The missing link: Predicting connectomes from noisy and partially observed tract tracing data

Predictability of cortico-cortical connections in the mammalian brain

Despite a five order of magnitude range in size, the brains of mammals share many anatomical and functional characteristics that translate into cortical network commonalities. Here we develop a machine learning framework to quantify the degree of predictability of the weighted interareal cortical matrix. Partial network connectivity data were obtained with retrograde tract-tracing experiments generated with a consistent methodology, supplemented by projection length measurements in a nonhuman primate (macaque) and a rodent (mouse). We show that there is a significant level of predictability embedded in the interareal cortical networks of both species. At the binary level, links are predictable with an area under the ROC curve of at least 0.8 for the macaque. Weighted medium and strong links are predictable with an 85%-90% accuracy (mouse) and 70%-80% (macaque), whereas weak links are not predictable in either species. These observations reinforce earlier observations that the formation and evolution of the cortical network at the mesoscale is, to a large extent, rule based. Using the methodology presented here, we performed imputations on all area pairs, generating samples for the complete interareal network in both species. These are necessary for comparative studies of the connectome with minimal bias, both within and across species.

The impact of input node placement in the controllability of structural brain networks

Network controllability refers to the ability to steer the state of a network towards a target state by driving certain nodes, known as input nodes. This concept can be applied to brain networks for studying brain function and its relation to the structure, which has numerous practical applications. Brain network controllability involves using external signals such as electrical stimulation to drive specific brain regions and navigate the neurophysiological activity level of the brain around the state space. Although controllability is mainly theoretical, the energy required for control is critical in real-world implementations. With a focus on the structural brain networks, this study explores the impact of white matter fiber architecture on the control energy in brain networks using the theory of how input node placement affects the LCC (the longest distance between inputs and other network nodes). Initially, we use a single input node as it is theoretically possible to control brain networks with just one input. We show that highly connected brain regions that lead to lower LCCs are more energy-efficient as a single input node. However, there may still be a need for a significant amount of control energy with one input, and achieving controllability with less energy could be of interest. We identify the minimum number of input nodes required to control brain networks with smaller LCCs, demonstrating that reducing the LCC can significantly decrease the control energy in brain networks. Our results show that relying solely on highly connected nodes is not effective in controlling brain networks with lower energy by using multiple inputs because of densely interconnected brain network hubs. Instead, a combination of low and high-degree nodes is necessary.

Mapping higher-order relations between brain structure and function with embedded vector representations of connectomes

Connectomics generates comprehensive maps of brain networks, represented as nodes and their pairwise connections. The functional roles of nodes are defined by their direct and indirect connectivity with the rest of the network. However, the network context is not directly accessible at the level of individual nodes. Similar problems in language processing have been addressed with algorithms such as word2vec that create embeddings of words and their relations in a meaningful low-dimensional vector space. Here we apply this approach to create embedded vector representations of brain networks or connectome embeddings (CE). CE can characterize correspondence relations among brain regions, and can be used to infer links that are lacking from the original structural diffusion imaging, e.g., inter-hemispheric homotopic connections. Moreover, we construct predictive deep models of functional and structural connectivity, and simulate network-wide lesion effects using the face processing system as our application domain. We suggest that CE offers a novel approach to revealing relations between connectome structure and function.

Generative models for network neuroscience: prospects and promise

Network neuroscience is the emerging discipline concerned with investigating the complex patterns of interconnections found in neural systems, and identifying principles with which to understand them. Within this discipline, one particularly powerful approach is network generative modelling, in which wiring rules are algorithmically implemented to produce synthetic network architectures with the same properties as observed in empirical network data. Successful models can highlight the principles by which a network is organized and potentially uncover the mechanisms by which it grows and develops. Here, we review the prospects and promise of generative models for network neuroscience. We begin with a primer on network generative models, with a discussion of compressibility and predictability, and utility in intuiting mechanisms, followed by a short history on their use in network science, broadly. We then discuss generative models in practice and application, paying particular attention to the critical need for cross-validation. Next, we review generative models of biological neural networks, both at the cellular and large-scale level, and across a variety of species including Caenorhabditis elegans, Drosophila, mouse, rat, cat, macaque and human. We offer a careful treatment of a few relevant distinctions, including differences between generative models and null models, sufficiency and redundancy, inferring and claiming mechanism, and functional and structural connectivity. We close with a discussion of future directions, outlining exciting frontiers both in empirical data collection efforts as well as in method and theory development that, together, further the utility of the generative network modelling approach for network neuroscience.