Fig 1.
Comparisons between simulation results (red solid lines) and experimental data of young and elderly adult males (blue solid and dotted lines, respectively) [1] with mean values (solid lines) and standard error (error bars) exclusively for young adult males of physiological values versus time during active short–term exercise involving knee flexions.
The yellow rectangles correspond the responses observed during the exercise. (a) Breathing rate (BR), (b) Tidal volume (TV), (c) Minute ventilation (MV), (d) Heart rate (HR), (e) Blood pressure (BP) vs. time, and (f) Power spectral density (PSD) of heart rate variability (HRV) vs. heart beat frequency. The light green, blue, and red rectangles in (f) represent the very–low–frequency (VLF: ∼0.05 Hz), low frequency (LF: 0.05–0.15 Hz), and high-frequency (HF: 0.15–0.4 Hz) components, respectively. Experimental data on HRV are not available in the referenced study [1]. The black dotted lines show the results of Model A simulating elderly males whose systemic arterial resistance was set to 0.082 mmHg⋅s/ml whereas the green dotted lines denote the results of model B simulating adult females whose vital capacity was set to 3.1 L.
Table 1.
Parameters to control respiratory states.
A parameter of APSR is set to 1.0 in all conditions.
Table 2.
Parameters characterizing the circulatory system [66].
Fig 2.
Comparisons of the simulation results (red solid lines) and experimental data (blue solid lines) [1] with mean values (solid lines) and standard error (error bars) of physiological values vs. time in passive short–term exercise involving knee flexions.
The yellow rectangles represent the responses during the exercise. (a) Breathing rate (BR), (b) Tidal volume (TV), (c) Minute ventilation (MV), (d) Heart rate (HR), (e) Blood pressure (BP) vs. time, and (f) Power spectral density (PSD) of heart rate variability (HRV) vs. heart beat frequency. Experimental data on HRV are not available in the referenced study [1].
Fig 3.
Simulation results of voluntary breathing controls in five respiratory states: Case A (BR = 14 bpm, TV = 0.5 L), B (BR = 12 bpm, TV = 0.67 L), C (BR = 10 bpm, TV = 0.8 L), D (BR = 8 bpm, TV = 1.0 L), E (BR = 6 bpm, TV = 1.33 L).
(a) Breathing rate (BR), (b) Tidal volume (TV), (c) Minute ventilation (MV), (d) Heart rate (HR) with experimental test data from Song et al. [2], including mean values (solid circles) and peak and trough values (dotted lines), (e) Blood pressure (BP) vs. time, and (f) Power spectral density (PSD) of heart rate variability (HRV) vs. heart beat frequency.
Fig 4.
Simulation results for mental stress loads: (a) Breathing rate (BR), (b) Tidal volume (TV), (c) Minute ventilation (MV), (d) Heart rate (HR), (e) Blood pressure (BP) vs. time, (f) Power spectral density (PSD) of heart rate variability (HRV) vs. heart beat frequency.
The yellow rectangles represent the responses during the mental stress loads. Five mental stress loads varying from 0.1 to 0.5 in steps of 0.1 were applied from 20 to 40 s in the automatic breathing condition (BR = 16 bpm, TV = 0.5 L).
Fig 5.
Comparative analysis of blood oxygen partial pressures during short–term exercise, voluntary controlled breathing, and mental stress loading: (a) active vs passive exercise, (b) controlled breathing at 6 or 14 bpm, and (c) mental stress loads of 0.1 and 0.5.
The yellow rectangles indicate data during short–term exercise and mental stress.
Fig 6.
HRV metrics of SDNN, Sample Entropy, and total power of HRV and LF/HF power ratio for all simulation conditions.
(a) SDNN, (b) Sample Entropy, (c) Total power of HRV, and (d) LF/HF power ratio.
Fig 7.
Comparisons of the Poincaré plots during short–term exercise, voluntary breathing control, and mental stress loading.
(a) active short–term exercise, (b) passive short–term exercise, (c) controlled breathing of 6 bpm, (d) controlled breathing of 14 bpm, (e) mental stress load of 0.1, and (f) mental stress load of 0.5. NNI indicates normal–to–normal interval.
Table 3.
Parameters describing the regulation effectors [66].
Fig 8.
Respiratory–circulatory system model.
The model integrates the respiratory CPG system with spiking neurons, as proposed by Molkov et al. (2014) [64], and the circulatory system utilizing a rate–coding approach, as described by Ursino (1998) [66]. The red, blue, light blue, and purple lines denote excitatory and inhibitory signals, CO2 signals as chemical feedback, and breathing control signals, respectively. The light green line indicates pulmonary stretch receptors as mechanical feedback. Thick black and orange lines represent blood vessels and the interactions between the respiratory and circulatory systems, respectively.
Table 4.
Parameters of respiratory CPG model.
Table 5.
Parameters adjusted for adult human respiratory system.
Fig 9.
Voluntary breathing control model.
The model incorporates a muscle controller utilizing actor–critic reinforcement learning to simulate the activity of respiratory muscles (diaphragm and abdominal muscles) during voluntary breathing. Additionally, it includes a breathing rhythm generation model analogous to the respiratory CPG system. The red lines denote muscle activation signals for the respiratory muscles.