COVID-19 and silent hypoxemia in a minimal closed-loop model of the respiratory rhythm generator

Figures

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  Figure 5:. Sensitivity of PaO2 vs M curves to variation of hemoglobin parameters. In both panels, all parameters are set to their values from the original 7D-O2 model except for the parameter being varied. A: PaO2 vs M curves for various hemoglobin binding affinities K (including the original value K=26mmHg). Color scale maps the lowest and highest maximum PaO2 values to blue and red, respectively. B: PaO2 vs M curves for 6 different values of hemoglobin concentration [Hb] (including the original value Hb=250gmL-1) with the same color scale as in (A).

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  Figure 6:. Simulations of putative silent hypoxemia model at high metabolic demand. A-F: Output from simulations of the normoxia model (the original 7D-O2 model) and the silent hypoxemia model (Hb=250gmL-1 curve from Fig. 3D) shown in red and blue, respectively, for M=0.97×10-5ms-1. Voltage traces showing multiple bursts (A) and zooming in on a single burst (B); lung volume (C) and blood oxygen (D) traces across multiple bursts.

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  Figure 1:. Schematic of the 7D-O2 model. Bursts of action potential firing (V,mV) in the respiratory central pattern generator (CPG) drive a pool of motor neurons (α, dimensionless) leading to expansions of lung volume (volL,L) and increases in lung and blood oxygen (PAO2 and PaO2, mmHg). Through a chemosensory pathway (gtonic,nS), the blood oxygen level affects the amount of excitatory current sent to the CPG, thereby closing the control loop (red arrow). Time (t, seconds) is the horizontal axis for all traces. The six parameters shown in blue are varied in this study to model silent hypoxemia. Redrawn, with modifications, from [17].

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  Figure 2:. Dynamics of 7D-O2 model and hypothetical silent hypoxemia PaO2 vs M curves. A: Blood oxygen PaO2 as a function of metabolic demand (M) in the original 7D-O2 model. There is a plateau region at low M values for which normoxia (green shading) is maintained, and a collapse point at approximately M=1.2×10-5ms-1 beyond which severe hypoxia occurs. In a model of silent hypoxemia, it seems clear that the plateau portion of the curve should shift lower (maroon arrow pointing down), but it is not as clear whether the collapse point should remain in the same location or shift horizontally (maroon arrows pointing left and right). B: Variables of the 7D-O2 model for M values in the plateau region (left column) or after the collapse point (right column). C-E: Hypothetical silent hypoxemia models (red) with a lower plateau and a collapse point shifted to a lower M value (C), in the same location (D), or shifted to a higher M value (E) compared to the 7D-O2 model (black).

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  Figure 3:. Sensitivity of PaO2 vs M curves to variation of model parameters. A: Chemosensory sigmoid of gtonic as a function of PaO2 with various parameter values for the maximum (ϕ), half-activation θg, and slope σg of the sigmoid. Default settings from the original 7D-O2 model ϕ=0.3nS,θg=85mmHg,σg=30mmHg) shown in gray. See panel (B) for the definition of the color scale used for the other curves. B: PaO2 vs M curves for 27 different combinations of the chemosensory sigmoid parameters ϕ=0.24,0.3,0.36;θg=70,85,100;σg=24,30,36 on a color scale with the lowest and highest maximum PaO2 values shown in blue and red, respectively, with the exception of the default parameter set which is shown in gray. C: Hemoglobin saturation curves (Eq. 18) for various hemoglobin binding affinities K. Default model has K=26mmHg. D: PaO2 vs M curves for the set of K values shown in (C). E: PaO2 vs M curves for 9 different combinations of oxygen flux and lung volume parameters τLB=100,500,900ms;vol0=1.6,2.0,2.4L, with a constant set of chemosensory sigmoid parameters ϕ=0.24,θg=70,σg=36 on a color scale with the lowest and highest M values at the collapse point PaO2=40 shown in blue and red, respectively, with…

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  Figure 4:. Simulations of putative silent hypoxemia model. A-F: Output from simulations of the normoxia model (the original 7D-O2 model) and the silent hypoxemia model ([Hb]=250 curve from Fig. 3D) shown in red and blue, respectively. Voltage traces showing multiple bursts (A) and zooming in on a single burst (B); lung volume (C) and blood oxygen (D) traces across multiple bursts. For panels (A-D), M=0.4×10-5ms-1. Interburst interval (E) and number of spikes per burst (F) as a function of metabolic demand.