Seminars



Quantitative Biology Seminar
Monday, November 7, 2016: 335 West Hall, 12:00p - 1:00p

PresenterDaniel Wójcik, PhD, Nencki Institute for Experimental Biology, Warsaw

Discussion Source reconstruction from extracellular potentials: from single cells to the whole brains

Abstract Extracellular recordings of electric potential remain a popular tool for investigations of brain activity on all scales in animals and humans, from single cells (spikes) to systems studied with depth electrodes (LFP, SEEG), subdural recordings (ECoG), and on the scalp (EEG). They are relatively easy to record but difficult to interpret: since electric field is long range one can observe neural activity several millimeters from its source. As a consequence, every recording reflects activity of many cells, populations and regions, depending on which level we focus. One way to overcome this problem is to reconstruct the distribution of current sources (CSD) underlying the measurement.

We recently proposed a kernel-based method of CSD estimation from multiple extracellular recordings from arbitrarily placed probes (i.e. not necessarily on a grid) which we called kernel Current Source Density method (kCSD). In my presentation, I will present the recent advances of this method, latest software implementations, and explain why it works. I will also show two recent developments, skCSD (single cell kCSD) and kESI (kernel Electrophysiological Source Imaging). skCSD assumes that we know which part of the recorded signal comes from a given cell and we have access to the morphology of the cell. This could be achieved by patching a cell, driving it externally while recording the potential on a multielectrode array, injecting a dye, and reconstructing the morphology. In this case we know that the sources must be located on the cell and this information can be successfully used in source estimation. In kESI we consider simultaneous recordings with subdural ECoG (strip and grid electrodes) and with depth electrodes (SEEG). Such recordings are taken on some epileptic patients prepared for surgical removal of epileptogenic zone. When MR scan of the patient head is taken and the positions of the electrodes are known as well as the brain’s shape, the idea of kCSD can be applied to constrain the possible distribution of sources facilitating localization of the foci.

More informationQuantitative Biology Seminars



Math 563 (2016): Advanced Mathematical Methods in Biology: Math, Music and the Brain
Monday, Wednesday, and Friday, 12-1pm. Mondays and Wednesdays in B735 East Hall, Fridays in the Community Lounge at the School of Public.

Instructor:Daniel Forger (Professor of Mathematics, Research Professor of Computational Medicine, AAGO); forger@umich.edu

Overview: How can our appreciation and performance of music be enhanced by understanding mathematics and basic principles of how the brain works? By studying music, can we learn about new mathematics and principles of signal processing in the brain? Can principles of music theory be deduced by analysis of the works by master composers? The connections between mathematics and music have been known for thousands of years. Yet, recent advances in technology, computational neuroscience and "big data" have provided new answers to these questions.

In this course, we study mathematical models for how the brain processes sound, and mathematical techniques for analyzing music performance. Although examples will be presented from ancient to contemporary music, we will focus on analyzing Bach's Trio Sonatas throughout the semester. Group work and original research will be encouraged. The class will meet alternately between a computer lab and a performance venue where live performances will regularly be included in class lectures.

Prerequisites: Granger causality (GC) analysis is one of the major approaches to explore the dynamical causal connectivity among individual neurons or neuronal populations. In this talk, focusing on the connectivity reconstruction of the conductance-based integrate-and-fire neuronal networks, we address two issues: (i) how the causal connectivity obtained from GC analysis can be mapped to the underlying anatomical connectivity; and (ii) how we can sample discretely from the time continuous quantities, e.g., membrane potential, to obtain a reliable GC network reconstruction. We numerically demonstrate that the anatomical connectivity can be successfully reconstructed from the GC analysis and theoretically establish a quadratic relation between the GC and the coupling strength. We also analyze in detail the impact of sampling interval length on the GC analysis of uniformly sampled data and propose a strategy to circumvent the possible sampling hazards for a reliable network reconstruction. In addition, we establish a nonuniform sampling GC analysis framework to achieve a reliable network reconstruction. Finally, we note that our analysis on the validity and reliability of GC analysis can be extended to more general dynamics.

Contact: Danny Forger at forger@umich.edu for more information