Modeling Unloading of the Left Ventricle by the Levitronix CentriMag LVAS using a Cardiovascular Simulator

Transcription

1 Modeling Unloading of the Left Ventricle by the Levitronix CentriMag LVAS using a Cardiovascular Simulator BMTE Lieke Cox Sandra Loerakker Internship at the Texas Heart Institute, Houston, USA Supervisors Eindhoven University of Technology: dr. ir. P.H.M. Boveerd prof. dr. ir. F.N. van de Vosse Supervisor Texas Heart Institute T.J. Myers, BS In collaboration with the Department of Cardiothoracic Surgery, Academic Medical Center, Amsterdam, The Netherlands

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3 Abstract The goal of this study was to evaluate if it is possible to simulate unloading of the heart by an assist device. For this goal, a Cardiovascular Simulator was used, that modeled the left atrium and ventricle, and the systemic circulation. With this Cardiovascular Simulator, dilated cardiomyopathy was simulated, after which the Levitronix CentriMag Left Ventricular Assist System (LVAS) was connected to the Simulator. Furthermore, the time-varying elastance model as described by Suga and Sagawa [1,2] was used to quantify and simulate the reaction of the left ventricle to the assist device. To simulate preload depence of the ventricular filling, air-filled ventricular balloons were used. Different simulation series were performed for a range of assist device speeds (0 3,000 rpm) under different conditions: series 1 and 2 without ventricular compliance and respectively constant and decreasing stroke volumes for each subsequent simulation, and series 3 and 4 with ventricular balloons for compliance and also constant (series 3) and decreasing (series 4) stroke volumes. For each simulation, the aortic pressure, the left ventricular pressure, the flow through the assist device, the flow generated by the ventricle, the total aortic flow, and the left ventricular volume were determined. From these data, other characteristics such as the stroke volume, the ejection fraction and the workload of the left ventricle were deduced. A decrease of the workload of the ventricle was used as criterion for unloading and the other data were used to interpret the changes in workload. Although the workload decreased for increased assist device speeds in simulation series 2 and 4, this did not prove that unloading of the ventricle by an assist device was simulated. The reason for this is that the decreases in stroke volume were chosen arbitrarily instead of dictated by the elastance model, due to limitations of the Cardiovascular Simulator, which made it impossible to attribute the decrease in workload to the assist device. Only one simulation (series 3 at 3,000 rpm) showed a decrease of the workload at a constant stroke volume and therefore proved unloading of the ventricle by the assist device. Although this particular simulation did show that ventricular unloading by an assist device can be simulated with the Cardiovascular Simulator, other simulations showed that unloading can only be simulated in case the aortic valve no longer opens because of both the rigidity of the ventricle, and even more important, the passive filling mechanism of the ventricle. For this reason, for future research, the Cardiovascular Simulator should be altered so that it contains a compliant ventricle and ensures active filling of the ventricle which makes it possible to change the preload of the ventricle. With this adjusted Simulator it would be possible to investigate the influence of different assist devices on the workload and the left ventricular and aortic pressures and flows.

4 Table of contents Abstract... 0 Section 1: Introduction... 2 Section 2: Materials and Methods Cardiovascular Simulator Description of components HemoLab software Operation of the Cardiovascular Simulator Physiological signals Pressure and flow signals Left ventricular pressure-volume loop The time-varying elastance model of the heart Frank-Starling mechanism Time-varying elastance model Use of the ESPVR to simulate the human heart Use of the ESPVR in the Cardiovascular Simulator Simulations Limitations of the Cardiovascular Simulator Compliance of the ventricular chamber Simulations with Levitronix CentriMag LVAS Levitronix CentriMag Set-up of the Levitronix CentriMag LVAS Adjusting Cardiovascular Simulator settings Simulation of dilated cardiomyopathy Dilated cardiomyopathy Calculation of variables Simulations Section 3: Results Simulation with a constant amplitude of piston movement Simulation with a decreasing amplitude of piston movement Simulation with a constant amplitude of piston movement and ventricular balloons Simulation with a decreasing amplitude of piston movement and ventricular balloons Section 4: Discussion Discussion of each of the four simulation series Discussion simulation series Discussion simulation series Discussion simulation series Discussion simulation series Comparison simulation series Influence of an increase in amplitude of the piston movement Influence of balloons in the ventricular chamber General discussion Section 5: Conclusions References Appix A: Calibration A.1 Calibration servomotor A.2 Calibration flow sensors A.3 Calibration pressure sensors A.4 Calibration balloons Appix B: Data processing B.1 Pressure and flow signals B.2 Left ventricular pressure volume loop Appix C: Matlab programs C.1 Physiologicalsignals.m C.2 Elastancemodel.m C.3 Assistdevice.m Appix D: Mathematical model

5 Section 1: Introduction In case of severe heart failure, when medical therapy is insufficient, sometimes a mechanical assist device is used to improve the condition of the patient [3,4,5]. The assist device is supposed to unload the heart, usually by pumping blood out of the ventricle into either the systemic or pulmonary circulation. Although it is possible to investigate the unloading mechanism in patients [6,7,8], it is difficult to compare the unloading effects of different assist devices, because they are all implanted in different patients. A potential solution would be to use a mock-loop to compare the unloading effects of different assist devices under equal circumstances. Because most assist devices are developed for supporting the left side of the heart [4,8], since the left ventricle has the highest workload and usually fails before the right ventricle does, a Cardiovascular Simulator was used that modeled the left atrium and ventricle, and the systemic circulation. Firstly, this Cardiovascular Simulator was used to generate physiological pressures and flows, i.e. model a healthy heart. When these physiological pressures were obtained, the piston movement that simulated the contraction of the left ventricle, was adjusted according to the time-varying elastance model [1,2]. This adjustment was necessary to be able to simulate the reaction of the heart to an assist device. After implementation of the elastance model, the Cardiovascular Simulator settings were changed to model dilated cardiomyopathy, a common form of heart muscle disease [9,10,11], since it is useless to connect an assist device to (the model of) a healthy heart. Finally, an assist device, the Levitronix CentriMag LVAS [12,13] was connected to the adjusted Cardiovascular Simulator. For this configuration, different simulation series were performed to simulate the reaction of the failing heart to the assist device, at varying assist device speeds, under different simulation conditions. The changes in simulation conditions included changes in stroke volume and compliance of the ventricle. For all simulations, the aortic pressure, the left ventricular pressure, the flow through the assist device, the flow generated by the ventricle, the total aortic flow, and the left ventricular volume were determined. From these data, other characteristics such as the stroke volume, the ejection fraction and the workload of the left ventricle could be deduced. The overall goal of this first study was to investigate if it was possible to model unloading of the heart by an assist device with the Cardiovascular Simulator. As the criterion for unloading of the ventricle, a decrease in workload was chosen. In section 2, the materials and methods used in this study are described, in section 3 the results of the different simulations are shown, in section 4 these results are discussed, and in section 5 conclusions are drawn. 2

6 Section 2: Materials and Methods 2.1 Cardiovascular Simulator Description of components For the measurements performed in this study a Cardiovascular Simulator (HemoLab), financially supported by the department of cardiothoracic surgery, Academic Medical Center Amsterdam, was used that simulated the left side of the heart and the systemic circulation, see figure 1 and 2. Figure 1: Overview of the Cardiovascular Simulator, as used at the Texas Heart Institute. Compliance chamber Adjustable resistances Atrium Aorta Servomotor Piston Aortic valve Mitral valve Left ventricle Vein Assist device connection Figure 2: Close-up of the mock-loop. 3

7 The Cardiovascular Simulator consisted of several components that are indicated in figure 2: Servomotor Compliance chamber Left ventricle Atrium Aorta Vein Adjustable resistances Valves Assist device connection The Servomotor controlled a piston that transferred a volume change to the ventricular chamber. A thin-walled polyurethane tube (representing the aorta) connected the aortic outlet port of the (left) ventricle to the inlet port of the compliance chamber. Rubber o-bands were used to obtain fixation of the aorta. A thick-walled PVC tube was used to connect the outlet port of the compliance chamber to the atrium. The atrium and left ventricle were interconnected via a PMMA (Plexiglas) tube (representing the veins), hereby closing the flow loop. The Servomotor was supplied with limit switches that prevented motion of the axis that could result in damage to the axis and its guiding system. Correct connection of the limit switches is described in more detail in the HemoLab manual [14]. In the compliance chamber, two variable resistances were present. Furthermore, a stopcock at the top of the compliance chamber could be used to set the fluid level inside the compliance chamber, thereby altering the compliance. The pressure and flow waves could be influenced by the two resistances, the amount of air entrapped inside the compliance chamber, the length and material properties of the model aorta used, and the piston movement. Furthermore, the following equipment was used to run the simulator and measure pressures and flows, see figure 3: Motion Controller board Data Acquisition board HemoLab software (LabView) Servo controller Connector box Limit switches BNC 2110 (National Instruments, part no: F-01, serial no: 113EFB1) Voltage converter (Simran, model: SM-500DE) Flow sensor (Transonic Systems Inc., Model number T106, Serial number T106 S A11894) Pressure sensors (not shown) Transducer (Gould Instrument Systems, model: , serial: 373) The Motion Controller board and Data Acquisition board were inserted in two empty PCI slots of a computer. From the PC (HemoLab software and Motion Controller board) the movement of the Servomotor was controlled via the connector box and the Servo controller, and the data measured by the pressure and flow sensors were 4

8 received via the transducer, BNC-2110 and the Data Acquisition board. In figure 3 a schematic representation of the components described above is given. Connector box Servo controller Motion Controller board Servomotor Personal Computer Cardiovascular Simulator Data Acquisition board Flow probe Pressure wire BNC-2110 Transducer Flow sensor Pressure sensor Figure 3: Schematic representation of Cardiovascular Simulator setup. The exact procedure of making the connections between the components can be found in the HemoLab manual [14] HemoLab software In the HemoLab software program the piston movement, as well as the signals to be recorded, and the length of the simulation were adjustable. Figure 4 displays the layout of the computer program. The piston movement was prescribed in a file with the piston coordinates. This file contained 100 sample points (normalized displacements from the origin) and the piston followed all these coordinates each second, resulting in 60 heart beats per minute (bpm). Initially, the file pulse_generator_100.dat was used. The graphical representation of this displacement file is shown in the figure below in the Loaded trajectory screen. Since the displacement file contained normalized coordinates, the amplitude of the piston movement was adjusted by the Amplitude (encoder counts) knob, where 25,000 counts (cts) corresponded with 6 cm. The number of cycles performed during a simulation was also set. The data channels that were displayed in the Acquired Data window were selected from the Physical Channels scroll button. Furthermore, the data of one particular channel could also be displayed separately in the Selected Channel window. Because the HemoLab software obtained the data in Volts, some data processing was needed to change these values in pressure (mm Hg) and flow (L/min) units. The Servomotor and the pressure and flow sensors were calibrated prior to starting any simulations. These calibrations are described in Appix A.1, A.2, and A.3. 5

9 The Start/Stop Motion button was used to start and stop simulations. With the Save data switch it was possible to save the recorded data to a text-file. Figure 4: HemoLab software used to perform simulations Operation of the Cardiovascular Simulator When the piston was moved forward by the Servomotor, the volume of the left ventricle became smaller. Due to the decrease in ventricular volume, water was moved through the aortic valve into the aorta. When the piston moved backwards again, water was sucked out of the atrium via the mitral valve into the ventricle, so the ventricle was always completely filled with fluid. From the aorta, the water had to pass a resistance to enter the compliance chamber. The compliance in this chamber consisted of the air volume that was compressed when new water entered the chamber. To leave the chamber, the water had to pass the peripheral resistance to enter the veins. After this it was transported to the atrium, where it subsequently entered the ventricle again. 6

10 2.2 Physiological signals Pressure and flow signals In order to obtain physiological pressure and flow signals, adjustments were made to the Cardiovascular Simulator. As described in section Description of Components, these adjustments included changes in the resistances, in the amount of air entrapped inside the compliance chamber, in the length and material properties of the aorta, and in the movement of the piston. The calibration equation of the Servomotor (Appix A.1) was used to determine that for a stroke volume of 70 to 80 ml, the amplitude of the piston movement should be set between approximately 17,500 and 20,000 cts. However, the Servomotor was unable to perform the movement at these amplitudes, due to the high speed and acceleration of the piston that were needed. To solve this problem, a different input file was created. This new input file was a sin 2 function Figure 5: New normalized displacement signal used as input to the Servomotor with its maximum shifted to the left as can be seen in figure 5. This maximum was chosen at sample point 40 because this resulted in the best resemblance of the previous input file that could be used at higher amplitudes: x t u piston sin sin t 4T 1 t 1 2T 4 4T T 1 t t T 1 1 (1) Here, x(t) is the normalized displacement at time point t, u piston is the amplitude of the piston movement in cts, and T 1 is the time point in s where the normalized displacement has its maximal value. Since a different input file might also lead to a different relationship between the amplitude of the piston movement and the stroke volume, the Servomotor was recalibrated using the method described in Appix A.1, only this time at 10,000, 12,500, 15,000, and 17,500 cts. This resulted in new calibration coefficients with an R 2 value of : V c u S 1 piston c 2 (2) Here V S is the stroke volume in ml, u piston the amplitude in cts and c 1 and c 2 are calibration coefficients. After recalibration of the Servomotor, the amplitude of the piston movement was set at 18,500 cts which was the highest number of cts at which the piston movement could be performed, even for the new input file. This movement resulted in a stroke volume of approximately 75 ml and a flow of approximately 4.5 L/min. 7

11 For obtaining physiological pressure signals, the pressure waves shown in figure 6A were used as an example. After some fine-tuning, the pressure signals as shown in figure 6B were obtained with the Cardiovascular Simulator, which seem to correspond reasonably to the reference signals. Figure 6: A) Physiological pressure signals as found in literature [15]; B) Pressure signals obtained with the Cardiovascular Simulator. Furthermore, the flow signal as found in literature (figure 7A) and the flow signal obtained with the Cardiovascular Simulator (figure 7B) are similar as well. The data processing that was performed on the data acquired with the HemoLab software is described in Appix B.1. Figure 7: A) Physiological flow aortic flow signal as found in literature [15]; B) Aortic flow signal as obtained with the Cardiovascular Simulator Left ventricular pressure-volume loop The data obtained with the settings used for the signals in figure 6B and 7B were also used to make a left ventricular pressure-volume loop, as can be seen in figure 8B. The volume of the ventricle was not measured during the simulations but could be deduced from the piston displacement because of the rigidity of the ventricular chamber of the Cardiovascular Simulator. The -diastolic volume (begin point of each simulation) was chosen at 120 ml and at each subsequent point in time, the volume was calculated using the volume change imposed by the piston movement. This -diastolic volume of 120 ml did not correspond to the actual ventricular diastolic volume of the Cardiovascular Simulator, which was approximately 1.3 L. 8

12 However, because the -diastolic volume value does not influence the course of the loop (it only induces a shift on the horizontal axis), the -diastolic volume was set at a physiological value of 120 ml. Figure 8: A) Left ventricular pressure volume loop as found in literature [16]; B) Left ventricular pressure-volume loop as obtained with the Cardiovascular Simulator. When the pressure-volume loop in figure 8B is compared with the pressure-volume loop in figure 8A, some differences in the shape of both graphs can be noticed. The main difference is that the pressure-volume loop generated with the Cardiovascular Simulator does not show isovolumic contraction and relaxation. This is caused by the rigidity of the ventricular chamber that ensured that the left ventricular volume constantly changed along with the movement of the piston. The exact data processing used to plot the pressure-volume loop is described in Appix B.2 and the Matlab program used for both the pressure and flow signals and the pressure-volume loop can be found in Appix C.1. 9

13 2.3 The time-varying elastance model of the heart After determining the Cardiovascular Simulator settings that led to physiological signals, a method had to be developed to simulate the reaction of the heart to changes in either pressure or flow. This was necessary, because the initially the Cardiovascular Simulator always performed the same piston movement, resulting in a constant stroke volume indepent of pre- and afterload. Because this is not physiological, the timevarying elastance model was implemented to adjust the movement performed by the piston in the Cardiovascular Simulator. This mechanism should make it possible to model heart disease and the response of the heart (up to a certain degree) to an assist device. The Frank-Starling mechanism is also included in the time-varying elastance model, so both mechanisms will be described below, as well as the implementation of the time-varying elastance model in the Cardiovascular Simulator Frank-Starling mechanism When the human body is at rest, the heart pumps approximately 4 to 6 liters of blood each minute [15]. However, during exercise, the heart may be required to pump much more blood. Therefore, a regulatory mechanism is needed to adjust the amount of blood that the heart pumps each minute to the demands of the body. One of these mechanisms is the Frank-Starling mechanism, which basically means that the more the heart is filled during diastole, the larger the quantity of blood pumped into the aorta will be [15]. When an extra amount of blood flows into the ventricles, the cardiac muscle is stretched to a greater length, which leads to a more optimal alignment of the actin and myosin filaments, see figure 9. Subsequently the muscle is able to contract with increased force and as a result of this, the stroke volume and cardiac output of the heart also increase [15]. Another very important mechanism to increase the cardiac output is to increase the heart rate. However, this mechanism was out of the scope of this paper. Figure 9: When the -diastolic left ventricular volume increases, the sarcomeres become stretched which leads to a better alignment of the actin and myosin filaments. This results in a larger contractile force and also a larger stroke volume [17]. 10

14 2.3.2 Time-varying elastance model The time-varying elastance model was developed by Suga and Sagawa, who described the contraction of the ventricle in the pressure-volume plane as an elastance that varies over the cardiac cycle [1,2]. Elastance is a measure of cardiac muscle stiffness. In diastole, the muscle is relaxed and the stiffness is low; in systole, the muscle contracts and becomes stiffer [18]. In the early 1970s Suga and Sagawa found that the isochronic points (points recorded after a given time from onset of contraction) in different contractions are located on a single line, characterized by its slope and intercept with the volume axis, see figure 10. The slope is the ratio of the increase in ventricular pressure and the associated increase in ventricular volume, and has the dimensions of stiffness or elastance (E; mm Hg/mL) [18]. The line connecting all -systolic points on the pressure-volume curves is called the End-Systolic Pressure Volume Relationship (ESPVR) and the line through the diastolic points is called the End-Diastolic Pressure Volume Relationship (EDPVR) [18]. The intercept with the volume axis was considered a correction volume (V 0 ). Stepping through the cardiac cycle, the intercept with the volume axis remains quasiconstant, while the slope varies from a low value in diastole to a maximal value reached at the of ejection. Furthermore, after normalizing the time-varying elastance curve E(t) with respect to amplitude (E N = E/E max ) and timing of the peak (t N = t/t Emax ), it was demonstrated that the intrinsic shape was essentially constant within one species and in a large range of cardiac diseases [18]. The time-varying elastance model can be considered as a global cardiac muscle property, or as a constitutive equation for the ventricle that linearly relates ventricular volume to intracavity pressure [18]. E t V lv p t lv t V 0 (3) Here, E(t) is the time-varying elastance in mm Hg/mL, p lv (t) is the time-varying pressure in the left ventricle in mm Hg, V lv (t) is the time-varying volume of the left ventricle in ml and V 0 is the point in ml where all lines of the elastance model intersect the volume axis. 11

15 Figure 10: Time-varying elastance concept as elaborated by Suga and Sagawa. A) The markers on a line indicate isochronic points on the different pressure-volume loops. The slope of the line varies in a cyclic way, while the intercept with the volume axis (V 0 ) remains constant; B) The slope of the line, which is equal to the elastance E(t), is shown in time; C) E(t) is normalized with respect to the amplitude and timing of the peak. [18] Pressure-volume loops with a smaller -diastolic volume are smaller, as can be observed from figure 10, since a smaller -diastolic volume leads to a smaller stroke volume. The relation between the -diastolic volume and stroke volume is also a characteristic of the Frank-Starling mechanism Use of the ESPVR to simulate the human heart In this study the ESPVR was used to simulate the human heart instead of the EDPVR. The reason for this was that the -diastolic pressures measured during the simulations were very low (even negative), which was caused by a lack of preload. The only option to increase the preload was to raise the water level in the atrium. However, the added water became distributed over all components, thereby changing the relationship between the stroke volume and the -systolic pressure. Since this would make it impossible to calculate the shift in -diastolic volume according to the ESPVR, it was decided only to take the ESPVR line into account. plv, ES Emax ( Vlv, ES V0 ) (4) Here, p lv,es is the -systolic pressure in the left ventricle in mm Hg, E max is the maximal elastance in mm Hg/mL, V lv,es is the -systolic volume of the left ventricle in ml and V 0 is the correction volume in ml. The -systolic volume can be calculated as follows: V lv, ES Vlv, ED VS (5) Here, V lv,ed is the -diastolic volume of the left ventricle in ml and V S is the stroke volume in ml, which is calculated as: 12

16 V V V V ) (6) S S, ref ( lv, ED lv, ED, ref Here, V S,ref is the stroke volume of the left ventricle at the reference situation which was used to calculate E max, is the slope of the Starling curve and V lv,ed,ref is the diastolic volume at the reference situation. dv dv S lv, ED (7) Here, dv S is the change in stroke volume in ml and dv lv,ed is the corresponding change in -diastolic volume in ml Use of the ESPVR in the Cardiovascular Simulator First, a pressure-volume loop of the reference situation (u piston = 18,500 cts, V S = 87 ml, V lv,ed = 120 ml) was made. The left ventricular pressure was measured while the left ventricular volume was calculated using the input file (see Pressure and flow signals). In this study, V 0 was chosen to be the origin of the pressure-volume plane (V lv = 0 ml and p lv = 0 mm Hg), because no general value for humans was found for V 0. V 0 and the -systolic point (minimal volume, V lv,ed is the maximal volume) of the reference pressure-volume loop were used to calculate the ESPVR. This is shown in figure 11. Figure 11: Determination of the ESPVR. It is defined by the elastance concept that each -systolic point of different pressure-volume loops is situated on the ESPVR. A change in stroke volume leads to a change in left ventricular pressure. The new pressure-volume loop is shifted over the volume-axis so that the -systolic point reaches the ESPVR. The left ventricular volume is calculated for each simulation. The calculated theoretical shift over the volume axis led to a new -diastolic volume, which was used to perform new simulations, see figure

17 A B Figure 12: Shift of pressure-volume loops. A) Unshifted loops; B) Shifted loops. However, since the ventricular chamber in the Cardiovascular Simulator was totally rigid, a change in initial ventricular volume does not influence the pressure, see figure 13. Therefore, it is not necessary to really change the -diastolic volume of the ventricular chamber. Instead, it is sufficient to calculate the change. Figure 13: Series of simulations where the amplitude of the piston movement as well as the diastolic volume were adjusted. To calculate the shift over the volume-axis, the relation between stroke volume and -systolic pressure was determined. In the Cardiovascular Simulator this was a linear relation, which can be seen in the figure below. Figure 14: Relationship between the amplitude of the piston movement and the -systolic pressure in the left ventricle. 14

18 So the -systolic pressure in the left ventricle was calculated with the following equation: plv, ES c1 u piston c2 (8) Here, p lv,es is the -systolic pressure in the left ventricle in mm Hg, u piston is the amplitude of the piston movement in cts and c 1 and c 2 are calibration coefficients. The -diastolic volume that matches the elastance model could be calculated by adding the stroke volume to the -systolic volume. Only this stroke volume was not the stroke volume described in section Pressure and flow signals, which was the actual water volume that passed the aortic valve each second, but the water volume that was displaced by the piston each second. These two volumes are not equal because of the leakage of the valves. The displacement volume of the piston per count could be calculated since an amplitude of the piston movement of 25,000 cts corresponded to 6 cm and the cross-section of the piston was 19.6 cm 2 : u cm u u piston, cm piston, cts (9) Here, u cm is the displacement of the piston in cm/ct, u piston,cm is the displacement of the piston in cm and u piston,cm is the displacement of the piston in cts. V S, piston x cm A u piston (10) Here, V S,piston is the displacement volume of the piston in ml, x cm is the displacement of the piston in cm/ct, A is the cross-section of the piston in cm 2 and u piston is the amplitude of the piston movement in cts. V S,piston was used to calculate the diastolic left ventricular volume: V lv, ED Vlv, ES VS, piston V p lv, ES,18500 lv, ES,18500 p lv, ES V S, piston (11) Here, V lv,ed is the -diastolic volume of the left ventricle in ml, V lv,es is the systolic volume of the left ventricle in ml, V S,piston is the displacement volume of the piston in ml as described in equation (10), V lv,es,18500 is the -systolic volume of the left ventricle in ml with an amplitude of the piston movement of 18,500 cts, p lv,es,18500 is the -systolic pressure in the left ventricle in mm Hg with an amplitude of the piston movement of 18,500 cts, and p lv,es is the -systolic pressure in the left ventricle in mm Hg as described in equation (8). The initial position of the piston was set at 0 cts. So in order to decrease the diastolic volume, the initial displacement of the piston had to be calculated to change the volume of the ventricle to become equal to the -diastolic volume as calculated in equation (11). V lv ED Vlv, ED,0 Vlv, ED, (12) 15

19 Here, V lv,ed is the change in -diastolic volume of the left ventricle in ml, V lv,ed,0 is the initial -diastolic volume of the left ventricle in ml, V lv,ed is the -diastolic volume of the left ventricle in ml. The shift of the initial piston position along the axis was calculated as: u Vlv, ED, (13) A u ED cts cm Here, u ED,cts is the shift of the initial piston position in cts, V lv,ed is the -diastolic volume change of the left ventricle in ml, A is the cross-section of the piston in cm 2, and u cm is the displacement of the piston in cm/ct. In figure 15 the relation between the stroke volume and the -diastolic volume is shown, which is the Frank-Starling curve of the Cardiovascular Simulator. This curve is linear instead of rounded, but around normal conditions (V lv,ed = 120 ml and V S = 75 ml), when it is compared with the curve in figure 9, this line seems to be within the physiological range. Figure 15: Frank-Starling curve of the Cardiovascular Simulator Simulations Some simulations were performed using the equations described in previous paragraphs. In one series of simulations the amplitude of the piston movement was successively chosen to be 15,500, 16,500, 17,500 and 18,500 cts, while the diastolic volume was changed according to the equations described above. When the piston was shifted at the beginning of a simulation, water was extracted from the Simulator to compensate for the smaller ventricle, because otherwise the relation between the amplitude of the piston movement and the -systolic pressure would change. In another series only the amplitude of the piston movement was changed, because it was expected that the shifts of the piston in the previous series of simulations would not have any effect on the results. Therefore the -diastolic volumes in the next series were only calculated. The results of both series of simulations are shown in figure

20 A B Figure 16: A) First series of simulations where the amplitude of the piston movement as well as the -diastolic volume were adjusted; B) Second series of simulations where only the amplitude of the piston movement was adjusted while the -diastolic volume was calculated. As can be observed from figure 16, the results of both series of simulations are almost identical. For this reason it was decided to only calculate the shifts in -diastolic volume in future simulations, instead of really altering the volume, because a single shift of the piston at the beginning of a simulation apparently did not make any real difference. The implemented elastance model makes it possible to calculate the stroke volume and -diastolic volume that will lead to a certain -systolic pressure or vice versa, which should be helpful in simulating the reaction of the heart to an assist device. The Matlab program elastancemodel.m that was used to generate the pressure-volume loops according to the elastance model as described above can be found in Appix C.2. The elastance curves of the Cardiovascular Simulator are shown in figure 17. The normalized elastance curve in figure 17B is quite similar to figure 10C. A B Figure 17: A) Elastance curve of the Cardiovascular Simulator; B) Normalized elastance curve of the Cardiovascular Simulator. 17

21 2.3.6 Limitations of the Cardiovascular Simulator According to the elastance concept, the heart should react to a larger -diastolic volume by raising its stroke volume. In the Cardiovascular Simulator however, the ventricle consisted of a rigid chamber where the volume could only be changed by the piston movement. Since the piston performed the same movement each second, the -diastolic left ventricular volume was always the same and therefore the stroke volume would not change either. Nor would the -diastolic pressure, due to passive filling from the atrium. For this reason it was attempted to add more compliance to the ventricular chamber by using balloons filled with air. This is described in the next section. 18

22 2.4 Compliance of the ventricular chamber The ventricular chamber was surrounded by rigid walls and a rigid (although moving) piston, and because the ventricle was completely filled with water, there was no compliance of the ventricle at all. It would have been better if the ventricle had had some compliance, because then it would have been possible to change the diastolic volume according to the preload. Therefore, some balloons filled with air were added to the ventricle, because air was expected to become compressed at physiological pressures. After several attempts (Appix A.4), two balloons were filled with only 80 ml of air each, so the stress on the balloon surface (which could reduce the air volume) would be minimal. The balloons were filled using a three-way stopcock, a small plastic tube and umbilical tape. One balloon was connected to an of the stopcock via the plastic tube (tightened with umbilical tape) and the other balloon was directly connected to another of the stopcock. A 30 ml syringe was connected to the third of the stopcock to push air into the balloons by adjusting the switch of the stopcock, see figure 18. The reason for using balloons to put the air into the ventricle was that the air could not leak through the aortic valve. Figure 18: Filling the balloons with a certain amount of air. Boyle s Law was used to calculate the pressure that was needed to reduce the air volume in the balloons to a certain amount: p V C (14) Here, p is the pressure in Pa, V is the volume in m 3 and C is a constant in J. Then for one balloon filled with 80 ml (at an atmospheric pressure of Pa) it can be calculated that: 5 5 C p V J (15) When the air volume would be reduced (by compression) with 20 ml (V = ), this would lead to a pressure of Pa, or 35 kpa above atmospheric pressure, which leads to a passive elastance of Pa/m 3. 19

23 To ensure that the stress on the surface of the balloon did not decrease the air volume within a balloon, it was tried to measure the pressure change in the balloon when the volume was reduced with 20 ml, as was calculated above. Therefore, two stopcocks were glued into the lid of an almost watertight jar. One balloon was put into the jar after which the jar was filled with water. One stopcock was used to put a pressure sensor into the jar while the other one was used to push 20 ml of water into the jar with a syringe, see figure 17A. The change in pressure signal can be observed from figure 19B. Figure 19: A) Measuring the pressure change in the balloon when its volume was reduced by compression; B) Change in pressure signal when the water was added to the jar. Before the 20 ml of water were added, the air volume in the balloon was equal to 80 ml and the pressure was assumed to be approximately equal to the atmospheric pressure. After the water was injected, the pressure in the balloon was approximately equal to 3 V (see figure 16), which corresponded with Pa, or 259 mm Hg, which is very close to the calculated value of Pa, or mm Hg. Therefore it was decided to use Boyle s Law to calculate the air volume in the balloons when the left ventricular pressure was known. Only two balloons fitted in the ventricle in such a way that they could be fixed at a certain location, see figure 20. This fixation was necessary to make sure that the balloons could not obstruct the inflow or outflow of the ventricle. The maximal pressure in the left ventricle is approximately 120 mm Hg, which corresponds with Pa. Under this pressure the air volume in the balloon would reduce with 11 ml, which corresponds to 22 ml when two balloons were used. Figure 20: Two balloons were fixed in the ventricle so that they could not obstruct the inflow or the outflow. 20

24 2.5 Simulations with Levitronix CentriMag LVAS Levitronix CentriMag [12,13] In order to be able to investigate the influence of an assist device on left ventricular pressure-volume loops, an assist device had to be connected to the Cardiovascular Simulator. In this study, the Levitronix CentriMag Left Ventricular Assist System (LVAS) was used. The CentriMag blood pumping system developed by Levitronix (Waltham, Massachusetts, a wholly owned subsidiary of Pharos, LLC) is designed to provide hemodynamic support for patients suffering from cardiogenic shock. It is a member of the new generation blood pumps that provide support with minimal blood trauma. In Europe, the CentriMag LVAS has CE Mark approval and is commercially available. The system was developed for use as an extracorporeal ventricular assist system to support patients in severe, potentially reversible ventricular failure for periods of up to 14 days. In the United States, the CentriMag LVAS is applied for investigational use only. A clinical trial to evaluate the safety and effectiveness of the technology for use in the treatment of postcardiotomy cardiogenic shock is in progress under an Investigational Device Exemption. The Levitronix CentriMag Blood Pumping System is comprised of three fundamental components; a single use blood pump, a motor, and a drive console. All three components are shown in figure 21. The CentriMag motor rotates a magnet within the CentriMag blood pump at a speed that is set by the CentriMag console. The speed can be increased with 500 rpm increments up to a maximum of 5,500 rpm with a corresponding flow of 9.9 L/min. The blood pump and rotor are made of medical-grade polycarbonate and the pump has 3/8 barbed inlet and outlet ports. The priming Figure 21: Levitronix console, motor and blood pump volume of the pump is 31 ml and its maximum operating pressure is 600 mm Hg. The console operates at VAC at 50/60 Hz with a power of 120 W. It is fairly small (8.35 x x ) and weighs 6.6 kg. Unlike most conventional devices, the Levitronix CentriMag blood pump does not contain seals or bearings. Instead it is driven by a low frictionless rotation of the impeller, leading to minimal vibration, noise free operation, and minimal friction and heat generation in the blood path. Together with the low priming volume of the system this results in a reduced risk of hemolysis and thrombus formation. Furthermore, the Levitronix pump does not contain flexing sacs, diaphragms, or valves, which may degrade and fail. By eliminating the bearings and avoiding flexing components, the CentriMag LVAS is designed for longer life and reliability and to ideally reduce the incidence of device-related adverse effects. Other important advantages of the system are that it is portable, it allows for fast preparation and easy insertion, and that it is easy to operate. Disadvantages of the CentriMag VAS include the necessity of anticoagulation with heparin and the risk of cannula displacement. 21

25 2.5.2 Set-up of the Levitronix CentriMag LVAS The inflow cannula of the Levitronix CentriMag LVAS was connected to the Cardiovascular Simulator by inserting the inflow cannula into the ventricular chamber through the assist device connection hole. Silicone rubber adhesive sealant was used to ensure a watertight connection. To connect the outflow cannula, a T-shaped connector tube was placed at the proximal of the aorta, after which multiple connector tubes were used to bridge the difference in diameter between the outflow cannula and the T-shaped tube. Although the Levitronix CentriMag LVAS was provided with a flow sensor for feedback to the controller, an extra flow sensor was connected to the BNC 2110 (to enable data saving) via a flow monitor (Transonic Systems Inc., Model number HT 11 OR, Serial number A00269A and HgXL flowprobe) to measure the flow trough the inflow cannula of the Levitronix CentriMag LVAS. The configuration of the components described above can be seen in figure 22. With the connection of the assist device, a continuous flow at a constant speed could be generated, which made it possible to use a different flow sensor calibration method. Both the new LVAS flow sensor and the aortic flow sensor were calibrated using this new method, that is described in Appix A.2. After calibration, the aortic sensor was clamped around the aorta behind the T-shaped connector, and the LVAS sensor was clamped around Levitronix CentriMag LVAS outflow cannula. The flow through the aortic valve was calculated with the Matlab-program assistdevice.m (see Appix C.3) by subtracting the flow through the Levitronix from the flow through the aorta. Figure 22: A) Cardiovascular Simulator connected to Levitronix Centrimag LVAS; B) Close-up of the assist device, its connection, and the flow probes as clamped for calibration (Appix A.2). 22

26 2.5.3 Adjusting Cardiovascular Simulator settings Since the changes made to the Cardiovascular Simulator for the connection of the Levitronix CentriMag LVAS also changed the pressure and flow signals, adjustments were made to the Cardiovascular Simulator settings to regain physiological signals. This was necessary to be able to calculate the settings needed to simulate heart disease. For this purpose, a clamp was placed on the outflow cannula of the Levitronix CentriMag. The reason for clamping the outflow cannula rather than the inflow cannula was that this was easier because of the material properties of the cannulas and connectors. The resulting pressure and flow signals are shown in figure 23. The waveforms of the pressure signals are basically the same as before the connection of the assist device (figures 6 and 7). The only difference is that the pulse pressure (difference between systolic and diastolic pressure) is higher. This is probably due to the shortening of the flexible aorta that was necessary to insert the rigid T-shaped connector tube. Like the pressure signals, the flow signals are within the physiological range. The average flow through the assist device is 0.2 L/min, which indicates that the clamp succeeded reasonably well in limiting flow through the device. The average flow through the aortic valve was 4.3 L/min. The leakage of the valves was calculated using equations (16) and (17). A B Figure 23: A) Pressure signals as simulated after connection of Levitronix CentriMag; B) Flow signals as simulated after connection of Levitronix CentriMag. L valves (1 q q av p ) 100 (16) Here, L valves is the percentage of valve leakage, aortic valve in m 3 /s and was calculated with equation 17. p q av is the average flow through the q is the average flow generated by the piston in m 3 /s that Ap um u piston q p (17) T 23

27 Here, A p is the cross-section of the piston in m 2, u m is the distance the piston moves in m/cts, u piston is the amplitude of the piston movement in cts and T is the period of the piston movement in s. q was m 3 /s (5.2 L/min) and L valves was 17%. This leakage of the valves p was probably mainly caused by the amount of water pushed into the atrium by the closing of the mitral valve. Table 1 shows some characteristics for the chosen Cardiovascular Simulator settings with a clamp on the outflow cannula of the assist device. Table 1: Characteristics for the chosen Cardiovascular Simulator settings. Characteristic Value Heart rate 60 bpm Cardiac output 4.3 L/min Stroke volume* 72 ml Stroke volume piston** 87 ml Leakage of the valves 17% End diastolic volume 120 ml End systolic volume 33 ml Ejection fraction 73% * Water volume that passes the aortic valve during each cycle. ** Water volume that is displaced by the piston during each cycle. Furthermore, the relationship between the amplitude of the piston movement and the systolic pressure was determined for the new settings, with an R 2 of Also the relationship between the amplitude of the piston movement and the stroke volume was determined for the new settings, with an R 2 of Like before, the left ventricular pressure volume loop at an amplitude of the piston movement of 18,500 cts, which is shown in figure 24A, was used to calculate the ESPVR as described in Implementation of the elastance model. Furthermore, the -diastolic volume for a certain amplitude of the piston movement was calculated using equation (11). The relationships described above were used to plot the Frank-Starling curve for the new settings. In figure 24B it can be seen that this new curve is almost the same as the old one. A B Figure 24: A) Left ventricular pressure volume loops for the Cardiovascular Simulator without assist device and with an assist device with a clamp on the outflow cannula. B) Frank-Starling curves for the Cardiovascular Simulator without assist device and with an assist device with a clamp on the outflow cannula. 24

28 2.6 Simulation of dilated cardiomyopathy Dilated cardiomyopathy To investigate the influence of an assist device on the pressure-volume loops of the left ventricle, heart failure was simulated. The choice was made to simulate dilated cardiomyopathy because this is the most common form of heart muscle disease [11]. Dilated cardiomyopathy is found most often in middle-aged people and more often in men than in women, but the disease has been diagnosed in people of all ages, including children [11]. In general, heart failure causes a decrease in cardiac output, which results from a decline in stroke volume that is due to systolic dysfunction, diastolic dysfunction, or a combination of the two. Systolic dysfunction is caused by a loss of heart muscle contractility, most likely due to either alterations in signal transduction mechanisms or loss of viable, contracting muscle as occurs following acute myocardial infarction. Diastolic dysfunction occurs when the ventricle becomes less compliant (i.e. stiffer), which impairs ventricular filling. Both systolic and diastolic dysfunction result in a higher ventricular -diastolic pressure [9,10]. Because of this increased diastolic pressure, the Frank-Starling mechanism as described in Frank-Starling mechanism acts as a compensatory mechanism by augmenting the force of contraction and therefore stroke volume. However, if the systolic or diastolic dysfunction becomes too severe, the capacity of this compensatory mechanism becomes exhausted after which the stroke volume can decline significantly. In dilated cardiomyopathy the ventricle Figure 25: Changes to the Frank - Starling curve for heart failure (C). dilates to very large volumes through remodeling in an attempt to maintain stroke volume and limit the increase in -diastolic pressure. For real severe cardiomyopathy, a condition of cardiogenic shock may develop, where the circulation of blood drops below the level needed to maintain life. Dilated cardiomyopathy causes changes of the pressure volume curves described by the elastance model. The EDPVR shifts to the right due to dilation of the heart, and reduced contractility results in a decreased slope and a right-shift of the ESPVR. Figure 25 shows an example of changes of the Starling curve due to heart failure. The -diastolic volume increases while the stroke volume decreases. This results in a reduction of work per heartbeat as could also be deduced from the changes of the pressure-volume loops. When an assist device is connected to a failing heart, the heart usually becomes smaller and the stroke volume also decreases due to the unloading. It was assumed that the pressure-volume loop in a failing heart would shift to the left according to the elastance model, so all points in time would stay at their isochronic line. In this way the work performed by the heart should decrease, because the stroke volume becomes smaller ( V decreases) and the -systolic pressure also decreases according to the elastance model ( p decreases). If the heart recovered, the ESPVR line would become steeper and therefore the systolic pressure would increase, as well as the work performed by the heart. However, in this study recovery of the heart was not simulated, so only shifts of the pressure-volume loops along the ESPVR line were simulated, instead of a shift of the ESPVR line itself. 25

29 2.6.2 Calculation of variables As a possible value for the -diastolic left ventricular volume per m 2 for a patient with dilated cardiomyopathy, 133 ml/m 2 was found [19]. Together with an average body surface area (BSA) of 1.73 Figure 26: ESPVRs for healthy hearts (open symbols) and hearts with dilated cardiomyopathy (filled symbols) [21]. [20] this leads to an diastolic volume of 230 ml. Figure 26 shows some ESPVRs for both healthy individuals and patients with heart failure. From these data, a V 0 of 100 ml was estimated for the patients with dilated cardiomyopathy (V 0 for the healthy individuals is approximately 0 ml as used in the previous simulations). Obviously, the values for both the diastolic left ventricular volume and V 0 are only rough estimations, but the only goal was to be within the proper range for a patient with dilated cardiomyopathy. The average value of the ejection fraction (EF) for the 5 patients whose ESPVRs are displayed in figure 26, was 17% [21]. This value was used to calculate a stroke volume (SV) of approximately 39 ml (EF. V ED ), a cardiac output (CO) of approximately 2.3 L/min (SV. HR. 10-3, where HR stands for heart rate) and a cardiac index (CI) of approximately 1.4 L/min/m 2 (CO / BSA). For the calculation of the stroke volume, the leakage of the valves was not taken into account since the exact leakage was not known for the new configuration. Instead, the choice was made to use the ejection fraction of 17% to calculate the stroke volume, after which the stroke volume could be used to calculate the -systolic left ventricular volume and thus the new ejection fraction. To obtain a left ventricular pressure-volume loop corresponding to the data described above, the new amplitude of the piston movement was calculated with equation (10) and the new calibration coefficients. This new amplitude was 12,871 cts, leading to a water displacement volume of 61 ml. Furthermore, equation (12) was used to calculate the shift of the initial piston position, which was -23,384 cts. Unfortunately, the previous initial position made it impossible to shift the initial piston position this far to the left. But since the initial volume does not have any influence on the signals because of the rigidity of the ventricular chamber of the Cardiovascular Simulator, the same (old) initial volume was used to simulate an diastolic volume of 230 ml. However, when a flexible ventricular sac is used for the simulations, it is possible and useful to have different -diastolic volumes. The new ESPVR was calculated as described before using equation (4). However, now the situation with an amplitude of the piston movement of 12,871 cts was chosen as a basis for the ESPVR. Table 2 shows some of the characteristics for the settings selected for dilated cardiomyopathy. m 2 26

30 Table 2: Characteristics for the Cardiovascular Simulator settings for dilated cardiomyopathy. Characteristic Value Heart rate 60 bpm Cardiac output 2.3 L/min Cardiac index 1.4 L/min/m 2 Stroke volume* 39 ml Stroke volume piston** 61 ml Leakage of the valves 35% End diastolic volume 230 ml End systolic volume 169 ml Ejection fraction 27% * Water volume that passes the aortic valve during each cycle. ** Water volume that is displaced by the piston during each cycle. Figure 27 shows the left ventricular pressure-volume loops and the Frank-Starling curves as simulated for a healthy heart and a heart with dilated cardiomyopathy. A B Figure 27: A) Left ventricular pressure volume loops for a healthy heart and a heart with dilated cardiomyopathy (DCM). B) Frank-Starling curves for a healthy heart and a heart with dilated cardiomyopathy (DCM). 27

31 2.7 Simulations Some adjustments to the Cardiovascular Simulator had to be made, in order to try to get a physiological response of the heart when the LVAD was turned on. The most significant change that was made was that the originally strictly ascing aorta was turned into a partially ascing and partially horizontal or slightly descing aorta by moving the compliance chamber downwards, see figure 28, because a nonphysiological totally ascing aorta would pressurize the left ventricle too much. Moreover, the assist device was now connected to the distal of the aorta. Also a clamp was placed onto the outflow cannula of the LVAD and onto the aorta proximal to the connection of the LVAD, to prevent the ventricle from being over-pressurized. Furthermore, due to the assist device, the pressure-volume relationships were changed in such a way that the -systolic pressures had become almost equal to zero. Therefore, the maximal instead of the -systolic left ventricular pressure was used for the elastance model in the simulations that are described in this section. The resulting pressure signals are shown in figure 29. A B Figure 28: A) Cardiovascular Simulator with ascing aorta; B) Cardiovascular Simulator with horizontal or slightly descing aorta. Figure 29: Left ventricular and aortic pressure signals as simulated with the Cardiovascular Simulator after alteration of the Cardiovascular Simulator configuration. 28

32 Four series of simulations were performed with the revised Cardiovascular Simulator. During the first series of simulations, the amplitude of the piston movement was kept at 12,871 cts (see section Calculation of variables), while the speed of the LVAD was raised from 0 to 3,000 rpm with increments of 500 rpm, as can be seen in table 3. Table 3: Simulations with a constant amplitude of piston movement. Simulation Amplitude of piston movement LVAD speed (rpm) Balloons in ventricle (cts) 1A 12,871 -* No 1B 12,871 0 No 1C 12, No 1D 12,871 1,000 No 1E 12,871 1,500 No 1F 12,871 2,000 No 1G 12,871 2,500 No 1H 12,871 3,000 No * The LVAD was turned off and a clamp was placed on the outflow cannula. When the heart is unloaded by an assist device, usually the (-diastolic) size of the left ventricle will decrease, resulting in a lower filling pressure. According to the elastance model, this lower -diastolic pressure will in turn result in a decrease in stroke volume. However, because of the rigidity of the ventricular chamber, no decrease in ventricular size and therefore -diastolic pressure could occur, which made it impossible to relate the decrease in stroke volume to the -diastolic left ventricular pressure. Therefore, in this study the stroke volume was decreased with 10% (1,287 cts) for each 500 rpm increase in LVAD speed. Because the unclamped assist device acted as a (passive) bypass resulting in a lower resistance even at 0 rpm, for this condition the stroke volume was also decreased with 10%. For the described conditions a second series of simulations was performed, see table 4. Table 4: Simulations with a decreasing amplitude of piston movement. Simulation Amplitude of piston movement LVAD speed Balloons in ventricle (cts) (rpm) 2A 12,871 -* No 2B 11,584 0 No 2C 10, No 2D 9,010 1,000 No 2E 7,723 1,500 No 2F 6,436 2,000 No 2G 5,149 2,500 No 2H 3,862 3,000 No * The LVAD was turned off and a clamp was placed on the outflow cannula. In the third and fourth series of simulations, the same simulations were performed as in the first and second series, respectively. However, now two balloons each filled with 80 ml of air were placed in the ventricle to investigate the effects of a higher compliance on the results of the first and second series. The settings of the third and fourth series can be found in table 5 and 6. 29

33 Table 5: Simulations with a constant amplitude of piston movement and ventricular balloons. Simulation Amplitude of piston movement LVAD speed Balloons in ventricle (cts) (rpm) 3A 12,871 -* Yes 3B 12,871 0 Yes 3C 12, Yes 3D 12,871 1,000 Yes 3E 12,871 1,500 Yes 3F 12,871 2,000 Yes 3G 12,871 2,500 Yes 3H 12,871 3,000 Yes * The LVAD was turned off and a clamp was placed on the outflow cannula. Table 6: Simulations with a decreasing amplitude of piston movement and ventricular balloons. Simulation Amplitude of piston movement LVAD speed Balloons in ventricle (cts) (rpm) 4A 12,871 -* Yes 4B 11,584 0 Yes 4C 10, Yes 4D 9,010 1,000 Yes 4E 7,723 1,500 Yes 4F 6,436 2,000 Yes 4G 5,149 2,500 Yes 4H 3,862 3,000 Yes * The LVAD was turned off and a clamp was placed on the outflow cannula. 30

34 Section 3: Results For all four simulation series, the left ventricular pressure-volume loops, the aortic and left ventricular pressures, the flow through the aortic valve, the flow through the LVAD and the total aortic flow, and some characteristics are displayed for the different simulations (A to H). 3.1 Simulation with a constant amplitude of piston movement For simulation series 1, the left ventricular pressure-volume loops are shown in figure 30, the aortic and left ventricular pressure signals are shown in figure 31A and 31B respectively, the flow through the aortic valve, the flow through the LVAD and the total aortic flow are shown in figure 32A, 32B, and 32C respectively, pressure characteristics are shown in table 7, flow characteristics are shown in table 8, and all other characteristics are shown in table 9. Figure 30: Left ventricular pressure-volume loops for simulations 1A 1H, at an amplitude of the piston movement of 12,871 cts, with no balloons in the ventricular chamber. 31

35 Figure 32 shows that the aortic valve opened for all rpm-settings. A B Figure 31: Pressure signals for simulations 1A 1H, at an amplitude of the piston movement of 12,871 cts, with no balloons in the ventricular chamber: A) Aortic pressure; B) Left ventricular pressure. A B C Figure 32: Flow signals for simulations 1A 1H, at an amplitude of the piston movement of 12,871 cts, with no balloons in the ventricular chamber: A) Flow through the aortic valve; B) Flow through the LVAD; C) Total aortic flow. 32

36 In table 7 it can be seen that the maximal left ventricular pressure, the maximal aortic pressure, the minimal aortic pressure, and the mean aortic pressure all increased for each increase in LVAD speed, while the pulse pressure decreased. Table 7: Pressure characteristics for simulations 1A 1H, at an amplitude of the piston movement of 12,871 cts, with no balloons in the ventricular chamber. Simulation Description p lv, max [mm Hg] p ao, max [mm Hg] p ao, min [mm Hg] p ao, mean [mm Hg] Pulse pressure [mm Hg] 1A Clamped LVAD B 0 rpm C 500 rpm D 1,000 rpm E 1,500 rpm F 2,000 rpm G 2,500 rpm H 3,000 rpm In table 8 it can be seen that the mean flow through the aortic valve decreased, while the mean flow through the LVAD and the mean total aortic flow increased for each increase in LVAD speed (and also for the removal of the clamp on the outflow cannula of the assist device). Table 8: Flow characteristics for simulations 1A 1H, at an amplitude of the piston movement of 12,871 cts, with no balloons in the ventricular chamber. Simulation Description q av, mean [L/min] q LVAD, mean [L/min] q ao, mean [L/min] 1A Clamped LVAD B 0 rpm C 500 rpm D 1,000 rpm E 1,500 rpm F 2,000 rpm G 2,500 rpm H 3,000 rpm In table 9 it can be seen that the -diastolic volume and the work increased, while the ejection fraction decreased for each increase in LVAD speed. Table 9: Other characteristics for simulations 1A 1H, at an amplitude of the piston movement of 12,871 cts, with no balloons in the ventricular chamber. Simulation Description Amplitude piston [cts] SV piston * [ml] V ED [ml] EF** [%] Work [J] 1A Clamped LVAD 12, x B 0 rpm 12, x C 500 rpm 12, x D 1,000 rpm 12, x E 1,500 rpm 12, x F 2,000 rpm 12, x G 2,500 rpm 12, x H 3,000 rpm 12, x 10-3 * SV piston = stroke volume, calculated as left ventricular volume change. ** EF = ejection fraction. 33

37 3.2 Simulation with a decreasing amplitude of piston movement For simulations series 2, the left ventricular pressure-volume loops are shown in figure 33, the aortic and left ventricular pressure signals are shown in figure 34A and 34B respectively, the flow through the aortic valve, the flow through the LVAD and the total aortic flow are shown in figure 35A, 35B, and 35C respectively, pressure characteristics are shown in table 10, flow characteristics are shown in table 11, and all other characteristics are shown in table 12. Figure 33: Left ventricular pressure-volume loops for simulations 2A 2H, with a 10% decrease of the amplitude of the piston movement for each subsequent simulation and no balloons in the ventricular chamber. 34

38 Figure 35 shows that the aortic valve did not open for an LVAD speed of 2,000 rpm or higher. A B Figure 34: Pressure signals for simulations 2A 2H, with a 10% decrease of the amplitude of the piston movement for each subsequent simulation and no balloons in the ventricular chamber: A) Aortic pressure; B) Left ventricular pressure. A B C Figure 35: Flow signals valve for simulations 2A 2H, with a 10% decrease of the amplitude of the piston movement for each subsequent simulation and no balloons in the ventricular chamber: A) Flow through aortic valve; B) Flow through LVAD; C) Total aortic flow. 35

39 In table 10 it can be seen that the maximal left ventricular pressure decreased from simulation A to C, then increased from simulation C to E, and finally decreased again from simulation E to H. The maximal and minimal aortic pressure decreased from simulation A to C, after which they increased from simulation C to H. The mean aortic pressure decreased from simulation A to B after which it increased from simulation B to H. The pulse pressure decreased for all subsequent simulations. Table 10: Pressure characteristics for simulations 2A 2H, with a 10% decrease of the amplitude of the piston movement for each subsequent simulation and no balloons in the ventricular chamber. Simulation Description p lv, max [mm Hg] p ao, max [mm Hg] p ao, min [mm Hg] p ao, mean [mm Hg] Pulse pressure [mm Hg] 2A Clamped LVAD B 0 rpm C 500 rpm D 1,000 rpm E 1,500 rpm F 2,000 rpm G 2,500 rpm H 3,000 rpm In table 11 it can be seen that the mean flow through the aortic valve decreased for all subsequent simulations, while the mean flow through the LVAD and the mean total aortic flow increased for each increase in LVAD speed from 500 rpm onward. Table 11: Flow characteristics for simulations 2A 2H, with a 10% decrease of the amplitude of the piston movement for each subsequent simulation and no balloons in the ventricular chamber. Simulation Description q av, mean [L/min] q LVAD, mean [L/min] q ao, mean [L/min] 2A Clamped LVAD B 0 rpm C 500 rpm D 1,000 rpm E 1,500 rpm F 2,000 rpm G 2,500 rpm H 3,000 rpm In table 12 it can be seen that the -diastolic volume and the work decreased or remained constant for each subsequent simulation, while no tr can be seen for the change in ejection fraction. Table 12: Other characteristics for simulations 2A 2H, with a 10% decrease of the amplitude of the piston movement for each subsequent simulation and no balloons in the ventricular chamber. Simulation Description Amplitude piston [cts] SV piston * [ml] V ED [ml] EF** [%] Work [J] 2A Clamped LVAD 12, x B 0 rpm 11, x C 500 rpm 10, x D 1,000 rpm 9, x E 1,500 rpm 7, x F 2,000 rpm 6, x G 2,500 rpm 5, x H 3,000 rpm 3, x 10-3 * SV piston = stroke volume, calculated as left ventricular volume change. ** EF = ejection fraction. 36

40 3.3 Simulation with a constant amplitude of piston movement and ventricular balloons For simulations series 3, the left ventricular pressure-volume loops are shown in figure 36, the aortic and left ventricular pressure signals are shown in figure 37A and 37B respectively, the flow through the aortic valve, the flow through the LVAD and the total aortic flow are shown in figure 38A, 38B, and 38C respectively, pressure characteristics are shown in table 13, flow characteristics are shown in table 14, and all other characteristics are shown in table 15. Figure 36: Left ventricular pressure-volume loops for simulations 3A 3H, at an amplitude of the piston movement of 12,871 cts, with two balloons in the ventricular chamber. 37

41 Figure 38 shows that the aortic valve did not open at an LVAD speed of 3,000 rpm. A B Figure 37: Pressure signals for simulations 3A 3H, at an amplitude of the piston movement of 12,871 cts, with two balloons in the ventricular chamber: A) Aortic pressure; B) Left ventricular pressure. A B C Figure 38: Flow signals valve for simulations 3A 3H, at an amplitude of the piston movement of 12,871 cts, with two balloons in the ventricular chamber: A) Flow through aortic valve; B) Flow through LVAD; C) Flow through aorta. 38

42 In table 13 it can be seen that the maximal left ventricular pressure decreased from simulation A to B, increased from simulation B to G, and decreased again from simulation G to H. The maximal aortic pressure, the minimal aortic pressure, and the mean aortic pressure all increased for each increase in LVAD speed from 500 rpm onward while the pulse pressure decreased from simulation C onward. Table 13: Pressure characteristics for simulations 3A 3H, at an amplitude of the piston movement of 12,871 cts, with two balloons in the ventricular chamber. Simulation Description p lv, max [mm Hg] p ao, max [mm Hg] p ao, min [mm Hg] p ao, mean [mm Hg] Pulse pressure [mm Hg] 3A Clamped LVAD B 0 rpm C 500 rpm D 1,000 rpm E 1,500 rpm F 2,000 rpm G 2,500 rpm H 3,000 rpm In table 14 it can be seen that the mean flow through the aortic valve decreased for all simulations, while the mean flow through the LVAD increases from simulation B onward, and the mean total aortic flow increased from simulation C onward. Table 14: Flow characteristics for simulations 3A 3H, at an amplitude of the piston movement of 12,871 cts, with two balloons in the ventricular chamber. Simulation Description q av, mean [L/min] q LVAD, mean [L/min] q ao, mean [L/min] 3A Clamped LVAD B 0 rpm C 500 rpm D 1,000 rpm E 1,500 rpm F 2,000 rpm G 2,500 rpm H 3,000 rpm In table 15 it can be seen that the stroke volume remained nearly constant. The diastolic volume and work increased from simulation B to G and decreased again from simulation G to H. The ejection fraction decreased from simulation B to G and increased again from simulation G to H. Table 15: Other characteristics for simulations 3A 3H, at an amplitude of the piston movement of 12,871 cts, with two balloons in the ventricular chamber. Simulation Description Amplitude piston [cts] SV piston * [ml] V ED [ml] EF** [%] Work [J] 3A Clamped LVAD 12, x10-3 3B 0 rpm 12, x10-3 3C 500 rpm 12, x10-3 3D 1,000 rpm 12, x10-3 3E 1,500 rpm 12, x10-3 3F 2,000 rpm 12, x10-3 3G 2,500 rpm 12, x10-3 3H 3,000 rpm 12, x10-3 * SV piston = stroke volume, calculated as LV volume change. ** EF = ejection fraction. 39

43 3.4 Simulation with a decreasing amplitude of piston movement and ventricular balloons For simulations series 4, the left ventricular pressure-volume loops are shown in figure 39, the aortic and left ventricular pressure signals are shown in figure 40A and 40B respectively, the flow through the aortic valve, the flow through the LVAD and the total aortic flow are shown in figure 41A, 41B, and 41C respectively, pressure characteristics are shown in table 16, flow characteristics are shown in table 17, and all other characteristics are shown in table 18. Figure 39: Left ventricular pressure-volume loops for simulations 4A 4H, with a 10% decrease of the amplitude of the piston movement for each subsequent simulation, with two balloons in the ventricular chamber. 40

44 Figure 41 shows that the aortic valve did not open for an LVAD speed of 2,000 rpm or higher. A B Figure 40: Pressure signals for simulations 4A 4H, with a 10% decrease of the amplitude of the piston movement for each subsequent simulation, with two balloons in the ventricular chamber: A) Aortic pressure; B) Left ventricular pressure. A B C Figure 41: Flow signals valve for simulations 4A 4H, with a 10% decrease of the amplitude of the piston movement for each subsequent simulation, with two balloons in the ventricular chamber: A) Flow through aortic valve; B) Flow through LVAD; C) Total aortic flow. 41

45 In table 16 it can be seen that the maximal left ventricular pressure decreased from simulation A to C, then increased from simulation C to E, and finally decreased again from simulation E to H. The maximal aortic pressure, the minimal aortic pressure, and the mean aortic pressure all increased from simulation C to H, while the pulse pressure decreased to zero. Remarkable is that the maximal, mean, and minimal pressures were equal for an rpm of 2,000 or higher. Table 16: Pressure characteristics for simulations 4A 4H, with a 10% decrease of the amplitude of the piston movement for each subsequent simulation with two balloons in the ventricular chamber. Simulation Description p lv, max [mm Hg] p ao, max [mm Hg] p ao, min [mm Hg] p ao, mean [mm Hg] Pulse pressure [mm Hg] 4A Clamped LVAD B 0 rpm C 500 rpm D 1,000 rpm E 1,500 rpm F 2,000 rpm G 2,500 rpm H 3,000 rpm In table 17 it can be seen that the mean flow through the aortic valve decreased, while the mean flow through the LVAD and the mean total aortic flow increased for each increase in LVAD speed. Table 17: Flow characteristics for simulations 4A 4H, with a 10% decrease of the amplitude of the piston movement for each subsequent simulation with no balloons in the ventricular chamber. Simulation Description q av, mean [L/min] q LVAD, mean [L/min] q ao, mean [L/min] 4A Clamped LVAD B 0 rpm C 500 rpm D 1,000 rpm E 1,500 rpm F 2,000 rpm G 2,500 rpm H 3,000 rpm In table 18 it can be seen that the work decreased or remained constant from simulation C onward, while no tr can be seen for the change in left ventricular -diastolic volume or the ejection fraction for each increase in LVAD speed. Table 18: Other characteristics for simulations 4A 4H, with a 10% decrease of the amplitude of the piston movement for each subsequent simulation with no balloons in the ventricular chamber. Simulation Description Amplitude piston [cts] SV piston * [ml] V ED [ml] EF** [%] Work [J] 4A Clamped LVAD 12, x B 0 rpm 11, x C 500 rpm 10, x D 1,000 rpm 9, x E 1,500 rpm 7, x F 2,000 rpm 6, x G 2,500 rpm 5, x H 3,000 rpm 3, x 10-3 * SV piston = stroke volume, calculated as LV volume change. ** EF = ejection fraction. 42

46 Section 4: Discussion First, all four simulation series are discussed separately. Then a comparison is made between simulation series 1 (constant amplitude of the piston movement, no balloons in the ventricle) and 2 (decreasing amplitude of the piston movement, no balloons in the ventricle), and between simulation series 3 (constant amplitude of the piston movement, two balloons in the ventricle) and 4 (decreasing amplitude of the piston movement, two balloons in the ventricle) to investigate the influence of decreasing the amplitude of the piston movement. Finally, simulation series 1 is compared to simulation series 3 while simulation series 2 is compared to simulation series 4 to investigate the influence of balloons in the ventricle. 4.1 Discussion of each of the four simulation series Discussion simulation series 1 In simulation series 1, the aortic valve opened for all rpm-settings. The aortic valve only remains closed when the flow through the assist device is equal to or greater than the maximal flow caused by the piston movement, at least when the leakage of the valves is not taken into account. Because of the opening of the aortic valve, the maximal left ventricular pressure increased for each increase in LVAD speed, since the higher flow through the aorta caused an increase in the aortic pressure. The maximal, minimal, and mean aortic pressure all increased due to the increase in LVAD speed, but the pulse pressure decreased, because each increase in flow through the LVAD automatically decreased the flow through the aortic valve. While the flow through the LVAD increased and the flow through the aortic valve decreased for obvious reasons, the total aortic flow increased because the assist device also sucked water out of the atrium. The -diastolic left ventricular volume increased for each increase in LVAD speed. This was due to the increase in maximal left ventricular pressure, since the pressurevolume loops were shifted in the pressure-volume plane according to the maximal left ventricular pressure-volume relationship described in section 2.7 Simulations. However, this shift is meaningless as long as the aortic valve still opens, because then an increase in maximal left ventricular pressure is caused by an increase in flow through the assist device and the resulting increase in aortic pressure. This left ventricular pressure increase has nothing to do with the maximal left ventricular pressure volume relationship or the elastance of the heart, so no conclusions can be drawn from the -diastolic volumes calculated by shifting the pressure-volume loops as long as the aortic valve still opens. For the calculation of the ejection fraction, the -diastolic volume was used, which means that it is also impossible to interpret this value unless the aortic valve remains closed. The work can be interpreted even though the aortic valve opened for all simulations, since shifting the pressure-volume loop does not influence the work. The workload increased for each increase in LVAD speed, which was caused by an increase in the aortic and thus ventricular pressure, while the stroke volume remained constant. From the increase of the workload, it can be concluded that the Levitronix CentriMag did not unload the ventricle in simulation series 1, with a constant amplitude of the piston movement. This was not unexpected, since normally the -diastolic left ventricular volume and thus pressure would decrease for each increase in LVAD speed, which 43

47 would result in a decrease in stroke volume according to the elastance model, which would in turn result in a decrease in work. Unfortunately, the rigidity of the ventricle prevented a decrease of the -diastolic left ventricular volume and pressure. This is a problem because these should have been the variables on which a decrease in stroke volume was based for each subsequent simulation according to the elastance model. Furthermore, because ventricular filling was only caused by backward movement of the piston instead of contraction of the atrium, the -diastolic pressure was almost equal to zero for every simulation. Even a more elastic ventricle would not have solved this problem Discussion simulation series 2 For simulation series 2, the aortic valve remained closed at an LVAD speed of 2,000 rpm or higher. For the same reason as described for simulation series 1, the maximal left ventricular pressure increased for each increase in LVAD speed as long as the aortic valve opened. For each increase in LVAD speed at which the aortic valve no longer opened, the maximal left ventricular pressure decreased because the assist device sucked more water out of the ventricle. The maximal, minimal, and mean aortic pressure increased for each increase in LVAD speed because of the increased flow through the aorta. The pulse pressure decreased until it became zero when the aortic valve remained closed. This pulse pressure did not necessarily have to be zero when the aortic valve no longer opened, because the piston movement could still have caused pulsatility in the LVAD flow and thus aortic flow and pressure. The flow through the aortic valve decreased while the flow through the assist device and the total aortic flow increased, which was all expected. From 2,000 rpm onward, regurgitation occurred due to leakage of the aortic valve. When the aortic valve no longer opened, the -diastolic left ventricular volume and stroke volume both decreased. The decrease in -diastolic left ventricular volume can be explained by the decrease in ventricular pressure, while the decrease in ejection fraction indicates that the -diastolic volume decreased relatively faster than the stroke volume. The work decreased for all simulations, which might lead to the conclusion that in simulation series 2, the assist device unloaded the heart. However, this decrease in work would also have occurred when the same decrease in stroke volume had been applied without increasing the LVAD speed or even without unclamping the assist device. Although it is not wrong to assume that the stroke volume will decrease for each increase in LVAD speed, the specific decreases applied in this simulation series were not based on the elastance model for reasons explained in section 4.1. Discussion simulation series 1. Instead they were chosen quite randomly which makes it not possible to unambiguously conclude that the assist device unloaded the heart. However, when the aortic valve remained closed, the work decreased dramatically, which is an indication that this decrease is probably at least partially caused by unloading by the Levitronix CentriMag LVAS Discussion simulation series 3 Because the aortic valve opened until an LVAD speed of 3,000 rpm, the maximal left ventricular pressures increased for each increase in LVAD speed, except for the increase to 3,000 rpm, at which speed it decreased. The maximal, minimal and mean aortic pressure increased for each increase in LVAD speed, while the pulse pressure 44

48 decreased as expected. The flows also showed the predicted trs: an increase in LVAD flow and total aortic flow, and a decrease in flow through the aortic valve. The stroke volume remained nearly constant, because the amplitude of the piston movement was constant while both the -diastolic and -systolic left ventricular pressure were very low, resulting in no significant change in -diastolic and systolic balloon volume. Because there was only one simulation for which the aortic valve did not open, it is not possible to detect a tr in the -diastolic left ventricular volume and ejection fraction for an increase in LVAD speed with a closed aortic valve. The work increased for each increase in LVAD speed as long as the aortic valve still opened. At 3,000 rpm however, when the aortic valve remained closed, the work had decreased compared to the simulation at 2,500 rpm. This decrease in work for the same stroke volume is very import, since it proves unloading of the ventricle by the Levitronix CentriMag LVAS for this particular rpm-setting Discussion simulation series 4 The maximal left ventricular pressure increased for an LVAD speed between 500 and 2,000 rpm, after which it decreased for an LVAD speed between 2,000 and 3,000 rpm. This can be explained by the opening of the aortic valve up to an LVAD speed of 2,000 rpm. The slight decrease in maximal left ventricular pressure between simulation B (0 rpm) and C (500 rpm) cannot be explained, which is also the case for the change in the aortic pressures between simulation B and C. After simulation C, the maximal, minimal and mean aortic pressure increased as expected while the pulse pressure decreased to zero for the rpm-settings at which the aortic valve remained closed. The flows showed the expected increase in both assist device flow and total aortic flow, and decrease in flow through the aortic valve. The stroke volume decreased, which was expected because of the decreased amplitude of the piston movement. However, the stroke volume increased after removal of the clamp on the outflow cannula of the assist device despite the decrease in amplitude of the piston movement. This was caused by the difference in the shape of the pressure-volume loops for the two simulations; the pressure-volume loop of the clamped LVAD showed a relatively high -systolic pressure, which resulted in a decreased balloon volume and an increased -systolic ventricular volume and thus decreased stroke volume. Furthermore, the -diastolic volume was higher for the unclamped LVAD, which resulted in an increased -diastolic left ventricular volume and thus increased stroke volume for this situation. When the aortic valve no longer opened, the -diastolic volume decreased as expected due to a decrease in both stroke volume and ventricular pressure. The decrease of the ejection fraction between simulation G and H indicates that the stroke volume decreased relatively more rapidly than the -diastolic volume. For reasons mentioned in section 4.2 Simulation series 2, from the decrease in work for increased LVAD speed it cannot be concluded that the ventricle is being unloaded by the assist device. However, the sudden decrease in work between the last simulation where the aortic valve still opens (1,500 rpm) and the first simulation where this valve remains closed (2,000 rpm) indicates that this decrease was probably at least partly caused by unloading of the ventricle with the Levitronix CentriMag LVAS. 45

49 4.2 Comparison simulation series Influence of an increase in amplitude of the piston movement When simulation series 1 is compared to simulation series 2, it can be seen that the aortic valve opened for all rpm-settings for simulation series 1, while it remained closed at LVAD speeds of 2,000 rpm or higher for simulation series 2. This difference is easily explained by the decrease in amplitude of the piston movement and thus stroke volume in simulation series 2. Also due to this difference in stroke volume, the maximal, minimal, and mean aortic pressures were higher for simulation series 1 than simulation series 2. The flow through the LVAD was almost equal for both simulation series, while the flow through the aortic valve and the mean total aortic flow were a bit higher for simulation series 1 than 2 as expected. It is not very useful to compare the -diastolic volumes and ejection fractions of series 1 and series 2, because the aortic valve opens for all rpm-settings in simulation series 1, which makes these data useless. The most important difference between the two simulation series is that for the second series the work decreased for each increase in LVAD speed, while for the first series the work increased. This indicates that a decrease in stroke volume is necessary to simulate unloading of the ventricle by an assist device. This at least seems to hold true for rpm-settings at which the aortic valve still opens, since the work can either decrease by a decrease in stroke volume or by a decrease in left ventricular pressure (or a combination of the two). When simulation series 3 is compared to simulation series 4, it can be seen that the aortic valve remained closed at an LVAD speed of 3,000 rpm for simulation series 3, while it remained closed at LVAD speeds of 2,000 rpm or higher for simulation series 4. This was obviously caused by the decrease of the amplitude of the piston movement in simulation series 4, which also caused the pressures of simulation series 4 to be lower than the pressures of simulation series 3. Although the tr for the flow signals for both simulations is the same, it cannot be explained why the flow through the assist device and the total aortic flow are lower for simulation series 3 than for simulation series 4. The stroke volume is larger for simulation series 3 than for simulation series 4, which is not surprising because of the decrease in amplitude of the piston movement in simulation series 4. Only the stroke volume of simulation 3B is lower than the stroke volume of simulation 4B. This can be explained by the high -diastolic left ventricular pressure for simulation 4B, which caused a decrease in -diastolic balloon volume and as a result of that an increase in -diastolic left ventricular volume and stroke volume. The only rpm-setting for which the aortic valve no longer opened for both simulation series, is 3,000 rpm. The -diastolic volume at 3,000 rpm of simulation series 3 was larger than of simulation series 4, due to the smaller stroke volume for the latter simulation. The workload was lower for simulation series 4 than for simulation series 3, which was firstly caused by the lower stroke volumes used in simulation series 4 and secondly by the earlier closure of the aortic valve for simulation series 4. This difference in work for simulation series 3 and 4 indicates that the workload is lower for a decreased stroke volume as was also seen for the comparison between simulation series 1 and 2. This obviously is not an unexpected result, since a decrease in stroke volume would also have led to a decrease in workload if no assist device had been in place. 46

50 4.2.2 Influence of balloons in the ventricular chamber Although the idea was to compare the simulations without balloons in the ventricle to the simulations with the balloons in the ventricle, this comparison appeared to be useless because the settings of the Cardiovascular Simulator apparently had changed too much during the insertion of the balloon into the ventricle. This was concluded from the fact that the left ventricular pressure was higher for the simulations with balloons in the ventricle than for the simulation without balloons in the ventricle for the same amplitude of the piston movement. These pressures should have been either equal to or lower than the pressures for the simulation series without balloons in the ventricle due to the damping effect of the balloons. The probable reason for the unexpected pressure increases was that because the Simulator needed to be taken apart in order to be able to insert the balloons, factors such as the configuration of the aorta, the total amount of water in the Cardiovascular Simulator, the water height in the compliance chamber, and the place of the clamp on the aorta had changed. Although it is unfortunate that no conclusions can be drawn about the influence of the balloons, it was not expected that the balloons would make an important difference anyway. The reason for this is that the -diastolic pressure was almost equal to zero for most simulations, thereby causing no significant change in -diastolic balloon and left ventricular volume. However, if a mock-loop with a contracting atrium had been used, it would have been useful to investigate the influence of balloons in the ventricle. 4.3 General discussion Due to limitations of the Cardiovascular Simulator, it was not possible to regulate the stroke volume of the heart by the -diastolic volume, because the left heart in the Simulator consisted of a rigid atrial and ventricular chamber, so in diastole the LVAD was only sucking water out of the atrium while the volume of the ventricle did not change. Therefore, the -diastolic pressure did not change even when an assist device was connected and thus it was impossible to change the stroke volume of the heart according to the -diastolic pressure. So instead of using the -diastolic pressure to adjust the stroke volume, the line connecting the maximal pressures in the left ventricle was used to shift the pressurevolume loops and thereby alter the stroke volume. However, when the LVAD speed was increased, the maximal left ventricular pressure rose, which according to the implemented elastance model resulted in an increase in -diastolic volume and stroke volume. This is not what would happen in a human heart, because unloading of the failing heart with an assist device would usually lead to a decrease in -diastolic volume and stroke volume. This contradiction can be explained by the fact that the rise in maximal left ventricular pressure was not caused by the properties of the heart or the elastance model, but by the LVAD. Therefore, it was incorrect to apply the elastance model by looking at the maximal left ventricular pressure instead of the diastolic left ventricular pressure for a heart in combination with an LVAD. For this reason, not all results from the simulations performed in this study are in correspondence with physiology. In simulation series 2 and 4 where the stroke volume was decreased with each increase in LVAD speed, a decrease in workload was observed, which suggests unloading of the heart. This could be true because the stroke volume usually decreases 47

51 when an LVAD is connected, but it is not proven since the workload of the heart would always decrease when the stroke volume was decreased and the specific decreases in stroke volume used in this study were not based on the elastance model for reasons explained earlier. The only way to observe unloading in the Cardiovascular Simulator that was only due to the LVAD was when the stroke volume was kept constant and the aortic valve did not open anymore, because then the systolic left ventricular pressure dropped, which resulted in a decrease in workload. This was only the case in simulation series 3. Here the workload was lower at 3,000 rpm than at 2,500 rpm, because the aortic valve did not open any more at 3,000 rpm. However, this still is no real proof of unloading by the assist device, since only one measurement was performed with a closed aortic valve at constant LVAD speed, but it was impossible to do measurements at higher speeds because then the Simulator was expected to collapse. Unfortunately, it was not possible to compare the simulation series with the balloons with the series without a balloon quantitatively, due to altered Cardiovascular Simulator settings. This is probably due to the fact that the -systolic and diastolic pressures were almost zero, which would not lead to a change in balloon volume and therefore would also not result in a change in left ventricular stroke volume. 48

52 Section 5: Conclusions The goal of this study was to investigate if it was possible to model unloading of the heart by an assist device with the Cardiovascular Simulator, with a decrease in workload as criteria for unloading of the heart. The conclusion is that it should be possible to simulate unloading of the ventricle with the Cardiovascular Simulator used in this study, at least for a series of simulations with a constant stroke volume and a closed aortic valve. Although in this study only one simulation was performed where a constant stroke volume resulted in a closed aortic valve and thus a lower workload, it should be possible to perform more of these simulations by either reinforcing the weaker connections of the Cardiovascular Simulator so that the LVAD speed can be increased or by decreasing the stroke volume so that the aortic valve remains closed at lower LVAD speeds. However, this still does not make it possible to simulate unloading in case the aortic valve still opens. This is a problem, because in patients a situation where the aortic valve does not open is usually not desirable due to the elevated risk of fusing valves and thrombus formation in the aortic root. Therefore, it would be better if the Cardiovascular Simulator is adjusted so that unloading of the heart can be simulated when the aortic valve still opens. A first improvement would be to use a ventricular sac enclosed by a compressible medium, e.g. a combination of water and air, in order to improve the compliance of the ventricle. This would make it possible to alter the volume entrapped in the ventricle at -diastole. Furthermore, a mechanism that ensures physiological filling of the ventricle is needed so that the preload can be altered. A possible solution would be to use another Servomotor and piston for contraction of the atrium, perhaps in combination with a balloon or atrial sac to take into account the elasticity of the atrium. However, an extra reservoir would then be needed for collecting water, a function that was now performed by the atrium. With this adjusted Simulator it would be possible to investigate the influence of different assist devices on the failing heart. It would not only be possible to compare changes in workload, but also changes in pressure and flow in the left ventricle and the aorta, which are important variables in tissue perfusion and oxygenation. Another option would be to make a mathematical model to simulate unloading of the left ventricle. A first attempt was made to model the Cardiovascular Simulator (without an LVAD), which is discussed in Appix D. However, this might be a less appropriate method for comparing different assist devices, because they cannot be physically tested this way. 49

53 References 1. Suga H, Sagawa K, Shoukas AA. Load Indepence of the Instantaneous Pressure- Volume Ratio of the Canine Left Ventricle and Effects of Epinephrine and Heart Rate on the Ratio. Circ. Res. 1973; 32: Suga H, Sagawa K. Instantaneous Pressure-Volume Relationships and Their Ratio in the Excised, Supported Canine Left Ventricle. Circ. Res. 1974; 35: Gemmato CJ, Forrester MD, Myers TJ, Frazier OH, Cooley DA. Thirty-Five Years of Mechanical Circulatory Support at the Texas Heart Institute. Texas Heart Institute Journal. 2005; 32: Frazier OH, Fuqua JM, Helman DN. Clinical Left Heart Assist Devices: A historical perspective. In: Goldstein DJ, Oz MC, eds. Cardiac Assist Devices. Armonk, NY: Futura Publishing Co., Inc Cooley DA, A Brief History of Transplants and Mechanical Assist Devices. In: Frazier OH, Radovancevic B, Macris MP, eds. Support and Replacement of the Failing Heart. Philadelphia, New York: Lippincott-Raven Xydas S, et al. Mechanical Unloading Leads to Echocardiographic, Electrocardiographic, Neurohormonal, and Histologic Recovery. The Journal of Heart and Lung Transplantation. 2006; 25: Matsumiya G, et al. Who would be a candidate for bridge to recovery during prolonged mechanical left ventricular support in idiopathic dilated cardiomyopathy? J Thorac Cardiovasc Surg. 2005; 130: Frazier OH, Myers TJ. Left Ventricular Assist System as a Bridge to Myocardial Recovery. Ann Thorac Surg. 1999; 68: Unverferth DV. Dilated Cardiomyopathy. 1985, Futura Publishing Company, Inc. Mount Kisco, New York. 10. Hosenpud JD, Greenberg BH. Congestive Heart Failure. 2000, 2 nd ed, Lippincott Williams & Wilkins, Philadelphia De Robertis F, et al. Clinical Performance with the Levitronix Centrimag Short-term Ventricular Assist Device. The Journal of Heart and Lung Transplantation. 2006; 25: Operation and Installation Manual Cardiovascular Simulator. HemoLab Cardiovascular Engineering, Eindhoven, The Netherlands. 15. Guyton AC, Hall JE. Textbook of Medical Physiology. 2000, 10 th ed. WB Saunders Publishing Co., Inc. Philadelphia. 16. Rhoades R, Pflanzer RG. Human Physiology. 2003, 4 th ed. WB Saunders Publishing Co., Inc. Philadelphia Segers P, et al. Systemic and Pulmonary Hemodynamics Assessed with a Lumped- Parameter Heart-Arterial Interaction Model. Journal of Engineering Mathematics. 2003; 47: Boxenbaum H. Pharmacokinetic Tricks and Traps: Drug Dosage Adjustment in Renal Failure. J Pharm Pharmaceut Sci. 1999; 2: Holubarsch C, et al. Existence of the Frank-Starling Mechanism in the Failing Human Heart. Circulation. 1996; 94: Milnor WR Hemodynamics Williams & Wilkins, Baltimore. 50

54 Appix A: Calibration A.1 Calibration servomotor To determine the relationship between the amplitude of the piston movement and the flow in the aorta, the aorta was disconnected from the compliance chamber and connected to the lid of a 2 L cardiotomy reservoir. This reservoir was placed at such height that approximately 2/3 of the atrium could be filled with water before water flowed from the aorta into the reservoir. During simulations the water level in the atrium was kept reasonably constant by pouring water into the atrium. Multiple simulations were performed for different piston movement amplitudes in the range of 5,000 to 12,500 cts. The number of cycles per measurement varied from 40 (for 12,500 cts) to 50 (for all other simulations) due to the limited volume of the cardiotomy reservoir, which made it impossible to collect water during 50 cycles at 12,500 cts. For each simulation the average stroke volume was determined by dividing the total volume of water collected in the cardiotomy reservoir by the number of cycles. Subsequently the different stroke volumes were averaged for each piston movement amplitude, resulting in an average stroke volume per number of counts. Figure A1 shows the resulting calibration graph. 50 Stroke volume [ml] y = 0,0045x - 8,6 R 2 = 0, Amplitude piston movement [cts] Figure A1: Initial calibration graph and equation of servomotor This graph clearly is a linear line, but its interception with the y-axis does not occur at an amplitude of 0 cts. This means that not all the water that is displaced by the piston passes the aortic valve to flow into the aorta. Because the ventricular chamber is rigid and there is no significant leakage of water, some water must flow into the atrium, which is caused by the closing of the mitral valve and some leakage of this valve. To find out if the relationship between the amplitude of the piston movement and the stroke volume deps on pre- or afterload, two new sets of simulations were performed. To investigate the influence of the preload six simulations were performed at 10,000 cts with different heights of water in the atrium (three with high and three with low water levels). After these simulations it was concluded that the preload does not influence the relationship between the amplitude of the piston movement and the stroke volume. To investigate the influence of the afterload, three simulations were performed at 10,000 cts with a clamp on the aorta. Comparison of the results of these simulations with the previous simulations without clamp led to the conclusion that like the preload, the afterload does not influence the calibration graph of the servomotor. 51

55 A.2 Calibration flow sensors Method A: Calibration equation of the Servomotor With the calibration of the servomotor (see Appix A.1), the mean flow through the aorta is known for each specified amplitude of the piston movement (stroke volume times heart rate, which is always set at 60 bpm). To calibrate the flow sensor, measurements were performed at four different piston movement amplitudes (10,000 cts, 12,500 cts, 15,000 cts, and 17,500 cts). At each setting three measurements of 200 s were performed, resulting in a total of 12 measurements. Matlab was used to cut off the first 100,000 data points and subsequently calculate the mean voltage of the remaining data points for each measurement. For each amplitude, the mean voltage was determined by averaging the three different measurements. The resulting calibration graph can be seen in figure A2. 4,5 Flow [L/min] 4 3,5 3 2,5 y = 10,705x - 0,1047 R 2 = 1 2 0,2 0,25 0,3 0,35 0,4 0,45 Flow [V] Figure A2: Calibration graph and equation of flow sensor Method B: Assist device After the assist device was connected, it was used to calibrate both flow sensors. To calibrate the sensors, both the LVAS sensor and the aortic sensor were clamped around the inflow cannula of the CentriMag LVAS after which the CentriMag console was set to different rpms resulting in different flows. For each rpm-setting, a simulation of 20 cycles was performed of which the average voltages were calculated in Matlab for both flow sensors. The number of cycles is much smaller than the 200 cycles used for the initial calibration for the flow sensor, but the reason for this is that this time, the flow was constant so no equilibrium had to be reached. The corresponding reference flow in L/min was displayed on the CentriMag console. The resulting calibration graphs and equations are shown in figure A3. A 6 B Flow [L/min] y = 2 x - 0, R 2 = 0, Flow [L/min] y = 10,705x - 0,1047 R 2 = 0, , ,2 0,4 0,6 Flo w [V ] Flo w [V ] Figure A3: A) Calibration graph and equation of LVAS flow sensor; B) Calibration graph and equation of aortic flow sensor. 52

56 A.3 Calibration pressure sensors Method A: Veri-Cal To calibrate the pressure sensors, the Veri-Cal of UTAH Medical Products was used to apply different pressures in the range of 0 to 200 V to the pressure sensors. For each pressure a simulation of 20 cycles was performed. Matlab was used to calculate the average voltage, leading to the calibration graphs shown in figure A4. A 200 B 200 Pressure [mm Hg] y = 100,43x + 0,1222 R 2 = ,5 1 1,5 2 Pressure [mm Hg] y = 100,42x - 31,666 R 2 = ,5 1 1,5 2 2,5 Pressure [V] Pressure [V] Figure A4: A) Initial calibration graph and equation of aortic pressure sensor; B) Initial calibration graph and equation of left ventricular pressure sensor. Method B: Water colon An alternative method to calibrate the pressure sensors is by using a colon of water to apply pressure to the pressure sensors. Because this is less accurate than the Veri-Cal, this method was performed on the aortic pressure sensor only, as a validation of method A. One of a tube with an inner diameter of 2.7 cm was closed off, while water was poured into the tube up to a height of 1 m. First, three measurements of 20 cycles were performed with the sensor opened to air, after which the sensor was placed on the bottom of the tube for three measurements. After calculating the average voltage per measurement in Matlab, the average voltage was determined for each set of three measurements. Using the equation of the Veri-Cal calibration, the corresponding pressures were calculated, which were 71 mm Hg for 1 m of water and 2 mm Hg in air. These values deviated only slightly from the expected values, so this deviation was attributed to inaccuracies of method B. 53

57 A.4 Calibration balloons Before the simulations described in section 2.4 Compliance of the ventricular chamber were performed, several other attempts were made to calculate the pressure change for a reduce of the air volume in the balloon. Method A: First the balloons were filled with 100 ml of water each and put into the jar mentioned in section 2.4 Compliance of the ventricular chamber. The 30 ml syringe was filled with water and during the experiment there were several injections of 5 ml to measure the pressure at different injection volumes. At each ejection the pressure in the jar rose a bit, but due to leakage of the jar, the pressure slightly dropped again after each injection, see figure A5. Figure A5: Pressure change in a jar with two balloons each filled with 100 ml of water, with several injections of 5 ml. Because the leakage of the jar was too large, this was not a very good method. Method B: After this, the same air volume of 100 ml in each balloon was used. However, it was decided to inject a larger volume (20 ml) at once, see figure A6. Figure A6: Pressure change in the jar when 20 ml of water was added. 54

58 This seemed to be a better method, because less leakage is observed. According to Boyle s Law (see equation (11)): 5 4 C p V J (A1) Then, when 20 ml of water is injected (the balloon volume becomes 80 ml), the pressure should become equal to Pa, or mm Hg. From figure A6 it can be observed that the pressure signal increased to 2.5 V after the injection. This corresponds with a pressure of Pa, or mm Hg, which is still quite a difference. Probably the surface of the balloon was stretched a bit, which caused the air to be compressed even before the balloon was put into the jar. As a result a slightly higher pressure was needed to reduce the air with another 20 ml. Therefore this experiment was repeated with a smaller air volume (80 ml), which is described in section 2.4 Compliance of the ventricular chamber. This experiment resulted in a better correspondence between the measured and the calculated pressure and so this volume was chosen to be used during the simulations with the Cardiovascular Simulator. 55

59 Appix B: Data processing B.1 Pressure and flow signals To obtain the pressure and flow signals, the data (txt-files) acquired with the HemoLab software were loaded in Matlab. After this, the data points between 100 and 151 s were selected (data points 100,001 to 150,000). The first 100,000 data points were deleted to be certain of a state of equilibrium, and because not all data files were of the same length, an interval of 50 s after these first 100 s was chosen for further data processing. The selected data were converted from V to Pa (pressure signals) and m 3 /s (flow signal) using the calibration equations of the pressure and flow sensors. The pressure signals were filtered using a 4 th order low pass digital Butterworth filter with a cutoff frequency of 5 Hz. According to Milnor [22] it was not necessary to include higher frequencies. Since the flow signal was already filtered by the flow sensor transducer, no further filtering was needed for this signal. Figure A7 shows both the filtered and unfiltered pressure signals. The filtered flow and pressure signals were converted to mm Hg (pressure) and L/min (flow), after which plots could be made. A B Figure A7: A) Unfiltered and filtered aortic pressure signals; B) Unfiltered and filtered LV pressure signals. 56

60 B.2 Left ventricular pressure volume loop For the pressure volume loop, the left ventricular volume had to be calculated in time. This left ventricular volume array was calculated with equation A2. V ) lv ( i) Vlv, ED, 0 x( i u piston um Ap (A2) Here, V lv (i) is the left ventricular volume at sample point i in m 3, V lv,ed,0 is the initial -diastolic volume of the left ventricle in m 3, x(i) is the normalized displacement at sample point i, u piston is the amplitude of the piston movement in cts, u m is the displacement of the piston in m/cts and A p is the cross-section of the piston in m 2. Furthermore, the filtered left ventricular pressure signal was averaged over the 50 selected cycles, resulting in an average left ventricular pressure wave. This was done because for the pressure volume loop, the left ventricular pressure had to be plotted against the left ventricular volume so it would be impossible to select just one loop by zooming in on the graph like could be done for the pressure and flow signals. The choice was made to calculate an average pressure volume loop as can be seen in figure A8. The averaged signal was sampled with 0.1 Hz to obtain a data array of 100 sample points, the same Figure A8: Left ventricular pressure volume loops number of sample points as the left ventricular volume array. The measured left ventricular pressure signal did not correspond to the volume signal in time resulting in double loop as can be seen in panel A of figure A9. To solve this problem, the -diastolic left ventricular pressure was detected, after which the pressure and flow signals were shifted in order to match this data point to the -diastolic volume data point. The shifted signals were converted to mm Hg (pressure signals), L/min (flow signal), and ml (ventricular volume) after which the plot could be made as seen in panel B of figure A9. A. B Figure A9: A) Left ventricular pressure volume loop with unshifted pressure signal; B) Left ventricular pressure volume loop with shifted pressure signal. 57