Lecture 7: General Linear Model (GLM) and fMRI Flashcards
Diagram of fMRI data and time series graph- (3)
- Selected at specific voxel with green lines on right
- After doing preprocessing steps, it shows graph of brightness of the voxel selected over time
- The red line in the graph shows you what the voxel’s signal looks like over time
- Its activity is preferred in some conditions over the other - peaks
What is the general idea of the general linear model?
- Brain activity in each voxels is explained in terms of set of mixture of different responses to each of the conditions in experiment
Data from early MRI experiment looking FFA (first papers explaining FFA is responsible for processing faces) time series plot show.. and statistical analysis used…- (6)
- Pps viewing pictures of faces (dark grey) or objects (light grey) in blocked design expeirment in specific voxel in FFA
- Response to faces higher than responses to objects
- Wanted to quantify statistical if height in face blocks higher than response to objects
- In early experiments analysis, averaging signal changes in blocks of faces vs objects and comparing the two using convential statistical tests
- Slightly imprecise way to analyse data as change in BOLD signal does not follow immediately after change in condition –> lag before hemodyanmic response kick in and takes a while to evolve
- Use info to provide more accurate info to estimate the signal changes and use across different designs –> GLM
The general linear model (GLM) allows us to
estimate the degree of signal change associated with each condition in the experiment
General linear model is more accurate than
simply averaging
GLM uses the (approximate) linearity of the BOLD signal means
GLM can be extended to a wide variety of experimental designs
What is this graph showing? - (6)
- Blue in one condition
- Green in another condition
- White is rest
- Time series across the x -axis
- fMRI signal is on y-axis
- Data is called X when talking about mathematically
Diagram of step 1 of GLM in which we specificy time periods corresponding to specifc task/stimulus conditions
In first step of GLM of speciifcying time periods corresponding to specific task/stimulus conditions we expect that.. - (2)
- We imagine ther is some neural activity that pps given one or another task
- Neural activity we are expecting to see in given (blue) condition of a specific voxel is expecting to arise at beginning of the task, plateau (constant) during the task block and at end of block neural activity drops to 0 until next blue block happens
Diagram of Seconed step of GLM creating hemodynamic regressors (by convolving with a canoical HRF) from the specifications of time periods corresponding to specific task/stimulus
Second step of GLM of producing hemodynamic regressors (by convolving with canoical HRF) means if this is the neural activity of neurons in a specific voxel in this graph then expect the
- expect following pattern of blood flow changes (modelled BOLD signal changes on y-axis) that we would expect happen at the specific voxel on second graph
In second step of GLM, to create the second graph on the right, the software..
convolving the modelled neural activity with canonical (typical) hemodynamic response function
The term canonical just means
typical
What does convolution?
- It is a mathematical operation that takes neural activity at each moment by the canoical HRF and then adds the moments together
What does this diagram show? - (2)
- At top shows canonical (typical) hemodynamic response function (HRF) looks like which is changes in BOLD signal we would expect to see for a single moment of neural activity (graph at middle = modelled neural activity)
- Convolution multiples canonical HRF * modelled neural activity for every moment in experiment and added together
What does convolution rely on?
the approximate linearity of the BOLD signal
What does HRF stand for?
Hemodynamic response function
Diagram of step 3 of GLM of repeating steps 1 and 2 (specificy time periods to specific task and produce hemodynamic regressors) which shows.. - (5)
- EV stands for explainatory variables
- Specificed time periods corresponding to each stimulus conditions of blue and green and created hemodynamic regressors as EV1 and EV2 show y axis of modelled BOLD signal change
- These EV used to produce the regressors
- EV1 of blue condition used to produce G1 regressor for blue condition
- EV2 of green condition used to produce G2 regressor for green condition
Diagram of step 4 of GLM of fitting regressors to the data of fMRI signal of specific voxel with aim of determining how much each regressor and bits leftover we can’t explain contributes to observed pattern of signal change which means.. - (2)
- Explain amount of response of fMRI signal to a specific voxel from data X to condition 1 in terms one regressor - G1
- Explain amount of response of fMRI signal to a specific voxel from data X to condition 2 in terms another regressor - G2
Step 4 of fitting regressors to the data
we also have a constant term in which - (2)
- Y axis is in arbitary units
- We fit constant term to whole experiment and to its data (Red) in our regression which represents how bright the voxel is throughout the experiment ignoring the activity the brain activity changes (activity of specific voxel is nothing is happening, no condition)
Step 4 of fitting regressors to data shows.. - (2)
- Best combination of G1 and G2 when added together (black line) looks quite similar to the data of activity of a voxel
- The residuals (diff between black and red line) at each moment in time and added together is as small as it can be
Summary of our GLM steps , our fitted model, is.. - (2)
- Our fitted model we call M is beta coefficient 1 of G1 (blue condition) + beta coefficient 2 of g2 (green condition) + some constant number called B3 + residuals
- Multiply by different beta coefficients to enable best possible fit of data
If residuals are huge then means the fitted GLM model is not a good fit
for the data
Steps of general linear model - (5)
- We begin to specificy time periods of modelled neural activity to specific task/stimulus
- From this, we produce the hemodynamic regressors (by modelled neural activity with canoical hemodynamic response function)
- This is done for each experimental condition
- We then fit regressors (G1 and G2) to the data of fMRI signal of specific voxel with aim of determining how much each regressor and bits leftover we can’t explain contributes to observed pattern of signal change
- We fit constant to the regression model as well