Comparing time and frequency domain numerical methods with Born-Rytov approximations for far-field electromagnetic scattering from single biological cells

TL;DR

This study benchmarks the Born-Rytov approximation (BRA) against full-wave Maxwell solvers—Discrete Dipole Approximation (DDA) and Yee-lattice Finite-Difference Time-Domain (FDTD)—and multi-slice Fourier transform (MSFT BRA) for electromagnetic scattering from a sphere and a tomographic Saccharomyces cerevisiae cell. By leveraging Mie theory as ground truth for spheres and tomographic RI reconstructions for yeast, it quantifies absolute and angular errors, compute time, and memory across near-field and far-field projections. The results show that BRA and DDA generally provide more accurate forward-scattering patterns for heterogeneous cells than FDTD, with BRA offering orders-of-magnitude faster performance suitable for rapid detector design and pattern-based classification, while DDA delivers robust quantitative accuracy for complex geometries. The findings inform practical choices for refractive-index reconstruction workflows and forward-scattering simulations in label-free cytometry and related applications, highlighting trade-offs between accuracy, memory, and speed. The work underscores the value of combining BRA/MSFT with higher-fidelity methods like DDA for comprehensive validation of scatter-based cell characterization pipelines.

Abstract

The Born-Rytov approximation estimates effective refractive index of biological cells from measurements of scattered light intensity, polarization and phase. Effective refractive index is useful for estimating a biological cell's dry mass, volume, and internal morphology directly from its elastic light scattering pattern. This work compares the Born-Rytov approximation with analytical, Yee-lattice finite-difference time-domain, and discrete-dipole approximations to Maxwell's equations in the cases of electromagnetic scattering from a sphere and a tomographic reconstruction of Saccharomyces cerevisiae. Practical advantages and limitations of each numerical method are compared for modeling electromagnetic scattering of both near-field intensity and the far-field projected intensity, in terms of accuracy, memory, and compute time. When compared with a commercial software implementation of the Yee-lattice finite-difference time domain method, the Born-Rytov scattering approximation and discrete dipole approximation show better agreement with the far-field light scattering pattern from Saccharomyces cerevisiae.

Figures (14)

• Figure 1: Empirically measured effective refractive index, which ranges from $n_b=1.33$ to $n_{\mathrm{nuc.}}=1.39$habaza2015tomographic. (a) The $xy$ cross section, (b) the $xz$ cross section, and (c) the $yz$ cross section. In general, the shape of refractive index regions in the cell are non-spherical and cannot be approximated by Mie scattering theory. In (c), sharp edges in the gray scale color map appear as a result of the Rytov approximation. This illustrated reconstruction is exact from measurements by Habaza et al.habaza2015tomographic.
• Figure 2: Illustration of cell partitioning. (a) Original cell refractive index down-sampled to 100 lattice units in each dimension, (b) mapped refractive index to seven discrete values. (c) and (d) are the top and side views of the cell, respectively, as Gaussian point distributions plotted in Paraview 5.12.0-RC2. (e-k) Gradations of $\mathcal{R}\{\Delta n\}=0.01$ in refractive index value from $n=1.33+i0.01$ to $n=1.39+i0.01$ plotted in Paraview 5.12.0-RC2 as a volume. The small extinction coefficient $\kappa=0.01$ is necessary for convergence of the solution within the empirically derived error tolerance. The same injection axis, cell dimensions, and orientation are used for direct comparison with ANSYS® Lumerical FDTD (Fig \ref{['fig:3']}). These cell dimensions are a factor of 0.625$\times$ lesser than measured by Habaza et al.habaza2015tomographic.
• Figure 3: Tomographic model of S. cerevisiae modeled in ANSYS® Lumerical FDTD using seven discrete refractive index values. Each refractive index value is given a small extinction coefficient, $\kappa=0.01$, to compare with DDSCAT 7.3.3, which cannot perform its analysis on a completely lossless system. (a) The trimetric view of the geometry with increasing transparency mapped to refractive index. (b-c) side views of the same geometry in (a). (e) Refractive index of the cell returned from an index monitor. (f-l) Gradations of $\mathcal{R}\{\Delta n\}=0.01$ in refractive index value from $n=1.33+i0.01$ to $n=1.39+i0.01$. These cell dimensions are a factor of 0.625$\times$ lesser than measured by Habaza et al.habaza2015tomographic, and identical to Fig. \ref{['fig:2']}.
• Figure 4: Near-field intensity ($\mathrm{S}_{11}$) predicted by (a, b, c) the discrete dipole approximation (DDA, DDSCAT 7.3.3draine1994discrete) and (e, f, g) Mie theoryZhu_2020 for the case of $N_\lambda\approx9$ along three different planes of incidence: (a, d) $xy$, (b, e) $xz$, and (c, f) $yz$. Each plot axis is in terms of free-space wavelength, $\lambda_0$.
• Figure 5: Near-field intensity ($\mathrm{S}_{11}$) predicted by (a, b, c) ANSYS® Lumerical FDTD and (e, f, g) Mie theoryZhu_2020 for the case of $N_\lambda\approx11$ along three different planes of incidence: (a, d) $xy$, (b, e) $xz$, and (c, f) $yz$. Each plot axis is in terms of free-space wavelength, $\lambda_0$.