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Evaluation of a parallel FDTD code and application to modeling of light scattering by deformed red blood cells

R. Scott Brock, Xin-Hua Hu, Ping Yang, and Jun Q. Lu

Open Access Open Access

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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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.

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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.

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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.

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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.

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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.

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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.

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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.

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Fig. 8.
Fig. 8. Same as Fig. 7 except for Mueller matrix element -S12/S11.

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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.

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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.

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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.

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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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