Research Papers

Volumetric Stress-Strain Analysis of Optohydrodynamically Suspended Biological Cells

[+] Author and Article Information
Sean S. Kohles1

Reparative Bioengineering Laboratory, Department of Mechanical and Materials Engineering, Portland State University, Portland, OR 97207; Department of Surgery, Oregon Health and Science University, Portland, OR 97239kohles@cecs.pdx.edu

Yu Liang

Center for Allaying Health Disparities Through Research and Education (CADRE), Department of Mathematics and Computer Science, Central State University, Wilberforce, OH 45384yliang@centralstate.edu

Asit K. Saha

Center for Allaying Health Disparities Through Research and Education (CADRE), Department of Mathematics and Computer Science, Central State University, Wilberforce, OH 45384asaha@centralstate.edu


Corresponding author.

J Biomech Eng 133(1), 011004 (Dec 22, 2010) (6 pages) doi:10.1115/1.4002939 History: Received September 15, 2010; Revised October 24, 2010; Posted November 02, 2010; Published December 22, 2010; Online December 22, 2010

Ongoing investigations are exploring the biomechanical properties of isolated and suspended biological cells in pursuit of understanding single-cell mechanobiology. An optical tweezer with minimal applied laser power has positioned biologic cells at the geometric center of a microfluidic cross-junction, creating a novel optohydrodynamic trap. The resulting fluid flow environment facilitates unique multiaxial loading of single cells with site-specific normal and shear stresses resulting in a physical albeit extensional state. A recent two-dimensional analysis has explored the cytoskeletal strain response due to these fluid-induced stresses [Wilson and Kohles, 2010, “Two-Dimensional Modeling of Nanomechanical Stresses-Strains in Healthy and Diseased Single-Cells During Microfluidic Manipulation,” J Nanotechnol Eng Med, 1(2), p. 021005]. Results described a microfluidic environment having controlled nanometer and piconewton resolution. In this present study, computational fluid dynamics combined with multiphysics modeling has further characterized the applied fluid stress environment and the solid cellular strain response in three dimensions to accompany experimental cell stimulation. A volumetric stress-strain analysis was applied to representative living cell biomechanical data. The presented normal and shear stress surface maps will guide future microfluidic experiments as well as provide a framework for characterizing cytoskeletal structure influencing the stress to strain response.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

Schematic representations of (a) the microchannel configuration facilitating the optohydrodynamic trap and (b) the relationship between Cartesian (x-y-z) and spherical polar (r-θ-ϕ) coordinate systems (19)

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Figure 2

Planar experimental flow velocities in an isolated quadrant surrounding an optically and hydrodynamically trapped analogous cell (20.6 μm diameter polystyrene microsphere) as measured with micrometer-resolution particle image velocimetry (6). Maximum velocity gradients are associated with maximum applied normal and shear stresses.

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Figure 3

The fully characterized volumetric pressure field at the geometric center of the cross-junction channel (a) with and (b) without the cell perturbing the flow field (Eq. 10). The balance in applied stresses leads to an efficient hydrodynamic trap. Axis units are locations relative to the radius of the cell (a/r).

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Figure 4

Individual components of the volumetric stress state applied to the surface (r=a) of a single cell as modeled within the optohydrodynamic trap. These stresses include (a) normal stress, σrr, (b) shear stress in the xy-plane, τrθ, and (c) shear stress in the xz-plane, τrϕ (Eq. 12). The colors of the full-field stress map indicate locations with positive (+red), negative (−blue), and zero (0 green) hydrodynamic stresses based on the prescribed coordinate system. Axis units are spatial locations relative to the radius of the cell (a/r).

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Figure 5

Volumetric stress versus strain of an optohydrodynamically trapped myoblast. The z-direction view cell images represent the cell under no dynamic load (left) and with the maximum applied hydrodynamic load (right). Volumetric strains are equivalent to that of the fractional change in volume of the spherical cell as well as those calculated from the orthogonal principal strains. Strain due to droplet deformation theory is shown for comparison (26).



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