^{1}

^{2}

^{3}

^{4}

^{5}

^{¤a}

^{6}

^{¤b}

^{6}

^{¤c}

^{6}

^{¤d}

^{7}

^{¤e}

^{8}

^{9}

^{10}

The authors have declared that no competing interests exist.

Current Address: Axinesis, Wavre, Belgium

Current Address: Philips, Vantaa, Finland

Current Address: Blend Labs, Inc., San Francisco, California, United States of America

Current Address: 1010data, New York, New York, United States of America

Current Address: FØCAL, Cambridge, Massachusetts, United States of America

Mindboggle (

This is a

This article summarizes years of work on the Mindboggle project (

Brain images have been used to derive biological markers of mental illness and disease for years, most notably to predict prognoses among patients with behavioral disorders, often more accurately than current behavioral instruments such as widely used scales and structured interviews. For example, brain images have been used to predict relapse in methamphetamine dependence [

A significant impediment to our understanding of mental health is variation in human brain anatomy, physiology, function, connectivity, response to treatment, and so on. The normal range of variation must first be established to determine what is outside of this range, and only then can we hope to address neuropsychiatric assessment, diagnosis, prognosis, treatment, or prevention. An effective biomarker traditionally consists of one or more measures that maximize the separability between groups while minimizing the variance within each group. Brain images provide many ways of measuring different aspects of the brain, but it is not always clear how to compare these measures over time or across individuals. Comparing brains presumes that a brain-to-brain correspondence or mapping has been solved. To do this, scientists ubiquitously co-register images to each other, either individually or in groups, commonly with the use of a standard template brain or labeled atlas. However, registration alone does not guarantee correspondence [

Neuroanatomists rely instead on high-level “features” such as distinctive cortical folding patterns and relative positions of subcortical structures to consistently identify anatomical structures or label brain regions ([

To compare features across individuals we need to quantify them. One quantification method is to characterize the quantities and distributions of grayscale values within a volume, but this does not work well for features of limited extent, such as a point, line, or surface patch. Another method is to coregister a given brain or brain feature with a reference and to define similarity with the reference based on the registration itself (deformation-based morphometry). Yet another method is to directly measure shape, where shape is defined as the geometrical information that remains when location, scale and rotation are removed from an object [

More subtle shape measures may provide more sensitive and specific biomarkers, and combining shape measures in a multivariate analysis can improve results over any single measure [

The Mindboggle project (

The anatomical labels included in the DKT cortical labeling protocol [

Software ported from Python 2 to Python 3

Docstring tests provided for almost every function

GitHub repository transferred to the nipy.org community’s GitHub account

Online documentation updated automatically

Online support via NeuroStars with the tag

Online tests run automatically

Mindboggle released as a Docker container

Mindboggle’s open source brain morphometry platform takes in preprocessed T1-weighted MRI data, and outputs volume, surface, and tabular data containing label, feature, and shape information for further analysis. Mindboggle can be run on the command line as “

The documentation is updated online (

Mindboggle’s flexible, modular, open source pipeline facilitates the addition of functions for computing almost any shape measure in any programming language. We initialized Mindboggle with shape measures that we thought have great potential for describing the shapes of brain structures and that complement shape measures supplied by existing software packages. It is just as easy to include functions in Mindboggle for volume-based as it is for surface-based measures, but we decided to focus primarily on surface-based shape measures to complement the volume-based methods available in standard brain image analysis packages. We also want to emphasize in this work intrinsic shape measures of brain structures rather than shapes inferred by registration-based methods such as voxel-based, tensor-based, and deformation-based morphometry that rely on a reference or canonical template and are sensitive to errors in registration. We also do not consider density values to be intrinsic shape measures, as they do not describe the shape of an object, but quantify values obtained within an object, in an analogous manner as one would quantify an fMRI signal or PET ligand binding within a voxel or region of interest.

For running individual functions on surface meshes, the only inputs to the software are outer cortical surface meshes constructed from T1-weighted MRI data by software such as FreeSurfer, Caret [

The

To refine segmentation, labeling, and volume shape analysis, Mindboggle optionally takes output from the Advanced Normalization Tools (ANTs, v2.1.0rc3 or higher recommended;

Links to the template and example input and output data can be found on the Mindboggle website. Output formats include NIfTI format for volume files, VTK format for surface meshes, and comma-delimited CSV format for tables. Each file contains integers that correspond to anatomical labels or features (0–24 for sulci or fundi for either hemisphere). All output data are in the original subject’s space, except for additional surfaces and mean coordinates in MNI152 space [

Mindboggle performs the following steps. We provide some details of the algorithms at the end of each step, but for full descriptions, see the relevant software documentation (

Convert FreeSurfer formats to NIfTI volumes and VTK surfaces.

Optionally combine FreeSurfer and ANTs gray/white segmented volumes and fill with labels.

Compute volumetric shape measures for each labeled region.

Compute shape measures for every cortical surface mesh vertex.

Extract cortical surface features.

Segment cortical surface features with labels.

Compute shape measures for each cortical surface label or sulcus.

Compute statistics for each shape measure in Step 4 for collections of vertices.

Mindboggle performs all of its processing in two open standard formats: NIfTI (.nii.gz; ^{3} per voxel (volume element). All surface-based shape measures are computed on the “pial surface” (cortical-cerebrospinal fluid boundary) by default, since it is sensitive to differences in cortical thickness.

This optional step of the pipeline will be skipped in the future when methods for tissue class segmentation of T1-weighted MR brain images into gray and white matter improve. FreeSurfer and ANTs make different kinds of mistakes while performing tissue class segmentation (

Left: Coronal slice of a T1-weighted brain MRI. Middle: Cross-section of FreeSurfer inner (magenta) and outer (green) cortical surfaces overlaid on top of the same slice. The red ellipse circumscribes a region where the FreeSurfer surface reconstruction failed to include gray matter on the periphery of the brain. Right: Cross-section of ANTs segmentation. The blue ellipse circumscribes a region where the ANTs segmentation failed to segment white matter within a gyrus that the FreeSurfer correctly segmented (compare with the middle panel). The purple box in the lower right highlights a region outside of the brain that the ANTs segmentation mistakenly includes as gray matter. To reconcile some of these discrepancies, Mindboggle currently includes an optional processing step that combines the segmentations from FreeSurfer and ANTs. This step essentially overlays the white matter volume enclosed by the magenta surface in the middle panel atop the gray/white segmented volume in the right panel.

The

The FreeSurfer/ANTs hybrid segmentation introduces new gray-white matter boundaries, so the corresponding anatomical (gyral-sulcal) boundaries generated by FreeSurfer and ANTs need to be updated accordingly. Mindboggle uses

volume

thickness of cortical labels (

As mentioned in the Introduction, the most common shape measures computed for brain image data are volume and cortical thickness for a given labeled region of the brain. Volume measurements are influenced by various factors such as cortical thickness, surface area [

Mindboggle’s

The ^{3} to 0.5mm^{3} voxel dimensions to better represent the contours of the cortex. Next it extracts outer and inner boundary voxels of the cortex by morphologically eroding the cortex by one (resampled) voxel bordering the outside of the brain and bordering the inside of the brain (non-cortex). Then it estimates the middle cortical surface area by the average volume of the outer and inner boundary voxels of the cortex. Finally, it estimates the thickness of a labeled cortical region as the volume of the labeled region divided by the middle surface area of that region. The

surface area

mean curvature

geodesic depth

travel depth

convexity (FreeSurfer)

thickness (FreeSurfer)

Aside from the convexity and thickness measures inherited from FreeSurfer, shape measures computed for each vertex of a cortical surface triangular mesh are generated by Mindboggle’s open source C++ code (using the Visualization Toolkit, VTK) developed by Joachim Giard: surface area, mean curvature, geodesic depth, and travel depth. Surface area is computed per vertex (as opposed to per face of the mesh to be consistent with all other Mindboggle shape measures) as the area of the Voronoi polygon enclosing the vertex (

Mindboggle computes surface area for each surface mesh vertex as the area of the Voronoi polygon enclosing the vertex. Left: Lateral view of a left cortical hemisphere colored by surface area per vertex. Right: Close-up of the surface mesh. Mindboggle uses area to normalize other shape values computed within a given region such as a gyrus or sulcus.

Curvature is an obvious shape measure for a curved and folded surface like the cerebral cortex and has the potential to help make inferences about other characteristics of the brain, such as sulcus width, atrophy [

Mindboggle computes curvature for each surface mesh vertex. Left: Lateral view of a left cortical hemisphere colored by mean curvature per vertex, where color indicates surface curving away from (purple for negative curvature) or toward (yellow for positive curvature) the local, outward-pointing normal vector. If the surface is locally flat or between negative and positive curvatures, the color is greenish-blue. Right: Mean curvature on the sulcus folds.

Depth is an important measure characterizing the highly folded surface of the human cerebral cortex. Since much of the surface is buried deep within these folds, an accurate measure of depth is useful for defining and extracting deep features, such as sulci [

We are aware of three predominant methods for measuring depth of points on the surface of the cerebral cortex, where depth is the distance between a given point on the brain surface to an outer reference surface of zero depth (the portions of the brain surface in contact with the outer reference surface are gyral crowns or crests). The first is Euclidean depth, the distance along a straight path from the point on the brain to the outer reference surface. A straight path has the undesirable property that it will cross through anything, which can make a highly folded surface indistinguishable from a slightly folded surface that fills the same volume. The second is geodesic depth, the shortest distance along the surface of the brain from the point to where the brain surface makes contact with the outer reference surface. Geodesic paths are very sensitive to slight or gradual changes in depth, resulting in exaggerated distances where the outer reference surface does not wrap the brain closely. Geodesic paths are also greatly affected by cavities, so distances can be exaggerated where there are irregularities, particularly in the bottoms of sulcus folds. The third measure, FreeSurfer software’s “convexity,” while not explicitly referred to as depth, is used to indicate relative depth. It is based on the displacement of surface mesh vertices after inflating the surface mesh [

Travel depth was introduced as a hybrid depth measure for macromolecules, defined as the shortest distance that a solvent molecule would travel from the convex hull of the macromolecule without penetrating the macromolecule surface. It was first defined for surfaces but using a voxel-based algorithm [

Mindboggle computes geodesic depth (left) and travel depth (right) for each surface mesh vertex. This medial view of the sulcus folds from the left cortical hemisphere is colored by depth, with the deepest vertices in yellow. Note that the deepest vertices according to geodesic depth reside toward the center of the insula (center fold), whereas the deepest vertices according travel depth run along the deepest furrows of the insula, as one would expect.

Mindboggle’s mean and Gaussian curvatures are based on the relative direction of the normal vectors in a small neighborhood, which works best for low resolution or for local peaks, but can be sensitive to the local linear geometry of the mesh. Increasing the radius of the neighborhood mitigates this sensitivity, so a neighborhood parameter corresponding to the radius of a geodesic disk is defined in the unit of the mesh. If coordinates are in millimeters, the default setting of 2 results in an analysis of the normal vectors within a 2mm radius disk. Other options include computing both mean and Gaussian curvatures based on the local ratios between a filtered surface and the original surface area (the filtering is done using Euclidean distances, so it's best for less accurate but fast visualization), or computing the mean curvature based on the direction of the displacement vectors during a Laplacian filtering (a good approximation based on the Laplacian, but underestimates very large, negative or positive, curvatures due to saturation).

The travel depth algorithm constructs a combination of Euclidean paths outside the cortical surface and estimated geodesic paths along the cortical surface. The principal idea of the algorithm lies in the classification of a surface into “visible” and “hidden” areas (

folds

fundus per fold

Mindboggle extracts hierarchical structures from cortical surfaces [

Top left: Lateral view of the left hemisphere of a brain with folds labeled red. Mindboggle extracts cortical surface folds based on a depth threshold that it computes from the distribution of travel depth values. Bottom left: individually colored folds from the same brain. The red surface shows that folds can be broadly connected, depending on the depth threshold, and therefore do not map one-to-one to anatomical region labels. Top right: The same folds with individually colored anatomical labels. These labels can be automatically or manually assigned (as in the case of this Mindboggle-101 subject). Bottom right: Individually colored sulci. Mindboggle uses the anatomical labels to segment folds into sulci, defined as folded portions of cortex whose opposing banks are labeled with sulcus label pairs in the DKT labeling protocol [

To extract folds, a depth threshold is used to segment deep vertices of the surface mesh. We have observed in the histograms of travel depth measures of cortical surfaces that there is a rapidly decreasing distribution of low depth values (corresponding to the outer surface, or gyral crowns) with a long tail of higher depth values (corresponding to the folds). Mindboggle’s

A fundus is a branching curve that runs along the deepest and most highly curved portions of a fold (

This figure shows three views of the outside of a single sulcus (taken from the top middle fold in

Mindboggle uses its

sulci from folds

fundus per sulcus

Since folds are defined as deep, connected areas of a surface, and since folds may be connected to each other in ways that differ across brains, there usually does not exist a one-to-one mapping between folds of one brain and those of another. To address the correspondence problem, we need to find just those portions of the folds that correspond across brains. To accomplish this, Mindboggle segments folds into sulci, which do have a one-to-one correspondence across non-pathological brains (right side of

The

surface area

Laplace-Beltrami spectrum

Zernike moments

In addition to shape measures computed for each vertex of a surface (Step 4), Mindboggle also computes shape measures that apply to collections of vertices such as gyri and sulci (Step 6): surface area (sum of surface areas across vertices), Laplace-Beltrami spectra, and Zernike moments.

Martin Reuter established important properties of the spectrum that relates to a shape’s intrinsic geometry with his “Shape-DNA” method [

Mindboggle computes a Laplace-Beltrami spectrum for each feature (gyrus, sulcus, etc.), which relates to its intrinsic geometry, after Reuter et al.’s “Shape-DNA” method [

The eigen-decomposition of the Laplace-Beltrami operator is computed via a finite element method (FEM). Mindboggle’s Python

To calculate the distance between the descriptors of two shapes, Reuter describes several approaches, e.g., L^{p}-norm, Hausdorff distance and weighted distances. One of the more prominent and simple distance measures is the Euclidean distance (L2 norm) of the first N smallest (non-zero) eigenvalues, where N is called the truncation parameter. To account for the linearly increasing magnitude of the eigenvalues (Weyl’s law), Reuter recommends dividing each value by its area and its index (done by default in Mindboggle). As an alternative, the Weighted Spectral Distance (WESD) [^{p}-norm of a weighted difference between the vectors of the N smallest eigenvalues. This approach forms a pseudo-metric and also avoids domination of higher components on the final distance, making it insensitive to the truncation parameter N (with a decreasing influence as N gets larger). Additionally, the choice of p (for the L^{p}-norm) influences how sensitive the metric is to finer as opposed to coarser differences in the shape; as p increases, WESD becomes less sensitive to differences at finer scales.

Moments can describe the shape of objects, images, or statistical distributions of points, and different types of moments confer different advantages [

Mikhno et al. [

median

median absolute deviation

mean

standard deviation

skewness

kurtosis

lower quartile

upper quartile

There can be thousands of vertices in a single feature such as a gyrus, sulcus, or fundus, so it makes sense to characterize a feature’s shape as a distribution of per-vertex shape values (Step 4) when the shape measures don’t apply to collections of vertices (Step 7). Mindboggle’s

Mindboggle has been and continues to be subjected to a variety of evaluations (

We compared shape measures with one another in a representative individual from the Mindboggle-101 data set (

In these plots, we compare a pair of shape measures for each vertex of each right cortical region in a representative individual from the Mindboggle-101 brains, colored arbitrarily by region. Top: In this plot comparing two measures of depth, geodesic depth is higher than travel depth, and may exaggerate depth, such as in the insula (gray dots extending to the upper left). Bottom: In this plot of mean curvature by travel depth, we again see that the shape measures are not independent of one another. As one might expect, we see greater curvature at greater depth.

This superposition of two box and whisker plots is a comparison between two measures of cortical surface depth applied to the 101 Mindboggle-101 brains: Mindboggle’s travel depth and geodesic depth. These surface measures are computed for every mesh vertex, so the plots were constructed from median depth values, with one value per labeled region. The pattern of geodesic depth and travel depth measures are very similar across the 62 cortical regions, but deviate considerably for the insular regions (far right); this is not surprising, given that geodesic paths are very sensitive to gradual changes in depth and to cavities.

This superposition of two box and whisker plots is a comparison between two measures of cortical surface curvature applied to the 101 Mindboggle-101 brains: Mindboggle’s mean curvature and FreeSurfer’s curvature measure. These surface measures are computed for every mesh vertex, so the plots were constructed from median curvature values, with one value per labeled region. The Mindboggle curvature measures were greater than the FreeSurfer curvature measures for almost all regions, with the notable exception of the entorhinal regions (fourth pair from the left).

This superposition of two box and whisker plots is a comparison between two measures of cortical thickness applied to the 101 Mindboggle-101 brains: Mindboggle’s

While it may be useful to compare the distributions of two different shape measures for each region over a population (as in Figs

To compare pairs of related (travel and geodesic depth, mean and FreeSurfer curvature) surface shape measures, we computed the distance correlation between vectors of shape values for all vertices in each cortical region, and averaged the distance correlations across the 101 Mindboggle-101 subjects. For

Cortical region | travel depth vs. geodesic depth | mean curvature vs. FreeSurfer curvature | thickinthehead vs. FreeSurfer thickness | |||
---|---|---|---|---|---|---|

left | right | left | right | left | right | |

caudal anterior cingulate | 0.97 | 0.96 | 0.83 | 0.83 | 0.39 | 0.38 |

caudal middle frontal | 0.99 | 0.99 | 0.88 | 0.88 | 0.72 | 0.70 |

cuneus | 0.99 | 0.99 | 0.84 | 0.83 | 0.52 | 0.51 |

entorhinal | 0.96 | 0.96 | 0.77 | 0.75 | 0.38 | 0.33 |

fusiform | 0.97 | 0.97 | 0.83 | 0.83 | 0.22 | 0.20 |

inferior parietal | 0.99 | 0.99 | 0.88 | 0.88 | 0.56 | 0.50 |

inferior temporal | 0.98 | 0.98 | 0.84 | 0.84 | 0.31 | 0.39 |

isthmus cingulate | 0.91 | 0.93 | 0.78 | 0.79 | 0.19 | 0.30 |

lateral occipital | 0.99 | 0.99 | 0.86 | 0.86 | 0.54 | 0.57 |

lateral orbitofrontal | 0.92 | 0.92 | 0.80 | 0.81 | 0.54 | 0.54 |

lingual | 0.97 | 0.98 | 0.83 | 0.82 | 0.45 | 0.62 |

medial orbitofrontal | 0.97 | 0.97 | 0.82 | 0.82 | 0.42 | 0.57 |

middle temporal | 0.99 | 1.00 | 0.88 | 0.88 | 0.49 | 0.40 |

parahippocampal | 0.96 | 0.97 | 0.81 | 0.84 | 0.44 | 0.26 |

paracentral | 0.99 | 0.99 | 0.87 | 0.87 | 0.64 | 0.59 |

pars opercularis | 0.98 | 0.98 | 0.89 | 0.89 | 0.65 | 0.47 |

pars orbitalis | 0.98 | 0.98 | 0.90 | 0.90 | 0.43 | 0.50 |

pars triangularis | 1.00 | 1.00 | 0.90 | 0.90 | 0.63 | 0.47 |

pericalcarine | 0.96 | 0.97 | 0.76 | 0.78 | 0.34 | 0.37 |

postcentral | 1.00 | 1.00 | 0.87 | 0.87 | 0.71 | 0.63 |

posterior cingulate | 0.99 | 0.99 | 0.84 | 0.83 | 0.29 | 0.38 |

precentral | 0.99 | 0.99 | 0.88 | 0.88 | 0.70 | 0.54 |

precuneus | 0.98 | 0.98 | 0.86 | 0.86 | 0.29 | 0.48 |

rostral anterior cingulate | 0.98 | 0.97 | 0.80 | 0.79 | 0.26 | 0.35 |

rostral middle frontal | 0.99 | 0.99 | 0.91 | 0.91 | 0.75 | 0.61 |

superior frontal | 0.99 | 0.99 | 0.89 | 0.89 | 0.80 | 0.71 |

superior parietal | 0.99 | 0.99 | 0.89 | 0.89 | 0.69 | 0.76 |

superior temporal | 0.99 | 0.99 | 0.86 | 0.85 | 0.59 | 0.52 |

supramarginal | 1.00 | 1.00 | 0.88 | 0.87 | 0.65 | 0.60 |

transverse temporal | 0.97 | 0.98 | 0.76 | 0.74 | 0.67 | 0.69 |

insula | 0.29 | 0.31 | 0.73 | 0.73 | 0.46 | 0.38 |

As described above, travel depth uses a reference wrapper surface that lies closer to the cortical surface than a convex hull would. In particular, the wrapper lies closer to the medial temporal lobe, so the gyri in this area have depth values equal to zero as one would want. FreeSurfer’s convexity measure [

We are aware of only one study directly comparing FreeSurfer with manual cortical thickness measures, where the manual estimates were made in nine gyral crowns of a post-mortem brain, selected for their low curvature and high probability of having been sampled perpendicular to the plane of section [

This section presents the first quantitative comparison of fundus extraction software algorithms. Since there exists no ground truth for fundus curves, we must resort to other means of evaluation. We leave it to future work to determine their utility for practical applications such as diagnosis and prediction of disorders. Since the DKT labeling protocol defines many of its anatomical label boundaries along approximations of fundus curves, we used the manually edited anatomical label boundaries in the Mindboggle-101 dataset as gold standard data to evaluate the positions of fundi extracted by four different algorithms in 2013. Specifically, for each of the 48 fundi/sulci defined by the DKT protocol, we computed the mean of the minimum Euclidean distances from the label boundary vertices in the sulcus to the fundus vertices in the sulcus, as well as from the fundus vertices in the sulcus to the label boundary vertices in the sulcus. The algorithms included Mindboggle’s default

All of the fundi, summary statistics, and results are available online (

For a shape measure to be useful in comparative morphometry, it should be more sensitive to differences in anatomy than to differences in MRI scanning setup or artifacts. To get a sense of the degree of scan/rescan consistency of our shape measures, we ran Mindboggle on 41 Mindboggle-101 subjects with a second MRI scan (OASIS-TRT-20 and MMRR-21 cohorts). We computed the fractional shape difference per cortical region as the absolute value of the difference between the region’s shape values for the two scans divided by the first scan’s shape value. For the volumetric shape measures (volume and

This table gives a statistical summary of the shape differences between two scans of the same brain for 41 brains. The “mean” column is the average of the mean values in

mean | std | min | 25% | 50% | 75% | max | >0.50 | >0.25 | |
---|---|---|---|---|---|---|---|---|---|

volume | 0.047 | 0.044 | 0.002 | 0.019 | 0.035 | 0.063 | 0.213 | 5 | 21 |

0.052 | 0.046 | 0.001 | 0.017 | 0.039 | 0.078 | 0.183 | 0 | 16 | |

area | 0.039 | 0.038 | 0.001 | 0.014 | 0.030 | 0.054 | 0.182 | 2 | 6 |

travel depth | 0.061 | 0.050 | 0.002 | 0.024 | 0.050 | 0.085 | 0.229 | 1 | 36 |

geodesic depth | 0.059 | 0.049 | 0.002 | 0.022 | 0.048 | 0.082 | 0.222 | 2 | 35 |

mean curvatures | 0.044 | 0.038 | 0.001 | 0.016 | 0.033 | 0.059 | 0.170 | 0 | 7 |

FreeSurfer curvature | 0.094 | 0.091 | 0.004 | 0.033 | 0.070 | 0.127 | 0.433 | 17 | 78 |

FreeSurfer thickness | 0.041 | 0.036 | 0.001 | 0.014 | 0.032 | 0.060 | 0.147 | 0 | 0 |

To measure interhemispheric shape differences, we computed the fractional shape difference per cortical region as in the preceding section, replacing inter-scan differences with interhemispheric differences (

This table gives a statistical summary of the interhemispheric shape differences for the 101 Mindboggle-101 brains. The “mean” column is the average of the mean values in

mean | std | min | 25% | 50% | 75% | max | >0.50 | >0.25 | |
---|---|---|---|---|---|---|---|---|---|

volume | 0.129 | 0.091 | 0.002 | 0.058 | 0.117 | 0.180 | 0.448 | 38 | 443 |

0.044 | 0.036 | 0.001 | 0.017 | 0.037 | 0.064 | 0.169 | 0 | 4 | |

area | 0.183 | 0.163 | 0.002 | 0.074 | 0.148 | 0.248 | 1.025 | 165 | 744 |

travel depth | 0.198 | 0.199 | 0.003 | 0.074 | 0.150 | 0.257 | 1.251 | 211 | 764 |

geodesic depth | 0.173 | 0.163 | 0.002 | 0.067 | 0.133 | 0.229 | 1.009 | 148 | 658 |

mean curvatures | 0.104 | 0.113 | 0.002 | 0.038 | 0.079 | 0.141 | 0.872 | 59 | 192 |

FreeSurfer curvature | 0.190 | 0.435 | 0.003 | 0.074 | 0.150 | 0.250 | 3.890 | 205 | 626 |

FreeSurfer thickness | 0.050 | 0.077 | 0.001 | 0.018 | 0.036 | 0.062 | 0.691 | 23 | 28 |

To estimate the normal range of variation in the shapes of healthy adult human brains, we applied Mindboggle software in 2015 to compute shape measures for our Mindboggle-101 dataset. The result is the largest set of shape measures computed on healthy human brain data (See the

The data we analyzed consist of repeated measurements on five distinct real-valued shape measures (mean curvature, geodesic depth, travel depth, FreeSurfer convexity, and FreeSurfer thickness) for each of 31 distinct regions per brain hemisphere in each of the 101 subjects. Each subject was scanned at one of five different laboratories. At the bottom of

Top: Overview of the variance results for five shape measures computed on each of 31 manually labeled cortical regions (combined across both hemispheres for this figure) in the 101 Mindboggle-101 healthy human brains. The blue color-coded heatmap shows the relative contributions of subject, hemisphere, and residual to describe the variability for each shape measure, with a greater contribution coded by a darker blue. For all shape measures and brain regions, most of the variability was concentrated in the residual. See the

We organized the data in a nested fashion: brain hemisphere is nested within subject, and subject is nested within laboratory. In addition to the five shape measurements and the three nested classification factors, the data also include three covariates: sex (male, female), age (integer variable), and handedness (left, right; we relabeled two ambidextrous subjects as left-handed). Given the grouped nature of the data, we used linear mixed models for the statistical modeling of the data. To assess the importance of each of the covariates and nested classification factors, we fitted 24 distinct linear mixed models for each shape measure and brain region combination to assess the importance of each of the covariates (sex, handedness, and age as fixed effects) and nested classification factors (laboratory, subject, and brain hemisphere as random effects). For each shape measure, we decomposed the total variance into the variance between laboratories, between subjects within a laboratory, between brain hemispheres within a subject, and within brain hemispheres.

For each shape measure and brain region combination, we used the Bayesian Information Criterion (BIC) score to select the best model among the 24 competing models. A BIC score is a goodness of fit measure used to perform model selection among models with different dimensions (number of parameters), and is proportional to the negative log likelihood of the model penalized by the number of parameters in the model. It strikes a balance between model fit (measured by the log-likelihood score) and model complexity (measured by the number of parameters in the model). In the context of linear models, an over-parameterized model will always have a larger log-likelihood score than a more parsimonious model, but it will also likely overfit the data. Nonetheless, by including a penalty proportional to the number of parameters in the model, the BIC score can be used to compare models with different dimensions since over-parameterized models are penalized to a greater extent. The smaller the BIC score, the better the model fits the data.

Two models stood out as the best models for the mean curvature, travel depth, FreeSurfer convexity, and FreeSurfer thickness shape measures across the 31 brain regions (

We repeated the same analysis as above on two scans acquired three years apart from hundreds of the ADNI participants (126 with Alzheimer’s, 199 healthy controls) as part of an international Alzheimer’s challenge (see “History of the Mindboggle project” section above) to see if we could find changes in brain shape measures that correlate with changes in ADNI-MEM cognitive scores over the course of three years. This resulted in the most detailed shape analysis of brains with Alzheimer's disease ever conducted [

We found that healthy brains and brains with Alzheimer’s disease have similar shape statistical summaries, but changes in the following shape measures after a three-year interval were significantly correlated with changes in ADNI-MEM cognitive score:

Volume for right caudal anterior cingulate and left: entorhinal, inferior parietal, (middle, superior) temporal, superior frontal, precuneus, and supramarginal gyri

FreeSurfer thickness for left and right: entorhinal, fusiform, inferior parietal, (inferior, middle, superior) temporal, superior frontal, precuneus, and supramarginal gyri; left: (caudal middle/lateral, orbito/rostral middle) frontal, and pars triangularis gyri; right lingual gyrus

Mean curvature for left and right rostral middle frontal gyri; left (middle, superior) temporal gyri; right inferior temporal gyri

In this article, we have documented the Mindboggle open source brain morphometry platform and demonstrated its use in studies of shape variation in healthy and diseased humans. There are many ways in which the open source software community can extend Mindboggle’s capabilities, and there are many possible applications for Mindboggle to brain and non-brain data. Here we will provide links to the software and data used in this study, briefly summarize the study results, and point toward possible further evaluations and alternative approaches.

Mindboggle home:

Mindboggle software:

Documentation:

Issues and bugs:

Support questions (post with tag “

Continuous integration tests:

BIDS-Apps Docker app:

Brain image viewer:

Third-party software dependencies:

Anaconda Python distribution:

Visualization Toolkit:

Nipype:

Nibabel:

ANTs:

FreeSurfer output:

Data:

Example preprocessed data:

Anatomical labeling protocol:

Anatomically labeled data:

In this section we summarize the findings of our evaluations in the Results section. The number of different shape measures and the size of the populations make this the largest and most detailed shape analysis of human brains every conducted. We computed over 8,000 values corresponding to statistical summaries of shape measures and coefficients of shape measures for each of the 101 brain images in the Mindboggle-101 dataset and for each of thousands of brain images in the ADNI and AddNeuroMed datasets. Shape measures are not independent of one another, and some related shape measures exaggerate values for certain morphological structures (such as geodesic vs. travel depth for the insula). Mindboggle’s

The Mindboggle software will continue to be subjected to evaluations of its algorithms as well as of its applicability to new datasets of healthy and diseased brains. Data exist to conduct evaluations of test/retest reliability and reproducibility [

There are many ways to enhance Mindboggle’s functionality and applicability to pathological brains. Taking advantage of different and multiple types of images, atlases, labels, features, and shape measures are clear ways to expand and improve Mindboggle, and the software was built using the Nipype framework specifically to enable modular and flexible inclusion of different algorithms, and to easily generate different outputs using different input data or parameter settings. We took advantage of this flexibility to generate multiple outputs for comparison in our evaluation studies. In the future, Mindboggle could accept different preprocessed inputs to take advantage of promising new algorithms that combine surface reconstruction with whole-brain segmentation in a way that is more robust to white-matter abnormalities [

The Mindboggle software extracts and identifies features for shape analysis. This approach is based on human-designed features (brain structure and label definitions and algorithmic implementations) and assumes the validity of the designed feature model. The tremendous success that machine learning (especially deep learning) approaches have had across domains [

(PDF)

Nipype automatically generates a flow diagram of the processing steps when running Mindboggle.

(PDF)

(PDF)

(PDF)

(PDF)

We sincerely thank everyone who has contributed to the Mindboggle open science project over the years, including Nolan Nichols, Oliver Hinds, Arthur Mikhno, Hal Canary, and Ben Cipollini. We also thank Gang Li, Denis Rivière, and Olivier Coulon for assistance with the fundus evaluation. Arno Klein would like to thank Deepanjana and Ellora for their continued patience and support, and dedicates this project to his mother and father, Karen and Arnold Klein.

Software and online resources that have benefitted the project include: GitHub.com, ReadtheDocs.org, and PyCharm for software development; Open Science Framework, Harvard Dataverse, and Synapse.org for public data storage; and D3, Bokeh, Paraview, and the Viridis colormap (