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 difference from standard GLM analysis? cyclical function? 1) key parameter is response phase, not 1) Fourier analysis (phase of a amplitude sinusoid) 2) no contrast, overlapping responses 2) Cross-correlation (phase of a contributes to efficiency of design specified model function) 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 FFT the amplitude and phase of each frequency component. 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 power spectrum peaks at 15 cycles! phase=angle(f(16)) %nth+1 value 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 Fluid waves + 30dB ! Air waves The cochlea essentially Tonotopic Map performs a Fourier transform. Time-dependent sound information is converted to its Action frequency spectrum. Potentials The map is called tonotopy. 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 High Human Auditory Cortex Tonotopic: fMRI freqat 7 Tesla Low freq low high frequency frequency tones tones anterior posterior from DaCosta et al. J. Neurosci 2011 The auditory cortex also has a topographic mapping of its sensory surface, the cochlea. these maps are tonotopic with a spatial mapping of the sound frequencies from low to high. so if your were to listen to a frequency sweep this would literally result in a wave of neural response across your auditory cortex, like so. This demo is actual fMRI data that we measured and these are the clearest auditory maps ever seen in the human. You see there are two maps here (high to low, low to high) and they allow us to identify auditory subregions A1 & R which together comprise primary auditory cortex. Human Auditory Cortex Tonotopic: fMRI at 7 Tesla high low frequencyhigh frequency tonesfrequency 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).