$μ$NeuFMT: Optical-Property-Adaptive Fluorescence Molecular Tomography via Implicit Neural Representation

TL;DR

μNeuFMT tackles the ill-posed problem of fluorescence molecular tomography under uncertain tissue optics by fusing an implicit neural representation (INR) with a differentiable, FEM-based forward model in a self-supervised framework. It introduces an optical-property adaptation module that jointly optimizes $μ_a$ and $μ_s'$ with the fluorophore distribution, enabling robust reconstruction across severe initial mis-specifications. Across numerical simulations, physical phantoms, and in vivo mouse imaging, μNeuFMT outperforms conventional, sparse-regularized, and supervised baselines in localization accuracy, shape fidelity, and depth resolution. This physics-informed, optics-adaptive INR paradigm offers a practical path to reliable, high-resolution fluorescence tomography for clinically relevant fluorescence-guided interventions.

Abstract

Fluorescence Molecular Tomography (FMT) is a promising technique for non-invasive 3D visualization of fluorescent probes, but its reconstruction remains challenging due to the inherent ill-posedness and reliance on inaccurate or often-unknown tissue optical properties. While deep learning methods have shown promise, their supervised nature limits generalization beyond training data. To address these problems, we propose $μ$NeuFMT, a self-supervised FMT reconstruction framework that integrates implicit neural-based scene representation with explicit physical modeling of photon propagation. Its key innovation lies in jointly optimize both the fluorescence distribution and the optical properties ($μ$) during reconstruction, eliminating the need for precise prior knowledge of tissue optics or pre-conditioned training data. We demonstrate that $μ$NeuFMT robustly recovers accurate fluorophore distributions and optical coefficients even with severely erroneous initial values (0.5$\times$ to 2$\times$ of ground truth). Extensive numerical, phantom, and in vivo validations show that $μ$NeuFMT outperforms conventional and supervised deep learning approaches across diverse heterogeneous scenarios. Our work establishes a new paradigm for robust and accurate FMT reconstruction, paving the way for more reliable molecular imaging in complex clinically related scenarios, such as fluorescence guided surgery.

Figures (5)

• Figure 1: Conceptual illustration of $\mu$NeuFMT. (a) The FMT setup: a scanned laser illuminates the sample while a CMOS camera with filter wheel on the opposite side records boundary images. The raster scanning method yields the raw 2D image stack $M^{real}$, serving as the input to the subsequent FMT reconstruction. (b) The difference between $M^{real}$ and the simulated measurement $\widehat{M}(\mu_a,\mu_s^\prime,C_\theta)$ is iteratively minimized until an optimized value of unknown fluorescence distribution $C$ is found. $R(C)$ is a regularization term and $\mu\in\{\mu_a,\mu_s'\}$ is the intrinsic optical properties consisting of absorption coefficient $\mu_a$ and scattering coefficient $\mu_s'$. (c) A $\mu$-adaption module is integrated into the FMT reconstruction. The stiffness matrix $S$ is determined by both $\mu_a$ and $\mu_s'$. (d) The FEM-based simulator predicts virtual measurement $\widehat{M}(\mu_a,\mu_s^\prime,C_\theta)$ based on the operator $S^{-1}(\mu)$ and predicted fluorescence distribution $C$. (e) Fluorescence distribution encoded in an INR. 3D node coordinate serves as input, while a continuous $C$ map is generated through positional encoding and an MLP network.
• Figure 2: Ablation test for the optical-property-adaption ($\mu$-adaption) module in $\mu$NeuFMT. (a-c) Effective test for the correction of $\mu_s'$. (a) For a homogeneous phantom simulation with a ‘S’-shaped fluorescence inclusion, the ground truth (GT) of $\mu_a$ and $\mu_s'$ values are $\text{0.1 mm}^{\text{-1}}$ and $\text{1.0 mm}^{\text{-1}}$ respectively. A mismatched initial guess of $\mu_s'$ was assumed for FMT reconstruction. The $\mu$-adaption module successfully corrects $\mu_s'$ with an average error of 0.55%, leading to significantly improved FMT reconstruction results compared to non-adaptive NeuFMT. (b) Convergence curve of $\mu_s'$ given more initial $\mu_s'$ values ranging from 0.5$\times$ to 2$\times$ GT value under the same setting of (a). (c) Convergence curve of $\mu_s'$ value across all cases with different $\mu_a$ values, given initial $\mu_s' = \text{1.5 mm}^{\text{-1}}$. (d-f) Effective test for the correction of the absorption coefficient ($\mu_a$). (d) For the same phantom in (a), a (mismatched) $\mu_a$ initial value is assumed for FMT reconstruction. The $\mu$-adaption module successfully corrects $\mu_a$ with an average error of 1.5%, leading to significantly improved FMT reconstruction results. (e) Convergence curve of $\mu_a$ given more initial $\mu_a$ values ranging from 0.5$\times$ to 2$\times$ GT value under the same setting of (d). (f) Convergence curve of $\mu_a$ value across all cases with different $\mu_s'$ values, given initial $\mu_a = \text{0.15 mm}^{\text{-1}}$. (g-h) Effective test for the correction of both absorption and diffusion coefficients. (g) For the same phantom in (a), given mismatched initial $\mu_a =$ 1.5 and $\mu_s' =$ 0.15, both of which are 50% higher than GT, the $\mu$-adaption module successfully corrects both $\mu_a$ and $\mu_s'$ at the same time. (h) Convergence curve given the iteration process in (g) for both optical coefficients.
• Figure 3: Results of numerical phantom simulations. (a)–(d) Ground truth (GT) and FMT reconstruction results from five methods ($L_2$-CG, $L_1$-FISTA, U-Net, direct NeuFMT, and $\mu$NeuFMT) across four numerical cases. For each method, two cross-sections (along XY- and XZ-planes), a 3D isosurface, and the Dice coefficient are displayed. (e) Intensity profiles along the dashed lines in the XY slices are compared for the four cases.
• Figure 4: Results of real phantom experiments. (a) Photograph of the real silicone phantoms and fluorescence inclusions. (b)–(e) Ground truth (GT) and FMT reconstruction results from five methods ($L_2$-CG, $L_1$-FISTA, U-Net, direct NeuFMT, and $\mu$NeuFMT) across four numerical cases. For each method, two cross-sections (along XY- and XZ-planes), a 3D isosurface, and the Dice coefficient are displayed. (f) Intensity profiles along the dashed lines in the XY slices are compared for the four cases.
• Figure 5: In vivo lymph node FMT imaging and reconstruction results. (a) The white-light image and preview via 2D fluorescence reflectance imaging (FRI) overlaid on the white-light image with the red aera indicating the concentrated distribution of Cy5 probe on the cites of three lymph nodes (LN-1, LN-2, LN-3) and the vein. (b) Comparison of FMT reconstruction results from different methods. The 3D segmentation, along with two slices at $z$ = 8 and 11 mm, are displayed. (c) Intensity profiles along the dashed lines in b. are compared for each ex vivo images of lymph nodes after sacrificing the animal. The gray zone represents the estimated size of LN, based on the ex vivo fluorescence images.