## 4 Discussion  
This study utilises a computational model simulating cardiovascular system dynamics and an integrated CF-LVAD model. The cardiovascular system model allows to simulate different physiological scenarios and mechanisms. For instance, the interaction between the preceding and pre-preceding RR intervals and left ventricular systolic function in patients with chronic AF and dilated cardiomyopathyy was simulated in this study. Therefore, the effect of RR interval distributions on the haemodynamic outcome CF-LVAD support can be simulated using the presented cardiovascular system model. The mean RR interval duration in the cardiovascular system model simulating AF with unimodal RR interval distribution was 0.512 s corresponding to a 117 bpm heart rate. Although such a high heart rate is common in untreated AF patients, the current guidelines suggest to reduce the heart rate below 100 bpm in AF patients [39]. The RR interval duration in the cardiovascular system model simulating AF with bimodal RR interval distribution was 0.884 s corresponding to 68 bpm. This is below the suggested target heart rate. It should also be noted that the RR interval durations used in this study are patient specific and the AF treatment is not included in the utilised numerical models. The left ventricular ejection fraction was relatively low in the cardiovascular system simulating AF with unimodal RR interval distribution. It has already been shown that there is a strong correlation between the ejection fraction and the ratio of preceding and pre-preceding RR intervals during AF [40]. A higher preceding and pre-preceding RR interval ratio results in high ejection fraction as in the cardiovascular system model simulating AF with bimodal RR interval distribution [40]. The low right ventricular ejection fraction during normal SR and AF with bimodal RR interval distribution increased above 50% under CF-LVAD support similar to a healthy cardiovascular system [41]. Although the right ventricular ejection fraction during AF with a unimodal RR interval distribution increased as well under CF-LVAD support, it was around 40% which indicates an impaired function. It is already known that the right ventricular function may be impaired in heart failure patients with AF under CF-LVAD support [42]. The cardiovascular system model produced impaired right ventricular function for relatively short cardiac cycles and unimodal RR interval distribution. Systolic pulmonary arterial pressures also reported to be relatively high in LVAD implanted heart failure patients with AF with respect to patients without AF [20]. Again, the cardiovascular system model produced relatively high systolic pulmonary arterial pressures for unimodal RR interval distribution under CF-LVAD support (Table 1). Higher aortic peak pressures and middle cerebral arterial peak flow rates may result in increased cerebral hypertensive events [24]. Relatively high aortic peak pressures and middle cerebral arterial peak flow rates were relatively high produced for bimodal RR interval distribution without CF-LVAD support (Figure 5). The peak values in the aortic pressure and middle cerebral arterial flow rate signals were reduced to similar values under CF-LVAD support for all the cases (Figure 5). Such a result may show the beneficial effect of CF-LVAD therapy on the patients with AF. However, it should be noted that the mean values of the aortic pressures and middle cerebral arterial flow rates were different in each case under heart pump support. Although cardiovascular system model generated similar cardiac outputs for each case, the mean pump outputs were remarkably different. The different mean pump outputs were obtained for each case depending on the duration of the cardiac cycles utilised in the simulations and varying CF-LVAD resistance used to describe CF-LVAD support (Equation (21)). The left and right atrial volumes are similar in healthy cardiovascular system [43; 44; 45].