Main

Identifying brain regions and circuits that give rise to neurological and psychiatric symptoms is a central goal of fundamental and clinical neuroscience. Charting the relationship between brain alterations and behavior has long served as a cornerstone of this effort, from linking brain injury to behavioral outcomes1,2,3 to systematic studies leveraging modern neuroimaging techniques4. Progress has, however, been more elusive for complex neurological and psychiatric conditions, where patients can often exhibit highly spatially distributed and heterogeneous brain abnormalities5,6,7.

The method of ‘lesion network mapping’ (LNM)8,9, also known in literature under alternative terms such as ‘causal brain mapping’10, ‘causal network localization’11, ‘lesion network-symptom mapping’12,13,14,15, ‘network localization’16,17, ‘atrophy network mapping’18, ‘remission network mapping’19, ‘coordinate network mapping’ or ‘coordinate-based network mapping’20,21,22, ‘activation network mapping’23, ‘network-based meta-analytic’ analysis24, among others (Supplementary Table 1), has rapidly gained traction as a framework to trace and unite topographically heterogenous lesions and other brain alterations to underlying brain circuits10,11,15. Collectively referred to as the LNM framework, this method maps the anatomical locations of brain alterations onto normative functional brain connectivity (FC) to examine whether, and if so how, these alterations converge onto a common underlying network. The framework posits that alterations in different brain regions can give rise to similar clinical symptoms when they disrupt the same functional brain network. Over the past years, LNM studies have reported such functional networks for a broad range of neurological and psychiatric disorders, including post-traumatic stress disorder (PTSD)25, epilepsy26,27, autism spectrum disorder (ASD)28, schizophrenia29, obsessive-compulsive disorder (OCD)30 and migraine20, among many others (see refs. 31,32,33 and a 2025 PubMed/ClinicalTrials.gov search for review; Supplementary Table 1 and Supplementary Note 1). Notable LNM findings include the ‘causal depression network’15,34,35,36, a ‘psychosis circuit’37 and brain circuits related to addiction38, all highlighted as promising for clinical application15,25,26,38,39,40.

However, many of these reported LNM networks—purportedly delineated as disease-specific—seem to converge on strikingly similar brain networks. As illustrated in Fig. 1a,b, the LNM networks reported for psychiatric conditions such as addiction38, migraine20, PTSD25 and schizophrenia29, but also for neurological conditions such as vertigo41, Capgras syndrome42, Parkinson’s disease43 and disrupted volition16, appear to implicate one and the same system, a network involving bilateral insular cortices, the anterior cingulate cortex (ACC) and parts of the frontopolar cortex, thalamus and cerebellum. This observation is unexpected, considering the substantial heterogeneity in etiology and symptomatology of these conditions.

Fig. 1: Observed similarity of published work using LNM networks from original and randomized lesions.

a,b, Images of LNM-related circuitry maps from recent LNM and sLNM publications (from refs. 16,20,25,29,38,41,42,43). Panel a is reproduced with permission. c, Correlation between sLNM networks for reduced PTSD risk25 and cognitive decline induced by DBS in Parkinson’s disease43 (shown in b). d, Recomputed LNM maps resulting from the application of voxel-wise Lead-DBS54 on publicly available lesions for addiction38, migraine20, neurogenic stuttering44, neglect syndrome53, insomnia53 and disrupted agency16. Reconstruction of LNM maps (d, first two images) compared to those reported in the original study (a) is high. e–g, Correlations between reconstructed LNM maps depicted in d are shown. h–j, Results show high similarity between LNM circuits derived from cortical deviations for six psychiatric conditions (BP and OCD are shown) and healthy controls; data taken from ref. 28. k, The most reported regions across 102 LNM networks from a literature survey (Supplementary Tables 1 and 2), highlighting the prevalence of the top 10% highest correlated and anticorrelated voxels. Extensive overlap is evident in the insula, ACC and frontal pole. l–n, LNM networks derived from random lesions also show highly similar LNM outcomes. For example, lesions that disrupted agency16 and spin-randomized versions of these lesions (middle row) across the brain, as well as completely randomized seed locations (bottom row), result in similar LNM outcomes (shown in n). o,q, Plot of the spatial correlation between the original LNM map (disrupted agency16) and a typical example from the randomized conditions. p,r, Randomization of lesions was repeated 1,000 times, with almost all occasions resulting in highly similar LNM maps between the original (disrupted agency) and random conditions (box plots show values of n = 1,000 permutations; (p) minima = 0.06, maxima = 0.92, center = (median) 0.75, bounds of box (Q1 25th percentile–Q3 75th percentile) = 0.66–0.81, whiskers = 0.43–0.92; (r) minima = 0.58, maxima = 0.96, center = (median) 0.84, bounds of box (Q1 25th percentile–Q3 75th percentile) = 0.81–0.87, whiskers = 0.72–0.96). s, The application of LNM (Lead-DBS) on lesions associated with addiction remission (top left, lesion masks taken from ref. 38). The panel also shows LNM outputs on the same lesion set but now spin-randomized across the cortex (top right, exemplary spin, r = 0.48), following a random selection of 100 lesions with mixed symptomatology (bottom left, ‘mixed lesions’, r = 0.93), and based on 100 synthetic lesions (bottom right, r = 0.71). All approaches yield very similar LNM maps. t–v, Plots show data (ASD28) from an alternative null analysis, with the connections of the group connectome C binarized and randomized (t, left = original matrix, right = randomized matrix). Once again, LNM analyses resulted in very similar maps. Plot in u shows a representative example (ASD) and v shows a box plot of all randomizations (box plot shows values of n = 1,000 permutations; minima = 0.93, maxima = 0.98, center = (median) 0.96, bounds of box (Q1 25th percentile–Q3 75th percentile) = 0.96–0.96, whiskers = 0.94–0.98). ADHD, attention-deficit/hyperactivity disorder; BP, bipolar disorder; MDD, major depressive disorder; OCD, obsessive-compulsive disorder; PTSD, post-traumatic stress disorder; s subjects; SCZ, schizophrenia.

Examining this spatial overlap between published LNM networks in more detail substantiates the observed high spatial alignment. For example, published LNM networks for PTSD25 and cognitive decline in Parkinson’s disease43 show high spatial correlation (r = 0.73; see Fig. 1b,c, Supplementary Note 2 and Supplementary Table 2 for data sources). Similar overlap is observed among networks for addiction38, migraine20, neurogenic stuttering44 and disrupted agency16 (r = 0.62–0.89; voxel-wise P < 0.001; Fig. 1d–g). This spatial alignment remains highly significant after correcting for spatial autocorrelation effects (spin test45 and BrainSMASH46; Pspin, Pbrainsmash < 0.001; r and P values for all examined networks are listed in Supplementary Table 3). Similar overlap is evident for LNM networks linked to aphasia47 and epilepsy27 (r = 0.40), amnesia48 and psychosis37 (r = 0.80), as well as for networks further linked to individual symptom data like networks related to risk of depression in multiple sclerosis34 and remission for smoking addiction38 (r = 0.57; all P, Pspin, Pbrainsmash < 0.001). LNM maps derived based on focal neurological lesions (for example, dyskinetic cerebral palsy49) or associated with deep brain stimulation (DBS)-related targets (for example, treatment for OCD50) also appear to show surprisingly high similarity (r = 0.64; P, Pspin, Pbrainsmash < 0.001; Supplementary Table 3).

Remarkably, several of these LNM networks—for example, disruption of agency16 (Fig. 1l–n), ASD28, addiction38, but also epilepsy27 (Supplementary Fig. 8)—seem to be indistinguishable from networks derived when lesions are randomly shuffled across the brain (r = 0.73–0.95; Fig. 1l–r), derived from a mix of lesions not associated with one specific disorder (Fig. 1s), or even from completely random synthetic lesions (Fig. 1s and Supplementary Note 6). Also, randomizing the connections of the normative connectome dataset does not appear to markedly disrupt the LNM outcomes, resulting in rather similar networks (degree-preserving randomization51,52; for example, LNM for neglect syndrome53, r = 0.66, addiction38, r = 0.72, agency16, r = 0.75, and ASD28, r = 0.94, illustrated in Fig. 1t–v; Supplementary Note 7 and Supplementary Fig. 3).

The breadth of this spatial similarity is indicated by a literature survey, identifying 201 studies that discussed and/or used the LNM framework in context of studying 101 neurological and psychiatric conditions (2015–2025; see details in Supplementary Notes 1 and Supplementary Table 1). Re-analyzing 102 LNM networks across 72 of these studies confirmed an overall high alignment of LNM maps (|r| = 0.40, s.d. = 0.25; Supplementary Notes 2 and 3), with regions such as the bilateral insula, ACC and frontal cortex appearing in up to 74% of reported LNM networks (Fig. 1k; see Supplementary Note 5 for details).

To explain this notable similarity among reported LNM networks, we examined the core principles of the method. Our systematic analysis reveals a fundamental limitation of LNM methods: LNM projects sets of lesions—regardless of their clinical association—onto only elementary properties of the standard connectivity matrix, primarily the row sum of that matrix (that is, node ‘degree’). Below, we provide a step-by-step walkthrough of the LNM pipeline, illustrating how its procedural stages can be expressed compactly in linear matrix notation. This formalization exposes the inherent constraint of the method that explains why the majority of published LNM networks converge to highly similar outcomes instead of identifying disorder-specific circuits.

Results

Step-by-step walkthrough of LNM

LNM (for methodologically equivalent variants and approaches published under different nomenclature, see Supplementary Table 1, from now on collectively referred to as LNM) typically consists of three methodological steps. Figure 2a presents a schematic of these steps, as implemented in popular LNM toolboxes like Lead-DBS54 (Supplementary Notes 8 and 17). We can consider a group of patients, each with one or more brain lesions, and study them using a large standard resting-state functional magnetic resonance imaging (fMRI) dataset from normative healthy individuals (for example, 1,000 healthy participants from the GSP1000 (ref. 55) or Human Connectome Project56). In step 1 of the LNM procedure, each lesion is mapped to corresponding voxels in the standardized space (for example, MNI152) of the normative dataset. Next, in step 2, the FC of a lesion is computed by correlating the average resting-state time series of the lesion’s matching voxels with all other voxels in the brain and standardizing the correlation values using a Fisher r-to-z transformation. This is repeated across all healthy datasets in the normative connectivity dataset, resulting in over 1,000 FC maps per lesion, which are then combined into a single map using a one-sample t test to assess voxel-wise deviation from zero FC. A threshold (for example, |t| > 7) can be applied to identify the strongest connections57. Steps 1 and 2 are repeated for all studied lesions, producing a set of individual FC t maps, one for each lesion.

Fig. 2: LNM pipeline and streamlined implementation.

a, The procedure of LNM involves three major steps—first, the lesion(s) of a single patient s (step 1) is placed into standard space. Next, the FC profile of that lesion m**s of patient s is computed by means of the fMRI resting-state data in a large normative dataset, with the FC maps combined in a one-sample t test (two-sided) to obtain a single FC map for each lesion of patient s. Optionally, the t map can be thresholded to select the strongest connections (step 2). Steps 1 and 2 are repeated for all lesions of the group of patients S. Afterwards, the individual FC lesion maps are combined in a group analysis (step 3) to define their underlying common network. b, Step 2 of the LNM procedure can be streamlined (left, middle row) using an atlas-based approach in which the cortex and subcortical areas are parcellated according to a high-resolution atlas—for example, the Yeo-Schaefer1000/Melbourne54 atlas107,108. Middle, an atlas-based approach allows for precomputation of all lesion-to-region FC for all datasets in the normative connectome dataset. Right, all individual matrices can be grouped into a single group connectome C, with the resulting group matrix containing the same information as the one-sample t test performed in step 2. c, Taken together, the entire LNM procedure is now compressed to selecting row i corresponding to lesion m**s of patient s from the group matrix C (optionally, threshold the resulting vector), repeat this for all lesions of all patients s in S, and summing over the selected rows Cm to obtain the final LNM network map. C, group connectivity matrix; GSP1000, Brain Genomics Superstruct Project 1000; h, normative participants; r, correlation coefficient; S, all participants.

Next, in the group-analysis step 3 of the LNM procedure, the lesion FC t maps are combined to produce the group LNM network. This is typically done by averaging the lesion FC t maps, identifying regions consistently connected across lesions (for example, ≥75% (ref. 17)). The resulting map is referred to as the LNM network9 or LNM sensitivity map8. Alternatively, when individual symptom data are available, the group-analysis step 3 can involve correlating the lesion FC maps with symptom scores (~16% of reviewed studies; Supplementary Table 1) or contrast subgroups with differing symptom levels (~11%); variants of the method referred to as ‛lesion network-symptom mapping’ or symptom-based LNM12,13,14,15. The sign of the resulting r values or t values in the symptom lesion network mapping (sLNM) depends on the behavioral scale that is used, and may indicate, for example, risk level11,25, symptom change15 or clinical state (for example, relapse versus remission)38.

Formal notion of LNM

We found that the LNM methodological steps can be considerably compressed, without losing information. This compression is illustrated in Fig. 2b,c, and a mathematical derivation is provided in Supplementary Note 18. First, precomputing the correlation among the time series of all brain voxels yields all possible lesion-to-voxel FC maps beforehand. These precomputed matrices, for all normative participants in the normative connectivity dataset (H), can replace step 2 in the LNM approach (Fig. 2b). To improve practical feasibility, a high-resolution brain atlas can be used to divide the brain into, for example, R = 1,000 equally sized regions58. Furthermore, inferring equal variance across the connections in H (which we empirically validated, r = 0.99; Supplementary Note 8), the one-sample t test in step 2 can be replaced by taking the mean of the precomputed individual matrices54. This allows replacing the entire set of 1,000 normative FC matrices with a single mean group connectivity matrix C (Fig. 2b). This approach eliminates the need for looping the procedure over all normative datasets for each lesion, repetitively, reducing the computation time for a standard dataset of 50 lesions from ~10–12 h using the Lead-DBS toolbox54 to under 10 s. We empirically validated this compressed approach, with both the full Lead-DBS implementation and the atlas-based accelerated version producing effectively identical LNM maps (examined across 100 patient and 100 synthetic lesions, mean r = 0.96; Supplementary Notes 8 and 20).

The compressed version (Fig. 2c) describes the LNM procedure now as: (step 1) matching lesion m**s of participant s to the region(s) i in the used brain atlas; (step 2) selecting the matching row(s) i in the group connectivity matrix C; repeat steps 1–2 for all lesions; and (step 3 group analysis) taking the sum (or mean, which are equivalent) of all selected rows to obtain the final LNM map.

Formally, we can express LNM as

$$\mathrm{LNM}=\mathop{\sum }\limits_{s=1}^{{S}}\left(\frac{1}{|{m}_{s}|}\mathop{\sum }\limits_{i\in {m}_{s}}{C}_{i,r}\right)\mathrm{for},\mathrm{all},r\in R$$

(1)

where S denotes the total set of patients, s one specific participant, m**s the lesion of participant s, |m**s| the size of lesion m**s, i the row(s) in C matching the region(s) of lesion m**s in participant s, C the group average functional matrix of size R × R, R all voxels or brain regions in the chosen brain mask or atlas and r a specific region in R (scaled with a fixed constant; for exact formal notation, see Supplementary Notes 8 and 18). We can also rewrite equation (1) in a vector notation:

$$\begin{array}{l}{\mathrm{LNM}}=\mathop{\sum}\limits_{s=1}^{{S}}\left({{{\bf{m}}}}_{s}\times C\right)\end{array}$$

(2)

where ({{\bf{m}}_{s}}) is a row vector of size 1 × R, indicating the lesion region with entries of 1 or 1/(\left|{m}_{s}\right|) when a lesion covers multiple rows, and 0 otherwise.

We can now make one final compression—combining all lesion vectors ({{\bf{m}}}_{s}) of all participants into a single lesion matrix M = (({\vec{{\bf{m}}}}_{1}), ({\vec{{\bf{m}}}}_{2}), …,({{\vec{\bf{m}}}}_{s})) (Fig. 2c). This summarizes the entire LNM procedure (steps 1, 2 and 3 combined) to a linear matrix multiplication:

$$\mathrm{LNM}=\mathop{\sum }\left(M\times C\right)$$

(3)

where M denotes the lesion matrix, C the standard group connectivity matrix.

In the sLNM variant, the group-analysis step is slightly modified (illustrated in Supplementary Fig. 1). In step 3, at each voxel, the FC values across the individual lesion maps (size S × 1) are further correlated with the participants’ symptom scores (size S × 1), instead of taking the mean over all maps without further weighting. With steps 1 and 2 the same (and given by M × C, equation (3)), it can be obtained that the calculation of the final sLNM r map of all voxels in step 3 scales with:

$$\mathrm{sLNM}=\mathop{{\bf{sv}}}\limits\times \left(M\times C\right)$$

(4)

where M and C are again the lesion matrix and the normative group connectivity matrix, and ({{\bf{sv}}}) now a standardized row vector describing the individual symptom scores (Supplementary Notes 9 and 19 provide a step-by-step and more formal derivation of sLNM).

We provide exemplary code for the voxel-wise Lead-DBS implementation of LNM and sLNM, along with the equivalent linear matrix form of equations (3) and (4) in Supplementary Note 20.

LNM converges to the elementary properties of the input matrix

The above formal characterization brings to light a key limitation at the core of the LNM method, explaining the observed similarity between published networks (Fig. 1). Specifically, the approach involves a repetitive sampling of one and the same matrix C, with the lesions M (and additionally the symptom scores sv in the sLNM variant) involving only lin