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Introduction: Neurovascular coupling (NVC) is an important mechanism for the regulation of cerebral perfusion during intensive cognitive activity. Thus, it should be examined in terms of its effects on the regulation dynamics of cerebral perfusion and its possible alterations during cognitive impairment. The dynamic dependence of continuous changes in cerebral blood velocity (CBv), which can be measured noninvasively using transcranial Doppler upon fluctuations in arterial blood pressure (ABP) and CO 2 tension, using end-tidal CO 2 (EtCO 2 ) as a proxy, can be quantified via data-based dynamic modeling to yield insights into two key regulatory mechanisms: the dynamic cerebral autoregulation (dCA) and dynamic vasomotor reactivity (DVR), respectively., Methods: Using the Laguerre Expansion Technique (LET), this study extracted such models from data in supine resting vs cognitively active conditions (during attention, fluency, and memory tasks from the Addenbrooke's Cognitive Examination III, ACE-III) to elucidate possible changes in dCA and DVR due to cognitive stimulation of NVC. Healthy volunteers (n = 39) were recruited at the University of Leicester and continuous measurements of CBv, ABP, and EtCO 2 were recorded., Results: Modeling analysis of the dynamic ABP-to-CBv and CO 2 -to-CBv relationships showed significant changes in dCA, but not DVR, under cognitively active conditions compared to resting state., Discussion: Interpretation of these changes through Principal Dynamic Mode (PDM) analysis is discussed in terms of possible associations between stronger NVC stimulation during cognitive tasks and enhanced sympathetic activation., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2024 Rizko, Beishon, Panerai and Marmarelis.)

Cerebral Autoregulation (CA) is an important physiological mechanism stabilizing cerebral blood flow (CBF) in response to changes in cerebral perfusion pressure (CPP). By maintaining an adequate, relatively constant supply of blood flow, CA plays a critical role in brain function. Quantifying CA under different physiological and pathological states is crucial for understanding its implications. This knowledge may serve as a foundation for informed clinical decision-making, particularly in cases where CA may become impaired. The quantification of CA functionality typically involves constructing models that capture the relationship between CPP (or arterial blood pressure) and experimental measures of CBF. Besides describing normal CA function, these models provide a means to detect possible deviations from the latter. In this context, a recent white paper from the Cerebrovascular Research Network focused on Transfer Function Analysis (TFA), which obtains frequency domain estimates of dynamic CA. In the present paper, we consider the use of time-domain techniques as an alternative approach. Due to their increased flexibility, time-domain methods enable the mitigation of measurement/physiological noise and the incorporation of nonlinearities and time variations in CA dynamics. Here, we provide practical recommendations and guidelines to support researchers and clinicians in effectively utilizing these techniques to study CA., Competing Interests: Declaration of conflicting interestsThe author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

We studied the regulation dynamics of cerebral blood velocity (CBv) at middle cerebral arteries (MCA) in response to spontaneous changes of arterial blood pressure (ABP), termed dynamic cerebral autoregulation (dCA), and end-tidal CO 2 as proxy for blood CO 2 tension, termed dynamic vasomotor reactivity (DVR), by analyzing time-series data collected at supine rest from 36 patients with Type-2 Diabetes Mellitus (T2DM) and 22 age/sex-matched non-diabetic controls without arterial hypertension. Our analysis employed a robust dynamic modeling methodology that utilizes Principal Dynamic Modes (PDM) to estimate subject-specific dynamic transformations of spontaneous changes in ABP and end-tidal CO 2 (viewed as two "inputs") into changes of CBv at MCA measured via Transcranial Doppler ultrasound (viewed as the "output"). The quantitative results of PDM analysis indicate significant alterations in T2DM of both DVR and dCA in terms of two specific PDM contributions that rise to significance (p < 0.05). Our results further suggest that the observed DVR and dCA alterations may be due to reduction of cholinergic activity (based on previously published results from cholinergic blockade data) that may disturb the sympatho-vagal balance in T2DM. Combination of these two model-based "physio-markers" differentiated T2DM patients from controls (p = 0.0007), indicating diabetes-related alteration of cerebrovascular regulation, with possible diagnostic implications., Competing Interests: Declaration of conflicting interestsThe author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Objective: Here, we demonstrate the first successful use of static neural stimulation patterns for specific information content. These static patterns were derived by a model that was applied to a subject's own hippocampal spatiotemporal neural codes for memory., Approach: We constructed a new model of processes by which the hippocampus encodes specific memory items via spatiotemporal firing of neural ensembles that underlie the successful encoding of targeted content into short-term memory. A memory decoding model (MDM) of hippocampal CA3 and CA1 neural firing was computed which derives a stimulation pattern for CA1 and CA3 neurons to be applied during the encoding (sample) phase of a delayed match-to-sample (DMS) human short-term memory task., Main Results: MDM electrical stimulation delivered to the CA1 and CA3 locations in the hippocampus during the sample phase of DMS trials facilitated memory of images from the DMS task during a delayed recognition (DR) task that also included control images that were not from the DMS task. Across all subjects, the stimulated trials exhibited significant changes in performance in 22.4% of patient and category combinations. Changes in performance were a combination of both increased memory performance and decreased memory performance, with increases in performance occurring at almost 2 to 1 relative to decreases in performance. Across patients with impaired memory that received bilateral stimulation, significant changes in over 37.9% of patient and category combinations was seen with the changes in memory performance show a ratio of increased to decreased performance of over 4 to 1. Modification of memory performance was dependent on whether memory function was intact or impaired, and if stimulation was applied bilaterally or unilaterally, with nearly all increase in performance seen in subjects with impaired memory receiving bilateral stimulation., Significance: These results demonstrate that memory encoding in patients with impaired memory function can be facilitated for specific memory content, which offers a stimulation method for a future implantable neural prosthetic to improve human memory., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The reviewer SS declared a shared affiliation with the author XS to the handling editor at the time of review., (Copyright © 2024 Roeder, She, Dakos, Moore, Wicks, Witcher, Couture, Laxton, Clary, Popli, Liu, Lee, Heck, Nune, Gong, Shaw, Marmarelis, Berger, Deadwyler, Song and Hampson.)

We present data from the Heart Rate Variability and Emotion Regulation (HRV-ER) randomized clinical trial testing effects of HRV biofeedback. Younger (N = 121) and older (N = 72) participants completed baseline magnetic resonance imaging (MRI) including T 1 -weighted, resting and emotion regulation task functional MRI (fMRI), pulsed continuous arterial spin labeling (PCASL), and proton magnetic resonance spectroscopy ( 1 H MRS). During fMRI scans, physiological measures (blood pressure, pulse, respiration, and end-tidal CO 2 ) were continuously acquired. Participants were randomized to either increase heart rate oscillations or decrease heart rate oscillations during daily sessions. After 5 weeks of HRV biofeedback, they repeated the baseline measurements in addition to new measures (ultimatum game fMRI, training mimicking during blood oxygen level dependent (BOLD) and PCASL fMRI). Participants also wore a wristband sensor to estimate sleep time. Psychological assessment comprised three cognitive tests and ten questionnaires related to emotional well-being. A subset (N = 104) provided plasma samples pre- and post-intervention that were assayed for amyloid and tau. Data is publicly available via the OpenNeuro data sharing platform., (© 2023. The Author(s).)

Heart rate variability is a robust biomarker of emotional well-being, consistent with the shared brain networks regulating emotion regulation and heart rate. While high heart rate oscillatory activity clearly indicates healthy regulatory brain systems, can increasing this oscillatory activity also enhance brain function? To test this possibility, we randomly assigned 106 young adult participants to one of two 5-week interventions involving daily biofeedback that either increased heart rate oscillations (Osc+ condition) or had little effect on heart rate oscillations (Osc- condition) and examined effects on brain activity during rest and during regulating emotion. While there were no significant changes in the right amygdala-medial prefrontal cortex (MPFC) functional connectivity (our primary outcome), the Osc+ intervention increased left amygdala-MPFC functional connectivity and functional connectivity in emotion-related resting-state networks during rest. It also increased down-regulation of activity in somatosensory brain regions during an emotion regulation task. The Osc- intervention did not have these effects. In this healthy cohort, the two conditions did not differentially affect anxiety, depression, or mood. These findings indicate that modulating heart rate oscillatory activity changes emotion network coordination in the brain., (© 2022. The Psychonomic Society, Inc.)

Background: Cerebral flow autoregulation (CFA) is a homeostatic mechanism critical for survival. The autonomic nervous system (ANS) plays a key role in maintaining proper CFA function. More quantitative studies of how the ANS influences CFA are desirable. Objective: To discover and quantify the dynamic effects of cholinergic blockade upon CFA in response to changes of arterial blood pressure and blood CO2 tension in healthy adults. Methods: We analyzed time-series data of spontaneous beat-to-beat mean arterial blood pressure (ABP) and cerebral blood flow velocity in the middle cerebral arteries (CFV), as well as breath-to-breath end-tidal CO2 (CO2), collected in 9 adults before and after cholinergic blockade, in order to obtain subject-specific predictive input-output models of the dynamic effects of changes in ABP and CO2 (inputs) upon CFV (output). These models are defined in convolutional form using "kernel" functions (or, equivalently, Transfer Functions in the frequency domain) that are estimated via the robust method of Laguerre expansions. Results: Cholinergic blockade caused statistically significant changes in the obtained kernel estimates (and the corresponding Transfer Functions) that define the linear dynamics of the ABP-to-CFV and CO2-to-CFV causal relations. The kernel changes due to cholinergic blockade reflect the effects of the cholinergic mechanism and exhibited, in the frequency domain, resonant peaks at 0.22 Hz and 0.06 Hz for the ABP-to-CFV and CO2-to-CFV dynamics, respectively. Conclusion: Quantitative estimates of the dynamics of the cholinergic component in CFA are found as average changes of the ABP-to-CFV and CO2-to-CFV kernels, and corresponding Transfer Functions, before and after cholinergic blockade., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Marmarelis, Shin, Hamner and Tan.)

Rationale: Deep brain stimulation (DBS) of the hippocampus is proposed for enhancement of memory impaired by injury or disease. Many pre-clinical DBS paradigms can be addressed in epilepsy patients undergoing intracranial monitoring for seizure localization, since they already have electrodes implanted in brain areas of interest. Even though epilepsy is usually not a memory disorder targeted by DBS, the studies can nevertheless model other memory-impacting disorders, such as Traumatic Brain Injury (TBI)., Methods: Human patients undergoing Phase II invasive monitoring for intractable epilepsy were implanted with depth electrodes capable of recording neurophysiological signals. Subjects performed a delayed-match-to-sample (DMS) memory task while hippocampal ensembles from CA1 and CA3 cell layers were recorded to estimate a multi-input, multi-output (MIMO) model of CA3-to-CA1 neural encoding and a memory decoding model (MDM) to decode memory information from CA3 and CA1 neuronal signals. After model estimation, subjects again performed the DMS task while either MIMO-based or MDM-based patterned stimulation was delivered to CA1 electrode sites during the encoding phase of the DMS trials. Each subject was sorted ( post hoc ) by prior experience of repeated and/or mild-to-moderate brain injury (RMBI), TBI, or no history (control) and scored for percentage successful delayed recognition (DR) recall on stimulated vs. non-stimulated DMS trials. The subject's medical history was unknown to the experimenters until after individual subject memory retention results were scored., Results: When examined compared to control subjects, both TBI and RMBI subjects showed increased memory retention in response to both MIMO and MDM-based hippocampal stimulation. Furthermore, effects of stimulation were also greater in subjects who were evaluated as having pre-existing mild-to-moderate memory impairment., Conclusion: These results show that hippocampal stimulation for memory facilitation was more beneficial for subjects who had previously suffered a brain injury (other than epilepsy), compared to control (epilepsy) subjects who had not suffered a brain injury. This study demonstrates that the epilepsy/intracranial recording model can be extended to test the ability of DBS to restore memory function in subjects who previously suffered a brain injury other than epilepsy, and support further investigation into the beneficial effect of DBS in TBI patients., Competing Interests: RH discloses a current consulting and advisory relationship with Braingrade, Inc., a component of Engram (Holding), Inc., a Delaware C-Corporation. This relationship was not in effect at the time of the study. The remaining authors declare that the research was otherwise conducted in the absence of any other commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Roeder, Riley, She, Dakos, Robinson, Moore, Couture, Laxton, Popli, Clary, Sam, Heck, Nune, Lee, Liu, Shaw, Gong, Marmarelis, Berger, Deadwyler, Song and Hampson.)

Background: Recent studies have utilized data-based dynamic modeling to establish strong association between dysregulation of cerebral perfusion and Mild Cognitive Impairment (MCI), expressed in terms of impaired CO 2 dynamic vasomotor reactivity in the cerebral vasculature. This raises the question of whether this is due to dysregulation of central mechanisms (baroreflex and chemoreflex) or mechanisms of cortical tissue oxygenation (CTO) in MCI patients. We seek to answer this question using data-based input-output predictive dynamic models. Objective: To use subject-specific data-based multivariate input-output dynamic models to quantify the effects of systemic hemodynamic and blood CO 2 changes upon CTO and to examine possible differences in CTO regulation in MCI patients versus age-matched controls, after the dynamic effects of central regulatory mechanisms have been accounted for by using cerebral flow measurements as another input. Methods: The employed model-based approach utilized the general dynamic modeling methodology of Laguerre expansions of kernels to analyze spontaneous time-series data in order to quantify the dynamic effects upon CTO (an index of relative capillary hemoglobin saturation distribution measured via near-infrared spectroscopy) of contemporaneous changes in end-tidal CO 2 (proxy for arterial CO 2 ), arterial blood pressure and cerebral blood flow velocity in the middle cerebral arteries (measured via transcranial Doppler). Model-based indices (physio-markers) were computed for these distinct dynamic relationships. Results: The obtained model-based indices revealed significant statistical differences of CO 2 dynamic vasomotor reactivity in cortical tissue, combined with "perfusivity" that quantifies the dynamic relationship between flow velocity in cerebral arteries and CTO in MCI patients versus age-matched controls ( p = 0.006). Significant difference between MCI patients and age-matched controls was also found in the respective model-prediction accuracy ( p = 0.0001). Combination of these model-based indices via the Fisher Discriminant achieved even smaller p -value ( p = 5 × 10 -5 ) when comparing MCI patients with controls. The differences in dynamics of CTO in MCI patients are in lower frequencies (<0.05 Hz), suggesting impairment in endocrine/metabolic (rather than neural) mechanisms. Conclusion: The presented model-based approach elucidates the multivariate dynamic connectivity in the regulation of cerebral perfusion and yields model-based indices that may serve as physio-markers of possible dysregulation of CTO during transient CO 2 changes in MCI patients., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2021 Marmarelis, Shin and Zhang.)

The study of dynamic cerebral autoregulation (DCA) in essential hypertension has received considerable attention because of its clinical importance. Several studies have examined the dynamic relationship between spontaneous beat-to-beat arterial blood pressure data and contemporaneous cerebral blood flow velocity measurements (obtained via transcranial Doppler at the middle cerebral arteries) in the form of a linear input-output model using transfer function analysis. This analysis is more reliable when the contemporaneous effects of changes in blood CO 2 tension are also taken into account, because of the significant effects of CO 2 dynamic vasomotor reactivity (DVR) upon cerebral flow. In this article, we extract such input-output predictive models from spontaneous time series hemodynamic data of 24 patients with essential hypertension and 20 normotensive control subjects under resting conditions, using the novel methodology of principal dynamic modes (PDMs) that achieves improved estimation accuracy over previous methods for relatively short and noisy data. The obtained data-based models are subsequently used to compute indexes and markers that quantify DCA and DVR in each subject or patient and therefore can be used to assess the effects of essential hypertension. These model-based DCA and DVR indexes were properly defined to capture the observed effects of DCA and VR and found to be significantly different ( P < 0.05) in the hypertensive patients. We also found significant differences between patients and control subjects in the relative contribution of three PDMs to the model output prediction, a finding that offers the prospect of identifying the physiological mechanisms affected by essential hypertension when the PDMs are interpreted in terms of specific physiological mechanisms. NEW & NOTEWORTHY This article presents novel model-based methodology for obtaining diagnostic indexes of dynamic cerebral autoregulation and dynamic vasomotor reactivity in hypertension.

We tested the influence of blood pressure variability on the reproducibility of dynamic cerebral autoregulation (DCA) estimates. Data were analyzed from the 2nd CARNet bootstrap initiative, where mean arterial blood pressure (MABP), cerebral blood flow velocity (CBFV) and end tidal CO2 were measured twice in 75 healthy subjects. DCA was analyzed by 14 different centers with a variety of different analysis methods. Intraclass Correlation (ICC) values increased significantly when subjects with low power spectral density MABP (PSD-MABP) values were removed from the analysis for all gain, phase and autoregulation index (ARI) parameters. Gain in the low frequency band (LF) had the highest ICC, followed by phase LF and gain in the very low frequency band. No significant differences were found between analysis methods for gain parameters, but for phase and ARI parameters, significant differences between the analysis methods were found. Alternatively, the Spearman-Brown prediction formula indicated that prolongation of the measurement duration up to 35 minutes may be needed to achieve good reproducibility for some DCA parameters. We conclude that poor DCA reproducibility (ICC<0.4) can improve to good (ICC > 0.6) values when cases with low PSD-MABP are removed, and probably also when measurement duration is increased., Competing Interests: The authors have declared that no competing interests exist.

There are currently intensified efforts by the scientific community world-wide to analyze the dynamics of the Covid-19 pandemic in order to predict key epidemiological effects and assist the proper planning for its clinical management, as well as guide sociopolitical decision-making regarding proper mitigation measures. Most efforts follow variants of the established SIR methodological framework that divides a population into "Susceptible", "Infectious" and "Recovered/Removed" fractions and defines their dynamic inter-relationships with first-order differential equations., Goal: This paper proposes a novel approach based on data-guided detection and concatenation of infection waves - each of them described by a Riccati equation with adaptively estimated parameters., Methods: This approach was applied to Covid-19 daily time-series data of US confirmed cases, resulting in the decomposition of the epidemic time-course into five "Riccati modules" representing major infection waves to date (June 18th)., Results: Four waves have passed the time-point of peak infection rate, with the fifth expected to peak on July 20th. The obtained parameter estimates indicate gradual reduction of infectivity rate, although the latest wave is expected to be the largest., Conclusions: This analysis suggests that, if no new waves of infection emerge, the Covid-19 epidemic will be controlled in the US (<5000 new daily cases) by September 26th, and the maximum of confirmed cases will reach 4,160,000. Importantly, this approach can be used to detect (via rigorous statistical methods) the emergence of possible new waves of infections in the future. Analysis of data from individual states or countries may quantify the distinct effects of different mitigation measures.

Background: Significant reduction of dynamic vasomotor reactivity (DVR) was recently reported in patients with amnestic mild cognitive impairment (MCI) relative to age-matched controls. These results were obtained via a novel approach that utilizes data-based predictive dynamic models to quantify DVR., Objective: Using the same methodological approach, we seek to quantify the dynamic effects of the CO2-driven chemoreflex and baroreflex upon heart-rate in order to examine their possible correlation with the observed DVR impairment in each MCI patient., Methods: The employed approach utilizes time-series data to obtain subject-specific predictive input-output models of the dynamic effects of changes in arterial blood pressure and end-tidal CO2 (putative "inputs") upon cerebral blood flow velocity in large cerebral arteries, cortical tissue oxygenation, and heart-rate (putative "outputs")., Results: There was significant dysregulation of CO2-driven heart-rate chemoreflex (p = 0.0031), but not of baroreflex (p = 0.5061), in MCI patients relative to age-matched controls. The model-based index of CO2-driven heart-rate chemoreflex gain (CRG) correlated significantly with the DVR index in large cerebral arteries (p = 0.0146), but not with the DVR index in small/micro-cortical vessels (p = 0.1066). This suggests that DVR impairment in small/micro-cortical vessels is not mainly due to CO2-driven heart-rate chemoreflex dysregulation, but to other factors (possibly dysfunction of neurovascular coupling)., Conclusion: Improved delineation between MCI patients and controls is achieved by combining the DVR index for small/micro-cortical vessels with the CRG index (p = 2×10-5). There is significant correlation (p < 0.01) between neuropsychological test scores and model-based DVR indices. Combining neuropsychological scores with DVR indices reduces the composite diagnostic index p-value (p∼10-10).

Objective: To compare the novel model-based hemodynamic physiomarker of Dynamic Vasomotor Reactivity (DVR) with biomarkers based on Diffusion Tensor Imaging (DTI) and some widely used neurocognitive scores in terms of their ability to delineate patients with amnestic Mild Cognitive Impairment (MCI) from age-matched cognitively normal controls., Materials & Methods: The model-based DVR and MRI-based DTI markers were obtained from 36 patients with amnestic MCI and 16 age-matched controls without cognitive impairment, for whom widely used neurocognitive scores were available. These markers and scores were subsequently compared in terms of statistical delineation between patients and controls., Results: It was found that statistically significant delineation between MCI patients and controls was comparable for DVR or DTI markers (p < 0.01). The performance of both types of markers was consistent with the scores of some (but not all) widely used neurocognitive tests., Conclusion: Since DTI offers a measure of cerebral white matter integrity, the results suggest that the model-based hemodynamic marker of DVR may correlate with cognitive impairment due to white matter lesions. This finding is consistent with the hypothesis that dysregulation of cerebral microcirculation may be an early cause of cognitive impairment, which has been recently corroborated by several studies., (© 2019 The Authors. Brain and Behavior published by Wiley Periodicals, Inc.)

Parameters describing dynamic cerebral autoregulation (DCA) have limited reproducibility. In an international, multi-center study, we evaluated the influence of multiple analytical methods on the reproducibility of DCA. Fourteen participating centers analyzed repeated measurements from 75 healthy subjects, consisting of 5 min of spontaneous fluctuations in blood pressure and cerebral blood flow velocity signals, based on their usual methods of analysis. DCA methods were grouped into three broad categories, depending on output types: (1) transfer function analysis (TFA); (2) autoregulation index (ARI); and (3) correlation coefficient. Only TFA gain in the low frequency (LF) band showed good reproducibility in approximately half of the estimates of gain, defined as an intraclass correlation coefficient (ICC) of >0.6. None of the other DCA metrics had good reproducibility. For TFA-like and ARI-like methods, ICCs were lower than values obtained with surrogate data ( p < 0.05). For TFA-like methods, ICCs were lower for the very LF band (gain 0.38 ± 0.057, phase 0.17 ± 0.13) than for LF band (gain 0.59 ± 0.078, phase 0.39 ± 0.11, p ≤ 0.001 for both gain and phase). For ARI-like methods, the mean ICC was 0.30 ± 0.12 and for the correlation methods 0.24 ± 0.23. Based on comparisons with ICC estimates obtained from surrogate data, we conclude that physiological variability or non-stationarity is likely to be the main reason for the poor reproducibility of DCA parameters.

Analysis of beat-to-beat spontaneous cerebral hemodynamic data has yielded predictive dynamic models of cerebral hemodynamics and has shown previously that patients with Mild Cognitive Impairment (MCI) exhibit significantly reduced cerebral vasomotor reactivity to CO 2 relative to cognitively normal control subjects [1]. The present work examines the heart-rate reflex (HRR) dynamics of 46 MCI patients compared to 20 control subjects, using closed-loop modeling of HRR under resting conditions of spontaneous variations of arterial blood pressure (baroreflex) and end-tidal CO 2 (chemoreflex). These subject-specific predictive dynamic models are obtained via the methodology of Principal Dynamic Modes [2] and allow the computation of model-based markers of baroreflex and chemoreflex function. We found that the chemoreflex gain is significantly weakened in MCI patients relative to controls (p=0.0086), while the baroreflex is not significantly affected. These findings offer another tool for diagnosis and monitoring of MCI (via model-based markers), when used in conjunction with current methods.

This letter proposes a novel method, multi-input, multi-output neuronal mode network (MIMO-NMN), for modeling encoding dynamics and functional connectivity in neural ensembles such as the hippocampus. Compared with conventional approaches such as the Volterra-Wiener model, linear-nonlinear-cascade (LNC) model, and generalized linear model (GLM), the NMN has several advantages in terms of estimation accuracy, model interpretation, and functional connectivity analysis. We point out the limitations of current neural spike modeling methods, especially the estimation biases caused by the imbalanced class problem when the number of zeros is significantly larger than ones in the spike data. We use synthetic data to test the performance of NMN with a comparison of the traditional methods, and the results indicate the NMN approach could reduce the imbalanced class problem and achieve better predictions. Subsequently, we apply the MIMO-NMN method to analyze data from the human hippocampus. The results indicate that the MIMO-NMN method is a promising approach to modeling neural dynamics and analyzing functional connectivity of multi-neuronal data.

Objective: Different methods to calculate dynamic cerebral autoregulation (dCA) parameters are available. However, most of these methods demonstrate poor reproducibility that limit their reliability for clinical use. Inter-centre differences in study protocols, modelling approaches and default parameter settings have all led to a lack of standardisation and comparability between studies. We evaluated reproducibility of dCA parameters by assessing systematic errors in surrogate data resulting from different modelling techniques., Approach: Fourteen centres analysed 22 datasets consisting of two repeated physiological blood pressure measurements with surrogate cerebral blood flow velocity signals, generated using Tiecks curves (autoregulation index, ARI 0-9) and added noise. For reproducibility, dCA methods were grouped in three broad categories: 1. Transfer function analysis (TFA)-like output; 2. ARI-like output; 3. Correlation coefficient-like output. For all methods, reproducibility was determined by one-way intraclass correlation coefficient analysis (ICC)., Main Results: For TFA-like methods the mean (SD; [range]) ICC gain was 0.71 (0.10; [0.49-0.86]) and 0.80 (0.17; [0.36-0.94]) for VLF and LF (p  =  0.003) respectively. For phase, ICC values were 0.53 (0.21; [0.09-0.80]) for VLF, and 0.92 (0.13; [0.44-1.00]) for LF (p  <  0.001). Finally, ICC for ARI-like methods was equal to 0.84 (0.19; [0.41-0.94]), and for correlation-like methods, ICC was 0.21 (0.21; [0.056-0.35])., Significance: When applied to realistic surrogate data, free from the additional exogenous influences of physiological variability on cerebral blood flow, most methods of dCA modelling showed ICC values considerably higher than what has been reported for physiological data. This finding suggests that the poor reproducibility reported by previous studies may be mainly due to the inherent physiological variability of cerebral blood flow regulatory mechanisms rather than related to (stationary) random noise and the signal analysis methods.

Objective: We demonstrate here the first successful implementation in humans of a proof-of-concept system for restoring and improving memory function via facilitation of memory encoding using the patient's own hippocampal spatiotemporal neural codes for memory. Memory in humans is subject to disruption by drugs, disease and brain injury, yet previous attempts to restore or rescue memory function in humans typically involved only nonspecific, modulation of brain areas and neural systems related to memory retrieval., Approach: We have constructed a model of processes by which the hippocampus encodes memory items via spatiotemporal firing of neural ensembles that underlie the successful encoding of short-term memory. A nonlinear multi-input, multi-output (MIMO) model of hippocampal CA3 and CA1 neural firing is computed that predicts activation patterns of CA1 neurons during the encoding (sample) phase of a delayed match-to-sample (DMS) human short-term memory task., Main Results: MIMO model-derived electrical stimulation delivered to the same CA1 locations during the sample phase of DMS trials facilitated short-term/working memory by 37% during the task. Longer term memory retention was also tested in the same human subjects with a delayed recognition (DR) task that utilized images from the DMS task, along with images that were not from the task. Across the subjects, the stimulated trials exhibited significant improvement (35%) in both short-term and long-term retention of visual information., Significance: These results demonstrate the facilitation of memory encoding which is an important feature for the construction of an implantable neural prosthetic to improve human memory.

Neurostimulation is a promising therapy for abating epileptic seizures. However, it is extremely difficult to identify optimal stimulation patterns experimentally. In this study, human recordings are used to develop a functional 24 neuron network statistical model of hippocampal connectivity and dynamics. Spontaneous seizure-like activity is induced in silico in this reconstructed neuronal network. The network is then used as a testbed to design and validate a wide range of neurostimulation patterns. Commonly used periodic trains were not able to permanently abate seizures at any frequency. A simulated annealing global optimization algorithm was then used to identify an optimal stimulation pattern, which successfully abated 92% of seizures. Finally, in a fully responsive, or closed-loop, neurostimulation paradigm, the optimal stimulation successfully prevented the network from entering the seizure state. We propose that the framework presented here for algorithmically identifying patient-specific neurostimulation patterns can greatly increase the efficacy of neurostimulation devices for seizures.

In order to build hippocampal prostheses for restoring memory functions, we build sparse multi-input, multi-output (MIMO) nonlinear dynamical models of the human hippocampus. Spike trains are recorded from hippocampal CA3 and CA1 regions of epileptic patients performing a variety of memory-dependent delayed match-to-sample (DMS) tasks. Using CA3 and CA1 spike trains as inputs and outputs respectively, sparse generalized Laguerre-Volterra models are estimated with group lasso and local coordinate descent methods to capture the nonlinear dynamics underlying the CA3-CA1 spike train transformations. These models can accurately predict the CA1 spike trains based on the ongoing CA3 spike trains during multiple memory events, e.g., sample presentation, sample response, match presentation and match response, of the DMS task, and thus will serve as the computational basis of human hippocampal memory prostheses.

This letter examines the results of input-output (nonparametric) modeling based on the analysis of data generated by a mechanism-based (parametric) model of CA3-CA1 neuronal connections in the hippocampus. The motivation is to obtain biological insight into the interpretation of such input-output (Volterra-equivalent) models estimated from synthetic data. The insights obtained may be subsequently used to interpretat input-output models extracted from actual experimental data. Specifically, we found that a simplified parametric model may serve as a useful tool to study the signal transformations in the hippocampal CA3-CA1 regions. Input-output modeling of model-based synthetic data show that GABAergic interneurons are responsible for regulating neuronal excitation, controlling the precision of spike timing, and maintaining network oscillations, in a manner consistent with previous studies. The input-output model obtained from real data exhibits intriguing similarities with its synthetic-data counterpart, demonstrating the importance of a dynamic resonance in the system/model response around 2 Hz to 3 Hz. Using the input-output model from real data as a guide, we may be able to amend the parametric model by incorporating more mechanisms in order to yield better-matching input-output model. The approach we present can also be applied to the study of other neural systems and pathways.

Computational neuroscience is a field that traces its origins to the efforts of Hodgkin and Huxley, who pioneered quantitative analysis of electrical activity in the nervous system. While also continuing as an independent field, computational neuroscience has combined with computational systems biology, and neural multiscale modeling arose as one offshoot. This consolidation has added electrical, graphical, dynamical system, learning theory, artificial intelligence and neural network viewpoints with the microscale of cellular biology (neuronal and glial), mesoscales of vascular, immunological and neuronal networks, on up to macroscales of cognition and behavior. The complexity of linkages that produces pathophysiology in neurological, neurosurgical and psychiatric disease will require multiscale modeling to provide understanding that exceeds what is possible with statistical analysis or highly simplified models: how to bring together pharmacotherapeutics with neurostimulation, how to personalize therapies, how to combine novel therapies with neurorehabilitation, how to interlace periodic diagnostic updates with frequent reevaluation of therapy, how to understand a physical disease that manifests as a disease of the mind. Multiscale modeling will also help to extend the usefulness of animal models of human diseases in neuroscience, where the disconnects between clinical and animal phenomenology are particularly pronounced. Here we cover areas of particular interest for clinical application of these new modeling neurotechnologies, including epilepsy, traumatic brain injury, ischemic disease, neurorehabilitation, drug addiction, schizophrenia and neurostimulation.

In this paper, we have introduced a general modeling approach for dynamic nonlinear systems that utilizes a variant of the simulated annealing algorithm for training the Laguerre-Volterra network (LVN) to overcome the local minima and convergence problems and employs a pruning technique to achieve sparse LVN representations with l 1 regularization. We tested this new approach with computer simulated systems and extended it to autoregressive sparse LVN (ASLVN) model structures that are suitable for input-output modeling of nonlinear systems that exhibit transitions in dynamic states, such as the Hodgkin-Huxley (H-H) equations of neuronal firing. Application of the proposed ASLVN to the H-H equations yields a more parsimonious input-output model with improved predictive capability that is amenable to more insightful physiological/biological interpretation.

Much of the research on cannabinoids (CBs) has focused on their effects at the molecular and synaptic level. However, the effects of CBs on the dynamics of neural circuits remains poorly understood. This study aims to disentangle the effects of CBs on the functional dynamics of the hippocampal Schaffer collateral synapse by using data-driven nonparametric modeling. Multi-unit activity was recorded from rats doing an working memory task in control sessions and under the influence of exogenously administered tetrahydrocannabinol (THC), the primary CB found in marijuana. It was found that THC left firing rate unaltered and only slightly reduced theta oscillations. Multivariate autoregressive models, estimated from spontaneous spiking activity, were then used to describe the dynamical transformation from CA3 to CA1. They revealed that THC served to functionally isolate CA1 from CA3 by reducing feedforward excitation and theta information flow. The functional isolation was compensated by increased feedback excitation within CA1, thus leading to unaltered firing rates. Finally, both of these effects were shown to be correlated with memory impairments in the working memory task. By elucidating the circuit mechanisms of CBs, these results help close the gap in knowledge between the cellular and behavioral effects of CBs.

Objective: As an extension to our study comparing a putative compartmental and data-based model of linear dynamic cerebral autoregulation (CA) and CO 2 -vasomotor reactivity (VR), we study the CA-VR process in a nonlinear context., Methods: We use the concept of principal dynamic modes (PDM) in order to obtain a compact and more easily interpretable input-output model. This in silico study permits the use of input data with a dynamic range large enough to simulate the classic homeostatic CA and VR curves using a putative structural model of the regulatory control of the cerebral circulation. The PDM model obtained using theoretical and experimental data are compared., Results: It was found that the PDM model was able to reflect accurately both the simulated static CA and VR curves in the associated nonlinear functions (ANFs). Similar to experimental observations, the PDM model essentially separates the pressure-flow relationship into a linear component with fast dynamics and nonlinear components with slow dynamics. In addition, we found good qualitative agreement between the PDMs representing the dynamic theoretical and experimental CO 2 -flow relationship., Conclusion: Under the modeling assumption and in light of other experimental findings, we hypothesize that PDMs obtained from experimental data correspond with passive fluid dynamical and active regulatory mechanisms., Significance: Both hypothesis-based and data-based modeling approaches can be combined to offer some insight into the physiological basis of PDM model obtained from human experimental data. The PDM modeling approach potentially offers a practical way to quantify the status of specific regulatory mechanisms in the CA-VR process.

A nonparametric model of smooth muscle tension response to electrical stimulation was estimated using the Laguerre expansion technique of nonlinear system kernel estimation. The experimental data consisted of force responses of smooth muscle to energy-matched alternating single pulse and burst current stimuli. The burst stimuli led to at least a 10-fold increase in peak force in smooth muscle from Mytilus edulis, despite the constant energy constraint. A linear model did not fit the data. However, a second-order model fit the data accurately, so the higher-order models were not required to fit the data. Results showed that smooth muscle force response is not linearly related to the stimulation power.

Very productive collaborative investigations characterized how multineuron hippocampal ensembles recorded in nonhuman primates (NHPs) encode short-term memory necessary for successful performance in a delayed match to sample (DMS) task and utilized that information to devise a unique nonlinear multi-input multi-output (MIMO) memory prosthesis device to enhance short-term memory in real-time during task performance. Investigations have characterized how the hippocampus in primate brain encodes information in a multi-item, rule-controlled, delayed match to sample (DMS) task. The MIMO model was applied via closed loop feedback micro-current stimulation during the task via conformal electrode arrays and enhanced performance of the complex memory requirements. These findings clearly indicate detection of a means by which the hippocampus encodes information and transmits this information to other brain regions involved in memory processing. By employing the nonlinear dynamic multi-input/multi-output (MIMO) model, developed and adapted to hippocampal neural ensemble firing patterns derived from simultaneous recorded multi-neuron CA1 and CA3 activity, it was possible to extract information encoded in the Sample phase of DMS trials that was necessary for successful performance in the subsequent Match phase of the task. The extension of this MIMO model to online delivery of electrical stimulation patterns to the same recording loci that exhibited successful CA1 firing in the DMS Sample Phase provided the means to increase task performance on a trial-by-trial basis. Increased utility of the MIMO model as a memory prosthesis was exhibited by the demonstration of cumulative increases in DMS task performance with repeated MIMO stimulation over many sessions. These results, reported below in this article, provide the necessary demonstrations to further the feasibility of the MIMO model as a memory prosthesis to recover and/or enhance encoding of cognitive information in humans with memory disruptions resulting from brain injury, disease or aging., (Copyright © 2016 Elsevier Inc. All rights reserved.)

We recently introduced model-based "physiomarkers" of dynamic cerebral autoregulation and CO2 vasomotor reactivity as an aid for diagnosis of early-stage Alzheimer's disease (AD) [1], where significant impairment of dynamic vasomotor reactivity (DVR) was observed in early-stage AD patients relative to age-matched controls. Milder impairment of DVR was shown in patients with amnestic mild cognitive impairment (MCI) using the same approach in a subsequent study [2]. The advocated approach utilizes subject-specific data-based models of cerebral hemodynamics to quantify the dynamic effects of resting-state changes in arterial blood pressure and end-tidal CO2 (the putative inputs) upon cerebral blood flow velocity (the putative output) measured at the middle cerebral artery via transcranial Doppler (TCD). The obtained input-output models are then used to compute model-based indices of DCA and DVR from model-predicted responses to an input pressure pulse or an input CO2 pulse, respectively. In this paper, we compare these model-based indices of DVR and DCA in 46 amnestic MCI patients, relative to 20 age-matched controls, using TCD measurements with their counterparts using Near-Infrared Spectroscopy (NIRS) measurements of blood oxygenation at the lateral prefrontal cortex in 43 patients and 22 age-matched controls. The goal of the study is to assess whether NIRS measurements can be used instead of TCD measurements to obtain model-based physiomarkers with comparable diagnostic utility. The results corroborate this view in terms of the ability of either output to yield model-based physiomarkers that can differentiate the group of aMCI patients from age-matched healthy controls.

To understand how memory information is encoded in the hippocampus, we build classification models to decode memory features from hippocampal CA3 and CA1 spatio-temporal patterns of spikes recorded from epilepsy patients performing a memory-dependent delayed match-to-sample task. The classification model consists of a set of B-spline basis functions for extracting memory features from the spike patterns, and a sparse logistic regression classifier for generating binary categorical output of memory features. Results show that classification models can extract significant amount of memory information with respects to types of memory tasks and categories of sample images used in the task, despite the high level of variability in prediction accuracy due to the small sample size. These results support the hypothesis that memories are encoded in the hippocampal activities and have important implication to the development of hippocampal memory prostheses.

Objective: Traditional hippocampal modeling has focused on the series of feedforward synapses known as the trisynaptic pathway. However, feedback connections from CA1 back to the hippocampus through the entorhinal cortex (EC) actually make the hippocampus a closed-loop system. By constructing a functional closed-loop model of the hippocampus, one may learn how both physiological and epileptic oscillations emerge and design efficient neurostimulation patterns to abate such oscillations., Approach: Point process input-output models where estimated from recorded rodent hippocampal data to describe the nonlinear dynamical transformation from CA3 → CA1, via the schaffer-collateral synapse, and CA1 → CA3 via the EC. Each Volterra-like subsystem was composed of linear dynamics (principal dynamic modes) followed by static nonlinearities. The two subsystems were then wired together to produce the full closed-loop model of the hippocampus., Main Results: Closed-loop connectivity was found to be necessary for the emergence of theta resonances as seen in recorded data, thus validating the model. The model was then used to identify frequency parameters for the design of neurostimulation patterns to abate seizures., Significance: Deep-brain stimulation (DBS) is a new and promising therapy for intractable seizures. Currently, there is no efficient way to determine optimal frequency parameters for DBS, or even whether periodic or broadband stimuli are optimal. Data-based computational models have the potential to be used as a testbed for designing optimal DBS patterns for individual patients. However, in order for these models to be successful they must incorporate the complex closed-loop structure of the seizure focus. This study serves as a proof-of-concept of using such models to design efficient personalized DBS patterns for epilepsy.

Fractality, represented as self-similar repeating patterns, is ubiquitous in nature and the brain. Dynamic patterns of hippocampal spike trains are known to exhibit multifractal properties during working memory processing; however, it is unclear whether the multifractal properties inherent to hippocampal spike trains reflect active cognitive processing. To examine this possibility, hippocampal neuronal ensembles were recorded from rats before, during and after a spatial working memory task following administration of tetrahydrocannabinol (THC), a memory-impairing component of cannabis. Multifractal detrended fluctuation analysis was performed on hippocampal interspike interval sequences to determine characteristics of monofractal long-range temporal correlations (LRTCs), quantified by the Hurst exponent, and the degree/magnitude of multifractal complexity, quantified by the width of the singularity spectrum. Our results demonstrate that multifractal firing patterns of hippocampal spike trains are a marker of functional memory processing, as they are more complex during the working memory task and significantly reduced following administration of memory impairing THC doses. Conversely, LRTCs are largest during resting state recordings, therefore reflecting different information compared to multifractality. In order to deepen conceptual understanding of multifractal complexity and LRTCs, these measures were compared to classical methods using hippocampal frequency content and firing variability measures. These results showed that LRTCs, multifractality, and theta rhythm represent independent processes, while delta rhythm correlated with multifractality. Taken together, these results provide a novel perspective on memory function by demonstrating that the multifractal nature of spike trains reflects hippocampal microcircuit activity that can be used to detect and quantify cognitive, physiological, and pathological states.

This paper presents a systems identification approach for studying the long-term synaptic plasticity using natural spiking activities. This approach consists of three modeling steps. First, a multi-input, single-output (MISO), nonlinear dynamical spiking neuron model is formulated to estimate and represent the synaptic strength in means of functional connectivity between input and output neurons. Second, this MISO model is extended to a nonstationary form to track the time-varying properties of the synaptic strength. Finally, a Volterra modeling method is used to extract the synaptic learning rule, e.g., spike-timing-dependent plasticity, for the explanation of the input-output nonstationarity as the consequence of the past input-output spiking patterns. This framework is developed to study the underlying mechanisms of learning and memory formation in behaving animals, and may serve as the computational basis for building the next-generation adaptive cortical prostheses., (Copyright © 2014 Elsevier B.V. All rights reserved.)

We develop an autoregressive model framework based on the concept of Principal Dynamic Modes (PDMs) for the process of action potential (AP) generation in the excitable neuronal membrane described by the Hodgkin-Huxley (H-H) equations. The model's exogenous input is injected current, and whenever the membrane potential output exceeds a specified threshold, it is fed back as a second input. The PDMs are estimated from the previously developed Nonlinear Autoregressive Volterra (NARV) model, and represent an efficient functional basis for Volterra kernel expansion. The PDM-based model admits a modular representation, consisting of the forward and feedback PDM bases as linear filterbanks for the exogenous and autoregressive inputs, respectively, whose outputs are then fed to a static nonlinearity composed of polynomials operating on the PDM outputs and cross-terms of pair-products of PDM outputs. A two-step procedure for model reduction is performed: first, influential subsets of the forward and feedback PDM bases are identified and selected as the reduced PDM bases. Second, the terms of the static nonlinearity are pruned. The first step reduces model complexity from a total of 65 coefficients to 27, while the second further reduces the model coefficients to only eight. It is demonstrated that the performance cost of model reduction in terms of out-of-sample prediction accuracy is minimal. Unlike the full model, the eight coefficient pruned model can be easily visualized to reveal the essential system components, and thus the data-derived PDM model can yield insight into the underlying system structure and function.

Although an anatomical connection from CA1 to CA3 via the Entorhinal Cortex (EC) and through backprojecting interneurons has long been known it exist, it has never been examined quantitatively on the single neuron level, in the in-vivo nonpatholgical, nonperturbed brain. Here, single spike activity was recorded using a multi-electrode array from the CA3 and CA1 areas of the rodent hippocampus (N = 7) during a behavioral task. The predictive power from CA3→CA1 and CA1→CA3 was examined by constructing Multivariate Autoregressive (MVAR) models from recorded neurons in both directions. All nonsignificant inputs and models were identified and removed by means of Monte Carlo simulation methods. It was found that 121/166 (73 %) CA3→CA1 models and 96/145 (66 %) CA1→CA3 models had significant predictive power, thus confirming a predictive 'Granger' causal relationship from CA1 to CA3. This relationship is thought to be caused by a combination of truly causal connections such as the CA1→EC→CA3 pathway and common inputs such as those from the Septum. All MVAR models were then examined in the frequency domain and it was found that CA3 kernels had significantly more power in the theta and beta range than those of CA1, confirming CA3's role as an endogenous hippocampal pacemaker.

Receptive field identification is a vital problem in sensory neurophysiology and vision. Much research has been done in identifying the receptive fields of nonlinear neurons whose firing rate is determined by the nonlinear interactions of a small number of linear filters. Despite more advanced methods that have been proposed, spike-triggered covariance (STC) continues to be the most widely used method in such situations due to its simplicity and intuitiveness. Although the connection between STC and Wiener/Volterra kernels has often been mentioned in the literature, this relationship has never been explicitly derived. Here we derive this relationship and show that the STC matrix is actually a modified version of the second-order Wiener kernel, which incorporates the input autocorrelation and mixes first- and second-order dynamics. It is then shown how, with little modification of the STC method, the Wiener kernels may be obtained and, from them, the principal dynamic modes, a set of compact and efficient linear filters that essentially combine the spike-triggered average and STC matrix and generalize to systems with both continuous and point-process outputs. Finally, using Wiener theory, we show how these obtained filters may be corrected when they were estimated using correlated inputs. Our correction technique is shown to be superior to those commonly used in the literature for both correlated Gaussian images and natural images.

In order to build hippocampal prostheses for restoring memory functions, we build multi-input, multi-output (MIMO) nonlinear dynamical models of the human hippocampus. Spike trains are recorded from the hippocampal CA3 and CA1 regions of epileptic patients performing a memory-dependent delayed match-to-sample task. Using CA3 and CA1 spike trains as inputs and outputs respectively, second-order sparse generalized Laguerre-Volterra models are estimated with group lasso and local coordinate descent methods to capture the nonlinear dynamics underlying the spike train transformations. These models can accurately predict the CA1 spike trains based on the ongoing CA3 spike trains and thus will serve as the computational basis of the hippocampal memory prosthesis.

One key problem in computational neuroscience and neural engineering is the identification and modeling of functional connectivity in the brain using spike train data. To reduce model complexity, alleviate overfitting, and thus facilitate model interpretation, sparse representation and estimation of functional connectivity is needed. Sparsities include global sparsity, which captures the sparse connectivities between neurons, and local sparsity, which reflects the active temporal ranges of the input-output dynamical interactions. In this paper, we formulate a generalized functional additive model (GFAM) and develop the associated penalized likelihood estimation methods for such a modeling problem. A GFAM consists of a set of basis functions convolving the input signals, and a link function generating the firing probability of the output neuron from the summation of the convolutions weighted by the sought model coefficients. Model sparsities are achieved by using various penalized likelihood estimations and basis functions. Specifically, we introduce two variations of the GFAM using a global basis (e.g., Laguerre basis) and group LASSO estimation, and a local basis (e.g., B-spline basis) and group bridge estimation, respectively. We further develop an optimization method based on quadratic approximation of the likelihood function for the estimation of these models. Simulation and experimental results show that both group-LASSO-Laguerre and group-bridge-B-spline can capture faithfully the global sparsities, while the latter can replicate accurately and simultaneously both global and local sparsities. The sparse models outperform the full models estimated with the standard maximum likelihood method in out-of-sample predictions.

A methodology for nonlinear modeling of multi-input multi-output (MIMO) neuronal systems is presented that utilizes the concept of Principal Dynamic Modes (PDM). The efficacy of this new methodology is demonstrated in the study of the dynamic interactions between neuronal ensembles in the Pre-Frontal Cortex (PFC) of a behaving non-human primate (NHP) performing a Delayed Match-to-Sample task. Recorded spike trains from Layer-2 and Layer-5 neurons were viewed as the "inputs" and "outputs", respectively, of a putative MIMO system/model that quantifies the dynamic transformation of multi-unit neuronal activity between Layer-2 and Layer-5 of the PFC. Model prediction performance was evaluated by means of computed Receiver Operating Characteristic (ROC) curves. The PDM-based approach seeks to reduce the complexity of MIMO models of neuronal ensembles in order to enable the practicable modeling of large-scale neural systems incorporating hundreds or thousands of neurons, which is emerging as a preeminent issue in the study of neural function. The "scaling-up" issue has attained critical importance as multi-electrode recordings are increasingly used to probe neural systems and advance our understanding of integrated neural function. The initial results indicate that the PDM-based modeling methodology may greatly reduce the complexity of the MIMO model without significant degradation of performance. Furthermore, the PDM-based approach offers the prospect of improved biological/physiological interpretation of the obtained MIMO models.

We propose a new variant of Volterra-type model with a nonlinear auto-regressive (NAR) component that is a suitable framework for describing the process of AP generation by the neuron membrane potential, and we apply it to input-output data generated by the Hodgkin-Huxley (H-H) equations. Volterra models use a functional series expansion to describe the input-output relation for most nonlinear dynamic systems, and are applicable to a wide range of physiologic systems. It is difficult, however, to apply the Volterra methodology to the H-H model because is characterized by distinct subthreshold and suprathreshold dynamics. When threshold is crossed, an autonomous action potential (AP) is generated, the output becomes temporarily decoupled from the input, and the standard Volterra model fails. Therefore, in our framework, whenever membrane potential exceeds some threshold, it is taken as a second input to a dual-input Volterra model. This model correctly predicts membrane voltage deflection both within the subthreshold region and during APs. Moreover, the model naturally generates a post-AP afterpotential and refractory period. It is known that the H-H model converges to a limit cycle in response to a constant current injection. This behavior is correctly predicted by the proposed model, while the standard Volterra model is incapable of generating such limit cycle behavior. The inclusion of cross-kernels, which describe the nonlinear interactions between the exogenous and autoregressive inputs, is found to be absolutely necessary. The proposed model is general, non-parametric, and data-derived.

Conformal ceramic electrodes utilized in prior recordings of nonhuman primate prefrontal cortical layer 2/3 and layer 5 neurons were used in this study to record tonic glutamate concentration and transient release in layer 2/3 PFC. Tonic glutamate concentration increased in the Match (decision) phase of a visual delayed-match-to-sample (DMS) task, while increased transient glutamate release occurred in the Sample (encoding) phase of the task. Further, spatial vs. object-oriented DMS trials evoked differential changes in glutamate concentration. Thus the same conformal recording electrodes were capable of electrophysiological and electrochemical recording, and revealed similar evidence of neural processing in layers 2/3 and layer 5 during cognitive processing in a behavioral task.

The right level of abstraction for a model mimicking a neural function is often difficult to determine. There are trade-offs between capturing biological complexities on one hand and the scalability and efficiency of the model on the other. In this work, we describe a nonlinear Laguerre-Volterra model of the synaptic temporal integration of input spikes to postsynaptic potentials. This model is then efficiently implemented using analog subthreshold circuits and can serve as a foundation for future large-scale hardware systems that can emulate multi-input multi-output (MIMO) spike transformations in populations of neurons. The normalized mean square error in estimating real data using the circuit implementation of this model is less than 15%. The model components are modular and its parameters are adjustable for modeling temporal integration by neurons in other brain regions. The total power consumption of this nonlinear Laguerre-Volterra system is less than 5nW.

The prefrontal cortex (PFC) has been postulated to play critical roles in cognitive control and the formation of long-term memories. To gain insights into the neurobiological mechanism of such high-order cognitive functions, it is important to understand the input-output transformational properties of the PFC micro-circuitry. In this study, we identify the functional connectivity between the Layer 2/3 (input) neurons and the Layer 5 (output) neurons using a previously developed generalized Volterra model (GVM). Input-output spike trains are recorded from the PFCs of nonhuman primates performing a memory-dependent delayed match-to-sample task with a customized conformal ceramic multi-electrode array. The GVM describes how the input spike trains are transformed into the output spike trains by the PFC micro-circuitry and represents the transformation in the form of Volterra kernels. Results show that Layer 2/3 neurons have strong and transient facilitatory effects on the firings of Layer 5 neurons. The magnitude and temporal range of the input-output nonlinear dynamics are strikingly different from those of the hippocampal CA3-CA1. This form of functional connectivity may have important implications to understanding the computational principle of the PFC.

It has previously been demonstrated that the detrimental effect on the performance of a delayed nonmatch to sample (DNMS) memory task by exogenously administered cannabinoid (CB1) receptor agonist, WIN 55212-2 (WIN), is reversed by the receptor antagonist rimonabant. In addition, rimonabant administered alone elevates DNMS performance, presumably through the suppression of negative modulation by released endocannabinoids during normal task performance. Other investigations have shown that rimonabant enhances encoding of DNMS task-relevant information on a trial-by-trial, delay-dependent basis. In this study, these reciprocal pharmacological actions were completely characterized by long-term, chronic intrahippocampal infusion of both agents (WIN and rimonabant) in successive 2-week intervals. Such long-term exposure allowed extraction and confirmation of task-related firing patterns, in which rimonabant reversed the effects of CB1 agonists. This information was then utilized to artificially impose the facilitatory effects of rimonabant and to reverse the effects of WIN on DNMS performance, by delivering multichannel electrical stimulation in the same firing patterns to the same hippocampal regions. Direct comparison of normal and WIN-injected subjects, in which rimonabant injections and ensemble firing facilitated performance, verified reversal of the modulation of hippocampal memory processes by CB1 receptor agonists, including released endocannabinoids.

To develop hippocampal prosthetic devices that can restore the memory-dependent cognitive functions lost in diseases or injuries, it is essential to build a computational model that sufficiently captures the transformations of multiple memories performed by hippocampal sub-regions. A universal model with a single set of coefficients for all memories is desirable, since it can transform the memories without explicitly knowing what those memories represent and thus avoids switching between multiple models for multiple memories in implementation. In this study, we test the feasibility of such universal models of hippocampal CA3-CA1 by estimating the multi-input, multi-output (MEMO) nonlinear dynamic models using input (CA3) and output (CA1) spike trains recorded during multiple behavioral events representing multiple memories from rats performing a delayed nonmatch-to-sample task. We further statistically evaluated the model performances of the MEMO models on the different events. Results show that the models accurately replicate the output spike patterns during those events, and thus can be used as event-invariant nonlinear dynamic models that continuously predict the ongoing CA1 spatio-temporal patterns as the ongoing CA3 spatio-temporal patterns unfold.

Developing a neural prosthesis for the damaged hippocampus requires restoring the transformation of population neural activities performed by the hippocampal circuitry. To bypass a damaged region, output spike trains need to be predicted from the input spike trains and then reinstated through stimulation. We formulate a multiple-input, multiple-output (MIMO) nonlinear dynamic model for the input-output transformation of spike trains. In this approach, a MIMO model comprises a series of physiologically-plausible multiple-input, single-output (MISO) neuron models that consist of five components each: (1) feedforward Volterra kernels transforming the input spike trains into the synaptic potential, (2) a feedback kernel transforming the output spikes into the spike-triggered after-potential, (3) a noise term capturing the system uncertainty, (4) an adder generating the pre-threshold potential, and (5) a threshold function generating output spikes. It is shown that this model is equivalent to a generalized linear model with a probit link function. To reduce model complexity and avoid overfitting, statistical model selection and cross-validation methods are employed to choose the significant inputs and interactions between inputs. The model is applied successfully to the hippocampal CA3-CA1 population dynamics. Such a model can serve as a computational basis for the development of hippocampal prostheses.

Despite the rich innervation of the cerebral vasculature by both sympathetic and parasympathetic nerves, the role of autonomic control in cerebral circulation and, particularly, cerebral hemodynamics is not entirely clear. Previous animal studies have reported inconsistent results regarding the effects of electrical stimulation or denervation on cerebral blood flow (CBF), cerebral pressure-flow relationship, and cerebral vessel response to metabolic stimuli. Moreover, with the advance of transcranial Doppler ultrasound (TCD), which yields accurate measurements of CBF velocity (CBFV) with high time resolution, it has been found that in humans CBFV in the middle cerebral artery decreased substantially during lower body negative pressure (LBNP) and head-up tilt in the absence of systemic hypotension, which suggests the presence of cerebral vasoconstriction associated with augmented sympathetic nerve activity during orthostatic stress. These observations were based on assessing static measures of cerebral circulation, i.e., mean values of artevial blood pressure (ABP) and CBF with a low time resolution.

This paper presents the results of a computational study that compares simulated compartmental (differential equation) and Volterra models of the dynamic effects of insulin on blood glucose concentration in humans. In the first approach, we employ the widely accepted "minimal model" and an augmented form of it, which incorporates the effect of insulin secretion by the pancreas, in order to represent the actual closed-loop operating conditions of the system, and in the second modeling approach, we employ the general class of Volterra-type models that are estimated from input-output data. We demonstrate both the equivalence between the two approaches analytically and the feasibility of obtaining accurate Volterra models from insulin-glucose data generated from the compartmental models. The results corroborate the proposition that it may be preferable to obtain data-driven (i.e., inductive) models in a more general and realistic operating context, without resorting to the restrictive prior assumptions and simplifications regarding model structure and/or experimental protocols (e.g., glucose tolerance tests) that are necessary for the compartmental models proposed previously. These prior assumptions may lead to results that are improperly constrained or biased by preconceived (and possibly erroneous) notions-a risk that is avoided when we let the data guide the inductive selection of the appropriate model within the general class of Volterra-type models, as our simulation results suggest.