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TECHNICAL PAPERS: Cell

# The Deformation of an Erythrocyte Under the Radiation Pressure by Optical Stretch

[+] Author and Article Information
Yong-Ping Liu, Alvin C. K. Lai

School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore

Chuan Li

School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singaporemcli@ntu.edu.sg

Kuo-Kang Liu

Institute of Science and Technology in Medicine, School of Medicine, Keele University, Thornburrow Drive, Hartshill, Stoke-on-Trent ST4 7QB, UK

J Biomech Eng 128(6), 830-836 (Apr 22, 2006) (7 pages) doi:10.1115/1.2354204 History: Received October 17, 2005; Revised April 22, 2006

## Abstract

In this paper, the mechanical properties of erythrocytes were studied numerically based upon the mechanical model originally developed by Pamplona and Calladine (ASME J. Biomech. Eng., 115, p. 149, 1993) for liposomes. The case under study is the erythrocyte stretched by a pair of laser beams in opposite directions within buffer solutions. The study aims to elucidate the effect of radiation pressure from the optical laser because up to now little is known about its influence on the cell deformation. Following an earlier study by Guck (Phys. Rev. Lett., 84, p. 5451, 2000; Biophys. J., 81, p. 767, 2001), the empirical results of the radiation pressure were introduced and imposed on the cell surface to simulate the real experimental situation. In addition, an algorithm is specially designed to implement the simulation. For better understanding of the radiation pressure on the cell deformation, a large number of simulations were conducted for different properties of cell membrane. Results are first discussed parametrically and then evaluated by comparing with the experimental data reported by Guck An optimization approach through minimizing the errors between experimental and numerical data is used to determine the optimal values of membrane properties. The results showed that an average shear stiffness around $4.611×10–6Nm−1$, when the nondimensional ratio of shear modulus to bending modulus ranges from 10 to 300. These values are in a good agreement with those reported in literature.

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## Figures

Figure 1

Schematic representation of a spherical cell trapped by a pair of laser beams aligned in opposite directions

Figure 2

The geometry and coordinate system of a spherical cell membrane: (a) the undeformed spherical membrane with diameter a and (b) the deformed membrane in dimensionless coordinates (R*, Z*) where R*=R∕a, Z*=Z∕a, S*=S∕a, and Z* is the axis of symmetry

Figure 3

The flowchart of numerical procedures

Figure 4

The profile of a spherical cell membrane after stretched by a pair of laser beams along the Z*-axis at R*=0 (σ0* is the magnitude of dimensionless stretching force)

Figure 5

Comparison of the deformation for a spherical cell with C=1.0 and 5.0

Figure 6

The transverse and longitudinal strains as function of the stretching forces for different membrane stiffness

Figure 7

Figure 8

The Taylor deformation parameter (D12=(z(0)−r(π∕2))∕(z(0)+r(π∕2))) as a function of the stretching force. Data are adapted from the experimental results in Refs. 9-10.

Figure 9

The contour of errors as a function of C and bending stiffness B. Corresponding shear stiffness G is shown in the top figure.

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