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.