= Differences Between Spin-Echo and Gradient-Echo Imaging =
= Differences Between Spin-Echo and Gradient-Echo Imaging =
Spin-Echo and Gradient-Echo imaging are two different methods of obtaining fMRI data that vary along various dimensions: the pulse sequence used to generate and obtain the signal, signal-to-noise ratio, and sensitivity to large blood vessels, to name a few.
Spin-Echo and Gradient-Echo imaging are two different methods of obtaining fMRI data that vary along various dimensions: the pulse sequence used to generate and obtain the signal, signal-to-noise ratio, and sensitivity to large blood vessels, to name a few.
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Note that this is a project template. Other styles are possible. For example, you could use [http://white.stanford.edu/teach/index.php/Main_Page#Multiple_page_format a multiple page format].
= Background =
= Background =
== Retinotopic maps ==
You can use subsections if you like.
Below is an example of a retinotopic map. Or, to be precise, below ''will'' be an example of a retinotopic map once the image is uploaded. To add an image, simply put text like this inside double brackets 'MyFile.jpg | My figure caption'. When you save this text and click on the link, the wiki will ask you for the figure.
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[[File:Example.jpg | Figure 1]]
Below is another example of a reinotopic map in a different subject.
<br>
[[File:Example2.jpg | Figure 2]]
Once you upload the images, they look like this. Note that you can control many features of the images, like whether to show a thumbnail, and the display resolution.
Once you upload the images, they look like this. Note that you can control many features of the images, like whether to show a thumbnail, and the display resolution.
MNI is an abbreviation for [http://en.wikipedia.org/wiki/Montreal_Neurological_Institute Montreal Neurological Institute].
= Methods =
= Methods =
== Measuring retinotopic maps ==
== MR Analysis ==
Retinotopic maps were obtained in 5 subjects using Population Receptive Field mapping methods [http://white.stanford.edu/~brian/papers/mri/2007-Dumoulin-NI.pdf Dumoulin and Wandell (2008)]. These data were collected for another [http://www.journalofvision.org/9/8/768/ research project] in the Wandell lab. We re-analyzed the data for this project, as described below.
=== Subjects ===
Subjects were 5 healthy volunteers.
=== MR acquisition ===
Data were obtained on a GE scanner. Et cetera.
=== MR Analysis ===
The MR data was analyzed using [http://white.stanford.edu/newlm/index.php/MrVista mrVista] software tools.
The MR data was analyzed using [http://white.stanford.edu/newlm/index.php/MrVista mrVista] software tools.
==== Pre-processing ====
=== Pre-processing ===
All data were slice-time corrected, motion corrected, and repeated scans were averaged together to create a single average scan for each subject. Et cetera.
All data were slice-time corrected, motion corrected, and repeated scans were averaged together to create a single average scan for each subject. Et cetera.
==== PRF model fits ====
PRF models were fit with a 2-gaussian model.
==== MNI space ====
After a pRF model was solved for each subject, the model was trasnformed into MNI template space. This was done by first aligning the high resolution t1-weighted anatomical scan from each subject to an MNI template. Since the pRF model was coregistered to the t1-anatomical scan, the same alignment matrix could then be applied to the pRF model. <br>
Once each pRF model was aligned to MNI space, 4 model parameters - x, y, sigma, and r^2 - were averaged across each of the 6 subjects in each voxel.
Et cetera.
= Results - What you found =
== Retinotopic models in native space ==
Some text. Some analysis. Some figures.
== Retinotopic models in individual subjects transformed into MNI space ==
Some text. Some analysis. Some figures.
== Retinotopic models in group-averaged data on the MNI template brain ==
Some text. Some analysis. Some figures.
== Retinotopic models in group-averaged data projected back into native space ==
= Results =
Some text. Some analysis. Some figures.
= Conclusions =
= Conclusions =
Here is where you say what your results mean.
= References - Resources and related work =
= References - Resources and related work =
References
Software: mrVista
Software
= Appendix I - Code and Data =
= Appendix I - Code and Data =
Line 83:
Line 34:
==Data==
==Data==
[[Media:MyDataZipFile.zip | zip file with my data]]
[[Media:MyDataZipFile.zip | zip file with my data]]
= Appendix II - Work partition (if a group project) =
Brian and Bob gave the lectures. Jon mucked around on the wiki.
= Test Equations =
''This is a test of equation use on our wiki. The text below is copied and pasted from [http://en.wikipedia.org/wiki/Discrete_Fourier_transform wikipedia's article on the DFT]''
==Definition==
The [[sequence]] of ''N'' [[complex number]]s ''x''<sub>0</sub>, ..., ''x''<sub>''N''−1</sub> is transformed into the sequence of ''N'' complex numbers ''X''<sub>0</sub>, ..., ''X''<sub>''N''−1</sub> by the DFT according to the formula:
:<math>X_k = \sum_{n=0}^{N-1} x_n e^{-\frac{2 \pi i}{N} k n} \quad \quad k = 0, \dots, N-1</math>
where i is the imaginary unit and <math>e^{\frac{2 \pi i}{N}}</math> is a primitive N'th [[root of unity]]. (This expression can also be written in terms of a [[DFT matrix]]; when scaled appropriately it becomes a [[unitary matrix]] and the ''X''<sub>''k''</sub> can thus be viewed as coefficients of ''x'' in an [[orthonormal basis]].)
The transform is sometimes denoted by the symbol <math>\mathcal{F}</math>, as in <math>\mathbf{X} = \mathcal{F} \left \{ \mathbf{x} \right \} </math> or <math>\mathcal{F} \left ( \mathbf{x} \right )</math> or <math>\mathcal{F} \mathbf{x}</math>.
The '''inverse discrete Fourier transform (IDFT)''' is given by
:<math>x_n = \frac{1}{N} \sum_{k=0}^{N-1} X_k e^{\frac{2\pi i}{N} k n} \quad \quad n = 0,\dots,N-1.</math>
A simple description of these equations is that the complex numbers <math>X_k</math> represent the amplitude and phase of the different sinusoidal components of the input "signal" <math>x_n</math>. The DFT computes the <math>X_k</math> from the <math>x_n</math>, while the IDFT shows how to compute the <math>x_n</math> as a sum of sinusoidal components <math>(1/N) X_k e^{\frac{2\pi i}{N}k n}</math> with [[frequency]] <math>k/N</math> cycles per sample. By writing the equations in this form, we are making extensive use of [[Euler's formula]] to express sinusoids in terms of complex exponentials, which are much easier to manipulate. In the same way, by writing <math>X_k</math> in [[Complex_number#Polar_form|polar form]], we immediately obtain the sinusoid amplitude <math>A_k</math> and phase <math>\phi_k</math> from the [[complex argument|complex modulus and argument]] of <math>X_k</math>, respectively:
Note that the normalization factor multiplying the DFT and IDFT (here 1 and 1/''N'') and the signs of the exponents are merely conventions, and differ in some treatments. The only requirements of these conventions are that the DFT and IDFT have opposite-sign exponents and that the product of their normalization factors be 1/''N''. A normalization of <math>1/\sqrt{N}</math> for both the DFT and IDFT makes the transforms [[unitary matrix|unitary]], which has some theoretical advantages, but it is often more practical in numerical computation to perform the scaling all at once as above (and a unit scaling can be convenient in other ways).
(The convention of a negative sign in the exponent is often convenient because it means that <math>X_k</math> is the amplitude of a "positive frequency" <math>2\pi k/N</math>. Equivalently, the DFT is often thought of as a [[matched filter]]: when looking for a frequency of +1, one correlates the incoming signal with a frequency of −1.)
In the following discussion the terms "sequence" and "vector" will be considered interchangeable.
Differences Between Spin-Echo and Gradient-Echo Imaging
Spin-Echo and Gradient-Echo imaging are two different methods of obtaining fMRI data that vary along various dimensions: the pulse sequence used to generate and obtain the signal, signal-to-noise ratio, and sensitivity to large blood vessels, to name a few.
Background
Once you upload the images, they look like this. Note that you can control many features of the images, like whether to show a thumbnail, and the display resolution.
Figure 3
Methods
MR Analysis
The MR data was analyzed using mrVista software tools.
Pre-processing
All data were slice-time corrected, motion corrected, and repeated scans were averaged together to create a single average scan for each subject. Et cetera.
