We analyzed clinical behavioral and MRI data of 272 patients (mean age 64.1 years, SD 11.3, 59.6% male) included in the GRECogVASC study (NCT01339195) assessing post-stroke cognitive and motor status and its determinants in French-speaking patients (Arnoux et al., 2018; Barbay et al., 2018; Godefroy et al., 2012). All patients gave their written informed consent to participation. The study was performed in accordance with institutional guidelines and was approved by the regional investigational review board (Comité de Protection de Personnes Nord-Ouest II, Amiens, France; reference: 2010/25). Table 1 reports the demographic and clinical characteristics of the study cohort. We included patients presenting unilateral and bilateral strokes due to both cerebral infarct and hemorrhage, because hemorrhage may extend outside the arterial territories, and consequently, the association of both stroke subtypes decreases multicollinearity (i.e., data correlations among neighboring voxels) (Kreisler et al., 2000). All patients were assessed at 6 months post-stroke, using MRI and the NIHSS to quantify symptom severity in stroke (Brott et al., 1989). NIHSS is composed of 11 items concerning specific functional abilities (see section “1 Introduction”). By using the NIHSS motor sub-scale, we assessed the presence of hemiparesis, a deficit frequently used in clinico-anatomical correlations studies because of its known anatomical basis centered on the motor system, including the corticospinal tract and the precentral cortex (Godefroy et al., 1998; Kassubek et al., 2005; Zhu et al., 2010). To this aim, we derived a global limb motor score able to quantify the motor deficit linked to dysfunction in the motor system (the facial paresis score was not included, as we focused on limb paresis). The score corresponded to 10 minus the sum of the upper and lower limb items in the NIHSS; a score of 10 corresponded to no impairment in the limbs motor system, whereas a score of two indicated major impairment. Left hemiparesis was defined by a left limb motor score < 10. We restricted our analyses to the left motor score, as the motor deficit was more frequent on the left side (n = 30) than on the right side (n = 24) (Table 1).

Magnetic resonance imaging scans included high-resolution T1-weighted images (inversion-recovery ultrafast gradient echo with magnetization preparation; fields of view (x, z): 205, 256; acquisition matrix (x, z): 256, 512; voxel size (x, y, z): 0.8 mm, 2 mm, 0.5 mm; sequence parameters: TR/TE: 13/4.5 ms; inversion time: 400 ms; flip angle: 15°; receiver bandwidth: 20.83 kHz; acquisition time: 3 mn 28 s), FLAIR, T2 and T2*-weighted sequences obtained at 6 months after stroke on a 3T machine (HDXt, General Electric Medical System) equipped with an eight-channel head coil. MRI datasets were registered into a template for older individuals (Rorden et al., 2012), using the pyramidal block-matching Diffeomorphic Demons algorithm (Garcia et al., 2010) implemented in the MedINRIA software package¹ (Toussaint et al., 2007). Lesion delineation was performed manually (by trained neurologists: M.B., A.A., O.G.) on 3DT1 MRI datasets by applying the levelset algorithm in Medical Image Processing, Analysis and Visualization software (Covington et al., 2010). Lesions were defined as cavitations on T1 sequence. Normalized lesioned brain structures (further called regions of interest, ROIs) were determined using NiiStatV9 (Rorden et al., 2007) and Automatic Anatomical Labelling (AAL) (Tzourio-Mazoyer et al., 2002) and NatbrainLab (Catani and Thiebaut de Schotten, 2008) templates, representing both gray and white matter structures (see Figure 1) and put together in the AALCAT atlas. The entire methodological pipeline is summarized in Figure 2.

The present study reflects the iterative estimated MSA, a novel MSA-based approach to characterize contributions of both gray matter structures and white matter connections simultaneously in a given function. A similar method has been used by Malherbe et al. (2021) in combination with VLSM, which allowed to pre-select a subset of regions in order to reduce the number of regions for the subsequent MSA. Due to methodological advances in computing the MSA, in the present study no preselection of ROIs needed to be performed. This advance allowed us to test directly the ability of the iterative estimated MSA approach for making causal functional inferences in motor function based on brain lesion deficits.

The MSA quantified relative contributions of both gray matter structures and white matter connections. Positive contributions obtained with MSA emphasized the roles of the internal capsule, corticospinal tract and cortico-ponto-cerebellum as principal contributors in motor function. First, the key roles of the corticospinal tract and internal capsule confirm previous findings reported in the motor function analysis by using alternative methods (Arnoux et al., 2018; Godefroy et al., 1998; Kassubek et al., 2005; Malherbe et al., 2021; Zhu et al., 2010) and emphasize the importance of white matter connections. These results suggest that the iterative MSA was able to rank positive contributors when jointly analysing gray matter structures and white matter connections as previously described (Kaufman et al., 2009; Malherbe et al., 2021; Ofir-Geva et al., 2023). Second, we inferred contributions of structures that had not been evident as playing a key role in motor deficit (Corbetta et al., 2015; Karnath and Rennig, 2017; Rorden et al., 2009). These structures involved the cortico-ponto-cerebellum bundle as a positive contributor. This pathway originates in the motor cortex, the prefrontal and temporal cortices (Salmi et al., 2010). The characterization of the cortico-ponto-cerebellum white matter network functional role in human is still challenging, but current findings suggest an involvement in both motor and cognitive functions (Palesi et al., 2017), although we cannot exclude that multicollinearity might also account for the present association.

We should note that the contribution of the RoB was non-significant in our MSA analyses. Specifically, the contribution of the RoB is a strong indicator of the absence of other potential structures involved in motor function that would have not been considered as regions of interest in the analyses. Of note, an important RoB contribution would indicate that the analyzed function is dependent on brain regions potentially missing from the analysis. However, we should note that the RoB reflects the different lesion patterns of many distinct regions. Small but critical regions may become “diluted,” preventing the RoB from reaching a significant level (Ofir-Geva et al., 2023). Alternatively, it can be hypothesized that the lack of a RoB contribution could be related to the inconsistency of lesion locations and to the weak signal of lesion load in regions that are functionally related to the deficit. As a result, this signal cannot be of much utility to the model. While this explanation is also possible, one should consider the substantial size of 272 patients’ sample in the present study, limiting such alternative explanations. Furthermore, the F1-score (considering recall and precision in the analyses) was very high (0.88).

It could be argued that regions such as the precentral gyrus (primary motor cortex) should also be involved in the motor function. Given that the present study has been conducted in chronic patients, it could be that the presence of lesions in these regions in the acute stage is potentially compensated by an intact corticospinal tract or internal capsule. Thus, lesions inducing temporary motor impairment resolve after the acute stage (Karnath and Rennig, 2017) and this may account for the absence of an independent effect of precentral lesions (el Quessar et al., 1999; Godefroy et al., 1998). Other possible explanations include the fact that isolated lesions in the primary motor cortex often recover in the chronic phase, leading to impaired dexterity that the NIHSS does not assess. Additionally, the combined NIHSS sub-scores for upper and lower limbs may dilute the signal, as the primary motor cortex may play a lesser role in lower limb function. Finally, this outcome might be due to an insufficient representation of primary motor cortex lesions in the cohort (10 out of 272 patients presented lesions of the superior corona radiata, including premotor and primary motor cortices lesions), which can occur even in large study populations.

Multi-perturbation Shapley Analysis was previously used in order to define brain-behavior relationships. Specifically, MSA was initially used in datasets from cooling deactivation experiments and permanent lesion experiments (e.g., Keinan et al., 2004b; Zavaglia et al., 2016) and results proved to be robust in ground truth simulations (Zavaglia et al., 2024). The plausibility of applying MSA on lesion data was also demonstrated in studies conducted in cohorts of stroke patients with visuospatial neglect (Malherbe et al., 2018; Toba et al., 2017; Toba et al., 2020c) that confirmed and specified contributions of fronto-parietal and occipital systems to visuospatial attentional behavior (Corbetta et al., 2008; He et al., 2007; Hilgetag et al., 2001; Kincade et al., 2005; Thiebaut de Schotten et al., 2005; Toba et al., 2018; Verdon et al., 2010; Toba et al., 2022; Toba et al., 2024; Kaufmann et al., 2025). However, caution is needed when interpreting MSA results. While MSA was proposed to address lesion-dependencies, this assumption holds mainly in theoretical scenarios where complete empirical data is available. In practice, MSA heavily depends on predictors and classifiers which can be biased by interdependencies within the data.

Generally, MSA results have been interpreted in the framework of inter-hemispheric rivalry theories (Keinan et al., 2004a; Keinan et al., 2004b) and find applications in studies conducted with non-invasive methods able to stimulate or disrupt different brain structures (see for details Valero-Cabre et al., 2019). Specifically, positive contributors (such as the corticospinal tract, the internal capsule, the cortico-ponto-cerebellum tract) represent structures that facilitate the performance and thus a clinical goal may be to enhance them. However, interpretations are more complex, because brain structures have intrinsic dynamics that allow them to compete for processing resources in order to accomplish brain functions. As a result, they may be at the same time positive and negative contributors in related functions.

Several limitations of the present study should be discussed. First, our analyses purposely concerned a well-known functional system (the motor system). While this choice allows to discuss the efficacy of the iterative estimated MSA in identifying important motor regions, it also limits the novelty of our results. Moreover, the use of a relatively coarse measure for motor function (i.e., NIHSS upper and lower limb scores), even in a large cohort, is not ideal for contributing novel biological insights. More precise measures should provide a finer-grained understanding of the motor system’s condition.

Second, the lesion-based approach used in this study is not the definitive gold standard for computing lesions-symptom mapping analyses. However, motor function is among the best-understood functions in terms of functional anatomy. For this reason, we chose to use it as a model to evaluate our methodological approach.

Third, the train-set to predict the behavior was performed with a graded database, whereas the test-set was binarized. This choice respects the need to use different train and test set of data but also involves that the model performance should be treated with caution.

Another limitation of this study concerns the choice of ROIs in MSA. ROIs are defined anatomically but not functionally. As a result, chosen ROIs can combine different functional units and thus the computation of a lesion load may not be entirely informative on the functional role of the region.

Last, another limitation of this study is represented by the inclusion of patients with a history of prior strokes and bilateral strokes, potentially confounding the results. However, additional analyses emphasized only minor results changes when these patients were left out.