ComBAT Harmonization for diffusion MRI: Challenges and Best Practices

F\'elix Dumais; Gabriel Girard; Guillaume Theaud; Jean-Christophe Houde; Manon Edde; Matthieu Dumont; Maxime Descoteaux; Pierre-Marc Jodoin; Yoan David

REVIEW 5 major objections 4 minor 44 references

ComBAT Harmonization for diffusion MRI: Challenges and Best Practices

T0 review · 5 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read ComBAT, the standard method for pooling MRI measurements across sites, works only when age's effect is identical at every site; violating that hidden assumption misaligns populations and corrupts variance estimates.

desk verdict A useful, honest practical evaluation of ComBAT's known limitations, but the new quantitative thresholds rest on simulations that mirror ComBAT's own linear assumptions and are not statistically grounded. read the letter →

arxiv 2505.14722 v1 pith:PU3MNTJH submitted 2025-05-19 stat.AP cs.CVcs.LGphysics.med-ph

Pierre-Marc Jodoin , Manon Edde , Gabriel Girard , Félix Dumais , Guillaume Theaud , Matthieu Dumont , Jean-Christophe Houde , Yoan David

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Maxime Descoteaux

This is my paper · ORCID

classification stat.APcs.CVcs.LGphysics.med-ph MSC 62P1062F1562J05

keywords ComBATharmonizationdiffusionMRImulti-siteimagingbatcheffectscovariateslopenormativemodelingsamplesizeempiricalBayes

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

ComBAT is the most widely used statistical tool for combining MRI-derived measurements collected at different hospitals and scanners, removing site-specific additive and multiplicative biases while trying to preserve genuine biological variability. This paper argues that ComBAT hides a strong assumption: the slope linking covariates such as age to the measured metric must be the same at every site, and when that fails the harmonization is misleading. Using a large healthy-aging cohort whose values are artificially rescaled with known factors, the authors show exactly when harmonization breaks and when it works, and they repackage ComBAT as a pairwise procedure that aligns each site to one fixed reference dataset. The payoff is a set of concrete conditions for safe use — at least 16 to 32 subjects per site, an age span of roughly 40 years, balanced sex composition, and parameters estimated from healthy controls only — which matters for any multi-site study, normative modeling effort, or clinical deployment that pools brain measurements.

What carries the argument

The load-bearing object is the linear generative model $y_{ijv} = \alpha_v + x_{ij}^T\beta_v + \gamma_{iv} + \delta_{iv}\varepsilon_{ijv}$, where $x_{ij}$ collects covariates such as age and sex, $\beta_v$ is the common population slope, $\gamma_{iv}$ the additive site effect, and $\delta_{iv}$ the multiplicative site effect. Because ComBAT standardizes data by removing the population trend $x_{ij}^T\hat{\beta}_v$, any site-specific multiplication of that slope — written as the factor $S$ in $y_{ijv} = \alpha_v + \gamma_{iv}A + x_{ij}^T\beta_v S + \delta_{iv}\varepsilon_{ijv}M$ — bypasses the correction and survives as a misalignment. The experimental vehicle is Pairwise-ComBAT, a reconfiguration that harmonizes each moving site independently onto a fixed reference population rather than onto a pooled average, and a synthetic-protocol design in which a real healthy-aging cohort is rescaled with known additive ($A$), slope ($S$), and variance ($M$) factors so that harmonization error can be measured exactly. A closed-form Bhattacharyya distance between rectified Gaussian populations serves as the quality metric.

What would settle it

Take two real sites whose age-versus-metric slopes are known to differ markedly, run standard ComBAT with more than 32 subjects and a full age span at each site, and measure the Bhattacharyya distance between the harmonized and reference distributions on held-out subjects: the paper predicts a large distance whenever the slope factor departs from 1, so near-zero distance on such a pair would contradict the central claim. A second check targets the variance claim: on two sites with matched slopes, compare ComBAT's estimated site variance with the empirical within-site variance; if they converge well before 100 subjects, the paper's claim that the prior keeps disproportionately high weight near 100 subjects would be refuted.

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Extended reading notes

Core claim

ComBAT models each measured value as a linear function of covariates plus an additive site effect and a multiplicative site effect, and assumes the covariate regression vector $\beta_v$ — the population slope relating age to the measured metric — is identical at every site. The central demonstration is that this slope assumption is often wrong: when a moving site has been rescaled by a slope factor $S \neq 1$ relative to the reference, ComBAT compensates the additive bias but leaves the multiplicative bias uncorrected, so the harmonized populations stay misaligned and the estimated site variance $\hat{\delta}^{2*}_{iv}$ carries a growing quadratic error. In controlled experiments with known injected bias, slope, and variance factors, harmonization quality deteriorates sharply for slope factors of 0 and 1.8 even though pure additive and pure multiplicative differences are handled well. The paper also shows that the variance estimator keeps a disproportionately large weight on its prior even for populations above roughly 100 subjects, and introduces a Bhattacharyya-distance measure on covariate-rectified data as a goodness-of-fit metric for harmonization.

Load-bearing premise

The experiments assume real inter-site differences are exactly the kind the authors inject — a global additive offset, a slope change, and a variance change applied to one healthy population — so if genuine site effects are messier, such as nonlinear age trajectories or acquisition-specific artifacts, the diagnosed failure modes and the recommended sample-size and age-range thresholds may not transfer to real data.

Editorial extensions

If this is right

Multi-site studies should verify that covariate slopes, such as the age-versus-metric relationship, are approximately equal across sites before running ComBAT, because large slope discrepancies predict failed harmonization even when additive and multiplicative biases are modest.
Reliable harmonization has concrete lower bounds on the moving site: at least 16 to 32 training subjects, an age span of roughly 40 years or more, and balanced male/female composition; below these, test-set generalization degrades even when training fits look good.
For normative modeling and clinical applications, harmonization parameters should be estimated on healthy control subjects only and then applied to pathological subjects; including pathology in the estimation compresses diseased populations into the normal range and erases the disease signal.
Harmonizing each site to a single fixed reference dataset, rather than to the pooled average of all sites, allows new sites to be added without re-estimating previously established parameters, a direct benefit for open-data sharing, longitudinal studies, and clinical data streams.
Because a slope mismatch corrupts the estimated site variance, any downstream statistic built from post-harmonization variance — such as normative deviation scores — inherits the bias unless the slope condition is checked first.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A cheap pre-flight check the authors do not propose: fit the covariate model inside each site separately, compare slope estimates and their confidence intervals, and restrict ComBAT harmonization to site pairs whose slopes overlap, turning the paper's negative result into a positive screening test.
Because the variance estimator keeps strong prior weight even near 100 subjects, a natural extension is a sample-size-aware prior or reporting both the shrunk and the empirical variance; the paper documents the symptom but does not propose the remedy.
The equal-slope requirement is stated for linear slopes, yet many diffusion metrics change nonlinearly with age; a testable prediction is that the 40-year age-range rule is necessary but not sufficient on cohorts with curvilinear age trajectories, where a global linear fit can mask locally mismatched slopes.
The reference-anchored framing implies a frozen-parameter protocol for live clinical data: estimate the harmonization function once on a normative reference, then harmonize each incoming subject with those fixed parameters, eliminating the moving-target problem by construction rather than by re-estimation.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

Here's my take on 2505.14722. The paper is worth a look if you use ComBAT, but it is not a theoretical advance. The main point—ComBAT assumes a common slope across sites and fails when that breaks—is already in Kim et al. and Bayer et al., and the authors say Pairwise-ComBAT is only a reconfiguration of the original. What they add is a systematic, controlled look at how sample size, age range, sex balance, and patient mix affect harmonization, with clear recommendations at the end. That is genuinely useful for applied multi-site dMRI work.

The theory section is correctly written and the slope-mismatch derivation (Eq. 14) is sound. I also credit them for treating harmonization as a train/test problem rather than just looking at training fit. The ADNI and NIMH examples are real data and support the qualitative conclusions: slope differences produce bad harmonization, and mixing patients into the parameter estimation compresses pathology.

The soft spots are in the quantitative recommendations. The '16-32 subjects' and 'at least 40 years of age span' thresholds come from the modified-CamCAN simulations, where the moving site is created by applying a linear transform to the same CamCAN data used as the reference. That means the simulation is self-consistent with ComBAT's own generative model; it does not test nonlinear age effects, voxel-dependent site effects, or the messy interactions you see across real scanners. The MAD curves in Figures 5 and 7 are averages over 30 repeats with no confidence intervals and no statistical tests, so the specific cutoffs are not well-grounded. The central qualitative claims hold up; the precise numbers should be treated as provisional.

A couple of other things: the code and data are promised only upon acceptance, which limits reproducibility now, and there are typos in key formulas (Eq. 10 and the Bhattacharyya distance expression). These are fixable, not fatal.

Who benefits? Practitioners who use ComBAT without knowing its failure modes, and normative modeling groups. I would cite it if I were writing a methods paper on multi-site harmonization, but not as the authoritative source for the thresholds.

My recommendation: send it to peer review. It is a solid, honest evaluation of a widely used tool, and the recommendations matter to a large community. The referee should insist on error bars, a public code release, and a discussion of how the simulated site effects might differ from real ones.

Referee Report

5 major / 4 minor

Summary. The manuscript re-derives the linear model underlying ComBAT harmonization and pinpoints the assumption that the covariate slope β_v is identical across sites. It introduces Pairwise-ComBAT, which harmonizes each site to a fixed reference dataset, and proposes a Bhattacharyya-distance goodness-of-fit measure. Using a synthetic "modified-CamCAN" dataset created by applying additive, slope, and multiplicative transforms to CamCAN, plus two real datasets (ADNI and NIMH), the authors run experiments varying bias magnitude, sample size, age range, sex covariates, and pathological contamination. They conclude with recommendations: ComBAT should not be used as a black box; covariate slopes should be matched; at least 16–32 subjects per site are recommended; the age range should span at least 40 years; sex distributions should be balanced; and harmonization parameters should be estimated on healthy controls only.

Significance. If the central claims hold, the paper is a useful service to the ComBAT user community. The formal observation around Eq. (14)—that a site-specific slope multiplier S_i leaves a residual x^T β(S_i−1) that no additive or multiplicative correction can remove—is correct and is illustrated in the synthetic and NIMH examples. The train/test decomposition of harmonization error is a good methodological instinct, and the recommendation to estimate batch parameters on healthy controls is clinically sensible. The ADNI pathology illustration in Fig. 10 convincingly shows the risk of compressing patient distributions into the normative range. However, the quantitative thresholds that are the paper's headline contribution rest on simulations that satisfy ComBAT's linear assumptions by construction, and no uncertainty is reported on the 30-repeat averages. The significance is therefore real, but the strength of the quantitative recommendations currently exceeds what the evidence supports.

major comments (5)

[Mathematical limitations and Dataset studied (Eqs. 14 and 16)] The generative model used to create the synthetic moving site is not the model analyzed in the theory. Eq. (14) shows that a slope multiplier S_i necessarily changes the intercept through the term γ_iv = α_v(S_i−1)+A_i, so slope and additive site effects are coupled. Eq. (16), by contrast, applies the additive factor A and slope factor S independently to the CamCAN baseline. The simulated failure modes in Figs. 3–7 therefore do not directly instantiate the theoretical failure mode of Eq. (14), and the measured effects may not transfer to situations where slope and intercept changes are coupled. Please justify the independent parameterization or rerun the central experiments under the coupled model derived in Eq. (14).
[Results (Figs. 5 and 7)] The recommendations "at least 16 to 32 subjects" and "age range at least 40 years" are read off MAD curves that are averaged over 30 repetitions but presented without confidence intervals, error bars, or any inferential test. In Fig. 5(a) and Fig. 7, the training and testing curves approach the reference floor smoothly, and it is not possible to tell whether the apparent plateau at N≈32 or age span≈40 is statistically distinguishable from the floor at larger N or wider age spans. Because these thresholds are a central product of the paper, please report per-condition variability (e.g., bootstrap CIs or box plots over the 30 repeats) and, where possible, a test comparing the error at the recommended operating point with the reference error.
[Experiments 2 and 3; Dataset studied (Modified-CamCAN)] The sample-size and age-range experiments are conducted exclusively on Modified-CamCAN, in which the moving site and the test set are generated by applying the same global linear transform to the same CamCAN distribution used as the reference. This means the data satisfy ComBAT's model assumptions by construction, with no nonlinear age trajectories, voxel-dependent scanner effects, or acquisition-specific artifacts. The experiments therefore test interpolation under a correct model, not robustness to model misspecification. The ADNI and NIMH analyses are qualitative illustrations rather than quantitative validation of the thresholds. The recommendations should be labeled as conditional on the synthetic model, or supported by additional real-data analyses with varying sample size and age range.
[Pairwise-ComBAT (Eq. 15)] Eq. (15) adds back the covariate effect as x^T_Rj β̂_v, i.e., using the covariates of a reference-site subject rather than those of the moving-site subject being harmonized. If this is not a typographical error, the method replaces each moving subject's age/sex effect with the reference subject's covariates and thereby destroys biological variability. If it is a typo, it should read x^T_Mj β̂_v. Either way, the current text cannot be implemented faithfully, and the accompanying code is not yet public, so a reader cannot resolve the ambiguity from the repository.
[Goodness of fit] The formula for the Bhattacharyya distance is inconsistent and, as printed, incorrect. The notation switches between subscripts R and T (z_Rjv is defined while the expression uses µ_Tv and σ_Tv), and the logarithmic term should have denominator 2 σ_Tv σ_Mv, not 2 σ_Tv + σ_Mv. Since all BD values in Figs. 3, 4, 9, and 10 are quantitative evidence for the paper's conclusions, the printed formula and notation must be corrected.

minor comments (4)

[Abstract and Recommendations] The abstract states "five essential recommendations," but the Recommendations section lists six bullet points and the Conclusion also says "six recommendations." Please align the count.
[Code and Data Availability] The availability statement says the code and data "will be rendered public upon acceptance." For a paper whose stated goals are reproducibility and open science, please make the Pairwise-ComBAT code and the modified-CamCAN generation scripts available during review, at least as supplementary material.
[Captions of Figs. 8 and 9] "Mean Absolution Difference" should be "Mean Absolute Difference." In addition, the MAD metric is used without a formal definition; please define it in the Method section or figure captions.
[Figure 5(a)] The label "Error Ref = 0.465e10-5" appears to mean 0.465×10⁻⁵ but the typesetting is confusing. Please write it unambiguously.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the slope-assumption failure follows from the paper's own Eq. (14), and experiments include external ADNI/NIMH validation, so the central claim does not reduce to its inputs.

full rationale

The paper's central claim is mathematical: ComBAT assumes a site-independent slope βv in Eq. (1), and when data are generated under Eq. (14) with a site-specific slope multiplier Si, the harmonized population retains a residual xTβv(Si−1) that no additive or multiplicative site correction removes. This is derived from the paper's own equations and is not an input restated as a conclusion. The simulation studies generate Modified-CamCAN via Eq. (16), which is deliberately within ComBAT's linear model family; measuring MAD/BD on such data is a controlled internal-consistency check, not a prediction equivalent to its inputs by construction. Crucially, the paper does not stop at the synthetic data: NIMH and ADNI datasets are harmonized and show qualitatively the same slope-mismatch and pathology-compression effects, providing independent external evidence. The recommendations on sample size and age range are empirical thresholds read from these simulations; while their portability to real, nonlinear, or confounded site effects may be a generalizability concern, that is a correctness/validity question, not circular reasoning. The only self-references (TractoFlow, response function) concern processing tools and are not load-bearing for the harmonization claims. No step was found in which a fitted parameter is renamed as a prediction or in which a uniqueness or prior-work citation is doing the argumentative work.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

No new entities are introduced. The paper relies on the standard ComBAT model, empirical Bayes priors, and a synthetic data assumption that is specific to its experimental design.

free parameters (1)

A, S, M factors in modified-CamCAN generation = A in {0.6, 0.8, 1.2}; S in {0, 0.8, 1.8}; M in {0.2, 0.8, 1.8}
These hand-chosen factors in Eq. (16) define the simulated site effects; the paper does not fit them to data, but the quantitative recommendations are conditional on this choice of simulation conditions.

assumptions (5)

domain assumption The ComBAT data model (Eq. 1) with a site-independent slope βv and Gaussian noise ε.
This is the core assumption of ComBAT that the paper reviews; the failure analysis is built on it.
domain assumption Empirical Bayes priors: Gaussian for γ, inverse Gamma for δ^2 (Eqs. 6-7).
Inherited from ComBAT; the posterior estimators in Eqs. 11-12 depend on these priors.
domain assumption The reference site R is well-populated and representative of healthy controls.
Stated in the Pairwise-ComBAT section: 'in all our experiments, we assume the reference site is well-populated.'
ad hoc to paper Synthetic site differences in modified-CamCAN follow Eq. (16) and are representative of real site effects.
This is the experimental setup used to produce the recommendations; it is not validated against a broader set of real site-effect structures.
domain assumption After rectification, harmonized populations are Gaussian so the Bhattacharyya closed-form applies.
Stated in the Goodness of fit section: after removing covariates and biases, the distributions are assumed Gaussian.

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Cite this review

Pith. "Pith review of ComBAT Harmonization for diffusion MRI: Challenges and Best Practices." pith.science (2026). https://pith.science/paper/PU3MNTJH

@misc{pith2026250514722,
  author       = {Pith},
  title        = {Pith review of: ComBAT Harmonization for diffusion MRI: Challenges and Best Practices},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PU3MNTJH}},
  note         = {Machine review of arXiv:2505.14722}
}

read the original abstract

Over the years, ComBAT has become the standard method for harmonizing MRI-derived measurements, with its ability to compensate for site-related additive and multiplicative biases while preserving biological variability. However, ComBAT relies on a set of assumptions that, when violated, can result in flawed harmonization. In this paper, we thoroughly review ComBAT's mathematical foundation, outlining these assumptions, and exploring their implications for the demographic composition necessary for optimal results. Through a series of experiments involving a slightly modified version of ComBAT called Pairwise-ComBAT tailored for normative modeling applications, we assess the impact of various population characteristics, including population size, age distribution, the absence of certain covariates, and the magnitude of additive and multiplicative factors. Based on these experiments, we present five essential recommendations that should be carefully considered to enhance consistency and supporting reproducibility, two essential factors for open science, collaborative research, and real-life clinical deployment.

Figures

Figures reproduced from arXiv: 2505.14722 by the authors.

**Figure 1.** Illustration of the seven steps of a typical Pairwise-ComBAT harmonization of two sites underlying the effect of each variable of Eq.(17). From the raw data in a) to the harmonized data in j). The gray curves in b) illustrate the overall trend of the population from site 1 and site 2, whereas the scatter plots show the values of the J subjects of each site. likelihood distribution as in L/S ComBAT[18] 1 . Following… view at source ↗

**Figure 2.** Pairwise-ComBAT harmonization of the mean diffusivity (MD) in the modified CamCAN dataset against the unbiased CamCAN (N=441). (a) The parameters A (additive), M (multiplicative), S (slope) used to generate the modified CamCAN version (c.f. Eq.(16). (b) (left) raw data with the slopes for CamCAN (solid black line), modified CamCAN (dashed black line), and the slope estimated by Pairwise-ComBAT (solid blue line). (ri… view at source ↗

**Figure 3.** Experiment 1. Harmonization of the Modified-CamCAN population (in gray) on the CamCAN population (in red). Results for different multiplicative factors on (a) the bias (A) (b) the Slope (S) and (c) the noise variance (M) as described in eq. (16). The left columns are the original data and the right columns are the harmonized data. Green checks indicate correct harmonization, red X’s indicate poor harmonization. allo… view at source ↗

Figures from the paper (27 more)

**Figure 4.** Figure 4: a) The quadratic error in the estimation of the moving site variance ˆδ 2∗ iv for different slope and variance multiplicative factors S and M. b) Harmonization of the mean diffusivity (MD) of the NIMH population (red) onto that of CamCAN (gray). The different slopes be…

**Figure 5.** Figure 5: (a) Mean Absolute Difference (MAD) training and testing harmonization errors for various number of training samples N from the Modified-CamCAN moving site. (b) and (c) illustrate the effect of using too few or enough training samples on the training and testing fit. Gr…

**Figure 6.** Figure 6: Effect of age range harmonization of the mean diffusivity (MD) metric between the modified CamCAN and CamCAN. Green checks indicate correct harmonization, red X’s indicate poor harmonization. yond N = 8 subjects, the testing and training errors begin to decrease, indic…

**Figure 7.** Figure 7: and 6 [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

**Figure 8.** Figure 8: Effect of covariate on Pairwise-ComBAT harmonization of the mean diffusivity (MD) metric between modified CamCAN and CamCAN datasets. a) Mean Absolution Difference (MAD) harmonization when considering male-only, female-only and a balance (male+female) populations. b)…

**Figure 9.** Figure 9: (a) and (b) illustrate a pathological population (purple triangles) exhibiting negative (top left) and positive (middle top) bias relative to a normative population (red). Below these, the harmonization results are shown both with and without the inclusion of pathologi…

**Figure 10.** Figure 10: Harmonization of ADNI-127-GE site with CamCAN. a) Raw data, b) Pairwise-ComBAT harmonization from HC group only, c) Pairwise-ComBAT harmonization from HC and pathological group. The gray (target site) and red (moving site) lines show the population mean trend of both …

**Figure 11.** Figure 11: This illustration is complementary to figure 3 in the paper. 17 [PITH_FULL_IMAGE:figures/full_fig_p017_11.png]

**Figure 12.** Figure 12: This illustration is complementary to figure 3 in the paper. A = 0.6 BD = 0.09 A = 1.2 BD = 0.023 S = 0 BD = 0.84 S = 0.8 BD = 0.051 S = 1.8 BD = 0.049 M=0.2, A=S=1 BD = 0.47 M=0.8, A=S=1 BD = 0.014 M=0.2, A=1,S=1.8 BD = 0.92 a. Additive (A) effect (M=S=1) c. Multipli…

**Figure 13.** Figure 13: This illustration is complementary to figure 3 in the paper. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_13.png]

**Figure 14.** Figure 14: This illustration is complementary to figure 3 in the paper. A = 0.6 BD = 11.33 A = 1.2 BD = 3.85 S = 0 BD = 0.89 S = 0.8 BD = 0.027 S = 1.8 BD = 0.028 M=0.2, A=S=1 BD = 0.47 M=0.8, A=S=1 BD = 0.012 M=0.2, A=1,S=1.8 BD = 0.67 a. Additive (A) effect (M=S=1) c. Multipli…

**Figure 15.** Figure 15: This illustration is complementary to figure 3 in the paper. 19 [PITH_FULL_IMAGE:figures/full_fig_p019_15.png]

**Figure 16.** Figure 16: This illustration is complementary to figure 3 in the paper. b) 2 < N < 32 c) N ≥ 32 Raw Train Test Total Apparent fiber density (AFDt) ✘ ✘ ✓ ✓ b) 2 < N < 32 c) N ≥ 32 Fractional anositropy (FA) ✘ ✘ ✓ ✓ b) 2 < N < 32 c) N ≥ 32 Isotropic volume fraction (isoVF) ✘ ✘ ✓ ✓…

**Figure 17.** Figure 17: This illustration is complementary to figure 5 in the paper. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_17.png]

**Figure 18.** Figure 18: This illustration is complementary to figure 5 in the paper. Full age range Total Apparent fiber density (AFDt) – AF Left Age matched Raw Train Test Full age range Age matched Full age range Age matched Age (years) Age (years) Age (years) Age (years) Age (years) Age (…

**Figure 19.** Figure 19: This illustration is complementary to figure 6 in the paper. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_19.png]

**Figure 20.** Figure 20: This illustration is complementary to figure 6 in the paper. Full age range Isotropic volume fraction (isoVF) – AF Left Age matched Raw Train Test Full age range Age matched Full age range Age matched Age (years) Age (years) Age (years) Age (years) Age (years) Age (ye…

**Figure 21.** Figure 21: This illustration is complementary to figure 6 in the paper. 22 [PITH_FULL_IMAGE:figures/full_fig_p022_21.png]

**Figure 22.** Figure 22: This illustration is complementary to figure 6 in the paper. Full age range Corticospinal tract left (CST L) – FA Age matched Raw Train Test Full age range Age matched Full age range Age matched Age (years) Age (years) Age (years) Age (years) Age (years) Age (years) 2…

**Figure 23.** Figure 23: This illustration is complementary to figure 6 in the paper. 23 [PITH_FULL_IMAGE:figures/full_fig_p023_23.png]

**Figure 24.** Figure 24: This illustration is complementary to figure 6 in the paper. HC only HC + Pathology Raw Train Test a) Pathology with A=M=0.8 b) Pathology with A=M=1.2 HC only HC + Pathology BD= 0.0003 BD=0.26 BD= 0.0006 BD=0.27 BD= 0.0039 BD=0.28 BD=0.0017 BD=0.29 BD= 1.89 BD= 1.96 C…

**Figure 25.** Figure 25: This illustration is complementary to figure 9 in the paper. 24 [PITH_FULL_IMAGE:figures/full_fig_p024_25.png]

**Figure 26.** Figure 26: This illustration is complementary to figure 9 in the paper. 25 [PITH_FULL_IMAGE:figures/full_fig_p025_26.png]

**Figure 27.** Figure 27: This illustration is complementary to figure 9 in the paper. 26 [PITH_FULL_IMAGE:figures/full_fig_p026_27.png]

**Figure 28.** Figure 28: This illustration is complementary to figure 9 in the paper. 27 [PITH_FULL_IMAGE:figures/full_fig_p027_28.png]

**Figure 29.** Figure 29: This illustration is complementary to figure 9 in the paper. 28 [PITH_FULL_IMAGE:figures/full_fig_p028_29.png]

**Figure 30.** Figure 30: This illustration is complementary to figure 9 in the paper. 29 [PITH_FULL_IMAGE:figures/full_fig_p029_30.png]

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

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