Medical Devices 06-�Functional Magnetic Resonance Imaging (fMRI)

Dalton H Bermudez, B.Eng

Medical Physics PhD Student

What is fMRI

• Medical devices that enables one to inference about neural activity

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• Different type of fMRI studies:

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• Resting State Study

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• Dynamic Study

Stimulus to BOLD Signal

Source: Arthur & Boniface, 2002. Tends in Neuroscience

Temporal and Spatial Resolution

Gazzaniga, Ivry & Mangun, Cognitive Neuroscience

Raw fMRI data

fMRI Acquisition & Analysis

Affine Transforms:

Types of Transform Matrix

• 2-D Scaling Transform Matrix:

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Types of Transform Matrix

• 2-D Translation Transform Matrix:

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Types of Transform Matrix

• 2D Rotational Transformation Matrix:

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Implementation of Scaling, shifting, and rotation in MATLAB using rigid registration

Types of Transform Matrix

• 2D Shearing Transformation Matrix:

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Motion Correction

• Motion Correction of fMRI deals with minimizing the differences between the FMRI volumes and reference structural MRI volume.

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• To estimate the parameters for the affine transform model to best align the fMRI images to the reference structural MRI images, the difference between the images needs to be determine.

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• The difference between images is referred to as the cost function.

Motion Correction- Cost Functions

• A proper cost function should be sufficiently small when two images are well-aligned and larger as they become misaligned

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• The type of cost function depends on types of images being registered or aligned.

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• If the images are of the same type, like the realignment of fMRI voxels units across different time-points, then the cost function can be determined by minimizing the difference between intensity values.

Motion Correction- Cost Functions

• The least square cost function measures the average squared difference between voxel intensities in each of the images begin registered.

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• A_v and B_v represent intensity of vth voxels in images A and B.
• Only appropriate to use this method in within-modality registration.

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Motion Correction- Cost Functions

• The Normalized correction considers the linear relationship between voxel intensities in the two images being aligned.

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• Measure is appropriate for within-modality registration only.

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Hemodynamic Response Function Model 

• When analyzing the shape of the estimated hemodynamic response function (HRF), summary measures of psychological interest (e.g., amplitude, delay, and duration) can be extracted and used to infer information regarding the intensity, onset latency, and duration of the underlying brain metabolic activity.

Hemodynamic Response Functions

• Mark Cohen’s Gamma-variate function used to represent Hemodynamic Response Function.

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• The terms b and c are constant with values of 8.6 and 0.547

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• To model HRF one includes both first and second temporal derivatives to capture peaks that occur earlier or later in the BOLD signal and to capture narrower or wider responses in the signal, respectively.

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Informed Basis Set

Canonical HRF (2 gamma functions)

Plus Multivariate Taylor expansion in:

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time (Temporal Derivative)

width (Dispersion Derivative)

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Temporal derivative can model (small) differences in the latency of peak response.

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Dispersion derivative can model (small) differences in the duration of the peak response.

Hemodynamic Response Functions

Hemodynamic Response Functions

• The sum of three gamma functions can also be used to generate the HRF:

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• A₁=−0.2, A₂=10, A₃=−3.6, α₁=1.5, α₂=6.6, α₃=15, β₁= 0.8, β₂=0.8, and β₃=1

Hemodynamic Response Function Model 

• The fMRI time course can then be modeled as the convolution of the Hemodynamic response function and the stimulus function.

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• Where h(t) and u(t) are the HRF and stimulus function, respectively.

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Temporal Basis Functions for fMRI

• Fits of a boxcar epoch model with (red) and without (black) convolution by a canonical HRF, together with the data (blue).

Generalized Linear Model (GLM)

Statistical Parametric Maps

• Statistical Parametric Maps (SPMs) is the construction of spatial statistical processes to test hypothesis about specific effects within a region.
• SPMs are processes with voxel values that are under the null hypothesis, which distributed with a known probability density function.

fMRI with Statistical Maps

Preliminary EEG-informed fMRI Analysis (Part 1)-in AFNI

Preliminary EEG-informed fMRI Analysis (Part 2) - in AFNI

Preliminary EEG-informed fMRI Analysis (Part 3) - in AFNI

What does the fMRI tell you?

• Each intensity value corresponds to the oxygenation supplied to that brain region

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• The higher the oxygenation to a brain region, the more neural activity in the region.

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• The fluctuation in the intensity of fMRI is known as the BOLD Signal.