In children, left ventricular assist devices (LVADs) are mostly used as a bridge to heart transplantation (HT) with a success rate up to 84%.1,2 Pulsatile (p-) LVAD, in particular, are mostly used in pediatrics where the continuous (c-) flow LVAD use is still limited but challenging and under development. The use of LVADs could successfully support both pediatric and adult patients, increasing the cardiac output (CO) and unloading the left ventricle (LV) with a LV reverse remodeling at different levels from histology to echocardiography. The LVAD could decrease the LV work because of flow distribution between the native LV and the LVAD.3 One of the major complications in LVAD patients is the right ventricular (RV) failure with an incidence among 13% to 44% in adults and an incidence of 42% in children.4–7 Different explanations about the increased risk of the RV failure in LVAD patients were proposed:
- - Right ventricular work increases due to RV venous return increase thanks to the LVAD because the RV and the LV work in series8,9
- - The leftward shift of the interventricular septum after the LVAD implantation could decrease the support given by the septum to the RV contraction.8,10
On the contrary, it has been considered that the LVAD could decrease the RV afterload, decreasing the pulmonary arterial pressure (Pap), possibly leading to a better RV pump functioning.11 In literature, there are different opinions3–11 and several authors performed animal experiments also to study the interventricular interaction during LVAD assistance.3–10 The aim of this work is to use a numerical model of the cardiovascular system to study the effects of different settings of continuous and pulsatile flow LVADs on LV and RV functions, energetics, preloads, and afterloads in pediatric patients.
Materials and Methods
A lumped parameter model of the cardiovascular system was adopted to this specific study,11–15 where
- Heart chambers are represented by variable elastance models
- - Pulmonary and systemic circulations are represented by windkessel models
- - The interventricular septum was modeled with a variable elastance model as an active membrane separating the two ventricles.14,15 The model of the interventricular septum permits to reproduce the interventricular interdependency that is described by the variation of ventricular volumes because of the deviation of septum position.14,15 The interventricular septum model was firstly described by Suga and Sagawa15 with the aim of modeling the changes in a ventricle as a function of the changes in the controlateral ventricle. In their work, Suga and Sagawa15 assumed that the heart has three different elastances and that when the RV and LV pressures are equal, the interventricular septum is in a neutral position and the pressure–volume relationship of one ventricle is not influenced by the pressure–volume relationship of the controlateral ventricle. On the contrary, when the left ventricular pressure is higher than the right ventricular pressure, the interventricular septum is pushed to the right causing changes in right ventricular volume and pressure. The septum position is represented by the septum volume calculated with the following equation introduced by Suga and Sakawa15:
where Vseptum(t) is zero in the neutral position (when Plv[t] = Prv[t]) and Vseptum(t)is >0 (<0) if the left (right) ventricular pressure is higher than the right (left) ventricular pressure. Moreover, the deviation of septum position increases if its elastance decreases. With the model of the septum, the variation of ventricular volumes are also due to the deviation of septum position. In fact, considering the interventricular septum, ventricular instantaneous left (Vlv[t]) and right (Vrv[t]) ventricular volumes Vlv(t) and Vrv(t) can be calculated as
where Vlv(t)fw (Vrv(t)fw) is the instantaneous left (right) ventricular volume of the free wall. Introducing the model of the interventricular septum, the instantaneous ventricular pressure in a ventricle becomes a function of its own parameters and of the other chamber parameters.14,15 A more detailed description of the model is presented in [14, 15].
Two LVADs were modeled in this study:
- - A c-LVAD was modeled starting from the pressure-flow characteristics of the Infant Jarvik pump, which is the most used continuous flow LVAD in pediatrics,16 with a polynomial equation for each pump speed (25,000–45,000 rpm).10,16 The VAD connections are realized between the LV and the aorta (Figure 1).
- - A p-LVAD was modeled including the separate representation of the filling and the ejection phases. The ejection (filling) is described by the air outflow from a high pressure tank (LV) connected to a pressure source toward the LV (lower pressure tank). A detailed description of the mathematical model of the pulsatile VAD is reported in . The interaction between the air and the blood is mediated by a membrane. The pressure drop across the membrane is negligible when the ventricular volume is far from the minimum and the maximum, whilst it increases at full fill-full empty positions with the membrane compliance.
Data of five pediatric patients undergoing LVAD implantation were retrospectively collected before the LVAD implantation including
- - Clinical data: gender, weight, age at the implantation, pathology, type of VAD, heart rate (HR);
- - Echocardiographic data: ejection fraction (EF), left ventricular end systolic (LVESV) and end diastolic (LVEDV) volumes;
- - Hemodynamic data: systolic/diastolic and mean pulmonary pressures, LV end systolic pressure (LVESP), left and right atrial pressures, arterial systemic pressure, CO.
Data were used to calculate model input parameters to reproduce the baseline hemodynamics for the five patients. Heart rate was set directly in the model. Left ventricular end systolic elastance (Elvs) was calculated from LVESP and the LVESV assuming the rest volume as zero as11–14:
LV end diastolic (Elvd) elastance was calculated from left atrial (Pla) pressure and the LVEDV assuming the rest volume as zero as11–14
The total arterial systemic resistance (Ras) was calculated from the CO and the difference between mean systemic arterial pressure (Pas) and right atrial pressure (Pra):
The total arterial pulmonary resistance (Rap) was calculated from the CO and the difference between mean Pap and right left atrial pressure (Pla):
From Pas waveforms, it was possible to evaluate the time decay that is the combination between resistances and compliances. From these time decay constants, it was possible to estimate the total arterial systemic compliance (Cas)15,17–19 as
where td is the duration of the diastolic phase, AoP(D) is the diastolic arterial systemic pressure, and AoP(S) is the systolic arterial systemic pressure.
All the other compliances were kept constant to default values (Table 1). Right ventricular end systolic and end diastolic elastances were set equal LV end diastolic and Elvs, respectively. Then RV elastances were empirically adjusted with an iterative procedure until the measured hemodynamics values were reached, according to the procedure described in [17, 18]. All other parameters were maintained equal to the default values reported in Table 1. The LV and RV external works were calculated by the model as the area of the LV and RV pressure–volume loops, whereas the artero-ventricular coupling was calculated as:
where LVAVC (RVAVC) is LV (RV) artero-ventricular coupling and Ea (Ep) is the systemic arterial (pulmonary) elastance calculated as
where RVESV (RVEDV) is RV end systolic (diastolic) volume calculated by the model and the RVESP is the RVESP.15
Once the baseline conditions of the five patients were reproduced, for each patient, the following simulations were performed:
- Simulation of the c-LVAD implantation collecting simulated hemodynamic outcomes for each pump speed.
- Simulation of the p-LVAD implantation collecting simulated hemodynamic outcomes, changing separately:
- a. the pump rate, to assure a patients perfusion ranging from 100 ml/kg to 200 ml/kg;
- b. the LVAD systolic duration (30%, 40%, 50%);
- c. the LVAD filling pressure (0 mm Hg, –35 mm Hg);
- d. the LVAD ejection pressure (100 mm Hg, 200 mm Hg).
During the simulation of the effect of one LVAD parameter changes, all other LVAD parameters were kept constant to the values of the starting point. The starting point of this set of simulations includes a LVAD rate equal to patients HR, a LVAD systolic duration of 30%, a LVAD filling pressure of 0 mm Hg, and a LVAD ejection pressure of 100 mm Hg.
Table 2 shows the patients baseline characteristics and a comparison between measured and simulated data at the baseline using the t-test, evidencing that the model can well reproduce patients baseline hemodynamics. Data of five patients (two males, 40%), with an average weight of 7.5 ± 4.5 kg and an average age of 15.5 ± 11.8 months were used. All patients were affected by idiopathic-dilated cardiomyopathy with severely dilated LV (LVESV: 53.2 ± 24.3 ml, LVEDV: 63.8 ± 28.1 ml) and a depressed right ventricular function (RV end systolic area 3.2 ± 2.5 cm2, RV end diastolic area 4.8 ± 3.0 cm2, RV fractional area change 31.8 ± 14.9%). At the baseline, the estimated RV end systolic (diastolic) elastance was 1.22 ± 0.47 mm Hg/ml (0.28 ± 0.21 mm Hg/ml).
Figure 2A shows the trend of RV and LV preload as a function of LVAD speed evidencing a decrease of left atrial pressure because of LV unloading assured by the LVAD, and a slight increase of the right atrial pressure. Figure 2B shows the trend of RV and LV afterload evidencing that arterial systemic pressure increases and Pap decreases if the LVAD speed increases. Figure 2C shows the trends of mean LV and RV volumes and of RV ejection fraction. The LVAD implantation permits to unload the LV, whereas increasing the LVAD speed, the RV volume and RV increased because of the increase of RV preload and the leftward shift of the interventricular septum. Right ventricular ejection fraction increases increasing the pump speed. In Figure 2D, the trends of LV external work (LVEW), RV external work (RVEW), and CO are shown. LVEW (RVEW) is decreased (increased) once the LVAD is implanted. Then, increasing the pump speed, the LVEW continues to decrease and the RVEW increases. Finally, Figure 2E shows the trends of ventriculo-arterial coupling as a function of LVAD speed. The left ventriculo-arterial coupling is improved by the presence of the LVAD and it reaches a physiological value (range 0.5–1)20,21 increasing the pump speed. Moreover, the presence of the LVAD, decreases the right ventriculo-arterial coupling mainly because of the reduction of RV afterload.
Figure 3 shows the trend of RV stroke volume and interventricular septum volume (Vseptum) as a function of LVAD speed for each patient evidencing a leftward shifting of the interventricular septum increasing the LVAD speed.
Figure 4A shows the trends of the total CO and the ratio between LV and RV volumes (LVV/RVV) as a function of LVAD rate. The total CO continuously increases because of the LVAD rate increase, whereas the ratio LVV/RVV continuously decreases evidencing a higher LV unloading. RVV increases as a consequence of LVAD rate increase and of the leftward shift of the interventricular septum. Figure 4B shows the trends of LVEW and RVEW as a function of LVAD rate. The LVEW (RVEW) is decreased (increased) by the increase of the LVAD rate.
Finally, changing the ejection pressure from 100 mm Hg to 200 mm Hg it has been observed: an increase by 3.5% of CO, an increase (decrease) by 6% (10.7%) in RVEW (LVEW), a reduction of 9% (6%) in LVESV (LVEDV), an increase of RVESV and RVEDV of 2.7%. Changing the LVAD filling pressure from 0 mm Hg to –35 mm Hg, it has been observed: an increase of the CO by 4.7%, an increase (decrease) by 3.7% (3.4) in LVEW (RVEW) and no changes in ventricular volumes (<1%). Changing the LVAD systole duration from 30% to 50%, it has been observed that the LVAD emptying improves and therefore the CO is increased by 8% as well as the Pas and the LVESV (LVEDV) is decreased by 15.7% (11%). It has been speculated that the effects of the changes of systole duration depends on the degree of LVAD filling and emptying. In fact, if the pump is working in full filled-full empty condition, the increase of systole duration reduced the VAD filling time, potentially reducing the LVAD CO. On the contrary, if the pump filling is adequate, but the pump emptying is not enough, the increment of the systole duration increases the CO. Finally, if the pump emptying is adequate, but the pump filling is not enough, the decrement of the systole duration could increase the CO. This parameter is also strongly influenced by the ratio between the LVAD rate and the patient rate and further investigation are ongoing on this topic.
Although the LV is unloaded by the presence of the LVAD, the effects on RV are controversial. The LVAD have both beneficial and detrimental effects on RV function. On one side, the reduction of the RV afterload and the increase of the RV preload could lead to a better RV performance.10,18 Jonge et al.22 compared the contractile myofilaments in cardiomyocytes of the LV and RV free walls after 215 ± 143 days of support in 13 adult patients evidencing identical immunohistochemic morphology of the contractile myofilaments between the LV and RV free walls. Kawai et al.23 assessed acute echocardiographic RV function during LVAD implantation in 25 adult patients evidencing a significant increase of RV fractional area changes after the LVAD implantation and discussed the possibility that also a pre-existing RV or interventricular septal pathology or elevated pulmonary vascular resistance could lead to a reduction of RV compensatory ability.18 These assumption was supported also by Mandarino et al.8 and Morita et al.24 Morita et al.24 aimed at studying the mechanism of RV ejection fraction improvement after the LVAD implantation using the ventriculo-arterial coupling in eight adult patients evidencing that the improvement of RV function could be explained by the reduction of the RV afterload leading to a better ventriculo-arterial coupling.24
On the other side, the LVAD causes a leftward shift of the interventricular septum decreasing the contribution of the interventricular septum to the RV systole.8 Moreover, the increase of the total CO because of LVAD could lead to RV overload. Barbone et al.3 studied LV and RV function on 34 adult patients assisted for 77 ± 71 days evidencing that LV volume was substantially decreased and RV volume was significantly increased one month after the implantation. Finally, Arakawa et al.18 tested on seven goats a LVAD counter-pulsation driving modality evidencing that a correction of the interventricular septum shift lead to a better support of the RV contraction. Umeki et al.25 demonstrated that a counter-pulsation mode permits also to decrease the RV afterload.
In our work, we aimed at evaluating the ventricular interdependency in p-LVAD and c-LVAD pediatric population changing the LVAD control parameters. Results evidenced that the LVAD could unload the LV reducing also the LVEW and improving the LV and RV ventriculo-arterial coupling especially in the case of c-LVAD. The LV and RV ventriculo-arterial coupling improvement is more evident with c-LVAD in comparison to p-LVAD. In fact, with p-LVAD, the LV and RV ventriculo-arterial coupling showed only a slight decrement from the baseline to the highest p-LVAD rate: from 5.4 ± 2.4 to 4.2 ± 2.0 for the LV and from 3.1 ± 1.3 to 2.9 ± 1.2 for the RV. Moreover the LVAD causes important changes in LVEW and RVEW passing from the baseline to the highest c-LVAD speed. In particular, LVEW is decreased by 60% by c-LVAD and 30% by p-LVAD, whilst RVEW is increased by 87% by c-LVAD and 15% by p-LVAD. In addition, the c-LVAD (p-LVAD) causes a decrement of LV preload by 50% (2%), an increment of RV preload by 27.3% (9%), an increment of the LV afterload by 48% (7.5%), and a decrement of the RV afterload by 36% (3.6%). The LVAD causes an increase of the RV ejection fraction and a decrease of the RV afterload. However, in the presence of LVAD, the RVEW increases with RV volumes even if the ventriculo-arterial coupling was improved. The changes in RV function are inversely proportional to the degree of the interventricular septum leftward shift that increased by increasing the LVAD contribution (Figure 3). Results reported in this study evidenced the necessity of careful LVAD programming in order to optimize both LV unloading and RV function. The intersection points (Figures 2–4) could represent an indication to optimize LVAD setting to reach a good compromise between the hemodynamic improvement and the RV overload. Optimizing the LVAD parameter setting, it could be theoretically possible to improve both LV and RV function because the LVAD causes a LV unloading, a RV afterload decrease and, consequently, both the LV and RV ventriculo-arterial coupling improvement.
Our study is a simulation study based on baseline data collected retrospectively on pediatric patients and the simulation outcome after the VAD implantation was not compared with measured data. Future work will be dedicated to data collection during the LVAD implantation to verify the model outcomes. Simulation results refer to pediatric population and should be extended to adults. Moreover, the model’s parameters are linear, the effects of the pericardium was neither modeled, nor the effects of autonomic controls and the effects of ventricular cannula position or the influence of regulating systemic and pulmonary resistance. As a consequence, the model could not reproduce the long-term evolution of RV function after changing the LVAD setting. Therefore in the acute phase after the VAD parameter changes (i.e., increase of LVAD speed or LVAD rate) CO, RVEF, and RVEW continue to increase, but the model could not predict a worsening of RV function changing automatically, for example, the end systolic right ventricular elastance. It should be underlined that changing the LVAD speed or the LVAD rate, the total CO increases, but the most important effects are the total CO repartition between the pump and the native ventricle. In this condition, the system works in a narrow band around a working point, thus reducing the effects of assuming linear components.
In this work, we focused on the study of the effect of pump parameters changes on the acute biventricular interaction. In a future work, we will model autonomic control subjects in order to better study the reaction of the cardiocirculatory system to the disturbance represented by the VAD. Moreover, we will deeply study the effects of the ratio of patients’ and LVAD rates and the effects of systole duration.
Finally, the acute hemodynamic changes evaluated in this study are usually small and not always reflect the long-term effects. Therefore, patients could potentially benefit from the periodically interventricular interdependency monitoring and the LVAD setting optimization on the base of the hemodynamics.
Ideally, an LVAD should provide not only a maximum flow support with a good LV unloading, but also a RV function support. The study of the interventricular interaction in the presence of the LVAD could lead to a better pump setting to maximize the benefits on both LV and RV. A numerical models could permit to study the interventricular interdependency and then to develop and test in silico a dedicated LVAD control algorithm.
Group CONAD sponsor of the project entitled “A new Heart.”
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