Membrane depolarization mediates both the inhibition of neural activity and cell-type-differences in response to high-frequency stimulation.

Neuromodulation using high frequency (>1 kHz) electric stimulation (HFS) enables preferential activation or inhibition of individual neural types, offering the possibility of more effective treatments across a broad spectrum of neurological diseases. To improve effectiveness, it is important to better understand the mechanisms governing activation and inhibition with HFS so that selectivity can be optimized. In this study, we measure the membrane potential (Vm) and spiking responses of ON and OFF α-sustained retinal ganglion cells (RGCs) to a wide range of stimulus frequencies (100-2500 Hz) and amplitudes (10-100 µA). Our findings indicate that HFS induces shifts in Vm, with both the strength and polarity of the shifts dependent on the stimulus conditions. Spiking responses in each cell directly correlate with the shifts in Vm, where strong depolarization leads to spiking suppression. Comparisons between the two cell types reveal that ON cells are more depolarized by a given amplitude of HFS than OFF cells-this sensitivity difference enables the selective targeting. Computational modeling indicates that ion-channel dynamics largely account for the shifts in Vm, suggesting that a better understanding of the differences in ion-channel properties across cell types may improve the selectivity and ultimately, enhance HFS-based neurostimulation strategies.

Nanoparticle-based optical interfaces for retinal neuromodulation: a review.

Degeneration of photoreceptors in the retina is a leading cause of blindness, but commonly leaves the retinal ganglion cells (RGCs) and/or bipolar cells extant. Consequently, these cells are an attractive target for the invasive electrical implants colloquially known as "bionic eyes." However, after more than two decades of concerted effort, interfaces based on conventional electrical stimulation approaches have delivered limited efficacy, primarily due to the current spread in retinal tissue, which precludes high-acuity vision. The ideal prosthetic solution would be less invasive, provide single-cell resolution and an ability to differentiate between different cell types. Nanoparticle-mediated approaches can address some of these requirements, with particular attention being directed at light-sensitive nanoparticles that can be accessed via the intrinsic optics of the eye. Here we survey the available known nanoparticle-based optical transduction mechanisms that can be exploited for neuromodulation. We review the rapid progress in the field, together with outstanding challenges that must be addressed to translate these techniques to clinical practice. In particular, successful translation will likely require efficient delivery of nanoparticles to stable and precisely defined locations in the retinal tissues. Therefore, we also emphasize the current literature relating to the pharmacokinetics of nanoparticles in the eye. While considerable challenges remain to be overcome, progress to date shows great potential for nanoparticle-based interfaces to revolutionize the field of visual prostheses.

Understanding visual processing of motion: completing the picture using experimentally driven computational models of MT.

Computational modeling helps neuroscientists to integrate and explain experimental data obtained through neurophysiological and anatomical studies, thus providing a mechanism by which we can better understand and predict the principles of neural computation. Computational modeling of the neuronal pathways of the visual cortex has been successful in developing theories of biological motion processing. This review describes a range of computational models that have been inspired by neurophysiological experiments. Theories of local motion integration and pattern motion processing are presented, together with suggested neurophysiological experiments designed to test those hypotheses.

Central stress pathways in the development of cardiovascular disease.

PURPOSE: Mental stress is of essential consideration when assessing cardiovascular pathophysiology in all patient populations. Substantial evidence indicates associations among stress, cardiovascular disease and aberrant brain-body communication. However, our understanding of the flow of stress information in humans, is limited, despite the crucial insights this area may offer into future therapeutic targets for clinical intervention. METHODS: Key terms including mental stress, cardiovascular disease and central control, were searched in PubMed, ScienceDirect and Scopus databases. Articles indicative of heart rate and blood pressure regulation, or central control of cardiovascular disease through direct neural innervation of the cardiac, splanchnic and vascular regions were included. Focus on human neuroimaging research and the flow of stress information is described, before brain-body connectivity, via pre-motor brainstem intermediates is discussed. Lastly, we review current understandings of pathophysiological stress and cardiovascular disease aetiology. RESULTS: Structural and functional changes to corticolimbic circuitry encode stress information, integrated by the hypothalamus and amygdala. Pre-autonomic brain-body relays to brainstem and spinal cord nuclei establish dysautonomia and lead to alterations in baroreflex functioning, firing of the sympathetic fibres, cellular reuptake of norepinephrine and withdrawal of the parasympathetic reflex. The combined result is profoundly adrenergic and increases the likelihood of cardiac myopathy, arrhythmogenesis, coronary ischaemia, hypertension and the overall risk of future sudden stress-induced heart failure. CONCLUSIONS: There is undeniable support that mental stress contributes to the development of cardiovascular disease. The emerging accumulation of large-scale multimodal neuroimaging data analytics to assess this relationship promises exciting novel therapeutic targets for future cardiovascular disease detection and prevention.

Video See-Through Pipelines for Virtual Reality Headsets and their Impact on Gait.

This study investigated the impact of different video see-through pipelines in virtual reality on gait. A mobility task was conducted with healthy participants to evaluate the gait adaptions using different video see-through pipelines. The gait parameters observed for this study were stride length, maximum toe clearance and walking speed. The results showed an impact on gait where the gait parameters were reduced when participants used a high latency and restricted field of view pipeline. However, when participants used a pipeline with low latency and a field of view closer to normal vision, less impact on gait was achieved. As virtual reality poses a promising future for gait rehabilitation in patients with Parkinson's disease, this result highlights the need to carefully consider the video see-through pipeline and display characteristics when considering its use for gait rehabilitation or mobility studies in general.Clinical relevance- This study demonstrates the impact of virtual reality systems on gait using different video see- through pipelines during a mobility task. This may be useful for clinicians who use virtual reality in gait rehabilitation and aid them in choosing the most suitable virtual reality system for therapy.

Self-Attention Based Vision Processing for Prosthetic Vision.

We investigate Self-Attention (SA) networks for directly learning visual representations for prosthetic vision. Specifically, we explore how the SA mechanism can be leveraged to produce task-specific scene representations for prosthetic vision, overcoming the need for explicit hand-selection of learnt features and post-processing. Further, we demonstrate how the mapping of importance to image regions can serve as an explainability tool to analyse the learnt vision processing behaviour, providing enhanced validation and interpretation capability than current learning-based methods for prosthetic vision. We investigate our approach in the context of an orientation and mobility (OM) task, and demonstrate its feasibility for learning vision processing pipelines for prosthetic vision.

Effect of Stimulation Current in Transcutaneous Vagus Nerve Stimulation (tVNS): A Study Using Concurrent Magnetoencephalography (MEG).

Transcutaneous vagus nerve stimulation (tVNS) is a non-invasive method of brain stimulation that has been investigated for its use in the clinical treatment of a number of different conditions. There has been little investigation into the stimulation current that is delivered and the effect on individual variability in response to tVNS.Seventeen participants underwent tVNS, and stimulation current was determined based on individual pain threshold. To investigate individual variability, brain dynamics were measured concurrently using magnetoencephalography (MEG) in response to two different stimulation protocols of tVNS. The first protocol consisted of a sequence of equally spaced short (1ms) stimulation pulses applied 24 times per second (24 Hz), and the second consisted of a sequence of 24 pulses per second spaced according to a 6 Hz pulse frequency modulation (PFM). Both stimulation sequences were delivered to the cymba concha in the left ear.The difference in brain responses to the two sequences was initially calculated using a one-sample t-test at the group level, based on z-scoring of the data at the individual level, and no statistically significant differences were observed. Further investigation of individual variability suggested that participants fell into two groups; one that responded more strongly to 24 Hz and one that responded more strongly to the irregular spacing of pulses in the PFM protocol.We tested whether the stimulation current that the participant received could predict how they would respond to the stimulation, but we did not observe any correlation. This supports the literature that suggests that selecting stimulation current based on individual pain threshold is a suitable procedure for tVNS, and higher stimulation intensities does not correspond to stronger brain response. Further investigation into individual variability in response to different frequencies and pulse spacing of tVNS should also be investigated further and may lead to the development of personalised stimulation protocols.Clinical relevance- The stimulation current at which tVNS is delivered does not appear to influence brain response to stimulation, and the value of stimulation current should be selected based on individual participant comfort.

Central mechanisms in sympathetic nervous dysregulation in obesity.

Cardiovascular and metabolic complications associated with excess adiposity are linked to chronic activation of the sympathetic nervous system, resulting in a high risk of mortality among obese individuals. Obesity-related positive energy balance underlies the progression of hypertension, end-organ damage, and insulin resistance, driven by increased sympathetic tone throughout the body. It is, therefore, important to understand the central network that drives and maintains sustained activation of the sympathetic nervous system in the obese state. Experimental and clinical studies have identified structural changes and altered dynamics in both grey and white matter regions in obesity. Aberrant activation in certain brain regions has been associated with altered reward circuitry and metabolic pathways including leptin and insulin signaling along with adiposity-driven systemic and central inflammation. The impact of these pathways on the brain via overactivity of the sympathetic nervous system has gained interest in the past decade. Primarily, the brainstem, hypothalamus, amygdala, hippocampus, and cortical structures including the insular, orbitofrontal, temporal, cingulate, and prefrontal cortices have been identified in this context. Although the central network involving these structures is much more intricate, this review highlights recent evidence identifying these regions in sympathetic overactivity in obesity.

Functional Connectivity Analysis of Transcutaneous Vagus Nerve Stimulation (tVNS) Using Magnetoencephalography (MEG).

Altered brain functional connectivity has been observed in conditions such as schizophrenia, dementia and depression and may represent a target for treatment. Transcutaneous vagus nerve stimulation (tVNS) is a form of non-invasive brain stimulation that is increasingly used in the treatment of a variety of health conditions. We previously combined tVNS with magnetoencephalography (MEG) and observed that various stimulation frequencies affected different brain areas in healthy individuals. We further investigated whether tVNS had an effect on functional connectivity with a focus on brain regions associated with mood. We compared functional connectivity (whole-head and region of interest) in response to four stimulation frequencies of tVNS using data collected from concurrent MEG and tVNS in 17 healthy participants using Weighted Phase Lag Index (WPLI) to calculate correlation between brain areas. Different frequencies of stimulation lead to changes in functional connectivity across multiple regions, notably areas linked to the default mode network (DMN), salience network (SN) and the central executive network (CEN). It was observed that tVNS delivered at a frequency of 24 Hz was the most effective in increasing functional connectivity between these areas and sub-networks in healthy participants. Our results indicate that tVNS can alter functional connectivity in regions that have been associated with mood and memory disorders. Varying the stimulation frequency led to alterations in different brain areas, which may suggest that personalized stimulation protocols can be developed for the targeted treatment of different medical conditions using tVNS.

Classification of Epileptic and Psychogenic Non-Epileptic Seizures Using Electroencephalography and Electrocardiography.

Patients with psychogenic non-epileptic seizures (PNES) may exhibit similar clinical features to patients with epileptic seizures (ES). Misdiagnosis of PNES and ES can lead to inappropriate treatment and significant morbidity. This study investigates the use of machine learning techniques for classification of PNES and ES based on electroencephalography (EEG) and electrocardiography (ECG) data. Video-EEG-ECG of 150 ES events from 16 patients and 96 PNES from 10 patients were analysed. Four preictal periods (time before event onset) in EEG and ECG data were selected for each PNES and ES event (60-45 min, 45-30 min, 30-15 min, 15-0 min). Time-domain features were extracted from each preictal data segment in 17 EEG channels and 1 ECG channel. The classification performance using k-nearest neighbour, decision tree, random forest, naive Bayes, and support vector machine classifiers were evaluated. The results showed the highest classification accuracy was 87.83% using the random forest on 15-0 min preictal period of EEG and ECG data. The performance was significantly higher using 15-0 min preictal period data than 30-15 min, 45-30 min, and 60-45 min preictal periods ( [Formula: see text]). The classification accuracy was improved from 86.37% to 87.83% by combining ECG data with EEG data ( [Formula: see text]). The study provided an automated classification algorithm for PNES and ES events using machine learning techniques on preictal EEG and ECG data.

Forecasting seizure likelihood from cycles of self-reported events and heart rate: a prospective pilot study.

BACKGROUND: Seizure risk forecasting could reduce injuries and even deaths in people with epilepsy. There is great interest in using non-invasive wearable devices to generate forecasts of seizure risk. Forecasts based on cycles of epileptic activity, seizure times or heart rate have provided promising forecasting results. This study validates a forecasting method using multimodal cycles recorded from wearable devices. METHOD: Seizure and heart rate cycles were extracted from 13 participants. The mean period of heart rate data from a smartwatch was 562 days, with a mean of 125 self-reported seizures from a smartphone app. The relationship between seizure onset time and phases of seizure and heart rate cycles was investigated. An additive regression model was used to project heart rate cycles. The results of forecasts using seizure cycles, heart rate cycles, and a combination of both were compared. Forecasting performance was evaluated in 6 of 13 participants in a prospective setting, using long-term data collected after algorithms were developed. FINDINGS: The results showed that the best forecasts achieved a mean area under the receiver-operating characteristic curve (AUC) of 0.73 for 9/13 participants showing performance above chance during retrospective validation. Subject-specific forecasts evaluated with prospective data showed a mean AUC of 0.77 with 4/6 participants showing performance above chance. INTERPRETATION: The results of this study demonstrate that cycles detected from multimodal data can be combined within a single, scalable seizure risk forecasting algorithm to provide robust performance. The presented forecasting method enabled seizure risk to be estimated for an arbitrary future period and could be generalised across a range of data types. In contrast to earlier work, the current study evaluated forecasts prospectively, in subjects blinded to their seizure risk outputs, representing a critical step towards clinical applications. FUNDING: This study was funded by an Australian Government National Health & Medical Research Council and BioMedTech Horizons grant. The study also received support from the Epilepsy Foundation of America's 'My Seizure Gauge' grant.

Activity of Retinal Neurons Can Be Modulated by Tunable Near-Infrared Nanoparticle Sensors.

The vision of patients rendered blind by photoreceptor degeneration can be partially restored by exogenous stimulation of surviving retinal ganglion cells (RGCs). Whereas conventional electrical stimulation techniques have failed to produce naturalistic visual percepts, nanoparticle-based optical sensors have recently received increasing attention as a means to artificially stimulate the RGCs. In particular, nanoparticle-enhanced infrared neural modulation (NINM) is a plasmonically mediated photothermal neuromodulation technique that has a demonstrated capacity for both stimulation and inhibition, which is essential for the differential modulation of ON-type and OFF-type RGCs. Gold nanorods provide tunable absorption through the near-infrared wavelength window, which reduces interference with any residual vision. Therefore, NINM may be uniquely well-suited to retinal prosthesis applications but, to our knowledge, has not previously been demonstrated in RGCs. In the present study, NINM laser pulses of 100 µs, 500 µs and 200 ms were applied to RGCs in explanted rat retinae, with single-cell responses recorded via patch-clamping. The shorter laser pulses evoked robust RGC stimulation by capacitive current generation, while the long laser pulses are capable of inhibiting spontaneous action potentials by thermal block. Importantly, an implicit bias toward OFF-type inhibition is observed, which may have important implications for the feasibility of future high-acuity retinal prosthesis design based on nanoparticle sensors.

Quantifying visual acuity for pre-clinical testing of visual prostheses.

Objective.Visual prostheses currently restore only limited vision. More research and pre-clinical work are required to improve the devices and stimulation strategies that are used to induce neural activity that results in visual perception. Evaluation of candidate strategies and devices requires an objective way to convert measured and modelled patterns of neural activity into a quantitative measure of visual acuity.Approach.This study presents an approach that compares evoked patterns of neural activation with target and reference patterns. A d-prime measure of discriminability determines whether the evoked neural activation pattern is sufficient to discriminate between the target and reference patterns and thus provides a quantified level of visual perception in the clinical Snellen and MAR scales. The magnitude of the resulting value was demonstrated using scaled standardized 'C' and 'E' optotypes.Main results.The approach was used to assess the visual acuity provided by two alternative stimulation strategies applied to simulated retinal implants with different electrode pitch configurations and differently sized spreads of neural activity. It was found that when there is substantial overlap in neural activity generated by different electrodes, an estimate of acuity based only upon electrode pitch is incorrect; our proposed method gives an accurate result in both circumstances.Significance.Quantification of visual acuity using this approach in pre-clinical development will allow for more rapid and accurate prototyping of improved devices and neural stimulation strategies.

Forecasting psychogenic non-epileptic seizure likelihood from ambulatory EEG and ECG.

Objective.Critical slowing features (variance and autocorrelation) of long-term continuous electroencephalography (EEG) and electrocardiography (ECG) data have previously been used to forecast epileptic seizure onset. This study tested the feasibility of forecasting non-epileptic seizures using the same methods. In doing so, we examined if long-term cycles of brain and cardiac activity are present in clinical physiological recordings of psychogenic non-epileptic seizures (PNES).Approach.Retrospectively accessed ambulatory EEG and ECG data from 15 patients with non-epileptic seizures and no background of epilepsy were used for developing the forecasting system. The median period of recordings was 161 h, with a median of 7 non-epileptic seizures per patient. The phases of different cycles (5 min, 1 h, 6 h, 12 h, 24 h) of EEG and RR interval (RRI) critical slowing features were investigated. Forecasters were generated using combinations of the variance and autocorrelation of both EEG and the RRI of the ECG at each of the aforementioned cycle lengths. Optimal forecasters were selected as those with the highest area under the receiver-operator curve (AUC).Main results.It was found that PNES events occurred in the rising phases of EEG feature cycles of 12 and 24 h in duration at a rate significantly above chance. We demonstrated that the proposed forecasters achieved performance significantly better than chance in 8/15 of patients, and the mean AUC of the best forecaster across patients was 0.79.Significance.To our knowledge, this is the first study to retrospectively forecast non-epileptic seizures using both EEG and ECG data. The significance of EEG in the forecasting models suggests that cyclic EEG features of non-epileptic seizures exist. This study opens the potential of seizure forecasting beyond epilepsy, into other disorders of episodic loss of consciousness or dissociation.

Preferential modulation of individual retinal ganglion cells by electrical stimulation.

Objective.Retinal prostheses have had limited success in vision restoration through electrical stimulation of surviving retinal ganglion cells (RGCs) in the degenerated retina. This is partly due to non-preferential stimulation of all RGCs near a single stimulating electrode, which include cells that conflict in their response properties and their contribution to visiual processing. Our study proposes a stimulation strategy to preferentially stimulate individual RGCs based on their temporal electrical receptive fields (tERFs).Approach.We recorded the responses of RGCs using whole-cell patch clamping and demonstrated the stimulation strategy, first using intracellular stimulation, then via extracellular stimulation.Main results. We successfully reconstructed the tERFs according to the RGC response to Gaussian white noise current stimulation. The characteristics of the tERFs were extracted and compared based on the morphological and light response types of the cells. By re-delivering stimulation trains that were composed of the tERFs obtained from different cells, we could preferentially stimulate individual RGCs as the cells showed lower activation thresholds to their own tERFs.Significance.This proposed stimulation strategy implemented in the next generation of recording and stimulating retinal prostheses may improve the quality of artificial vision.

Measuring brain response to transcutaneous vagus nerve stimulation (tVNS) using simultaneous magnetoencephalography (MEG).

Objective.Transcutaneous vagus nerve stimulation (tVNS) is a form of non-invasive brain stimulation that delivers a sequence of electrical pulses to the auricular branch of the vagus nerve and is used increasingly in the treatment of a number of health conditions such as epilepsy and depression. Recent research has focused on the efficacy of tVNS to treat different medical conditions, but there is little conclusive evidence concerning the optimal stimulation parameters. There are relatively few studies that have combined tVNS with a neuroimaging modality, and none that have attempted simultaneous magnetoencephalography (MEG) and tVNS due to the presence of large stimulation artifacts produced by the electrical stimulation which are many orders of magnitude larger than underlying brain activity.Approach.The aim of this study is to investigate the utility of MEG to gain insight into the regions of the brain most strongly influenced by tVNS and how variation of the stimulation parameters can affect this response in healthy participants.Main results.We have successfully demonstrated that MEG can be used to measure brain response to tVNS. We have also shown that varying the stimulation frequency can lead to a difference in brain response, with the brain also responding in different anatomical regions depending on the frequency.Significance.The main contribution of this paper is to demonstrate the feasibility of simultaneous pulsed tVNS and MEG recording, allowing direct investigation of the changes in brain activity that result from different stimulation parameters. This may lead to the development of customised therapeutic approaches for the targeted treatment of different conditions.

Seizure Forecasting Using Long-Term Electroencephalography and Electrocardiogram Data.

Electroencephalography (EEG) has been used to forecast seizures with varying success. There is an increasing interest to use electrocardiogram (ECG) to help with seizure forecasting. The neural and cardiovascular systems may exhibit critical slowing, which is measured by an increase in variance and autocorrelation of the system, when change from a normal state to an ictal state. To forecast seizures, the variance and autocorrelation of long-term continuous EEG and ECG data from 16 patients were used for analysis. The average period of recordings was 161.9 h, with an average of 9 electrographic seizures in an individual patient. The relationship between seizure onset times and phases of variance and autocorrelation in EEG and ECG data was investigated. The results of forecasting models using critical slowing features, seizure circadian features, and combined critical slowing and circadian features were compared using the receiver-operating characteristic curve. The results demonstrated that the best forecaster was patient-specific and the average area under the curve (AUC) of the best forecaster across patients was 0.68. In 50% of patients, circadian forecasters had the best performance. Critical slowing forecaster performed best in 19% of patients. Combined forecaster achieved the best performance in 31% of patients. The results of this study may help to advance the field of seizure forecasting and lead to the improved quality of life of people who suffer from epilepsy.

Neural activity shaping utilizing a partitioned target pattern.

Electrical stimulation of neural tissue is used in both clinical and experimental devices to evoke a desired spatiotemporal pattern of neural activity. These devices induce a local field that drives neural activation, referred to as an activating function or generator signal. In visual prostheses, the spread of generator signal from each electrode within the neural tissue results in a spread of visual perception, referred to as a phosphene.Objective.In cases where neighbouring phosphenes overlap, it is desirable to use current steering or neural activity shaping strategies to manipulate the generator signal between the electrodes to provide greater control over the total pattern of neural activity. Applying opposite generator signal polarities in neighbouring regions of the retina forces the generator signal to pass through zero at an intermediate point, thus inducing low neural activity that may be perceived as a high-contrast line. This approach provides a form of high contrast visual perception, but it requires partitioning of the target pattern into those regions that use positive or negative generator signals. This discrete optimization is an NP-hard problem that is subject to being trapped in detrimental local minima.Approach.This investigation proposes a new partitioning method using image segmentation to determine the most beneficial positive and negative generator signal regions. Utilizing a database of 1000 natural images, the method is compared to alternative approaches based upon the mean squared error of the outcome.Main results.Under nominal conditions and with a set computation limit, partitioning provided improvement for 32% of these images. This percentage increased to 89% when utilizing image pre-processing to emphasize perceptual features of the images. The percentage of images that were dealt with most effectively with image segmentation increased as lower computation limits were imposed on the algorithms.Significance.These results provide a new method to increase the resolution of neural stimulating arrays and thus improve the experience of visual prosthesis users.

Response of primary auditory neurons to stimulation with infrared light in vitro.

OBJECTIVE: Infrared light can be used to modulate the activity of neuronal cells through thermally-evoked capacitive currents and thermosensitive ion channel modulation. The infrared power threshold for action potentials has previously been found to be far lower in the in vivo cochlea when compared with other neuronal targets, implicating spiral ganglion neurons (SGNs) as a potential target for infrared auditory prostheses. However, conflicting experimental evidence suggests that this low threshold may arise from an intermediary mechanism other than direct SGN stimulation, potentially involving residual hair cell activity. APPROACH: Patch-clamp recordings from cultured SGNs were used to explicitly quantify the capacitive and ion channel currents in an environment devoid of hair cells. Neurons were irradiated by a 1870 nm laser with pulse durations of 0.2-5.0 ms and powers up to 1.5 W. A Hodgkin-Huxley-type model was established by first characterising the voltage dependent currents, and then incorporating laser-evoked currents separated into temperature-dependent and temperature-gradient-dependent components. This model was found to accurately simulate neuronal responses and allowed the results to be extrapolated to stimulation parameter spaces not accessible during this study. MAIN RESULTS: The previously-reported low in vivo SGN stimulation threshold was not observed, and only subthreshold depolarisation was achieved, even at high light exposures. Extrapolating these results with our Hodgkin-Huxley-type model predicts an action potential threshold which does not deviate significantly from other neuronal types. SIGNIFICANCE: This suggests that the low-threshold response that is commonly reported in vivo may arise from an alternative mechanism, and calls into question the potential usefulness of the effect for auditory prostheses. The step-wise approach to modelling optically-evoked currents described here may prove useful for analysing a wider range of cell types where capacitive currents and conductance modulation are dominant.

Learning receptive field properties of complex cells in V1.

There are two distinct classes of cells in the primary visual cortex (V1): simple cells and complex cells. One defining feature of complex cells is their spatial phase invariance; they respond strongly to oriented grating stimuli with a preferred orientation but with a wide range of spatial phases. A classical model of complete spatial phase invariance in complex cells is the energy model, in which the responses are the sum of the squared outputs of two linear spatially phase-shifted filters. However, recent experimental studies have shown that complex cells have a diverse range of spatial phase invariance and only a subset can be characterized by the energy model. While several models have been proposed to explain how complex cells could learn to be selective to orientation but invariant to spatial phase, most existing models overlook many biologically important details. We propose a biologically plausible model for complex cells that learns to pool inputs from simple cells based on the presentation of natural scene stimuli. The model is a three-layer network with rate-based neurons that describes the activities of LGN cells (layer 1), V1 simple cells (layer 2), and V1 complex cells (layer 3). The first two layers implement a recently proposed simple cell model that is biologically plausible and accounts for many experimental phenomena. The neural dynamics of the complex cells is modeled as the integration of simple cells inputs along with response normalization. Connections between LGN and simple cells are learned using Hebbian and anti-Hebbian plasticity. Connections between simple and complex cells are learned using a modified version of the Bienenstock, Cooper, and Munro (BCM) rule. Our results demonstrate that the learning rule can describe a diversity of complex cells, similar to those observed experimentally.