Table 6 Typical applications of 0D model

Analysis of the systemic arterial flow characteristics

Only the arterial network is modelled

Characteristics of the three- and four-element Windkessel models [13, 15, 16, 43, 114, 167, 169, 170];

Advantages and disadvantages of using the three element RCR model as aortic input impedance [14];

Comparison of different configurations of three element and four element models as the embryonic aortic impedance [110];

Investigation of aortic input impedance in infants and children by curve fitting to two, three and four element Windkessel models [17];

Study of the linear and nonlinear formulations of the three element Windkessel model by considering the pressure-dependent capacitance effect in the arterial network [89, 90, 92];

Two port analysis to extend the Windkessel models by considering the venous side flow pulsations in the systemic loop [19, 20];

Ventricular-systemic arterial coupling [171].

Hemodynamic response in the native cardiovascular system under various healthy and diseased conditions

Complete description of the native cardiovascular system

Cardiovascular response in normal healthy subjects [31];

Study of the ventricular interaction effect [32].

Modelling the dysfunction in regional stunned myocardium of the left ventricular [69];

Modelling of cardiac muscles in the study of mechanics and energetics of fibrillating ventricle [49];

Study of changes in pulmonary venous pressure after the onset of left ventricular dysfunction [30].

Hemodynamic changes under various surgical and therapeutical interventions.

The native cardiovascular system was partly changed.

Circulation dynamics in the presence of the bidirectional cavopulmonary anastomosis in children with a uni-ventricular heart [50];

Rest and exercise hemodynamics in patients with total cavopulmonary connection [172];

Modelling the hemodynamic characteristics in patients with hypoplastic left heart syndrome after the palliative Norwood operation [51];

Study of the cardiovascular response in patients with right ventricular bypass and uni-ventricular circulation support [173];

Modelled the cardiovascular control adaptations in chronic renal failure patients [166];

Modelling of the hemodynamic response to hemodialysis induced hypovolemia [54].

Modelling of the cardio-pulmonary response under step-leap respiration exercise for the treatment of patients with Cor Pulmonale [84].

Ventricular assist device support for heart failure

The native cardiovascular system was in heart failure condition, and a VAD model is coupled.

Studies of cardiovascular response in the heart failure condition supported with various types of VADs [70, 85, 99, 174–178];

Studies of cardiovascular response in the heart failure condition supported with intra-aortic balloon pumps [48];

Comparison of the assistance action of different types of VAD and VAD motion profiles [179];

Study of the effect of the inlet and outlet cannulation sites for connecting the VADs to the native cardiovascular system [180];

Study of the physiological control of pulsatility gradient in rotary blood pump [33, 181].

Study of cardiovascular response under neuro-regulation

The native cardiovascular system was coupled with the models for the nervous system

Simulate the cardiovascular responses under neuro-regulation in various conditions of isocapnic hypoxia [41, 76], hemorrhage [40], hypercapnia and hypocapnic hypoxia [77], carotid occlusion [27];

Simulation of cardiopulmonary response in Valsalva manoeuvre [35];

Simulation of circulation system response to acceleration stress [78];

Simulation of the cardiovascular response to orthostatic stress [22].

Study of special and local circulation loops in the cardiovascular system.

Only the local circulation loop was modelled, and arterial pressure or flow-rate was applied as upstream boundary condition.

Simulation of human foetal cardiovascular system [23];

Studies of cerebral auto-regulation effect [100, 103], cerebral vasospasm [80], acute brain damage [102], and cerebral hemodynamics during arterial and CO₂ pressure change [101];

Modelling of coronary local circulation loop [104];

Study of dependence of intra-myocardial pressure and coronary flow on ventricular loading and contractility [52, 93];

Study of venous valves in pressure shielding in the lower extremity [87];

Simulation of venous circulation in lower extremities [37].

As boundary condition in multi-scale simulation of cardiovascular dynamics

The 0D circulation system model was coupled with the distributed parameter models (1D, 2D or 3D).

Multi-scale simulation of the cardiovascular dynamics [147, 151, 153, 159, 160].