A quantitative model of relation between respiratory-related blood pressure fluctuations and the respiratory sinus arrhythmia

Figures

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  Fig. 1. Model setup. Cardiopulmonary, arterial and venous compartment are denoted as CC, AC and VC respectively. The flows between the compartments are: venous return (VR), ventricular outflow (VO) related with cardiac output (CO), and flow through the total peripheral resistance (TPR). The transmural pressure acting on the cardiopulmonary compartment is the intrathoracic pressure (ITP)

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  Fig. 2. Schematic of the neural input in the kicked Windkessel model. From the top there are: respiratory phase Φ(t), intrathoracic pressure (peak of inspiration related to the minimum of pI. Zero phase at onset of inspiration, where the pI attains the maximum. Third curve, marked as rn shows a single kick, as defined by Eq. 10. Kicks are delivered at a short delay τ after each reset of Φ (bemark a small phase shift between the Φ and the rn). Fourth panel shows the r.h.s of Eq. 5, i.e., the cumulated effect of neural input, acting through the phase sensitive curve (9). The phase velocity r(t) is either increased (like in breath 2 and 3) or decreased (like in breath 1). As the decay of the neural force is slow, the net effect on phase velocity r may be bipolar. Bottom row shows the resulting heart phase φ(t)

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  Fig. 3. Example of numerical output of the model. The first row shows the arterial blood pressure pa. The second row shows pressures in venous compartment pv (thick curve), and cardiopulmonary compartment pc (thin curve). Blood pressure in the venous compartment is constant in this scale of the plot. The third row shows the phase of the heart φ(t) mod 1 (line) and the phase of the respiratory rhythm Φ(t) mod 1 (area curve). Control is applied at time τ after each maximum of Φ(t) mod 1. The fourth row shows the resulting RR interval variability, which is seemingly in-phase with the intrathoracic pressure pI, shown in the fifth row

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  Fig. 4. Magnitude of the fluctuations of BP as function of the delay time τ. Three ABP-derived variables are shown: the MAP (thick solid curve), the SAP (thin curve) and the DAP (thick dashed curve). Hatched area mark the ranges of ineffective control of the MAP

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  Fig. 5. Magnitude of the fluctuations of BP as a function of the control amplitude r0. Three ABP-related variables are shown: MAP (thick solid curve), SAP (thin curve) and DAP (thick dashed curve). Hathed area marks ranges of an ineffective control of the DAP