Distinct brain-wide presynaptic networks underlie the functional identity of individual cortical neurons.

Neuronal connections provide the scaffolding for neuronal function. Revealing the connectivity of functionally identified individual neurons is necessary to understand how activity patterns emerge and support behavior. Yet, the brain-wide presynaptic wiring rules that lay the foundation for the functional selectivity of individual neurons remain largely unexplored. Cortical neurons, even in primary sensory cortex, are heterogeneous in their selectivity, not only to sensory stimuli but also to multiple aspects of behavior. Here, to investigate presynaptic connectivity rules underlying the selectivity of pyramidal neurons to behavioral state 1-12 in primary somatosensory cortex (S1), we used two-photon calcium imaging, neuropharmacology, single-cell based monosynaptic input tracing, and optogenetics. We show that behavioral state-dependent neuronal activity patterns are stable over time. These are not determined by neuromodulatory inputs but are instead driven by glutamatergic inputs. Analysis of brain-wide presynaptic networks of individual neurons with distinct behavioral state-dependent activity profiles revealed characteristic patterns of anatomical input. While both behavioral state-related and unrelated neurons had a similar pattern of local inputs within S1, their long-range glutamatergic inputs differed. Individual cortical neurons, irrespective of their functional properties, received converging inputs from the main S1-projecting areas. Yet, neurons that tracked behavioral state received a smaller proportion of motor cortical inputs and a larger proportion of thalamic inputs. Optogenetic suppression of thalamic inputs reduced behavioral state-dependent activity in S1, but this activity was not externally driven. Our results revealed distinct long-range glutamatergic inputs as a substrate for preconfigured network dynamics associated with behavioral state.

Manifold learning for fMRI time-varying functional connectivity.

Whole-brain functional connectivity (FC) measured with functional MRI (fMRI) evolves over time in meaningful ways at temporal scales going from years (e.g., development) to seconds [e.g., within-scan time-varying FC (tvFC)]. Yet, our ability to explore tvFC is severely constrained by its large dimensionality (several thousands). To overcome this difficulty, researchers often seek to generate low dimensional representations (e.g., 2D and 3D scatter plots) hoping those will retain important aspects of the data (e.g., relationships to behavior and disease progression). Limited prior empirical work suggests that manifold learning techniques (MLTs)-namely those seeking to infer a low dimensional non-linear surface (i.e., the manifold) where most of the data lies-are good candidates for accomplishing this task. Here we explore this possibility in detail. First, we discuss why one should expect tvFC data to lie on a low dimensional manifold. Second, we estimate what is the intrinsic dimension (ID; i.e., minimum number of latent dimensions) of tvFC data manifolds. Third, we describe the inner workings of three state-of-the-art MLTs: Laplacian Eigenmaps (LEs), T-distributed Stochastic Neighbor Embedding (T-SNE), and Uniform Manifold Approximation and Projection (UMAP). For each method, we empirically evaluate its ability to generate neuro-biologically meaningful representations of tvFC data, as well as their robustness against hyper-parameter selection. Our results show that tvFC data has an ID that ranges between 4 and 26, and that ID varies significantly between rest and task states. We also show how all three methods can effectively capture subject identity and task being performed: UMAP and T-SNE can capture these two levels of detail concurrently, but LE could only capture one at a time. We observed substantial variability in embedding quality across MLTs, and within-MLT as a function of hyper-parameter selection. To help alleviate this issue, we provide heuristics that can inform future studies. Finally, we also demonstrate the importance of feature normalization when combining data across subjects and the role that temporal autocorrelation plays in the application of MLTs to tvFC data. Overall, we conclude that while MLTs can be useful to generate summary views of labeled tvFC data, their application to unlabeled data such as resting-state remains challenging.

Manifold Learning for fMRI time-varying FC.

Whole-brain functional connectivity ( FC ) measured with functional MRI (fMRI) evolve over time in meaningful ways at temporal scales going from years (e.g., development) to seconds (e.g., within-scan time-varying FC ( tvFC )). Yet, our ability to explore tvFC is severely constrained by its large dimensionality (several thousands). To overcome this difficulty, researchers seek to generate low dimensional representations (e.g., 2D and 3D scatter plots) expected to retain its most informative aspects (e.g., relationships to behavior, disease progression). Limited prior empirical work suggests that manifold learning techniques ( MLTs )-namely those seeking to infer a low dimensional non-linear surface (i.e., the manifold) where most of the data lies-are good candidates for accomplishing this task. Here we explore this possibility in detail. First, we discuss why one should expect tv FC data to lie on a low dimensional manifold. Second, we estimate what is the intrinsic dimension (i.e., minimum number of latent dimensions; ID ) of tvFC data manifolds. Third, we describe the inner workings of three state-of-the-art MLTs : Laplacian Eigenmaps ( LE ), T-distributed Stochastic Neighbor Embedding ( T-SNE ), and Uniform Manifold Approximation and Projection ( UMAP ). For each method, we empirically evaluate its ability to generate neuro-biologically meaningful representations of tvFC data, as well as their robustness against hyper-parameter selection. Our results show that tvFC data has an ID that ranges between 4 and 26, and that ID varies significantly between rest and task states. We also show how all three methods can effectively capture subject identity and task being performed: UMAP and T-SNE can capture these two levels of detail concurrently, but L E could only capture one at a time. We observed substantial variability in embedding quality across MLTs , and within- MLT as a function of hyper-parameter selection. To help alleviate this issue, we provide heuristics that can inform future studies. Finally, we also demonstrate the importance of feature normalization when combining data across subjects and the role that temporal autocorrelation plays in the application of MLTs to tvFC data. Overall, we conclude that while MLTs can be useful to generate summary views of labeled tvFC data, their application to unlabeled data such as resting-state remains challenging.

Landmark constrained genus-one surface Teichmüller map applied to surface registration in medical imaging.

We address the registration problem of genus-one surfaces (such as vertebrae bones) with prescribed landmark constraints. The high-genus topology of the surfaces makes it challenging to obtain a unique and bijective surface mapping that matches landmarks consistently. This work proposes to tackle this registration problem using a special class of quasi-conformal maps called Teichmüller maps (T-Maps). A landmark constrained T-Map is the unique mapping between genus-1 surfaces that minimizes the maximal conformality distortion while matching the prescribed feature landmarks. Existence and uniqueness of the landmark constrained T-Map are theoretically guaranteed. This work presents an iterative algorithm to compute the T-Map. The main idea is to represent the set of diffeomorphism using the Beltrami coefficients (BC). The BC is iteratively adjusted to an optimal one, which corresponds to our desired T-Map that matches the prescribed landmarks and satisfies the periodic boundary condition on the universal covering space. Numerical experiments demonstrate the effectiveness of our proposed algorithm. The method has also been applied to register vertebrae bones with prescribed landmark points and curves, which gives accurate surface registrations.

Genus-one surface registration via teichmüller extremal mapping.

This paper presents a novel algorithm to obtain landmark-based genus-1 surface registration via a special class of quasi-conformal maps called the Teichmüller maps. Registering shapes with important features is an important process in medical imaging. However, it is challenging to obtain a unique and bijective genus-1surface matching that satisfies the prescribed landmark constraints. In addition, as suggested by [11], conformal transformation provides the most natural way to describe the deformation or growth of anatomical structures. This motivates us to look for the unique mapping between genus-1 surfaces that matches the features while minimizing the maximal conformality distortion. Existence and uniqueness of such optimal diffeomorphism is theoretically guaranteed and is called the Teichmüller extremal mapping. In this work, we propose an iterative algorithm, called the Quasi-conformal (QC) iteration, to find the Teichmüller extremal mapping between the covering spaces of genus-1 surfaces. By representing the set of diffeomorphisms using Beltrami coefficients (BCs), we look for an optimal BC which corresponds to our desired diffeomorphism that matches prescribed features and satisfies the periodic boundary condition on the covering space. Numerical experiments show that our proposed algorithm is efficient and stable for registering genus-1 surfaces even with large amount of landmarks. We have also applied the algorithm on registering vertebral bones with prescribed feature curves, which demonstrates the usefulness of the proposed algorithm.