PsPM course session 2: LTI & GLM -...
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[email protected] PsPM course session 2: LTI & GLM Dominik R Bach Wellcome Centre for Human Neuroimaging & Max Planck UCL Centre for Computational Psychiatry and Ageing, University College London Clinical Research Priority Program "Synapse & Trauma" & Department of Psychiatry, Psychotherapy, and Psychosomatics, University of Zurich 09.04.2020 www.bachlab.org [email protected] @bachlab_cog WELLCOME CENTRE FOR HUMAN NEUROIMAGING MAX PLANCK UCL CENTRE FOR COMPUTATIONAL PSYCHIATRY AND AGEING RESEARCH SNA SCR = RF
Transcript of PsPM course session 2: LTI & GLM -...
PsPM course session 2: LTI & GLM
Dominik R BachWellcome Centre for Human Neuroimaging & Max Planck UCL Centre for Computational Psychiatry and Ageing, University College London
Clinical Research Priority Program "Synapse & Trauma" & Department of Psychiatry, Psychotherapy, and Psychosomatics, University of Zurich
09.04.2020
@bachlab_cog
WELLCOME CENTRE FOR HUMAN NEUROIMAGINGMAX PLANCK UCL CENTRE FOR COMPUTATIONAL PSYCHIATRY AND AGEING RESEARCH
SNA SCR � = RF
Psychological variable Neural activity Physiological
signal
Neural model
Peripheral LTI model
CS+/CS- US Memory Memory difference between CS+/CS-?
The "best possible" approximation to the true psychological variable.
Course overview
Lecture 2: 09.04.2020
Lecture 3: 16.04.2020 Lecture 4: 23.04.2020Lecture 5: 30.04.2020 Lecture 6: 07.05.2020Lecture 6: 07.05.2020
Lecture 7: 14.05.2020
PsPM file:Data time-series
(Marker time stamps)Recorded file
Analogue data recording Digitisation
Preprocessing:Trim unnecessary data
Detect missing fixation and exclude/(correct) pupil sizeHeart beat detection & interpolation
Respiration cycle detection & interpolationStartle eyeblink EMG filtering and rectification
Import
Model inversion:GLM, non-linear models
1st (participant) level model files
Group-level model (t-test,
ANOVA, LME, ...)
If possible, only anti-aliasing filter
High sampling rate if no anti-aliasing
filter
Each step usually generates a new file with a prefix
(SPM-style)
2nd-level t-test
Export parameters to SPSS, R, ...
2nd (group) level model file
All necessary filters applied on-the-fly
during model inversion
PsPM pipeline overview
Psychological variable
Neural activity
Physiological signal
Neural model
Peripheral LTI model
Examples: Instantaneous impulse with constant latency Short Gaussian impulse
Basic formalism
Bach & Friston (2013), Bach et al. (2018)
Psychological variable Neural activity Physiological
signal
Peripheral LTI model
All published model-based methods make LTI assumptionsSome don't say so which has been interpreted as an "advantage" over PsPM (see e.g. Boucsein 2012, page 171)
LTI assumptions in hybrid approaches
Alexander et al. (2005), Benedek & Kaernbach (2010ab), Greco et al. (2016)
Psychological variable
Neural activity
Physiological signal
Neural model
Peripheral LTI model
Examples: Instantaneous impulse with constant latency Short Gaussian impulse
Example SCR
Gerster et al. (2017) Psychophysiology
1.Time invariance: output depends only on input but not on time. The same input always produces the same output. Variability in the output is due to variability in the input.
2. Linearity: the output after two inputs is the sum of the output that would follow the individual inputs.
What is LTI?
SNA SCR � = RF
LTI system is unambiguously characterised by its response function.
This is the equation for convolution. It is the same as a linear filter.
Convolution with response function (RF)
LTI systems are idealised versions of reality, even in standard engineering
applications.
How good is this approximation?Under what circumstances does it break?
Fidelity of the LTI formalism
Dynamic range• Under what conditions is the LTI system plausible? • Hard biophysical constraints (e.g. pupil size)
Noise within dynamic range• Random noise (measurement noise, spontaneous activity, etc.)
Data preprocessing• Non-linearities more prevalent in some frequency bands -> filtering (e.g. SCR)
Non-linearities• Can occur across the entire dynamic range, but more likely towards the limits• Can potentially be modelled (e.g. Volterra kernels in fMRI)
Quantification• How much signal variance can be explained under an LTI model?
Fidelity of the LTI formalism
Time invariance• Compare responses at different points in time
Direct tests• Neural recording or stimulation
Linearity• Does response depend on baseline?
Indirect test• Assume that external stimuli
elicit very brief neural activity with constant latency
Neural signal
External stimulus
Testing the LTI formalism
LTI model assumes 1 RF per condition/subject
Canonical RF• Estimated from large data base (e.g. SCR: 1278 SCRs from 64 individuals
with ~ 30 s ITI)
Constrained RF• Add components to canonical RF to capture subject-specific variation• SCR: best retrodictive validity for canonical RF + time derivative
Often difficult to estimate RF for each subject• Not enough data• Responses overlapping• Experiment events not suitable
Canonical vs individual RF
Instantaneous neural impulse with constant latency: Dirac/Kronecker delta function (all GLMs)
Gaussian neural impulse with constrained latency and dispersion, and free amplitude (non-linear SCR model)
Gaussian neural impulse with constant dispersion, and free latency/amplitude (SF models)
Gamma neural impulse with free amplitude, latency, shape and scale (Pupil models Korn & Bach 2016, not yet in PsPM)
Possible neural models
=SCR X1 X2 X3β1β0 + + β3+ β2 + ε
General Linear Model
Intercept(per segment of continous data,
termed "session" in PsPM)
Events in condition 1
Events in condition 2
Events in condition 3
General linear model
Constrained RF• One regressor per function in the basis set (all orthogonalised)• Response amplitude estimate: reconstruct response, amplitude of highest
peak (unlike SPM)
Basis set
Events in condition 1 Events in condition 2 "Start break|" Intercept
Design matrix
Events in condition 1 Events in condition 2 "Start break|" Intercept
Design orthogonality
Events in condition 1 Events in condition 2 "Start break|"
Model fit
Events in condition 1 Events in condition 2 "Start break|"
implausible RF
plausible RF
Estimated RF
Name for 1st level model file ...
... and directorySeconds, samples, markers?Data file (1 per session)Timings (specify in GUI or 1 file per session)
SPM style timing files:
names = {'Neutral', 'Aversive'};onsets = {[1, 5], [2, 3, 4]};
pmod(1).name{1} = 'Arousal_rating';pmod(1).param{1} = [0.1 1.3];
pmod(2).name{1} = 'Arousal_rating';pmod(2).param{1} = [4.7, 8.3, 7.0];
GUI implementation
Events in condition 1
Equivalent for 1 BF if only mean per condition is required
Estimability issues if many missing data point• Can be problematic for pupil size (loss of fixation), unconstrained parameter
values, currently working on solution within PsPM
A priori hypotheses better tested with pmods• ... but single trial estimates can be useful e.g. for trial-by-trial LMEs, for
comparing computational learning models without re-estimating PsPMs, or as input for computational fMRI
Estimability issues if RF longer than ITI• SCR, respiration• Successfully used for pupil
Modelling events or conditions?
Thank you!Project teamGiuseppe CastegnettiSamuel GersterSaurabh KhemkaChristoph KornFilip Melinčšak Karita OjalaPhilipp PaulusMatthias StaibAthina Tzovara Yanfang Xia
ProgrammersLaure CiernikGabriel GräniTobias MoserEshref ÖzdemirIvan RojkovLinus Rüttimann
Project collaboratorsJean DaunizeauRay DolanMikael ElamGuillaume FlandinSteve FlemingKarl FristonBarbara NamerManuel Voelkle
Funders
