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Affect and Choice: Background Information
Imagine deciding which of two equally priced and equally appropriate pictures to buy for a home office. Faced with such a decision, people are thought to consult their feelings and ask, “How do I feel about each option?” (Schwarz & Clore, 2003). A choice between the two affective states is thought to determine which picture is chosen.
Now imagine deciding whether to invest in risky high-yield stocks or safer lower-returning bonds. This decision involves considerations that are not purely affective. However, a growing literature suggests that even in such cases affective choice may play a pivotal role in decision making. Indeed, it has been suggested that affect serves as the “common currency” of decision making (Peters, Västfjäll, Gärling & Slovic, 2006). Decision makers decompose complex thoughts into affective states (Mellers, 2000; Pfister et al., 2008) that are then compared with each other, as in the picture example.
Despite the centrality of affective choice to decision making, it is not at all clear how choices between two affective states are made. Our starting point in addressing this issue is a distinction between two fundamental dimensions of affect—valence and arousal. The first, valence, represents the pleasantness/unpleasantness of the affect. The second, arousal, represents the degree of activation associated with the affect. These dimensions capture most of the variance in self-reported mood ratings (Osgood, Suci & Tanenbaum, 1957; Russell 1980; Barrett & Russell, 1999). In addition, cross cultural (Larsen & Diener, 1992), neurobiological (Posner et al., 2009), and developmental data (Russell & Bullock, 1985) demonstrate that – as Wundt (1912) postulated – valence and arousal are core components of affective states. Valence and arousal are often drawn as perpendicular dimensions to create an affective 2-space (Figure 1).
Experiment Structure
60 IAPS pictures (images with affective content) were split into 30 pairs. Within a pair, one picture was designated as Picture 1 and the other as Picture 2. Picture 1 and Picture 2 were counterbalanced for valence and arousal (IAPS population ratings).
In the fMRI, subjects were shown Picture 1 for 500ms followed by Picture 2 for 500ms. They were asked to make a choice between the two pictures. The chosen picture was displayed for 4s—a duration long enough to ensure that the preferred picture was viewed and processed; this attached real affective consequences to each choice.
Outside the fMRI, subjects were asked to rate each image on a 1-7 scale for valence and arousal
Hypothesis
We expected to see 2 sets of results:
1) Distinct areas of the brain would be active for high vs. low valence pictures and for high vs. low arousal pictures. Since a variety of independent sources confirm that valence and arousal are core dimensions of affect, finding neural bases that underlie these dimensions is central to the understanding of affect.
2) We expect activations in these regions to drive choice. In particular a greater positive arousal (PA) would predict choice in cases where both pictures have PA > 0. Similarly in cases where NA > 0, we expect that lower NA would predict choice.
fMRI Methods
Expected Bases of A/V
Based on prior work in the Knutson Lab [1] we expected particular sub-cortical areas to show differential activation:
For Positive Arousal (PA) we expected to see some activation in the Ventral Striatum (Nucleus Accumbens in particular
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. Maybe some equations.
Equations
If you want to use equations, you can use the same formats that are use on wikipedia.
See wikimedia help on formulas for help.
This example of equation use is copied and pasted from wikipedia's article on the DFT.
The sequence of N complex numbers x0, ..., xN−1 is transformed into the sequence of N complex numbers X0, ..., XN−1 by the DFT according to the formula:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X_k = \sum_{n=0}^{N-1} x_n e^{-\frac{2 \pi i}{N} k n} \quad \quad k = 0, \dots, N-1}
where i is the imaginary unit and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Xk can thus be viewed as coefficients of x in an orthonormal basis.)
The transform is sometimes denoted by the symbol Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal{F}} , as in Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{X} = \mathcal{F} \left \{ \mathbf{x} \right \} } or Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal{F} \left ( \mathbf{x} \right )} or Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal{F} \mathbf{x}} .
The inverse discrete Fourier transform (IDFT) is given by
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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.}
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
Software
Appendix I - Code and Data
Code
Data
Appendix II - Work partition (if a group project)
Brian and Bob gave the lectures. Jon mucked around on the wiki.