{"id":"6b3cf645-d746-4fb3-9400-3bae8ca611f9","arxiv_id":"2501.15689","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A multi-compartment extension of 3D-SHORE with ℓ1 sparsity approximates diffusion-relaxation MRI signals more accurately than mono-exponential dictionary methods and enables free-water-suppressed tissue maps.","lead":"MC-SHORE is a new way to represent brain MRI signals that combine diffusion and relaxation contrasts, using spherical harmonic basis functions and multiple tissue compartments per voxel. On simulated and human brain data it approximates the measured signal more accurately than existing single- and multi-compartment methods, and it can remove free-water contributions from microstructural maps.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The initial SPIJN-based T1 compartment detection is the load-bearing step: any compartment missed or falsely added at b=0 is permanently absent or extra in the MC-SHORE dictionary, so both the approximation and the FW-separation claims inherit its errors.","rationale":"The reader's weakest assumption matches my own: the dictionary support is fixed before the main estimation. I reviewed whether another issue (e.g., in-sample evaluation, single ζ scaling, threshold-based separation) is more fundamental. In-sample evaluation is appropriate for a representation claim; single ζ is a modeling choice that could be tested but is not obviously wrong; the T1 threshold is a stated assumption. The b0 SPIJN step, however, is both acknowledged by the authors as lossy and unquantified. The in silico data are constructed with T1s far apart, so the initial detection is nearly guaranteed to succeed; the in vivo data have no ground truth. A simple sensitivity experiment (adding a short-T1 compartment or perturbing the detected support) would settle whether the method degrades gracefully or catastrophically when the initial spectrum is imperfect. Since the authors already flag this as a limitation and the reader's conditional verdict requests additional validation, my stress-test does not move the verdict.","tokens_in":23464,"tokens_out":5975,"duration_ms":56446,"concrete_test":"Generate in silico data with the same ZEBRA protocol but add a third compartment with T1 = 150 ms (myelin-like, deliberately suppressed by λ=1) alongside the existing 1000/2000 ms pools, with known volume fractions. Run the full pipeline: b0 SPIJN with λ=1, dictionary reduction (Eq. 12), then MC-SHORE(s) signal fitting. Compare the estimated FW fraction and signal approximation MSE to ground truth. If the short-T1 compartment is undetected and its signal is folded into IEW or FW, the separation and approximation claims fail exactly in the regime the method is designed to exclude.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claims—more accurate signal approximation and separation of IEW/FW contributions—both depend on the reduced dictionary constructed in Eq. (12) from the b0-only SPIJN T1 spectrum with λ=1 (Section 4.2). That first step is not a preprocessing detail: it defines the support of the dictionary. Any compartment whose T1 bin has zero estimated coefficient at b=0 is absent from D, and because the subsequent MC-SHORE optimization (13)–(16) only selects among atoms already present, a missed compartment can never be recovered. Conversely, a false-positive T1 bin adds spurious atoms that can absorb signal and bias the T1-threshold-based IEW/FW split (1800 ms cutoff, Section 3.3). The authors acknowledge this in Section 6.1: non-detected compartments cause information loss that 'cannot be recovered later,' and false positives affect microstructural indices. Yet the in silico validation uses only well-separated T1 values (1000/2000 ms) and never perturbs the initial spectrum; the in vivo evaluation has no ground truth for compartment fractions. Thus the fragility of the b0 SPIJN step is the most load-bearing unexamined assumption.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces MC-SHORE, a multi-compartment signal representation for diffusion-relaxation MRI. The diffusion kernel is the 3D-SHORE basis combined with an inversion-recovery T1 term; a reduced dictionary is constructed by first estimating a T1 spectrum from b=0 data with SPIJN and keeping only detected T1 compartments (Eq. 12). Coefficient estimation uses three ℓ1/sparsity-regularized objectives solved by ADMM, with λ1 and λ2 selected by GCV. The method is evaluated in silico (two crossing fibers, varying free-water fractions and SNRs) and on the MUDI in vivo data, against Relax-ADC, Relax-DTI, Relax-SHORE, and MC-ADC. The authors claim more accurate signal approximation with fewer dictionary atoms than mono-exponential multi-compartment methods, and demonstrate IEW/FW separation through T1-thresholded aggregation of coefficients.","tokens_in":23723,"tokens_out":6935,"duration_ms":58823,"significance":"The proposed representation is a plausible and useful extension of Relax-SHORE to multi-compartment tissue models. If the claims hold, it offers a route to richer multi-parametric signal representation with closed-form microstructural measures and free-water partial volume suppression. The paper is strong on methodology: the objective functions are clearly specified, the ADMM update rules are given, the evaluation uses a public multi-parametric dataset (MUDI), and the in silico experiments cover a range of SNRs, crossing angles, and free-water fractions. The main unresolved risks are the dependence of the dictionary support on the b=0 SPIJN estimate and the in-sample nature of the in vivo approximation errors.","major_comments":[{"comment":"The reduced dictionary is defined by the support of the T1 spectrum estimated from b=0 data by SPIJN with λ=1. Because the subsequent optimizations in Eqs. (13)–(16) select only among atoms already present in D, any compartment with a zero b0 coefficient is permanently excluded, and any false-positive compartment remains in the dictionary and can bias the T1-thresholded IEW/FW split. This limitation is acknowledged in §6.1 ('non-detected compartments... cannot be recovered later'; false positives affect indices). The in silico model in §4.1.4 uses only two well-separated T1 values (1000 and 2000 ms) and no experiment perturbs the initial SPIJN estimate or compares reduced versus full-dictionary performance. I request a sensitivity analysis: vary SPIJN λ, add noise to the b0 data, simulate a missed compartment, and report how often compartments are recovered and how approximation MSE and IEW/FW fractions change.","section":"§3.2, Eq. (12); §4.2; §6.1"},{"comment":"The in vivo approximation results are in-sample: the coefficients are estimated from all 448 volumes and the MSE is computed on the same volumes (Table 1, Fig. 3). No train/test split, cross-validation, or per-subject error bars are reported, so the lower MSE of MC-SHORE compared with the baselines may partly reflect overfitting of a more flexible dictionary. Please provide out-of-sample evaluation (e.g., estimate on a subset of acquisitions or volumes and compute MSE on held-out volumes), and report variability across the five subjects and a statistical comparison of the methods.","section":"§5.1, §5.2; Table 1; Fig. 3"},{"comment":"The abstract and contribution list claim that the dictionary maintains a low number of atoms, but the in vivo experiments do not report the actual number of atoms used per voxel or per ROI. The reduced dictionary size depends on the number of detected T1 compartments, and without this information the comparison to the fixed 2500-atom MC-ADC dictionary is incomplete. Please report the distribution of dictionary sizes (or atom counts) for the tested voxels and ROIs.","section":"§5.2; abstract and §1 contributions"}],"minor_comments":[{"comment":"The definition of r^{k+1}_2 appears to omit the term '- h^{k+1}_v'; compare Algorithm 1, line 8.","section":"Eq. (21a)"},{"comment":"The sentence 'Each stick population has 25% contribution...' is ambiguous; the subsequent example (fiso=0.2 giving 0.2 per population) suggests a normalization rule that should be stated explicitly.","section":"§4.1.4"},{"comment":"There is a typo: 'nad' should be 'and' in the paragraph following Eq. (14).","section":"§3.4"},{"comment":"The region dubbed 'arteria corona radiata' is likely 'anterior corona radiata' (ACR).","section":"§4.1.3"},{"comment":"The x-axis label is unclear; please define the 'n25/n50/n100' notation (number of T1 values) in the caption.","section":"Figure 1(d)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript fits the journal's scope and the methodology is a genuine extension of the authors' prior Relax-SHORE work. I see no citation or novelty concerns. The main revision demands are the sensitivity analysis of the initial compartment support and out-of-sample in vivo evaluation; without those, the central claims are not fully supported."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a solid extension of the authors' own Relax-SHORE into a multi-compartment T1 dictionary, and the approximation experiments back the main signal-approximation claim. The FW-separation claim is weaker, and the stress-test note is right: the whole pipeline rests on a b0-only SPIJN step that fixes the dictionary support, and that step is never perturbed or validated.\n\nThe genuinely new piece is replacing the mono-exponential ADC kernel inside each T1 compartment with a 3D-SHORE expansion, and then estimating coefficients with l1, joint-sparsity, and fused-lasso objectives. The method description is complete enough to reproduce: dictionary construction, ADMM updates, GCV for lambda, and the in silico protocol with Rician noise across SNR, fiso, and radial order. The in silico results show MC-SHORE beats Relax-SHORE and MC-ADC in approximation MSE for realistic fiso, and the in vivo table shows the same pattern in WM and GM. That is a real, if incremental, improvement. The authors also state the main limitation honestly in Section 6.1: compartments missed at the b0 step cannot be recovered later, and false positives bias the indices.\n\nThe soft spots are in the evaluation, not in the writing. The in silico design uses only two well-separated T1 values (1000/2000 ms), so the initial SPIJN support is effectively perfect by construction; no experiment perturbs the initial spectrum or tests overlapping T1 peaks. The in vivo MSE is computed on the same volumes used for fitting, so it is in-sample approximation, and no error bars or significance tests are reported. The IEW/FW separation is demonstrated only via qualitative ODFs and boxplots; there is no ground truth for free-water fraction or orientation. Given the abstract's claim about separating intra-/extra-axonal and free-water contributions, that claim needs held-out validation or a phantom/ground-truth experiment before I'd trust it. None of this kills the paper; it means the approximation result is solid and the separation result is promising but unproven.\n\nWho benefits: researchers working on diffusion-relaxometry signal representation, especially those building dictionaries for ZEBRA/MUDI-type acquisitions. It deserves a serious referee and should be sent out with requests for held-out validation, a perturbation analysis of the b0 SPIJN step, and error bars. I'd cite it if I needed a baseline for multi-compartment SHORE.","headline":"Solid extension of the authors' Relax-SHORE to multi-compartment T1, with a real but untested fragility in the b0-based dictionary support.","tokens_in":24283,"tokens_out":2280,"would_cite":true,"duration_ms":22712,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that a sparse, compartment-wise 3D-SHORE basis represents diffusion-relaxation MR signals more accurately than mono-exponential multi-compartment dictionaries with fewer atoms, and that its coefficients can separate…","keywords":["Diffusion-relaxometry","multi-parametric sequence","3D-SHORE","signal representation","sparse dictionary","free-water elimination","microstructure","brain MRI"],"falsifier":"Acquire diffusion-relaxation data at echo times short enough (below roughly 40 ms) that myelin water contributes a measurable signal: because the paper deliberately chooses the initial SPIJN regularization so that the myelin compartment (T1 below about 200 ms) is absent, the same pipeline should show a systematic approximation residual and biased GFA or RTOP maps wherever myelin is present. Alternatively, in an in silico three-compartment experiment where the initial detection omits one compartment, MC-SHORE's approximation error should fail to improve when the dictionary is enlarged and the recovered free-water fraction should drift from its true value.","tokens_in":23210,"feed_emoji":"🧠","tokens_out":7582,"duration_ms":60853,"temperature":0.7,"pith_summary":"This paper sets out to show that the diffusion-relaxation MR signal can be represented as a sparse sum over a small number of tissue compartments, where each compartment's non-Gaussian, direction-dependent diffusion is described by a 3D-SHORE spherical basis rather than a mono-exponential decay. The authors build a dictionary whose atoms are products of an inversion-recovery T1 kernel and 3D-SHORE basis functions, then estimate coefficients with ℓ1 and fused-Lasso sparsity penalties. On in silico and in vivo ZEBRA data, they report that this multi-compartment SHORE representation approximates the measured signal more accurately than single-compartment SHORE and than multi-compartment mono-exponential dictionaries, while using a small number of atoms. The practical payoff, if true, is that sparse multi-parametric acquisitions can yield per-compartment microstructural maps and suppress free-water partial-volume contamination at tissue boundaries.","feed_headline":"3D-SHORE basis sharpens multi-compartment diffusion-relaxation MRI","feed_subtitle":"Replacing mono-exponential diffusion with a spherical SHORE kernel separates free water from tissue in one dictionary.","key_machinery":"The load-bearing object is the compartment-wise dictionary atom $d_{nlm}(TI, q, u \\mid T_1, \\zeta) = \\left(1 - 2\\exp\\left(-\\frac{TI}{T_1}\\right)\\right)\\phi_{nlm}(q, u \\mid \\zeta)$, the product of the inversion-recovery T1 kernel and a 3D-SHORE basis function whose radial part is a Laguerre polynomial and whose angular part is a spherical harmonic. Each T1 compartment carries the full SHORE expansion, so anisotropic and non-Gaussian diffusion is modelled per compartment without geometrically sampling diffusion parameters; the dictionary is then pruned to the compartments detected in the b=0 signal by SPIJN (with λ chosen so myelin water is absent), and the coefficients are estimated by ADMM under three sparsity-promoting objectives, including a fused-Lasso variant with voxel-similarity weights. This machinery is what lets the atom count stay low while accuracy improves.","core_discovery":"The paper's central claim is that replacing the mono-exponential diffusion kernel in a continuum diffusion-relaxation model with the 3D-SHORE basis per T1 compartment yields a dictionary representation, MC-SHORE, that is both more expressive and more economical than the standard MC-ADC dictionaries: with the same or fewer atoms it achieves lower approximation MSE across SNR, free-water fraction, and b-value regimes, and its coefficients can be aggregated by T1 to separate intra-/extra-axonal from free-water signal. The discovery is that the dictionary size is set by the spherical-basis order times the number of detected T1 compartments, not by the sampling density of the diffusion parameter space, so adding non-Gaussian diffusion does not multiply the atom count. From the estimated coefficients the method computes ensemble propagator measures and ODFs compartment-wise, and the authors show that dropping the free-water compartment from the aggregation sharpens fibre orientation estimates and raises GFA in white matter.","pith_inferences":["Because dictionary size scales with the SHORE radial order rather than diffusion parameter discretization, the same compartment-wise construction should extend to a second relaxation axis such as T2 without the geometric dictionary explosion that afflicts MC-ADC-style methods; the paper does not implement this extension.","The initial T1 detection step is the bottleneck: replacing SPIJN with a Bayesian or off-the-grid compartment estimator could remove the 'missed compartments are unrecoverable' failure without changing the SHORE machinery.","The free-water separation claim is demonstrated qualitatively through ODF and GFA maps; a quantitative in silico test with known ground-truth free-water fraction and crossing angles below the roughly 45-degree angular-resolution limit of 3D-SHORE would show whether FW suppression actually improves fibre-orientation accuracy or merely sharpens the angular response.","A comparison against multi-compartment versions of other spherical bases (e.g., MAP-MRI, BFOR, mq-DPI) would test whether the multi-compartment sparsity structure rather than the specific 3D-SHORE basis is what drives the accuracy gain."],"forward_implications":["On the same number of dictionary atoms, MC-SHORE approximates in vivo diffusion-relaxation signals with lower MSE than MC-ADC under DR-CSI and SPIJN, Relax-SHORE, Relax-DTI, and Relax-ADC in both white and gray matter.","The dictionary atom count is the number of detected T1 compartments times the SHORE basis size (e.g., about 100 atoms for two compartments at radial order L=6), rather than a product of densely sampled diffusion and relaxation parameters.","Removing the free-water compartment from the coefficient aggregation sharpens ODFs and raises GFA in white matter, which the authors interpret as reduced partial-volume contamination at tissue boundaries.","The same framework yields per-compartment ensemble propagator measures (RTOP, RTAP, RTPP), mean-squared displacement, and ODFs, so microstructural indices can be computed for tissue fractions rather than the whole voxel.","The voxel-similarity-weighted fused-Lasso variant (MC-SHORE(wl)) delivers the lowest approximation error, particularly at high b-values."],"supporting_citations":[{"why":"Supplies the 3D-SHORE/MAP-MRI basis functions and the closed-form formulas for ensemble propagator measures that MC-SHORE inherits.","marker":"Özarslan et al., 2013"},{"why":"Provides the 3D-SHORE representation as a diffusion kernel and the estimation of microstructural measures and ODFs used throughout the paper.","marker":"Zucchelli et al., 2016"},{"why":"Defines Relax-SHORE, the single-compartment method that MC-SHORE extends and a principal comparison baseline, including the ζ scaling recipe.","marker":"Bogusz et al., 2022"},{"why":"SPIJN provides the initial T1 spectrum that selects compartments and builds the reduced dictionary, and also serves as a multi-compartment mono-exponential baseline.","marker":"Nagtegaal et al., 2020"},{"why":"Introduces the ZEBRA acquisition protocol and the Relax-ADC baseline, defining the acquisition setup and the dictionary construction scheme that MC-SHORE replaces.","marker":"Hutter et al., 2018"},{"why":"DR-CSI is a multi-compartment ADC-based continuum model used as a baseline and a source of the spatial smoothness constraint idea.","marker":"Kim et al., 2017"},{"why":"MADCO establishes the continuum-modeling Fredholm equation formulation and the discretized dictionary approach that MC-SHORE builds upon.","marker":"Benjamini and Basser, 2016"},{"why":"Provides the ADMM optimization framework used to solve the sparse objective functions with stopping criteria.","marker":"Boyd et al., 2011"},{"why":"Supplies the MUDI challenge in vivo diffusion-relaxation data set used for the in vivo validation.","marker":"Pizzolato et al., 2020"}],"fun_headline_variants":["MC-SHORE: sparse diffusion-relaxation MRI with compartment separation","Spherical SHORE basis shrinks diffusion-relaxation dictionary","New MC-SHORE model separates free water in MRI","Sparse 3D-SHORE improves multi-compartment MRI","MC-SHORE: efficient multi-compartment diffusion-relaxation imaging"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The pipeline assumes the first T1 spectrum estimated from b=0 data with a fixed sparsity level has already found every real tissue compartment; any compartment missed there is unrecoverable, and any false positive contaminates the later microstructural indices.","fun_headline_variants_meta":{"raw":{"variants":["MC-SHORE: sparse diffusion-relaxation MRI with compartment separation","Spherical SHORE basis shrinks diffusion-relaxation dictionary","New MC-SHORE model separates free water in MRI","Sparse 3D-SHORE improves multi-compartment MRI","MC-SHORE: efficient multi-compartment diffusion-relaxation imaging"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000174,"raw_usage":{"total_tokens":1332,"prompt_tokens":1046,"completion_tokens":286,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":662,"completion_tokens_details":{"reasoning_tokens":196}},"tokens_in":662,"tokens_out":286,"duration_ms":2782,"temperature":1.0,"reasoning_tokens":196,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T14:02:58.784263+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Acquire diffusion-relaxation data at echo times short enough (below roughly 40 ms) that myelin water contributes a measurable signal: because the paper deliberately chooses the initial SPIJN regularization so that the myelin compartment (T1 below about 200 ms) is absent, the same pipeline should show a systematic approximation residual and biased GFA or RTOP maps wherever myelin is present. Alternatively, in an in silico three-compartment experiment where the initial detection omits one compartment, MC-SHORE's approximation error should fail to improve when the dictionary is enlarged and the recovered free-water fraction should drift from its true value.","supporting_citations":[{"cited_title":"title What lies beneath? D iffusion EAP -based study of brain tissue microstructure","cited_arxiv_id":null,"evidence_quote":"Provides the 3D-SHORE representation as a diffusion kernel and the estimation of microstructural measures and ODFs used throughout the paper."},{"cited_title":"title Diffusion-relaxation scattered mr signal representation in a multi-parametric sequence","cited_arxiv_id":null,"evidence_quote":"Defines Relax-SHORE, the single-compartment method that MC-SHORE extends and a principal comparison baseline, including the ζ scaling recipe."},{"cited_title":"title Fast multi-component analysis using a joint sparsity constraint for mr fingerprinting","cited_arxiv_id":null,"evidence_quote":"SPIJN provides the initial T1 spectrum that selects compartments and builds the reduced dictionary, and also serves as a multi-compartment mono-exponential baseline."},{"cited_title":"title Integrated and efficient diffusion-relaxometry using ZEBRA","cited_arxiv_id":null,"evidence_quote":"Introduces the ZEBRA acquisition protocol and the Relax-ADC baseline, defining the acquisition setup and the dictionary construction scheme that MC-SHORE replaces."},{"cited_title":"title Diffusion-relaxation correlation spectroscopic imaging: a multidimensional approach for probing microstructure","cited_arxiv_id":null,"evidence_quote":"DR-CSI is a multi-compartment ADC-based continuum model used as a baseline and a source of the spatial smoothness constraint idea."},{"cited_title":"title Use of marginal distributions constrained optimization (madco) for accelerated 2d mri relaxometry and diffusometry","cited_arxiv_id":null,"evidence_quote":"MADCO establishes the continuum-modeling Fredholm equation formulation and the discretized dictionary approach that MC-SHORE builds upon."},{"cited_title":"title Distributed optimization and statistical learning via the alternating direction method of multipliers","cited_arxiv_id":null,"evidence_quote":"Provides the ADMM optimization framework used to solve the sparse objective functions with stopping criteria."}],"review_version":1}