Statistical analysis and modeling of olfactory bulb activation patterns using unmarked spatial point processes

Shcherban I.V., Lysenko L.V., Shcherban O.G., Kalitin K.Y.
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In neuroscience, the study of odor coding mechanisms requires the analysis of spatial activation patterns of olfactory structures (glomeruli) reconstructed from multiphoton microscopy data. However, the lack of a formal statistical framework for analyzing population-level summary maps limits result reproducibility and hinders the development of predictive models. To address these limitations, we developed a novel methodology for the analysis of olfactory activity maps aggregated across multiple animals, based on the theory of unmarked spatial point processes. The methodology includes a data preprocessing procedure and a numerical analysis algorithm implemented in the R environment using the spatstat package.

The proposed approach enables: (1) transformation of raw glomerular activity maps into point patterns while preserving information about glomerular sizes (replacing size information with local point density is a methodological compromise reflecting the “functional weight” of glomerular input); (2) analysis of point patterns based on spatial morphometric characteristics of domains — regions of stable glomerular activation in the olfactory bulb, each approximated by an ellipse, with ellipse parameters (center coordinates in stereotaxic space, major and minor axis lengths, orientation angles), areas, and intra-ellipse point densities reflecting odorant-specific response signatures; (3) statistical hypothesis testing for spatial randomness (Complete Spatial Randomness) using Ripley’s $K$-function, the nearest-neighbor G-function, and Monte Carlo simulations; (4) synthesis of a parametric pairwise interaction model (Strauss process), whose parameters $(r_{PI}, \gamma)$ have a clear biological interpretation — the spatial interaction scale of glomeruli and the strength of response comodulation, respectively.

The methodology was validated using experimental data obtained from 24 laboratory rats: 10 animals stimulated with camphor and 14 with methyl benzoate. The fitted Strauss models yielded close but odorant-specific parameters: interaction radii $r_{PI}$ of 150 $\mu$m (camphor) and 120 μm (methyl benzoate); interaction parameters $gamma$ of 0.95 and 0.89, respectively. The total domain areas (0.60 mm2 and 0.73 mm2) and point densities (38 and 43 points/mm2) calculated at the first stage of analysis are fully consistent with the parametric signatures $(r_{PI}, \gamma)$ of the Strauss model. Model validation using $Q$-$Q$ plots of smoothed residuals confirmed their adequacy.

Our results are consistent with data previously obtained using genetic labeling and functional mapping techniques, demonstrating the correctness of the proposed methodology and the effectiveness of multiphoton laser scanning microscopy for such applications. The proposed framework provides reproducible quantitative assessment of glomerular domains within a unified stereotaxic coordinate system and can be extended to other odorants and biological species. All findings were obtained under anesthesia; extrapolation to active olfactory strategies in awake animals requires further investigation.

Keywords: unmarked point processes, Ripley's $K$-function, nearest-neighbor $G$-function, Monte Carlo method, Strauss model, multiphoton microscopy, spatial patterns of olfactory activity
Citation in English: Shcherban I.V., Lysenko L.V., Shcherban O.G., Kalitin K.Y. Statistical analysis and modeling of olfactory bulb activation patterns using unmarked spatial point processes // Computer Research and Modeling, 2026, vol. 18, no. 4, pp. 1005-1019
Citation in English: Shcherban I.V., Lysenko L.V., Shcherban O.G., Kalitin K.Y. Statistical analysis and modeling of olfactory bulb activation patterns using unmarked spatial point processes // Computer Research and Modeling, 2026, vol. 18, no. 4, pp. 1005-1019
DOI: 10.20537/2076-7633-2026-18-4-1005-1019
URL: http://crm-en.ics.org.ru/journal/article/3756/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Copyright © 2026 Shcherban I.V., Lysenko L.V., Shcherban O.G., Kalitin K.Y.

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