Reconstruction of three-dimensional shapes of normal and disease-related erythrocytes from partial observations using multi-fidelity neural networks

TL;DR

This work tackles reconstructing full 3D erythrocyte shapes from partial microscope-like observations. It introduces a multi-fidelity neural network (MFNN) that combines a low-fidelity sphere-to-RBC deformation model with a high-fidelity correlation network, underpinned by a sphere–RBC homeomorphism and morphologies generated by dissipative particle dynamics to model stomatocyte, discocyte, and echinocyte forms. The MFNN achieves high coordinate accuracy (>95%) with at least two cross-sections, and informative oblique cross-sections further improve reconstruction, while the area–volume constraint enhances robustness to noisy data. The approach offers a data-efficient, generalizable path toward quantitative RBC morphology analysis and could enable 3D geometry reconstruction in normal and disease-related RBC samples from partial observations. Future work includes expanding morphologies, incorporating experimental data, and developing adaptive/rotation-invariant sampling strategies to improve real-world applicability.

Abstract

Reconstruction of 3D erythrocyte or red blood cell (RBC) morphology from partial observations, such as microscope images, is essential for understanding the physiology of RBC aging and the pathology of various RBC disorders. In this study, we propose a multi-fidelity neural network (MFNN) approach to fuse high-fidelity cross-sections of an RBC, with a morphologically similar low-fidelity reference 3D RBC shape to recover its full 3D surface. The MFNN predictor combines a convolutional neural network trained on low-fidelity reference RBC data with a feedforward neural network that captures nonlinear morphological correlations, and augments training with surface area and volume constraints for regularization in the low-fidelity branch. This approach is theoretically grounded by a topological homeomorphism between a sphere and 3D RBC surfaces, with training data generated by dissipative particle dynamics simulations of stomatocyte-discocyte-echinocyte transformation. Benchmarking across diverse RBC shapes observed in normal and aged populations, our results show that the MFNN predictor can reconstruct complex RBC morphologies with over 95% coordinate accuracy when provided with at least two orthogonal cross-sections. It is observed that informative oblique cross-sections intersecting spicule tips of echinocytes improve both local and global feature reconstruction, highlighting the value of feature-aware sampling. Our study further evaluates the influence of sampling strategies, shape dissimilarity, and noise, showing enhanced robustness under physically constrained training. Altogether, these results demonstrate the capability of MFNN to reconstruct the 3D shape of normal and aged RBCs from partial cross-sections as observed in conventional microscope images, which could facilitate the quantitative analysis of RBC morphological parameters in normal and disease-related RBC samples.

Figures (10)

• Figure 1: SDE representatives' images (Stomatocyte-II, Stomatocyte-I, Discocyte, Echinocyte-I, Echinocyte-II, Echinocyte-III) observed by SEM (the first images row) and their numerical correspondence obtained by the improved two-component RBC model (the second images row). The SEM images are from the experimental reference geekiyanage2019coarse with authorization.
• Figure 2: Illustrative sketch of the identical process demonstrated by Homeomorphism theory, DPD simulation, and MFNN predictor
• Figure 3: Illustrative vertices selection of training set in MFNN: A. Stomatocyte-I, $\delta = \text{0.1}\mu m,N_\text{train}=\text{242}$; B. Discocyte, $\delta = \text{0.2}\mu m,N_\text{train}=\text{231}$; C. Echinocyte-III, $\delta = \text{0.1}\mu m,N_\text{train}=\text{263}$. Yellow dots are the highlighted selected samples on three orthogonal cross-sections with a small thickness of 2$\delta$, $N_\text{train}$ is the total number of selected vertices.
• Figure 4: Test error $\varepsilon$ versus training data size $N_\text{train}$ in low-fidelity CNN illustrated in A. error bar and B. two-log axis (scaling exponents and minimum test error at $N_\text{train}=\text{2,000}$ for each representative shape are Sto.II: $\alpha=\text{0.8634}$, Sto.I: $\alpha=\text{0.8854}$, Dis.: $\alpha=\text{0.7284}$, Ech.I: $\alpha=\text{0.6931}$, Ech.II: $\alpha=\text{0.7163}$, and Ech.III: $\alpha=\text{0.6488}$).
• Figure 5: Test error $\varepsilon$ versus inserted noise level $\eta$ in low-fidelity CNN illustrated in scenarios of six shapes: (a).Sto.II, (b).Sto.I, (c).Dis., (d).Ech.I, (e).Ech.II, and (f).Ech.III. In each scenario, cases of varying $\eta=\text{1\%},\text{5\%},\text{10\%},\text{15\%},\text{20\%}$ and $N_\text{train}=\text{300},\text{500},\text{1,000}$ are given for comparison.