Abstract

A parallel Finite-Difference-Time-Domain (FDTD) code has been developed to numerically model the elastic light scattering by biological cells. Extensive validation and evaluation on various computing clusters demonstrated the high performance of the parallel code and its significant potential of reducing the computational cost of the FDTD method with low cost computer clusters. The parallel FDTD code has been used to study the problem of light scattering by a human red blood cell (RBC) of a deformed shape in terms of the angular distributions of the Mueller matrix elements. The dependence of the Mueller matrix elements on the shape and orientation of the deformed RBC has been investigated. Analysis of these data provides valuable insight on determination of the RBC shapes using the method of elastic light scattering measurements.

© 2005 Optical Society of America

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References

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ACES Journal (1)

J. Lumpp, S. K. Maxumdar,S. D. Gedney, "Performnce Modeling of the Finite-Difference Time-Domain Method on Parallel Systems," ACES Journal 13, 147-159, (1998).

Am. J. Physiol. Heart Circ. Physiol. (1)

T. W. Secomb, R. Hsu, A. R. Pries, "Motion of red blood cells in a capillary with an endothelial surface layer: effect of flow velocity," Am. J. Physiol. Heart Circ. Physiol. H629-H636, (2001).
[PubMed]

Appl. Comput. Electromagn. Soc. J. (1)

P. S. Excell, A. D. Tinniswood, K. Haigh-Hutchinson, "Parallel computation of large-scale electromagnetic field distributions," Appl. Comput. Electromagn. Soc. J. 13, 179-187, (1998).

Appl. Opt. (3)

Biorheology (1)

S. Chien, R. G. King, R. Skalak, S. Usami,A. L. Copley, "Viscoelastic properties of human blood and red cell suspensions," Biorheology 12, 341-6, (1975).
[PubMed]

Computational Methods for Fluid-Solid In (1)

P. R. Zardar, S. Chien,R. Skalak, "Interaction of viscous incompressible fluid with an elastic body," in Computational Methods for Fluid-Solid Interaction Problems, T. L. Geers, Ed. (American Society of Mechanical Engineers, New York: 1977) pp. 65-82.

IEEE Antennas and Wireless Propag. Lett (1)

X. Li, A. Taflove, V. Backman, "Modified FDTD near-to-far-field transformation for improved backscattering calculation for strongly forward-scattering objects," IEEE Antennas and Wireless Propagation Lett. 4, 35-38, (2005).
[CrossRef]

IEEE J. Sel. To. Quantum Electron. (1)

A. Dunn, R. Richard-Kortum, "Three-dimensional computation of light scattering from cells," IEEE J. Sel. To. Quantum Electron 2, 898-890, (1996).
[CrossRef]

IEEE Microwave Guided Wave Lett. (1)

V. Varadarajan, R. Mittra, "Finite-difference time-domain analysis using distributed computing," IEEE Microwave Guided Wave Lett. 4, 144-145, (1994).
[CrossRef]

IEEE Trans. Antennas. Propg. (1)

S. K. Yee, "Numerical solutions of initial boundary problems involving Maxwell's equations in isotropic materials," IEEE Trans. Antennas. Propg. 14, 302-307, (1966).
[CrossRef]

IEEE Trans. Biomed. Eng. (1)

A. Karlsson, J. He, J. Swartling, and S. Andersson-Engels, "Numerical simulations of light scattering by red blood cells," IEEE Trans. Biomed. Eng. 52, 13-18 (2005)
[CrossRef] [PubMed]

IEEE Trans. Microwave Theory Techniques (1)

S. Gedney, "Finite-difference time-domain analysis of microwave circuit devices on high performance vector/parallel computers," IEEE Trans. Microwave Theory Techniques 43, 2510-2514, (1995).
[CrossRef]

Int. J. Numerical Modeling (1)

K. C. Chew, V. F. Fusco, "A parallel implementaiton of the finite-difference time-domain algorithm," Int. J. Numerical Modeling 8, 293-299, (1995).
[CrossRef]

Int. J. of High Speed Computing (1)

H. Hoteit, R. Sauleau, B. Philippe, P. Coquet, J. P. Daniel, "Vector and parallel implementations for the FDTD analysis of milimeter wave planar antennas," Int. J. of High Speed Computing 10, 209-234, (1999).
[CrossRef]

J. Biomech. (1)

P. R. Zarda, S. Chien, R. Skalak, "Elastic deformations of red blood cells," J. Biomech. 10, 211-21, (1977).
[CrossRef] [PubMed]

J. Biomed. Opt. (2)

J. Q. Lu, P. Yang,X. H. Hu, "Simulations of Light Scattering from a Biconcave Red Blood Cell Using the FDTD method," J. Biomed. Opt. 10, 024022, (2005).
[CrossRef] [PubMed]

R. Drezek, M. Guillaud, T. Collier, I. Boiko, A. Malpica, C. Macaulay, M. Follen, R. Richards-Kortum, "Light scattering from cervical cells throughout neoplastic progression: influence of nuclear morphology, DNA content, and chromatin texture," J. Biomed. Opt. 8, 7-16, (2003).
[CrossRef] [PubMed]

J. Fluid Mech. (1)

T. W. Secomb, R. Skalak, N. Ozkaya, J. F. Gross, "Flow of axisymmetric red blood cells in narrow capillaries," J. Fluid Mech. 163, 405-423, (1986).
[CrossRef]

J. Opt. Soc. Am. A (2)

Microvasc Res. (1)

E. Evans,Y. C. Fung, "Improved measurements of the erythrocyte geometry," Microvasc Res. 4, 335-47, (1972).
[CrossRef] [PubMed]

Opt. Lett. (1)

Rev. Sci. Instrum. (1)

V. P. Maltsev, "Scanning flow cytometry for individual particle analysis," Rev. Sci. Instrum. 71, 243-255 (2000)
[CrossRef]

Science (1)

R. Skalak,P. I. Branemark, "Deformation of red blood cells in capillaries," Science 164, 717-9, (1969).
[CrossRef] [PubMed]

SPIE Proc. (1)

R. S. Brock, X. H. Hu, P. Yang, J. Q. Lu, "Simulation of light scattering by a pressure deformed red blood cell with a parallel FDTD method," SPIE Proc. 5702, 69-75, (2005).
[CrossRef]

Other (5)

A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, Mass., 2000).

A. J. Grimes, Human Red Cell Metabolism, (Blackwell Scientific Pub, Oxford: 1980) pp. 57.

C. F. Bohren, D. R. Huffman, Absorption and scattering of light by small particles, (Wiley, New York, 1983).

H. C. van de Hulst, Light scattering by small particles, (Wiley, New York, 1957).

C. D. Bortner, J. A. Cidlowski, "Flow Cytometric Analysis of Cell Shrinkage and Monovalent Ions during Apoptosis," in Methods in Cell Biology: Apoptosis, vol. 66, J. Ashwell and L. Schmanti, Eds. (Academic Press, San Diego, 2000).

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Figures (11)

Fig. 1.
Fig. 1.

(a) The arrangement of E and H components, offset from each other by ½ increments along each principle axis, in a Yee grid cell. (b) Data communication between two neighboring sections with the boundary plane perpendicular to the y-axis. (1) and (2) indicate the different directions of data communications.

Fig. 2.
Fig. 2.

Comparison of the parallel FDTD calculations with the Mie theory for the case of a sphere of r=2.5µm: (a) angular distributions of S11; (b) errors of the Mueller matrix elements.

Fig. 3.
Fig. 3.

Comparison of the extinction efficiency σe and the anisotropy factor g obtained by the parallel FDTD code with those by the Mie theory versus the radius of the spheres. The lines are provided as the visual aids.

Fig. 4.
Fig. 4.

FDTD simulation run times per PE and the speedup of the parallel code versus the number of PEs used in the calculation for the case of a sphere of r=1.60µm with grid size 159×159×159 and 2397 time marching steps: (a) on DSC; (b) on LSC; (c) on BLLC, and for the case of r=2.5µm with grid size 231×231×231 and 3421 time marching steps: (d) on DSC; (e) on LSC; (f) on BLLC.

Fig. 5.
Fig. 5.

The deformed RBCs and orientation definitions: (a) cross-sectional views of the RBCs under different pressure drops of ΔP (taken from Ref. [27]); (b) the 3D views with the numbers indicating the ΔP value; (c) the configuration of light scattering by a deformed RBC with the two dashed lines defining the scattering plane.

Fig. 6.
Fig. 6.

(a) The anisotropy factor g and (b) the scattering cross section σs of a RBC versus the orientation angle θi for three different values of pressure drop ΔP. The lines are provided as the visual aids.

Fig. 7.
Fig. 7.

The angular distribution of the Mueller matrix element S11 of deformed RBCs at 3 values of ΔP with 5 values of θi. The averaged distribution was obtained over 7 values of θi.

Fig. 8.
Fig. 8.

Same as Fig. 7 except for Mueller matrix element -S12/S11.

Fig. 9.
Fig. 9.

The angular distribution of the Mueller matrix element S33/S11 with the same definition of the averaged distribution as in Fig. 7. In the lower-right panel an extra dash-dot-dot line is added to represent S33/S11 calculated from the Rayleigh-Gans (R-G) theory.

Fig. 10.
Fig. 10.

The angular distribution of the normalized Mueller matrix element S22/S11 with the same definition of the averaged distribution as in Fig. 7.

Fig. 11.
Fig. 11.

The angular distribution of the normalized Mueller matrix element S34/S11 with the same definition of the averaged distribution as in Fig. 7.

Equations (6)

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H x i , j , k n + 1 2 = H x i , j , k n 1 2 + Δ t μ 0 ( E y i , j , k + 1 2 n E y i , j , k 1 2 n Δ z E z i , j + 1 2 , k n E z i , j 1 2 , k n Δ y ) ,
E x i , j , k n + 1 = E x i , j , k n + Δ t ε i , j , k ( H z i , j + 1 2 , k n + 1 2 H z i , j 1 2 , k n + 1 2 Δ y H y i , j , k + 1 2 n + 1 2 H y i , j , k 1 2 n + 1 2 Δ z ) .
( E s E s ) = e i k ( r z ) i k r ( S 2 S 3 S 4 S 1 ) ( E i E i )
S = ( F , x F , y F , x F , y ) ( cos ( θ ) sin ( θ ) sin ( θ ) cos ( θ ) ) ,
[ F , x F , x ] = i k 3 4 π V ( ε ( r ' , ω ) ε 0 1 ) [ E , x ( r ' , ω ) E , x ( r ' , ω ) ] e i k · r d 3 r ,
[ F , y F , y ] = i k 3 4 π V ( ε ( r ' , ω ) ε 0 1 ) [ E , y ( r ' , ω ) E , y ( r ' , ω ) ] e i k · r d 3 r ,

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