Cardiovascular Fluid Dynamics

The cardiovascular dynamics is studied by means of lumped (0D) and multiscale (0D-1D) models. The lumped parameterization, consisting of a network of compliances, resistances, and inductances, allows to describe the complete cardiovascular system: the pumping heart together with the systemic and pulmonary circuits. The multiscale model focuses on the heart-arterial interaction. A lumped parameterization of the left heart and distal circulation is implemented, while 1D modeling of large-to-medium systemic arteries is accounted for.

The modeling resolution leads to describe the cardiovascular system in terms of the characteristic fluid dynamics variables (pressures, volumes, flow rates) and the hemodynamic parameters able to evaluate the cardiac efficiency and performance. Both models are developed and used to study cardiac pathologies, with particular attention to the cardiac arrhythmia and related altered clinical conditions.

 

LUMPED-PARAMETER MODELING

In the lumped parameterization the anatomical details are neglected and the whole cardiovascular system (with both systemic and pulmonary loops) is represented through the windkessel model by a set of electrical components, such as compliances, resistances and inductances.

Figure 1: scheme of the cardiovascular system.

Particular attention is paid to the physiologic and fibrillated beating features: (i) the normal beating (NSR, in blue) with full atrial contractility and RR beats extracted from a Gaussian distribution, and (ii) the fibrillated beating (AF, in red), with no atrial contraction and RR beats extracted from an Exponentially Modified Gaussian distribution. Interbeat analysis is also carried out on real RR series collected in the MIT database.

Figure 2: RR beating features. (left) RR temporal series; (middle) RR distributions; (right) autocorrelation functions, R (real RR recordings).

An overview of the main outcomes, computed over thousands of cardiac cycles and focused on the leaft heart, compares the normal sinus rhythm (NSR, in blue) and the atrial fibrillation (AF, in red). The model predictions well agree with the state-of-the-art clinical measures regarding AF: there is an overall deterioration of the hemodynamic framework with reduced cardiac efficiency and performance. The present stochastic modeling turns out to be an efficient and powerful tool for a deeper comprehension of the arrhythmia impact on the whole cardiovascular system.

Figure 3: left heart dynamics. From left to right: PV loops during NSR; PV loops during AF; systemic arterial pressure series; left atrial volume series.

Figure 4: LV performance and flow rates. From left to right: cardiac output (CO) and ejection fraction (EF) series; rate pressure product (RPP) values averaged over 10000 cardiac cycles (RR from real recordings); mitral flow rate (Qmi) temporal series; aortic flow rate (Qao) temporal series. 

 

MULTISCALE MODEL

With a stochastic modeling of the RR beating similar to the one used in the lumped parameterization, the multiscale model focuses on the effects of AF on the cerebral and aortic circulation. Preliminary results along the aortic tree are shown.

Figure 5: pressure time series along the aorta. (top) aortic arch; (middle) descending aorta; (bottom) abdominal aorta.

 

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