On the accuracy of implicit neural representations for cardiovascular anatomies and hemodynamic fields

TL;DR

The paper systematically evaluates implicit neural representations (INRs) for compressing and representing cardiovascular hemodynamics and anatomy via signed distance fields. By testing nine architectures (including SIREN, MFN, and MHE) across 2D, 3D, and 4D datasets, it identifies spectral-bias mitigation strategies that yield high-accuracy pressure and velocity fields and sub-centimeter SDF reconstructions. Key findings show that SIREN and MFN-Gabor consistently deliver robust performance with limited hyperparameter tuning, while MHE is competitive but sensitive to encoding choices and data sampling. The work demonstrates substantial compression (up to ~230x in some cases) and provides open-source code and data to facilitate reproducibility and adoption in cardiovascular modeling and digital-twin contexts.

Abstract

Implicit neural representations (INRs, also known as neural fields) have recently emerged as a powerful framework for knowledge representation, synthesis, and compression. By encoding fields as continuous functions within the weights and biases of deep neural networks-rather than relying on voxel- or mesh-based structured or unstructured representations-INRs offer both resolution independence and high memory efficiency. However, their accuracy in domain-specific applications remains insufficiently understood. In this work, we assess the performance of state-of-the-art INRs for compressing hemodynamic fields derived from numerical simulations and for representing cardiovascular anatomies via signed distance functions. We investigate several strategies to mitigate spectral bias, including specialized activation functions, both fixed and trainable positional encoding, and linear combinations of nonlinear kernels. On realistic, space- and time-varying hemodynamic fields in the thoracic aorta, INRs achieved remarkable compression ratios of up to approximately 230, with maximum absolute errors of 1 mmHg for pressure and 5-10 cm/s for velocity, without extensive hyperparameter tuning. Across 48 thoracic aortic anatomies, the average and maximum absolute anatomical discrepancies were below 0.5 mm and 1.6 mm, respectively. Overall, the SIREN, MFN-Gabor, and MHE architectures demonstrated the best performance. Source code and data is available at https://github.com/desResLab/nrf.

Figures (23)

• Figure 1: Schematic of multiresolution hash encoding (MHE).
• Figure 2: Spatial locations outside of geometries are positive (blue), whereas locations inside are negative (pink). Points on the surface form the zero level set.
• Figure 3: Visualization of examples from the selected test cases: greyscale zebra image, cylindrical pipe, and aortic anatomy.
• Figure 4: Flow profiles in mL/s for pipe and aorta test cases.
• Figure 5: Selected test cases: ideal spherical geometry, pulmonary, and aortic anatomies.