Analytic Model of fMRI BOLD Signals for Separable Metrics of Neural and Metabolic Activity

Abstract

The applications of fMRI (functional magnetic resonance imaging) are broad covering diagnostic and clinical extents of brain function, which involves the analysis of BOLD (blood oxygen level-dependent) contrast signals. The BOLD signals are sourced from both neural and metabolic functions, and thus to enable a detailed examination of fMRI studies, methods are sought to separate the neural and metabolic functions, such that the neural component, which is often the metric of interest, can be independently examined, especially in relation to neural connectivity. In this work, a modeling approach is developed that separates the neural and metabolic functions from the overall BOLD signal. The newly developed model is initially developed within a linear framework and demonstrates excellent comparison in data fit at 97.4% to the three Gamma function, which has been widely used to characterize fMRI BOLD experimental data. The neural component of the model formulation is comprised of a proper transfer function of two poles and two zeros, and characterizes the salient features of the BOLD signal, including the initial dip, peak, undershoot, and stabilization period. The linear model is extended to characterize nonlinear fMRI BOLD signal responses through the integration of saturation functions to both the leading and trailing edges of the signal. The nonlinear model representation not only explains the muted response in amplitude and oscillations, but also explains nuanced oscillations during the hold and settling phases of fMRI BOLD responses as exemplified in comparison to published data of sensorimotor responses. Further, the newly developed decomposition is derived within a framework for modeling neurovascular coupling environments, and thus lends credibility to the modeling framework. In developing the decomposition of the neural and metabolic transfer functions, it is a conclusion that the BOLD signal correlates very well with the fast dynamics associated with neural response to external stimuli. * charlesschaper@comcast.net Graphical AbstractThe normalized impulse response of the BOLD signal and the corresponding neural activity according to the newly developed model. There is a correspondence of the critical points for the oscillatory response of the neural function and metabolic reactivity, including the initial dip, peak and subsequent undershoot. Thus, the BOLD signal is a correlated representation of the underlying neural response.

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“…The key “players” of the system are neuroactivating ion-conducting systems. As in most neurodynamic processes, the final stage of a nerve impulse is the inclusion of Ca 2+ ions in the process. , In the case of neurovascular coupling, the key role of the calcium ions is the activation of two fundamentally important participants in the processphospholipase A 2 and NO synthase. Calcium ions activate phospholipase A 2 , which is a product of arachidonic acid, and ultimately activate the synthesis of a vasodilator prostaglandin (PG) producer.…”

“…Dynamics of Ca 2+ ions and R changes in system (1) over time. (a) The results of the calculations of system (1) are normalized by the amplitude of the variables; (b) data from ref .…”

“…When the parameters ( k ′ = 0.5 s –1 , σ 1 = 0.25 s –1 , and σ 2 = 0.56 s –1 ) are chosen, the theoretical dynamics of the neuronal and metabolic responses of the system effectively describe the “classical” ratio of dynamic responses at neuronal and biochemical stages (Figure ). For comparison, the data from ref are shown in Figure . An adequate agreement of the results is observed.…”

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