Computation of frequency- and time-domain Jacobians in optical tomography with Monte Carlo simulations

TL;DR

This paper extends Monte Carlo simulations to directly compute frequency- and time-domain Jacobians in optical tomography, improving accuracy especially in low-scattering tissues and with realistic detector models.

Contribution

It introduces a comprehensive framework and open-source software for calculating Jacobians in optical tomography using Monte Carlo methods, including realistic detector modeling.

Findings

MC-derived Jacobians agree with diffusion approximation in high-scattering regimes

Detector modeling affects surface sensitivity and tissue depth sensitivity

The framework enables accurate Jacobian computation in low-scattering tissues

Abstract

Significance: Jacobians, or spatially resolved sensitivity profiles, are central to image reconstruction in model-based optical tomography of biological tissue. Although Monte Carlo (MC) simulations are the gold standard for modeling light transport in turbid media, methodology for frequency- and time-domain Jacobians remains incomplete. Aim: This work extends MC to directly compute absorption and scattering Jacobians for frequency-domain (amplitude and phase) and time-domain (intensity and mean time-of-flight) measurements and prism-terminated optical fiber detectors. Approach: Jacobians are derived in the perturbation MC framework and implemented in the high-performance, open-source Monte Carlo eXtreme (MCX) simulator. Results are validated against the diffusion approximation (DA) solved using the finite element method in neonatal head models. MC with split voxels on curved surfaces is extended to Jacobian computation. The detector model is implemented in post-processing and compared with isotropic reception at surface. Results: MC- and DA-derived Jacobians show excellent agreement only in high-scattering regimes, highlighting the importance of MC for low-scattering domains. The detector model reduces surface sensitivity and marginally increases sensitivity to deeper tissues at short (< 2 cm) source-detector separations. Conclusion: A complete theoretical framework and MC software for computing frequency- and time-domain Jacobians is provided. Realistic detector modeling is encouraged for short-separation channels.