Framework for parametric fMRI fitting
Poster No:
1357
Submission Type:
Abstract Submission
Authors:
Michael Woletz1, David Linhardt2, Siddharth Mittal1, Christian Windischberger3
Institutions:
1Medical University of Vienna, Vienna, Vienna, 2Medical University of Vienna, Wien, Vienna, 3Medical University of Vienna, Vienna, Austria
First Author:
Co-Author(s):
Introduction:
Most task-based fMRI analysis designs make use of a general linear model (GLM) (Friston, 1995), where a regression matrix is constructed based on the task design and the research question and fitted, along with additional nuisance regressors to the data in a least-squares way. Other, specialized methods, such as population receptive field mapping (PRF), employ models where the regression matrix is not only depending on the task, but also additional parameters, which are in turn estimated from the data using optimization methods. In this work we present a simple framework, allowing the fast comparison of different parameters during the optimization process, as well as the computation of derivatives.
Methods:
A mathematical framework was developed, by making use of algebraic properties of the regressors, which simplifies the fitting process. Instead of performing least squares fitting, the fitting problem can be reduced to a matrix multiplication by enforcing orthonormality constraints, without changing the overall fit. That is, the static regressors are made orthonormal using a QR decomposition and the model regressor by subtraction of the static regressor fits (see Figure 1 for details).
The constructed matrix consists of time courses, corresponding to different sets of parameters, which can be used for a coarse fitting routine on all measured voxels at once. Once approximate parameters are found, the framework allows for the computation of derivatives with respect to the estimated parameters, which enables the use of efficient derivative based methods for the estimation of all parameters in all measured voxels.
The proposed framework was tested on simulated data, simulating a PRF acquisition. Noisy time-courses were generated, representing a moving bar stimulus for a Gaussian PRF at a given position and size. Time courses were generated using the equations in Figure 1, as well as the derivative for the optimization function and used to compare the simulated ground truth results with the result from the parametric fitting framework.
The constructed matrix consists of time courses, corresponding to different sets of parameters, which can be used for a coarse fitting routine on all measured voxels at once. Once approximate parameters are found, the framework allows for the computation of derivatives with respect to the estimated parameters, which enables the use of efficient derivative based methods for the estimation of all parameters in all measured voxels.
The proposed framework was tested on simulated data, simulating a PRF acquisition. Noisy time-courses were generated, representing a moving bar stimulus for a Gaussian PRF at a given position and size. Time courses were generated using the equations in Figure 1, as well as the derivative for the optimization function and used to compare the simulated ground truth results with the result from the parametric fitting framework.
Results:
The calculated error function and its partial derivatives as a function of the location parameters for a simulated PRF experiment can be seen in Figure 2. Our framework is very efficient, allowing the computation of both the error function and the gradient as simple matrix multiplications, enabling a fast evaluation of both for many voxel time-courses at once, without reducing the fitting accuracy.
Conclusions:
By reformulatiing the GLM model, we have presented a framework, which allows fitting of parameters in an fMRI experiment. The new framework allows for faster fitting routines and gradient based fitting routines, not only on CPUs, but GPUs, enabling not only faster results, but also more complicated models.
Modeling and Analysis Methods:
Activation (eg. BOLD task-fMRI) 1
Methods Development 2
Novel Imaging Acquisition Methods:
BOLD fMRI
Perception, Attention and Motor Behavior:
Perception: Visual
Keywords:
Computational Neuroscience
FUNCTIONAL MRI
Modeling
1|2Indicates the priority used for review