Modeling And Interpretation Of Extracellular Potentials

CNS2012 Tutorial, 21.03.2012Modeling and interpretation ofextracellular potentialsGaute T. Einevoll1, Szymon Łęski2, Espen Hagen11ComputationalNeuroscience Group (compneuro.umb.no)Norw. Univ of Life Sci. (UMB), Ås; Norwegian Node of INCFNencki Institute of Experimental Biology, WarsawPolish Node of INCF21

Overall plan for tutorial 9.00-9.50: Lecture 1 (Gaute)9.50-10.05: Break10.05-10.55: Lecture 2(Gaute & Szymon)10.55-11.10: Break11.10-12.00: Lecture 3 (Szymon)12.00-13.00: Lunch break13.00-: Tutorials (Espen & Szymon)2

Physiological measures of neural activityMembrane potentialSpikeVoltage-sens. die imaging (VSDI)Intrinsic optical imagingLocal field potential (LFP)Two-photon calcium imagingMultiunit Activity (MUA)Functional MRIEEGMEGPET Look for correlations between measurementsand stimulus/behavior Typical multimodal analysis: Look forcorrelations between different experiments

Physics-type multimodal modelingVSDI: Weighted sumover membranepotentials close tocortical surfaceSpike, MUA: WeightedLFP,EEG,MEG:Weighted sum overtransmembranecurrents all overneuronsum over transmembranecurrents in soma region Need to work out mathematical connections between neuron dynamicsand different experimental modalities (”measurement physics”)4

’Modeling what you can measure’ A candidate model for, say, network dynamics in a cortical columnshould predict all available measurement modalitiesSpikesMulti-unit activity (MUA)Local field potential (LFP)Voltage-sensitive dye imagingTwo-photon calcium imaging And we need neuroinformaticstools to make this as simple aspossiblehttp://compneuro.umb.no/LFPy5

Measuring electrical potentials in the brain Among the oldest and (conceptually) simplestmeasurents of neural activity Richard Caton (1875): Measures electrical potentialsfrom surfaces of animal brains (ECoG)RECORDINGELECTRODEΦREFERENCEELECTRODEFAR AWAYPIECE OF CORTEX6

Typical data analysis Recorded signal split into two frequency bands: High-frequency band ( 500 Hz): Multi-unit activity (MUA),measures spikes in neurons surrounding electron tip Low-frequency band ( 300 Hz): Local field potential (LFP),measures subthreshold activity LFP often discarded Sometimes used for current-source density(CSD) analysis with laminar-electroderecordings spanning cortical layers7

Revival of LFP in last decade LFP is unique window intoactivity in populations(thousands) of neurons New generation of siliconbased multielectrodes with upto thousands of contacts offersnew possibilities Candidate signal for braincomputer interfaces (BCI);more stable than spikes8

Rat whisker system:laminar electrode recordings(Anna Devor, Anders Dale, UC San Diego;Istvan Ulbert, Hungarian Acad. Sci, )”RETINA”Brainstem”EYE”Whisker9

Laminar electrode recordings from ratbarrel cortex – single whisker flicktop ofcortexLow-pass filter( 500 Hz):LOCAL FIELDPOTENTIAL(LFP) bottomMeasure ofdendriticprocessingof synapticinput?of cortexstimulusonsetHigh-pass filter( 750Hz),rectification :MULTI-UNITACTIVITY (MUA)Einevoll et al, J Neurophysiol 2007Measure ofneuronalactionpotentials?10

Physical origin of LFP and MUA Source of extracellular potential: Transmembrane currentsREFERENCEELECTRODEFAR AWAY(Φ 0)Φ(t)EXTRACELLULAR RECORDINGELECTRODEcurrent sink: I1(t)r1r2PIECE OF NEURAL TISSUEcurrent source: I2(t)FORWARD SOLUTION: : extracellular conductivity11

Note: Current monopoles do not existcurrent sink: I1(t)current source: I2(t) -I1(t) Conservation of electric charge requires(capacitive currents included!): From far away it looks like a current dipole12

Assumptions underlying:I. Quasistatic approximation to Maxwell’s equations- sufficiently low frequencies so that electrical andmagnetic fields are decoupled (OK for f á 10 kHz)- here: not interested in magnetic fields- then: 13

Assumptions underlying:II. Coarse-grained extracellular medium described byextracellular conductivity Φ(t)r1r2I1(t)-I1(t)Φ(t) r1I1(t)-I1(t)r214

Assumptions underlying:III. Linear extracellular mediumj: current density (A/m2)E: electric field (V/m) IV. Extracellular medium tropic15

Assumptions underlying:IV.1: Ohmic: σ is real, that is, extracellular medium isnot capacitive OKIV.2: Homogeneous: σ is the same at all positions OK inside cortex, but lower σ in white matter Formula can be modified my means of «method of images»from electrostaticsIV. 3: Frequency-independent: σ is same for all frequencies Probably OK (I think), but still somewhat debated But if frequency dependence is found, formalism can easily beadapted16

Assumptions underlying:IV.4 Isotropic: σ is the same in all directions- σ is in general a tensor(σx ,σy ,σz)- Easier to move alongapical dendrites thanacross (σz σx and σy)zx - Cortex: σz 1-1.5 σx,yGeneralized formula:17

Forward-modelingformula formulticompartmentneuron modelΦ(r)Current conservation:18

Inverse electrostatic solution No charge pileup inextracellular medium:transmembrane currents Inversesolution:Φ(r) Forwardsolution:19

Current source density Neural tissue is a spaghettilike mix of dendrites, axons,glial branches at micrometerscale In general, theextracellular potentialwill get contributions froma mix of all these Current source density (CSD) [C(x,y,z)]: density ofcurrent leaving (sink) or entering (source) extracellularmedium in a volume, say, 10 micrometers across [A/m3]20

Electrostatic solution for CSD Definition of CSD: Inversesolution: Forwardsolution:21

Generalization to cases withposition- and direction-dependent σ Generalized Poisson equation: Can always be solved with Finite Element Modeling (FEM) Example use: Modeling of MEA experiments (slice, cultures)22

New book Chapter on modeling ofextracellular potentials:23

Forward-modelingformula formulticompartmentneuron modelΦ(r)Current conservation:24

Multicompartmental modeling scheme Example dendritic segment[non-branching case]:Vi-1 Kirchhoff’s current law(”currents sum to zero”):CURRENTS TONEIGHBOURINGSEGMENTSPASSIVEMEMBRANECURRENTViVi 1transmembrane currentACTIVE MEMBRANECURRENTSSYNAPTICCURRENTS25

Forward modellingof spikesWhat does an actionpotential look like as seen byan extracellular electrode?[neuron model fromMainen & Sejnowski, 1996]From Henze et al (2000):26

How does theextracellularsignature of actionpotentials dependon neuronal morphology? Amplitude is (i) roughly proportional to sum ofcross-sectional areas of dendrites connected tosoma, (ii) independent of membrane resistance Rm, Spike width increases with distance from soma,i.e., high-frequency dampening also with simpleohmic extracellular mediumPettersen & Einevoll, Biophysical Journal 2008amplitudespike width27

Spike sorting problem Electrodes pick up signalsfrom many spiking neurons;must be sorted At present spike sorting is:o labor intensiveo unreliable Need automated spikesorting methods which areo accurateo reproducibleo reliableo validatedo fastto take advantage of newQuian Quiroga et al. 2005generation of multielectrodes28[from Buzsaki, Nature Neurosci, 2004]

Steps in spike sorting29Einevoll et al, Current Opinion Neurobiology 2012

Test data for spike-sorting algorithms30

Example model test dataSPIKESORTING Can make test data of abitrary complexity by, for example,(i) varying dendritic morphologies(ii) vary spike shapes(iii) include adapting or bursting neurons(iv) add arbitrary recorded or modeled noise(v) tailor correlations in spike times across neurons31

Collaborative effort on development and validation of suitableautomatic spike-sorting algoritms needed Collaborate website shosted by Gnode, the German node of theInternational NeuroinformaticsCoordinating Facility (INCF)http://www.g-node.org/spikeCurrent Opinion in Neurobiology, 201232

Poster on Tuesday: P14333

Example LFP from multicompartment modelBasal excitation gives ”inverted” LFPpattern compared to apical excitationLinden et al, Journal of Computational Neuroscience 201034

Generated LFP depend on morphologyPyramidal(L5 cat V1):Stellate(L4 cat V1):Linden et al, Journal of Computational Neuroscience 201035

LFP dipole from single L5 pyramidal neuron1 Hz oscillatory current into apical synapse:36

Frequency dependence of LFP dipole1 Hz100 Hz37

Intrinsic dendritic filtering of LFPTransmembrane currentfrequency [Hz]Membrane potentialLinden et al, Journal of Computational Neuroscience 2010frequency [Hz] 38

Origin of low-pass filtering effect of LFP Depth profiles of return current:1 Hz100 Hzmembraneareatransmembranecurrent100 Hz10 Hz1 HzEffective current-dipole moment decreases withincreasing frequency due to cable properties of dendrites39

How ’local’ is thelocal field potential? Modeling study forpopulations of neurons:? Uncorrelated neuronal LFP sources: spatial reach 0.2 mm Correlated neuronal LFP sources:o spatial reach set by spatial range of correlations of synaptic inputo effect of correlations depends sensitively on synaptic input distributionLinden et al, Neuron 201140

Poster on«Frequency dependenceof spatial reach»,Tuesday: P14341

Collaborators on modeling and analysis ofextracellular electrical potentialsNorw. Univ. Life Sci.Klas PettersenEspen HagenHenrik Lindén (KTH)Tom Tetzlaff (Jülich)Eivind S. NorheimAmir KhosrowshahiTorbjørn Bækø NessPatrick BlomquistHåkon EngerHans E. PlesserUC San DiegoAnders DaleAnna DevorEric HalgrenSergei GratiyFZ JülichMarkus DiesmannSonja GrünNencki Inst, WarsawSzymon LeskiDaniel WojcikHungarian Acad SciIstvan UlbertRadboud, NijmegenDirk SchubertRembrandt BakkerETH Zürich/BaselFelix FrankeTU BerlinKlaus ObermayerLMU Munich (INCF G-node)Thomas WachtlerAndrey SoboloevFunding:Research Council of Norway (eScience, NOTUR, NevroNor)EU (BrainScaleS)National Institute of Health (NIH)International Neuroinformatics Coordination Facility (INCF)Polish-Norwegian Research FoundationEND42

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like mix of dendrites, axons, glial branches at micrometer scale In general, the extracellular potential will get contributions from a mix of all these. 21 Electrostatic solution for CSD . increasing frequency due to cabl