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A Pulsed Finite-Difference Time-Domain (FDTD) Method for Calculating Light Scattering from Biological Cells Over Broad Wavelength Ranges

Rebekah Drezek, Andrew Dunn, and Rebecca Richards-Kortum

Open Access Open Access

Abstract

We combine the finite-difference time-domain method with pulse response techniques in order to calculate the light scattering properties of biological cells over a range of wavelengths simultaneously. The method we describe can be used to compute the scattering patterns of cells containing multiple heterogeneous organelles, providing greater geometric flexibility than Mie theory solutions. Using a desktop computer, we calculate the scattering patterns for common homogeneous models of biological cells and also for more complex representations of cellular morphology. We find that the geometry chosen significantly impacts scattering properties, emphasizing the need for careful consideration of appropriate theoretical models of cellular scattering and for accurate microscopic determination of optical properties.

©2000 Optical Society of America

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Figures (4)
Fig. 1.
Fig. 1. Validation of the pulse response FDTD code. Comparison of FDTD pulse response results with Mie theory predictions for a 4 µm circular object (m=1.02, λ=1 µm and λ=2 µm). Curves are normalized to scattered intensity at 0°.

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Fig 2.
Fig 2. Validation of the pulse response FDTD code. Calculated scattering diagrams for a series of infinite cylinders (m=1.50, x=1.2 to 2.4). The left graph shows curves obtained by plotting the intensity data corresponding to particular size parameters. The right image displays the calculated scattering over a range of size parameters. The color scale corresponds to the log of the scattered intensity. Each curve in the graph on the left corresponds to a horizontal line through the image on the right.

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Fig 3.
Fig 3. Four models of cellular scattering: (1) nucleus only, (2) cytoplasm only, (3) nucleus and cytoplasm, and (4) nucleus and cytoplasm containing organelles. The color scale corresponds to the log of the scattered intensity.

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Fig 4.
Fig 4. Top: Scattering from normal (left) and dysplastic (right) cervical cell. Note elevated scattering in dysplastic cell. The increased scattering at small angles is due to a larger nucleus to cytoplasm ratio. The increased scattering at high angles is due to alterations in chromatin structure, resulting in increased heterogeneity in nuclear refractive index. The color scale corresponds to the log of the scattered intensity. Bottom: Integrated scattered intensities over three angular ranges (0–20°, 80–100°, and 160–180°) for normal (left) and dysplastic (right) cervical cells

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Equations (1)

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G ( k Δ f ) = Δ t ∑ n = 0 N − 1 g ( n Δ t ) exp ( − j 2 π kn N ) , k = 0 , 1 , 2 , … , NF
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