Download Topographic Mapping with fMRI

Topographic Mapping with fMRI
Retinotopy in visual cortex
Tonotopy in auditory cortex
Topographic maps are ordered representations of sensory surfaces
(retina, cochlea, skin) in the brain.
Detecting these maps with functional MRI allows us to identify
specific sensory brain regions in individual patients.
Departure from the GLM ...
Recall that GLM is associated
with the amplitudes of
different components in the
measured fMRI signal
Today, we’ll learn a new technique that cares about the phase of the signal, using
the Fourier transform. It is very simple.
Overview:
1) Neuroscience background: visual system
2) Phase-encoded method for mapping visual cortex (use of Fourier
Analysis), “traveling wave method”
3) Examples from auditory and somatosensory cortex
Background Visual System & Retinotopy
Motor cortex
Somatosensory cortex
Different sensory surfaces project to different regions of the brain
retina --> Visual cortex
cochlea --> Auditory cortex
skin surface --> Somatosensory cortex
Motor cortex --> Muscle surface in body
Visual Cortex response fMRI
whole field stimulus stimulates all of retina, and all of visual cortex map.
Background Visual System & Retinotopy
The eye focuses light onto the 2D retinal surface at the back of the eye. (the retinal
picture)
The 2-D array of cells in the retina project in an orderly manner to neurons in visual cortex,
creating a 2D cortical picture. (actually multiple times)
This is the retinotopic map.
Background Visual System & Retinotopy
Retina cells (photoreceptors) have receptive fields - each responds to light from one location
of visual space. The array of cells are tiled to cover the whole 2D field of view.
V1 neurons have a receptive field of about 1 deg visual angle. The array of neurons are tiled
to form a 2D retinotopic map.
Background Visual System & Retinotopy
imaged with high-resolution functional MRI (1mm3)
Polimeni et al. Neuroimage 2011
Here is an example of the retinal image projected onto human V1.
Now imagine: an image moving across your field of view ... What activity would result in V1?
V1 lesion causes loss of vision
Lesions in V1 produce blind spots in the corresponding region of visual space.
V1 stimulation causes perception of light
a thought experiment: what if you could stimulate impossible visual space?
It is possible to stimulate local regions of V1
with transcranial magnetic stimulution (TMS)
which results in light perception in the
corresponding region of visual space.
Background Visual System & Retinotopy
Wandell, Dumoulin, & Brewer Neuron 2007
V1 is the first and largest visual area in cortex, but there are many more
areas V2, V3, V4, ...
Each area has its own retinotopic map.
If we could identify all the maps, we know the location of each visual
area ( locations not known by anatomical landmarks)
Retinotopic Mapping with fMRI
Dougherty et al. Journal of Vision 2003
Retinotopic mapping can be achieved with fMRI. Mapping stimuli trace out the visual
field in eccentricity and polar angle. Color mappings show associated areas of visual
cortex.
“Phase-encoded” or “Traveling wave” mapping method:
Engel et al. Nature 1994, Sereno et al. Science 1995
polar angle:
eccentricity:
idealized response of visual cortex voxels with blue and green receptive fields:
•
•
•
Periodic stimuli map out visual space in polar angle in eccentricity
Voxel responses are periodic, having the same frequency but different phases
So, parameter of interest is response phase because it tags visual field location
“Phase-encoded” or “Traveling wave” mapping method:
Engel et al. Nature 1994, Sereno et al. Science 1995
polar angle:
eccentricity:
Stimulus is cyclical, so response is cyclical
how to measure the phase of a
cyclical function?
1) Fourier analysis (phase of a
sinusoid)
2) Cross-correlation (phase of a
specified model function)
difference from standard GLM analysis?
1) key parameter is response phase, not
amplitude
2) no contrast, overlapping responses
contributes to efficiency of design
Fourier analysis for retinotopic mapping
here’s the actual fMRI time series of a good single voxel.
you can see by eye that there are 15 cycles (the stimulation frequency)
and we want to know the phase of that signal
This is an excellent Fourier problem!
The Fourier Transform breaks down a signal into its component sinusoids, giving
the amplitude and phase at each frequency.
Fourier transform:
Any temporal signal (just about) can be represented as a sum of sine and cosine waves
(circular motion) of different frequencies and amplitudes.
the green oscillation with
w=1 has big impact on result, so
let’s say its Fourier coeff f(1) = 1.
the blue sine wave (w=3) has
some impact but the amplitude is
smaller: f(2) = 0.13
If we know the Fourier coeff. for all
frequencies, we can approximate
any function f.
Mathematically, the Fourier Series in an infinite sequence of sines and cosines,
f(x) = a0 + a1cos(x) + b1sin(x) + a2cos(2x) + b2sin(2x) + ...
this describe a continuous function f and the Fourier coefficients can be solved for
by integration
In actual calculations, we compute the Discrete Fourier Transform (DFT) in finite
dimensions using matrix algebra. (FFT “fast Fourier transform” in Matlab)
It helps to remember Euler’s formula, and the Fourier series can be expressed as:
where each coefficient Cn is expressed as
complex number with a real and imaginary
component: Cn = a+ bi
Now to get back to our retinotopic mapping signal ....
here’s the actual fMRI time series of a good single voxel.
you can see by eye that there are 15 cycles (the stimulation frequency)
and we want to know the phase of that signal
Fourier analysis for Retinotopy (how to in Matlab):
1) Zero center the time series (if not already)
series=series-mean(series)
2) Apply Fast Fourier Transform (FFT).
Produces array of complex numbers giving
the amplitude and phase of each frequency
component.
FFT
f=FFT(series);
3) plot the amplitude spectrum
amplitudes=abs(f)
bar(0:30, amplitudes(1:31))
4) get the phase at stimulation frequency n
phase=angle(f(16))
%nth+1 value
power spectrum peaks at 15 cycles!
Finally, plot the phases with a color code, and notice how they change
smoothly. Each retinal image is revealed by a complete cycle of phases.
Retinotopic mapping with the ‘traveling wave’ has been used to study:
organization on function of the visual system
So far, at least 18 human visual areas identified
based on their retinotopic maps
individual differences and perception
Schwartzkopf, Song, & Rees Nature Neuroscience 2009
clinical applications in vision loss
Baselar et al. Nature Neuroscience 2011
Topographic Mapping with fMRI
SUMMARY:
1) Retinotopic maps in visual cortex
2) Retinotopic mapping techniques depend on the phase
of the fMRI response
3) Examples from other sensory systems (hearing, touch,
movement)
Perception!
How hearing works: tonotopy
+ 30dB !
Fluid waves
Air waves
The cochlea essentially
performs a Fourier transform.
Time-dependent sound
information is converted to its
frequency spectrum.
The map is called tonotopy.
Tonotopic Map
Action
Potentials
Auditory Pathway in the Brain
Tonotopic maps in the brain: cochlear surface projects in orderly manner to the brain.
In the brain, each neuron responds to a small frequency range (receptive fields) and the
neurons are layed out in maps from low to high-frequency response.
Sound presentation and phase mapping.
1) Present tones from 88 to 8000 Hz in 1/2 octave steps, in repeating cycles
2) For each voxel, determine the response phase at the stimulation frequency
Human Auditory Cortex Tonotopic:
High
fMRI freq
at
7 Tesla
Low
freq
low
frequency
tones
high
frequency
tones
anterior
posterior
from DaCosta et al. J. Neurosci 2011
Human Auditory Cortex Tonotopic: fMRI at 7 Tesla
low
frequency
tones
high
high
frequency
frequency
tones
tones
anterior
posterior
• A1is the primary auditory cortex.
• Neurons in A1 are hyperactive in tinnitus (animal models)
Somatosensory cortex and Motor Cortex
Topographic mapping of motor cortex with fMRI
used to studying phantom pain and other
disorders
Zaharia et al. PNAS 2012
You should be able to ...
• Explain the principles of retinotopic and tonotopic organization in the
brain
Neurons in the brain form a continuous map of the sensory surface. Nearby neurons on
the map represent nearby locations in sensory space.
In vision, the sensory surface is the retina with a spatial map called retinotopy. In hearing,
the sensory surface is the cochlea with a map of sound frequencies called tonotopy.
Another example, is the somatosensory system which maps the body surface.
• Why is the mapping technique called “phase-encoded”?
The mapping stimuli are periodic, cycling through sensory space. They produce a
periodic response across the brain maps. Different locations on the map will differ by
the phase of the response (as opposed to amplitude or frequency of response)