# Implicit neural representations for accurate estimation of the Standard Model of white matter

## TL;DR

This paper introduces a self-supervised neural method to improve the accuracy of estimating white matter properties from MRI data, especially in noisy conditions.

## Contribution

A novel self-supervised implicit neural representation framework for estimating Standard Model parameters with improved accuracy and robustness.

## Key findings

- The INR method shows superior accuracy in estimating SM parameters, especially in low signal-to-noise conditions.
- The method enables anatomically plausible spatial upsampling and supports joint estimation with high spherical harmonics orders.
- The INR framework is robust to noise and accommodates gradient non-uniformity corrections.

## Abstract

Diffusion magnetic resonance imaging (dMRI) enables non-invasive investigation of tissue microstructure. The Standard Model (SM) of white matter aims to disentangle dMRI signal contributions from intra- and extra-axonal water compartments. However, due to the model’s high-dimensional nature, accurately estimating its parameters poses a complex problem and remains an active field of research, in which different (machine learning) strategies have been proposed. This work introduces an estimation framework based on implicit neural representations (INRs), which incorporate spatial regularization through the sinusoidal encoding of the input coordinates. The INR method is evaluated on both synthetic and in vivo datasets and compared to existing methods. Results demonstrate superior accuracy of the INR method in estimating SM parameters, particularly in low signal-to-noise conditions. Additionally, spatial upsampling of the INR can represent the underlying dataset anatomically plausibly in a continuous way. The INR is self-supervised, eliminating the need for labeled training data. It achieves fast inference, is robust to noise, supports joint estimation of SM kernel parameters and the fiber orientation distribution function with spherical harmonics orders up to at least 8, and accommodates gradient non-uniformity corrections. The combination of these properties positions INRs as a potentially important tool for analyzing and interpreting diffusion MRI data.

In this work a self-supervised implicit neural representation framework for estimating Standard Model of white matter parameters is presented, improving fitting accuracy under noise conditions, enabling spatial upsampling, and allowing for integrated gradient non-uniformity correction.