Mathematical Modeling seminars

First, a new measure of MI for reaction times is proposed that takes the entire RT distribution into account. Second, we present some recent developments in TWIN modeling, including a new proposal for the sound-induced flash illusion (SIFI).

In the current virtual journal club Dr Di Luca will present findings from a series of psychophysical investigations where he measured sensitivity and bias in the perception of the timing of stimuli. He will present how improved detection with longer sequences and biases in reporting isochrony can be accounted for by optimal statistical predictions. Among his findings was also that the timing of stimuli that occasionally deviate from a regularly paced sequence is perceptually distorted to appear more regular. Such change depends on whether the context these sequences are presented is also regular. Dr Di Luca will present a Bayesian model for the combination of dynamically updated expectations, in the form of a priori probability, with incoming sensory information. These findings contribute to the understanding of how the brain processes temporal information to shape perceptual experiences.

Psychology and neuroscience are increasingly looking to fine-grained analyses of decision-making behaviour, seeking to characterise not just the variation between subjects but also a subject's variability across time. When analysing the behaviour of each subject in a choice task, we ideally want to know not only when the subject has learnt the correct choice rule but also what the subject tried while learning. I introduce a simple but effective Bayesian approach to inferring the probability of different choice strategies at trial resolution. This can be used both for inferring when subjects learn, by tracking the probability of the strategy matching the target rule, and for inferring subjects use of exploratory strategies during learning. Applied to data from rodent and human decision tasks, we find learning occurs earlier and more often than estimated using classical approaches. Around both learning and changes in the rewarded rules the exploratory strategies of win-stay and lose-shift, often considered complementary, are consistently used independently. Indeed, we find the use of lose-shift is strong evidence that animals have latently learnt the salient features of a new rewarded rule. Our approach can be extended to any discrete choice strategy, and its low computational cost is ideally suited for real-time analysis and closed-loop control.

Over the past decade we have demonstrated that the fusion of subject-specific structural information of the human brain with mathematical dynamic models allows building biologically realistic brain network models, which have a predictive value, beyond the explanatory power of each approach independently. The network nodes hold neural population models, which are derived using mean field techniques from statistical physics expressing ensemble activity via collective variables. Our hybrid approach fuses data-driven with forward-modeling-based techniques and has been successfully applied to explain healthy brain function and clinical translation including aging, stroke and epilepsy. Here we illustrate the workflow along the example of epilepsy: we reconstruct personalized connectivity matrices of human epileptic patients using Diffusion Tensor weighted Imaging (DTI). Subsets of brain regions generating seizures in patients with refractory partial epilepsy are referred to as the epileptogenic zone (EZ). During a seizure, paroxysmal activity is not restricted to the EZ, but may recruit other healthy brain regions and propagate activity through large brain networks. The identification of the EZ is crucial for the success of neurosurgery and presents one of the historically difficult questions in clinical neuroscience. The application of latest techniques in Bayesian inference and model inversion, in particular Hamiltonian Monte Carlo, allows the estimation of the EZ, including estimates of confidence and diagnostics of performance of the inference. The example of epilepsy nicely underwrites the predictive value of personalized large-scale brain network models. The workflow of end-to-end modeling is an integral part of the European neuroinformatics platform EBRAINS and enables neuroscientists worldwide to build and estimate personalized virtual brains. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2023-12-06. Recording duration: 00:50:07.

Neurodegenerative diseases involve accumulation of aberrant proteins in the brain, leading to brain damage and progressive cognitive and behavioral dysfunction. Many gaps exist in our understanding of how these diseases initiate and how they progress through the brain. However, evidence has accumulated supporting the hypothesis that aberrant proteins can be transported using the brain’s intrinsic network architecture — in other words, using the brain’s natural communication pathways. This theory forms the basis of connectome-based computational models, which combine real human data and theoretical disease mechanisms to simulate the progression of neurodegenerative diseases through the brain. In this talk, I will first review work leading to the development of connectome-based models, and work from my lab and others that have used these models to test hypothetical modes of disease progression. Second, I will discuss the future and potential of connectome-based models to achieve clinically useful individual-level predictions, as well as to generate novel biological insights into disease progression. Along the way, I will highlight recent work by my lab and others that is already moving the needle toward these lofty goals.

Navigation requires orienting oneself relative to landmarks in the environment, evaluating relevant sensory data, remembering goals, and convert all this information into motor commands that direct locomotion. I will present models, highly constrained by connectomic, physiological and behavioral data, for how these functions are accomplished in the fly brain.

A central question in neuroscience is how the structure of brain circuits determines their activity and function. To explore this systematically, we developed a 230,000-neuron model of mouse primary visual cortex (area V1). The model integrates a broad array of experimental data:Distribution and morpho-electric properties of different neuron types in V1.

Working memory (WM) is a cognitive function that allows the short-term maintenance and manipulation of information when no longer accessible to the senses. It relies on temporarily storing stimulus features in the activity of neuronal populations. To preserve these dynamics from distraction it has been proposed that pre and post-distraction population activity decomposes into orthogonal subspaces. If orthogonalization is necessary to avoid WM distraction, it should emerge as performance in the task improves. We sought evidence of WM orthogonalization learning and the underlying mechanisms by analyzing calcium imaging data from the prelimbic (PrL) and anterior cingulate (ACC) cortices of mice as they learned to perform an olfactory dual task. The dual task combines an outer Delayed Paired-Association task (DPA) with an inner Go-NoGo task. We examined how neuronal activity reflected the process of protecting the DPA sample information against Go/NoGo distractors. As mice learned the task, we measured the overlap between the neural activity onto the low-dimensional subspaces that encode sample or distractor odors. Early in the training, pre-distraction activity overlapped with both sample and distractor subspaces. Later in the training, pre-distraction activity was strictly confined to the sample subspace, resulting in a more robust sample code. To gain mechanistic insight into how these low-dimensional WM representations evolve with learning we built a recurrent spiking network model of excitatory and inhibitory neurons with low-rank connections. The model links learning to (1) the orthogonalization of sample and distractor WM subspaces and (2) the orthogonalization of each subspace with irrelevant inputs. We validated (1) by measuring the angular distance between the sample and distractor subspaces through learning in the data. Prediction (2) was validated in PrL through the photoinhibition of ACC to PrL inputs, which induced early-training neural dynamics in well-trained animals. In the model, learning drives the network from a double-well attractor toward a more continuous ring attractor regime. We tested signatures for this dynamical evolution in the experimental data by estimating the energy landscape of the dynamics on a one-dimensional ring. In sum, our study defines network dynamics underlying the process of learning to shield WM representations from distracting tasks.

Changes in ocular hemodynamics may be indicative of pathological conditions in the eye (e.g. glaucoma, age-related macular degeneration), but also elsewhere in the body (e.g. systemic hypertension, diabetes, neurodegenerative disorders). Thanks to its transparent fluids and structures that allow the light to go through, the eye offers a unique window on the circulation from large to small vessels, and from arteries to veins. Deciphering the causes that lead to changes in ocular hemodynamics in a specific individual could help prevent vision loss as well as aid in the diagnosis and management of diseases beyond the eye. In this talk, we will discuss how mathematical and computational modelling can help in this regard. We will focus on two main factors, namely blood pressure (BP), which drives the blood flow through the vessels, and intraocular pressure (IOP), which compresses the vessels and may impede the flow. Mechanism-driven models translates fundamental principles of physics and physiology into computable equations that allow for identification of cause-to-effect relationships among interplaying factors (e.g. BP, IOP, blood flow). While invaluable for causality, mechanism-driven models are often based on simplifying assumptions to make them tractable for analysis and simulation; however, this often brings into question their relevance beyond theoretical explorations. Data-driven models offer a natural remedy to address these short-comings. Data-driven methods may be supervised (based on labelled training data) or unsupervised (clustering and other data analytics) and they include models based on statistics, machine learning, deep learning and neural networks. Data-driven models naturally thrive on large datasets, making them scalable to a plethora of applications. While invaluable for scalability, data-driven models are often perceived as black- boxes, as their outcomes are difficult to explain in terms of fundamental principles of physics and physiology and this limits the delivery of actionable insights. The combination of mechanism-driven and data-driven models allows us to harness the advantages of both, as mechanism-driven models excel at interpretability but suffer from a lack of scalability, while data-driven models are excellent at scale but suffer in terms of generalizability and insights for hypothesis generation. This combined, integrative approach represents the pillar of the interdisciplinary approach to data science that will be discussed in this talk, with application to ocular hemodynamics and specific examples in glaucoma research.

Over the past decade we have demonstrated that the fusion of subject-specific structural information of the human brain with mathematical dynamic models allows building biologically realistic brain network models, which have a predictive value, beyond the explanatory power of each approach independently. The network nodes hold neural population models, which are derived using mean field techniques from statistical physics expressing ensemble activity via collective variables. Our hybrid approach fuses data-driven with forward-modeling-based techniques and has been successfully applied to explain healthy brain function and clinical translation including aging, stroke and epilepsy. Here we illustrate the workflow along the example of epilepsy: we reconstruct personalized connectivity matrices of human epileptic patients using Diffusion Tensor weighted Imaging (DTI). Subsets of brain regions generating seizures in patients with refractory partial epilepsy are referred to as the epileptogenic zone (EZ). During a seizure, paroxysmal activity is not restricted to the EZ, but may recruit other healthy brain regions and propagate activity through large brain networks. The identification of the EZ is crucial for the success of neurosurgery and presents one of the historically difficult questions in clinical neuroscience. The application of latest techniques in Bayesian inference and model inversion, in particular Hamiltonian Monte Carlo, allows the estimation of the EZ, including estimates of confidence and diagnostics of performance of the inference. The example of epilepsy nicely underwrites the predictive value of personalized large-scale brain network models. The workflow of end-to-end modeling is an integral part of the European neuroinformatics platform EBRAINS and enables neuroscientists worldwide to build and estimate personalized virtual brains.

Higher cortical areas carry a wide range of sensory, cognitive, and motor signals supporting complex goal-directed behavior. These signals mix in heterogeneous responses of single neurons, making it difficult to untangle underlying mechanisms. I will present two approaches for revealing interpretable circuit mechanisms from heterogeneous neural responses during cognitive tasks. First, I will show a flexible nonparametric framework for simultaneously inferring population dynamics on single trials and tuning functions of individual neurons to the latent population state. When applied to recordings from the premotor cortex during decision-making, our approach revealed that populations of neurons encoded the same dynamic variable predicting choices, and heterogeneous firing rates resulted from the diverse tuning of single neurons to this decision variable. The inferred dynamics indicated an attractor mechanism for decision computation. Second, I will show an approach for inferring an interpretable network model of a cognitive task—the latent circuit—from neural response data. We developed a theory to causally validate latent circuit mechanisms via patterned perturbations of activity and connectivity in the high-dimensional network. This work opens new possibilities for deriving testable mechanistic hypotheses from complex neural response data.

To understand subjective evaluation of an option, various disciplines have quantified the interaction between reward and effort during decision making, producing an estimate of economic utility, namely the subject ‘goodness’ of an option. However, those same variables that affect the utility of an option also influence the vigor (speed) of movements to acquire it. To better understand this, we have developed a mathematical framework demonstrating how utility can influence not only the choice of what to do, but also the speed of the movement follows. I will present results demonstrating that expectation of reward increases speed of saccadic eye and reaching movements, whereas expectation of effort expenditure decreases this speed. Intriguingly, when deliberating between two visual options, saccade vigor to each option increases differentially, encoding their relative value. These results and others imply that vigor may serve as a new, real-time metric with which to quantify subjective utility, and that the control of movements may be an implicit reflection of the brain’s economic evaluation of the expected outcome. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2023-10-18. Recording duration: 00:45:32.

The neurobiological mechanisms of arousal and anesthesia remain poorly understood. Recent evidence highlights the key role of interactions between the cerebral cortex and the diffusely projecting matrix thalamic nuclei. Here, we interrogate these processes in a whole-brain corticothalamic neural mass model endowed with targeted and diffusely projecting thalamocortical nuclei inferred from empirical data. This model captures key features seen in propofol anesthesia, including diminished network integration, lowered state diversity, impaired susceptibility to perturbation, and decreased corticocortical coherence. Collectively, these signatures reflect a suppression of information transfer across the cerebral cortex. We recover these signatures of conscious arousal by selectively stimulating the matrix thalamus, recapitulating empirical results in macaque, as well as wake-like information processing states that reflect the thalamic modulation of largescale cortical attractor dynamics. Our results highlight the role of matrix thalamocortical projections in shaping many features of complex cortical dynamics to facilitate the unique communication states supporting conscious awareness.

Understanding communication and information processing in nervous systems is a central goal of neuroscience. Over the past two decades, advances in connectomics and network neuroscience have opened new avenues for investigating polysynaptic communication in complex brain networks. Recent work has brought into question the mainstay assumption that connectome signalling occurs exclusively via shortest paths, resulting in a sprawling constellation of alternative network communication models. This Review surveys the latest developments in models of brain network communication. We begin by drawing a conceptual link between the mathematics of graph theory and biological aspects of neural signalling such as transmission delays and metabolic cost. We organize key network communication models and measures into a taxonomy, aimed at helping researchers navigate the growing number of concepts and methods in the literature. The taxonomy highlights the pros, cons and interpretations of different conceptualizations of connectome signalling. We showcase the utility of network communication models as a flexible, interpretable and tractable framework to study brain function by reviewing prominent applications in basic, cognitive and clinical neurosciences. Finally, we provide recommendations to guide the future development, application and validation of network communication models.

Myopia is predicted to affect 50% of all people worldwide by 2050, and is a risk factor for significant, potentially blinding ocular pathologies, such as retinal detachment and glaucoma. Thus, there is significant motivation to better understand the process of myopigenesis and to develop effective anti-myopigenic treatments. In nearly all cases of human myopia, scleral remodeling is an obligate step in the axial elongation that characterizes the condition. Here I will describe the development of a biomechanical assay based on transient unconfined compression of scleral samples. By treating the scleral as a poroelastic material, one can determine scleral biomechanical properties from extremely small samples, such as obtained from the mouse eye. These properties provide proxy measures of scleral remodeling, and have allowed us to identify all-trans retinoic acid (atRA) as a myopigenic stimulus in mice. I will also describe nascent collaborative work on modeling the transport of atRA in the eye.

Humans and animals are not always rational. They not only rationally exploit rewards but also explore an environment owing to their curiosity. However, the mechanism of such curiosity-driven irrational behavior is largely unknown. Here, we developed a decision-making model for a two-choice task based on the free energy principle, which is a theory integrating recognition and action selection. The model describes irrational behaviors depending on the curiosity level. We also proposed a machine learning method to decode temporal curiosity from behavioral data. By applying it to rat behavioral data, we found that the rat had negative curiosity, reflecting conservative selection sticking to more certain options and that the level of curiosity was upregulated by the expected future information obtained from an uncertain environment. Our decoding approach can be a fundamental tool for identifying the neural basis for reward–curiosity conflicts. Furthermore, it could be effective in diagnosing mental disorders.

To effectively move in complex and changing environments, animals must control locomotor speed and gait, while precisely coordinating and adapting limb movements to the terrain. The underlying neuronal control is facilitated by circuits in the spinal cord, which integrate supraspinal commands and afferent feedback signals to produce coordinated rhythmic muscle activations necessary for stable locomotion. I will present a series of computational models investigating dynamics of central neuronal interactions as well as a neuromechanical model that integrates neuronal circuits with a model of the musculoskeletal system. These models closely reproduce speed-dependent gait expression and experimentally observed changes following manipulation of multiple classes of genetically-identified neuronal populations. I will discuss the utility of these models in providing experimentally testable predictions for future studies.

The dominant theoretical framework to account for reinforcement learning in the brain is temporal difference (TD) reinforcement learning. The TD framework predicts that some neuronal elements should represent the reward prediction error (RPE), which means they signal the difference between the expected future rewards and the actual rewards. The prominence of the TD theory arises from the observation that firing properties of dopaminergic neurons in the ventral tegmental area appear similar to those of RPE model-neurons in TD learning. Previous implementations of TD learning assume a fixed temporal basis for each stimulus that might eventually predict a reward. Here we show that such a fixed temporal basis is implausible and that certain predictions of TD learning are inconsistent with experiments. We propose instead an alternative theoretical framework, coined FLEX (Flexibly Learned Errors in Expected Reward). In FLEX, feature specific representations of time are learned, allowing for neural representations of stimuli to adjust their timing and relation to rewards in an online manner. In FLEX dopamine acts as an instructive signal which helps build temporal models of the environment. FLEX is a general theoretical framework that has many possible biophysical implementations. In order to show that FLEX is a feasible approach, we present a specific biophysically plausible model which implements the principles of FLEX. We show that this implementation can account for various reinforcement learning paradigms, and that its results and predictions are consistent with a preponderance of both existing and reanalyzed experimental data.