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Engineering Aspects–Pulsatile vs Nonpulsatile Flow

Energy Equivalent Pressure and Total Hemodynamic Energy Associated with the Pressure-Flow Waveforms of a Pediatric Pulsatile Ventricular Assist Device

Weiss, William J.*; Lukic, Branka*; Ündar, Akif

Author Information
doi: 10.1097/01.mat.0000179341.95404.f8
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Abstract

The Penn State Pediatric Ventricular Assist Device (PVAD) is a pulsatile, pneumatically actuated assist pump, similar in design to the adult-size Pierce-Donachy VAD (Thoratec VAD).1 The pump uses a segmented poly(ether polyurethane urea) blood sac and diaphragm. The dynamic stroke volume ranges from approximately 10 to 15 ml, depending on valve type and operating conditions.

The PVAD is a positive-displacement pump with a stroke volume similar to that of the infant native ventricle. Although the PVAD is inherently pulsatile, the length of the ejection phase (PVAD systole) may be adjusted by setting the systolic duration and systolic drive pressure. Short systolic duration and high drive pressure produces the highest pulsatility but also results in higher shear stresses in the outlet cannula due to the significant impedance of the small diameter pediatric cannulae. This study was undertaken to study the effect of operating conditions on PVAD pulsatility by quantifying pulsatility in terms of the energy equivalent pressure (EEP),2 and to quantify the cannula hemodynamic energy losses.

Materials and Methods

A test version of The Penn State PVAD, as shown in Figure 1, was constructed for particle image velocimetry, high-speed video flow visualization, and in vitro testing. Björk-Shiley tilting disk valves were used in this study.

Figure 1.
Figure 1.:
The Pediatric VAD flow visualization pump on the mock circulatory loop.

The PVAD was connected to a Penn State mock circulatory loop. Each cannula consisted of Tygon tubing 15 cm in length with an internal diameter of 9.52 mm (0.375 in) at the pump end, tapering to 6.35 mm (0.250 in) at the mock loop end. The loop connector included an orifice of internal diameter 4.44 mm (0.175 in) and 20.6 mm (0.81 in) in length, which simulated the reduced diameter of the cannulae tip. The PVAD was positioned with the plane of the diaphragm horizontal, at the height of the inlet and outlet compliances.

The systemic arterial compliance spring length was adjusted for pediatric simulation so that the arterial systolic and diastolic pressures were approximately 90/60 mm Hg with the PVAD stroke volume of approximately 12 ml and the systolic duration of 300 milliseconds. The arterial compliance was not re-adjusted for changes in systolic duration. Mean inlet pressure was adjusted by adjusting the height of a venous reservoir.

The following measurements were obtained:

  • Venous pressure (pV) measured at the inlet compliance
  • Arterial pressure (pA) measured at the arterial compliance
  • Outlet pressure (pO) measured at the outlet cannula approximately 1 cm from the pump outlet connector
  • Driveline pressure (pD) measured at the pump
  • Outlet cannula flow (qO) measured with a model T206 Transonic flowmeter (Transonic Systems Inc., Ithaca, NY)
  • Systemic flow (qS) measured with a rotameter (ABB model 10A4555SYBH, Warminster, PA)

Data were acquired using a National Instruments SCXI system and BioBench software (National Instruments, Austin, TX) with a sampling rate of 1000 samples/s. Approximately 1 minute of data was recorded at each test condition.

The mean nominal flowrate was set at 0.50, 0.75, 1.00, and 1.25 l/min by adjusting the PVAD rate, inlet pressure, and diastolic vacuum (see Table 1). The systolic duration was set at either 230 or 400 milliseconds, although at the highest flow condition the longest duration for which the target flow of 1.25 l/min could be achieved was 350 milliseconds.

Table 1
Table 1:
Results for Four Nominal Flowrate Conditions, Comparing Rapid Systolic Ejection (230 milliseconds) with Slow Systolic Ejection (350–400 milliseconds)

A program was written in Matlab and Simulink (Mathworks, Cambridge, MA) to calculate the following parameters for each PVAD beat of interval T:

Each parameter was recorded at the end of each beat. EEP as defined by Shepard et al.2 is the energy per unit volume of blood pumped. EEP has the units of J/m3, and is equivalent to units of pressure. The arterial EEP is that “seen” by the patient at the aortic anastomosis, distal to the outlet cannula. The pump EEP is measured at the proximal end of the cannula. The difference between proximal and distal EEP is a measure of energy loss across the cannula.

Results

An example of the waveforms for the 0.75 l/min (nominal) condition is shown in Figure 2. The overall results are summarized in Table 1. Mean arterial pressure was kept nearly constant, ranging from 72.7 to 75.6 mm Hg. Mean and standard deviations are shown for approximately one minute of data in each condition, such that the number of MAP and EEP data points ranges from 45 beats to 103 beats. A higher pump rate was required in all cases for the longer duration systole to obtain a mean flowrate equivalent to the shorter systolic duration.

Figure 2.
Figure 2.:
Examples of waveforms obtained at a nominal mean flowrate of 0.75 l/min systolic with systolic duration of 230 milliseconds and systolic driving pressure of 350 mm Hg (left column) and systolic duration of 400 milliseconds and systolic driving pressure of 120 mm Hg (right column). Arterial pressure is measured in the arterial compliance chamber, and pump outlet pressure is measured directly at the pump outlet connector, proximal to the outlet cannula.

As shown in Figure 3, for all conditions the systemic arterial EEP was significantly higher than the MAP. The difference between arterial EEP and MAP was more pronounced at the shorter systolic duration, as expected for a more pulsatile duty cycle. The effect of experimental variations in MAP is eliminated in Figure 4, where the increase in EEP relative to MAP is shown. The greatest difference (8.4%) occurred at the lowest mean flowrate (0.50 l/min) and shortest systolic duration (230 milliseconds).

Figure 3.
Figure 3.:
The arterial energy equivalent pressure (EEP) compared with the mean arterial pressure (MAP).
Figure 4.
Figure 4.:
The same data as Figure 3 expressed as arterial EEP relative to MAP. EEP is also seen to decrease as mean flow (and beat rate) increases.

The equivalent energy loss due to the outlet cannula is shown in Figure 5, where the EEP calculated at the pump end of the outlet cannula is highly dependent on systolic duration, demonstrating the importance of cannula impedance in pulsatile flow.

Figure 5.
Figure 5.:
A comparison of energy equivalent pressure measured at the proximal and distal ends of the outlet cannula demonstrates significantly higher mean energy losses with a shorter systolic ejection time.

Discussion

Energy equivalent pressure is a measure of hemodynamic energy that is useful in comparing the effect of systolic duration and cannula design. This quantitative approach may be used to assess the tradeoffs in delivering a high level of pulsatility to the patient versus minimizing the energy loss in the small diameter pediatric cannulae.

The highest arterial EEP, relative to the MAP, was found at the lowest flowrate (and pump beat rate). Arterial EEP decreased as the flowrate and beat rate increased, for a given systolic duration, in nearly all cases. A similar increase in EEP at lower beat rates was observed using the adult pneumatic VAD.3

Referring to the 0.75-l/min mean flowrate data in Figure 2, the peak outlet flowrate reached approximately 4.7 l/min at 230 milliseconds systolic duration, and only 2.4 l/min at 400 milliseconds systolic duration. As expected, longer systolic ejection time results in a reduced EEP relative to the shorter ejection times.

The pressure drop in the outlet cannula may be estimated from the pressure differential (equal to pump outlet pressure minus arterial pressure) at any point in time, as seen in Figure 2. Alternatively, a single parameter such as the differential EEP (equal to pump EEP minus arterial EEP) may be useful. For example, for the 0.75-l/min condition, the cannula differential EEP (mean) was 158.1 mm Hg at 230 milliseconds, and 25.2 mm Hg at 400 mm Hg. The outlet cannula differential EEP for all flowrate conditions, shown in Figure 6, is relatively constant and may be used as metric for comparing cannulae in pulsatile modes.

Figure 6.
Figure 6.:
The differential EEP for the outlet cannula.

Conclusion

This study demonstrates the use of the energy equivalent pressure to quantify the changes in pulsatility due to variations in beat rate and systolic duration in a pulsatile pediatric VAD. Additionally, the EEP difference across the outlet cannula may be a useful parameter for cannula comparisons in pulsatile flow.

Acknowledgment

This research is funded by the National Heart, Lung, and Blood Institute Contract N01-HV-48191.

References

1. Pierce WS, Rosenberg G, Donachy JH, et al: Postoperative cardiac support with a pulsatile assist pump: techniques and results. Artif Organs 11: 247–251, 1987.
2. Shepard R, Simpson D, Sharp J: Energy equivalent pressure. Arch Surg 93: 730–740, 1966.
3. Undar A, Zapanta CM, Reibson JD, et al: Precise quantification of pressure flow waveforms of a pulsatile ventricular assist device. ASAIO J 51: 56–59, 2005.
Copyright © 2005 by the American Society for Artificial Internal Organs