Computational models of the respiratory central pattern generator (rCPG) are usually based on biologically-plausible Hodgkin Huxley neuron models. Such models require numerous parameters and thus are prone to overfitting. The HH approach is motivated by the assumption that the biophysical properties of neurons determine the network dynamics. Here, we implement the rCPG using simpler Izhikevich resonate-and-fire neurons. Our rCPG model generates a 3-phase respiratory motor pattern based on established connectivities and can reproduce previous experimental and theoretical observations. Further, we demonstrate the flexibility of the model by testing whether intrinsic bursting properties are necessary for rhythmogenesis. Our simulations demonstrate that replacing predicted mandatory bursting properties of pre-inspiratory neurons with spike adapting properties yields a model that generates comparable respiratory activity patterns. The latter supports our view that the importance of the exact modeling parameters of specific respiratory neurons is overestimated.
Respiration is one of the vital processes of life. While in simple single cell organisms respiration is driven by passive diffusion, complex organisms have developed complex breathing organs for the uptake of atmospheric oxygen and excretion of CO2 (e.g. gills and lungs). In mammals, airflow in and out of the lungs is generated by a variety of respiratory thoracic and abdominal muscles [1], while the strength and duration of pulmonary airflow is regulated by valving muscles in the upper airways [2,3]. The former include the diaphragm, the primary inspiratory muscle, expiratory and intercostal and finally expiratory abdominal muscles. The latter include laryngeal adductor and abductor muscles, as well as the tongue and various muscles of the soft palate and pharynx.
Besides the bronchomotor muscles, all respiratory muscles are skeletal and are therefore controlled by the brain. The brain breathing centers of mammals are organized in neuronal columns that span the medulla oblongata and the pons, which form the anatomical substrate for the central respiratory pattern generator (rCPG). Specific compartments of the rCPG are seen to serve a specific function in respiratory rhythm generation and formation of a three-phase sequential motor pattern compromising inspiration, postinspiration (stage I expiration) and expiration (stage II expiration) [4][5][6][7][8][9][10][11].
Over the last century, experimental data accumulated that identified the basic behavior of respiratory neurons that are distributed within specific compartments of rCPG. The class of neurons traditionally encodes the phase of neuronal activity in relation to the inspiratory activity of the diaphragm or the phrenic nerve. In addition, augmenting and decrementing discharge frequencies of these neurons are considered for classification. There is a general consensus that 5 classic respiratory neuron types form the core of the neural circuit that generates the respiratory rhythm and motor pattern: (1) rhythmogenic pre-Inspiratory (pre-I), (2) early-Inspiratory (early-I) with a decrementing discharge pattern (thus also called I-Dec), (3) Inspiratory neurons with augmenting discharge pattern (I-Aug, or ramp-I), post-Inspiratory neurons (post-I) with decrementing discharge pattern, which are active during the first part of expiration (thus also called E-Dec) and finally expiratory neurons that show augmenting discharge (E-Aug) pattern during the second phase of the expiratory interval. These neuron types form the basis for a substantial number of computational models that describe the putative function of the r-CPG. Mathematical models have focused on several dynamical mechanisms including the biophysical bursting properties of rhythmogenic pre-I that are seen to initiate the respiratory cycle [12][13][14], network oscillation based on reciprocal synaptic inhibition [15] and hybrid models based on excitatory rhythmogenic cell properties and inhibitory synaptic inhibition [7,16,23]. The latter sometimes even implement sensory feedback loops [17,18]. The contemporary hybrid models are complex Hodgkin-Huxley-based models. The main driver for Hodgkin-Huxley-based modeling has largely arisen from the finding in the early nineties that a specific subset of neurons located in the pre-Bötzinger complex (pre-BötC) remain rhythmogenic when isolated from the larger network [19]. Electrophysiological studies of pre-BötC neurons revealed the biophysical basis of pacemaker pre-I neurons and the excitatory synaptic coupling underlying group pacemaker mechanisms [20]. However, the biophysical properties of neurons outside the pre-BötC remain largely unexplored. Thus, the biophysical properties of non-pre-BötC neurons in modeling approaches are often based on speculation. Even more compelling is that fact that biophysical properties (ion channel composition) of bursting neurons in the somatogastric ganglion, an invertebrate model system of a CPG network, are extremely diverse in functionally homogenous neurons and therefore do not define the function of neurons in a rhythmogenic circuit [21] that shares significant similarity with the rCPG.
To simplify the complex and difficult to assess Hodgkin-Huxley-based models of the respiratory CPG, we implement the rCPG using Izhikevich resonate-and-fire neurons. These neurons are simple enough to be computationally efficient and tractable for bifurcation analysis and at the same time can account for various neural activity patterns Modeling the respiratory Central Pattern Generator with resonate-and-fire Izhikevich-Neurons 3 observed within the respiratory circuit in vivo, including intrinsic bursting and spike adaptation [22]. The remainder of the manuscript is organized as follows. In Section 2, we present a description of the model. In Section 3, we present our results regarding how the model can reproduce previous experimental and theoretical observations, and how the model can be used to test the hypothesis that intrinsic
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