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Statistical parametric mapping

Statistical parametric mapping (SPM) is a statistical framework and software package for analyzing neuroimaging data, involving the construction and assessment of spatially extended statistical processes to test hypotheses about regionally specific effects in functional brain images from modalities such as positron emission tomography (PET), functional magnetic resonance imaging (fMRI), electroencephalography (EEG), and magnetoencephalography (MEG).^[1] It employs the general linear model to characterize regionally specific effects while accounting for the inherent spatial correlations in imaging data, enabling inference on distributed brain responses to experimental stimuli or conditions.^[2] Developed primarily by Karl Friston and colleagues at the Wellcome Trust Centre for Neuroimaging (formerly the MRC Cyclotron Unit) in the late 1980s and early 1990s, SPM originated from efforts to analyze PET scans for brain activation studies, with its foundational concepts introduced in Friston et al.'s 1990 paper addressing global and local changes in cerebral blood flow. The approach was formalized through subsequent works incorporating Gaussian random field theory for multiple comparison corrections, as detailed in Worsley et al. (1992), and evolved to handle the temporal dynamics of fMRI data following its emergence in 1992. Key milestones include the release of SPM'91 in 1991, SPM'94 with enhanced preprocessing tools, and ongoing updates like SPM 25 (2025), which support advanced Bayesian inference, machine learning integrations, and novel analysis methods such as optimized beamforming for MEG/EEG data.^[3]^[4] SPM's core workflow encompasses spatial realignment, normalization to standard anatomical space, smoothing to enhance signal-to-noise ratio, model specification using design matrices, and parametric statistical inference via t- or F-maps thresholded for significance.^[5] Widely adopted in cognitive neuroscience, clinical research, and pharmacology, it facilitates group-level analyses through fixed- and random-effects models, ensuring robust detection of task-related activations or pathological alterations across subjects.^[6] As an open-source MATLAB-based toolbox, SPM promotes reproducibility and has influenced extensions to other fields like biomechanics, underscoring its versatility in handling high-dimensional spatiotemporal data.^[7]

Introduction

Definition and principles

Statistical parametric mapping (SPM) is a statistical framework for performing inference on neuroimaging data by constructing spatially extended statistical processes to test hypotheses about functional anatomy and physiology. It enables the identification of regionally specific effects, such as brain activations, without requiring a priori specification of regions of interest, treating the brain as a continuous random field.^[8] At its core, SPM employs a voxel-wise, mass-univariate approach, applying statistical tests independently to each voxel in the image volume to generate parametric maps of brain activity or structure. Key principles include the use of voxel-based morphometry for analyzing structural variations, such as gray matter concentration in MRI data, and the application of the general linear model (GLM) to time-series data from functional imaging modalities like fMRI or PET. Hypothesis testing occurs at each voxel to assess effects of experimental conditions, with results forming statistical maps (e.g., t- or F-maps) that highlight significant regions. The GLM underpins SPM's modeling, expressed as

\mathbf{Y} = \mathbf{X}\boldsymbol{\beta} + \boldsymbol{\epsilon},

where \mathbf{Y} is the observed data vector, \mathbf{X} is the design matrix encoding experimental effects, \boldsymbol{\beta} are the parameters to estimate, and \boldsymbol{\epsilon} is the error term assumed to follow a multivariate Gaussian distribution. This parametric assumption of Gaussian noise facilitates flexible modeling of complex experimental designs, including factorial or parametric variations, by convolving regressors with physiological models like the hemodynamic response function. In contrast to non-parametric approaches, which rely on permutation tests or rank-based statistics and can be computationally intensive for high-dimensional data, SPM's parametric framework leverages known distributional properties for efficient inference, offering greater statistical power when assumptions hold, particularly for detecting distributed effects across the brain. Random field theory then corrects for multiple comparisons inherent in voxel-wise testing, controlling family-wise error rates more sensitively than conservative methods like Bonferroni correction.

Historical development

Statistical parametric mapping (SPM) originated in the late 1980s at the MRC Cyclotron Unit in Hammersmith Hospital, London, where Karl Friston and colleagues developed methods to analyze positron emission tomography (PET) data from brain activation studies using short half-life radio tracers. The approach addressed limitations in traditional region-of-interest (ROI) analyses by enabling voxel-wise statistical inferences across the entire brain, marking a shift toward whole-brain inference in neuroimaging. The first application of SPM appeared in a 1989 study on color processing by Lueck et al., published in Nature. Foundational papers followed in 1990 and 1991: Friston et al. introduced SPM using T- and F-statistics to relate global and local changes in PET scans, while a subsequent paper addressed multiple comparisons via Gaussian random field theory for assessing significant changes in functional images. These works, both in the Journal of Cerebral Blood Flow & Metabolism, established the core principles of SPM for PET data.^[3] In 1994, Friston and collaborators released SPM'94, the first major software revision implemented in MATLAB, primarily authored by Friston during that summer with contributions from Andrew Holmes and others. This version formalized SPM as a general linear model (GLM) approach for functional imaging, detailed in a seminal paper that outlined statistical parametric maps for testing regionally specific effects. The Wellcome Department of Imaging Neuroscience (then the Wellcome Department of Cognitive Neurology) at University College London became the hub for SPM development after Friston's group relocated there in 1994, fostering its widespread adoption. SPM99, released in January 2000, integrated advanced GLM specifications for more flexible experimental designs, enhancing its utility for complex neuroimaging studies. By 2002, SPM2 extended SPM's capabilities to better handle functional magnetic resonance imaging (fMRI) data, incorporating hemodynamic response modeling and serial correlation corrections, as adaptations for fMRI had begun following its introduction in 1992.^[1]^[2]^[9]^[10]^[11]^[3] A notable extension emerged in 2003 with the introduction of dynamic causal modeling (DCM) by Friston, Harrison, and Penny, which built on SPM to infer effective connectivity in neural systems using Bayesian frameworks for fMRI and other modalities. This advancement expanded SPM beyond univariate inference to model interactions among brain regions. Overall, SPM's evolution from PET-focused tools in the early 1990s to versatile software for fMRI and beyond enabled large-scale, population-level studies of brain function, revolutionizing neuroimaging by prioritizing hypothesis-driven, whole-brain analyses over localized ROI methods.^[12]^[3]

Methodology

Experimental design

In statistical parametric mapping (SPM) analyses of functional neuroimaging data, such as functional magnetic resonance imaging (fMRI) and positron emission tomography (PET), experimental designs are structured to maximize the detection of task-related brain activations while minimizing noise and biases.^[13] Common design types include blocked, event-related, and factorial approaches, each tailored to the temporal characteristics of the hemodynamic response function (HRF) and the research question.^[14] These designs ensure that the resulting parametric maps reflect true neural activity rather than artifacts, with careful planning essential before data acquisition to account for later preprocessing steps like motion correction.^[13] Blocked designs present conditions in alternating epochs of sustained activity, typically lasting 20-40 seconds, to elicit robust, cumulative responses that align well with the slow HRF in fMRI and PET.^[14] This approach enhances statistical efficiency for detecting large-scale activations but can introduce confounds if order effects or anticipation build up across blocks.^[13] In contrast, event-related designs model transient responses to individual stimuli, using randomized inter-stimulus intervals (often 4-8 seconds) to deconvolve overlapping HRFs and allow estimation of trial-specific effects, making them suitable for studying dynamic cognitive processes. Factorial designs extend these by crossing multiple factors (e.g., task type × attention level in a 2×2 setup), enabling assessment of main effects and interactions through contrasts in the general linear model, which is particularly powerful for disentangling overlapping influences in SPM.^[14] Power analysis in SPM experimental design evaluates the ability to detect true effects, influenced by factors such as sample size, expected effect size (e.g., 0.5-1% BOLD signal change in fMRI), and temporal resolution of the scanning protocol.^[13] Efficiency metrics, including the variance of the design's contrast (lower variance indicating higher power), guide optimization; for instance, randomized event-related designs often outperform blocked ones for estimating onset latencies, while longer scan durations or larger samples (e.g., 12-20 subjects) boost power by reducing between-subject variance. Early studies often used sample sizes of 6-12 for group-level inferences in PET/fMRI, but contemporary guidelines recommend at least 20 subjects for fMRI to ensure robust power, with larger sizes (30+) preferred for reproducibility; power increases non-linearly with sample size, effect size, and reduced noise.^[13]^[16] To enhance interpretability, designs incorporate control conditions like baseline tasks (e.g., fixation cross or rest periods) and randomization of trial order via methods such as Latin squares or jittered onsets, which minimize biases from serial correlations or habituation.^[14] Confounding variables, particularly head motion in fMRI, are addressed through design choices like short acquisition times per run or counterbalanced block orders to limit displacement artifacts.^[13] A representative example is a cognitive activation study contrasting rest versus a word generation task in PET, where subjects alternate between silent rest and overt word production in blocked epochs, randomized across sessions to control for fatigue; this design isolates language-related activations in regions like Broca's area while using rest as a low-level baseline to subtract non-specific physiological noise.

Data preprocessing

Data preprocessing in statistical parametric mapping (SPM) prepares raw neuroimaging data, such as functional magnetic resonance imaging (fMRI) time series, for subsequent statistical modeling by addressing spatial misalignment, motion artifacts, temporal discrepancies, and noise. These steps ensure that voxel-wise statistical inferences are valid across subjects and sessions, assuming a known experimental design structure. The process typically follows a sequential pipeline, beginning with motion correction and culminating in smoothing, as implemented in SPM software developed by the Wellcome Centre for Neuroimaging.^[17] Motion correction, or realignment, compensates for subject head movements during scanning by estimating rigid-body transformations that minimize differences between successive volumes and a reference image, often the first or mean volume. This is achieved through least-squares optimization of the six parameters (three translations and three rotations) using an iterative algorithm that aligns images based on intra-modal similarity measures like normalized mutual information. The resulting realigned images are prefixed with "r" in SPM, and motion parameter estimates are saved for potential inclusion as regressors in later modeling; for MRI data, smoothing during estimation is typically set to 5 mm full-width at half-maximum (FWHM). This step is crucial for fMRI, where even small displacements can introduce spurious activations.^[17] Spatial normalization registers individual brain images to a standard stereotactic space, such as the Montreal Neurological Institute (MNI) template derived from the ICBM152 atlas, facilitating group-level comparisons. It employs an affine transformation (6 or 12 parameters for rigid-body and linear scaling/shearing) followed by non-linear warping using discrete cosine transform (DCT) basis functions or advanced methods like DARTEL for diffeomorphic registration. Resampling to the template's voxel grid uses interpolation methods such as trilinear or B-spline to preserve image integrity, with sinc interpolation applied in some contexts for higher accuracy in periodic signals. Outputs include warped images (prefixed with "w") and deformation fields, enabling inverse transformations back to native space.^[17] Smoothing applies an isotropic Gaussian kernel to the normalized images to enhance signal-to-noise ratio, reduce inter-subject anatomical variability, and satisfy the assumptions of Gaussian random field theory for multiple comparison corrections in SPM. Common kernel sizes range from 6 to 12 mm FWHM, with 8 mm as a default for fMRI to balance noise suppression and localization; the kernel is convolved with the image data, producing smoothed volumes prefixed with "s" or integrated into subsequent files. This step increases the effective degrees of freedom in statistical tests but can blur fine-scale activations if over-applied.^[17] Temporal filtering addresses low-frequency drifts and acquisition timing issues in fMRI data. High-pass filtering removes scanner-related slow variations (e.g., baseline drifts) using a discrete cosine transform basis set with a default cutoff of 128 seconds, implemented as part of the general linear model setup but often applied post-realignment. Slice-timing correction, specific to interleaved or sequential fMRI acquisitions, interpolates voxel time series to a common acquisition time (e.g., the middle slice) via sinc interpolation or Fourier phase shifting, correcting for within-TR delays that could otherwise alias hemodynamic responses; corrected files are prefixed with "a". These procedures ensure temporal alignment without introducing spatial distortions.^[17]

Statistical modeling

In statistical parametric mapping (SPM), the core statistical modeling relies on the general linear model (GLM) to relate observed neuroimaging data, such as blood-oxygen-level-dependent (BOLD) signals from functional magnetic resonance imaging (fMRI), to underlying neural processes. The GLM assumes that the measured signal at each voxel can be expressed as a linear combination of explanatory variables plus an error term, formulated as Y = X \beta + \epsilon, where Y is the vector of observed data, X is the design matrix, \beta is the vector of parameters to be estimated, and \epsilon represents the residual errors. This framework enables voxel-wise estimation of effects across the brain volume. To model the delayed and dispersed nature of the BOLD response, neural events—such as stimulus onsets or task conditions—are convolved with a hemodynamic response function (HRF). The canonical HRF in SPM is a double gamma function approximating the typical 4-6 second peak and subsequent undershoot following neural activation, transforming discrete event trains into continuous regressors that capture the expected signal shape. The design matrix X is constructed by assembling these convolved regressors for experimental conditions (e.g., separate columns for different tasks or stimuli) alongside nuisance regressors to account for confounds like head motion parameters, global signal intensity, or physiological noise, ensuring that the model isolates effects of interest. Parameter estimation in SPM begins with ordinary least squares (OLS) to obtain the beta weights \hat{\beta} = (X^T X)^{-1} X^T Y, which minimize the sum of squared residuals under the assumption of independent and identically distributed errors (sphericity). However, neuroimaging data often exhibit serial correlations due to temporal autocorrelations in the BOLD signal, violating sphericity; SPM addresses this using a variance components approach with an autoregressive model of order 1 (AR(1)) plus white noise to parameterize the error covariance structure V. The hyperparameters of V are estimated via restricted maximum likelihood (ReML), enabling pre-whitening of the data and design matrix to restore sphericity before re-estimating \beta. Contrasts are defined to test specific hypotheses about the parameters, such as differences between conditions or overall effects. A t-contrast, for group differences or simple effects, is specified as a vector c where the test statistic evaluates c^T \beta, assessing whether the linear combination deviates significantly from zero (e.g., c = [1, -1] for condition A minus B).

c^T \hat{\beta} \sim \mathcal{N}(c^T \beta, \sigma^2 c^T (X^T V^{-1} X)^{-1} c)

An F-contrast, for main effects or omnibus tests involving multiple parameters, uses a matrix C to evaluate the joint significance of subspaces, such as C \beta = 0. Model fitting incorporates non-sphericity corrections through an iterative reweighted least squares (IRLS) procedure within the ReML framework, where the data are iteratively whitened by updating the covariance estimate until convergence, yielding unbiased parameter estimates and valid inference. This process operates on preprocessed data, such as motion-corrected and spatially smoothed images, to enhance signal stability.

Inference procedures

In statistical parametric mapping (SPM), inference procedures begin with hypothesis testing at the voxel level using t-statistics for single contrasts and F-statistics for multiple contrasts within the general linear model framework.^[13] The t-statistic is computed as t = \frac{c^T \hat{\beta}}{\sqrt{\hat{\sigma}^2 c^T (X^T X)^{-1} c}}, where c is a contrast vector, \hat{\beta} are parameter estimates, \hat{\sigma}^2 is the error variance, and X is the design matrix; this tests the null hypothesis H_0: c^T \beta = 0, corresponding to no activation or effect in the signal.^[13] Similarly, the F-statistic assesses multiple parameters under the null, following an F-distribution under Gaussian assumptions.^[13] These univariate tests generate a statistical parametric map, but due to the high dimensionality of imaging data (e.g., millions of voxels), multiple comparisons correction is essential to control false positives. The primary approach for multiple comparisons in SPM is controlling the family-wise error rate (FWER) using random field theory (RFT), which accounts for spatial smoothness and autocorrelation in the imaging data modeled as a continuous Gaussian random field.^[13] RFT provides thresholds such that the probability of any false positive exceeding the threshold across the entire search volume is below a specified level (e.g., 5%), by approximating the distribution of the maximum statistic using the field's topological properties.^[13] As an alternative, the false discovery rate (FDR) method controls the expected proportion of false positives among significant voxels, offering less conservative thresholding for exploratory analyses, as implemented via the Benjamini-Hochberg procedure.^[13] To address spatial autocorrelation, SPM employs extent-based thresholding on clusters of contiguous suprathreshold voxels, where inference is based on cluster size rather than individual voxels, reducing the multiple comparisons burden.^[13] Under RFT, the probability of a cluster extent s exceeding a threshold u in a D-dimensional field is approximated as P(S > s \mid u, k) \approx e^{- \mathrm{[EC](/page/EC)}_D(u) \cdot (s / c)^{ (D+1)/D }}, where k indexes the field, c incorporates the full-width at half-maximum (FWHM) smoothness, and \mathrm{[EC](/page/EC)}_D(u) is the expected Euler characteristic.^[13] The expected Euler characteristic, a key RFT quantity approximating the number of distinct features (e.g., blobs or clusters) in the field, is given by E[\chi] = \sum_{i=0}^D \rho_i (4 \log 2)^{i/2} H_{i}(z) e^{-z^2 / 2}, with \rho_i as resels (resolution elements) in dimension i, H_i as Hermite polynomials, and z the standardized threshold; this enables precise control of FWER for smoothed fields typical in neuroimaging.^[13] Bayesian extensions in SPM provide non-parametric complements through posterior probability maps (PPMs), which estimate the probability that an effect exceeds a threshold at each voxel, integrating prior beliefs with observed data via empirical Bayes methods. PPMs, available since early SPM versions (e.g., SPM2), were enhanced in SPM8 for group-level Bayesian model selection, avoiding explicit multiple comparisons corrections by assessing conditional probabilities directly, such as P(\theta > \theta_0 \mid y) > p_T, where \theta is the effect size, y the data, and p_T a probability threshold (e.g., 0.95).^[18] This approach, building on variational Bayes approximations, offers a probabilistic framework for inference that is particularly useful in hierarchical models.

Visualization and analysis

Parametric maps

Parametric maps in statistical parametric mapping (SPM) represent the core output of voxel-wise statistical analyses, visualizing the spatial distribution of test statistics across brain images to identify regions of significant activation or effect. These maps are generated by applying the general linear model (GLM) to neuroimaging data, such as functional MRI (fMRI) or positron emission tomography (PET), after preprocessing steps like spatial normalization and smoothing.^[5] The primary types of parametric maps include SPM{T} and SPM{F}. SPM{T} maps are derived from univariate t-tests, assessing the significance of a single contrast, such as the difference in brain activity between two conditions, and are commonly used for hypothesis-driven tests of localized effects. In contrast, SPM{F} maps employ F-statistics to evaluate multiple linear contrasts simultaneously, accommodating complex designs like factorial analyses or interactions, where the overall significance of several effects is examined. Additionally, contrast-specific maps can depict effect sizes, providing a quantitative measure of the magnitude of regional responses beyond mere statistical significance.^[13]^[5] Interpretation of these maps focuses on key features such as peak coordinates and associated z-scores. Peak coordinates pinpoint the location of maximal activation within a cluster, reported in standardized spaces: the Talairach system, based on proportional scaling from a single postmortem atlas, or the more precise Montreal Neurological Institute (MNI) space, derived from averaged MRI templates for improved inter-subject alignment. Z-scores, obtained by transforming t- or F-statistics under the null hypothesis, quantify the deviation from expected noise levels, with higher values indicating stronger evidence against the null; for instance, a z-score exceeding 3.0 often corresponds to uncorrected p < 0.001, though maps incorporate corrected p-values from inference procedures like random field theory to account for multiple comparisons.^[13]^[5] For localization, parametric maps are typically rendered as volume overlays on anatomical templates, such as T1-weighted structural images or glass brain projections, allowing researchers to contextualize statistical findings within neuroanatomical structures. This visualization facilitates the identification of functionally relevant regions, such as cortical areas involved in sensory processing.^[13] A representative example is the interpretation of an SPM{T} map from a motor task paradigm, where participants perform unilateral hand movements. The map reveals significant activations in contralateral primary motor cortex (e.g., peak at MNI coordinates -36, -24, 60 mm with z = 5.2), reflecting the hemispheric lateralization of motor control, while ipsilateral regions show minimal deviation from the null.^[13]

Thresholding and clustering

In statistical parametric mapping (SPM), thresholding is applied to parametric maps to identify voxels or regions exceeding a specified significance level, refining the raw statistical outputs from earlier modeling stages.^[13] Height thresholding operates at the primary (voxel-level) scale, where individual voxel statistics are compared against thresholds derived from uncorrected p-values, Bonferroni correction for multiple comparisons, or family-wise error (FWE) rates controlled via random field theory (RFT). Voxel-level thresholds can also incorporate false discovery rate (FDR) procedures, which balance sensitivity and specificity by controlling the expected proportion of false positives among significant voxels, often outperforming strict FWE control in sparse activation scenarios. Cluster-level thresholding complements height thresholding by focusing on the spatial extent of activations, requiring contiguous suprathreshold voxels to form clusters that surpass an extent threshold, thereby enhancing detection power for spatially extended signals. Clusters are identified as connected components of voxels above the height threshold, typically using 3D or 2D connectivity criteria (e.g., face-adjacent voxels), with minimum cluster sizes estimated from the image's smoothness, quantified in resolution elements (resels) via RFT to account for spatial autocorrelation.^[19] This approach leverages the Gaussian random field properties of smoothed images, where expected cluster extents under the null hypothesis are predicted to set significance thresholds, reducing false positives from isolated noise peaks. Topological inference extends cluster-based methods by controlling false positives through the Euler characteristic (EC), a topological descriptor that captures the overall shape of excursion sets (suprathreshold regions) as the difference between the number of clusters and holes. Under RFT, the expected EC is approximated using intrinsic volumes of the search space, providing threshold-free or set-level inference that is robust to non-stationary smoothness variations across heterogeneous data, such as in neuroimaging with varying tissue types.^[19] For non-stationary fields, corrections involve local estimates of smoothness (e.g., via variance components) to normalize resel counts, ensuring valid FWE control without assuming uniform autocorrelation. In practice, within the SPM graphical user interface (GUI), users set height thresholds (e.g., p < 0.001 uncorrected) and extent thresholds (e.g., k > 10 voxels) in the results window to generate cluster reports, balancing exploratory analyses with liberal thresholds against confirmatory ones using conservative FWE or FDR corrections.^[13] This interactive process allows visualization of surviving clusters and peaks, with options to export statistics for further reporting, emphasizing the trade-off between sensitivity and specificity based on study goals.^[20]

Graphical outputs

Graphical outputs in Statistical Parametric Mapping (SPM) extend beyond raw parametric maps to provide interpretable visualizations that facilitate the exploration, validation, and communication of neuroimaging results. These displays integrate statistical inferences with anatomical context, often reflecting thresholded clusters from prior inference procedures to highlight significant effects (e.g., p < 0.05 family-wise error corrected). By rendering activations in intuitive formats, they enable researchers to assess spatial patterns, temporal dynamics, and network interactions efficiently.^[13]^[21] Glass brain projections offer a concise overview of significant activations through maximum intensity projections (MIPs) onto a translucent 3D brain outline, typically in sagittal, coronal, and axial orientations. This format collapses the full three-dimensional statistical map into two-dimensional views, emphasizing the location and extent of suprathreshold voxels without occluding underlying structure. In SPM software, these projections are generated automatically upon results inspection, using color-coded intensity scales to represent t- or F-statistic values, aiding rapid identification of distributed effects across the brain.^[13]^[21] Volume views provide detailed orthogonal sections of the brain, overlaying color-scaled statistical maps (e.g., z-scores or probability values) onto high-resolution anatomical templates like the MNI152. Users can navigate through axial, coronal, and sagittal slices via interactive crosshairs, zooming into regions of interest to evaluate local maxima, cluster sizes, and anatomical correspondence. These views support customizable colormaps and transparency levels, enhancing the discernment of subtle gradients in activation strength and facilitating precise reporting of coordinates in standard space.^[13]^[21] Time-series extraction visualizes signal fluctuations from user-defined regions of interest (ROIs), such as clusters or spheres centered on peaks, by plotting eigenvariates or adjusted BOLD responses over time. In SPM, this is achieved through the Volume of Interest (VOI) tool, which deconvolves raw data using the hemodynamic response function to reveal event-related dynamics, often displayed as peristimulus time histograms with confidence intervals. These plots validate model fits by comparing predicted versus observed signals, supporting further analyses like psychophysiological interactions. Complementary toolboxes like MarsBaR extend this by enabling batch extraction and graphical plotting of ROI time courses for multiple subjects.^[13]^[21]^[22] Advanced visuals in SPM include 3D rendered brains, where statistical overlays are projected onto inflated cortical surfaces or volume-rendered anatomies for immersive spatial interpretation. Surface rendering, often using meshes from tools like FreeSurfer integrated via SPM extensions, highlights hemispheric asymmetries and sulcal patterns, with rotatable views for publication-quality figures. In connectivity extensions such as Dynamic Causal Modeling (DCM) or psychophysiological interactions (PPI), results are depicted as graphs or adjacency matrices, illustrating directed influences or correlations between regions with node-link diagrams and edge weights scaled by Bayesian posteriors or coupling parameters. These formats elucidate network topology, aiding the reporting of functional integration in complex paradigms.^[13]^[21]^[23]

Applications and extensions

Neuroimaging applications

Statistical parametric mapping (SPM) has been extensively applied in neuroimaging to detect and characterize brain activity and structural changes across various modalities, particularly in functional magnetic resonance imaging (fMRI) and positron emission tomography (PET).^[6] In fMRI studies, SPM enables the analysis of task-evoked responses by modeling the blood-oxygen-level-dependent (BOLD) signal within a general linear framework, allowing inference on regionally specific activations.^[13] For instance, in task-based paradigms investigating language processing, SPM has identified key activations in the left inferior frontal gyrus and superior temporal gyrus during semantic and phonological tasks, supporting models of hemispheric specialization for language comprehension.^[24] Similarly, in resting-state fMRI, SPM facilitates connectivity analyses that reveal the default mode network (DMN), characterized by coherent low-frequency fluctuations in regions such as the posterior cingulate cortex and medial prefrontal cortex, which are implicated in self-referential thought and mind-wandering.^[25] In PET and single-photon emission computed tomography (SPECT) imaging, SPM is used to quantify regional metabolic or ligand binding differences by normalizing images to a standard space and applying voxel-wise statistics.^[26] A prominent application involves assessing glucose metabolism with 18F-fluorodeoxyglucose (FDG)-PET in Alzheimer's disease, where SPM reveals hypometabolism in temporoparietal and precuneus regions, with early-onset cases showing more extensive reductions compared to late-onset, correlating with cognitive decline severity.^[27] In pharmacological studies, SPM analyzes receptor binding potentials from PET tracers, such as those targeting dopamine D2/3 receptors, to evaluate drug occupancy and receptor availability in the striatum, aiding in the development of antipsychotics and addiction therapies.^[28] Clinically, SPM supports pre-surgical planning in epilepsy by mapping eloquent cortex through task-based fMRI, effectively identifying language-dominant hemispheres in temporal lobe cases, thus minimizing postoperative deficits.^[29] For stroke recovery, longitudinal SPM analyses of fMRI data from the 2000s demonstrate dynamic shifts in motor network activation, such as increased contralesional primary motor cortex recruitment in the subacute phase, which normalizes with improved hand function over months.^[30] Voxel-based morphometry (VBM), an extension of SPM for structural MRI, segments gray matter and applies deformation-based normalization to detect atrophy patterns in neurodegenerative diseases.^[31] In conditions like Alzheimer's and frontotemporal dementia, VBM identifies focal volume reductions in the hippocampus and frontal lobes, providing biomarkers for disease progression.^[32]

Broader scientific uses

Statistical parametric mapping (SPM), originally developed for neuroimaging, has been extended to broader scientific domains, leveraging its framework for hypothesis testing on spatially extended data to analyze patterns in diverse datasets. In genomics, SPM adaptations enable the mapping of gene expression patterns across tissue arrays, particularly through methods like SpatialSPM, which reconstructs spatial transcriptomics data into multi-dimensional image matrices for cross-sample comparability and generates parametric maps such as T-scores and correlation coefficients to identify differential expression regions.^[33] This approach builds on earlier parametric analyses for microarray data, such as the Parametric Analysis of Gene Set Enrichment (PAGE) introduced in 2005, which applies modified statistical models to rank and test predefined gene sets for enrichment in expression profiles.^[34] In environmental imaging, SPM supports the analysis of satellite and microscopy data to detect spatial patterns, including pollution mapping and anomaly identification in remotely sensed imagery. For instance, in geoscience applications, SPM performs t-tests on simulated or geophysical images to highlight significant anomalies, such as 5027-pixel regions in noisy datasets with full-width at half-maximum (FWHM) smoothing of 5–72 pixels, aiding in environmental monitoring like groundwater transmissivity variations that influence pollution dispersion.^[35] These methods quantify differences, for example, detecting regions with p-values around 1.0 × 10⁻⁴ in groundwater models where drawdown exceeds 2.00 m across 155 realizations.^[35] Beyond these, SPM finds use in fields like electroencephalography (EEG) and magnetoencephalography (MEG) for source localization, where dynamic SPM integrates these signals with functional MRI to achieve high-resolution imaging of cortical activity, modeling data as arising from time-varying current dipoles.^[36] Extensions to diffusion tensor imaging (DTI) further apply SPM for quantitative voxel-wise analysis of microstructural properties, such as fractional anisotropy in fiber tracts, using statistical parametric mapping to compare patient groups against controls.^[37] A primary challenge in these non-neuroimaging applications involves adapting SPM's Gaussian field assumptions to handle non-Gaussian noise, such as spatial correlations in environmental or genomic data, often requiring multi-Gaussian modeling or robust preprocessing to maintain inference validity.^[35]

Limitations and alternatives

Statistical parametric mapping (SPM) relies on the assumption of stationarity in the residual error distribution, which posits that the statistical properties of the data are consistent across space; however, this assumption often fails in heterogeneous neuroimaging data, such as arterial spin labeling (ASL) perfusion maps, leading to confounded thresholded clusters and biased inferences regardless of sample size or filtering.^[38] Large-scale spatial covariance structures in real data violate this stationarity, particularly in observational studies of individual differences, resulting in characteristic patterns of false activations that persist even in mixed-effects models.^[38] Additionally, SPM's mass-univariate approach treats each voxel independently using the general linear model (GLM), ignoring multivariate interactions and spatial dependencies across voxels, which limits its ability to capture complex neural network dynamics or distributed brain responses.^[39] This voxel-wise independence assumption overlooks connectivity and joint information, potentially missing subtle, spatially extended effects in functional magnetic resonance imaging (fMRI) data.^[39] Post-2010 critiques have highlighted SPM's over-reliance on spatial smoothing to meet random field theory assumptions for multiple comparisons correction, as smoothing can distort non-Gaussian spatial autocorrelations and inflate false-positive rates in cluster-level inference, reaching up to 70% at nominal 5% family-wise error (FWE) levels with 6-mm full-width at half-maximum (FWHM) kernels.^[40] These issues stem from deviations in real fMRI data's smoothness from the Gaussian shape required by SPM's parametric framework, prompting recommendations for stricter cluster-defining thresholds (e.g., P < 0.001) or nonparametric alternatives to mitigate inflated errors.^[40] SPM analyses are also highly sensitive to preprocessing choices, such as motion correction, physiological noise regression, and temporal detrending, with effects varying by subject and task; for instance, motion parameter regression can degrade overall reproducibility in low-motion cases while benefiting high-motion subjects, leading to up to 10.4% variability in activation maps across pipelines.^[41] As alternatives, nonparametric methods like Statistical non-Parametric Mapping (SnPM) employ permutation testing to avoid parametric assumptions, offering exact P-values based on maximal statistics (e.g., cluster size or peak height) and proving more robust for small samples or non-normal data in fMRI and positron emission tomography (PET).^[42] SnPM integrates seamlessly as an SPM toolbox, using pseudo t-statistics for low degrees of freedom and often yielding comparable or superior power without relying on Gaussian random field theory.^[42] Machine learning approaches, such as multivariate pattern analysis (MVPA), address SPM's univariate limitations by jointly analyzing voxel patterns with classifiers like support vector machines, enabling detection of subtle, distributed disease effects (e.g., in Alzheimer's) that univariate methods overlook.^[43] In recent developments as of 2025, SPM continues to evolve with integrations of artificial intelligence, including deep learning for improved preprocessing such as image registration, enhancing adaptive modeling in neuroimaging analysis.^[39]

Implementation

Software tools

Statistical Parametric Mapping (SPM) software originated in the early 1990s at the Wellcome Department of Imaging Neuroscience, University College London, with the initial release of SPM91 written in MATLAB by Karl Friston.^[6] The package has evolved through several major versions, including SPM95, SPM96, SPM99 (released January 2000), SPM2 (2003), SPM5 (December 2005), SPM8 (April 2009), and SPM12 (October 2014), incorporating advancements such as Bayesian inference and machine learning modules for enhanced statistical modeling.^[44] The latest major release, SPM 25.01 in January 2025, builds on SPM12 with optimizations, novel analysis methods like spectral decomposition and active inference frameworks, while maintaining core functionalities.^[45] SPM is distributed as free, open-source software under the GNU General Public License (GPL), enabling widespread adoption and community contributions through its GitHub repository, where users submit enhancements and bug fixes.^[44] The primary implementation, including SPM 25.01, is MATLAB-based with compiled C routines for efficiency, featuring a batch processing system for streamlined workflows, support for Dynamic Causal Modelling (DCM) with extensions like Parametric Empirical Bayes for random effects, and multivariate tools for behavioral and hierarchical modeling.^[45] It also includes Python wrappers via spm-python for broader accessibility.^[46] SPM offers standalone versions for Windows, macOS, and Linux, as well as Docker and Singularity containers for reproducible environments.^[47] Beyond SPM, other prominent open-source tools support statistical parametric mapping in neuroimaging. The FMRIB Software Library (FSL) offers FEAT (FMRI Expert Analysis Tool), a graphical interface for general linear model (GLM) analyses, including higher-level mixed-effects modeling with FLAME for group inference. The Analysis of Functional NeuroImages (AFNI) suite provides alternatives for preprocessing tasks such as motion correction and slice-timing adjustment, often used in pipelines complementary to SPM.^[48] For integration across packages, Nipype (Neuroimaging in Python: Pipelines and Interfaces) facilitates Python-based workflows that wrap SPM, FSL, and AFNI, enabling seamless interoperability without requiring MATLAB. These tools collectively address computational demands in SPM analyses, though optimization remains key for large datasets.

Computational considerations

Statistical parametric mapping (SPM) analyses, particularly for functional magnetic resonance imaging (fMRI), impose significant computational demands due to the high-dimensional nature of neuroimaging data. Processing a single subject's 4D fMRI dataset, which can exceed 1 GB in size for standard resolutions, requires substantial memory and processing power to handle spatial normalization, smoothing, and general linear model (GLM) fitting without excessive swapping to disk.^[49] SPM documentation recommends adjusting memory settings to utilize available RAM effectively, keeping temporary files in memory where possible to avoid performance degradation.^[50] Graphics processing unit (GPU) acceleration can optimize specific steps, such as image registration and spatial smoothing, yielding speedups of up to 14-fold compared to central processing unit (CPU)-only implementations in compatible SPM workflows.^[51] Parallel processing enhances SPM's efficiency, especially for group-level analyses involving multiple subjects. Multi-core CPUs enable implicit parallelization through MATLAB's threading, while the MATLAB Parallel Computing Toolbox allows explicit distribution of tasks like contrast estimation across cores or nodes in a cluster environment.^[52] For large cohorts, cluster computing is essential, as SPM supports job distribution via tools like pSPM or integrated schedulers, reducing group analysis times from hours to minutes on high-performance computing (HPC) systems with dozens of nodes.^[50] Scalability challenges arise with 4D fMRI data volumes that can reach 100 GB or more per subject in high-resolution or multi-modal studies, including structural and diffusion imaging, leading to terabyte-scale group datasets.^[53] Optimization strategies include subsampling volumes during exploratory phases or leveraging memory-mapped files to manage RAM constraints, though full-resolution processing often necessitates HPC resources to prevent out-of-memory errors during GLM inversion. Best practices for modern workflows emphasize integration with cloud computing platforms like Amazon Web Services (AWS), where scalable EC2 instances and S3 storage facilitate on-demand resource allocation for neuroimaging pipelines, including those using SPM. Benchmarking local execution times against cloud costs, using spot instances for non-urgent jobs, ensures cost-effective scaling, with CPU-optimized instances recommended for core SPM operations and GPU instances for accelerated preprocessing.^[55]

References

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SPM - Statistical Parametric Mapping - FIL | UCL
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[PDF] a short history of statistical parametric mapping in functional
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The analysis in this work used a primitive version of the Statistical Parametric Mapping (SPM) software. Karl wrote the original SPM in MATLAB, and it was ...Spm99 · Spm2 · Spm8
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SPM'99 - released 25th January 2000. SPM99 is very old now. Consider using SPM12. If you really want SPM99, then: Complete the download ...Missing: date | Show results with:date
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Aug 15, 2012 · SPM2. The release of SPM2 saw the beginning of the end of the frequentist era of SPM, as the software began to enter its Bayesian period of ...
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In Friston (2002) we focussed on the biophysical parameters of a hemodynamic response in a single region. The most important parameter was the efficacy with ...
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This book will be particularly useful to neuroscientists engaged in any form of brain mapping; who have to contend with the real-world problems of data analysis ...
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An example of a parametric modulation of event-related responses is shown in Chapter 14. Factorial designs. Many experiments manipulate more than one factor con ...
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Oct 15, 2021 · Correct differences in image acquisition time between slices. Slice-time corrected files are prepended with an 'a'.
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This chapter previews the ideas and procedures used in the analysis of brain imaging data. It serves to introduce the main themes covered, in depth, by the ...
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May 29, 2015 · Render: overlay on a volume rendered brain. Thresholded SPMs can be saved as NIfTI image files in the working directory by using the. “Save ...<|separator|>
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Running the ROI analysis — MarsBaR 0.45 documentation
Plot data (simple). draws time course plots of the ROI data to the SPM graphics window. Plot data (full) has options for filtering the data with the SPM ...
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The current release is designed for the analysis of resting-sate fMRI. VDB 1.0 software package had been tested in Windows 7/Windows 10(32 and 64 bit) ...
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This study constitutes, to our knowledge, the first resting-state connectivity analysis of the default mode and provides the most compelling evidence to date.Sign Up For Pnas Alerts · Methods · Discussion
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Glucose metabolism in early onset versus late onset Alzheimer's ...
The aims of this study thus were to examine, using an SPM analysis of 2-[18F]fluoro-2-deoxy-d-glucose (FDG)-PET in a large sample of Alzheimer's disease ...
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Overall glucose hypometabolism of early onset Alzheimer's disease patients was much greater in magnitude and extent than that of late onset patients.
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The software SPM is most often used. fMRI programs inconsistently include input from experts with all required skills (imaging, cognitive assessment, MR physics ...
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Recovery of motor function after stroke may occur over weeks or months and is often attributed to cerebral reorganization. We have investigated the ...
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Voxel-based morphometry (VBM) using structural brain MRI has been widely used for assessment of normal aging and Alzheimer's disease (AD).
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Aug 5, 2009 · It uses statistics to identify differences in brain anatomy between groups of subjects, which in turn can be used to infer the presence of atrophy.
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Apr 27, 2024 · We propose a method, SpatialSPM, that reconstructs ST data into multi-dimensional image matrices to ensure comparability across different samples through ...
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Jul 18, 2013 · This study aimed to quantitatively analyze data from diffusion tensor imaging (DTI) using statistical parametric mapping (SPM) in patients ...
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Spatial Autocorrelation Function of the Noise. SPM and FSL depend on Gaussian random-field theory (RFT) for FWE-corrected voxelwise and clusterwise inference.
[38]
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Most fMRI analyses are performed under the implicit assumptions that either the results are relatively insensitive to the chosen set of preprocessing steps ( ...
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Nipype (Neuroimaging in Python) has an SPM interface. Tutorials can be found at: https://miykael.github.io/nipype_tutorial/ · https://pythonhosted.org/nipype/ ...SPM and Python · Python interface to SPM · External projects
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afni.nimh.nih.gov
AFNI is a software suite for analyzing and displaying MRI data, including anatomical, functional, and diffusion weighted data. It is freely available.Documentation · Bootcamp · About · Class Handouts
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... data for a single subject in an fMRI study can range in size from 50 MB to more than 1 GB, and most studies have at least 15 subjects. Datasets of this size ...
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To speed up SPM, adjust memory settings, keep temporary files in memory, use 'nodesktop' mode, and utilize GPU for some operations.
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Parallel Computing Toolbox - MATLAB - MathWorks
Parallel Computing Toolbox enables you to harness a multicore computer, GPU, cluster, grid, or cloud to solve computationally and data-intensive problems.Missing: SPM | Show results with:SPM
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s guide to working with large, open-source neuroimaging datasets
For example, in the ABCD dataset, the raw data in NifTI format takes up ∼1.35 GB per individual or ∼13.5 TB for the entire first release of ∼10,000 individuals.
[51]
Running Neuroimaging Applications on Amazon Web Services
In this paper we describe how to identify neuroimaging workloads that are appropriate for running on AWS, how to benchmark execution time, and how to estimate ...Missing: SPM | Show results with:SPM