2009 Max Halvorson

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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.
Note that this is a project template. Other styles are possible. For example, you could use a multiple page format.

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.

Below is another example of a reinotopic map in a different subject.
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.

Figure 3

MNI space

MNI is an abbreviation for Montreal Neurological Institute.

Methods

Measuring retinotopic maps

Retinotopic maps were obtained in 5 subjects using Population Receptive Field mapping methods Dumoulin and Wandell (2008). These data were collected for another 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 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.

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.
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

Some text. Some analysis. Some figures.

Conclusions

Here is where you say what your results mean.

References - Resources and related work

References

Software

Appendix I - Code and Data

Code

zip file with code

Data

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 wikipedia's article on the DFT

Definition

The sequence of N complex numbers x₀, ..., x_N−1 is transformed into the sequence of N complex numbers X₀, ..., X_N−1 by the DFT according to the formula:

$X_{k}=\sum _{n=0}^{N-1}x_{n}e^{-{\frac {2\pi i}{N}}kn}\quad \quad k=0,\dots ,N-1$

where i is the imaginary unit and $e^{\frac {2\pi i}{N}}$ 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_k can thus be viewed as coefficients of x in an orthonormal basis.)

The transform is sometimes denoted by the symbol ${\mathcal {F}}$, as in $\mathbf {X} ={\mathcal {F}}\left\{\mathbf {x} \right\}$ or ${\mathcal {F}}\left(\mathbf {x} \right)$ or ${\mathcal {F}}\mathbf {x}$.

The inverse discrete Fourier transform (IDFT) is given by

$x_{n}={\frac {1}{N}}\sum _{k=0}^{N-1}X_{k}e^{{\frac {2\pi i}{N}}kn}\quad \quad n=0,\dots ,N-1.$

A simple description of these equations is that the complex numbers $X_{k}$ represent the amplitude and phase of the different sinusoidal components of the input "signal" $x_{n}$. The DFT computes the $X_{k}$ from the $x_{n}$, while the IDFT shows how to compute the $x_{n}$ as a sum of sinusoidal components $(1/N)X_{k}e^{{\frac {2\pi i}{N}}kn}$ with frequency $k/N$ 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 $X_{k}$ in polar form, we immediately obtain the sinusoid amplitude $A_{k}$ and phase $\phi _{k}$ from the complex modulus and argument of $X_{k}$, respectively:

$A_{k}=|X_{k}|={\sqrt {\operatorname {Re} (X_{k})^{2}+\operatorname {Im} (X_{k})^{2}}},$

$\varphi _{k}=\arg(X_{k})=\operatorname {atan2} {\big (}\operatorname {Im} (X_{k}),\operatorname {Re} (X_{k}){\big )}.$

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 $1/{\sqrt {N}}$ for both the DFT and IDFT makes the transforms 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 $X_{k}$ is the amplitude of a "positive frequency" $2\pi k/N$. 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.