Acta Polytechnica doi:10.14311/AP.2017.57.0367 Acta Polytechnica 57(5):367–372, 2017 © Czech Technical University in Prague, 2017 available online at http://ojs.cvut.cz/ojs/index.php/ap RELATION BETWEEN LEFT VENTRICULAR UNLOADING DURING ECMO AND DRAINAGE CATHETER SIZE ASSESSED BY MATHEMATICAL MODELING Svitlana Struninaa, ∗, Jiri Hozmana, Petr Ostadalb a Faculty of Biomedical Engineering, Czech Technical University in Prague, Nám. Sítná 3105, 272 01 Kladno, Czech Republic b Cardiovascular Center, Na Homolce Hospital, Roentgenova 2/37, 15030 Prague, Czech Republic ∗ corresponding author: svitlana.strunina@fbmi.cvut.cz Abstract. The flow-dependent left ventricle overload is a well-known complication of the veno-arterial extracorporeal membrane oxygenation in a severe cardiogenic shock, which leads to a distension of the left ventricle and, frequently, to a severe pulmonary edema. Recently, an unloading of the left ventricle using a catheter inserted to the left ventricle and connected to the extracorporeal membrane oxygenation circuit has been proposed. The computational method was used to simulate the blood flow in the extracorporeal membrane oxygenation system with a drainage catheter incorporated to the left ventricle and connected to the inflow part of the extracorporeal membrane oxygenation circuit by a Y-shaped connector. The whole system was modelled in Modelica modelling language. The impact of various catheter sizes (from 5 Fr to 10 Fr) and extracorporeal blood flow values (from 1 L/min to 5 L/min) were investigated. In our simulation model, the extracorporeal blood flow only modestly affected the value of volume that was withdrawn from the left ventricle by a catheter. Conversely, the size of the drainage catheter was the principal factor responsible for the achievement of the adequate left ventricle decompression. A 10 Fr drainage catheter, inserted into the left ventricle and connected to the venous part of the ECMO system, presents a promising solution to the unloading of the left ventricle during a extracorporeal membrane oxygenation. Keywords: catheter; decompression; extracorporeal membrane oxygenation; mathematical modeling; Modelica modeling language; overload. 1. Introduction The heart function improvement following a cardiac support was reported early [1]. The veno-arterial extracorporeal membrane oxygenation (VA-ECMO) currently represents the most effective minimally in- vasive circulatory support system. The VA-ECMO provides a sufficient support to enable an adequate tissue perfusion even in the case of cardiac arrest. However, a marked increase in systemic blood pres- sure caused by the VA-ECMO may also impair the function of the left ventricular (LV). In the presence of a severe left ventricle dysfunction, the left ventricle is unable to eject a sufficient blood volume, this leads to the increased afterload caused by the extracorporeal membrane oxygenation blood flow (EBF) and, conse- quently, to an impairment of the LV performance. In the extreme situation, the aortic valve remains closed even during systole. This results in the LV overload with distension, increased wall stress and increased myocardial oxygen consumption [2]. Insufficient de- compression of the left ventricle during the VA-ECMO is considered as a major factor preventing an adequate LV recovery [3]. Several methods are used for the LV decompression during the VA-ECMO therapy: a sur- gical approach with a minimally invasive thoracotomy, percutaneous approaches via the pulmonary artery or aortic valve, or through a septostomy, percutaneously inserted microaxial pump or intraaortic balloon pump. The LV decompression, during the ECMO therapy, seems to be associated with a significant improve- ment of the LV function [4]. The left ventricle can be unloaded by an insertion of a pigtail catheter into the LV through the aortic valve and connected to the inflow line of the ECMO circuit by an Y-shaped connector [2]. Figure 1 shows the unloading method during the ECMO therapy by the catheter inserted in the LV. There is a lack of information about the impact of the drainage catheter diameter and extra- corporeal blood flow value on the LV decompression by the catheter inserted in the LV. The main objec- tive of this study is to assess the unloading capacities of various diameters of the drainage catheter and various EBF values. Modelica modelling language was employed to identify the association between the catheter diameter and volume value withdrawn from the left ventricle in a big animal model with cardio- genic shock during the ECMO and, consequently, to evaluate the effect of the catheter diameter on the LV unloading. Modelica language is an object oriented, hierarchical, equation based and acausal modeling language, in which models can be created and graph- 367 http://dx.doi.org/10.14311/AP.2017.57.0367 http://ojs.cvut.cz/ojs/index.php/ap S. Strunina, J. Hozmana, P. Ostradal Acta Polytechnica Figure 2. System diagram. PPC – pulses pressure change, LV – left ventricle, RA – right atrium, CAT – vent, VS – volume sensor, VCP – venous circuit part, OXY – oxygenator, ACP – arterial circuit part, AC – arterial cannula, A – aorta, IC – inflow cannula. Oxygenator Drainage catheter Mechanical blood pump Y-shaped connector Figure 1. Unloading method during ECMO therapy by catheter. ically represented from pre-prepared components or by connecting instances of classes from libraries [5, 6]. Modelica language is acausal, which means that the equations can be expressed declaratively and the Mod- elica tool determine which of variables are dependent and independent based on the context upon a compi- lation [7]. The models are prepared to simulate just by a simple setting of the parameters. In the result of the simulation, the user can examine the change of variable values over time [6]. The main problem of medical research, articles, and experiments is using ob- scure units from medicine, pharmacology, biology and non-physics disciplines. One of the advantages of the Modelica environment is the support of non-SI units in the parameter dialog of each component. Values are represented by SI-units in the text code, but the Modelica environment supports non-SI units in the parameter dialog of each component. Physiological units are implemented as the displayUnits for each variable. Using displayUnits, the user can establish and observe the “physiological” values [8]. 2. Materials and methods In this study, a computer model was used to assess the LV unloading capacities of various diameters of drainage catheter inserted in the LV and EBF values. 2.1. Computer model The whole system was modelled in Modelica modeling language, which uses a hierarchical object-oriented modelling. The model is described using the follow- ing compartments: left ventricle, right atrium, aorta, oxygenator, pump, tube set of ECMO system and integrated drainage catheter incorporated into the LV and connected to ECMO system (Figure 2). Each compartment is modelled using a mathematical rela- tionship between blood volume Vi(t), input flow rate Fi(t) and output flow rate Fi,out(t) relative to the ith compartment given as dVi(t) dt = Fi(t) − Fi,out(t). (1) With a flow rate Fij (t) between compartments i and j defined in general by [9] Fij (t) = Pi(t) − Pj (t) Rij , j = i − 1. (2) Analogous to Kirchhoff’s current law, which is applied in the electrical domain, the law sum-to-zero is applied 368 vol. 57 no. 5/2017 Relation Between Left Ventricular Unloading and Drainage Catheter Size Extracorporeal blood flow [L/min] 1 2 3 4 5 End-systolic volume (ESV) [mL] 64 ± 11 70 ± 11 74 ± 11 78 ± 12 83 ± 14 Systolic blood pressure (SBP) [mmHg] 60 ± 7 72 ± 7 81 ± 6 89 ± 7 97 ± 8 LV end-diastolic pressure (EDP) [mmHg] 17.2 ± 1.4 18.2 ± 0.7 18.6 ± 1.5 18.9 ± 2.4 19.0 ± 2.9 Heart rate (HR) 94 ± 4 89 ± 3 84 ± 3 80 ± 2 77 ± 2 Table 1. Initial values of state variables and parameters of the model in Modelica. Figure 3. Withdrawal volume value for cardiac cycle according to the catheter size. The values can be found in Table 2. in the hydraulic domain to the flow variables. The sum of all mass flows at any given point is zero [10] Fin − Fout = 0. (3) The left ventricular pressures were established accord- ing to a single cycle of cardiac activity time given as [11] pressure = diaPressure if tc < TD1, diaPressure + sin ( tc − TD1π ) (sysPressure − diaPressure) if tc < TD2, diaPressure otherwise. (4) The blood flow in the system components can be completely described by Hagen–Poiseuille equation. The equation brings together all of the variables that determine flow Q = π∆Pr4 8µL . (5) Hagen–Poiseuille equation states that the maximum flow is inversely proportional to the lumen length and directly proportional to the fourth power of the radius for a circular cross-section of lumen [12]. The radius and length of components were various, as a consequence of required quantities. The dynamic viscosity of blood 0.001 Pa s was chosen [13]. The pump element was used from Modelica library for physiological calculations — Physiolibrary. For the simulation purpose, the pump flow rate was gradually increased from 1 L/min to 5 L/min. The oxygenator was modelled as a compartment with a pressure gradient. ∆P = Pin − Pout. (6) The simulation in this study is based on data from a standard in vivo experiment on large animal models. The initial parameter values were derived from mea- surements on a female swine [14]. The parameters for the simulations are presented in Table 1. 2.2. Model output The output variables consisted of time-varying flow rate value and pressure in different parts of the ECMO circuit and time-varying volume value withdrawn from the LV. The values are presented in the following units: time-varying flow rate value in ml/s and volume value withdrawn from the LV in ml. 2.3. Simulations For the simulation purpose, the pump volume flow rate was gradually increased from 1 L/min to 5 L/min 369 S. Strunina, J. Hozmana, P. Ostradal Acta Polytechnica Figure 4. The effect of veno-arterial extracorporeal membrane oxygenation blood flow on withdrawal volume value for cardiac cycle. The values can be found in Table 2. (Table 2). For each value of the extracorporeal blood flow, the value of systolic blood pressure, the LV end- diastolic blood pressure and heart rate were changed in accordance with the obtained data from the exper- iment on big animal models. The internal diameter of the drainage catheter was gradually increased from 5 Fr to 10 Fr (Table 2) for a various EBF value. The entire process was done for each unique combination of the EBF, catheter size and vital parameters. 3. Results The conducted study indicates that the size of the drainage catheter is a crucial factor when the insertion of a pigtail catheter into the LV through the aortic valve is used as a method of the LV decompression during the ECMO therapy. Figure 3 depicts the with- drawal volume value for the cardiac cycle according to the catheter size. The results of the simulation have indicated that the EBF does not greatly affect the withdrawal volume value from the LV by drainage catheter. The relationship between the withdrawal volume value for the cardiac cycle and the EBF is shown in Figure 4. Figure 5 depicts the flow rate profiles throughout the cardiac cycles and the varying-in-time volume value withdrawn from the LV by the drainage catheter according to the catheter size. The red circles depict the volume values withdraw from the LV for a one cardiac cycle. Table 2 presents the simulation results of volume values withdrawn from the LV for a one cardiac cycle. The drainage catheter size ranges from 5 Fr to 10 Fr, the EBF value varies from 1 L/min to 5 L/min. The outcomes of the simulation have shown that the 10 Fr drainage catheter withdraws 5.38 ± 0.76 ml during one cardiac cycle during the EBF from 1 L/min to 5 L/min (Table 2). Extracorporeal blood flow EBF [L/min] 1 2 3 4 5Drainage catheter size [Fr] Blood withdrawal for cardiac cycle [ml] 5 0.25 0.27 0.32 0.36 0.41 6 0.52 0.58 0.67 0.76 0.85 7 0.96 1.06 1.24 1.41 1.56 8 1.63 1.82 2.12 2.41 2.67 9 2.63 2.90 3.37 3.84 4.26 10 3.96 4.37 5.08 5.78 6.41 Table 2. Volume rate value withdraw from LV during VA ECMO in Modelica. 4. Discussion An increase of the LV afterload, together with severe systolic dysfunction during the VA-ECMO, often re- quires an urgent LV unloading. A number of sources mention that the drainage catheter is successfully used for the LV unloading during the ECMO therapy [3, 16– 20], but there is very little knowledge of the catheter size for an adequate LV unloading. This study was focused on the withdrawn blood volumes from the LV for a one cardiac cycle. One common complica- tion of the ECMO is the LV overload and distention, primarily due to the increased afterload caused by the EBF [2]. The ECMO application causes an in- crease of end-systolic volume (ESV) and can induce deterioration of LV the function [1]. The end-systolic volume is the amount of blood left in the ventricle at the end of the contraction [15]. Therefore, the objective was to identify the appropriate size of the drainage catheter for the extraction of the excessive 370 vol. 57 no. 5/2017 Relation Between Left Ventricular Unloading and Drainage Catheter Size Figure 5. Flow rate profiles throughout the cardiac cycle and varying in time volume value withdraw from LV by drainage catheter, EBF 3 L/min. ESV, to maintain adequate emptying of the LV at the end of each cardiac cycle, and thereby decompres- sion of the LV during the ECMO. As you can see in Table 1, with an increase of the EBF from 1 L/min to 5 L/min, the LV end-systolic volume increases, at average, to 4.75 ± 0.95 milliliters per liter (Table 1). The outcomes of the simulation have shown that the 10 Fr drainage catheter withdraws 5.38 ± 0.76 ml dur- ing one cardiac cycle during the EBF from 1 L/min to 5 L/min (Table 2). Thereby, the 10 Fr catheter presents a promising solution to achieve the purpose of the LV unloading during the ECMO by a drainage catheter inserted in the LV and connected to the ve- nous part of the ECMO system. The present study demonstrates that the withdrawal volume value by drainage catheter, connected to the inflow part of the ECMO system, depends mainly on the size of the catheter. The EBF did not demonstrate a notable effect. When the catheter diameter was kept constant and the EBF varied, the flow in the drainage catheter varied marginally. The limitations of the study are related to the mathematical model. Created model replicates the general specification of the flow in the ECMO circuit. The model does not completely be- have the same way as the ECMO system. It has been assumed that blood is modelled as an incompressible, Newtonian fluid. The flow is considered to be laminar with no acceleration of the fluid in the ECMO cir- cuit, gravitational effects were neglected. To make the study results clinically feasible, future work should be verified with the ECMO system specific model. 5. Conclusions Unloading capacities of various drainage catheter di- ameters and various EBF values during the ECMO by applying a numerical method is presented in this paper. The results suggest that the catheter diame- ter is the crucial factor when an insertion of a pigtail catheter into the LV through the aortic valve is used as a method of the LV decompression during the ECMO therapy. The EBF hardly affects a withdrawal vol- ume value by the drainage catheter from the LV. The model used in the presented work provides interesting answers to the question regarding determining param- eters in the ECMO circuit. The model can predict details of the pressure, withdrawal volume and flow rate value at any position in the system throughout the cardiac cycles. List of symbols Vi Blood volume [m3] Fi,in Input flow rate [m3/s] Fi,out Output flow rate [m3/s] Fij Flow rate between compartments i and j [m3/s] Pi Pressure of compartment i [Pa] Pj Pressure of compartment j [Pa] Rij Resistance between compartments i and j [(N/m2) (m3/sec)−1] Fin Input flow [m3/s] Fout Output flow [m3/s] diaPressure Diastolic blood pressure [Pa] sysPressure Systolic blood pressure [Pa] 371 S. Strunina, J. Hozmana, P. Ostradal Acta Polytechnica tc Relative time in cardiac cycle [s] TD1 Relative time of start of systole [s] TD2 Relative time of end of systole [s] Q Volumetric flow rate [m3/s] µ Dynamic viscosity [Pa s] r Pipe radius [m] L Length of pipe [m] ∆P Pressure reduction [Pa] Pin Input pressure [Pa] Pout Output pressure [Pa] References [1] S. Vandenberghe, P. Segers, B. Meyns and P. Verdonck. 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