Mathematical modelling of periodic breathing in chronic heart failure to design novel real-time dynamic therapy
Creators: name: Mebrate, Yoseph
Publisher: name: Imperial College London
Year: 2014

description: Periodic breathing (PB) is common in chronic heart failure (CHF) and has poor prognosis. The most commonly used therapy option involve continuous positive airway pressure, which is not acceptable to all patients. In this thesis I present a mathematical model providing a novel approach to treat PB with carefully controlled dynamic administration of supplementary CO2. I explored the consequences of phasic CO2 administration, with different timing and dosing algorithms. I found an optimal time window within the ventilatory cycle in which therapy reduces ventilation oscillations by more than 95%. Outside this window therapy increases ventilatory oscillations by more than 30%. A quadratic grading of CO2 dose (combined gradation of both concentration and duration) increased treatment efficiency. The undesired increase in mean CO2 caused by dynamic therapy was negligible compared with static therapy, to achieve the same degree of ventilatory stabilisation. Similarly, the increase in average ventilation was much smaller with dynamic than static therapy. In collaboration with my clinical and engineering colleagues we tested my model findings on seven healthy subjects simulating voluntary PB and seven heart failure (HF) patients with day time spontaneous PB. Dynamic CO2 administered at hyperventilation phase achieved the greatest reduction in ETCO2 oscillations caused by voluntary PB, and practically abolished spontaneous PB in the HF patients. During dynamic CO2 administration the mean ETCO2 and ventilation levels were not different to baseline and much lower than during continuous CO2 administration, in both groups of subjects. I developed the model further to investigate the effect of random physiological fluctuations on dynamic CO2 therapy and investigated, which is the best single parameter to guide dynamic CO2 therapy. I found that if alveolar CO2 could be measured to guide therapy, it would be as effective as using ventilation. However ETCO2, the clinically observable variable, is less effective because during severe hypopnoea it markedly diverges from alveolar CO2. Dynamic CO2 therapy ameliorated both sustained PB in unstable systems and intermittent PB in stable systems, although both guidance methods became less effective with a large noise component, regardless of the underlying system stability. I investigated further the emergence of intermittent ventilatory periodic patterns, on normally stable systems (loop gain&lt;1), following the introduction of random physiological fluctuations into the model. This was due to the amplification of the added noise by the delay feedback system, at its natural frequency. The development of this intermittent periodic breathing pattern is dependent on the proximity of the feedback system's loop gain to its tipping point (loop gain=1.0). To investigate the possibility of modulating heart rate by using implantable pacemaker in HF patients with PB, as a tool to manipulate ETCO2 and subsequently ventilation, I devised a novel analytical model equation that demonstrated how a change in cardiac output alters alveolar CO2. We implemented this model equation and found that ETCO2 and ventilation developed consistent oscillations with period 60s during the heart rate alternations. Furthermore, we verified the mathematical prediction that the amplitude of these oscillations would depend on those in cardiac output.