Nonlinear Analysis of Multimodal Dynamic Brain Imaging Data

In the context of realizing the functional requirements of a task, brain dynamics organize brain activities that cause biophysical and physiological signals, which the instruments of various neuroimaging modalities can measure. An ultimate goal is to make joint inferences about the underlying activity, dynamics, and functions by exploiting complementary information from multimodal datasets, acquired from the same subject who performed the same task. An intermediate problem is to design cross-modal analyses that improve the spatial and temporal resolution of one modality by incorporating complementary information from another modality. Given that M/EEG and fMRI BOLD signals are complementary in time and space with respect to a common subspace of brain activity, is there an fMRIrelated M/EEG analysis that spatially and temporally enhances the M/EEG signal? Likewise, is there an M/EEG-related fMRI analysis that temporally and spatially enhances the BOLD signal? A theoretical principle is to design cross-modal analyses that maximize the dynamic coupling between jointly observed signals within the framework of nonlinear system identification. In particular, we define a linear spatial estimator that maximizes the empirical coupling of the estimated M/EEG source activity as driven by local BOLD signal, and a nonlinear dynamic transform that maximizes the coupling of BOLD signal as driven by the estimated M/EEG signal. The latter transformation can be the basis for fMRI statistical parametric maps that couple more tightly with neuronal activity compared with task-derived maps. For M/EEG and fMRI datasets obtained from different sessions, we describe a method of temporal alignment that uses separately identified nonlinear system models to simulate “virtual simultaneous” datasets. The critical criterion for empirical evaluation of these methods is between-session reliability. In: International Journal of Bioelectromagnetism 3(1) http://www.tut. fi/ijbem/ Special issue on: Fusion of EEG, MEG and fMR Data Correspondence: Mark E. Pflieger Source Signal Imaging 2323 Broadway, Suite 102 San Diego, CA 92102 USA http://www.sourcesignal.com mep@sourcesignal.com Pflieger & Greenblatt IJBEM 3(1) 2 Introduction Brain dynamics implement brain functions by organizing brain activity; but we do not directly observe functions, activity, or dynamics in a functional neuroimaging experiment. Although the successful performance of a task manifests brain functions, we observe only the sensory and motor task variables— not the underlying brain functions that coordinate, monitor, predict, plan, and control these variables. We observe shadows of brain activity via the spatiotemporal signals obtained from a modality, such as BOLD (blood oxygenation level dependent) signals from fMRI, or fields/potentials from M/EEG. However, in order to make inferences about the underlying brain activity, we must apply biophysical, physiological, and biostatistical theories to the given task variables and measured signals. Finally, we clearly do not directly observe the underlying brain dynamics, which are the deterministic and/or stochastic laws that govern brain activity to realize functional requirements. In all three cases, we must combine the available data with a body of theory in order to make inferences about the interesting, underlying unknowns. Different modalities measure different signals that may reflect essentially the same underlying brain activity, dynamics, and functions. Armed with complementary datasets such as fMRI and M/EEG that have different spatial and temporal characteristics, the general question is: Can we make stronger inferences about each of the interesting unknowns via spatiotemporally improved signal detection and parameter estimation? Clearly, we will need some common theoretical machinery in order to make joint, multimodal inferences. To begin, let us make an assumption. When different-session fMRI and M/EEG datasets are available for the same subject who performed realizations of the same task, let us assume that the underlying brain dynamics were statistically equivalent across sessions. Although the brain activities must have differed in details across sessions, we assume that the underlying dynamics were substantially equivalent in the sense that between-session differences were statistically small compared with other experimentally significant variables. Based on this testable assumption, our goals are (A) to design cross-modal analyses of both datasets (fMRI and M/EEG) that improve, spatially and temporally, the estimation and detection of the common brain activity, and (B) to characterize the underlying dynamics. Ultimately, we seek (C) to understand how the dynamics implement brain functions in the context of successful task performances. While keeping in mind the larger context of problem C, this paper presents an approach for solving problem A that leads to the threshold of problem B. Problem C: Spatiotemporal integration functions In the long term, an ideal analysis of spatiotemporal imaging data should permit us to make inferences about brain processes as realizations of brain functions, i.e., as solutions to natural problems that engage the brain. Thus, we ultimately seek methods that can bridge the gap between (i) raw neuroimaging measurements from various modalities and (ii) descriptions of underlying brain processes in terms of the problems they solve. Such descriptions call for “functional insight” that is attuned to the “native interests” of the brain regions under study (e.g., Lettvin et al., 1959). We can approach this objectively if we express a putative functional insight as a testable hypothesis that explicitly formulates the problem that a brain process solves. Because the analysis we ultimately seek should permit us to test such functional hypotheses, it follows that the technical problem of designing imaging algorithms depends on the scientific problem of formulating functional theories about the natural problems solved by the brain. In short, our methods must match the subject matter. On the other hand, because the subject matter comprises unresolved functional issues that our methods should address, we must design the analysis to match a general theoretical framework that is relatively neutral, which can accommodate various specific functional hypotheses. Some viable candidates for such a framework are: adaptive system theory (Ashby, 1960; Sommerhoff, 1974); schema theory (Arbib et al., 1998); and information theory used as a language to express functional hypotheses, e.g., as used by Phillips and Singer (1997) to formulate the coherent infomax hypothesis of cortical processing. To our knowledge, these frameworks remain undeveloped along lines that would render them immediately useful for the design of imaging analysis algorithms. Pflieger & Greenblatt IJBEM 3(1) 3 However, in spite of this present lack of a suitable general framework for describing brain function, these basic considerations nevertheless can guide our current efforts toward the long-term goal. Spatiotemporal integration functions play a central role in solving various problems that engage the brain, which we classify as extrinsic or intrinsic. “Extrinsic problems” challenge the brain to dynamically organize skeletal and visceral behaviors that can achieve co-adaptations between the organism’s environment and the organism’s physiology. Two extremes of such co-adaptive processes are environment-directed and physiology-directed brain processes. Environment-directed processes adaptively control environment variables around the organism by coordinating, in space and time, two streams of brain processes: (a) motor planning and control of skeletal effector variables, and (b) sensory monitoring and prediction of the environment variables. (We use the terms “coordination”, “planning”, “control”, “monitoring”, and “prediction” to describe objective forms of brain function without ascribing subjective content.) To illustrate, consider Sommerhoff’s (1974) example of a bird pecking at a grain of seed, the position of which may be subject to wind perturbations: The planned/controlled trajectory of the beak must be coordinated with the monitored/predicted trajectory of the grain. In a formally similar way, physiology-directed processes modulate the autonomic regulation of physiological variables in the organism by coordinating, in space and time, two streams of brain processes: (a) planning and control of visceral effector variables, and (b) monitoring and prediction of the physiological variables. For example, efforts of biomedical engineers to externally control hemodynamic variables (Isaka and Sebald, 1993; Palerm et al., 1999) underscore the highly nonlinear nature of these dynamic physiological control problems. More generally, co-adaptive processes are bi-directional and higher-order in the sense that they coordinate environment-directed (somatic) and physiology-directed (visceral) processes (Yates and Stocker, 1998) as, for example, when a runner’s physiology responds to meet the increased demand of climbing a steep grade. In summary, the requirement for coordination of multiple brain processes in space and time implies that spatiotemporal integration functions play a key role in solving extrinsic problems. “Intrinsic problems” are self-referential problems that the brain solves (in the context of solving extrinsic problems) by coordinating brain architectural development processes and brain physiological regulation processes. Thus, two extreme types of processes that solve intrinsic problems are neurophysiological self-regulation and neuroarchitectural self-organization. Processes of the former type modulate the regulation of physiological variables in the brain itself, and so are special cases of the physiology-directed processes discussed above. An example is the regulation of the coupling between brain hemodynamic variables (such as regi