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Mammalian Brain as a Complex Adaptive System
A complex system is a collection of a number of building blocks interacting nonlin-early and giving rise to properties as a whole that are not evident from the prop-erties of the individual parts. Some basic characteristics of complex systems are summarized in Figure 1. Complex systems emerge from self-organization of the co-ordinative behavior of simple units in order to maintain energy optimization. Even though the building blocks seem to be fairly simple, nonlinear interactions between them may change the state of the whole. Smooth changes of the parameters that define the interaction between single units may change the behavior of the whole in a drastic way.
The brain is a “complex temporally and spatially multiscale structure that gives rise to elaborate molecular, cellular, and neuronal phenomena that together form the physical and biological basis of cognition” (Bassett and Gazzaniga, 2011). As any complex system, the nervous system is organized at several levels of organization, which are “separable conceptually but not detachable physically” (Churchland and Sejnowski, 1988). Still, the brain is much more “complex” than any other classically studied “complex system”. This complexity is a result of the vast number of different levels of organization, and the very rich nature of the emergent and immergent properties. Our limited knowledge about each level obstructs the “simplification” of building blocks, which is necessary in order to study the brain with the tools provided by the complex systems literature.
Brain is also an adaptive system. One of the biggest difficulties for brain func-tioning arises from the unpredictability of the nature. Brains have to retrieve the information collected from the dynamic and often “noisy” environment, in the sense that the information is not always present the same way in the same context. This requires the brain to act by adapting the organism to the new state of the environ-ment. Structure of the brain is plastic, hence not only the behavior, but also the material adapts to the environment in order to increase efficiency. Therefore, every brain has its own structure, as a function of both its own properties and the natural environment in which the structure is shaped (Koch and Laurent, 1999).
The levels of organization in the brain include molecules, synapses, single neurons, columns, hypercolumns, maps, cortical areas, sensory systems, and finally, the whole central nervous system (see Figure 1.1, which will be explained more in de-tails in Section 1). Organization at each level emerges from the interactions between the micro-level “agents” of the inferior level. Once the structure is stable, the whole is insensitive to the individual activities of the members of the inferior level (Wolf and Geisel, 2003).
Figure 2 – Archimboldo’s painting of Rudolf II represented as Vertumnus, the Roman god of the seasons. When the painting is seen from a short distance, the image is a collection of fruits, vegetables and flowers. If the painting is seen from a longer distance, the image of a person appears as a result of the good continuation of the forms of the individual parts.
The concept of “Perception” can be thought as an emergent property arising from the central nervous system, even though there is no physical layer corresponding to this level of organization. Self-organization at the perceptual level is revealed by the Gestalt psychology. Gestalt principles indicate that the sole interpretation of individual parts is not enough to explain the whole. In this sense, if the individual parts are not linked by the Gestalt laws, there is no information provided by a single part that would change the interpretation of the whole. The works of the medieval artist Archimboldo are good examples. For instance in the painting presented in Figure 2, Emperor Rudolf II is presented as the Roman god of seasons. The image is a collection of fruits, vegetables and flowers; which form the portrait of the emperor as a result of the Gestalt law of good continuation of the forms. In mental disorders such as schizophrenia or visual agnosia, this nice organization may be deteriorated, resulting in the loss of the concept of the whole, and a perception that is affected by the inner abnormal activity of the brain (hallucinations).
Perception emerges as the neuronal circuits are shaped by the information received from the natural environment. The organization schemes that will be explained in the following chapters are dependent on the initial training of the genetically-predefined neuronal networks. For example, development of the cortical maps can be explained by a self-organizing neural network trained by retinal waves and the natural environment (Mikkulainen, 2005), and animals that grow up in a different natural environment show biases in cortical map development (Tanaka et al., 2006).
As functionality of each brain is shaped by its own experience in the natural envi-ronment, individual experiences can be subjective. Different emergent properties of each individual brain may hence lead to the philosophical notion of qualia, i.e. how a certain mental state is felt or perceived by an individual. Mainzer (2007) argued that the qualia emerge by the interaction of the individual with the environment, and that this interaction can be explained by the nonlinear dynamics of complex systems. Understanding the limits of variability in how the brain respond to a par-ticular stimulation may help us to understand the objective limits of qualia, and study of the dynamics of the brain activity involving a single experience may give a quantitative measure of a certain quale.
In summary, a complex systems approach to study the brain would be useful to understand how individual units at a certain level (for example ion channels, single cells or columns) interact in order to give rise to the properties observed at the higher level. An illustration of levels of organization (or levels of abstraction) in the visual system is shown in Figure 3. Mesoscale level can be further divided into local and global population levels. Each level has a particular connectivity and coding strategy in order to solve a certain goal that would link the levels.
The work presented in this thesis is focused on population level processing in pri-mary visual cortex: We investigate how small groups of neurons coordinate in order to perform a common task that would give rise to global activity patterns. Un-derstanding of a particular level requires an intuition of what is done in inferior and superior levels. In our case, inferior level corresponds to the cellular level: each neuron has a way of handling the incoming information. Superior level can be considered as the system level: we are studying the primary visual cortex (V1) which has a particular task of local information extraction, but which acts also as a read-out buffer of the whole visual system (Lee and Mumford, 2003). We will first explain the basic properties of neurons that involve microscopic scale activ-ity in the brain. Then, we will introduce the macroscopic scale organization of the visual system, which corresponds to the regions and pathways. For each region, we will explain the region-specific characteristics of the microscopic organization which corresponds to the individual neurons. Finally, we will elaborate the meso-scopic scale organization which emerges from the interactions between individual neurons, corresponding to the population level. Before explaining the anatomy and physiology of the visual system, it is convenient to remind available tools which help us investigate the neuronal activity in different levels of organization.
Measures of neuronal activity at different scales
Our knowledge of the function of the brain has evolved very fast since the first ob-servations of Santiago Ramón y Cajal, Camillo Golgi and Heinrich Wilhelm Gottfried von Waldeyer-Hart at the end of the 19th century about the existence, structure and connectivity of neurons. Early studies were mostly based on anatomical investiga-tions of the neuronal tissue. The beginning of recordings with electrodes made a revolutionary contribution to the field, permitting to study real-time electrical activi-ties of the neurons. Since several decades, multichannel recordings and techniques that provide recording of the brain at various scales were developed. Combination of all these tools now will hopefully let us investigate the brain activity in all the aspects. In this chapter, we will briefly explain techniques used in neuroscience to study the function of the brain at different scales.
Neuronal tissues can be studied in-vitro, or in-vivo. In-vitro studies often involve working on slices of brain and are useful to determine the individual properties of isolated neurons independent of the interactions with other brain regions. However, in most cases, slicing procedures destroy most of the axons and dendritic trees, isolating the individual cell from the local network but it is still possible to study physical properties of the cellular membrane by injecting ionic solutions.
In order to understand the function of the living tissue in its context, network interactions need to be taken into account. If we want to study how the local and global activities interact together, in-vivo studies are more suitable. In-vivo studies involve working on intact animal, taken into account ethical considerations which may involve working with anesthetizers.
These two approaches combined may allow one to understand how brain tissue function at different scales and bridge together multiple levels of organization. The-oretical, computational, or hardware models of the neuronal systems permit deeper but more speculative investigations of the neuronal theories without the complica-tions of working with the living tissue. Modeling is especially useful for investigating parameter scales not reachable with in-vitro or in-vivo studies, or to bridge various studies performed at different scales. It is generally fruitful to combine analytical and computational tools with classical in-vitro and in-vivo studies in order to verify the consequences and limits of experimental findings.
Levels of organization in the nervous system and the spatio-temporal limits of the most well-known tools available in neuroscience are shown in Figure 1.1. The clas-sification of levels is based on the spatial scale. However, it should be noted that in the lower levels dynamics are faster than in the higher levels. It is important to choose an appropriate method that provides information about the level of organi-zation of interest.
Figure 1.1 – Levels of organization in the brain, and available methods to investigate the dynamics at each level. Adapted from Churchland and Sejnowski (1988) and Grinvald and Hildesheim (2004).
Electrophysiology
Most of our knowledge today about the brain is based on electrophysiological stud-ies. Depending on the type of recording, electrophysiological studies provide in-formation about the electrical activity in a certain level using electrodes. More conventional techniques involve single unit recordings. For intracellular studies, recordings are done with different types of electrodes. Micropipette electrodes in patch clamp provide recording of single or multiple channels, and sharp electrodes provide a measure of the voltage or current across the membrane. With these techniques, it is possible to record action potentials created by the neuron in a mil-lisecond range. These recordings provide also the measures of the fluctuations of the sub-threshold membrane potential that reflects more mesoscopic interactions in the local network.
Transmembrane currents can also be observed on the extracellular medium. Single unit activities revealed as action potentials and local field potentials (LFP) created by multiple neurons in a small volume can be recorded with microelectrodes placed in the extracellular space. LFP is a measure of the potential between two nearby but sufficiently apart electrodes, which gives information about the local current flow in the extracellular medium. Any activity of any excitable tissue around the recording site contributes to the LFP signal. The raw signal obtained by the recording elec-trode is low-pass filtered around a cut-off about 200 Hz for analysis. This process eliminates any fast events such as action potentials, and consequently the resulting signal reflects a more mesoscopic activity rather than fast individual activation of nearby neurons.
Even though the extracellular field provides a pooling of the activation of multiple neurons in the area, biases in sampling may arise from a number of reasons such as the geometry of the neurons, distance of a neuron from the electrode, and packing density (Buzsáki et al., 2012). Moreover, the reference electrode should be placed nearby in the brain, and this area often has very similar properties as the recording region. It is very difficult to choose a reference region that does not have any dominant local activity. Therefore, placement of the reference electrode introduces a second bias in LFP measurements.
In the last decades, development of multielectrode arrays provided means to record activity from a grid of multiple channels simultaneously. These improvements opened the way to study spatial arrangement of the cortical tissue at a mesoscopic scale. Multichannel recordings provide means to record spatiotemporal patterns of activity in the brain by sampling from multiple sites. Advances in recording and computation devices opens the way to record the data simultaneously from a high number of channels, however analysis of the large datasets provided by mul-tichannel recordings require development of appropriate algorithms that optimize computation. This is a common problem with neuroimaging techniques which may also be considered as multichannel recordings.
Strong extracellular potentials originate mostly from correlated activity of the neu-rons, as any uncorrelated activity will result in a flat profile. Correlated activity on an even more global scale can be observed with electrocorticography, which corre-sponds to the recording of the electrical activity using subdural surface electrodes. On the most global end of electrophysiology, we find electroencephalography (EEG). This is the oldest and the only noninvasive electrophysiological technique, which involves recording the activity filtered by the skull using scalp electrodes. Modern EEG caps provide up to 256 channels of recording.
Neuroimaging
Alternative methods to electrophysiology involve indirect measures of the neuronal activity. In the last decades, development of various neuroimaging techniques pro-vided noninvasive measures of the brain activity. Especially fMRI become very pop-ular as a result of the high-resolution non-invasive dynamic measurements pro-vided by the method. fMRI is a special case of magnetic resonance imaging. It benefits the different relaxation times of magnetization between oxygenated and non-oxygenated tissue. As the neural populations get activated, local blood vol-ume, oxyhemoglobin and deoxyhemoglobin concentrations change, giving rise to the blood oxygen level dependent (BOLD) signal. Time scales of activation and dynamics of the BOLD signal is relatively very slow with respect to the electrical activity. The time constant of the hemodynamic transfer function is in the order of a few seconds while electrophysiological activity may occur at a range of mil-liseconds. BOLD signal reflects the metabolic changes that result from oxygenation and energy consumption of the tissue, therefore not only neurons but also glial cells and neurovascular coupling contribute to this signal (Logothetis and Wandell, 2004). fMRI method provides a three dimensional recording of the brain activity with high spatial resolution and sampling. High spatial resolution up to tens of mi-crometers may be obtained using stronger magnetic field (>7 Tesla) using external contrast agents and smaller scanners, while human recordings can be done up to a millimeter range using 3-4 Tesla magnetic field.
Other indirect measures of the macroscale brain activity are positron emission to-mography (PET), Magnetoencephalography (MEG) and 2-deoxy-D-glucose (2-DG) method. PET was the most popular tool before the invention of the fMRI and is still used in neuroimaging. It involves usage of radioactive tracers which either stay in blood vessels or bind to receptors. These tracers emit gamma rays which are then detected by the PET scanner, reflecting the dynamics of the binding sites. MEG provides measure of the magnetic field created by the brain activity at high temporal but low spatial resolution. 2-DG method provides a metabolic measure of active brain areas. Using 2DG marking, it is then possible to perform post-mortem visualization of active brain areas, networks or single cells. This method has been very useful in order to image the functional architecture of the cortex before optical imaging methods were developed. However, real-time observation of the dynamics is not possible with this technique. 2-DG can also be used as a tracer for in-vivo functional near infrared imaging, similar to the radioactive agents used in PET scan.
Optical Imaging
As we see in Figure 1.1, optical imaging covers the widest spatial and temporal bandwidth for recording the brain activity. In reality, spatio-temporal resolution that is available while doing optical imaging is not limited by the nature of the interactions that are reflected by optical imaging, but the recording devices often limit the resolution of the recordings to a certain degree.
Optical imaging is less invasive than the other electrophysiological tools available in the micro and mesoscales. Recordings can be repeated over years on the same animal. The method also provides the possibility to work on behaving animals.
Optical imaging can be divided into two subcategories: intrinsic and extrinsic imag-ing. Intrinsic imaging involves recording of the metabolic changes of the tissue only by optical techniques. In extrinsic imaging, contrast agents that are sensi-tive to a particular change in the neuronal activity are used. Voltage Sensitive Dye (VSD) imaging falls into the extrinsic imaging category. Optical imaging is also a neuroimaging tool, and VSD imaging can be considered as both neuroimaging and electrophysiological recording technique. Good reviews of the optical imaging tech-nique are available (see Grinvald et al. (1999) for a general overview, Grinvald and Hildesheim (2004) and Chemla and Chavane (2010b) for VSD imaging). Here we will briefly introduce the basic principles of optical imaging, but the nature of the VSD signal and the important bibliography will be further detailed in the text.
Intrinsic imaging is a measure of metabolic changes due to neuronal activity. The underlying mechanism in intrinsic imaging is the BOLD signal, as it is for fMRI. When light is shed on the brain, these metabolic changes result in scattering and absorption of the light reflected by the tissue.
Optical signal observed by intrinsic imaging follows the BOLD signal activation range. Following the sensory stimulation, deoxyhemoglobin concentration increases in active regions as a result of initial oxygen consumption, resulting in darkening of the cortex. This signal is equivalent to the “initial dip” observed in the fMRI record-ings. Following this signal, delayed blood supply arrives in the tissue, decreasing he deoxyhemoglobin concentration and increasing oxyhemoglobin concentration. On a more precise time resolution, highly localized oxygen delivery to the active neuronal tissue occurs 200-400 ms after stimulus onset. This oxygen delivery is followed by the increase in blood volume 300-400 ms later, and finally oxyhemoglobin concen-tration starts to increase after 1000 ms (Frostig et al., 1990). The last contribution to the intrinsic signal is the light scattering that arises from the ion and water movement, volume changes of extracellular space, capillary expansion and neuro-transmitter release (Grinvald et al., 1999).
Figure 1.2 – Time courses of intrinsic signal compared to oxyhemoglobin and deoxyhe-moglobin concentrations. A: Time course of the global intrinsic signal on awake (solid line) and anesthetized (dashed line) monkey B: Oxyhemoglobin concentration and C: Deoxyhemoglobin concentration on awake monkey (solid lines) and anesthetized cat (dashed lines). Modified from Shtoyerman et al. (2000).
The relationship between the intrinsic signal and hemodynamic changes can be measured by image spectroscopy (Malonek and Grinvald, 1996; Vanzetta and Grin-vald, 1999; Shtoyerman et al., 2000). This method is based on the differences of reflection resulting from the amount of absorption by capillaries, small arteri-oles, and venules at different wavelengths. Time courses of the intrinsic signal and oxyhemoglobin and deoxyhemoglobin concentrations observed by Shtoyerman and colleagues are shown in Figure 1.2. Following these observations, Vanzetta and Grinvald (1999) measured the oxygenation level in the tissue directly by phospho-rescence and showed that the global intrinsic signal can be predicted by a linear combination of the oxyhemoglobin and deoxyhemoglobin concentrations (Vanzetta and Grinvald, 1999).
VSD imaging provides a more direct and temporally precise measurement of the neuronal activity. Voltage sensitive dyes are molecules that bind to the external surface of membranes of neurons. The dye’s sensitivity to voltage changes can be explained by a direct electro-chromic effect or the motion of the dye molecule in and out of the membrane. These effects reflect the changing electric field across the membrane and result in an increase of fluorescence. The blue dye (RH 1691, Optical Imaging, Rehovoth, Israel) filters out most of the hemodynamic artefacts because of the wavelength of light that is recorded (Shoham et al., 1999). Fluores-cence is captured by exciting the tissue on the peak of the optimum wavelength for the dye (~630nm), and then by filtering the emitted light above the peak of the optimum response range (~665nm). For intrinsic imaging, the cortex is illuminated at 605nm wavelength light and no other filter is used. The use of the second filter in VSD imaging is one of the major differences between VSD imaging and intrinsic imaging: in VSD imaging, only the fluorescent light is recorded while in intrinsic imaging the reflected light is recorded at all wavelengths. This provides filtering of an important amount of blood flow related artefacts.
Dyes provide information about the local change of the membrane potential. Flu-orescence that is reflected by the dye can be captured over different levels of or-ganization with a good choice of recording equipment. Therefore, the resolution indicated in Figure 1.1 represents the limitation of the dye technology only, but the recording limitations should also be taken into account.
In order to record population activity from V1, the dye which is diluted in an appro-priate solvent is applied on the cortical surface in a glass-covered chamber mounted on the skull opened over the areas to be recorded, and washed out after 2-3 hours of staining. This provides the dye to penetrate the cortical surface. In rodents, it is possible to stain the cortex without removing the dura (Lippert et al., 2007).
Due to the limit of penetration in the six layered cortex and filtering out of the signal coming from the deep layers, VSD signal reflects mostly the activity from layer II/III (Ferezou et al., 2006). However, dendritic trees of the neurons in different layers spread over other layers. A recent modeling study suggested that the 45% of the VSD signal originates from layer II/III activity, 20% from layer IV and 35% from layer V (Chemla and Chavane, 2010a).
Population recordings pool activity of tens of neurons under a single pixel. This single pixel reflects the activation of all the dye molecules under the recorded area (plus the light scattering from the nearby neurons) in a millisecond resolution. As the action potentials are very fast events that move very locally on the axon, and as the dendritic surface is very large compared to axonal surface, action potentials are filtered out in VSD recordings and the origin of the signal is mostly dendritic (Ferezou et al., 2006). Nevertheless, Chemla and Chavane (2010a) estimated the contribution of the pure spiking activity on the axons in VSD signal to be around 14%.
In contrast to multielectrode arrays, VSD imaging at population level provides pool-ing of multiple neurons under a pixel. Extracellular electrodes are sensitive to single unit activities over a region, but the recordings are biased as a result of the geometry and electrode placement (see the previous section). Instead, VSD imaging provides a more even pooling of all the excitable membrane surfaces under a pixel, which reflects direct intracellular membrane potential including the fine structure of the dendrites and axons. Chemla and Chavane (2010a) estimated the different contributions to this signal. They showed that the VSD imaging reflects mostly the dendritic signals (77%) of excitatory neurons (83%). Glial cells also contribute to the signal. However,e glial cells have very slow activation dynamics; hence their contribution is not present during the first seconds of recording.
As a result of this rich pooling, synchronous activity of nearby neurons is essential in order to obtain a high quality recording. As we will see in the following chapters, modular organization of the cortex provides packing of functionally similar neurons in nearby regions. This is the crucial mechanism that makes VSD imaging possi-ble in the population level. One other consequence of the pooling of all excitable membranes under a pixel is the over-representation of dendritic activities over the activities going on the somata and the axons. This is a result of the greater volume of dendrites compared to somata and axons in the cortex, especially on the layers 2/3 where horizontal connections between cells are prominent.
Even though the same cameras are often used for VSD imaging and intrinsic imag-ing, lower temporal resolution of intrinsic imaging permits sacrificing the temporal resolution for higher spatial resolution. Lower temporal resolution is also a factor that increases the signal-to-noise ratio in intrinsic imaging. As we go to higher temporal resolutions, the number of photons detected per frame will decrease, in-creasing the shot noise detected by the camera.
VSD imaging provides the optimal spatial and temporal resolution range to date for investigating mesoscopic dynamics of neural population activity. Extracellular recordings via multichannel arrays and two-photon imaging of calcium signal are the other techniques that offer comparable resolution. Multielectrode arrays pro-vide fast and direct recording of electrical activity in the brain, however the spatial sampling is low compared to VSD imaging. Moreover, multielectrode arrays record the activity on the extracellular media, and adequate methods are needed in order to extract single cell responses. The advantage over VSD imaging is the temporal resolution and the possibility to record supra-threshold activity.
Calcium imaging is another method that is comparable to the VSD imaging spec-trum. This method measures the calcium in the cells by using chemical or genet-ically encoded indicators, which bind to calcium ions. When this binding occurs, a fluorescence change which permits visualization of intracellular calcium concen-tration takes place. When combined with 2-photon microscopy, calcium imaging provides very good spatial resolution that make observation of single cell activity possible. However, calcium dynamics are relatively slow with respect to membrane potential measures. Calcium signal is also biased towards supra-threshold activity (Peterka et al., 2011).
Berger et al. (2007) performed simultaneous recording of VSD and calcium imaging in order to quantify the differences between the measures provided by these meth-ods. They showed that calcium signal is slower than membrane potential revealed by VSD to return to baseline, and calcium signal filters fast fluctuations of the membrane potential. Moreover, the VSD signal spread more than the calcium sig-nal, which is expected from the differences between subthreshold and suprathresh-old activities revealed by VSD and calcium imaging respectively. It should be noted that as it is the case for VSD imaging, calcium signal itself offers a high resolu-tion measure (it occupies the lower two-thirds of the optical imaging resolution in Figure1.1 (Grinvald, 2005)), but the main restriction is the recording and staining technology.
Overall, VSD imaging overcomes the low temporal dynamics of intrinsic and cal-cium imaging, while providing a much higher spatial sampling than multielectrode arrays. Moreover, subthreshold potential recorded by VSD imaging reflects local neuronal interactions avoiding the bias of individual cell spiking, which provides a better measure of mesoscopic activity in the brain.
Table of contents :
I Introduction
1 Measures of neuronal activity
1.1 Electrophysiology
1.2 Neuroimaging
1.3 Optical Imaging
2 Functional Organization of the Visual Cortex
2.1 Neuron as a Basic Processing Unit
2.2 Overview of the Visual System
2.2.1 Early Visual System
2.2.2 The Primary Visual Cortex
2.2.3 Higher Visual Areas
2.3 Mesoscale Organization at the Population Level in V1
2.3.1 Columnar organization of the cortex
2.3.2 Connectivity inside a column: Spanning the layers of the cortex
2.3.3 Connectivity between columns: Horizontal connections
2.3.4 Cortical Maps
3 Dynamics of Visual Cortical Activity
3.1 Coding strategies
3.1.1 Temporal vs. rate coding
3.1.2 Coding by synchrony
3.1.3 Propagation in a cascade
3.1.4 Sparse coding
3.1.5 Dynamics of inhibition and excitation in shaping neuronal responses
3.1.6 Dynamics of orientation tuning
3.2 Operating Regimes of the Visual Cortex
3.2.1 Variability of Neuronal Responses
3.2.2 Structure and Role of the “Cortical Noise”
3.3 Attractor States and Transient States
4 Analysis Approach for VSD Imaging
4.1 Composition of VSD Imaging Recordings
4.2 Denoising strategies
4.2.1 Conventional Methods for Denoising VSD Imaging Data
4.2.2 Statistical Methods for Source Separation
II Methodology
5 Experimental Setup and Data Analysis
5.1 Animal Preparation
5.2 Visual Stimulation
5.3 Data Analysis
5.4 Stimulus locked time-frequency analysis
III Results
6 Source Separation for Denoising of VSD Imaging Data
6.1 Introduction
6.2 Results
6.2.1 Blank Subtraction and Division on VSD Imaging Data
6.2.2 Source Separation on Raw Data for Denoising
6.2.3 Variations of the Denoising Model
6.3 Discussion
7 Source Separation for Dimensionality Reduction
7.1 PCA on Denoised Recordings
7.1.1 Stimulus selective and nonselective components revealed by PCA
7.1.2 Dynamics of Orientation Selectivity on a 3-Dimensional Principal Component Space
7.1.3 Anisotropies of the ring attractor
7.1.4 Orientation preference on the ring attractor compared to the orientation map
7.1.5 Detection of the Area 17/18 Border by PCA
7.2 ICA on Denoised Recordings
7.3 Discussion
8 VSD Imaging in Response to Stimuli with Different Statistics
8.1 Denoising of Long Recordings
8.2 Variability of Neural Population Activity
8.3 PCA on Natural Image Response
8.4 Discussion
IV Conclusion
