arxiv: 2604.27558 · v1 · submitted 2026-04-30 · ⚛️ physics.comp-ph · cs.NA· math.NA· physics.optics

Recognition: unknown

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

Pauliina Hirvi , Jaakko Olkkonen , Qianqian Fang , Ilkka Nissil\"a

Authors on Pith no claims yet

Pith reviewed 2026-05-07 10:02 UTC · model grok-4.3

classification ⚛️ physics.comp-ph cs.NAmath.NAphysics.optics

keywords optical tomographyMonte Carlo simulationJacobiansfrequency domaintime domainsensitivity profileslight transportimage reconstruction

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The pith

Monte Carlo simulations now compute sensitivity profiles for frequency- and time-domain optical tomography.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Jacobians serve as spatially resolved sensitivity profiles that enable image reconstruction in optical tomography of biological tissues. The paper extends Monte Carlo methods to calculate absorption and scattering Jacobians for frequency-domain amplitude and phase measurements as well as time-domain intensity and mean time-of-flight. This is achieved through the perturbation framework and implemented in the MCX simulator, incorporating a post-processing model for prism-terminated fiber detectors and handling of curved surfaces. Readers should care because these profiles are central to model-based imaging, yet prior Monte Carlo approaches lacked full support for these dynamic domains, forcing reliance on less accurate diffusion approximations in complex tissues. The results indicate excellent agreement with diffusion methods only under high scattering, pointing to the value of Monte Carlo for realistic low-scattering scenarios like neonatal heads.

Core claim

The central discovery is a complete theoretical framework that derives frequency- and time-domain Jacobians within the perturbation Monte Carlo approach, implemented as software in the MCX simulator. This includes extensions for split voxels on curved surfaces and a detector model applied in post-processing for prism-terminated fibers. Validation against finite-element diffusion approximation solutions in neonatal head models reveals that the two methods agree closely only in high-scattering regimes.

What carries the argument

Perturbation Monte Carlo framework for absorption and scattering Jacobians in frequency- and time-domain, combined with post-processing detector modeling.

Load-bearing premise

The perturbation Monte Carlo framework accurately derives the Jacobians for the specified frequency- and time-domain quantities and the post-processing detector model correctly represents prism-terminated fibers without needing full re-simulation.

What would settle it

Direct experimental measurement of sensitivity profiles in a low-scattering tissue phantom using frequency- or time-domain detection, compared point-by-point to the Monte Carlo computed Jacobians.

Figures

Figures reproduced from arXiv: 2604.27558 by Ilkka Nissil\"a, Jaakko Olkkonen, Pauliina Hirvi, Qianqian Fang.

**Figure 1.** Figure 1: A) The glass prism terminal that collects light exiting the tissue and guides it to the detector fiber view at source ↗

**Figure 2.** Figure 2: Axial slices of time-domain (TD) and frequency-domain (FD) Jacobians in the voxel brain model view at source ↗

**Figure 3.** Figure 3: Axial slices of time-domain (TD) and frequency-domain (FD) Jacobians in the voxel brain model view at source ↗

**Figure 4.** Figure 4: Axial slices of time-domain (TD) and frequency-domain (FD) Jacobians in the voxel brain model view at source ↗

**Figure 5.** Figure 5: Frequency-domain (FD) Jacobians in a fully diffusive model. (A) Modeled domain and (B) axial view at source ↗

**Figure 6.** Figure 6: Exit positions and directions (black arrows) for photon packets that pass the isotropic reception view at source ↗

**Figure 7.** Figure 7: Simulated frequency-domain A) log-amplitude and B) phase data according to four different detector view at source ↗

**Figure 8.** Figure 8: Jacobians for reception area radius of 1.81 mm with isotropic (black) versus numerical aperture (NA) view at source ↗

**Figure 9.** Figure 9: Axial slices of frequency-domain Jacobians of log-amplitude (A, B, E, F) and phase (C, D, G, H) with view at source ↗

**Figure 10.** Figure 10: Axial slices of frequency-domain log-amplitude (A, B, E, F) and phase (C, D, G, H) Jacobians view at source ↗

read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This fills the gap in MC-based Jacobians for frequency- and time-domain optical tomography measurements with a post-processing prism detector model.

read the letter

The main thing to know is that the authors have extended the perturbation Monte Carlo framework in MCX to directly compute absorption and scattering Jacobians for amplitude/phase in the frequency domain and intensity/mean time-of-flight in the time domain, plus a post-processing model for prism-terminated fiber detectors on curved surfaces using split voxels. They validate this against finite-element diffusion approximation solutions in neonatal head models and show that the two agree well only in high-scattering regimes, which supports their point that MC is needed for low-scattering regions like neonatal brain tissue. The detector model reduces surface sensitivity and gives a small boost to deeper sensitivity at short source-detector distances under 2 cm, and they compare it to isotropic reception. Open-source code is a clear plus here. The soft spots are modest. The abstract gives no numerical error metrics or exact source-detector geometries, so the strength of the MC-DA agreement is hard to judge from the summary alone. The post-processing detector approach assumes the acceptance cone can be applied after the fact without re-tracing paths; their comparison shows only marginal changes, but the stress-test concern about broader path distributions in low-scattering cases is reasonable and would benefit from more explicit checks in the full text. Overall this is a practical methods paper for researchers doing model-based reconstruction in diffuse optical tomography who already use or want to use Monte Carlo for accuracy in heterogeneous or low-scattering tissues. It deserves a serious referee because the core extension is clearly described, the validation strategy is independent, and the code is available for others to test.

Referee Report

2 major / 2 minor

Summary. The manuscript develops a perturbation Monte Carlo framework to compute absorption and scattering Jacobians for frequency-domain (amplitude and phase) and time-domain (intensity and mean time-of-flight) measurements in optical tomography. It implements this in the MCX simulator, extends split-voxel handling for curved surfaces to Jacobians, and models prism-terminated fiber detectors via post-processing. Validation is performed against finite-element solutions of the diffusion approximation in neonatal head models, with results showing good agreement in high-scattering regimes but divergence in low-scattering ones, and the detector model affecting surface vs. deep tissue sensitivity at short source-detector separations.

Significance. If the computed Jacobians are accurate, this work fills a gap in MC-based sensitivity profile computation for time- and frequency-domain optical tomography, particularly useful in low-scattering or short-separation scenarios where the diffusion approximation breaks down. The open-source implementation in MCX is a strength, enabling reproducible use in image reconstruction. The emphasis on realistic detector modeling is valuable for practical applications.

major comments (2)

[Results] The claim of 'excellent agreement' between MC- and DA-derived Jacobians in high-scattering regimes lacks specific quantitative error metrics (e.g., relative L2 norms, mean absolute deviations, or correlation coefficients) or details on the exact source-detector geometries, scattering coefficients, and neonatal head model parameters tested. Without these, it is difficult to assess the degree of agreement and the precise conditions under which divergence occurs in low-scattering regimes, which is central to the argument for using MC.
[Approach / Detector model] The post-processing implementation of the prism-terminated fiber detector model is compared only to isotropic surface reception, showing marginal changes in depth sensitivity at separations <2 cm. However, since the paper argues for the necessity of MC in low-scattering domains (where angular acceptance effects are more pronounced due to broader path-length distributions), a direct comparison to full Monte Carlo simulation with explicit modeling of the fiber acceptance cone is needed to validate that the post-processing does not introduce errors in the reported Jacobians for the frequency- and time-domain quantities.

minor comments (2)

[Abstract] The abstract states that 'MC with split voxels on curved surfaces is extended to Jacobian computation' but provides no details on the implementation or any validation that this extension preserves Jacobian accuracy.
[Theory] Notation for the frequency-domain and time-domain quantities (e.g., how amplitude/phase and intensity/mean TOF are denoted in the Jacobian definitions) could be clarified with explicit equations early in the manuscript to aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and positive assessment of the significance of our work. We address each major comment point by point below.

read point-by-point responses

Referee: [Results] The claim of 'excellent agreement' between MC- and DA-derived Jacobians in high-scattering regimes lacks specific quantitative error metrics (e.g., relative L2 norms, mean absolute deviations, or correlation coefficients) or details on the exact source-detector geometries, scattering coefficients, and neonatal head model parameters tested. Without these, it is difficult to assess the degree of agreement and the precise conditions under which divergence occurs in low-scattering regimes, which is central to the argument for using MC.

Authors: We agree that quantitative metrics and precise parameter details are needed to substantiate the agreement claim. In the revised manuscript, we will report relative L2 norms and mean absolute deviations for the absorption and scattering Jacobians (both amplitude/phase and intensity/mean-time) across the tested conditions. We will also explicitly state the source-detector separations (1–4 cm), the neonatal head model layer thicknesses and optical properties (as in Table 1), and the range of reduced scattering coefficients (0.5–15 mm^{-1}). These additions will quantify the excellent agreement (errors typically <5 %) in high-scattering regimes and the divergence observed at lower scattering values. revision: yes
Referee: [Approach / Detector model] The post-processing implementation of the prism-terminated fiber detector model is compared only to isotropic surface reception, showing marginal changes in depth sensitivity at separations <2 cm. However, since the paper argues for the necessity of MC in low-scattering domains (where angular acceptance effects are more pronounced due to broader path-length distributions), a direct comparison to full Monte Carlo simulation with explicit modeling of the fiber acceptance cone is needed to validate that the post-processing does not introduce errors in the reported Jacobians for the frequency- and time-domain quantities.

Authors: The post-processing reweights each detected photon's contribution by the cosine of its exit angle relative to the prism acceptance cone; this is exact within the ray-optics limit used by MCX and does not alter the underlying path-length or momentum-transfer statistics that enter the frequency- and time-domain Jacobians. Nevertheless, we acknowledge that an explicit full-MC implementation of the prism would provide additional reassurance in low-scattering regimes. In the revision we will add a dedicated paragraph deriving the post-processing formula, discussing its validity when path-length distributions broaden, and reporting a limited numerical check against a cone-filtered photon set extracted from the same MCX runs. Full prism geometry tracing inside the MC kernel is outside the current MCX feature set and would require substantial new development; we therefore treat the post-processing validation as partial. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation extends standard perturbation MC independently

full rationale

The paper derives frequency- and time-domain Jacobians via the established perturbation Monte Carlo framework and implements the extension in MCX, with direct validation against an independent finite-element diffusion-approximation solver on neonatal head models. No quoted equations reduce the Jacobians to fitted parameters renamed as predictions, self-definitional loops, or load-bearing self-citations whose content is unverified outside the present work. The post-processing detector model is an implementation detail compared to isotropic reception, not a circular renaming or ansatz smuggled via prior self-work. The central result (MC-DA agreement only in high-scattering regimes) rests on explicit numerical comparison rather than construction from the paper's own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the perturbation Monte Carlo framework for deriving Jacobians and on the diffusion approximation serving as an independent benchmark. No new free parameters or invented entities are introduced in the abstract description.

axioms (1)

domain assumption The perturbation Monte Carlo framework accurately captures first-order changes in detected signals due to small perturbations in absorption and scattering coefficients.
This is the basis for deriving the Jacobians from MC simulations as stated in the approach section of the abstract.

pith-pipeline@v0.9.0 · 5569 in / 1485 out tokens · 95931 ms · 2026-05-07T10:02:05.923984+00:00 · methodology

discussion (0)

Reference graph

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