Effect of hemodynamic variability on Granger causality analysis of fMRI - PubMed (original) (raw)

Effect of hemodynamic variability on Granger causality analysis of fMRI

Gopikrishna Deshpande et al. Neuroimage. 2010 Sep.

Abstract

In this work, we investigated the effect of the regional variability of the hemodynamic response on the sensitivity of Granger causality (GC) analysis of functional magnetic resonance imaging (fMRI) data to neuronal causal influences. We simulated fMRI data by convolving a standard canonical hemodynamic response function (HRF) with local field potentials (LFPs) acquired from the macaque cortex and manipulated the causal influence and neuronal delays between the LFPs, the hemodynamic delays between the HRFs, the signal-to-noise ratio (SNR), and the sampling period (TR) to assess the effect of each of these factors on the detectability of the neuronal delays from GC analysis of fMRI. In our first bivariate implementation, we assumed the worst-case scenario of the hemodynamic delay being at the empirical upper limit of its normal physiological range and opposing the direction of neuronal delay. We found that, in the absence of HRF confounds, even tens of milliseconds of neuronal delays can be inferred from fMRI. However, in the presence of HRF delays which opposed neuronal delays, the minimum detectable neuronal delay was hundreds of milliseconds. In our second multivariate simulation, we mimicked the real situation more closely by using a multivariate network of four time series and assumed the hemodynamic and neuronal delays to be unknown and drawn from a uniform random distribution. The resulting accuracy of detecting the correct multivariate network from fMRI was well above chance and was up to 90% with faster sampling. Generically, under all conditions, faster sampling and low measurement noise improved the sensitivity of GC analysis of fMRI data to neuronal causality.

Copyright (c) 2009 Elsevier Inc. All rights reserved.

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Figures

Figure 1

Figure 1

Schematic showing the procedure to derive the four time series of the multivariate network from a single channel of LFP data, x(n). x1(n), x2(n), x3(n) and x4(n) represent the four time series derived from x(n) and d1 and d2 represent the inherent neuronal delays in the simulated system governing the relationship between the four time series

Figure 2

Figure 2

The multivariate network expected to be obtained from the time series x1(n), x2(n), x3(n) and x4(n)

Figure 3

Figure 3

Variation of ρo, which determines the detectability of the neuronal influence in the absence of HRF confounds, as a function of neuronal delay dn, TR and noise for the case of simple delay. The black line represents the statistical threshold of _ρo_=3

Figure 4

Figure 4

Variation of ρo, which determines the detectability of the neuronal influence in the absence of HRF confounds, as a function of neuronal delay dn, TR and noise for the case of simple delay plus intrinsic dynamics. The black line represents the statistical threshold of _ρo_=3. Blue, red and black curves represent C values of 0.5, 0.7 and 0.9, respectively

Figure 5

Figure 5

Variation of ρd, which determines the detectability of the neuronal influence in the presence of HRF confounds, as a function of neuronal delay dn, TR and noise for the case of simple delay. The hemodynamic delay _dh_=0.5 s opposed the neuronal delay dn. The black line represents the statistical threshold of _ρd_=3

Figure 6

Figure 6

Variation of ρd, which determines the detectability of the neuronal influence in the presence of HRF confounds, as a function of neuronal delay dn, TR and noise for the case of simple delay plus intrinsic dynamics. The hemodynamic delay _dh_=0.5 s opposed the neuronal delay dn. The black line represents the statistical threshold of _ρd_=3. Blue, red and black curves represent C values of 0.5, 0.7 and 0.9, respectively.

Figure 7

Figure 7

Variation of ρd, which determines the detectability of the neuronal influence in the presence of HRF confounds, as a function of neuronal delay dn, TR and noise for the case of simple delay. The hemodynamic delay _dh_=2.5 s opposed the neuronal delay dn. The black line represents the statistical threshold of _ρd_=3

Figure 8

Figure 8

Variation of ρd, which determines the detectability of the neuronal influence in the presence of HRF confounds, as a function of neuronal delay dn, TR and noise for the case of simple delay plus intrinsic dynamics. The hemodynamic delay _dh_=2.5 s opposed the neuronal delay dn. The black line represents the statistical threshold of _ρd_=3. Blue, red and black curves represent C values of 0.5, 0.7 and 0.9, respectively.

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