Optical Inversion and Spectral Unmixing of Spectroscopic Photoacoustic Images with Physics-Informed Neural Networks

TL;DR

Spectroscopic photoacoustic imaging enables mapping of chromophore concentrations but is hampered by nonlinear, ill-posed inversion. The authors introduce SPOI-AE, a physics-informed autoencoder that jointly estimates optical parameters and chromophore concentrations by embedding a deterministic forward model in the decoder and training self-supervised on in vivo mouse lymph node data. Compared with linear baselines, SPOI-AE achieves superior reconstruction across wavelengths and yields biologically coherent SO2 estimates, with validation on a simulated ground-truth phantom showing competitive accuracy (e.g., SO2 MAE of 2.63 pp for optimized configurations). This framework provides a robust, physics-consistent path to optical inversion and spectral unmixing in sPA imaging and suggests future extensions to semi-supervised learning and uncertainty quantification.

Abstract

Accurate estimation of the relative concentrations of chromophores in a spectroscopic photoacoustic (sPA) image can reveal immense structural, functional, and molecular information about physiological processes. However, due to nonlinearities and ill-posedness inherent to sPA imaging, concentration estimation is intractable. The Spectroscopic Photoacoustic Optical Inversion Autoencoder (SPOI-AE) aims to address the sPA optical inversion and spectral unmixing problems without assuming linearity. Herein, SPOI-AE was trained and tested on \textit{in vivo} mouse lymph node sPA images with unknown ground truth chromophore concentrations. SPOI-AE better reconstructs input sPA pixels than conventional algorithms while providing biologically coherent estimates for optical parameters, chromophore concentrations, and the percent oxygen saturation of tissue. SPOI-AE's unmixing accuracy was validated using a simulated mouse lymph node phantom ground truth.

Figures (11)

• Figure 1: The complete architecture of SPOI-AE. For each sPA pixel numbered $i$, the inputs are $\mathbf{p}_i$ and $|\mathbf{r}_i|$, the input pixel and the pixel's distance from the origin, respectively. The reconstructed output pixel is denoted with $\widehat{\mathbf{p}}_i$. The FCNNs $\boldsymbol{\mu}_s'$-Net and $\boldsymbol{\mu}_a$-Net generate estimates for the absorption coefficient $\boldsymbol{\mu}_{a,i}$ and the reduced scattering coefficient $\boldsymbol{\mu}_{s,i}'$. The spectral unmixing block produces chromophore concentration estimates $\boldsymbol{c}_i$ from $\boldsymbol{\mu}_{a,i}$. A low-rank reconstruction of $\boldsymbol{\mu}_{a,i}$ is recreated from the chromophore concentration estimates denoted as $\widehat{\boldsymbol{\mu}}_{a,i}$. Finally, the decoding stage implementing the photoacoustic optical forward problem described in section \ref{['sec:fwd']}, reconstructs $\widehat{\mathbf{p}}_i$ from $\widehat{\boldsymbol{\mu}}_a$ and $\boldsymbol{\mu}_s'$.
• Figure 2: Pixel intensity histograms for the training dataset (TR) and testing dataset (TS). Pixel counts are binned as a function of normalized intensity of the photoacoustic signal across all imaging wavelengths used. In other words, each point represents a single $p(\mathbf{r}_i, \lambda_l)$ from either the training set or testing set.
• Figure 3: Example highlighting segmentation of a sPA image using Chan-Vese active contours. (US) Ultrasound image of a mouse lymph node. (Hand) Initial hand-drawn segmentation of the associated sPA image before the Chan-Vese active contour method was applied. (C-V) Evolved segmentation of the sPA image using the Chan-Vese active contour method initiated from the (Hand) segmentation. Note the exclusion of the background pixels and the inclusion of more of the biologically relevant foreground.
• Figure 4: Ground-truth phantom oxygenated hemoglobin and deoxygenated hemoglobin concentration images ((HbO2) and (HHb), respectively), with oxygenation of each inclusion annotated. Blood inclusions are embedded one centimeter deep into the simulation volume. Blood concentrations are ultimately mapped to initial pressure images, and two example wavelengths ($\lambda$=760nm and $\lambda$=850nm) are plotted in P. Scalebars represent five millimeters.
• Figure 5: $R^2$ results for the training set (TR) and the testing set (TS) as a function of imaging wavelength in nm.