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Bosco Tjan, Pinglei Bao, Christopher Purington; Problems associated with a nonlinear relationship between neural and fMRI BOLD responses and a solution. Journal of Vision 2016;16(12):872. doi: https://doi.org/10.1167/16.12.872.
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© ARVO (1962-2015); The Authors (2016-present)
Using the unique organization of an achiasmic individual's visual cortex, we showed that the amplitude of an evoked BOLD response is proportional to the amplitude of the evoked neural response raised to a power of approximately 0.5 (Bao, Purington & Tjan, 2015, eLife). Specifically, we found that in V1-V3 of an achiasmic individual, there are two nearly identical but non-interacting neural populations that are finely intermingled in the same cortical location. Their population receptive fields are spatially disjointed, allowing independent control of each population with visual stimuli. Since the neural populations do not interact, presenting two identical stimuli, each to one of the receptive fields, doubles the local neural activity relative to presenting just one. This in-vivo system lets us identify the nonlinearity between neural and BOLD responses independently from any nonlinearity between stimuli and neural responses. In the current study, we analyzed data from several experiments with the achiasmic participant and found that a simple linear-nonlinear model can approximate the neural-BOLD relationship in time. This model postulates a hemodynamic "control signal" that is linearly related to the evoked neural response during a stimulus event. The resulting BOLD time course is the sum of such control signals, raised to a power of 0.5 in a sign-preserving manner. This model suggests that nonlinearities associated with spatial summation, adaptation, and surround suppression observed with fMRI can be considerably contaminated by hemodynamic nonlinearity, an observation supported by recent findings (Bao et al., 2014VSS). The model also predicts that functional connectivity inferred from task states by linearly regressing out task-related activities can be misleading, since task harmonics produced by the nonlinear hemodynamics will be present in the residual. Squaring a baseline-subtracted BOLD response before applying any general linear model and using a modified hemodynamic response function can reduce the effects of hemodynamic nonlinearity on results.
Meeting abstract presented at VSS 2016
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