Rapid event-related (ER) functional magnetic resonance imaging (fMRI) is one of the most popular imaging methods in cognitive neuroscience. In the rapid ER fMRI studies, individual stimuli are presented every few seconds or faster. Although less efficient for localizing activation, rapid ER fMRI has several advantages over the traditional block design, including the ability to randomize trial types and to sort data based on behavioral responses.
The standard analysis for rapid ER fMRI models activation as a linear system [2
]; the hemodynamic response to multiple input stimuli is assumed to be a superposition of the responses to individual stimuli. This approach estimates the impulse response function, also known as the hemodynamic response function (HRF), of this linear system via de-convolution, and compares the estimates to the null hypothesis or to estimates from other experimental conditions.
fMRI signals commonly do not comply with the linear assumption. Independent studies have demonstrated a substantial adaptation effect in the hemodynamic response [1
], i.e., if two stimuli are presented within the adaptation period, the amplitude of the response to the second stimulus is reduced. Furthermore, the adaptation effect strengthens as the inter-stimulus interval (ISI) decreases. Several studies demonstrated that when a pair of visual stimuli is presented less than 1 sec apart, the response amplitude to the second stimulus is approximately 55% of that to the first stimulus, with recovery to 90% at a 6 sec ISI [12
]. This evidence suggests that the adaptation effect must be modeled in the analysis, especially when stimuli are presented frequently.
The adaptation effect is expected to vary spatially due to differences in neural and hemodynamic properties of functional areas in the brain [1
]. While physiological mechanisms for adaptation are not clearly understood, it is still useful to model it for the purposes of improving detection.
Previous studies of the adaptation effect separated detection and adaptation modeling [12
], fitting the adaptation model to the estimated HRF obtained using the standard general linear model (GLM) [9
]. This approach ignores the trial-to-trial variation. Work by Buxton et al.
] introduced the biophysical balloon model for fMRI signals where the adaptation effect is captured through interactions among blood flow, blood volumes, and de-oxyhemoglobin content, instead of an explicit interaction between stimuli. Friston et al.
] proposed a statistical model using the Volterra kernels to capture interaction between stimuli. The interaction can be efficiently estimated and statistically examined via the F
-test. However, the physiological interpretation of the model parameters is challenging, since the model treats the stimuli symmetrically, effectively ignoring the causal nature of the adaptation effect.
In this work, we extend the basic GLM by incorporating a region-specific model of adaptation. In addition to the stimulus onset, our design matrix also depends on the ISIs between stimuli via a single-parameter exponential function. Specifically, this model captures the decrease in the magnitude of the hemodynamic response if the time interval to the preceding stimuli is short. In other words, we only model causal interactions among stimuli, in contrast to the bidirectional interaction model in [10
]. By combining detection and adaptation modeling, the proposed method takes into account trial-to-trial variation. It is expected that the adaptation effect strengthens when more stimuli are presented prior to the current stimulus. We summarize this effect from multiple stimuli through a multiplicative model. This extension allows for a more flexible choice of an experimental paradigm in contrast to previous fMRI adaptation studies which were restricted to presentations of stimulus pairs [12
We jointly estimate the decay parameter of the exponential function for each region and the HRF for each location in the brain. The estimated parameter of the exponential function reflects the length of the adaptation period for the corresponding region, and the estimated HRF indicates the activation status of the corresponding location. Our experimental results demonstrate a significant improvement in detection sensitivity and confirm previously known adaptation phenomena in the sensory systems.