Zoran Tiganj

A Unified Mathematical Framework for Coding Time, Space, and Sequences in the Hippocampal Region

The medial temporal lobe (MTL) is believed to support episodic memory, vivid recollection of a specific event situated in a particular place at a particular time. There is ample neurophysiological evidence that the MTL computes location in allocentric space and more recent evidence that the MTL also codes for time. Space and time represent a similar computational challenge; both are variables that cannot be simply calculated from the immediately available sensory information. We introduce a simple mathematical framework that computes functions of both spatial location and time as special cases of a more general computation. In this framework, experience unfolding in time is encoded via a set of leaky integrators. These leaky integrators encode the Laplace transform of their input. The information contained in the transform can be recovered using an approximation to the inverse Laplace transform. In the temporal domain, the resulting representation reconstructs the temporal history. By integrating movements, the equations give rise to a representation of the path taken to arrive at the present location. By modulating the transform with information about allocentric velocity, the equations code for position of a landmark. Simulated cells show a close correspondence to neurons observed in various regions for all three cases. In the temporal domain, novel secondary analyses of hippocampal time cells verified several qualitative predictions of the model. An integrated representation of spatiotemporal context can be computed by taking conjunctions of these elemental inputs, leading to a correspondence with conjunctive neural representations observed in dorsal CA1.

Time Cells in Hippocampal Area CA3

Studies on time cells in the hippocampus have so far focused on area CA1 in animals performing memory tasks. Some studies have suggested that temporal processing within the hippocampus may be exclusive to CA1 and CA2, but not CA3, and may occur only under strong demands for memory. Here we examined the temporal and spatial coding properties of CA3 and CA1 neurons in rats performing a maze task that demanded working memory and a control task with no explicit working memory demand. In the memory demanding task, CA3 cells exhibited robust temporal modulation similar to the pattern of time cell activity in CA1, and the same populations of cells also exhibited typical place coding patterns in the same task. Furthermore, the temporal and spatial coding patterns of CA1 and CA3 were equivalently robust when animals performed a simplified version of the task that made no demands on working memory. However, time and place coding did differ in that the resolution of temporal coding decreased over time within the delay interval, whereas the resolution of place coding was not systematically affected by distance along the track. These findings support the view that CA1 and CA3 both participate in encoding the temporal and spatial organization of ongoing experience. SIGNIFICANCE STATEMENT Hippocampal “time cells” that fire at specific moments in a temporally structured memory task have so far been observed only in area CA1, and some studies have suggested that temporal coding within the hippocampus is exclusive to CA1. Here we describe time cells also in CA3, and time cells in both areas are observed even without working memory demands, similar to place cells in these areas. However, unlike equivalent spatial coding along a path, temporal coding is nonlinear, with greater temporal resolution earlier than later in temporally structured experiences. These observations reveal both similarities and differences in temporal and spatial coding within the hippocampus of importance to understanding how these features of memory are represented in the hippocampus.

An Algebraic Method for Eye Blink Artifacts Detection in Single Channel EEG Recordings

Single channel EEG systems are very useful in EEG based applications where real time processing, low computational complexity and low cumbersomeness are critical constrains. These include brain-computer interface and biofeedback devices and also some clinical applications such as EEG recording on babies or Alzheimer’s disease recognition. In this paper we address the problem of eye blink artifacts detection in such systems. We study an algebraic approach based on numerical differentiation, which is recently introduced from operational calculus. The occurrence of an artifact is modeled as an irregularity which appears explicitly in the time (generalized) derivative of the EEG signal as a delay. Manipulating such delay is easy with the operational calculus and it leads to a simple joint detection and localization algorithm. While the algorithm is devised based on continuous-time arguments, the final implementation step is fully realized in a discrete-time context, using very classical discrete-time FIR filters. The proposed approach is compared with three other approaches: (1) the very basic threshold approach, (2) the approach that combines the use of median filter, matched filter and nonlinear energy operator (NEO) and (3) the wavelet based approach. Comparison is done on: (a) the artificially created signal where the eye activity is synthesized from real EEG recordings and (b) the real single channel EEG recordings from 32 different brain locations. Results are presented with Receiver Operating Characteristics curves. The results show that the proposed approach compares to the other approaches better or as good as, while having lower computational complexity with simple real time implementation. Comparison of the results on artificially created and real signal leads to conclusions that with detection techniques based on derivative estimation we are able to detect not only eye blink artifacts, but also any spike shaped artifact, even if it is very low in amplitude.

A Simple biophysically plausible model for long time constants in single neurons

Recent work in computational neuroscience and cognitive psychology suggests that a set of cells that decay exponentially could be used to support memory for the time at which events took place. Analytically and through simulations on a biophysical model of an individual neuron, we demonstrate that exponentially decaying firing with a range of time constants up to minutes could be implemented using a simple combination of well‐known neural mechanisms. In particular, we consider firing supported by calcium‐controlled cation current. When the amount of calcium leaving the cell during an interspike interval is larger than the calcium influx during a spike, the overall decay in calcium concentration can be exponential, resulting in exponential decay of the firing rate. The time constant of the decay can be several orders of magnitude larger than the time constant of calcium clearance, and it could be controlled externally via a variety of biologically plausible ways. The ability to flexibly and rapidly control time constants could enable working memory of temporal history to be generalized to other variables in computing spatial and ordinal representations.

A non-parametric method for automatic neural spike clustering based on the non-uniform distribution of the data.

In this paper, we propose a simple and straightforward algorithm for neural spike sorting. The algorithm is based on the observation that the distribution of a neural signal largely deviates from the uniform distribution and is rather unimodal. The detected spikes to be sorted are first processed with some feature extraction technique, such as PCA, and then represented in a space with reduced dimension by keeping only a few most important features. The resulting space is next filtered in order to emphasis the differences between the centers and the borders of the clusters. Using some prior knowledge on the lowest level activity of a neuron, such as e.g. the minimal firing rate, we find the number of clusters and the center of each cluster. The spikes are then sorted using a simple greedy algorithm which grabs the nearest neighbors. We have tested the proposed algorithm on real extracellular recordings and used the simultaneous intracellular recordings to verify the results of the sorting. The results suggest that the algorithm is robust and reliable and it compares favorably with the state-of-the-art approaches. The proposed algorithm tends to be conservative, it is simple to implement and is thus suitable for both research and clinical applications as an interesting alternative to the more sophisticated approaches.

Sequential Firing Codes for Time in Rodent Medial Prefrontal Cortex

Abstract A subset of hippocampal neurons, known as “time cells” fire sequentially for circumscribed periods of time within a delay interval. We investigated whether medial prefrontal cortex (mPFC) also contains time cells and whether their qualitative properties differ from those in the hippocampus and striatum. We studied the firing correlates of neurons in the rodent mPFC during a temporal discrimination task. On each trial, the animals waited for a few seconds in the stem of a T‐maze. A subpopulation of units fired in a sequence consistently across trials for a circumscribed period during the delay interval. These sequentially activated time cells showed temporal accuracy that decreased as time passed as measured by both the width of their firing fields and the number of cells that fired at a particular part of the interval. The firing dynamics of the time cells was significantly better explained with the elapse of time than with the animals’ position and velocity. The findings observed here in the mPFC are consistent with those previously reported in the hippocampus and striatum, suggesting that the sequentially activated time cells are not specific to these areas, but are part of a common representational motif across regions.

Neural spike sorting using iterative ICA and a deflation-based approach.

We propose a spike sorting method for multi-channel recordings. When applied in neural recordings, the performance of the independent component analysis (ICA) algorithm is known to be limited, since the number of recording sites is much lower than the number of neurons. The proposed method uses an iterative application of ICA and a deflation technique in two nested loops. In each iteration of the external loop, the spiking activity of one neuron is singled out and then deflated from the recordings. The internal loop implements a sequence of ICA and sorting for removing the noise and all the spikes that are not fired by the targeted neuron. Then a final step is appended to the two nested loops in order to separate simultaneously fired spikes. We solve this problem by taking all possible pairs of the sorted neurons and apply ICA only on the segments of the signal during which at least one of the neurons in a given pair was active. We validate the performance of the proposed method on simulated recordings, but also on a specific type of real recordings: simultaneous extracellular-intracellular. We quantify the sorting results on the extracellular recordings for the spikes that come from the neurons recorded intracellularly. The results suggest that the proposed solution significantly improves the performance of ICA in spike sorting.

Influence of extracellular oscillations on neural communication: a computational perspective.

Neural communication generates oscillations of electric potential in the extracellular medium. In feedback, these oscillations affect the electrochemical processes within the neurons, influencing the timing and the number of action potentials. It is unclear whether this influence should be considered only as noise or it has some functional role in neural communication. Through computer simulations we investigated the effect of various sinusoidal extracellular oscillations on the timing and number of action potentials. Each simulation is based on a multicompartment model of a single neuron, which is stimulated through spatially distributed synaptic activations. A thorough analysis is conducted on a large number of simulations with different models of CA3 and CA1 pyramidal neurons which are modeled using realistic morphologies and active ion conductances. We demonstrated that the influence of the weak extracellular oscillations, which are commonly present in the brain, is rather stochastic and modest. We found that the stronger fields, which are spontaneously present in the brain only in some particular cases (e.g., during seizures) or that can be induced externally, could significantly modulate spike timings.

Encoding the Laplace transform of stimulus history using mechanisms for persistent firing

Persistent firing has been observed in slice preparations from a variety of brain regions believed to be important in memory [1-3]. Information about a transient stimulus can be reflected in persistently elevated firing rate over many minutes. What computation could persistent firing cells support? In particular the lack of forgetting observed in slice preparations seems difficult to reconcile with the finding that memory degrades over time. A scale-invariant model for representing past stimuli has been proposed in [4]. This model utilizes two layers of nodes. The first layer is composed of leaky integrators and computes the Laplace transform of the input function. The first layer projects to the second through a linear operator which approximates the inverse Laplace transform so the activity of the second layer at any point of time gives a fuzzy representation of the input history leading up to the present moment. Comparison with behavioral results suggests that the history should be retained over at least a few thousand seconds. If we assume that each node of the above model corresponds to an individual neuron, the neurons encoding the Laplace transform should respond to a particular stimulus with a firing rate that decays exponentially over time. Critically, in order to encode the Laplace transform we require different rates of decay for different neurons in this layer. Moreover, the longest time constant across neurons determines the longest time scale that can be maintained in representation of the history. Persistent firing cells [5] are basically perfect integrators. We have been exploring the conditions under which persistently firing cells observed in the slice could be adapted to give rise to a set of leaky integrators whose rate constants are under external control. The basic idea is to modulate the channels responsible for persistent firing using divisive dendritic inhibition [6]. Under these circumstances, constructing a set of cells with different rate constants amounts to providing a set of identical cells with different levels of inhibitory input. We explore the potential of this mechanism using biophysical simulations centered on a calcium-dependent cationic current - Ican and hyperpolarization-activated, voltage and calcium-dependent cationic current - Ih. We also describe a simple integrate and fire model that yields an explicit analytical solution describing the conditions under which persistent firing can be modulated to yield exponential decay.

Is working memory stored along a logarithmic timeline? Converging evidence from neuroscience, behavior and models

HighlightsBehavioral evidence suggests WM can draw on a compressed temporal record of the past.Neurophysiological evidence shows a compressed temporal record of the past.Thus this compressed temporal record of the past in the brain could support WM. Abstract A growing body of evidence suggests that short‐term memory does not only store the identity of recently experienced stimuli, but also information about when they were presented. This representation of ‘what’ happened ‘when’ constitutes a neural timeline of recent past. Behavioral results suggest that people can sequentially access memories for the recent past, as if they were stored along a timeline to which attention is sequentially directed. In the short‐term judgment of recency (JOR) task, the time to choose between two probe items depends on the recency of the more recent probe but not on the recency of the more remote probe. This pattern of results suggests a backward self‐terminating search model. We review recent neural evidence from the macaque lateral prefrontal cortex (lPFC) (Tiganj, Cromer, Roy, Miller, & Howard, in press) and behavioral evidence from human JOR task (Singh & Howard, 2017) bearing on this question. Notably, both lines of evidence suggest that the timeline is logarithmically compressed as predicted by Weber‐Fechner scaling. Taken together, these findings provide an integrative perspective on temporal organization and neural underpinnings of short‐term memory.