Functional MRI studies have typically investigated the amplitude of activation in regions of interest (ROI); however, increasing interest has focused on the possibility of exploiting the dynamic components of the fMRI time-series to explore connectivity within the brain. While neuroscientists often speak anecdotally about brain “circuitry,” there exists the exciting and largely unexplored possibility of using fMRI BOLD activation to quantify the strength of “excitatory” and “inhibitory” pathways, treating ROI time-series as signal inputs and outputs in a control systems model. A control system may be defined as “a collection of interconnected components that can be made to achieve a desired response in the face of external disturbances” [Khoo, 2000
]. In the case of physiology, the desired response is not only excitatory, to address the external disturbance, but also inhibitory, to maintain homeostasis by bringing the system back to baseline. Within this context, “inhibitory” activation is not to be understood as “lack of activation,” but rather reflects increase in BOLD signal of those ROIs that work to suppress the excitatory component of the circuit.
Control mechanisms are present at almost every level of physiology. At the molecular scale, the dynamics between potassium, chloride, and sodium ions regulate the action potential and its return to baseline [Hodgkin and Huxley, 1952
]. At the level of neurotransmitters, antagonistic neuro-receptors provide the excitatory (glutamate) and inhibitory (GABA) components of a negative feedback loop that maintain homeostasis [Calabresi et al., 1991
]. Equivalent regulatory mechanisms are present at other scales, such as that of the autonomic nervous system via interactions between sympathetic and parasympathetic components [Kandel et al., 2000
], of the endocrine system via interactions between cortisol and DHEA [Charney, 2004
], of the balance of glucose and insulin [Insel et al., 1975
], and the maintenance of core body temperature via vasodilation [Heldman, 2003
]. In a well-regulated control system, the excitatory and inhibitory components work closely together. Thus, in the absence of an environmental need for an extended excitatory response, the time-series describing the excitatory and inhibitory components should be highly correlated with minimum lag. This tight coupling results in dampening the impact of the chaotic external environment, or maintenance of homeostasis.
As shown by , the excitatory and inhibitory components of the limbic system have, by now, been relatively well-mapped out in the animal literature [LeDoux, 2000
; Maren, 2005
], making the dynamic regulation between these regions a plausible candidate for control systems modeling. In spite of numerous parallel pathways within the system, the medial central nucleus of the amygdala forms the chief excitatory component of the arousal response [Davis and Whalen, 2001
], with the lateral amygdala providing inhibitory modulation of the medial central nucleus, and the basal amygdala providing either positive modulation of the medial central nucleus (via direct pathways) or negative modulation of the medial central nucleus (via the intercalated nuclei) [Maren, 2005
]. The primary inhibitory pathways, identified primarily by intracellular recording/lesion studies of fear extinction, are the medial prefrontal cortex [Baxter et al., 2000
; Blair et al., 2005
; Izquierdo and Murray, 2005
; Izquierdo et al., 2005
; Phelps et al., 2004
; Rosenkranz et al., 2003
; Sotres-Bayon et al., 2006
] and the hippocampus—the latter hypothesized to provide a “context” for potentially aversive stimuli [Corcoran et al., 2005
; Sotres-Bayon et al., 2004
]. Two distinct models have been proposed for the interactions between the amygdala, medial prefrontal cortex, and hippocampus [Sotres-Bayon et al., 2004
]. In the first (“Model A”), the hippocampus and the medial prefrontal cortex are modeled as two independent components that inhibit the activation of amygdala. In the second (“Model B”), the hippocampus is hypothesized to modulate the medial prefrontal cortex, which then inhibits the amygdala. For both Models A and B, limbic outputs from the amygdala project to the hypothalamus. The hypothalamus controls the autonomic nervous system, itself another negative feedback loop with excitatory (sympathetic) and inhibitory (parsympathetic) components [Kandel et al., 1991
]. This same circuitry has been identified with anxiety disorders in the human as well [Cannistraro and Rauch, 2003
Figure 1 Viewed as a control system, the limbic system acts a negative feedback loop, with excitatory (medial central nucleus of the amygdala) and inhibitory (medial prefrontal cortex, hippocampus) components that, when well-regulated, serve to respond to arousing (more ...)
Basic research in control systems physiology surgically isolates the feed-forward and feedback components of the circuit, thereby permitting separate quantification. Under normal circumstances, this is not possible with neural research on human subjects; therefore, one of the central challenges in using fMRI signals for control systems analysis is quantifying limbic dysregulation from a self-interacting, intact circuit. This challenge, of quantifying dysregulation from an intact circuit, has already been largely addressed for the autonomic nervous system by the development of newer methods of heart-rate variability analysis (HRV). Thus, approaches developed for HRV analysis may ultimately be of help in suggesting techniques for quantifying limbic dysregulation using fMRI.
HRV measures variability between successive heartbeats (R–R intervals), and is thought to reflect homeostatic regulation between sympathetic and parasympathetic components of the autonomic nervous system. Because certain pathological conditions, such as heart disease [Goldstein et al., 1975
], hypertension [Abboud, 1982
; Julius et al., 1975
] and sudden cardiac death [Schwartz and De Ferrari, 1987
], are accompanied by disruptions in the balance between these two components, HRV has received much attention within the cardiology literature as a potentially valuable noninvasive tool to detect and understand cardiac illness. HRV has historically developed from two separate and conceptually divergent approaches: the first quantifies dysregulation indirectly by deconvolving a complex waveform into its excitatory and inhibitory contributions, while the second quantifies dysregulation directly by calculation of the amount of “complexity” or “chaos” in the system. For both approaches, power is increased by typically collecting HRV data over 24-h; however, the measurements themselves reflect short-acting (0.04–0.50 Hz) autonomic regulation in response to environmental fluctuations.
Original work on HRV was focused on the first approach, via estimation of the power spectrum of instantaneous heart rate fluctuations [Akselrod et al., 1981
; Pomeranz et al., 1985
]. Using sympathetic and parasympathetic blockers, several bandwidths were identified as being particularly physiologically significant: frequencies between below 0.04 Hz (Very Low Frequency, or VLF); 0.04–0.15 Hz (Low Frequency, or LF); and 0.15–0.40 Hz (High Frequency, or HF) [Akselrod et al., 1981
]. The VLF represents hormonal and temperature fluctuations, the LF represents both sympathetic and parasympathetic influences, and the HF represents parasympathetic contributions alone [Malik and Camm, 1993
]. The ratio of the LF/HF spectrum was shown to provide a reasonable approximation of the sympathovagal balance, with high LF/HF indicating sympathetic dominance, and low LF/HF indicating predominantly vagal control.
In spite of the predictive value of the sympathovagal balance in predicting disease, the power spectrum density (PSD) method has not been widely accepted by cardiologists as a clinical instrument. This is predominantly because of a well-known deficiency in the PSD method: the LF bandwidth is not solely representative of the sympathetic influence ; therefore a LF/HF ratio cannot be a precise measure of the balance between sympathetic and parasympathetic components. Moreover, the PSD method may be further compromised by the fact that the LF/HF ratio is linear, which cannot account for the significant nonlinear components of heart rate variability [Braun et al., 1998
The principal dynamic modes (PDM) analysis of heart rate variability was developed to address the problem of more precisely separating out the sympathetic and parasympathetic components of heart rate variability, and is explicitly nonlinear. The PDM are calculated using Volterra–Wiener kernels based on expansion of Laguerre polynomials [Zhong et al., 2004
]. Originally the method, applied to physiological systems, required both input and output signals [Marmarelis, 1997
; Marmarelis et al., 1999
; Marmarelis and Orme, 1993
], although later work [Zhong et al., 2004
] modified the method to include only a single output signal. Comparisons of PDM to PSD using sympathetic and parasympathetic blockers (atropine and propanolol) [Chon et al., 2006
; Zhong et al., 2006
; Zhong et al., 2004
] have demonstrated that PDM is significantly more accurate than PSD in separating out the sympathetic and parasympathetic components of heart rate variability in humans.
The “nonlinear complexity with shannon entropy” method of HRV represents the second approach, that of directly quantifying dysregulation of a system by measuring the degree of complexity or chaos in the system [Kurths et al., 1995
; Voss et al., 1995
, 1996]. Symbolic dynamics is estimated by first binning R–R intervals into four groups, represented by “symbols” “0,” “1,” “2,” and “3”:
where tn − tn−1 = R–R interval, μ = mean R–R interval, and a = 0.1. Each “word” is composed of combinatorial arrangements of the symbols, with three symbols per word. If the probability of occurrence of a word is less than a set threshold, in this case: 0.001, then the word is defined as a “forbidden word.” Increased forbidden word count therefore indicates both decreased chaos in the system as well as lowered heart rate (R–R) variability. Shannon entropy, a measure of chaos, is calculated as: Hk = ΣWk p(ω) log2 p(ω) where Wk is the set of all words of length kand p(ω) is the probability of occurrence of words.
Diagnoses of regulatory diseases typically involve testing by perturbing the system and then observing the dynamics by which the body returns to homeostasis; for example, by ingesting a bolus of glucose to screen for diabetes [Graci et al. 1999
; Kernohan et al., 2003
; Lucas et al., 1986
; Rolandsson et al., 2001
] or a bolus of dexamethasone to screen for Cushing's disease [Sriussadaporn et al., 1996
; Tyrrell et al., 1986
]. Other diagnostic tests avoid the use of bolus inputs, but instead quantify dysregulation in terms of the degree of output chaos in response to mild and chaotic inputs. One such method is the nonlinear complexity with Shannon entropy method of calculating HRV [Voss et al., 1995
] described earlier, which has shown promise in predicting risk for myocardial infarction [Bauernschmitt et al., 2004
; Huikuri and Makikallio, 2001
; Huikuri et al., 2003
; Lombardi, 2002
; Makikallio et al., 2002
; Swynghedauw et al., 1997
; Vigo et al., 2004
; Voss et al., 1995
, 1996]. By analogy, our results suggest the potential utility of using fMRI time-series as outputs in neural control systems, an approach that has been proven to be useful in modeling physiology, and which may also have practical applications in diagnosis—or even identification of vulnerability towards—stress-related disorders.
We hypothesized that individuals with greater trait anxiety were unable to maintain homeostasis of the neural emotional arousal response as effectively as their less-anxious colleagues, shifting the emphasis from an abnormal variable to an abnormal dynamic between the excitatory and inhibitory influences responsible for modulating one another. This would imply that vulnerability towards anxiety would be characterized by lowered cross-correlation between the functional activation of the excitatory and inhibitory limbic components of the emotional arousal response, while inversely, resilience towards anxiety would be characterized by heightened cross-correlation between these same limbic components. Moreover the dynamics of the data might themselves be able to shed light on the respective roles of the different limbic areas in modulating the arousal response and its effects on the excitatory (sympathetic) and inhibitory (parasympathetic) components of short-term cardiovascular regulation, measured via heart rate variability [Breiter et al., 1996
]. Our long-range goal is to characterize limbic dysregulation using nonlinear transfer functions, the tools normally used for control systems analyses. However, given the ambitiousness of applying BOLD signals to control systems, for this preliminary study we had a more modest aim: to apply coarse-grained statistical techniques—specifically correlational analyses—to investigate whether there might be a relationship between limbic regulation, autonomic regulation, and trait anxiety. If so, then these preliminary findings would provide support for a more mathematically nuanced characterization of dysregulation, with potential utility in developing fMRI-based diagnostic tools for stress-related disorders.