Dual oscillator model of the respiratory neuronal network generating quantal slowing of respiratory rhythm.

We developed a dual oscillator model to facilitate the understanding of dynamic interactions between the parafacial respiratory group (pFRG) and the preBötzinger complex (preBötC) neurons in the respiratory rhythm generation. Both neuronal groups were modeled as groups of 81 interconnected pacemaker neurons; the bursting cell model described by Butera and others [model 1 in Butera et al. (J Neurophysiol 81:382-397, 1999a)] were used to model the pacemaker neurons. We assumed (1) both pFRG and preBötC networks are rhythm generators, (2) preBötC receives excitatory inputs from pFRG, and pFRG receives inhibitory inputs from preBötC, and (3) persistent Na(+) current conductance and synaptic current conductances are randomly distributed within each population. Our model could reproduce 1:1 coupling of bursting rhythms between pFRG and preBötC with the characteristic biphasic firing pattern of pFRG neurons, i.e., firings during pre-inspiratory and post-inspiratory phases. Compatible with experimental results, the model predicted the changes in firing pattern of pFRG neurons from biphasic expiratory to monophasic inspiratory, synchronous with preBötC neurons. Quantal slowing, a phenomena of prolonged respiratory period that jumps non-deterministically to integer multiples of the control period, was observed when the excitability of preBötC network decreased while strengths of synaptic connections between the two groups remained unchanged, suggesting that, in contrast to the earlier suggestions (Mellen et al., Neuron 37:821-826, 2003; Wittmeier et al., Proc Natl Acad Sci USA 105(46):18000-18005, 2008), quantal slowing could occur without suppressed or stochastic excitatory synaptic transmission. With a reduced excitability of preBötC network, the breakdown of synchronous bursting of preBötC neurons was predicted by simulation. We suggest that quantal slowing could result from a breakdown of synchronized bursting within the preBötC.

What does the multi-peaked respiratory output pattern tell us about the respiratory pattern generating neuronal network?

The respiratory neuronal network activity can be optically recorded from the ventral medulla of the in vitro brainstem-spinal cord preparation using a voltage-sensitive dye. To assess the spatiotemporal dynamics of respiratory-related regions of the ventral medulla, we developed a novel non-linear response model called the sigmoid and transfer function model. It regards the respiratory motor activity recorded from the fourth cervical ventral root (C4VR) as the response to optical signals from pixels within respiratory-related regions. When the C4VR activity had less than three peaks, optical time series of a single suitably chosen pixel could precisely estimate the activity. However, it was difficult to find a single explanatory pixel for multi-peaked C4VR activity. In this paper, we show that the multi-input single-output (MISO) STF model that takes a few different pixels as inputs greatly improves the precision of the estimation. We interpret this result that multi-peaked respiratory output patterns are caused by "migration of recruited area". Here the term "migration" denotes the phenomenon that the transition of respiratory-recruited subareas on the ventral medulla is observed within a single breath. In conclusion, the STF model is useful for analyzing spatiotemporal dynamics of optically recorded respiratory neuronal activities.

A novel statistical analysis of voltage-imaging data by structural time series modeling and its application to the respiratory neuronal network.

The respiratory neuronal network activity can be optically recorded from the ventral medulla of the in vitro brainstem-spinal cord preparation using a voltage-sensitive dye. To assess the synchronicity between respiratory-related neurons and the breath-by-breath variability of respiratory neuronal activity from optical signals, we developed a novel method by which we are able to analyze respiratory-related optical signals without cycle-triggered averaging. The model, called the sigmoid and transfer function model, assumes a respiratory motor activity as the output and optical signals of each pixel as the input, and activity patterns of respiratory-related regions are characterized by estimated model parameter values. We found that rats intermittently showing multi-peaked respiratory motor activities had a relatively low appearance frequency of respiratory-related pixels. Further, correlations between respiratory-related pixels in rats with such unstable respiratory motor activities were poor. The poor correlations were caused by respiratory neurons recruited in the late inspiratory phase. These results suggest that poor synchronicity between respiratory neurons, which are recruited at various timings of inspiration, causes intermittent multi-peaked respiratory motor output. In conclusion, analyses of respiratory-related optical signals without cycle-triggered averaging are feasible by using the proposed method. This approach can be widely applied to the analysis of event-related optical signals.

Detection and visualization method of dynamic state transition for biological spatio-temporal imaging data.

In the statistical analysis of functional brain imaging data, regression analysis and cross correlation analysis between time series data on each grid point have been widely used. The results can be graphically represented as an activation map on an anatomical image, but only activation signal, whose temporal pattern resembles the predefined reference function, can be detected. In the present study, we propose a fusion method comprising innovation approach in time series analysis and statistical test. Autoregressive (AR) models were fitted to time series data of each pixel for the range sufficiently before or after the state transition. Then, the remaining time series data were filtered using these AR parameters to obtain its innovation (filter output). The proposed method could extract brain neural activation as a phase transition of dynamics in the system without employing external information such as the reference function. The activation could be detected as temporal transitions of statistical test values. We evaluated this method by applying to optical imaging data obtained from the mammalian brain and the cardiac sino-atrial node (SAN), and demonstrated that our method can precisely detect spatio-temporal activation profiles in the brain or SAN.