A tutorial in connectome analysis: Topological and spatial features of brain networks
High-throughput methods for yielding the set of connections in a neural system, the connectome, are now being developed. This tutorial describes ways to analyze the topological and spatial organization of the connectome at the macroscopic level of connectivity between brain regions as well as the microscopic level of connectivity between neurons. I will describe topological features at three different levels: the local scale of individual nodes, the regional scale of sets of nodes, and the global scale of the complete set of nodes in a network. Such features can be used to characterize components of a network and to compare different networks, e.g. the connectome of patients and control subjects for clinical studies. At the global scale, different types of networks can be distinguished and we will describe random, scale-free, small-world, modular, and hierarchical archetypes of networks. Finally, the connectome also has a spatial organization and we describe methods for analyzing wiring lengths of neural systems. As an introduction for new researchers in the field of connectome analysis, I will discuss the benefits and limitations of each analysis approach.
Suggested reading before the tutorial:
- Preferential Detachment During Human Brain Development: Age- and Sex-Specific Structural Connectivity in Diffusion Tensor Imaging (DTI) Data
- Mechanisms of Connectome Development
- A tutorial in connectome analysis: topological and spatial features of brain networks
The development of neural connections obeys to algorithmic principles
Brain functioning critically depends on the intricate interconnections between neurons. How can axons find the correct target among the many alternative possibilities? Since the controversy between Paul Weiss end Roger Sperry in the fifties, the mechanisms responsible for the development of neural connections has become a major theme of contemporary neuroscience. Today we can list a number of mechanisms, which together delineate algorithms which might inspire another main enterprise of contemporary neuroscience: the tracing of neural connections in vivo, non-invasively, using diffusion tractography.
Open challenges in tractography: Addressing tractography biases and tackling the false-positive problem
In this talk, I will cover some of the important current tractography limitations such as the length, position, shape and gyral biases, and will present some solutions that start addressing these limitations. The lack of ground truth on long‐range connectivity of the human brain makes it hard to quantitatively evaluate results. I will thus also introduce a novel brain-like numerical phantom dataset, which has a known ground truth connectivity that we used for the ISMRM 2015 international tractography challenge, evaluated with the Tractometer. Results from 96 submissions covering state of the art methods reveal substantial numbers of false‐positive bundles that are not part of the ground truth and yet consistently extracted by most algorithms. These findings should inspire future algorithmic developments and may help to test them. A key challenge for future tractography algorithms will be to control for false positives, while identifying the full extent of existing fiber bundles.
Advances in structural and functional connectivity visualization using the Fibernavigator
Scientific data visualization is constantly challenged by the continuously growing diffusion and functional MRI fields. Exploring and interacting with high-dimensional datasets is central to every analysis pipeline, allowing us to better understand the behavior of a certain tracking algorithm, for example. In this presentation, I will present a brief overview of the recent advances in data analysis & visualization available inside the Fibernavigator package that aim at enhancing data visualization.
Phantomas: Validating tractography pipelines with the help of simulated phantoms
Diffusion MRI is increasingly used for the numerical characterization of brain structural connectivity using fiber tractography. The technique is known to suffer from several pitfalls, and over the last decade a whole branch of the community started working on validating results provided by tractography. In this lecture, I will present an overview of different research projects and results which aim at validating some aspects of tractography. Then I will focus on the use of simulated phantoms, and propose a hands-on tutorial on how to design, generate and use simulated diffusion MRI images for the validation of your tractography pipeline using Phantomas  and the associated web interface.
Dipy: From Diffusion Data to Bundle Analysis
Dipy (Diffusion Imaging in Python) is a free and open source software project for computational neuroanatomy, focusing mainly on diffusion-weighted magnetic resonance imaging analysis. It implements a broad range of algorithms for denoising, registration, local reconstruction, tractography, and streamlines clustering. In this talk, I will present an overview of the project and the new algorithms and developments coming with the release of Dipy 0.14 in January 2018. I will then give a Dipy tutorial specifically on the processing of diffusion-weighted images in order to do streamline bundles analysis.
Advances in diffusion MRI from the human connectome project
I will give an overview of the developments carried out for diffusion MRI at 3 Tesla and 7 Tesla, in the Human Connectome Project (HCP). Next, I will describe some recent work which stemmed from data or technological advances achieved under the HCP. In particular, I will discuss cortical depth dependent analysis of fiber orientations, sparse reconstruction of white matter fiber orientations, as well as microstructure mapping of crossing fibers. I will conclude with on-going work on Friedreich’s ataxia, an autosomal recessive genetic disease, which has leveraged image acquisition acceleration techniques developed and improved under the HCP.
Multidimensional encoding of brain connectomes
This presentation will cover primarily the following references:
- Multidimensional encoding of brain connectomes
- Evaluation and statistical inference for human connectomes
- Ensemble Tractography
- The visual white matter: The application of diffusion MRI and fiber tractography to vision science
- White-Matter Tract Connecting Anterior Insula to Nucleus Accumbens Correlates with Reduced Preference for Positively Skewed Gambles
- A Major Human White Matter Pathway Between Dorsal and Ventral Visual Cortex
- Functionally Defined White Matter Reveals Segregated Pathways in Human Ventral Temporal Cortex Associated with Category-Specific Processing
Seeding connectivity: Cortical parcellation
In this talk I will be presenting cortical parcellation schemes and their use to infer cortical brain connectivity. The aim is to provide a overview of existing parcellation schemes that can be used in the context of connectivity inference, and to understand the fundamental and practical aspects of building a cortical parcellation. I will first introduce the motivations and the general concept of cortical parcellation. I will then discuss what can be expected from a cortical parcellation in terms of properties (e.g. resolution or geometry) and general relations with function, connectivity, of microstructure. We will then move on to the different types of information that can be used to parcellate the cortex and the different classes of atlases they lead to. Existing parcellation techniques and associated softwares will be briefly reviewed.
Forward models for multimodal functional imaging
Electro- and magneto-encephalography provide measurements of brain activity at very high time resolution. Being non-invasive, these techniques are a method of choice in human neuroscience. Interpretation of EEG and MEG measurements is however intricate because they mix various sources of activity coming from different regions. This talk reviews the physiological bases of electro- and magneto-encephalography, and establishes the models which are required for extracting brain source activity from EEG and MEG data. Conductivity models establish the relation between sources and electromagnetic measurements. For the EEG forward problem, the skull conductivity is of particular importance. To represent the geometry and conductivity of tissues, and compute the forward problems, boundary element methods have been developped and implemented in opensource software, OpenMEEG. With this type of software, several electrophysiological measurements can jointly be modeled. This is of particular interest in order to use multimodal datasets to validate source localization results.
Methods for functional brain imaging with MEG and EEG: Better preprocessing, better inverse methods and better group studies … with better software tools
Electroencephalography (EEG) and Magnetoencephalography (MEG) are noninvasive techniques used in clinical and cognitive neuroscience in order to image the active brain at a millisecond time scale. Yet to do so, challenging optimization and statistical problems need to be solved. In this talk I will first review the physics behind MEG/EEG measurements before diving into some recent methodological contributions. I will cover the problem of covariance estimation from a limited number of samples with shrinkage and latent factor models (Bayesian PCA, Factor Analysis). This is useful for data prewhitening which is a necessary preprocessing for joint MEG/EEG modeling . Then I will explain how sparsity promoting regularizations and time-frequency representations can improve the problem of source localisation, and how block block-coordinate descent and so called “safe rules” to speed up the solvers [1,2,3,4]. I will then conclude but doing a live demo using Jupyter notebooks of the different methods using the MNE software .
-  Automated model selection in covariance estimation and spatial whitening of MEG and EEG signals. D. A. Engemann, A. Gramfort. NeuroImage, 2015.
-  Mixed-norm estimates for the M/EEG inverse problem using accelerated gradient methods. A Gramfort, M Kowalski, M Hämäläinen. Physics in medicine and biology, 2012.
-  Time-Frequency Mixed-Norm Estimates: Sparse M/EEG imaging with non-stationary source activations. A Gramfort, D Strohmeier, J Haueisen, M Hämäläinen, M Kowalski, NeuroImage, 2013.
-  The Iterative Reweighted Mixed-Norm Estimate for Spatio-Temporal MEG/EEG Source Reconstruction. D Strohmeier, Y Bekthi, J Haueisen, A Gramfort, IEEE Trans. Medical Imaging 2016 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5533305/
-  Mind the duality gap: safer rules for the Lasso. O Fercoq, A Gramfort, J Salmon, Proc. ICML Conf. 2015
-  MNE software for processing MEG and EEG data. A Gramfort, M Luessi, E Larson, D Engemann, D Strohmeier, C Brodbeck, L Parkkonen and M Hämäläinen. NeuroImage, 2014.
Quality assessment and correction methods for diffusion MRI data
With its unique ability to investigate tissue microstructure in vivo, diffusion MRI (dMRI) is the preferred approach for investigating the brain’s structural connectivity. While dMRI plays a key role in connectomics, it suffers from limitations and imperfections which, if not adequately addressed, will have a profound impact on the validity of neuroscientific findings. In the first part of this lecture, I will show some tips and tricks to assess dMRI data quality and I will present several preprocessing steps that are required before starting with dMRI analysis. In the second part, I will give an ExploreDTI demo highlighting some of the tools to process and analyze dMRI data.
Image quality transfer
Hardware advances such as the Connectom scanner are heralding the future of MRI scanners. However, such high-end technology remains inaccessible and decades away for most hospitals due to their exorbitant price tags, especially in developing nations. Image Quality Transfer (IQT) aims to use machine learning to capture the fine details present in the high-quality scans, such as the data produced by the Human Connectome Project (HCP) and propagate it to enhance standard clinical data through computational methods. In this talk I will present our work where we first used random forests and more recently neural networks along with uncertainty estimation for IQT.
Sudhir K. Pathak
Hollow nanotube textile based phantoms for ground validation of truth measurement of diffusion MR images: Testing compartmental models and fiber tractography
The advancement of diffusion MR imaging acquisition, post-processing, and clinical diagnostic precision would be accelerated if the field had cross-laboratory anisotropic diffusion phantoms with ground truth non-MRI measurement of a configuration of fiber bundle and geometry at the nanoscale. These phantoms would provide an idealized axonal geometry of microstructure of human brain tissue. The diameter of axons in the corpus callosum of the human brain follows the gamma distribution, with the range from 0.6 to 5-micron inner diameter with a mean of 1 micron and packing density of a million per mm2 (see Liewald 2014). High packing density and small diameters of axons allow selectively to image fiber bundles with diffusion MRI. With recent advancements in textile engineering and phantom construction, our group can now provide the textile-based hollow fiber at nanometer diameter to centimeters length range with different geometrical configuration and packing density patterns. The phantoms use hollow fibers whose diameter ranging from 950 nanometers to 12 microns filled with water, called Taxons (Textile axon). We have created a Standard Taxon Filament (STF) that contains 950-nanometer internal diameter Taxons with a density of a million per mm2. SFT is purely restricted compartment with water volume fraction of 70%, matched human brain histology, and MRI-based metrics. We can create cortical networks such as the eye to LGN using Taxon filaments (e.g., human eye to the optic nerve of 9 million Taxons and 256 controlled paths with 100-micron precision placement). Select Taxonal filaments that include/exclude the restricted and hindered compartment can be used to test diffusion MRI based models. We can vary the diameter of the Taxons (0.2 to 18 microns diameter), and include tracers to enhance MRI, micro CT or optical microscope imaging. Non-MRI measurement with Micro CT, light, and electron microscope imaging of Taxons and Taxonal fiber tract provide ground truth configuration and microstructural information. We are testing bio-physical models like NODDI or spherical mean techniques (SMT) for packing density pattern and amount of Taxons. We have found the intra-cellular volume fraction correlates with a number of Taxons (r2 = 0.96). For geometrical configuration, we have tested Constrained Spherical Deconvolution techniques which show promising results to resolve more than 45-degree crossing. We will also present the effect of small/big delta on diffusivities at multiple packing densities of the Taxonal bundle. We plan to provide phantoms across laboratories and release public data sets to drive MRI-based quantitative calibration and discovery of improved techniques. We expect the phantoms to provide a set of ground truth challenges to advance MRI diffusion physics and Tractography.
Dimitri Van De Ville
Functional connectivity models: from blobs to (dynamic) networks
Over the past years, brain mapping techniques have become increasingly computational—largely inspired by approaches from signal processing and network theory—to overcome the shortcomings of voxel-wise detection of task-evoked activity. First of all, brain function does not rely exclusively on local specialization, but also on interactions between brain regions, a principle known as functional integration. New approaches that quantify such interactions have allowed to identify networks consisting of brain regions that exhibit temporally coherent signals. Second, the brain is always active, functionally and metabolically. Therefore, spontaneous activity between task periods cannot be considered as constant, but carries meaningful information, even during complete “resting state”; i.e., the subject is asked to relax and let his mind wander. Data-driven analysis has been used to extract resting-state networks that show close resemblance to activation patterns extracted from conventional task-evoked data. Moreover, these intrinsic functional networks are altered by almost any brain disease or disorder. Together with minimal patient compliance (no task needed), these networks are promising candidates for non-invasive biomarkers for diagnosis and prognosis in a single patient, and for facilitating the translation of fMRI into the clinical realm. We will give an overview of multivariate and graph-based techniques for fMRI data processing, as well as how machine-learning approaches can be made of good use in this field. Recently, the quest for better understanding of brain dynamics has triggered new ways to approach functional connectivity—conventionally measured as the correlation between timecourses over the whole run; i.e., using time-resolved rather that summarizing measures.
- M. G. Preti, T. Bolton, D. Van De Ville. The Dynamic Functional Connectome: State-of-the-Art and Perspectives. NeuroImage, in press [DOI:10.1038/s41598-017-12993-1]
- F. I. Karahanoglu, D. Van De Ville. Dynamics of Large-Scale fMRI Networks: Deconstruct Brain Activity to Build Better Models of Brain Function. Current Opinion in Biomedical Engineering, 2017, 3, 28-36 [DOI:10.1016/j.cobme.2017.09.008]
The enriched connectome: From links between functional and structural connectivity to quantitative plasticity of brain connectivity
This lecture will start with an overview of possibilities to relate functional- and structural connectivity. It was shown that local neural models can generate oscillatory neural signals. These neural masses can be coupled by the structural connectivity between areas to generate a signal which is similar to functional brain activations. This connectome can be enriched by quantitative MRI measurements of myelination and other parameters computed from multiparametric measurements. Additionally, micro-structural measurements and axonal diameter distributions can be estimated in vivo using advanced diffusion imaging models such as CHARMED and AxCaliber. Recently the model was extended to 3D to measure the axonal diameters in the entire brain. Now it is possible to measure those properties in vivo using the strong gradient system of the Connectome MRI system. By enriching the connectome with measurement of the axonal diameter and the local myelination, this model allows to compute effective connectivity and even infer on the directionality of the information flow. Thisopens new possibilities to measure brain structure and function. As example, the lecture will end with an application of multimodal assessment of plasticity of brain connectivity in a language learning study of adults.
Inferring information flow in the white matter of the brain: New information provided by the fusion of dMRI and M/EEG
Recent advances in microstructure determination: from confinement tensors to the orientationally-averaged signal
Characterizing compartmentalized specimens via diffusion MR necessitates a reliable representation of diffusion within local compartments. In the first part of the talk, I will discuss the recently introduced confinement tensor formalism, which is based on a Hookean force assumption. I will argue that the effective potential energy landscape associated with restricted diffusion is indeed Hookean for a wide range of experimental parameters and compartment size of practical interest.
By ridding a three-dimensional diffusion-weighted signal profile of its directional features, one can obtain a one-dimensional signal, which could exhibit the signature of the underlying microstructure. In the second part of the talk, I will discuss the effects of diffusion along neural projections on such orientationally-averaged signal.
Multidimensional diffusion MRI
A generalized SMT-based framework for diffusion MRI microstructural model estimation
Diffusion Magnetic Resonance Imaging (DMRI) has been widely used to characterize the principal directions of white matter fibers, also known as fiber Orientation Distribution Function (fODF), and axonal density in brain tissues.
Recently, different multi-compartment models have been proposed allowing the joint estimation of both the fODF and axonal densities following different approaches. In this work, the problem has been cast in a unified framework using the Spherical Mean Technique (SMT), where the presence of multiple compartments is accounted for and the fODF is expressed in a parametric form allowing the estimation of the whole set of parameters. In this formulation, the fODF is expressed by its Spherical Harmonics (SH) representation and different multi-compartment models can be easily plugged in, enabling a structured and simple comparison of the respective performance.
Starting from a general multi-compartment formulation, four simplified 2-parameters models are considered: Fiber ORientation Estimated using Continuous Axially Symmetric Tensors (FORECAST), Multi Compartment Microscopic Diffusion Imaging (MC-MDI), Neurite Orientation Dispersion and Density Imaging (NODDI), and Ball&Stick (BS). The proposed formulation, relying on SMT and SH representation, allows unifying several microstructural models proposed in diffusion MRI literature under the same mathematical framework, providing the mean for easily comparing their performance while highlighting their similarities and differences, thus facilitating the choice of the model to use for on in-vivo data.
Riemannian and Finslerian geometry for diffusion weighted magnetic resonance imaging
Riemannian geometry has been advocated as a mathematical framework for diffusion tensor imaging (DTI).
The reason for this is the conjectural yet intuitively natural identification of a (dual) Riemannian metric and the diffusion tensor, each carrying six degrees of freedom per spatial base point in 3-space.
This one-to-one mapping between local geometry and local diffusivity characteristics is an essential but at the same time limiting feature of the Riemannian paradigm for DTI, appropriate only
in a mildly anisotropic medium (notably white matter pathways in the brain with ‘single fiber coherence’).
The advent of more sophisticated models in diffusion weighted magnetic resonance imaging (collectively referred to as high angular resolution diffusion imaging or HARDI models)
calls for a geometric paradigm that is in principle capable of retaining a one-to-one mapping regardless of the number of degrees of freedom of the HARDI model.
The option I pursue and illustrate in this lecture is a natural extension of Riemann geometry already hinted upon by Bernhard Riemann in his seminal work and nowadays known as Finsler geometry.
Finslerian geometry incorporates Riemannian geometry as a limiting case and therefore appears to be appropriate for those type of HARDI (or DSI) models that can be likewise viewed as natural extensions of DTI.
The mathematics behind Finsler geometry is mind-boggling, and a rigorous closed-form connection with HARDI has not yet been established except in certain asymptotic regimes.
The lecture serves as a small step towards such a connection, and as a source of inspiration for future work.
Invariants and shape: Application to diffusion MRI
The notion of “shape” is an integral part of our experience in perceiving the world. Yet, it is often difficult to give its precise definition. Mathematically, a shape is what defines an object once its variations by several transforms (e.g. translations or rotations) are removed. Such a shape is characterized by a set of numbers called invariants.
In diffusion MRI, invariants and shape are also important notions as they characterize the diffusion properties independently of the position/orientation of the subject. Thus, they constitute the basic blocks over which can be built biomarkers.
This talk will present some basics principles and properties on invariance, in a tutorial like presentation. Those principles and properties will first be illustrated by examples in diffusion tensor MRI. Then, we will explore how these notions can be extended for higher order tensors.
Geometric statistics for computational anatomy
At the interface of geometry, statistics, image analysis and medicine, computational anatomy aims at analyzing and modeling the biological variability of the organs shapes and their dynamics at the population level. The goal is to model the mean anatomy, its normal variation, its motion / evolution and to discover morphological differences between normal and pathological groups. Since shapes and deformations live in non-linear spaces, this requires a consistent statistical framework on manifolds and Lie groups, which has motivated the development of Geometric Statistics during the last decade.
I will first present simple statistics (mean, Covariance) in Riemannian manifolds, which are allowed by the reformulation of the norion of mean as a minimization (Fréchet or Karcher mean) or as an implicit locus (exponential barycenter). This allows also to extend a number of image processing algorithms (interpolation, filtering, restoration of missing data) to manifold valued images. The we will turn to the generalization of Principal Component Analysis (PCA). Tangent PCA is often sufficient for analyzing data which are sufficiently centered around a central value (unimodal or Gaussian-like data), but fails for multimodal or large support distributions (e.g. uniform on close compact subspaces). Other existing generalizations like Principal Geodesic Analysis (PGA) and Geodesic PCA (GPCA) minimize the distance to Geodesic Subspaces (GS) that remain parametrized by a unique central point. A more general family of subspaces called barycentric subspaces are implicitly defined as the locus of points which are weighted means of k+1 reference points. Like PGA, barycentric subspaces can naturally be nested, allowing the construction of inductive forward or backward nested subspaces. The joint optimization of this whole hierarchy of properly embedded affine subspaces of increasing dimension (a flag) in called Barycentric Subspaces Analysis (BSA). The method will be illustrated on spherical and hyperbolic spaces, and on diffeomorphisms encoding the deformation of the heart in cardiac image sequences.
In a second part, I will investigate data living in transformation groups. The geometric structure generally considered is that of (right) invariant metrics Riemannian on groups of diffeomorphisms (LDDMM). However, efficient image processing methods based on diffeomorphisms parametrized by stationary velocity fields (SVF) have been developed in parallel with a great success from the practical point of view but with less theoretical support. This talk will detail and partially extend the Riemannian framework for geometric statistics to affine connection spaces and more particularly to Lie groups provided with the canonical Cartan-Schouten connection (a non-metric connection). In finite dimension, this provides strong theoretical bases for the use of one-parameter subgroups. The generalization to infinite dimensions would grounds the SVF-framework. From the practical point of view, we show that it leads to quite simple and very efficient models of atrophy of the brain in Alzheimer’s disease.
Functional connectomics: extracting and quantifying functional connectivity in fMRI
Fluctuations in the functional brain activity measure by functional magnetic resonnance imaging (fMRI) can reveal neural interactions. These can be systematicaly mapped and represented as a brain-wide graph, a “functional connectome”.
In this lecture, I will discuss the statistical modeling of building connectomes from fMRI data: the estimation choices, what they teach us about the brain, and the computational problems that they entail. I will cover: how to define regions that form nodes of the connectome; how to estimate graphical models that representation interactions between brain regions, and how to compare the resulting connectomes across subjects.
Practical work: using scikit-learn and nilearn for resting-state fMRI biomarkers
Scikit-learn is one of the reference machine-learn toolbox. Nilearn is a tool dedicated to supervised and unsupervised analysis of brain imaging. I will teach how they can be used to extract brain networks from resting-state fMRI and to learn biomarkers of a condition on these. The packages have a simple-to-use Python interface. Participants are invited to follow along.
Moo K. Chung
Persistent homological brain network analysis
Persistent homology, a branch of recently popular computational topology, provides a coherent mathematical framework for quantifying the topological structures of brain networks. Instead of looking at networks at a fixed scale, as usually done in many standard brain network analysis, persistent homology observes the changes of topological features of the network over multiple resolutions and scales. In doing so, it reveals the most persistent topological features that are robust under noise perturbations. This robustness in performance under different scales is needed for obtaining more stable quantification of the network. For the first half of the talk, we will review the basics of persistent homology. The remaining half of the talk will be focused on its applications in EEG and dMRI based brain network analysis. The talk is based on doi.org/10.1109/TMI.2012.2219590.
The talk will cover methodological aspects of multimodal connectomics, and it’s application to various pathologies. It will discuss the motivation for and issues with combining structural and functional connectivity information, from diffusion and functional imaging, and pathology specific solutions. Applications to autism, neuro-ongological planning and traumatic brain injury will be presented, to demonstrate study specific method development.
Structure-function relationship in epilepsy: insights from multimodal imaging and computational models
Structure-function relationship in epilepsy: insights from multimodal imaging and computational models
Despite the large amount of data describing localization-related epilepsy as a network disease, the links between macroscopic structural connectivity and: 1) functional network (dis)organisation; 2) seizure organization are still poorly understood. Using multimodal connectivity imaging, intracerebral EEG recordings as well as computational models of epilepsy informed by empiric structural connectivity, the tight relationship between anatomy and epilepsy will be illustrated. I will show that anatomical connectivity not only reflects the pathological impact of epilepsy on functional brain networks (link with cognitive impairment) but also shapes seizure organization and propagation. The need for a multimodal approach will be particularly emphasized and the possible extension of this framework to other neurological diseases will be discussed.
Computational neuroanatomy of the human brain white matter and beyond
The motivation of this talk is the computational encoding of neuroanatomy in terms of tissue characteristics as well as classical neuroanatomical knowledge.
The first problem to address will be the in vivo dissection of the human brain’s white matter from diffusion magnetic resonance imaging. We address this through representing current anatomical knowledge computationally. In this talk I will introduce computational tools to represent human anatomy. More precisely, I will introduce a domain specific programming language to represent and automatically extract the major white matter structures in the human brain’s white matter, the white matter query language (WMQL) as well as applications of these techniques to dyscalculia and schizophrenia.
Then I will move on to presenting techniques to perform group-based studies to parcel the cortical mantle based on white matter connectivity. Specifically, I will show how leveraging a consistent mathematical model of axonal-based cortical connectivity we are able to separate subject and parcel-specific characteristics in a random effects model. In particular, the motor and sensory cortex are subdivided in agreement with the human homunculus of Penfield. We illustrate this by comparing our resulting parcels with the motor strip mapping included in the Human Connectome Project data.
Finally, I will provide an prospective view on future directions of computational neuroanatomy.