Guide Quantitative Methods in Neuroscience: A Neuroanatomical Approach

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Table of contents

Similarly for statements about the total length of nerve fibres, capillaries etc. This reflects the founders' idea that stereology also offers insights and rules for the qualitative interpretation of sections. Stereologists have helped to detect many fundamental scientific errors arising from the misinterpretation of plane sections.

Such errors are surprisingly common. For example:.

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Stereology is a completely different enterprise from computed tomography. A computed tomography algorithm effectively reconstructs the complete internal three-dimensional geometry of an object, given a complete set of all plane sections through it or equivalent X-ray data. On the contrary, stereological techniques require only a few 'representative' plane sections, from which they statistically extrapolate the three-dimensional material. Stereology exploits the fact that some 3-D quantities can be determined without 3-D reconstruction: for example, the 3-D volume of any object can be determined from the 2-D areas of its plane sections, without reconstructing the object.

This means that stereology only works for certain quantities like volume, and not for other quantities. In addition to using geometrical facts, stereology applies statistical principles to extrapolate three-dimensional shapes from plane section s of a material.

Statisticians regard stereology as a form of sampling theory for spatial populations. To extrapolate from a few plane sections to the three-dimensional material, essentially the sections must be 'typical' or 'representative' of the entire material.

Course Descriptions

There are basically two ways to ensure this:. The first approach is the one that was used in classical stereology. Extrapolation from the sample to the 3-D material depends on the assumption that the material is homogeneous. This effectively postulates a statistical model of the material. This method of sampling is referred to as model-based sampling inference. The second approach is the one typically used in modern stereology. Instead of relying on model assumptions about the three-dimensional material, we take our sample of plane sections by following a randomized sampling design, for example, choosing a random position at which to start cutting the material.

Extrapolation from the sample to the 3-D material is valid because of the randomness of the sampling design, so this is called design-based sampling inference. Design-based stereological methods can be applied to materials which are inhomogeneous or cannot be assumed to be homogeneous. These methods have gained increasing popularity in the biomedical sciences, especially in lung-, kidney-, bone-, cancer- and neuro-science. Many of these applications are directed toward determining the number of elements in a particular structure, e. Many classical stereological techniques, in addition to assuming homogeneity, also involved mathematical modeling of the geometry of the structures under investigation.

These methods are still popular in materials science, metallurgy and petrology where shapes of e. Such geometrical models make it possible to extract additional information including numbers of crystals. However, they are extremely sensitive to departures from the assumptions.

In the classical examples listed above, the target quantities were relative densities: volume fraction, surface area per unit volume, and length per unit volume. Often we are more interested in total quantities such as the total surface area of the lung's gas exchange surface, or the total length of capillaries in the brain. Sampling principles also make it possible to estimate total quantities such as the total surface area of lung. Using techniques such as systematic sampling and cluster sampling we can effectively sample a fixed fraction of the entire material without the need to delineate a reference volume.

This allows us to extrapolate from the sample to the entire material, to obtain estimates of total quantities such as the absolute surface area of lung and the absolute number of cells in the brain. Undergraduate Program.


Courses: Schedules and Links. Neuroscience-related programs at NYU. Lectures and readings cover basic biophysics and cellular, molecular, and developmental neuroscience. Lectures and readings concentrate on neural regulation of sensory and motor systems. The first semester includes histology and cellular and molecular neuroscience. The second semester includes neuroanatomy, sensory neurophysiology, modern neuroanatomical tracer techniques, psychophysics, and computational neuroscience. Lectures, readings, and laboratory exercises cover neuroanatomy, cognitive neuroscience, learning, memory, and emotion.

Lecture, readings, and homework exercises cover basic mathematical techniques for analysis and modeling of neural systems. Students participate in the research activities in several different laboratories to learn current questions and techniques in neuroscience. We will approach these issues from multiple perspectives, drawing on theoretical, behavioral, and neural data from economics, psychology, and neurobiology. Major topics include: decision under risk and uncertainty; multiplayer interactions and social preferences; the role of learning in evaluating options; and choice mechanisms.

Each week a different disorder will be addressed in a 2.

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Part of each class session will include an overview by a clinical expert, who will provide a clinical understanding of the disease, including signs and symptoms. A second part will be given by a scientist who does basic research in the field, who will discuss experimental strategies and current hypotheses about pathophysiological mechanisms at the cellular and genetic level. Readings will be provided from each of these experts for each topic. Topics may include post-traumatic stress disorder, Autism, Parkinson's disease, epilepsy, addiction, and schizophrenia. Special Topics Courses: These are advanced 3 point seminars led by the faculty to provide in-depth consideration of specific topic areas in neural science.

Priority is given to doctoral students in neural science but others may be able to register if they meet the pre-requisites and there is room in the course.

Spiking and firing rate mechanistic treatments of network dynamics as well as probabilistic behavioral descriptions will be covered. Students will undertake computing projects related to the course material: some in homework format and a term project with report and oral presentation. Readings are from research papers and some secondary sources.

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Students present critical reviews of one of the papers on the reading list. A paper is required by end of the course on a topic mutually agreeable to student and instructor. Both analytical perturbation and bifurcation methods and numerical techniques will be described and used, serving as an applied introduction to these methodologies.

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Students will undertake computing projects related to the course material. It covers the basic ideas and methods of modeling single neurons, recurrent neural networks, synaptic plasticity and learning. The focus is on the neural circuit mechanisms of core cognitive functions such as decision-making and working memory, both in local neural networks and multi-regional large-scale brain systems.

This course is not about Bayesian data analysis, but about theories that the brain itself is a Bayesian decision-maker.

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Nevertheless, we will spend some time on model fitting and model comparison. The course will be taught at an introductory level, with many examples and basic exercises. Didactic principles will be strictly adhered to. If you wish to analyze your own data in a Bayesian framework, there will be an opportunity to do so in a final project.

Students will collect data using whole-cell recording, dynamic clamp, and optogenetic stimulation techniques in the in vitro slice or culture preparation. Several approaches to modeling the data will be discussed, including spiking Hodgkin-Huxley, integrate-and-fire neurons and variants , rate, and mean field models. The goal is to choose the simplest model that will account for the intrinsic and statistical properties of individual neurons and networks. Each class consists of a short lecture covering the main cellular components of a particular circuit, followed by a round table discussion of key papers selected to highlight specific and distinguishing features of the circuit.

Topics include: imaging and optics, color, estimation and representation of position, alignment, displacement, and local orientation, Fourier and multi-scale image decompositions wavelets , statistical image modeling and its use in compression, estimation, enhancement, synthesis and classification.

Neuroanatomy made ridiculously simple

Throughout, relationship of these computations to biological vision will be discsused. The format will be mixed: lectures, journal-club- like presentation of papers, and exploration with computer-driven stimuli. We will discuss neuronal mechanistic models and computational models to go with the behavior.

Our approach will be case-study; relevant background will be presented. We will emphasize auditory perception spatial hearing, pitch, auditory scene analysis but we will likely include case studies from vision e. We will simulate cellular neurophysiology experiments to explore resting and action potentials, firing properties, synaptic conductances and synaptic integration.