Sensorimotor Transformations

Sensorimotor TransformationsMaurice J. Chacron and Kathleen E. CullenOutlineLecture 1: - Introduction to sensorimotor transformations - The case of linear sensorimotor transformations: refuge tracking in electric fish - introduction to linear systems identification techniques

- Example of sensorimotor transformations: Vestibular processing, the vestibulo-occular reflex (VOR). OutlineLecture 2: - Nonlinear sensorimotor transformations - Static nonlinearities - Dynamic nonlinearitiesLecture 1Sensorimotor transformation:

if we denote the sensory input as a vector S and the motor command as M, a sensorimotor transformation is a mapping from S to M : M =f(S)Where f is typically a nonlinear function

Examples of sensorimotor transformationsVestibulo-occular reflex

Reaching towards a visual target, etc

Example: Refuge tracking in weakly electric fish

Refuge tracking

Refuge tracking

Sensory inputMotor outputError8Results

(Cowan and Fortune, 2007)Tracking performance is best when the refuge moves slowly

Tracking performance degrades when the refuge moves at higher speeds

There is a linear relationship between sensory input and motor outputLinear systems identification techniquesLinear functionsWhat is a linear function?

So, a linear system must obey the following definition:

Linear functions (continued)This implies the following:

a stimulus at frequency f1 can only cause a response at frequency f1 Linear transformations

assume output is a convolutionof the input with a kernel T(t) withadditive noise. Well also assume that allterms are zero mean. Convolution is the most general linear transformation that can be done to a signal

An example of linear coding:Rate modulated Poisson processtime

time dependent firing rateLinear Coding:

Example:

Recording from a P-typeElectroreceptor afferent.

There is a linear relationship betweenInput and outputGussin et al. 2007 J. Neurophysiol.

Instantaneous input-output transfer function:Fourier decomposition and transfer functions- Fourier Theorem: Any smooth signal can be decomposed as a sum of sinewavesSince we are dealing with linear transformations, it is sufficient to understand the nature of linear transformations for a sinewaveLinear transformations of a sinewaveScaling (i.e. multiplying by a non-zero constant)

Shifting in time (i.e. adding a phase)

Cross-Correlation Function

For stationary processes:

In general,Cross-SpectrumFourier Transform of the Cross-correlation function

Complex number in general

a: real partb: imaginary partRepresenting the cross-spectrum:

: amplitude

: phaseTransfer functions (Linear Systems Identification)

assume output is a convolutionof the input with a kernel T(t) withadditive noise. Well also assume that allterms are zero mean.

Transfer functionCalculating the transfer function

multiply by:

and average over noise realizations

=0

Gain and phase:

Sinusoidal stimulationat different frequencies

StimulusResponse20 msec

GainCombining transfer functionsinput

output

Where transfer functions fail

Vestibular systemCullen and Sadeghi, 2008Example: vestibular afferents

CV=0.044CV=0.35

`Regular afferentFiring rate(spk/s)Head velocity(deg/s)120100806040200-20-40

`

Irregular afferentFiring rate(spk/s)Head velocity(deg/s)160140120100806040-20-40200Signal-to-noise Ratio:

Borst and Theunissen, 1999Using transfer functions to characterize and model refuge tracking in weakly electric fish

Sensory inputMotor outputErrorCharacterizing the sensorimotor transformation

1st order2nd orderModeling refuge tracking using transfer functionssensory input sensoryprocessing motor processing motor outputModeling refuge tracking using transfer functionssensory input sensoryprocessing motor output

NewtonSimulink demos

Mechanics constrain neural processing

SummarySome sensorimotor transformations can be described by linear systems identification techniques.These techniques have limits (i.e. they do not take variability into account) on top of assuming linearity.