Topographic Mapping with fmri

Transcription

1 Topographic Mapping with fmri Retinotopy in visual cortex Tonotopy in auditory cortex signal processing + neuroimaging = beauty!

2 Topographic Mapping with fmri Retinotopy in visual cortex Tonotopy in auditory cortex Overview: 1) background on brain topographic maps with emphasis on visual cortex 2) traveling wave method for mapping visual cortex, use of Fourier Analysis 3) examples from auditory and motor cortex

3 Topographic Mapping with fmri Retinotopy in visual cortex Tonotopy in auditory cortex Topographic maps: in the brain we find ordered projections of the body s sensory surfaces (retina, cochlea, body surface) Imaging these maps allows identification of these sensory regions, in individual subjects, just a few minutes of fmri scan time required. Many applications in clinical and perceptual neuroscience.

4 Background Visual System & Retinotopy Motor cortex Somatosensory cortex Different sensory surfaces project to different regions of the brain The 2-D array of cells in the retina project in an orderly manner to visual cortex, such that the cortex a has 2D retinal image of the visual field. Visual cortical neurons each have a limited view (receptive field) of the visual field and are neighbored by neurons with adjacent views.

5 Background Visual System & Retinotopy Left Visual field projects to Right brain hemisphere Right Visual field projects to Left brain hemisphere

6 Background Visual System & Retinotopy A hierarchy of visual areas each with its own retinal image : retina to thalamus (LGN) to V1 to V2 to V3, etc... V1 is the first visual area in the cortex and is necessary for visual perception. Local lesions of V1 produce blindspots in the corresponding region of visual space Each visual areas is hard to define by anatomy. But could be identified if we could just visualize its retinal image

7 Retinotopy: retinal images on the brain classic demonstration of retinotopy in macaque V1 flattened V1 is labelled by radioactive glucose after viewing of flickering target pattern. Tootell et al. Science 1983 latest high-res demonstration in human V1 fmri response (1mm 3, 7 Tesla) to viewing flickering letter M (warped by inverse of cortical magnification) Polimeni et al. Neuroimage 2011

8 Measurement of visual responses with fmri

9 Visual Cortex has Multiple Retinotopic Maps Each visual area (V1, V3, V3, etc.. ) has its own retinotopic map resulting in a patchwork of such maps across the cortical surface. Visualizing these maps with allows identification of the individual areas. This can be achieved with fmri. Typically, mapping stimuli trace out the visual field in eccentricity and polar angle. Color mappings show associated areas of visual cortex. Dougherty et al. Journal of Vision 2003

10 A Closer look at Retinotopic Organization Left Visual cortex Right hemifield upper upper quadrant quadrant lower lower quadrant quadrant V3v upper quadrant V2v V2v upper quadrant V1 V1 full hemifield V2d V2d V3d V3d lower quadrant lower quadrant Mirror-image reversals at visual area borders patchwork of hemifields and quadrants in flattened area of visual cortex

11 A Hierarchy of Cortical Visual Areas Wandell, Dumoulin, & Brewer Neuron 2007 So far, at least 18 human visual areas identified based on their retinotopic maps

12 Now that we know about retinal images in brain, here is 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.

13 Topographic Mapping with fmri Overview: 1) background on brain topographic maps with emphasis on visual cortex 2) traveling wave method for mapping visual cortex, use of Fourier Analysis 3) examples from auditory and motor cortex

14 Traveling wave or phase-encoded 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

15 Traveling wave or phase-encoded mapping method: Engel et al. Nature 1994, Sereno et al. Science 1995 polar angle: eccentricity: Stimulus is cyclical, so response is cyclical idealized response of visual cortex voxels with blue and green receptive fields 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

16 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.

17 The Fourier transform is universal in signal processing (1820 s Joseph Fourier) Fourier s insight: Any temporal signal (just about) can be represented as a sum of sine and cosine waves (circular motion) of different frequencies and amplitudes.

18 Why this is useful: if earthquake vibrations can be separated into frequency components, buildings can be designed to avoid interacting with the strongest ones. if sound waves can be separated into frequency components, we can boost the frequencies we want to hear and ignore the ones we don t. (btw: Shazam compares the FT, not raw audio clips) if 2D images can be separated into frequency components, we can keep the important ones and ignore the rest to drastically decrease file size. ( lossy compression used in JPEG and MP3 files)

19 Fourier transform transforms the signal from the time domain to the frequency domain. time domain frequency domain the amplitudes squared are the power spectrum

20 Fourier transform transforms the signal from the time domain to the frequency domain. 5 Hz 12 Hz FFT Hz Time domain frequency domain (power spectrum)

21 Mathematically, the Fourier Series expressed as a sum of sine and cosine basis functions: If we instead sum to a finite number N>0, then partial sums of the Fourier series. Fourier coefficients can be solve for by projecting the function onto its bases and integrating for the area under the curve:

22 Intuition for why this works: sines and cosines form an orthonormal set: example of cosine-sine multiplication:

23 Fourier Series more conveniently expressed in complex notation: Euler s formula: where each coefficient Cn is expressed as complex number with a real and imaginary component: Cn = a + bi, where a is the amplitude and b the phase of the Fourier component at frequency n. So, any signal can be expressed as the sum of circular basis functions! For each component we need to know frequency N (how fast do we go around the circle?), the amplitude (what is the radius of the circle?) and the phase angle (where do we start on the circle?)

24 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 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.

25 Fourier analysis for Retinotopy (how to in Matlab): 1) Apply Fast Fourier Transform. FFT produces an array of complex numbers (real plus imaginary components) giving the amplitude and phase of each frequency component. FFT f=fft(series); 2) plot the amplitude spectrum amplitudes=abs(f) bar(0:30, amplitudes(1:31)) 3) get the phase at stimulation frequency n phase=angle(f(16)) %n th +1 value power spectrum peaks at 15 cycles!

26 Finally, plot the phases with a color code, and notice how the change smoothly. Each retinal image is revealed by a complete cycle of phases.

27 Linear Cross-correlation analysis 1) stimulus position is cyclical over time: 0s cont... 0s 40s 2) construct cyclical time-lagged regressors: 80s Lag = 1 Lag = 2 Lag = 3... Lag = 20 3) For each voxel, calculate correlation (R) between the voxel time course and all lagged regressors (i.e. if 20 lag functions then each voxel gets 20 R values) 4) Assign each voxel to the lag with the highest R (winner-take-all) 5) Correlation value can be thresholded for display

28 Retinotopic mapping with the traveling wave has been used to study: homologies with monkey visual system functions of individual visual areas individual differences and perception Schwartzkopf, Song, & Rees Nature Neuroscience 2009 visual cortex plasticity Baselar et al. Nature Neuroscience 2011

29 Topographic Mapping with fmri SUMMARY: Sensory topographic maps throughout the brain traveling wave method is an efficient way to measure these maps relies on methods to measure the PHASE of the fmri time course (Fourier or cross-correlation) Allows localization of individual brain regions in individual human subjects

30 Topographic Mapping with fmri Overview: 1) background on brain topographic maps with emphasis on visual cortex 2) traveling wave method for mapping visual cortex, use of Fourier Analysis 3) examples from auditory and motor cortex

31 Cochlea creates tonotopy The cochlea is a biological structure that essentially performs a Fourier transform! Incoming time-dependent sound information is converted to its frequency spectrum. Human hearing range: 20 Hz to 20,000 Hz. High-frequency hearing loss with age associated with loss of high-frequency cochlear hair cells.

32 High freq Human Auditory Cortex Tonotopic: fmri at 7 Tesla Low freq low frequency tones high frequency tones anterior posterior DaCosta et al. J. Neurosci 2011

33 Human Auditory Cortex Tonotopic: fmri at 7 Tesla low frequency tones high frequency high tones frequency tones anterior posterior useful for studying language and music processing, tinnitus DaCosta et al. J. Neurosci 2011

34 Sound presentation (phase mapping) 1) Present tones from 88 to 8000 Hz in 1/2 octave steps, in repeating cycles 2) For each voxel, calculate linear correlation to all time lags of the model function. LO HI LO HI LO HI time 0s 32s 64s cont... Lag = 1 Lag = 2 Lag = 3... Lag = 14

35 Somatosensory cortex

36 Topographic mapping of motor cortex with fmri useful for studying phantom pain and other disordors Zaharia et al. PNAS 2012

37 Topographic Mapping with fmri SUMMARY: Sensory topographic maps throughout the brain, and have smoothly changing representations traveling wave method is an efficient way to measure these maps relies on methods to measure the PHASE of the fmri time course (Fourier or cross-correlation)