Pneumatic LVAD can be connected "in serie" or "in parallel" mode. When LVAD pump is connected "in serie" ("in parallel") mode, it takes blood from the left ventricle (atrium) and ejects it into the aorta. In the reported configuration the cardiocirculatory network is composed by: systemic (pulmonary) arterial section modelled with a 4-MW (RLC elements) where Ras (Rap) is a variable peripheral resistance; systemic (pulmonary) venous section modelled by a variable resistace Rvs (a resistance Rvp) and a compliance Cvs (Cvp). HEART: the ejection and contraction phases of both ventricles are reproduced using the variable elastance model; the right (left) atrium is described as a linear capacity characterised by constant value of compliance Cra (Cla) and unstressed volume, i.e. the contractile activity of the atrium is neglected (see the Numerical Heart Model (1) section). The connection of the ventricles to the circulatory network is realised by means of valves (mitral (MV), aortic (AV), tricuspid (TV) and pulmonary (PV)), which are assumed to be ideal.

Upper left panel shows the general layout of the driving unit-pneumatic ventricle system. Ts and Td represent the systole and diastole time respectively. Upper right panel illustrates the pneumatic ventricle. Dashed and countinuous lines inside the ventricle represent two different position of the membrane. Vair and Pair (Vvad and Pvad) are the volume and pressure into the part of the ventricle connected to the air tube (into the ventricle). Lower panel shows the pressure-volume relationship which has been assumed for the pneumatic ventricular diaphragm in its end-systolic and end-diastolic position. Ced and Ces are the diaphragm compliance at end-diastolic and end-systolic position respectively. Vmin and Vmax are the minimum and the maximum pneumatic ventricular volume respectively.

Rvi (Rvo) represents the input (output) valve resistance. Pd (Pv) is the driving (vacuum) pressure; Pair is the pressure into the part of the VAD connected to the air tube;  Ppv is the pressure inside the VAD.

Electrical analogue model of the cardiovascular simulator. The cardiovascular model is divided in different sections: left (right) heart, systemic (pulmonary) arterial section, systemic (pulmonary) venous section and coronary section. PUCA pump aspirates blood from the left ventricle and ejects it into the aorta. In the electric analogue the behavior of the heart was implemented using the equations reported in the Numerical Heart Model (2) section.

The electric analogue of the cardiovascular system (CVS) consists of left and right herat (described in Numerical Heart Model (1) section), systemic arterial section, splanchnic peripheral and venous circulation, extrasplanchnic peripheral and venous circulation, peripheral and venous circulation in active muscle compartment, systemic thoracic vein section, pulmonary arterial, peripheral and veins sections and coronary circulation. QiHEMO (QoHEMO) is the input (output) LVAD pump flow. The electrical analogue and equations of Hemopump are shown in countinuous flow pump section. Qartery (Qvenous) is the coronary artery (venous) blood flow.

LAP (LVP) is the left atrial (ventricular) pressure; Qli (Qlo) is the left input (output) ventricular flow; AoP (Qas) is the systemic arterial pressure (flow); Rli (Rlo) is the left ventricular input (output) resistance; Ras (Las) is the systemic arterial resistance (inertance); Cas is the systemic arterial compliance; Qartery is the input coronary flow; Pt is the mean intrathoracic pressure; Psp (Psv) is the splanchnic peripheral (venous) pressure; Pev is the extasplanchnic venous pressure; Pmv is the pressure of the venous circulation in active muscle compartment; PSTV is the systemic thoracic vein pressure; QoHEMO is the outpul LVAD pump flow; Qsp (Qep) is the splanchnic (extrasplanchnic) peripheral flow; Qsv (Qev) is the splanchnic (extrasplanchnic) venous flow; Qmp (Qmv) is the pheriperal (venous) flow in active muscle compartment; Csp (Csv) is the splanchnic peripheral (venous) compliance; Cep (Cev) is the extrasplanchnic peripheral (venous) compliance; Cmp (Cmv) is the peripheral (venous) compliance in active muscle compartment; Rsp (Rsv) is the splanchnic peripheral (venous) resistance; Rep (Rev) is the extrasplanchnic peripheral (venous) resistance; Rmp (Rmv) is the peripheral (venous) resistance in active muscle compartment. Qartery is the coronary artery blood flow.

RVP is the right ventricular pressure; Qri (Qro) is the right input (output) ventricular flow; RAP (LAP) is the right (left) atrial pressure; Rri (Rro) is the right ventricular input (output) resistance; Rstv is the systemic thoracic vein resistance; Cap (Cpp) is the pulmonary arterial (peripheral) compliance; Cvp is the pulmonary venous compliance; Qvenous is the output coronary flow; PAP (PPP) is the pulmonary arterial (peripheral) pressure; Pvp is the pulmonary venous pressure; Qap (Qpp) is the pulmonary arterial (peripheral) flow; Qvp is the pulmonary venous flow; Rap (Rpp) is the pulmonary arterial (peripheral) resistance; Rvp is the pulmonary venous resistance. Qvenous is the coronary venous blood flow.

Cla (Cra) is the left (right) atrial compliance; QiHEMO is the input LVAD pump flow; Vlv (Vlv ) is the left (right) ventricular volume.  

The behavior of systemic venous bed is simulated by the compliance Cvs and the variable resistances (Rvs). The pulmonary arterial circulation is modelled with RLC elements. The pulmonary venous bed is modelled with the resistance Rvp and the compliance Cvp. The LVAD (Berlin Heart INCOR^®) takes blood from the left ventricle and ejects it into the aorta. In this electric analogue configuration the behavior of the heart was implemented using the equations reported in the Numerical Heart Model (2) section.

In the network LVP is the left ventricular pressure and AoP is the systemic arterial pressure. The input and output pump cannulae are modelled with the resistances R_vpi and R_vpo, the compliance C_vpi and C_vpo and the inertance L_vpi and L_vpo. Q_VAD is the pump flow; Q_vpi and Q_vpo are the flows of the input and output cannulae.