MEASURING EFFECTS OF LATENCY IN BRAIN ACTIVITY WITH FMRI Firdaus Janoos 1 , Raghu Machiraju 1 , Steffen Sammet 1 , Michael V. Knopp 1 , Simon K. Warfield 2 and Istv´ an ´ Akos M´ orocz 2 1 The Ohio State University, USA 2 Harvard Medical School, USA ABSTRACT In fMRI analysis, general linear modelling (GLM) is com- monly used because of its explanatory power, statistical sim- plicity and computational efficiency. Such models primarily measure the parametric effects of experimental conditions on amplitude of activation, and neglect other important effects on nature of the hemodynamic response, including its temporal characteristics such as relative latency (delay). In this paper, we present a GLM approach to estimate experimental effects on, not only activation amplitude, but also latency. We validate the statistical properties of our method through simulations, and show that on in vivo fMRI data, latency can characterize aspects of neural recruitment during different cognitive tasks, that amplitude alone cannot. Index Terms— fMRI, GLM, latency, parametric-effects 1. INTRODUCTION Functional magnetic resonance imaging (fMRI) is a very pow- erful tool for studying the “functional localization” of brain ac- tivity, although methods for understanding the “functional in- tegration” have become a important research agenda in recent years. Conventional methods for analyzing fMRI are designed to localize the functional substrates activated during specific mental activities. However, the temporal characteristics of the activity, such the delay in the hemodynamic response (HR) to a neurological stimulus, which are an important aspect of brain function [1] and provide information about how functionally specialized regions respond to different types of mental tasks – are typically not measured by these methods. Analysis methods based on general linear models (GLM) of brain response and linear least squares estimation of their parameters are very popular because of their computational ef- ficiency, statistical simplicity and explanatory power [2]. While most GLMs are used to estimate the amplitude of the HR to a stimulus at each voxel, it is possible to estimate the response latency using a first-order Taylor series expansion of the hemo- dynamic response function (HRF) in the GLM [3]. This esti- mator, however, is numerically unstable and biased. Here, we suggest a low-bias estimator for latency and provide an analyti- cal formulation for its variance, needed for deriving confidence intervals. An alternative approach to estimate the activation amplitude and delay uses an orthogonal basis derived from a spectrum of time-shifted HRFs [4]. Using GLM methods, it is possible to study the effects of experimental parameters on functional activation [5], in one of two ways: a) parametric effect analysis or b) factorial analysis. The first method is used when testing whether a real-valued (in- terval) experimental parameter p has a statistically significant effect f ( p) on the amplitude of activation by adding a regressor weighted by f ( p) (typically, a polynomial function) and test- ing its effect. One drawback is that the correct relationship f between the parameter and amplitude may not be known a pri- ori. Moreover, it assumes that the parameter modulates only the amplitude of the HR while all other aspects remain unchanged, which is known not to be the case [1]. Therefore, it only tests the effect of the parameter on the amplitude, not the latency of the response. The other alternative, a factorial analysis is used with categorical parameters, by adding a regressor correspond- ing to each level of the variable. The difference in response at each level can be used to deduce the presence of an effect on both amplitude and latency. While this method does not suffer from the drawbacks of the parametric effect analysis, it cannot be used for real-valued parameters. In this paper, we propose a method that combines the strengths of both approaches by measuring the effect of an interval parameter on both HR amplitude and latency, without requiring that the relationship to test for be specified a priori. The idea, as explained in section 2, is to quantize the real- valued parameter into a finite number of levels and analyze it with a factorial design. The loss in statistical power that would result from such a partitioning of the design is avoided by a regularization of the estimation procedure which significantly improves the quality of the inferences. In section 3 we validate our method on simulated data and present a case study on real data that demonstrates the addi- tional information about brain physiology that is available from examining parametric effects on latency. 2. METHOD 2.1. Estimating Response Amplitude and Latency Let s i (t ), t = 1...N, be the stimulus function representing the onsets and durations of the neurological stimuli corresponding to a mental task of type i = 1...q. In conventional GLM anal- ysis of fMRI data, the following model is used to explain the observed signal y(t ) at each voxel: y(t )= q ∑ i=1 [β i x i (t )+ γ i ˙ x i (t )] + ε (t ), (1) where x i (t )= s i ⋆ h(t ) is the expected HR (with no delay) ob- tained by convolving s i (t ) with a hemodynamic response func- 1141 978-1-4244-4126-6/10/$25.00 ©2010 IEEE ISBI 2010