Neural data-analysis Workshop Ben-Gurion University of the Negev Dept. of Cognitive and Brain Sciences Neural data-analysis Workshop

Objectives Objectives of the course: Objectives for today: To be capable of applying classical analysis techniques on typical recordings of brain activity using MATLAB ® Such recordings include: EEG (MEG), extra / intra cellular neuronal activity, electrode array pre-processed experimental data Develop professional attitude / abilities regarding analysis of neural data in general Objectives for today: Elaborate on the course objectives ;-) A quick introduction to digital signals in general and to brain activity signals 1st MATLAB exercise Presentation / hands on experience

Digital signals – Basics Example – Sinusoidal signal 𝑆(𝑡)=𝐴∙𝑐𝑜𝑠 (2𝜋𝑓𝑡+𝜑) t – time (Sec) A – amplitude f – frequency (Hz) = 1 / CycleTime (Sec) φ – phase

Digital signal processing – preview To analyze electrical signals, we use a converter of the measured signals from analog to digital (A2D) Sampling rate – frequency at which the analog signal is sampled and converted to digital form – measured in Hertz (1/Sec) Digital sampling of analog electrical signals results in a sequence of integer numbers with a length that equals the product of the signal duration (sec) and the sampling rate (1/sec) http://en.wikipedia.org/wiki/Sampling_rate

Brain activity signals Macroscopic level EEG (MEG) fMRI Microscopic level: Action potentials Intracellular Extracellular

From the lowest to the highest The macro and micro levels are related, as shown below. This study recorded EEG and intra-cellular voltage simultaneously. Contreras D, Steriade M. Cellular basis of EEG slow rhythms: a study of dynamic corticothalamic relationships. J Neurosci (1995)

Ex. 1 – Analyzing Intracellular data Download the exercise. Start working on the section “Qualitative observation of the given signals”

Finding spike times using threshold After looking at the signal (blue curve) we chose to have a threshold of -30 (green line). The black curve represents the binary vector (SaTH = (Si > TH)): It gets a value of “1” for every sample of the signal that is above the threshold It is “0” otherwise The red curve is the “derivative” (SaTHdiff = diff (SaTH)): It gets a value of “1” when the signal crosses the threshold in the positive direction It gets a value of “-1” when the signal crosses the threshold in the negative direction

Firing rate The basic way to calculate the firing rate is to divide the spike count with the segment length – in this example it is 7/0.2 = 35 spikes/sec (note, the usage of 200 mSec segment represents the stimulus time length as expressed in the exercise). The advantages of using this method is simplicity and strait forwardness The disadvantages is that here, there’s no way to learn about the statistics of the spike times ensemble. In other words, in this way we cannot estimate the measurement error. 11th segment of S1 Spike times: 3.0503 3.0597 3.0892 3.1209 3.1535 3.1865 3.2215

inter-spike interval (ISI) statistics ISIs of the previous example: 0.0094 0.0295 0.0317 0.0326 0.0330 0.0350 An alternate method of calculating the firing rate is to calculate the inverse of the time interval between 2 consecutive spikes (named “Inter Spike Interval” or ISI). In the given example we have 7 spikes → 6 ISIs i.e., 6 different rates could be defined here – what shall we do? We have 4 options: 1/mean(ISI) = 35.0467 spikes/sec mean(1./ISI) = 43.5627 spikes/sec 1/median(ISI) = 31.1042 spikes/sec median(1./ISI) = 31.1103 spikes/sec the methods using mean are more sensitive to the outliers – in our case the 1st ISI (9.4 mSec) is very far from the other ISI (29-35 mSec). The median is more robust to outliers. 1/std(ISI) or std(1./ISI) can be applied to estimate the measurement error…