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

TL;DR

This paper evaluates the accuracy of implicit neural representations (INRs) in modeling cardiovascular anatomies and hemodynamic fields, demonstrating high compression ratios and low errors in realistic simulations and anatomies.

Contribution

It provides a comprehensive assessment of INR performance for cardiovascular applications, exploring strategies to mitigate spectral bias and identifying architectures with optimal results.

Findings

INRs achieved compression ratios up to 230 for hemodynamic fields.

Maximum absolute errors were 1 mmHg for pressure and 10 cm/s for velocity.

Anatomical discrepancies were below 1.6 mm on average.

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.