Mathematical modeling of retinal pigment epithelium (RPE) autofluorescence (AF) with Gaussian mixture models and non-negative matrix factorization (NMF)

A. Johri, R. Post, B. Ganti, A. A. Fawzi, Paul Sajda, T. Ach, C. Curcio, T. Smith

To devise a mathematical algorithm that can extract individual spectral fluorophor components and their spatial localizations from hyperspectral autofluorescence (AF) emission data taken from RPE and Bruch’s membrane (BrM) human donor flat mounts (ex vivo).

Step 1: Hyperspectral cube acquisition: The AF of eleven pure human RPE/BrM flatmounts was studied at 3 locations (fovea, parafovea and periphery) via excitation at wavelengths 436-460 nm and 480-510 nm at 40X magnification. The corresponding hyperspectral emission data (hypercubes of two spatial and one spectral dimension) were captured using the Nuance FX camera (Caliper Life Sciences, US). (Further details in K. Agarwal abstract); Step 2: Gaussian modeling: We fit the original RPE spectra with mixtures of four Gaussian curves (Fig. 1), which provided single peak, smooth candidates for individual fluorophor components; Step 3: NMF modeling: We used these candidate spectra to initialize an NMF technique that factors the entire hypercube to recover constituent source spectra and their spatial localizations minimizing error. We also initialized the NMF with the emission signal from a patch of bare BrM because BrM, underlying the RPE, contributes its signal throughout.

NMF models with Gaussian/BrM initialization consistently decomposed RPE AF hypercubes into smooth individual candidate spectra with histologically plausible localizations within the flat-mount images (Fig. 2). For example, the shorter wavelength spectral component C3 localized to BrM (Fig. 2, Spatial Abundance C3), while the other four, emitting from 575 nm to 700 nm, localized to the lipofuscin compartment.

The Gaussian/NMF mixture model enabled consistent recovery of candidate spectra for individual RPE fluorophor emission signals with histologically plausible localizations. These spectra should now be matched to their corresponding biochemical components with techniques like imaging mass spectroscopy.

Accepted 1 April 2014
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