Parameter distributions in retinotopic pRF mapping
Poster No:
2076
Submission Type:
Abstract Submission
Authors:
Michael Woletz1, David Linhardt1, Siddharth Mittal2, Christian Windischberger2
Institutions:
1Medical University of Vienna, Vienna, Austria, 2Medical University of Vienna, Vienna, Vienna
First Author:
Co-Author(s):
Introduction:
Population receptive field (pRF) mapping (Dumoulin, 2008) is a popular method for estimating the mapping from the visual field onto the visual cortex. Previous studies have shown that the estimated parameters will depend on several factors, such as the stimulus (Linhardt, 2021; Alvarez, 2015) or the presence of an artificial scotoma (Binda, 2013; Prabhakaran 2020).
Generally, some effects seen in pRF mapping can only be properly understood, if the underlying distributions and the dependencies between parameters are known. In this study, we introduce a new methodology for assessing the expected distributions of the estimated parameters, based on simulations, by describing them as functions of the true model parameters.
Generally, some effects seen in pRF mapping can only be properly understood, if the underlying distributions and the dependencies between parameters are known. In this study, we introduce a new methodology for assessing the expected distributions of the estimated parameters, based on simulations, by describing them as functions of the true model parameters.
Methods:
In order to facilitate large scale simulations of pRF mapping results, the standard least-squares fitting method was reformulated, which allows for efficient implementation on GPU servers, as well as the use of gradient-based optimisation methods. A Levenberg-Marquardt optimiser was implemented on the GPU and used for simulating pRF mapping results with an isotropic Gaussian pRF model on a moving bar stimulus. Gaussian white noise with various contrast-to-noise ratios (CNRs) was added to time-courses for different parameter combinations (µx, µy, σ), resulting in a total of 990 combinations, with 10,000 samples each.
Initial results showed that distributions were oriented in eccentricity direction. We thus introduced a new coordinate system denoted as (µx', µy', σ) to adjust analyses to this feature (see Figure 1). All subsequent results will therefore be reported in this coordinate system. In order to account for different ratios between target parameters and stimulus size, all parameters are reported relative to the stimulus radius. Only datasets, where at least 99.5% of the data converged to true optima were used in the analysis.
To increase the flexibility and accuracy of the approach, the multivariate distributions were modeled using Sklar's theorem, i.e. using their marginal distributions and a multivariate copula for modeling the dependencies between the parameters. A vine-copula with a fixed bivariate copula was used for modeling the dependencies. A model selection approach was used for selecting the best marginal distribution and bivariate copula for all simulated datasets.
For each simulated dataset, maximum-likelihood parameter estimates (MLE) were obtained as well as a polynomial model of the parameters as a function of non-linear transforms of the input parameters. Model selection was again used to reduce the number of parameters for this model.
Initial results showed that distributions were oriented in eccentricity direction. We thus introduced a new coordinate system denoted as (µx', µy', σ) to adjust analyses to this feature (see Figure 1). All subsequent results will therefore be reported in this coordinate system. In order to account for different ratios between target parameters and stimulus size, all parameters are reported relative to the stimulus radius. Only datasets, where at least 99.5% of the data converged to true optima were used in the analysis.
To increase the flexibility and accuracy of the approach, the multivariate distributions were modeled using Sklar's theorem, i.e. using their marginal distributions and a multivariate copula for modeling the dependencies between the parameters. A vine-copula with a fixed bivariate copula was used for modeling the dependencies. A model selection approach was used for selecting the best marginal distribution and bivariate copula for all simulated datasets.
For each simulated dataset, maximum-likelihood parameter estimates (MLE) were obtained as well as a polynomial model of the parameters as a function of non-linear transforms of the input parameters. Model selection was again used to reduce the number of parameters for this model.
Results:
The skew normal distribution (Azzalini, 2013) was selected for the marginal distributions, while for the vine-copula the bivariate Hüsler-Reiss copula (Joe, 2014) best fitted the data. Significant dependencies between the pRF parameters and statistics of the distributions can be seen in Figure 2.
The distributions of µx' showed a slight bias in the mean and its skewness increased in a sigmoid fashion for pRFs approaching the stimulus border. The standard deviation of both µx' and σ increased non-linearly with the proximity to the stimulus border and was proportional to the inverse of the CNR. There was also a strong correlation between the estimated µx' and σ values, which increased with the true µx' and σ values in a sigmoid fashion.
The distributions of µx' showed a slight bias in the mean and its skewness increased in a sigmoid fashion for pRFs approaching the stimulus border. The standard deviation of both µx' and σ increased non-linearly with the proximity to the stimulus border and was proportional to the inverse of the CNR. There was also a strong correlation between the estimated µx' and σ values, which increased with the true µx' and σ values in a sigmoid fashion.
Conclusions:
Our approach, for the first time, allows for a direct prediction of the estimated distribution of pRF parameters for given true parameters. While the estimates showed little bias for the employed bar stimulus, the distributions showed clear dependencies in their spread, as well as skewness and non-linear dependencies with respect to the input parameters. Especially, the overlap between the simulated pRF and the stimulated area was crucial to understanding these relationships.
This method will help to better characterise the efficiency of a given pRF stimuli, and increase the interpretability of pRF mapping results.
This method will help to better characterise the efficiency of a given pRF stimuli, and increase the interpretability of pRF mapping results.
Modeling and Analysis Methods:
Activation (eg. BOLD task-fMRI) 2
Perception, Attention and Motor Behavior:
Perception: Visual 1
Keywords:
Design and Analysis
FUNCTIONAL MRI
Modeling
Vision
1|2Indicates the priority used for review
Abstract Information
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Were any human subjects research approved by the relevant Institutional Review Board or ethics panel? NOTE: Any human subjects studies without IRB approval will be automatically rejected.
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Provide references using APA citation style.
Azzalini, A. (2013). The Skew-Normal and Related Families. Cambridge: Cambridge University Press.
Binda, P. (2013). ‘Minimizing biases in estimating the reorganization of human visual areas with BOLD retinotopic mapping’. Journal of vision, 13(7), 13.
Dumoulin, S.O. (2008), 'Population receptive field estimates in human visual cortex', Neuroimage, vol. 39(2), pp. 647-660
Joe, H. (2014). Dependence Modeling with Copulas (1st ed.). Chapman and Hall/CRC.
Linhardt, D. (2021). ‘Combining stimulus types for improved coverage in population receptive field mapping’. NeuroImage, 238, 118240.
Prabhakaran, G. T. (2020). ‘Foveal pRF properties in the visual cortex depend on the extent of stimulated visual field’. NeuroImage, 222, 117250.