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Using high-resolution microscopy data to generate realistic structures for electromagnetic FDTD simulations from complex biological models

Nature Protocols (2024)Cite this article

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Abstract

Finite-difference time-domain (FDTD) electromagnetic simulations are a computational method that has seen much success in the study of biological optics; however, such simulations are often hindered by the difficulty of faithfully replicating complex biological microstructures in the simulation space. Recently, we designed simulations to calculate the trajectory of electromagnetic light waves through realistically reconstructed retinal photoreceptors and found that cone photoreceptor mitochondria play a substantial role in shaping incoming light. In addition to vision research and ophthalmology, such simulations are broadly applicable to studies of the interaction of electromagnetic radiation with biological tissue. Here, we present our method for discretizing complex 3D models of cellular structures for use in FDTD simulations using MEEP, the MIT Electromagnetic Equation Propagation software, including subpixel smoothing at mesh boundaries. Such models can originate from experimental imaging or be constructed by hand. We also include sample code for use in MEEP. Implementation of this algorithm in new code requires understanding of 3D mathematics and may require several weeks of effort, whereas use of our sample code requires knowledge of MEEP and C++ and may take up to a few hours to prepare a model of interest for 3D FDTD simulation. In all cases, access to a facility supercomputer with parallel processing capabilities is recommended. This protocol offers a practical solution to a significant challenge in the field of computational electrodynamics and paves the way for future advancements in the study of light interaction with biological structures.

Key points

  • This protocol provides a detailed roadmap for scientists interested in performing FDTD computational simulations to probe the interactions of electromagnetic waves (e.g., visible light or microwave radiation) with complex structures such as organs or biological cells.

  • This approach converts 3D models obtained by using microscopy to a ‘discretized’ form compatible with FDTD; the model surface data are used to perform subpixel smoothing to increase simulation accuracy.

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Fig. 1: Discretizing structures from 3D microscopy images for computational simulations.
Fig. 2: Determining whether a test point lies within or outside a closed contour.
Fig. 3: Simplifying the point-in-polygon problem in three dimensions by subdivision and interpolation.
Fig. 4: Calculating the shortest distance between a triangle and a point in 3D space.
Fig. 5: Subpixel averaging: determining whether a voxel surrounding a test point p overlaps a boundary with a finite thickness.
Fig. 6: Subpixel averaging: calculating the overlapping volume (fill fraction) between a voxel and a boundary with a finite thickness.
Fig. 7: Optimizing the discretization of a complex simulation domain.
Fig. 8: Anticipated discretization and FDTD simulation results for three different cone photoreceptor models.
Fig. 9: Mie scattering calculations for a lossless sphere using discretized icosahedrons of increasing accuracy.

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Data availability

The data used in this protocol to make these figures have been made available as part of a Figshare public repository41. It is shared under a GPL 3.0+ license.

Code availability

The code used in this protocol to make these figures has been made freely available as part of a Figshare public repository41. It is shared under a GPL 3.0+ license.

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Acknowledgements

This research was supported by the Intramural Research Program of the National Institutes of Health, National Eye Institute. We thank J. Angueyra for providing comments on an earlier version of the paper. FDTD simulations and execution of the discretization code were performed by using the computational resources of the NIH HPC Biowulf cluster (https://hpc.nih.gov).

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Authors and Affiliations

  1. Retinal Neurophysiology Section, National Eye Institute, National Institutes of Health, Bethesda, MD, USA

    John M. Ball & Wei Li

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Contributions

J.M.B. developed the protocol, wrote the manuscript and prepared figures. W.L. provided supervision as well as editing and feedback on the manuscript.

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Correspondence to John M. Ball.

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The authors declare no competing interests.

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Key reference using this protocol

Ball, J. M. et al. Sci. Adv. 8, eabn2070 (2022): https://doi.org/10.1126/sciadv.abn2070

Extended data

Extended Data Fig. 1 Example general workflow for classifying a point p within a grid of voxels by using a 3D model defined by a set of nested structures at three hierarchical levels (top, middle and bottom).

Compare to Extended Data Figs. 3–8 for further details. Blocks with light red and blue backgrounds represent ROI checks using exclusive and inclusive ROIs, respectively.

Extended Data Fig. 2 Schematized diagrams for the hierarchical file structures output by the discretization protocol provided here.

Dashed vertical lines and ellipses represent implied additional elements that have been omitted here for clarity. Bracketed descriptors indicate the size and type of data stored for key elements or provide other clarifying details.

Extended Data Fig. 3 Top-level point-classification flow diagram.

Note that lowercase n values here and in Extended Data Figs. 4–6 represent iteration count variables and should not be confused with normal vectors; e.g., ‘nmito’ represents the current mitochondria object index. Steps marked ‘STOP’ indicate end conditions in which classification of a point can be definitively identified as indicated. Diamond blocks indicate branching decision points. Double-plus (++) signs are used to increment element counts within loops. Proceed to ‘precise checks’ (Extended Data Fig. 4) where indicated.

Extended Data Fig. 4 ‘Precise check’ flow diagram to classify points as needed when simple checks (Extended Data Fig. 3) fail to classify p.

See Extended Data Fig. 3 for symbol clarification. When indicated, proceed to subpixel averaging calculations (Extended Data Fig. 5) to calculate fill fractions for boundary intersection voxels.

Extended Data Fig. 5 Top-level flow diagram to calculate subpixel averaging parameters for voxels identified as boundary intersections (Extended Data Fig. 4; see also Extended Data Fig. 3 for symbol clarification).

After transformation of the intersecting triangle (see Procedure and our public data repository41 for additional explanation), use the transformed normal vector n′′ to determine whether a 3D, 2D or 1D calculation is required (Extended Data Figs. 6–8, respectively).

Extended Data Fig. 6 Flow diagram to perform 3D fill fraction calculations when directed during subpixel averaging (Extended Data Fig. 5).

See Extended Data Figs. 3–5 for additional information. Note that for a finite boundary of width θ′ centered upon T′′, two sets of fill fraction calculations must be performed: once for the portion of the unit cube behind the inner surface (lower boundary) and a second time for the portion of the unit cube behind the outer surface (upper boundary).

Extended Data Fig. 7 Flow diagram to perform 2D fill fraction calculations when directed during subpixel averaging (Extended Data Fig. 5).

See Extended Data Figs. 3–6 for additional information. The first step is to determine which 2D plane (i.e., X-Y, Y-Z or X-Z) is appropriate for computations and to calculate appropriate plane parameters. In the block marked ‘Determine case for fill fraction calculation’, each block presents a calculation whose negative versus positive result determines which case number (in gray) to use for the remainder of this diagram. Note that the height and width of the squares in the final block are 1.

Extended Data Fig. 8 Flow diagram to perform 1D fill fraction calculations when directed during subpixel averaging (Extended Data Fig. 5).

See Extended Data Figs. 3–7 for additional information. The unit-cube normalization performed previously (Extended Data Fig. 5) simplifies the calculation.

Supplementary information

Supplementary Information

Supplementary Tutorial

Supplementary Video 1

Animation depicting the use of the rigid body physics engine in Blender to fill the cone photoreceptor inner segment membrane ‘container’ with arbitrary shapes representing alternative mitochondria morphologies. The development of this model is detailed in the tutorial found in Supplementary Information.

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Ball, J.M., Li, W. Using high-resolution microscopy data to generate realistic structures for electromagnetic FDTD simulations from complex biological models. Nat Protoc (2024). https://doi.org/10.1038/s41596-023-00947-z

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