Elsevier

NeuroImage

Volume 50, Issue 1, March 2010, Pages 72-80
NeuroImage

Power spectrum scale invariance quantifies limbic dysregulation in trait anxious adults using fMRI: Adapting methods optimized for characterizing autonomic dysregulation to neural dynamic time series

https://doi.org/10.1016/j.neuroimage.2009.12.021Get rights and content

Abstract

In a well-regulated control system, excitatory and inhibitory components work closely together with minimum lag; in response to inputs of finite duration, outputs should show rapid rise and, following the input's termination, immediate return to baseline. The efficiency of this response can be quantified using the power spectrum density's scaling parameter β, a measure of self-similarity, applied to the first derivative of the raw signal. In this study, we adapted power spectrum density methods, previously used to quantify autonomic dysregulation (heart rate variability), to neural time series obtained via functional MRI. The negative feedback loop we investigated was the limbic system, using affect-valent faces as stimuli. We hypothesized that trait anxiety would be related to efficiency of regulation of limbic responses, as quantified by power-law scaling of fMRI time series. Our results supported this hypothesis, showing moderate to strong correlations of trait anxiety and β (r = 0.45−0.54) for the amygdala, orbitofrontal cortex, hippocampus, superior temporal gyrus, posterior insula, and anterior cingulate. Strong anticorrelations were also found between the amygdala's β and wake heart rate variability (r =  0.61), suggesting a robust relationship between dysregulated limbic outputs and their autonomic consequences.

Introduction

Negative feedback loops that maintain homeostatic control are ubiquitous within the body (Khoo, 2000); the same mechanism, involving imbalance or “dysregulation” between excitatory and inhibitory components, can produce very different diseases depending upon the particular system affected. Dysregulatory diseases range from diabetes (Muscogiuri et al., 2008), Cushing's disease (Miller and O'Callaghan, 2002), hypertension (Grassi, 2009), cancer (Bosl and Li, 2005, Engelmann and Bauer, 2000, Ichimura et al., 2000), as well as autoimmune diseases such as asthma (Braman, 1995) and rheumatoid arthritis (Stenberg et al., 1992). As such, one diagnostic technique that has shown success in assessing risk for dysregulatory diseases is to provide a system perturbation (bolus) and then observe as a single instance the dynamics of the excitatory and inhibitory responses in modulating return to baseline; well-known examples include the glucose tolerance test for diabetes (Norris et al., 2008) and the dexamethasone suppression test for Cushing's disease (Elamin et al., 2008). Where strong perturbations are not feasible, one can maintain signal detection power by using a larger number of milder perturbations as inputs. For example, the nonlinear complexity with Shannon entropy method of heart rate variability analysis (Kurths et al., 1995, Voss et al., 1995) measures responses to endogenously and exogenously produced perturbations for up to 24 h at a time. These are assumed to be chaotic; therefore, the degree to which resulting cardiac outputs are also chaotic is an indicator of a well-regulated system, with increased chaos associated with improved cardiovascular health.

In a well-regulated control system, the excitatory and inhibitory components work closely together with minimum lag: in response to an input of finite duration, outputs should show rapid rise and, following the input's termination, efficient return to baseline (i.e., minimum latency and extinction times). As neuroimaging develops increasingly sophisticated methods of characterizing connectivity between neural regions associated with control circuits, this raises the exciting possibility of using neural time series to quantify dysregulation within those circuits. Doing so would provide sensitive neurobiological markers for the dynamics associated with risk for neurological and psychiatric illnesses that are dysregulatory in nature.

This manuscript builds directly upon our previous research which, having modeled the limbic system as a control circuit based upon animal and human research (Baxter et al., 2000, Blair et al., 2005, Davis and Whalen, 2001, Izquierdo and Murray, 2005, Izquierdo et al., 2005, LeDoux, 2000, Maren, 2005, Morgane and Mokler, 2006, Phan et al., 2002, Phelps et al., 2004, Rosenkranz et al., 2003, Sotres-Bayon et al., 2004, Sotres-Bayon et al., 2006), found that dysregulation of the excitatory (amygdala) and inhibitory (Brodmann Area 45) components positively correlated with trait anxiety in healthy adults (Mujica-Parodi et al., 2009). Moreover, limbic dysregulation was positively correlated with autonomic dysregulation, suggesting a mechanism by which patients with mental illnesses such as paranoid schizophrenia show lowered heart rate variability (Mujica-Parodi et al., 2005), since outputs from the limbic system, via the lateral hypothalamus, project to the lateral medulla and provide inputs for the autonomous nervous system's control circuit. Upon this model, we hypothesized that the observed autonomic dysregulation seen in patients does not result from autonomic abnormalities but rather from the autonomic nervous system's dysregulated limbic outputs (Radulescu and Mujica-Parodi, 2009, Radulescu and Mujica-Parodi, 2008).

The method we used previously to characterize dysregulation was to measure cross-correlations (“coupling”) between time series for nodes within the circuit. While the method showed a relationship to trait anxiety in healthy individuals, it had several important limitations as diagnostic or risk-assessment technique for patients. First, although analyses of the dynamics showed that the most dominant control was exerted by BA45 upon the amygdala, the cross-correlation method showed that trait anxiety was associated with uncoupling between different node-pairs within the circuit. To maximize clinical utility, it would be preferable that systemic uncoupling be characterized by a single output, as per the nonlinear complexity method of heart rate variability analysis (Voss et al., 1995, Mujica-Parodi et al., 2005). Second, the method made certain assumptions about the dynamics that seem to be violated by the more severe dysregulation seen in patients (Radulescu and Mujica-Parodi, 2008). While the most straightforward method of accomplishing both of these aims would be to measure Shannon entropy of the system, we found that entropy measures are unstable for the limited temporal resolution obtained by fMRI time series. Therefore, the approach we took was to measure variability directly by looking at frequency analyses (i.e., power spectrum density) of the time series.

Power spectrum scale invariance (PSSI) has been conventionally used as an efficient tool for analyzing irregular time series (Shelhamer, 2007) by measuring the relative frequency content of a signal. In our study of temporal variability of human brain activity, we utilize the fact that the time series of functional magnetic resonance imaging (fMRI) data show power-law scaling behavior (Thurner et al., 2003, Zarahn et al., 1997). Scaling or scale invariance means that there is no preferred temporal scale, and that the power spectrum density of the signal follows the power law:S(f)fβ,where β is the scaling exponent. This form of the PSSI, peculiar to fractional Brownian motion (Beran, 1994, Hurst, 1951, Mandelbrot, 1982, Mandelbrot and van Ness, 1968), is related to statistical self-similarity or fractal property of the signal.

Temporal scaling laws in biological time series are usually explained by the existence of the underlying complex control system involving various feedback mechanisms (Bak et al., 1987, Bak et al., 1988, Tang and Bak, 1988). The absence of characteristic time scales gives to the system important biological advantages, such as adaptability of response to a constantly changing environment (Goldberger et al., 1990). Scaling behavior in human brain oscillations using electroencephalogram (EEG) time series (Linkenkaer-Hansen et al., 2001) suggests that power-law scaling behavior of spontaneous oscillations can be explained within the theory of self-organized criticality, in which a system contains a critical point as an attractor. Conceptualized in these terms, a well-regulated control system is “self-organizing” in a sense that it arranges itself naturally without any external mechanism. The criticality of the system is in its balancing between structural stability in response to perturbations and the ability to react to perturbations without the need to tune the control parameters.

The scaling parameter β (Shelhamer, 2007 and references therein) serves as a measure of the auto-correlations within the signal. Estimating the β exponent for a time series provides a measure of whether the data are a pure random walk or have underlying trends. A flat spectrum (β = 0) corresponds to the uncorrelated time series; i.e., white noise. Increasing (negative) values of the scaling exponent indicate the persistence in the time series (i.e., the system's “memory”) over many different time scales. However, for reasons explained below, many of the physiological applications of the scaling parameter calculate β not from the raw signal but from its first derivative. The derivative shifts β by a constant, making negative values of β across the brain positive without changing between-voxel relationships.

Our approach is similar to that used in heart rate variability analysis. The scale-invariant properties of heartbeat sequences have been studied by various groups and methods (Ivanov et al., 1999, Ivanov et al., 2001, Peng et al., 1993, Thurner et al., 1998). It has been found that the scaling laws strongly depend upon the state of the underlying physiologic control system and are consistent with a nonlinear feedback system that shifts the signal away from the extremes (Ivanov et al., 2001). The PSSI analysis of the time series defines the complexity of heartbeat dynamics through its scale-free behavior, thus identifying a single scaling exponent as an index of healthy or pathological regulation (Peng et al., 1993).

While power spectrum density has long been used for analyzing inter-beat (R-R) intervals for heart rate variability analysis (Akselrod et al., 1981, Pagani et al., 1986, Pomeranz et al., 1985), applying the method to neural time series required some modifications. Heart rate variability analyses assume chaotic inputs and therefore by extension that well-regulated (i.e., highly adaptive) systems should also be characterized by high degrees of variability. However, given the inherent design limitations placed upon fMRI time series, by both TR as well as hemodynamic lag, inputs for most fMRI studies, even those that are event related, cannot be truly chaotic. For block designs, in which the stimuli are presented at regular intervals of consistent duration, this is even more so the case. Therefore, to be able to adapt the PSSI method to as many different types of fMRI designs as possible, we took the power spectrum not of the raw time series but of its first derivative (Shelhamer, 2007). This allowed us to quantify the suppleness of the system in responding quickly to new inputs (both endogenous and exogenous) and also returning to baseline quickly following input termination, without the assumption that inputs must be chaotic. For clarity it is important to note that in contrast to PSSI, what is normally known as “power spectrum density” or “spectral” analysis of heart rate variability measures not the degree to which all frequencies are represented, but specifically upon frequency ranges associated with excitatory (sympathetic) and inhibitory (parasympathetic) components (Task Force of the European Society of Cardiology, 1996). For fMRI, this need is somewhat ameliorated, since unlike R-R intervals, fMRI time series permit gross discrimination of their influences via spatial localization. However, in performing fMRI PSSI analyses, it is important to exclude frequencies associated with physiological factors such as respiration and heart rate, as these may provide confounds in interpreting the neural response.

For this study, we “perturbed the system” using visual stimuli (affect-valent faces) known to reliably provoke a limbic response. Since frequency analyses optimally require a larger number of data points than would typically be found for one condition, we included the entire time series in our analyses rather than specifying condition. We hypothesized that individuals with higher levels of trait anxiety would show less efficient regulation (β > 0) of limbic responses.

Section snippets

Participants

We recruited 50 healthy adult subjects into this study (N = 22 males, N = 28 females; μage = 26 yrs; SD = 7.7; max/min age = 18–49). A lengthy phone screening, as well as the Scheduled Clinical Interview for DSM-IV (Ventura et al., 1998), were administered to rule out subjects with current or prior psychiatric illness. All subjects received a history and physical; subjects were excluded if they had a history of drug abuse, traumatic brain injury, cardiovascular illness (including high blood pressure),

Trait anxiety

The trait anxiety scale, like the characteristic it represents, is a continuous measure that, in our sample of N = 50, provided a normal distribution (Shapiro–Wilk: W = 0.98, p = 0.4; μtrait anxiety score = 38; SD = 10; max/min score = 21–58). Trait anxiety was not correlated with age (r =  0.04, p = 0.8) nor was it different for males and females (t = 0.5, p = 0.6).

Power spectrum scale invariance method

Power spectrum logarithmic slope β, a measure of frequency spectrum density, was > 0 for all individuals and correlated with trait anxiety (r = 0.49, p = 

Discussion

Our aim was to develop a more sensitive global measure of limbic regulation. We started from a control systems model, in which the bilateral amygdala and hippocampus, as well as right BA9 and BA45, were defined – on the basis of previous research – as excitatory and inhibitory components of a negative feedback loop modulating emotional arousal to these same stimuli. By definition, the more supple the control circuit, the more tightly outputs should couple inputs; i.e., respond quickly to new

Acknowledgments

This research was supported by the Office of Naval Research no. N0014-04-1-005 (LRMP) and the National Institutes of Health grant no. 5-MO1-RR-10710 (Stony Brook University Hospital General Clinical Research Center).

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