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Based on the promising results of randomized controlled trials, deep brain stimulation (DBS) and responsive neurostimulation (RNS) are used increasingly in the treatment of patients with drug-resistant epilepsy. Drug-resistant temporal lobe epilepsy (TLE) is an indication for either DBS of the anterior nucleus of the thalamus (ANT) or temporal lobe (TL) RNS, but there are no studies that directly compare the seizure benefits and adverse effects associated with these therapies in this patient population. We, therefore, examined all patients who underwent ANT-DBS or TL-RNS for drug-resistant TLE at our center.We performed a retrospective review of patients who were treated with either ANT-DBS or TL-RNS for drug-resistant TLE with at least 12 months of follow-up. Along with the clinical characteristics of each patient's epilepsy, seizure frequency was recorded throughout each patient's postoperative clinical course.Twenty-six patients underwent ANT-DBS implantation and 32 patients underwent TL-RNS for drug-resistant TLE. The epilepsy characteristics of both groups were similar. Patients who underwent ANT-DBS demonstrated a median seizure reduction of 58% at 12-15 months, compared to a median seizure reduction of 70% at 12-15 months in patients treated with TL-RNS (p .05). The responder rate (percentage of patients with a 50% decrease or more in seizure frequency) was 54% for ANT-DBS and 56% for TL-RNS (p .05). The incidence of complications and stimulation-related side effects did not significantly differ between therapies.We demonstrate in our single-center experience that patients with drug-resistant TLE benefit similarly from either ANT-DBS or TL-RNS. Selection of either ANT-DBS or TL-RNS may, therefore, depend more heavily on patient and provider preference, as each has unique capabilities and configurations. Future studies will consider subgroup analyses to determine if specific patients have greater seizure frequency reduction from one form of neuromodulation strategy over another.

Low statistical power is a recognized problem in many fields. We performed a systematic review to determine the median statistical power of studies of epilepsy surgery outcomes. We performed a PubMed search for studies reporting epilepsy surgery outcomes for the years 1980-2020, focusing on studies using stereoelectroencephalography (SEEG). We extracted patient count data for comparisons of surgical outcome between two groups, based on a reported prognostic factor. We defined a clinically meaningful difference as the difference in seizure freedom for MRI positive (66.9%) versus negative (45.5%) from the largest study found. Based on 69 studies of surgery outcomes in patients undergoing SEEG, the median sample size was 38 patients, and the median statistical power was 24%. This implies at least a 17% chance a study with a significant result is false, assuming 1:1 pre-test odds. Results from simulation studies suggest that, if a typical SEEG study finds a significant effect, then the median observed effect size will be more than double the true effect size. We conclude that studies of epilepsy surgery outcomes using SEEG are often statistically underpowered, which limits the reproducibility and reliability of the literature. We discuss how statistical power could be improved.SHORT SUMMARYWe performed a systematic review to determine the median statistical power of studies of epilepsy surgery outcomes, focused on stereoelectroencephalography. We extracted patient count data for comparisons of outcomes between two groups. We defined a clinically meaningful difference as the prognostic value of a normal versus abnormal MRI. Based on 69 studies, the median sample size was 38 patients, and the median statistical power was 24%. Underpowered studies will overestimate the size of true effects and are more likely to report false positive results. We discuss how statistical power, and thus reproducibility and reliability of results, can be improved.

Purpose Corticocortical evoked potentials (CCEPs) resulting from single pulse electrical stimulation are increasingly used to understand seizure networks, as well as normal brain connectivity. However, we observed that when using depth electrodes, traditional measures of CCEPs amplitude using a referential montage can be falsely localizing, often to white matter. Methods We pooled 27 linear electrode arrays targeting the amygdala, hippocampus, or cingulate cortex from eight participants. Using postoperative imaging, we classified contacts as being in gray matter, white matter, or bordering each and measured the amplitude using the root-mean-squared deviation from baseline in a referential, common average, bipolar, or Laplacian montage. Results Of 27 electrode contacts, 25 (93%) had a significantly higher mean amplitude when in gray matter than in white matter using a Laplacian montage, which was significantly more than the 12 of 27 electrodes (44%) when using a referential montage (P = 0.0003, Fisher exact test). The area under the curve for a receiver operating characteristic classifying contacts as gray or white matter was significantly higher for either the Laplacian (0.79) or the bipolar (0.72) montage when compared with either the common average (0.56) or the referential (0.51) montage (P ≤ 0.005, bootstrap). Conclusions Both the Laplacian and bipolar montages were superior to the common average or referential montage in localizing CCEPs to gray matter. These montages may be more appropriate for interpreting CCEPs when using depth electrodes than the referential montage, which has typically been used in prior studies of CCEPs with subdural grids.

ObjectiveStudies of epilepsy surgery outcomes are often small and thus underpowered to reach statistically valid conclusions. We hypothesized that ordinal logistic regression would have greater statistical power than binary logistic regression when analyzing epilepsy surgery outcomes.MethodsWe reviewed 10 manuscripts included in a recent meta-analysis which found that mesial temporal sclerosis (MTS) predicted better surgical outcome after a stereotactic laser amygdalohippocampectomy (SLAH). We extracted data from 239 patients from eight studies which reported four discrete Engel surgical outcomes after SLAH, stratified by the presence or absence of MTS.ResultsThe rate of freedom from disabling seizures (Engel I) was 64.3% (110/171) for patients with MTS compared to 44.1% (30/68) without MTS. The statistical power to detect MTS as a predictor for better surgical outcome after a SLAH was 29% using ordinal regression, which was significantly more than the 13% power using binary logistic regression (paired t-test, pConclusionOrdinal regression should be considered when analyzing ordinal outcomes (such as Engel surgical outcome), especially for datasets with small sample sizes.

Robotic systems have fundamentally altered the landscape of functional neurosurgery. These allow automated stereotaxy with high accuracy and reliability, and are rapidly becoming a mainstay in stereotactic surgeries such as deep brain stimulation (DBS), stereoelectroencephalography (SEEG), and stereotactic laser ablation/MRI guided laser interstitial thermal therapy (MRgLITT). Robotic systems have been effectively applied to create a minimally invasive approach for diagnostics and therapeutics in the treatment of epilepsy, utilizing robots for expeditious and accurate stereotaxy for SEEG and MRgLITT. MRgLITT has been shown to approach open surgical techniques in efficacy of seizure control while minimizing collateral injury. We describe the use of robot assisted MRgLITT for a minimally invasive laser anterior temporal lobotomy, describing the approach and potential pitfalls. Goals of MRgLITT are complete ablation of the epileptogenic zone and avoiding injury to uninvolved structures. In the middle fossa these include structures such as cranial nerves in the skull base and cavernous sinus and the thalamus. These can be mitigated with careful trajectory planning and control of laser ablation intensity.

PURPOSE Previous work has shown that quantitative EEG measures correlate with the severity of ischemic stroke. This has not been systematically validated in patients with acute ischemic stroke who have undergone mechanical thrombectomy. METHODS Data were collected from 73 patients who underwent mechanical thrombectomy and had a standard head set EEG performed during their hospital admission. For each patient, the global delta-alpha ratio (DAR) and its difference between the two hemispheres were calculated. Associations between the global and interhemispheric DAR difference with the patients' National Institutes of Health Stroke and Modified Rankin Scale scores at discharge and 3 months after thrombectomy were assessed. RESULTS The interhemispheric DAR difference correlated with the National Institutes of Health Stroke scores at discharge (Spearman R = 0.41, P = 0.0008), National Institutes of Health Stroke scores at 3 months (Spearman R = 0.60, P = 0.02) and Modified Rankin Scale scores at 3 months (Spearman R = 0.27, P = 0.01). In contrast, the global DAR did not correlate significantly with any of these clinical outcomes when evaluated as continuous variables. In a multivariate logistic regression model, both the interhemispheric DAR difference (β = 0.25, P = 0.03) and the infarct volume (β = 0.02, P = 0.03) were independently predictive of good versus poor functional outcome (Modified Rankin Scale score ≤2 vs. >2) at 3 months. CONCLUSIONS The quantitative EEG measure of interhemispheric slow relative to fast frequencies power asymmetry correlated with the discharge and 3-month National Institutes of Health Stroke and Modified Rankin Scale scores and provided added value to infarct volume in predicting functional outcome at 3 months. These data support the prognostic value of quantitative EEG in ischemic stroke patients who have undergone mechanical thrombectomy.

Introduction Previous work has shown that review of quantitative EEG (QEEG) alone has reasonable sensitivity for identifying seizure onset. The objectives of this study are: (1) To evaluate whether QEEG can be also used to identify seizures in intracranial EEG recordings. (2) To explore whether QEEG can be used to triage the review of raw EEG records and assist in prioritizing the review of records with the highest probability of seizure Methods 66 one-hour EEG epochs were chosen from 6 temporal lobe epilepsy patients who underwent intracranial monitoring using bilateral foramen ovale (FO) electrodes. 33 clips were seizure free, and 33 clips contained at least one seizure, for a total of 36 seizures. Seizure onset was determined by review of the raw EEG by an epilepsy attending. We generated standard QEEG panels using Persyst (Prescott, AZ). Three blinded reviewers were asked to: (1) mark each area of concern for seizure on these QEEG panels and (2) rank the likelihood of that area containing a seizure as “probable,” “possible,” or “unlikely.” Epochs with no marked areas of concern were considered to be “low risk” for containing a seizure. Seizure identification was considered positive for an epoch if there was an area of concern marked and there was also a seizure anywhere within the 1 h-clip. We examined sensitivity and specificity as a function of the highest likelihood assigned to any area of concern. However, analysis of the “possible” and “unlikely” groups were combined because their sensitivity was not statistically different. Results Marking an epoch with at least one “probable” seizure had 52% sensitivity and 94% specificity for that one-hour epoch actually containing a seizure. Marking an epoch with at least one “possible” or “unlikely” seizure had 40% sensitivity and 73% specificity. Marking an epoch with any area of concern (“probable,” “possible”, or “unlikely”) had 92% sensitivity and 67% specificity, which implies that one-hour epochs containing a seizure had only a 8% false negative rate for being classified “low risk.” Conclusion QEEG can be used to identify seizures in standardized intracranial recordings, such as FO electrodes, and can also classify a sub-set of epochs as either very likely or very unlikely to contain a seizure. This suggests that QEEG can be used to triage the review of the intracranial raw EEG recordings, so the review of higher yield studies can be prioritized over lower yield records.

The use of chronic intracortical multielectrode arrays has become increasingly prevalent in neurophysiological experiments. However, it is not obvious whether neuronal signals obtained over multiple recording sessions come from the same or different neurons. Here, we develop a criterion to assess single-unit stability by measuring the similarity of 1) average spike waveforms and 2) interspike interval histograms (ISIHs). Neuronal activity was recorded from four Utah arrays implanted in primary motor and premotor cortices in three rhesus macaque monkeys during 10 recording sessions over a 15- to 17-day period. A unit was defined as stable through a given day if the stability criterion was satisfied on all recordings leading up to that day. We found that 57% of the original units were stable through 7 days, 43% were stable through 10 days, and 39% were stable through 15 days. Moreover, stable units were more likely to remain stable in subsequent recording sessions (i.e., 89% of the neurons that were stable through four sessions remained stable on the fifth). Using both waveform and ISIH data instead of just waveforms improved performance by reducing the number of false positives. We also demonstrate that this method can be used to track neurons across days, even during adaptation to a visuomotor rotation. Identifying a stable subset of neurons should allow the study of long-term learning effects across days and has practical implications for pooling of behavioral data across days and for increasing the effectiveness of brain–machine interfaces.

Biphasic insulin secretion in response to glucose, consisting of a transient first phase followed by a progressive second phase, is well described in pancreatic islets. Using single canine beta-cells we have compared the time courses of electrical activity and insulin granule exocytosis to biphasic insulin secretion. Short trains of action potentials, similar those found during first phase insulin secretion, trigger phasic exocytosis from a small pool of insulin granules, likely an immediately releasable pool docked near voltage activated Ca(2+) channels. In contrast, plateau depolarizations to between -35 and -20 mV resembling those during second phase insulin secretion, trigger tonic exocytosis from a larger pool of insulin granules, likely a highly Ca(2+)-sensitive pool farther from Ca(2+) channels. Both phasic and tonic modes of exocytosis are enhanced by glucose, via its metabolism. Hence, in canine beta-cells two distinct components of exocytosis, tuned to two components of electrical activity, may contribute significantly to biphasic insulin secretion.

In response to depolarizations that open voltage dependent Ca2+ channels single porcine beta-cells display heterogeneous time courses of exocytosis. Some cells display phasic exocytosis that is triggered by individual or short burst of action potentials typically characteristic of glucose-induced electrical activity or brief voltage clamp depolarization. Other cells, singularly or additionally, display tonic exocytosis that (i) is triggered during prolonged (up to seconds-long) depolarizations to voltages (-30 to -20 mV), and (ii) coincides with rises in global cytosolic [Ca2+] >500 nM. We suggest that tonic exocytosis (i) likely results from a recently described pool of granules that is more Ca2+ sensitive and less co-localized with voltage-sensitive Ca2+ entry channels than that contributing to phasic exocytosis and (ii) helps tune exocytosis to glucose-induced electrical activity when the latter consists of spike activity followed by intervals of plateau depolarization to nearly -20 mV.

Studies of stimulus-secretion coupling in human beta-cells have been hampered by poor availability of tissue due to variability of the supply of cadaver pancreati and in the adequacy of enzymatic liberation of islets as well as by the shunting of isolates into transplant trials. Here we establish that aliquots of islets, several from high-quality but low-yield islet isolates (50,000-100,000 islets), cryopreserved and then thawed as needed, respond to glucose in a calcium- and metabolic-dependent fashion. Insulin secretion is modulated by blockers of voltage-dependent Na+ and Ca2+ channels, and paracrine hormones (glucagon and somatostatin) in manners indistinguishable from fresh tissue preparations. Using single-cell electrophysiological and electrochemical assays we demonstrate that single beta-cells from cryopreserved islets display (1) stimulus-depolarization coupling based on rapid closure of K+ (ATP) channels; (2) action potential electrogenesis with upstrokes based on voltage-dependent Na and Ca currents; and (3) Ca2+ entry-mediated depolarization-exocytosis coupling sustained over multiple bouts of stimulation and modulated by paracrine hormones. All of these features are indistinguishable from those seen in single cells from freshly harvested islets. These results support the utility of cryopreservation, even of low-yield but functional isolates, as a means of ensuring a steady source of repeatedly accessible tissue for research on normal and diabetic islets.

α-Latrotoxin (α-LT), a potent excitatory neurotoxin, increases spontaneous, as well as action potential-evoked, quantal release at nerve terminals and increases hormone release from excitable endocrine cells. We have investigated the effects of α-LT on single human, mouse and canine β-cells. In isolated and combined measurements, α-LT, at nanomolar concentrations, induces: (i) rises in cytosolic Ca2+, into the micromolar range, that are dependent on extracellular Ca2+; (ii) large conductance non-selective cation channels; and (iii) Ca2+-dependent insulin granule exocytosis, measured as increases in membrane capacitance and quantal release of preloaded serotonin. Furthermore, at picomolar concentrations, α-LT potentiates depolarization-induced exocytosis often without evidence of inducing channel activity or increasing cytosolic Ca2+. These results strongly support the hypothesis that α-LT, after binding to specific receptors, has at least two complementary modes of action on excitable cells. (i) α-LT inserts into the plasma membrane to form Ca2+ permeable channels and promote Ca2+ entry thereby triggering Ca2+-dependent exocytosis in unstimulated cells. (ii) At lower concentrations, where its channel forming activity is hardly evident, α-LT augments depolarization-evoked exocytosis probably by second messenger-induced enhancement of the efficiency of the vesicle recruitment or vesicle fusion machinery. We suggest that both modes of action enhance exocytosis from a newly described highly Ca2+-sensitive pool of insulin granules activated by global cytosolic Ca2+ concentrations in the range of ∼1 μm.

The primary goals of this chapter are to consolidate and generalize what you know about data collection in MATLAB®. Moreover, we will elaborate on data analysis in MATLAB beyond simple correlations. You will also learn how reaction time data can be used to infer the mental process of spatial attention.

Publisher Summary This chapter defines the MATLAB Tutorial that introduces the functionality and power of the MATLAB® software, a powerful tool. MATLAB contains a large number of diverse operators and functions, covering virtually all applied mathematics, with particularly powerful functions in calculus and linear algebra. It is a high-performance programming environment for numerical and technical applications. If one would like to explore these functions, the MATLAB help function provides an excellent starting point. One can summon the help with the help command. The basic structure of this tutorial is as follows: each new concept is introduced through an example, an exercise, and some suggestions on how to explore the principles that guide the implementation of the concept in MATLAB. While working through the examples and exercises is indispensable, taking the suggestions for exploration seriously is also highly recommended. It has been shown that negative examples are very conducive to learning; in other words, it is very important to find out what does not work, in addition to what does work.

The purpose of this chapter is to familiarize you with simulating a stochastic process. We will be modeling a large-scale network of firing neurons through the analogy of forest fires. In the process, you will become more adept at using convolutions and creating movies of neural population dynamics.

In this chapter, you will be introduced to the use of wavelets and wavelet transforms as an alternative method of spectral analysis. We will discuss a number of common wavelets and introduce the Wavelet Toolbox of the MATLAB® software.

The purpose of this chapter is to examine the cone and horizontal cell system using a qualitative visualization technique called phase plane analysis. The chapter also includes exercises that defines the phase portraits drawn using a downloadable M-file called pplane7.m. The phase plane consists of three basic features: the nullclines intersecting at the fixed point of the system, the vector field showing how the solutions change over time, and trajectories showing how the solution approaches its steady-state from a given initial condition. It involves writing a simple version of pplane7. Several functions built into MATLAB will aid in coding each of the basic features of the phase plane. The chapter also examines more detail the model of retinal feedback between cone cells and horizontal cells of the retina.

This chapter pursues dual goals. First, we want to build on the data collection within a psychophysical paradigm approach. Second, and more importantly, this chapter will introduce the concept of a graphical user interface (GUI) within MATLAB® and demonstrate its gainful use.

In this chapter, we will apply phase plane analysis to a model of two interacting neuronal populations, an excitatory and an inhibitory population known as the Wilson-Cowan (W-C) equations. Rather than relying on the pplane7 program, we will apply the knowledge we possess to write our own rudimentary phase plane code for nonlinear systems.

The primary goal of this chapter is to collect and analyze reaction time data using MATLAB®. Reaction time measures to probe the mind have been the backbone of experimental psychology at least since the time of Donders (1868). The basic premise underlying the use of reaction times in cognitive psychology is the assumption that cognitive operations take a certain and measurable amount of time. In addition, it is assumed that additional mental processes add (more or less) linearly. If this is the case, increased reaction times reflect additional mental processes. Let us assume for the time being that this is a reasonable framework. Then, it is highly useful to have a program that allows you to quickly collect reaction time data.

In this chapter, you will learn how to use MATLAB® to do psychophysics. Once you master these fundamentals, you can use MATLAB to address any psychophysical question that might come to mind. While—in principle—all sensory modalities are open to psychophysical investigation, we will focus on visual psychophysics in this chapter.

This chapter has two primary goals. The first goal is to be introduced to the concept of supervised learning and how it may relate to synaptic plasticity in the nervous system, particularly in the cerebellum. The second goal is to learn to implement single-layer and multi-layer neural network architectures using supervised learning rules to solve particular problems.

This chapter introduces the short-time Fourier transform, nonstationary signals, and, spectrograms. It shows the Fourier spectrum for two subsections of song. The two subsections have very different distributions of power over frequency. A Fourier transform of the full song returns the power distribution over the entire song. Any localization of frequency information to a time point or an interval is lost. When applied to a signal, the term stationary indicates that certain statistical properties of the signal are uniform throughout. In other words, a subset of the signal is sufficient for analysis of the entire signal. The distribution of power over frequency remains the same over the whole signal. A similar idea is the concept of ergodicity. Imagine an ensemble of related signals. Going with the example of zebra finch vocalizations, an appropriate ensemble would be the set of vocalizations from a set of birds. An ergodic ensemble is one in which each sample and the ensemble approach the same mean. In other words, analyzing one sample or a subset of the signals from the group can approximate the analysis of the ensemble. Ergodicity and stationarity are independent qualities.

During a reach, neural activity recorded from motor cortex is typically thought to linearly encode the observed movement. However, it has also been reported that during a double-step reaching paradigm, neural coding of the original movement is replaced by that of the corrective movement. Here, we use neural data recorded from multi-electrode arrays implanted in the motor and premotor cortices of rhesus macaques to directly compare these two hypotheses. We show that while a majority of neurons display linear encoding of movement during a double-step, a minority display a dramatic drop in firing rate that is predicted by the replacement hypothesis. Neural activity in the subpopulation showing replacement is more likely to lag the observed movement, and may therefore be involved in the monitoring of the sensory consequences of a motor command.

Given the growing interest in porcine islets as model tissue for studying the pathogenesis of human diabetes mellitus and its treatment by transplantation, we investigated stimulus-exocytosis coupling in single porcine beta-cells using patch clamp electrophysiology, Ca2+ imaging, capacitance tracking and amperometry. We establish that porcine beta-cells display several features prominently seen in beta-cells from human islets of Langerhans. These include: (i) wide heterogeneity of electrical responsiveness to glucose; (ii) dependence of action potential activity on voltage-dependent Na(+) as well as high voltage activated Ca2+ current; (iii) heterogeneity of time course of depolarization-evoked insulin granule exocytosis; and (iv) the dependence of vigorous single cell electrical activity and insulin granule exocytosis on the presence of agents that enhance cytosolic cAMP concentration. These findings promote the usefulness of porcine beta-cells as a model for studying beta-cell function in large mammals, including humans, as well as an appropriate source of tissue for xenotransplantation.

Publisher Summary This chapter introduces the methodology used in a series of papers by Richmond and Optican exploring temporal encoding in a primate visual area. They used principal components analysis and information theory to argue that a temporal code provided more information about the stimulus than a rate code did. Richmond and Optican studied pattern discrimination in a primate visual area, the inferior temporal (IT) cortex. They addressed the question of temporal coding in IT in a well-known series of papers in the Journal of Neurophysiology. They found that the firing rate of IT neurons modulated in response to the presentation of one of 64 two-dimensional visual stimuli. They also saw evidence of temporal modulation that was not captured by the firing rate. To quantify the relevance of this temporal modulation, Richmond and Optican converted the raster plot for each trial into a spike density function. They then computed principal components (PCs) of these functions. They computed the mutual information between the stimulus and either the firing rates (rate code) or the first three PCs (temporal code). Their results indicated that the temporal code carried on average twice the information as the rate code.

Publisher Summary This chapter defines how to use the MATLAB® software to do psychophysics. Psychophysics deals with the nature of the quantitative relationship between physical and mental qualities. The practice of psychophysics is ubiquitous in all fields of neuroscience that involve the study of behaving organisms, be they man or beast. Curiously enough, the origins of systematic psychophysics can be traced to a single individual. The key to visual psychophysics is to elicit relatively simple mental phenomena that lend themselves to quantification by presenting physical stimuli that are easily described by just a few parameters such as luminance, contrast, or spatial frequency. One way to create these stimuli is to use commercially available graphics editors, most prominently Photoshop®. While this practice is very common, it comes at a cost. The chapter also introduces methods by which one can create and present visual stimuli of any kind on the screen. MATLAB includes a large library of adequate functions and it visualizes images by assuming triples in a 256-element RGB space. Each element of the triplet has to be an integral value between 0 and 255. This corresponds to a range of 8 bit. Hence, these elements can be represented by variables of the type uint8.

This chapter defines the most common method of decomposing a time series into frequency components, Fourier analysis. It also describes the MATLAB implementation of the Fast Fourier Transform (FFT), an efficient algorithm for calculating Fourier transformations and application to the analysis of human speech sounds. With a few special tricks, a faster algorithm, the FFT, that scales in N log N time can be formulated. One of these tricks involves taking advantage of datasets exactly 2N elements long. The increase in processing speed has made the FFT ubiquitous in signal processing. The chapter illustrates the project that defines Fourier decomposition to analyze vowel sounds produced by human speakers. The human vocal tract has multiple cavities in which speech sounds resonate. As such, most sounds have multiple strong frequency components. In classifying speech sounds, the lowest strong frequency band is termed the first formant. The next highest is termed the second formant, and so on. Vowels lend themselves to a particularly simple characterization through their formants. Typically, vowel sounds have distinguishable first and second formants.

Publisher Summary This chapter explains the Markov processes and how one can use them to model many phenomena, including human behavior. It also defines how to build a hidden Markov model to characterize the spiking behavior of a neuron. A Markov model describes a system as a set of discrete states and transition probabilities of moving from any one state to any other state of the model. Beyond a set of states and probabilistic transitions, a Markov model also adheres to the Markov property, which states that the transition probability from any state in the network depends only on some finite set of prior states. Thus, given a current state, knowing the probabilities for the next state of the system is merely a question of knowing some n previous states and not the entire state trajectory of the system.

This chapter describes the basic structure of the retina and to see how to create simple models of neuronal interactions. It helps in building a simple model describing the interaction between cone cells and horizontal cells of the retina and solves it exactly by taking advantage of the capability of the MATLAB® software to easily manipulate matrices. The retina is the part of the eye that transforms light into an electrochemical message sent to the brain for processing. Light first contacts the cornea, a transparent tissue covering the pupil and the iris. The cornea helps converge light through the pupil. Next, light passes through the lens, where it is further focused onto the retina in the back of the eye. The retina has five distinct classes of neurons arranged into cell layers. Light first contacts the innermost layers of the retina, but it is the outermost layer that first processes the incoming light signal. The layer responsible for processing the incoming light is composed mainly of two different cell types: cones and rods. Rods are mainly responsible for sensing brightness, and cones are responsible for detecting color. Cones have a G-protein coupled receptor on their cell surface called rhodopsin. This receptor is closely associated with a chromophore called 11-cis-retinal.

This chapter focuses on functional magnetic imaging (fMRI) as a fundamental noninvasive tool in understanding brain functioning in humans. It describes the basic physics behind structural and functional magnetic resonance imaging, and after that it explains the major experimental paradigms used in fMRI research and the kinds of data that are collected in an fMRI experiment. Functional magnetic resonance imaging has emerged as the dominant form of noninvasive functional imaging in humans. Although it is a relatively young technology that began in the early 1990s, it now plays a major role in many subfields of psychology, cognitive science, and neuroscience. It is even creeping up in other disciplines such as sociology and economics. As of the beginning of 2008, a quick online search of articles on PubMed revealed over 180,000 papers that reference the use of fMRI. Some have criticized fMRI as a scientific tool, claiming that it is little more than modern phrenology. Finally, using existing fMRI data from a simple finger-tapping task, it shows how to analyze and visualize the data to come up with a statistical parametric map of activation in the brain.

This chapter introduces the fundamental methods of analyzing spike trains of single neurons that are used to characterize their encoding properties: raster plots, peri-stimulus time histograms, and tuning curves. There are prepackaged tools available for these methods. These tools analyze behavioral data recorded from motor areas of a macaque monkey. In general, neuroscientists are interesting in knowing what neurons are doing. More specifically, neuroscientists are often interested in neural encoding—how neurons represent stimuli from the outside world with changes in their firing properties. If one is studying a neuron from a motor area, the stimuli might be a set of stereotyped movements which the subject performs. Using standard electrophysiological techniques, one can record the response of the neuron to each stimulus. This chapter also examines what features these responses have in common by averaging over all responses to create a peri-stimulus time histogram.

This chapter addresses how to decode the instantaneous hand position from a population of motor cortical neurons recorded from a macaque monkey. It also defines how information about how the hand position changes over time can be used to improve the decoding. It also examines how neurons in the motor cortex carry information about upcoming movements. This information can be used to decode the direction of a movement made to one of eight targets. The chapter discusses the linear filter approach. The advantage of this approach is that one can easily add more neurons or more kinematics to the model. The linear filter can be used on data recorded outside the motor cortex. The main advantage of this approach is that it is very fast and it is easy to calculate.

This chapter focuses on the principal components analysis (PCA) that performs a linear transformation on data and can be used to reduce multidimensional data down to a few dimensions for easier analysis. The idea is that many large datasets contain correlations between the dimensions, so that a portion of the data is redundant. PCA will transform the data so that as much variation as possible will be crammed into the fewest possible dimensions. This allows to compress the data by ignoring other dimensions. To apply PCA, first, it is needed to understand how the correlations between dimensions can be described by a covariance matrix. One common application of PCA is the spike sorting of neural data. Typically, a data acquisition system monitors a raw voltage trace. Every time the voltage crosses some threshold, the raw voltage is sampled during a time window surrounding this crossing to produce the recorded spike waveform.

This chapter deals with neural networks using Neural Networks Toolbox built into the MATLAB® software to address a particular problem. The major goal is to become familiar with the general concept of unsupervised neural networks and how they may relate to certain forms of synaptic plasticity in the nervous system. Neural networks have assumed a central role in a variety of fields. They are actually quite abstract computing structures. In fact, they are sometimes referred to as artificial neural networks. The nature of this role is fundamentally dualistic. On the one hand, neural networks can provide powerful models of elementary processes in the brain, including processes of plasticity and learning. On the other hand, they provide solutions to a broad range of specific problems in applied engineering, such as speech recognition, financial forecasting, or object classification.

This chapter examines the dynamics of ion channels using methods similar to those introduced by Hodgkin and Huxley in 1952. Ion channels are a class of multimeric transmembrane proteins with a hydrophilic pore that facilitates transport of ions across the cell membrane. The size of the ion channel pore and the charge of amino acids near the opening of the pore help exclude entry of some ions while promoting the entry of others. This confers upon the ion channel a selective permeability to different ions. Several factors can induce conformational changes in the ion channel, altering its quaternary structure and therefore its permeability. These factors are referred to as gating variables because they function as a gate between the ion channels' different conformational states. Most ion channels are classified according to the nature of their gating and their selectivity of ions. The largest subclasses of ion channels classified by gating are the ligand-gated and voltage-gated ion channels. Ligand-gated ion channels change conformation when a ligand binds to them. The most common ligand-gated ion channels found at the post-synaptic membrane of neurons include NMDA, kainate, AMPA, and GABAA receptors.

This chapter introduces the models of voltage-gated ion channels into a model of single neuron dynamics. Neurons communicate with each other by transmitting and receiving electrochemical signals called action potentials. These action potentials are transient fluctuations in the cell's membrane potential, which propagate down a cell's axon without attenuation. In the central nervous system, action potentials have a duration in the order of milliseconds and can often be divided into three phases. The first phase of the action potential is a rapid depolarization of the membrane called the rising phase or upstroke of the action potential. This is followed by a repolarization of the membrane called the falling phase or downstroke of the action potential. The last phase follows a hyperpolarization of the membrane and is called the undershoot.

Publisher Summary This chapter defines the number of methods to characterize the processes surrounding synaptic transmission, in particular the release and diffusion of neurotransmitters. It also introduces handles for graphic objects to update images dynamically. It also helps in understanding different random variables, discrete distributions, finite difference approximations to partial differential equations, and the use of graphic handles for rudimentary animation. Chemical synapses use the release of chemical neurotransmitters to propagate signals from one neuron (presynaptic) to another (postsynaptic). The two cells are separated by the synaptic cleft, a gap of approximately 40 nm between the presynaptic and postsynaptic membranes. The chapter focuses on the neuromuscular junction, the site of innervation of skeletal muscle. We will also focus on the steps of neurotransmitter release and neurotransmitter diffusion.

This chapter describes the use of signal detection theory to analyze data generated in psychophysical—and hypothetical neurophysiological—experiments. Signal detection theory (SDT) represents a way to optimally detect a signal in purely statistical terms without and explicit link to decision processes in particular or cognitive processes in general. SDT provides a rich view of the problem of how to detect a given signal. In particular, it reframes the task as a decision process, adding a cognitive dimension to understand this matter. Signal detection theory constitutes a formal, stochastic way to estimate the probability by which some things are the case and others are not; by which some effects are real and others are not, and so on. As such, it has the broadest possible implications. Signal detection theory is used by pharmaceutical companies as well as oil prospectors, and it has even made its mark in public policy considerations.

This chapter presents an open-ended approach toward solving the problem of neural decoding. Specifically, it addresses how to predict the upcoming direction of movement from a population of neuronal signals recorded from motor areas of a macaque monkey. Neural decoding is a mathematical mapping from the brain activity to the outside world. In the sensory domain, the outside world consists of the received visual, auditory, or other sensory information. In the motor domain, the outside world consists of the state of the skeletomuscular system. This is the inverse of neural encoding, which maps the outside world to brain activity. Neural decoding can also be thought of as pattern recognition. A set of neuronal spike times represents a pattern, and the goal of the decoder is to figure out which stimuli or movements are associated with which patterns. This is a common problem in science. Doctors perform pattern recognition when they produce a diagnosis from a collection of physical and physiological findings.

This chapter focuses on a computationally efficient spiking cortical neuron model and also generalizes this model to a network of neurons. The task of understanding how different areas of the brain interact with each other to perform higher level functions such as motor coordination and speech is a major interest of modern neuroscience but also an extremely difficult one. Many factors contribute to the global dynamics of neural networks. First, neurons isolated from a network exhibit a variety of patterns and behaviors. Some examples include regular spiking neurons, fast spiking neurons, intrinsic bursting neurons, and subthreshold membrane oscillations. Some of these behaviors are more common than others. The synaptic coupling between neurons can have a large impact on the network's dynamics leading to synchronization among the neurons and network oscillations. The chapter also defines the network oscillations in the brain are often categorized by their frequency. Oscillations with a frequency less than 4 Hz are called delta rhythms. Oscillations between 4 and 8 Hz are called theta rhythms. Rhythms from 8 to 12 Hz are called alpha rhythms, and rhythms from 12 to 30 Hz are called beta rhythms. Rhythms above 30 Hz are called gamma rhythms.

This chapter introduces the techniques of phase plane analysis to analyze a simplified model of action potential generation in neurons known as the Fitzhugh-Nagumo (FN) model. Unlike the Hodgkin-Huxley model, which has four dynamical variables, the FN model has only two, so the full dynamics of the FN model can be explored using phase plane methods. The FN model can be created from the Hodgkin-Huxley model by combining the variables V and m into a single variable Ʋ and combining the variables n and h into a single variable r . In the exercise section the chapter also explains the pplane7 program. This program was used to make the figures in the Background. Finally, it defines the Fitzhugh-Nagumo model that is set-up with pplane7 by injecting different levels of current and examining how the behavior of the model neuron mimics that of a real neuron.