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# ps_7 - Massachusetts Institute of Technology Biological...

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Massachusetts Institute of Technology Biological Engineering Division Department of Mechanical Engineering Department of Electrical Engineering and Computer Science BEH.410/2.798J/6.524J/10.539J Molecular, Cellular & Tissue Biomechanics, Spring 2003 Problem Set # 7 (Electrokinetics / muscle) Issued: Wed., 4/23/03 Due: Mon., 4/28/03 READING ASSIGNMENT: Grodzinsky, Chapter 8 (still) Kamm, Chapter 2.3, p. 18-31 PROBLEMS: Do problems 1-2 attached.

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Problem 1: Electromechanical Interactions in Charged Poroelastic Tissue A tissue specimen in the form of a cylindrical disk of thickness L is placed in the radially confining geometries of Fig. 1 and Fig. 2, in a buffer of 0.15 Molar NaCl. Assume that the tissue can be modeled as a hydrated, linear, isotropic, homogeneous matrix having negative fixed charge groups. Fig. 1 p = P 0 D Tissue x 1 x 1 = L p = 0 U = U 0 + V - a) Write the 1-dimensional equations of motion that describe the response of the tissue to mechanical or electrical stimuli in any experimental configuration. These equations include (i) conservation of momentum, (ii) conservation of mass, (iii) a stress-strain constitutive law, (iv-v) constituve laws for relative fluid velocity and electrical current density caused by pressure and voltage gradients (expressed in terms of the coupling
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ps_7 - Massachusetts Institute of Technology Biological...

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