, pp. 7242-7251,

*Chemical,* Vol.128, No.2, pp. 399-406, ISSN 0925-4005

*Soft Matter,* Vol.7, No.2, pp. 332-342, ISSN 1744-683X

technique. *J. Bacteriol.,* Vol.181, No.17, pp. 5210-5218,

833, ISSN 0968-4328

1097-0290

Kuznetsova, T. G., Starodubtseva, M. N., Yegorenkov, N. I., Chizhik, S. A. & Zhdanov, R. I. (2007). Atomic force microscopy probing of cell elasticity. *Micron,* Vol.38, No.8, pp. 824-

Le Guillou-Buffello, D., Gindre, M., Johnson, P., Laugier, P. & Migonney, V. (2011). An alternative quantitative acoustical and electrical method for detection of cell adhesion process in real-time. *Biotechnology and Bioengineering,* Vol.108, No.4, pp. 947-962, ISSN

Lee, C.-W., Lin, C.-C., Lin, W.-N., Liang, K.-C., Luo, S.-F., Wu, C.-B., Wang, S.-W. & Yang, C.-M. (2007). Tnf-{alpha} induces mmp-9 expression via activation of src/egfr, pdgfr/pi3k/akt cascade and promotion of nf-{kappa}b/p300 binding in human tracheal smooth muscle cells. *Am J Physiol Lung Cell Mol Physiol,* Vol.292, No.3, pp. L799-812, Lee, H., Contarino, M., Umashankara, M., Schön, A., Freire, E., Smith, A., Chaiken, I. & Penn, L. (2010). Use of the quartz crystal microbalance to monitor ligand-induced conformational rearrangements in hiv-1 envelope protein gp120. *Anal. Bioanal. Chem.,* 

Li, F., Wang, J. H. C. & Wang, Q.-M. (2008). Thickness shear mode acoustic wave sensors for characterizing the viscoelastic properties of cell monolayer. *Sensors and Actuators B:* 

Marx, K. A., Zhou, T., Montrone, A., McIntosh, D. & Braunhut, S. J. (2005). Quartz crystal microbalance biosensor study of endothelial cells and their extracellular matrix following cell removal: Evidence for transient cellular stress and viscoelastic changes during detachment and the elastic behavior of the pure matrix. *Anal. Biochem.,* Vol.343,

Matsuda, T., Kishida, A., Ebato, H. & Okahata, Y. (1992). Novel instrumentation monitoring in situ platelet adhesivity with a quartz crystal microbalance. *ASAIO Journal,* Vol.38,

McManus, M. J., Boerner, J. L., Danielsen, A. J., Wang, Z., Matsumura, F. & Maihle, N. J. (2000). An oncogenic epidermal growth factor receptor signals via a p21-activated kinase-caldesmon-myosin phosphotyrosine complex. *Journal of Biological Chemistry,* 

Melzak, K. A., Moreno-Flores, S., Lopez, A. E. & Toca-Herrera, J. L. (2011). Why size and speed matter: Frequency dependence and the mechanical properties of biomolecules.

Nimeri, G., Fredriksson, C., Elwing, H., Liu, L., Rodahl, M. & Kasemo, B. (1998). Neutrophil interaction with protein-coated surfaces studied by an extended quartz crystal microbalance technique. *Colloids and Surfaces B: Biointerfaces,* Vol.11, No.5, pp. 255-264,

Ono, M. & Kuwano, M. (2006). Molecular mechanisms of epidermal growth factor receptor (egfr) activation and response to gefitinib and other egfr-targeting drugs. *Clinical Cancer* 

Otto, K., Elwing, H. & Hermansson, M. (1999). Effect of ionic strength on initial interactions of escherichia coli with surfaces, studied on-line by a novel quartz crystal microbalance

Papakonstanti, E. A. & Stournaras, C. (2008). Cell responses regulated by early reorganization of actin cytoskeleton. *FEBS Lett.,* Vol.582, No.14, pp. 2120-2127, ISSN 0014-5793


Sauerbrey, G. (1959). Verwendung von schwingquarzen zur wägung dünner schichten und zur mikrowägung. *Zeitschrift für Physik A Hadrons and Nuclei,* Vol.155, No.2, pp. 206-222,

**Chapter 9** 

© 2012 Kitawaki, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

Numerical flow simulation is useful for understanding fluid phenomena such as blood flow or pulse wave propagation in the systemic arteries. For numerical analysis of intravascular flow, it is important to consider not only incompressible assumption and blood viscosity but also the viscoelasticity of the blood vessel wall; however, blood flow *in vivo* is complicated because of the unsteadiness of pulsatile flow and complex viscoelastic properties of the blood vessel wall. In order to conduct such numerical flow analysis in a viscoelastic blood vessel, it is effective to use the one-dimensional distributed parameter model, which can analyze flow along with the blood vessel axis. This distributed parameter model, pressure, flow volume and cross-section of the tube for every section element are defined and the time

According to previous research, quantitative numerical simulation requires a model which take in both effects of unsteady viscous friction and viscoelasticity of the vessel wall in case flow unsteadiness is large (Reuderink et al., 1989). Conventional one-dimensional numerical simulation models can be classified into a linear distributed parameter model (Snyder et al., 1968; Avolio et al., 1980) and a nonlinear distributed parameter model (Anliker & Rockwall, 1971; Schaaf & Abbrecht, 1972; Porenta et al., 1986). The linear distributed parameter model has the feature that is easy to take in the influence of viscoelasticity and to conduct numerical analysis of the flow unsteadiness, since superposition of a periodic solution is possible; however, the influence of fluid nonlinearity cannot be disregarded. On the other hand, the conventional nonlinear distributed parameter model does not involve the effects of such flow unsteadiness and the viscoelastic behavior of the blood vessel wall concurrently with the difficulty of model construction. Hence, these models can be used

**Numerical Simulation Model with** 

**Viscoelasticity of Arterial Wall** 

Additional information is available at the end of the chapter

**1.1. Numerical analysis of intravascular flow** 

Tomoki Kitawaki

**1. Introduction** 

change is analyzed.

only for qualitative discussion.

http://dx.doi.org/10.5772/49976

