J Artif Organs (2013) 16:149–156 DOI 10.1007/s10047-013-0691-7
ORIGINAL ARTICLE
Continuous-flow pump model study: the effect on pump performance of pump characteristics and cardiovascular conditions Gianfranco Ferrari • Maciej Kozarski • Libera Fresiello • Arianna Di Molfetta Krzysztof Zielin´ski • Krystyna Go´rczyn´ska • Krzysztof J. Pałko • Marek Darowski
•
Received: 26 July 2012 / Accepted: 27 January 2013 / Published online: 5 March 2013 The Japanese Society for Artificial Organs 2013
Abstract This model study evaluates the effect of pump characteristics and cardiovascular data on hemodynamics in atrio–aortic VAD assistance. The model includes a computational circulatory sub-model and an electrical submodel representing two rotary blood pumps through their pressure–flow characteristics. The first is close to a pressure generator—PG (average flow sensitivity to pressure variations, -0.047 l mmHg-1); the second is closer to a flow generator—FG (average flow sensitivity to pressure variations, -0.0097 l mmHg-1). Interaction with VAD was achieved by means of two interfaces, behaving as impedance transformers. The model was verified by use of literature data and VAD onset conditions were used as a control for the experiments. Tests compared the two pumps, at constant pump speed, in different ventricular and circulatory conditions: maximum ventricular elastance (0.44–0.9 mmHg cm-3), systemic peripheral resistance (781–1200 g cm-4 s-1), ventricular diastolic compliance Cp (5–10–50 cm3 mmHg-1), systemic arterial compliance (0.9–1.8 cm3 mmHg-1). Analyzed variables were: arterial and venous pressures, flows, ventricular volume, external work, and surplus hemodynamic energy (SHE). The PG pump generated the highest SHE under almost all conditions, in particular for higher Cp (?50 %). PG pump flow is G. Ferrari (&) L. Fresiello (&) A. D. Molfetta CNR, Institute of Clinical Physiology, Section of Rome, Rome, Italy e-mail:
[email protected] L. Fresiello e-mail:
[email protected] M. Kozarski L. Fresiello K. Zielin´ski K. Go´rczyn´ska K. J. Pałko M. Darowski PAS, Nałecz Institute of Biocybernetics and Biomedical Engineering, Warsaw, Poland
also the most sensitive to Emax and Cp changes (-26 and -33 %, respectively). The FG pump generally guarantees higher external work reduction (54 %) and flow less dependent on circulatory and ventricular conditions. The results are evidence of the importance of pump speed regulation with changing ventricular conditions. The computational sub-model will be part of a hydro-numerical model, including autonomic controls, designed to test different VADs. Keywords Lumped parameter model Computational model Physical model Heart assist device Rotary blood pump
Introduction The potential for ventricular assist devices (VADs) to foster heart recovery has led to new research opportunities and new challenges [1–3]. Continuous flow pumps (CFP), characterized by their pressure–flow curves, interact with the circulatory system and result in different scenarios, depending on several variables. A circulatory model could be therefore an attractive tool when studying circulatory assistance, considering the reliability, the low cost, and the repeatability of experiments performed using the model. Research on this topic has exploited computational [4, 5], hydraulic [6], and hybrid modeling approaches [7–9]. The hybrid model, applied in this study, merges computational and physical (electrical) environments. The purpose of the work reported in this paper was to analyze the hemodynamics under different ventricular and circulatory conditions during atrial–aortic assistance, modeled using two different pressure–flow characteristics. The first is close to a pressure generator (PG) that is typical for most current
123
150
pumps; the second is close to a flow generator (FG) to evaluate how different pressure sensitivity could affect interactions among the pump, the circulatory system, and the heart. This study completes a previous one [10] in which the same computational model was connected to a pulsatile VAD, then also represented by an electrical model.
Materials and methods The modular circulatory model, already described in the previous study [10], belongs to a family of circulatory models that can be used as purely computational models [11, 12] or for merging computational and physical environments [10, 13]. The closed loop lumped parameter model (Fig. 1) is divided into five functional blocks: left and right hearts, systemic, pulmonary and coronary circulation. Each block embeds a library of selectable models. The corresponding equations are solved by use of Euler’s method. The heart rate (HR) is set manually and controls ventricular ejection and filling onset. The block VAD-(CFP) in Fig. 1 works in a different environment, electrical in this case, and will be described later. An additional block, not used in this study but shown in Fig. 1, takes into account autonomic controls, including the baroreflex control. It can control ventricular Emax, peripheral resistances, venous tone, and HR [14]. Abbreviations and default values of lumped parameters are reported in Table 1.
Fig. 1 Block diagram of the circulatory–VAD model. Interfaces I1 and I2 are the points where the computational sub model is connected to the assist device. The autonomic controls block includes the baroreflex control and was not used in this work. Pla, Pas and VADF are the variables exchanged between the two environments, separated by the thick dashed line
123
J Artif Organs (2013) 16:149–156
The model was developed in a LabVIEWTM (National InstrumentsTM, Austin, TX, USA) environment (Release 7.1 for Windows). The user interface presents essential information and gives access to a dedicated sub-panel to start and control CFP. Computational and physical environments are connected by an interface which behaves as an impedance transformer [13]. In CFP the flow depends on the pump speed (PS) and on the pressure drop (DP) applied at the input and output ports of the pump. In atrial–aortic connection, DP is proportional to Pas - Pla (Fig. 1). VADF is the input variable to the computational sub-model. The interaction between the computational and CFP sub-models (Fig. 1) is described by the equations: dPla ðtÞ þ QinVAD ðtÞ dt Pla ðtÞ Plv ðtÞ Qli ðtÞ ¼ for Pla ðtÞ [ Plv ðtÞ Rli Qli ðtÞ ¼ 0 for Pla ðtÞ Plv ðtÞ Qvp ðtÞ ¼ Qli ðtÞ þ Cla
dPas ðtÞ þ QoutVAD ðtÞ dt dðQlo ðtÞÞ Ls þ Qlo ðtÞ Plv ðtÞ Pas ðtÞ ¼ dt ðRcs þ Rlo Þ for Plv ðtÞ [ Pas ðtÞ
ð1Þ
Qlo ðtÞ ¼ Qas ðtÞ þ Cas
Qlo ðtÞ ¼ 0
ð2Þ
for Plv ðtÞ Pas ðtÞ
The interfaces (I1–I2) enable application of the DP to the CFP electrical model, realized by means of operational
J Artif Organs (2013) 16:149–156
151
Table 1 Glossary of terms
Table 1 continued
Symbol
Meaning
Default value
Units
HR
Heart rate
60
bpm
Emaxl/ Emaxr
Left/right ventricular end-systolic elastance
2/0.5
Symbol
Meaning
LVF
Left ventricular output flow
l min-1
VADF
Ventricular assist device flow
l min-1
ESPVR
Ventricular end systolic pressure-volume relationship
A/D–D/A
Analog to digital– digital to analog conversion
Out var
Variable calculated in the computational environment and transmitted to the physical environment by D/A conversion
In var
Variable calculated in the physical environment and transmitted to the computational environment by D/A conversion
PG/FG
Pressure/flow generator
SHE
Surplus hemodynamic energy
erg cm-3
EW
Left ventricular external work
J
-3
mmHg cm 3
V0l/V0r
Left/right ventricular rest volume
5/5
cm
Cp
Left ventricular diastolic compliance
10
cm3 mmHg-1
Cla/Cra
Left/right atrial compliance
30/30
cm3 mmHg-1
Rli/Rlo
Left ventricular valves input/output resistance
10/10
g cm-4 s-1
Ls/Lp
Systemic/pulmonary inertia
7.4 9 10-5/ 5.5 9 10-5*
g cm-4
Rcs/Rcp
Systemic/pulmonary characteristic resistance
90/25
g cm-4 s-1
3
-1
Cas/Cap
Systemic/pulmonary arterial compliance
1.8/1.0
cm mmHg
Ras/Rap
Systemic/pulmonary arterial resistance
1300/80
g cm-4 s-1
Cvs/Cvp
Systemic/pulmonary venous compliance
82.5/5
cm3 mmHg-1
Rvs/Rvp
Systemic/pulmonary venous resistance
20/1
g cm-4 s-1
S/D
Systole/diastole ratio
CO
Cardiac output
l min-1
AOP/Pas LAP/Pla
Aortic pressure Left atrial pressure
mmHg mmHg
Plv
Left ventricular pressure
mmHg
Pap
Pulmonary arterial pressure
CVP
LV
Left ventricle
VAD
Ventricular assist device
CFP
Continuous flow pump
mmHg
DP-flow
Pump pressure-flow (characteristics)
Central venous pressure
mmHg
VCCG
ESV
Ventricular end-systolic volume
cm
3
Voltage controlled current generator
EDV
Ventricular enddiastolic volume
cm3
QinVAD/ QoutVAD
LVAD input/output blood flow
cm3 s-1
Qli/Qlo
Left ventricular input/ output blood flow
cm3 s-1
Qcla
Left atrial compliance blood flow
cm3 s-1
Qvp
Pulmonary venous blood flow
cm3 s-1
Qas
Systemic arterial blood flow
cm3 s-1
R2 ¼ RF R3
Qcas
Systemic arterial compliance blood flow
cm3 s-1
Iout ¼ 2 Vin
Qcor
Total coronary blood flow
cm3 s-1
Default value
Units
amplifiers. The input stage of the CFP model (Fig. 2) is therefore a differential amplifier. The remaining blocks enable construction of different characteristics (PG and FG). The last block (VCCG) is used to select the pump type (from PG to FG) and deserves some comments. From the schematics in Fig. 2, output current, Iout, is given [15] by Eq. (3), assuming that: RF ¼ R4 ¼ R5 RF R3 ðRF R3Þ
ð3Þ
A switch is used to select different pairs of resistors R2 and R3 to control the slope of the relationship between Iout and Vin, generating the characteristics shown in Fig. 2. FG
123
152
J Artif Organs (2013) 16:149–156
Fig. 2 Block diagram of the pump electrical sub-model. The pump characteristics are shown in the lower graph. PG pump, dashed lines. FG pump, continuous lines
characteristics were not intended to simulate a specific pump type but rather to provide an understanding of how pressure sensitivity (that is to say, the quantitative relationship between DP and pump flow variations) can affect pump performance under different cardiovascular conditions. Data are A/D and D/A converted through a data acquisition board (PCI-MIO-16E-4; National InstrumentsTM, Austin, TX, USA). Signal conversion factors (20 (mmHg V-1) for pressure–voltage conversions and 104 (cm3 s-1 A-1) for current-flow conversions) do not represent a specific pump and were chosen arbitrarily to keep all variables in the correct ranges.
Experimental method Experimental activity was conducted in two steps: model verification and specific experiments Model verification was performed by use of literature data [1, 2] on the basis of continuous-flow partial ventricular support. In particular, the study described in Ref. [1]
123
reports hemodynamic data before pump implantation and in the acute phase and 24 h after implantation of an atrial– aortic VAD. These data were used for model verification by feeding it with values extracted from literature data (Ras, Rap, Cas, and HR) and estimating the remaining variables to obtain appropriate pressures and flows [11]. Hemodynamic data after VAD (PG) onset were used to set up the control condition (CNT-2 in Table 2) applied to all the experiments described in this paper. PG pump characteristics were chosen because they are closer to the pump characteristics used in Ref. [1]. Tests were repeated under different circulatory and ventricular conditions (Table 3), comparing PG and FG pumps. The study included analysis of the left ventricular external work (EW) and of the surplus hemodynamic energy (SHE) [16]. SHE was calculated as the difference between energy equivalent pressure (EEP) and mean arterial pressure and is a measure of vascular pulsatility. Comparison of FG and PG pump characteristics was used to evaluate the effect of pump pressure sensitivity in the pump–heart–circulatory system interaction. The different patho-physiological conditions likely to arise during the assistance are taken into account by setting circulatory and
•
Values represent total cardiac output/(LVAD flow)
Column CO: the percentage (%) variation is calculated over total CO. The number in brackets is the LVAD flow contribution to CO
Simulations were in good agreement with literature data (Table 2). The CNT-2 set of values was used as a control for the next experiments in which pump type and ventricular and circulatory data were modified (Table 3). We are aware that by following this approach, the main results come from a simulation; however, having shown that the model can reproduce hemodynamic conditions before and after pump onset, it is realistic to extend the analysis to pumps PG–FG and to changes in ventricular and circulatory conditions. In these experiments PS was kept constant. Some remarks about the pump characteristics are necessary:
•
The pump electrical model does not reproduce the nonlinearities typical of CFPs. However, the pump working point moved in a relatively narrow band determined by DP (Table 3) range 33–100 mmHg. Most data lie in the range 33–80 mmHg. Under these conditions, the lack of non-linear parts of the characteristics may be regarded as not critical, at least for evaluation of the trends of the variables of interest. FG pump characteristics are rather narrow on the flow axis (Fig. 2) but, considering that the experiments were conducted at constant PS, a single curve of the whole family is enough. The analysis of the experiments (Table 3) reveals that:
•
Pump characteristics affect SHE, even if the dynamics of this variable could be negatively affected by the decision to represent the pump with linear characteristics. In general, the FG pump is less affected by changes in ventricular and circulatory variables.
b
a
% is the percentage variation between 1 and 2
CNT-2, after LVAD assistance onset
CNT-1, before LVAD assistance onset
Simulations reported in this table were conducted using a PG pump type
-38.6
-37.6 133
133 200 -39
-39
781
781
1184
1179 -6.5
– – 228
231 1.7
–
216
–
184
181
181
–
24
–
17.5 14.1
13.4 -28
Discussion
-31
38.9
28
Literature and simulated data (pump PG) are compared in Table 2. Percentage difference between the two data sets is less than 10 % for all available hemodynamic variables. Table 3 shows experiment results and includes all hemodynamic data, comparing the two pump types. Figure 3 shows CO, VADF, and LVF normalized to CNT-2 (circulatory condition after VAD onset but with pump off).
36.7
-38.8
-37.8
18
18.4
29.4
Results
29.6 ?14
?9.1 72
73.2
66
64.2
?58
?49
6.0/(3.0)
5.8/(3.2)
3.8
3.9 0
79
79
79
79
[1]
Simul.
0
ventricular variables. EXP4-Emax mimics partial ventricular recovery, EXP2-Cas and EXP3-Ras mimic, respectively, more compliant vessels or vasoconstriction. Finally, EXP5Cp1 and EXP6-Cp2 mimic changes in ventricular filling conditions as they can occur in hypertrophic and dilated cardiomyopathy.
25.2
% % 2 1 1 1 2b 2 CNT-1 CNT-2
1
%
1
%
2
%
1
2
%
2
%
CVP (mmHg) Pap (mmHg) LAP (mmHg) AOP (mmHg) COa (l min-1) HR (bts min-1)
Table 2 Comparison of VAD literature data [1] with simulation results
153
200
% 2 1 % 2 1 1 2 1
2
EDV (cm3) ESV (cm3)
%
Ras (g cm-4 s-1)
Rap (g cm-4 s-1)
J Artif Organs (2013) 16:149–156
123
154
J Artif Organs (2013) 16:149–156
Table 3 Results VAD
Emaxl (mmHg cm-3)
Cp (cm3 mmHg-1)
Cas (cm3 mmHg-1)
Ras (g cm-4 s-1)
CO (l min-1)
LVF (l min-1)
PG
PG
FG
CNT-2 [1]
Off
0.44
10
1.8
781
5.1
EXP1
On
0.44
10
1.8
781
5.73 12.4
% EXP2-Cas
On
0.44
10
0.9
781
EXP3-Ras
On
0.44
10
1.8
1200
EXP4-Emax
On
0.9
10
1.8
781
EXP5-Cp1
On
0.44
5
1.8
781
5.79 13.5
% %
% EXP6-Cp2
On
0.44
50
1.8
Pap (mmHg)
ESV (cm )
PG
PG
PG
FG
FG
CNT-2 [1]
26.7
EXP1
18.4
18.4
25.2
28.9
-31.1
-31.1
-28.8
-18.4
EXP2-Cas EXP3-Ras EXP4-Emax EXP5-Cp1 EXP6-Cp2
35.4
158
21.4
19.7
31.3
-19.9
-26.2
-11.6
30
26.7
24.1
35.4
33.3
0.0
-9.7
0.0
-5.9
-15.3
12.4
15.0
25.6
26.6
-53.6
-43.8
-27.7
-24.9
27.8
26.5
36.4
35.4
4.1
-0.7
2.8
0.0
7.1
6.4
22.6
22.3
-73.4
-76.0
-36.2
-37.0
184 16.5 185 17.1 198 25.3
13.9 185 17.1 200 26.6
17.6
-52.9
5.5
7.6
6.76
-58.8
-54.3 2.21 -56.7 1.71 -66.5
5.24 2.7 1.07
-2.0
2.0
76.5
2.33
2.1
5.2
-79.0
9.28
-36.1
FG
-75.3 15.5
330
-3.1
-5.8
-68.4
-73.8
216
212
1299
1060
-3.1
-4.9
224
220
201
121
-1.3
-84.0
-90.4
1291
1094
135
192
202
-14.6
-13.9
-9.4
2.5
-15.8
-13.1
126
126
140
139
83
79
-20.3
-20.3
-37.2
-37.7
-93.4
-93.7
299
299
387
375
1916
1403
89.2
89.2
73.5
68.2
52.2
77.9 29.4
3.39
3.79
74.4
76.4
5.6
0.5
23.6
26.9
3.0
3.67
91
94.6
3.93 22.4 2.14 -33.3
14.3
51.2
57.1
3.5
94.8
105.5
-7.2
57.5
75.2
3.94
65.1
65.2
4.5
8.1
8.3
107.9
110.8
79.2
84.1
3.39 -10.1
FG 0.584
398
125
21.6
PG
210
-20.9
0
PG
216
0.4
0
EW (J)
1259
60.2 73.2
SHE (erg cm ) FG
FG
3.77
-26.5
5.89
34.7
3.2
PG
3.21
2.36
1.26
6.87
82.0
FG
-6.5
3.26
-3
223 180
2.4
0.0
EDV (cm ) PG
6.0 5.38
3
FG
-50.6
32.5
% LAP (mmHg)
19.6
AOP (mmHg)
0
2.52
5.1
9.0
PG
5.1 6.1
5.0
781
3
FG
49.0
%
VADF (l min-1)
11.4
0.35 -40.1 0.33 -43.5 0.33 -43.5 0.96 64.4 0.12 -79.5 1.46 150
0.33 -43.5 0.3 -48.6 0.27 -53.8 1.05 79.8 0.12 -79.5 1.26 115.8
The control condition CNT-2 was obtained by setting in the model the same values as in Table 2, columns 2, with VAD off. Underlining indicates the variables modified in each experiment The lines marked as % report for each variable and each experiment the percentage variation in relation to control condition (CNT-2)
•
• •
•
•
A stiffer arterial system enhances the pulsatility and the effect is marked for the PG pump. This is a phenomenon observed for other types of assistance, for example the IABP [14]. SHE is affected by changes in ventricular filling characteristics. CO depends on circulatory and ventricular conditions and, for the same PS, maximum CO is obtained with the maximum ventricular diastolic compliance. VAD flow, with the same pump type and speed, depends on DP and it is at its highest with lower ventricular diastolic compliance. Finally, Fig. 3 shows that the FG pump flow is less sensitive than the PG pump to changes of conditions.
123
Fig. 3 Flows for all the experiments comparing PG and FG pump types. CO and LVF are normalized to CNT-2 CO and LVF. VADF is normalized to EXP1 VADF, because in CNT-2 the pump is switched off
J Artif Organs (2013) 16:149–156
The sensitivity of flow to changes of conditions could be an issue to be taken into account when suction detection algorithms are developed, especially those based on measurements of such pump variables as motor current. The circulatory and ventricular conditions have a different effect. In fact, in Fig. 3, for EXP4-Emax, pump PG flow drop is much higher than that for pump FG, and a simultaneous increase in EW (Table 3) can be observed. The rise in Emax provokes a re-distribution of blood flow, because of the increase in DP, between the pump flow (;) and the LV flow (:), increasing total CO also. Similar considerations are valid for EXP5-Cp1 and EXP6-Cp2. In general (Table 3), the relative contributions of LVF and VADF to CO are slightly sensitive to changes of circulatory conditions but are strongly affected by changes of ventricular conditions, especially for pump PG. The increase of LV contributions to CO is reflected by the rise in EW that could be interpreted as a signal of ventricular recovery or at the same time as the need to tune the PS to preserve the ventricle reducing its EW. For the same pump type, adequate PS control, based on the estimation of ventricular data (Emax and Cp) could adapt the pump flow to specific patients’ conditions that change dynamically during the assistance, especially for ventricular recovery. An example based on pump PG, more sensitive to changes of ventricular and circulatory conditions, can better explain the last point. EXP1, EXP6-Cp2, and EXP4-Emax were repeated, changing the PS from minimum to maximum in five steps. The variables analysed were EW, total CO, and VADflow. SHE was excluded because its retrospective verification on the basis of literature data only is rather difficult. The results are shown in Fig. 4. Data in the figure are normalised in relation to a control condition measured before VAD onset. Full verification of the data shown in Fig. 4 is rather difficult on the basis of literature data, because they are not homogeneous. Some researchers have analyzed the effects of PS variations on ventricular p–v loops [17], using a pump with apical connection. p–v loop data for atrial–aortic bypass are reported for a pulsatile VAD [18]. The two sets of data indicate: •
•
Total CO tends to remain constant with changing PS. The relative contributions of the VAD and of the LV change accordingly [17]. The same trends are shown by Figs. 3 and 4. Any change in ventricular conditions affects total CO and EW [18], also modifying the relative contributions of the VAD and of the LV.
Referring to Fig. 4 and assuming that the purpose of the assistance is to minimize EW and maximize CO, this is achieved by use of different pump speeds in each experiment. This implies that PS should be regulated in relation
155
Fig. 4 Effects of PS modulation for five different speeds (RPM-1 to RPM-5) on normalized EW, VADF, and CO. The first value is a control condition (C) obtained with the pump off. Experiments were conducted starting from conditions corresponding to EXP1, control CNT-2 (a), EXP6-Cp2, control EXP6-Cp2-pump off (b) and EXP4Emax, control EXP4-Emax-pump off (c)
to the patient’s ventricular (and circulatory) conditions. This scenario could become even more complex taking into account the patient’s physical activity and autonomic control reactions, especially in long-term VAD assistance.
Conclusions The hydraulic version of the model used in this paper is being developed in the framework of Integrated Project SensorART [19, 20]. Besides its research applications, the model could be a useful education and training tool because it enables easy creation of realistic patho-physiological conditions by use of different simulation modules, including autonomic controls. Acknowledgments This work was supported by European Union (EU) Integrated Project SensorART (Grant Number: 248763).
123
156
J Artif Organs (2013) 16:149–156
References 1. Meyns B, Klotz S, Simon A, Droogne W, Rega F, Griffith B, Dowling R, Zucker MJ, Burkhoff D. Proof of concept: hemodynamic response to long-term partial ventricular support with the synergy pocket micro-pump. J Am Coll Cardiol. 2009;54:79–86. 2. Umezu M, Yamazaki K, Ymazaki S, Iwasaki K, Miyakoshi T, Kitano T, Tokuno T. Japanese-made implantable centrifugal type ventricular assist system (LVAS): EVAHEART. Biocybern Biomed Eng. 2007;27:111–9. 3. Bartley PG, Kormos RL, Borovetz HS, Litwak K, Antaki JF, Poirier VL, Butler KC. HeartMate II left ventricular assist system: from concept to first clinical use. Ann Thorac Surg. 2001;71:S116–20. 4. Zhou J, Armstrong GP, Medvedev AL, Smith WA, Golding LA, Thomas JD. Numeric modeling of the cardiovascular system with a left ventricular assist device. ASAIO J. 1999;45:83–9. 5. Shi Y, Korakianitis T. Bowles C numerical simulation of cardiovascular dynamics with different types of VAD assistance. J Biomech. 2007;40:2919–33. 6. Knierbein B, Reul H, Eilers R, Lange M, Kaufmann R, Rau C. Compact mock loops of the systemic and pulmonary circulation for blood pump testing. Int J Artif Organs. 1992;15:40–8. 7. Ferrari G, Kozarski M, De Lazzari C, Clemente F, Merolli M, Tosti G, Guaragno M, Mimmo R, Ambrosi D, Głapinski J. A hybrid (numerical-physical) model of the left ventricle. Int J Artif Organs. 2001;24:456–62. 8. Colacino FM, Arabia M, Danieli GA, Moscato F, Nicosia S, Piedimonte F, Valigi P, Pagnottelli S. Hybrid test bench for evaluation of any device related to mechanical cardiac assistance. Int J Artif Org. 2005;28:817–26. 9. Gwak KW, Paden BE, Antaki JF, Ahn IS. Experimental verification of the feasibility of the cardiovascular impedance simulator. IEEE Trans Biomed Eng. 2010;57:1176–83. 10. Ferrari G, Kozarski M, Zielin´ski K, Fresiello L, Di Molfetta A, Go´rczyn´ska K, Pałko KJ, Darowski M. A modular computational circulatory model applicable to VAD testing and training. J Artif Organs. 2011;15:32–43. 11. Ferrari G, Kozarski M, Gu YJ, De Lazzari C, Di Molfetta A, Pałko KJ, Zielin´ski K, Go´rczyn´ska K, Darowski M, Rakhorst G.
123
12.
13.
14.
15.
16.
17.
18.
19.
20.
Application of a user friendly comprehensive circulatory model for hemodynamic and ventricular variables estimate. Int J Artif Organs. 2008;31:1043–54. Di Molfetta A, Santini L, Forleo G, Minni V, Mafhouz K, Della Rocca D, Fresiello L, Romeo F, Ferrari G. Towards a personalized and dynamic CRT-D: a computational cardiovascular model dedicated to therapy optimization. Methods Inform Med. 2012. doi:http://dx.doi.org/10.3414/ME12-01-0011. Kozarski M, Ferrari G, Zielin´ski K, Go´rczyn´ska K, Pałko KJ, Tokarz A, Darowski M. A new hybrid electro-numerical model of the left ventricle. Comput Biol Med. 2008;38:979–89. Fresiello L, Khir AW, Di Molfetta A, Kozarski M and Ferrari G. Effects of Iabp timing on baroreflex activities in a closed loop cardiovascular hybrid model. Artif Organs. 2012. doi:10.1111/ j.1525-1594.2012.01540.x. Linear circuits applications: voltage to current converters. In: Graeme JG, Tbey GE, Huelsman LP, editors. Operational amplifiers. Design and applications. Tokyo: McGraw–Hill International; 1981. p. 225–9. ¨ ndar A, Ji B, Lukic B, Zapanta C, Kunselman AR, Reibson JD, U Weiss WJ, Rosenberg G, Myers JL. Quantification of perfusion modes in terms of surplus hemodynamic energy levels in a simulated pediatric CPB model. ASAIO J. 2006;52:712–7. Moscato F, Vollkron M, Bergmeister H, Wieselthaler G, Leonard E, Schima H. Left ventricular pressure–volume loop analysis during continuous cardiac assist in acute animal trials. Artif Organs. 2007;31:369–76. Kawaguchi O, Sapirstein JS, Daily WB, Pae WE, Pierce WS. Left ventricular mechanics during synchronous left atrial–aortic bypass. J Thorac Cardiovasc Surg. 1994;107:1503–11. Kozarski M, Ferrari G, Zielinski K, Go´rczynska K, Palko KJ, Fresiello L, Di Molfetta A, Darowski M. A hybrid (hydronumerical) cardiovascular model application to investigate continuous-flow pump assistance effect. Biocybern Biomed Eng. 2012;32:77–91. SensorART. A remote controlled Sensorized ARTificial heart enabling patients empowerment and new therapy approaches— Integrated Project funded within the framework of the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 248763 (http://www.sensorart.eu).