The term neural modeling refers to a variety of different computational schemes (Arbib 2003), a spectrum if you will, ranging from those using percep-trons and backpropagation (McClelland & Rumelhart 1986) that often lack biological plausibility, to neural neworks that incorporate elements with biologically realistic properties (Dayan & Abbott 2001). Although, as we shall see, models at various points along this spectrum are now being utilized in conjunction with neuroimaging data, this review will emphasize the use of biologically realistic neural models.
Until recently, the focus of most mammalian neural modeling work centered on the behavior of single neurons, or small populations of neurons, usually located in a single brain area (Arbib 2003; Dayan & Abbott 2001; Rolls & Treves 1998), although there were some important exceptions, such as Tononi et al. (1992). The reason for such a focus was clear: most neural data suitable for modeling were acquired from single unit electrophysiological recordings. Beginning in the early 1990s, investigators started employing various types of computational network modeling methods that were directed at functional brain imaging data (e.g., Arbib et al. 1995; Friston 1994; Friston et al. 1991; Horwitz 1990; Mcintosh & Gonzalez-Lima 1991; Mcintosh et al. 1994; Tagamets & Horwitz 1998). Hemodynamic-based functional brain imaging has the ability to provide information about brain activity during the performance of cognitive tasks with a spatial resolution ranging from several millimeters to 1-2 centimeters from essentially all brain regions simultaneously. Moreover, because these methods are relatively non-invasive and can be performed in normal subjects, they enable brain researchers to investigate the brain basis of human cognition (for a review, see Frackowiak et al. 2004). However, the temporal resolution of these types of data are much inferior to the millisecond scale of neural dynamics (for PET, the temporal resolution is about 30-60sec; for fMRI, it is several seconds). Other techniques, such as electroencephalography (EEG) and magnetoencephalograpy (MEG) can also be used, and these methods do provide the requisite temporal information, but spatial localization is less well defined than is the case for fMRI and PET (see Horwitz et al. (2000) and Horwitz & Poeppel (2002) for brief discussions of the various neuroimaging methods and for the difficulties in combining them). Nonetheless, EEG/MEG has also elicited a number of computational neural modeling efforts (e.g., David & Friston 2003; Jirsa & Haken 1997; May et al. 1999; Nunez 1981; Robinson et al. 2005).
The central role that functional neuroimaging now plays in human cognitive neuroscience cannot be emphasized enough. Although there are numerous tasks that can be similarly performed in humans and nonhumans (especially nonhuman primates), there are many cognitive functions that are difficult, if not impossible, to study in nonhumans, especially those related to language, to some aspects of social cognition, and to high level executive function. Until the advent of functional neuroimaging the only ways to investigate the neural basis of human cognition were: (1) analysis of the behavioral consequences of brain lesions (e.g., strokes); (2) electrophysiological studies in neurosurgi-cal patients; (3) examination of behavior following pharmacologic intervention or in relation to genetic analysis; and, (4) extrapolation from nonhuman neurophysiological and other neuroscientific approaches. The hemodynamic functional neuroimaging methods (fMRI and PET) allowed numerous investigators to view the changes in brain activity between tasks and/or groups of subjects (e.g., normal volunteers and subjects with neurological or psychiatric disorders) with a spatial scale of a few millimeters, and, most importantly, to view these changes in most of the brain at the same time. The interpretation of these patterns of activity, involving the interaction of multiple and distributed neuronal populations, generated the need for computational modeling.
Modeling serves a number of purposes in this regard, including a way to keep track of the complex interactions between the various neural populations and a way to relate these patterns to neural mechanisms (e.g., Horwitz & Glabus 2005) or to hypothesized cognitive mechanisms (e.g., Anderson et al. 2003). Moreover, neural modeling is necessary, we would argue, for another reason. As indicated in the last paragraph, there are numerous and diverse sources of neuroscientific data that relate to the neural basis of cognitive function. All these types of data have different spatial, temporal and featural properties that make them hard to relate to one another. Furthermore, each type of data has its own interpretational limitations. The net effect is that no one kind of neuroscientific data can be thought of as being a "gold standard". That is, all these different types of data (lesions, electrophysiological, functional neuroimaging, etc.) are providing us with some information about the neural basis of a cognitive function, but there is no easy and straightforward way to put all these types of information together. We have argued for a long time now (e.g., Horwitz et al. 1999) that computational neural modeling provides a method by which all relevant neuroscientific data pertaining to a cognitive task can be accounted for in terms of the dynamic interactions of multiple neuronal populations. We will illustrate this later in this paper.
Conceptually, there are two different ways to employ computational modeling, although both can be used in conjunction with one another. In simulation mode, a model is constructed (i.e., a set of model parameters is defined and values for each parameter are assigned) and data are generated from each of the elements of the model. These data are then compared with appropriate experimental data and the model is considered successful if there is close agreement between the experimental and simulated data. In data-fitting mode, some computational procedure is used to vary the model parameters until there is agreement between experimental data and data generated by the model. Examples of data-fitting modeling are (1) the use of Structural Equation Modeling (SEM) with PET or fMRI data (e.g., Buechel et al. 1999; Mcintosh et al. 1994) and (2) the use of Dynamic Causal Model with fMRI data (Friston et al. 2003) (see also Stephan and Friston, this volume). Several papers in this volume focus on data-fitting modeling. Although the distinction between simulation and data-fitting is fuzzy, it is often the case that the models used in data-fitting are less detailed and less specific about the model parameters than are the models used in simulation. Importantly, the parameters used in simulation models often have their values based on a different set of data than on the data to which the model is being applied.
Simulation modeling can also be used directly at the level of PET/fMRI data (e.g., using SEM to simulate new results; see Horwitz 1990; Kronhaus & Willshaw in press). However, its main use has been to relate neurobiological data to fMRI or PET results, or conversely, to relate the performance of cognitive models to such data. The focus of this paper is on the former, but we shall also briefly review the latter.
Another way to think about the different types of modeling is that some are "bottom-up" and some are "top-down". In a bottom-up approach, the data one tries to explain are at one level, and the explanatory variables are at a "lower" level (lower can mean such things as more fundamental, more microscopic, more basic). As will be shown, this means, for example, trying to account for fMRI data in terms of the activity of neurons. Importantly, the goal of such modeling is to propose neural mechanisms that result in particular cognitive functions. In essence, one wants the cognitive function to appear as an emergent phenomenon. In a top-down approach, the hypothesized mechanisms are cognitive, and the goal is to locate the brain regions that implement these cognitive mechanisms. The way this is done is to find the brain region(s) whose fMRI signals behave as proposed by the model.
In the next section, we will review some recent top-down approaches. In the following section, we will review some bottom-up studies. We will end with some concluding comments.
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