Elsevier

Neurocomputing

Volume 69, Issues 13–15, August 2006, Pages 1553-1560
Neurocomputing

A neurocomputational model of stochastic resonance and aging

https://doi.org/10.1016/j.neucom.2005.06.015Get rights and content

Abstract

Stochastic resonance (SR) is fundamental to physical and biological processes. Here, we use a stochastic gain-tuning model to investigate interactions between aging-related increase of endogenous neuronal noise and external input noise in affecting SR. Compared to networks that have optimal system gain parameter of the activation function, networks with attenuated endogenous gain tuning at the system level, simulating aging neurocognitive systems with more intrinsic neuronal noise but less plasticity, continue to exhibit the general SR effect; however, this effect is smaller and requires more external noise. This set of finding suggests that determining the optimal proportion of resonance-inducing external noise as a function of internal-system stochastic gain tuning properties promotes unified theorizing about sensory and cognitive aging at behavioral and neural levels of analysis.

Introduction

Stochastic resonance (SR), the phenomenon of noise-enhanced responses to weak signals, is fundamental in many physical as well as physiological processes [10], [44]. For instance, recent evidence of SR in neurobiological systems’ sensory processing suggests that SR increases phase locking and coherence, thus promoting synchronization of neuronal activities (for a review, see [29]). Specifically, in humans, an optimal level of noise externally added to subthreshold signals can improve tactile sensory detection [6], [7], [25], balance control [12], [32], and visual perception [38]. A recent fMRI study [39] also showed that SR enhanced the activation level of neuronal activity in human visual cortex.

Other than external noise, intrinsic stochasticity of the nervous system is also inherently present in the components of neurons, such as synapses, that are central for neurotransmission [17]. Sensory and cognitive processes entail constant exchanges between neuronal activities and external stimulations. Thus, interactions between internal and external noise are inevitable. In order to study such interactions, it has been suggested recently that computational approaches need to explore how between-system differences in endogenous system parameters that regulate internal stochasticity interact with the commonly observed SR that is induced by external noise [14], [46]. With respect to gerontological applications, it has been suggested that senescence is associated with increasing internal noise. For instance, a classical hypothesis in neurocognitive aging research states that the aging brain is noisier [42], due to deteriorations in various transmitter systems [1], [2], [13], [15], [35], [36], [45], such as acetylcholine (Ach) and monoamines (e.g., dopamine, norepinephrine, and serotonin), and degenerations in structural integrity, such as reductions in gray and white matter density and brain volume shrinkages in prefrontal cortex and hippocampus [4], [33] as well as attenuated functional connectivity between these cortical regions [11]. Brain electrophysiological activities captured by EEG recordings show aging-related increase in variability [16]. Noisy fluctuations in cognitive and sensorimotor processes also increase with aging [19], [22], [23], [27]. A handful of studies have examined the effect of external input noise on tactile sensation or balance control in young and old adults [6], [7], [12], [25], [32], and provided first evidence of the continued existence of external-noise-enhanced SR in aging neurocognitive systems. However, little is known about how interactions between external input noise and aging-related increase of endogenous neuronal noise may modulate the general SR effect.

Tuning the gain parameter of neural networks’ activation function is a common system-based approach for modeling neuromodulation and its effect on neural plasticity [8], [37]. We extended a stochastic gain-tuning model of neurocognitive aging [18] to investigate interactions between external-noise-enhanced SR and aging-related increase of endogenous neuronal noise derived from deficits in the intrinsic system neuromodulatory process. Rather than assuming additive internal noise [9], [26], here we capture aging-related increase of intrinsic neuronal noise that may be attributable to decline in neuromodulation, particularly dopaminergic modulation, by attenuating the gain parameter of neuronal networks’ sigmoid activation function (Eq. (1)). The gain parameter is a system parameter that affects the slope and non-linearity of the neural network's activation function. Modeled as such, the net input a given processing unit i receives from afferent channels at the simulated discrete time step t is gated by the gain parameter (Git) before the unit emits its activation and further propagates the activity. At each processing step, indexed in discrete time steps, the value of the gain parameter associated with a given unit is randomly sampled from a uniform distribution with a given mean and standard deviation. The stochastic gain manipulation implemented as such incorporates the probabilistic nature of transmitter release [30]:Act(Git,inputit)=11+e-(Git·inputit+bias).

Whereas the level of external noise that is part of the stimulus environment may vary leading to various extents of external-noise-induced tuning, systems may also differ in the efficacy of their endogenous gain control mechanism. The stochastic gain manipulation we propose here is aimed at capturing aging-related differences in endogenous neuromodulatory gain control, in order for us to explore the effects of aging on the commonly observed external-noise-enhanced SR. Differences in neuromodulatory gain control between young and older neurobiological systems can be simulated by neural networks with a larger or smaller mean G. Fig. 1 shows three families of activation functions that are associated with three ranges of G. The slopes and non-linearity of activation functions associated with smaller G are reduced in comparison to the functions with larger G, i.e., comparing the set of curves on the right (G ranges from 0.4 to 0.6, with a mean of 0.5) and the set of curves in the middle (G ranges from 0.6 to 0.8, with a mean of 0.7) with that on the left (G ranges from 1.0 to 1.2, with a mean of 1.1). Extant evidence suggests that across various brain regions, there is about 5–10% decline in the efficacy of dopaminergic modulation per decade starting at about age 20 years [1], [15]. Assuming a 10% decline per decade, changing the level of mean G from 1.1 to 0.7 numerically corresponds to about four decades (36%) of decline (i.e., about the decline from 20 to 60 years of age), whereas changing the level of mean G from 1.1 to 0.5 numerically reflects about six decades (55%) of decline (i.e., about the decline from 20 to 80 years of age). These parameter ranges are also comparable to empirically observed aging-related increase in perceptual/cognitive processing fluctuation (noise), which was found to be about 7% increase in processing noise per decade from age 30 to 90 years in one study [23].

Attenuating the system-parameter-based stochastic gain regulation reduces the responsivity, thus the signal transmission efficiency, of the processing units, which subsequently increases intra-network activation noise and reduces representation distinctiveness [18]. This sequence of effects integrates findings of aging-related decline in neuromodulation [1], [15] and various cognitive aging deficits (e.g., adult age differences in learning rate, susceptibility to interference, working memory, associative binding, and performance variability) at the behavioral level [19], [20], [21], [22]. However, the question of whether similar mechanisms may also affect SR in aging neurobiological systems still needs to be investigated.

In principle, the within-system manipulation of neural network's gain parameter is related to typical concepts of input or output signal-to-noise ratio (SNR), as it is related to the SNR gain frequently encountered in the literatures of perceptual/sensory discrimination or signal processing. However, there is one clear difference: whereas the typically SNR gain [34] is often defined as the ratio of the system's output SNR (e.g., a person's perceptual performance measured at the behavioral level) to input SNR (e.g., the quality of the input stimuli), the within-system stochastic gain regulation of the activation function as implemented here is a manipulation of a system parameter that is intrinsic to the neural network. Conceptually, the importance of comparing SR phenomena derived from adding external noise and tuning system parameters as well as studying their interactions have been emphasized in recent work [14], [46]. With respect to gerontological applications, it is important to arrive at computational frameworks within which between-person differences in endogenous neurobioloical processes, such as the effect of aging on neuromodulation, can be directly modeled by an intrinsic system parameter. If this is done, we are enabled to study how gain regulation of the network's activation function at the system level interacts with the effect of external noise on SR. From an applied perspective, computational and empirical findings on this interaction between external noise and internal gain tuning properties open the possibility for determining optimal levels of noise [cf. 14] for human systems with suboptimal gain tuning characteristics.

Two important earlier studies have shown that external, context-dependent noise linearizes the input–output transfer function of model neuron ensembles [3] and changes the frequency tuning properties of actual sensory neurons [14]. Building on these earlier findings regarding external-noise-induced tuning of SR, particularly the so-called aperiodic SR, our effort here is to illuminate how external-noise-induced SR effects vary as a function of between-system differences in the efficacy of endogenous gain regulation. Although external noise may affect the input–output transfer function in both young and old neurobiological systems, mechanisms underlying age differences in brain integrity between the young and old that affect the efficacy of neuromodulation add another layer of influence at the system level, that may, in turn, interact with the effects of external noise tuning.

Section snippets

Analytic analysis of gain tuning and SR in a single-neuron model

To analytically characterize the effects of attenuating G on SR, we first considered a single-unit model. The aging deficit of neuromodulation is modeled by sampling G of the processing unit's activation function from uniform distributions with smaller means. Across a range of white Gaussian external input noise, we compute how accurate a single unit can distinguish between two relatively similar signals that represent the presence or absence of a stimulus. For each level of external noise, the

Gain tuning and SR of sensory detection in multi-neuron networks

We next expanded the G modulation of SR in the single-unit model to multi-unit networks to study adult age differences in external-noise-enhanced sensory detection. Multi-layer, feedforward backpropagation networks with full connections were implemented (see Fig. 3) to simulate sensory detection in paradigms analogous to earlier experiments [6], [7], [25]. For all reported simulations, the ensemble of processing units at the sensory layer (n1=12) encoded a pattern of signal amplitude in

Results

The results show that the details of SR depend on the interaction between external noise and G. In line with SR observed in old people [25], the G-reduced networks also exhibit SR. The magnitudes of peak SR are, however, smaller in G-reduced networks and the peaks are again right-shifted to greater levels of external noise (Fig. 4(a)). These findings indicate that increased internal noise in the G-reduced networks reduces the relative efficiency of external noise in producing SR. These results

Discussion and conclusion

Juxtaposing our findings of reduced and right-shifted peak SR with decreasing G tuning and previous analytical models [5], [9] showing similar effects with limiting the number of processing units suggests a conjecture: networks with attenuated G function as if they have a more limited number of processing units. This sheds new light for understanding cognitive and sensory aging both at the neurochemical and neuroanatomical levels. Current evidence suggests that the effect of anatomical neuronal

Shu-Chen Li is a research scientist in the Center for Lifespan Psychology at the Max Planck Institute for Human Development. Her research interests include behavioral studies of lifespan cognitive and sensorimotor development, and cognitive and computational neuroscience. Theoretically, she is particularly interested in modeling behavioral phenomena of lifespan development by computationally implementing neurobiological mechanisms that have bearings on memory, binding, attention, and processing

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