The Influence of a Nonlinear Resistance Element Upon In Vitro Aortic Pressure Tracings and Aortic Valve Motions : ASAIO Journal

Secondary Logo

Journal Logo

Medical Instrumentation

The Influence of a Nonlinear Resistance Element Upon In Vitro Aortic Pressure Tracings and Aortic Valve Motions

Scharfschwerdt, Michael; Misfeld, Martin; Sievers, Hans-H.

Author Information
ASAIO Journal 50(5):p 498-502, September 2004. | DOI: 10.1097/01.MAT.0000137038.03251.35
  • Free


In vitro testing of biological heart valves requires pressure and flow waveforms closely simulating natural conditions, which are mainly influenced by the characteristics of the vascular system. Simulation of the arterial function in artificial circulations was mostly performed by the useful Windkessel model but sometimes failed by generating inadequate systolic pressures. The integration of a novel nonlinear resistance element may improve the Windkessel function. Native porcine aortic valves were studied in a mock circulation with a novel nonlinear resistance element combined with the Windkessel compared with an aperture plate resistance. Pressure and flow measurements were performed at varying heart rates and stroke volumes and analyzed in the time and frequency domain. Aortic valve motions were evaluated using high speed video recording. With the classical afterload configuration including an aperture plate resistance, the pressure tracings showed a nonphysiologic decrease of pressure during systole after early peak pressure. By integration of the novel nonlinear resistance, peak systolic pressure occured later, peak pressure was higher, and the pressure waveform was more physiologically shaped. Leaflet motions of the aortic valves were less oscillatory and compared well with in vivo characteristics. In conclusion, a novel nonlinear resistance element in a mock circulation has the potential to provide more physiologic aortic pressure waveforms as influencing aortic valve dynamics and thus may be a helpful tool for investigation of biological heart valves.

Testing new valve devices and studying physiologic heart valve characteristics in vitro requires not only the generation of an adequate ventricular volume displacement but also the simulation of the hydraulic properties of the arterial system.

The pulse in the arteries generated by the heart is modulated by many factors, such as the Windkessel of the great arteries, reflections of pulse waves, and neurologic and humoral characteristics. 1–4 The concert of all of these parameters results in the well known pressure and flow curves in the ascending aorta. Simplified, the vascular system can be described by a peripheral resistance, a characteristic resistance or impedance, and an arterial compliance, together called the Windkessel. This useful model corresponds to physiologic counterparts and provides hydraulic practibility, but it does not completely account for wave travel. O’Rourke 1 described the arterial system as a more complex transmission line where the major functions, which are blood distribution in the conduit and attentuation of pulsations (cushioning function), were strictly combined in the aorta and the central elastic arteries. Both functions were furthermore influenced by geometric and viscoelastic nonuniformities. 4

Simulation of these conditions in an artificial circulation is limited by material properties and constructive means. A few complex hydraulic models of the arterial tree were presented 5–8; indeed, in most reports classical Windkessel configurations were used, with restrictor clamps or aperture plates for simulating peripheral resistance and central air chambers together simulating the arterial function. By doing so, these artificial pressure tracings often show a typical nonphysiologic pressure decrease during systole after early generation of peak pressure. 9–12 To overcome this obstacle, we combined a novel nonlinear resistance device with the central air compliance chamber and evaluated its influence upon aortic pressure and valve motion.

Materials and Methods

Test Apparatus

The principle structure of the pulse duplicator system is depicted in Figure 1. An open reservoir 1 with its fluid level adjustable above the valve position provides the atrial pressure load. The pulsatile flow is generated by a short stroke piston pump 2 driven by waveform adapted cam plates 3 at various frequencies and stroke volumes. The piston has a diameter of 110 mm and is built of light acrylic material for small inertia. A plain latex membrane acts as sealing and lead. To minimize negative pressure while filling the pump in diastole, the input of the pump is built with two specially designed disc valves representing the mitral valve 4 with little inertia during opening and nonleakage closure. An adjustable air compliance chamber 5 at the pump outflow simulates ventricular impedance to avoid pressure and flow oscillations in systole. 9 The aortic roots are mounted straight ahead of the pump, free standing between two holders in a fluid reservoir 6 to keep the material moist. Above the aortic root section, a box with an optical window at the upper side is mounted, 7 which permits a view of the investigated valve.

Figure 1.:
Scheme of the test apparatus. 1) Atrial reservoir; 2) Piston pump; 3) Waveform adapted cam plate; 4) Disc valves; 5) Adjustable input compliance; 6) Fluid reservoir; 7) Visualization chamber; 8) Height variable fluid column; 9) Adjustable aortic compliance; 10) Nonlinear resistance element; 11) Pressure sensors; 12) Ultrasonic flow probe; 13) High speed camera.

The afterload system consists of three elements: a height variable fluid column 8 providing constant diastolic pressure, an adjustable air compliance chamber 9 to provide the characteristic aortic compliance, and the newly developed nonlinear resistance element. 10 The element is a cylindrical block of 100 mm height and 48 mm diameter, mounted inside the upper end of the afterload column (Figure 2, upper). To prevent movement of the element, wide meshed grids were mounted above and below. The resistance element was made of a compressible plastic material (Eulastic HR23, Kabelwerk Eupen, Belgium) with fine open pores of approximately 0.9 mm (Figure 2, lower). The characteristics of the material were a low density (ρ = 21 kg/m3) and a low deformation coefficient of approximately 0.5 N/mm. During the simulated cardiac cycle, the block is compressed (Figure 3, a and b), forced by the dynamic pressure of the flowing liquid. This deformation causes a decrease of pore diameter and therefore an increase of flow resistance with a nonlinear characteristic following a third order polynomial (Figure 3, c).

Figure 2.:
Photographs of the resistance device. Above, device mounted inside the afterload column. Below, cross-section of the element illustrating the fine porous structure of the material.
Figure 3.:
Scheme of the nonlinear resistance element. Diastolic state (a) compression of the element during systole (b) pressureflow relationship of the novel resistance element (c).

Data Acquisition

For the determination of pressure differences across the investigated native aortic porcine valves, pressure values were measured 4 cm upstream and 6.5 cm downstream of the valve using Envec Ceracore M capacitive pressure transducers (Endress+Hauser, Maulburg, Germany). 11 The flow through the valves was measured upstream of the valve mounting with a HT207 ultrasonic flowmeter (Transonic Systems Inc., Ithaca, NY). 12 Both pressure and flow signals were low pass filtered at 100 Hz. Data were collected using a 16 bit multichannel analog to digital converter for 10 seconds each, run at a rate of 500 samples per second or, if combined with the valve motion recording, for 2 seconds (1,024 frames) at the same sampling rate.

Valve motions were recorded with a Motionscope HR-1000 high-speed camera (Redlake Imaging Corp., Morgan Hill, CA) at a rate of 500 frames per second, positioned straight above the valve outflow. Video data were digitized and analyzed with a custom made motion evaluation software. Both video and data recording were started simultaneous and synchronized by trigger signals from the high speed camera. Time delay between measured data and video recording was less than 3 ms.

System Evaluation

The hydraulic performance of the mock circulation was evaluated by testing native porcine aortic roots in a normal vascular state using the newly designed nonlinear resistance device in comparison with an aperture plate resistance. Tests were performed at different heart rates (40, 52, 64, and 80 bpm) and stroke volumes (54 and 82 ml), representing cardiac output in a range of 2–6.5 L/min. Diastolic pressure was set to 80 mm Hg, atrial pressure was 10 mm Hg, and systolic forward flow was fixed at 32% of the cycle time. Aortic compliance was adjusted to 1.0 mm Hg/ml. Experiments were performed with eight native aortic roots; measurements were repeated 10 times for each root and test condition. Mean pressure drop, peak flow, mean flow, closing volume, leakage volume, and total regurgitation were calculated from the data using a commercial spreadsheet analyses program following the ISO 5840. 13 Data are presented as mean ± SD, and for comparison between the different setups, Student’s t-test was applied.

Additionally, Fourier analyses were performed upon the aortic pressure and flow signals to determine the characteristics of the afterload systems. Arterial input impedance was calculated from the corresponding pressure and flow harmonics. Total peripheral resistance (impedance at zero frequency) and characteristic impedance (average of impedance moduli from 5–15 Hz) were estimated from the impedance spectrum and compared with in vivo data.


Total values of hemodynamic parameters increased with heart rate and stroke volume, but differences between the investigated afterload models were similar at all test conditions. Values were given for a common heart of 64 bpm and a stroke volume of 54 ml.

With only a fixed arterial resistance combined with the classical air compliance chamber, the pressure curve showed a typical decrease of pressure during systole after early peak pressure increase (Figure 4, above right). With the novel nonlinear resistance pressure tracings (Figure 4, above left) simulated more closely the natural systolic pressure waveform. Peak systolic pressure occurred later (138 ± 5 ms vs. 75 ± 2 ms; p = 0.004) and peak pressure was higher (124.5 ± 0.1 mm Hg vs. 111.7 ± 0.3 mm Hg; p = 0.0003), whereas the maximum rate of left ventricular pressure change dp/dt was similar in both groups (539.1 mm Hg/s for the nonlinear resistance vs. 536.3 mm Hg/s for the fixed resistance). Peak systolic flow was higher for the group with the fixed resistance (15.21 ± 0.09 L/min vs. 14.68 ± 0.04 L/min; p = 0.026) and also mean systolic flow (9.70 ± 0.02 L/min vs. 8.95 ± 0.01 L/min; p ± 0.011). Pressure gradients were not affected by the resistance type (3.91 ± 0.02 mm Hg vs. 3.93 ± 0.16 mm Hg) and also closing volume (3.52 ml ± 0.08 vs. 3.68 ± 0.12 ml).

Figure 4.:
Example aortic pressure, flow and valve opening plots at a heart rate of 64 bpm. Left, afterload with novel nonlinear resistance. Right, Classical afterload configuration with an aperture plate resistance.

The different modes (Windkessel with aperture plate and Windkessel with nonlinear resistance) led to different leaflet motion characteristics of the tested biological valves depicted in Figure 4. Initial opening was comparable between both models (42.1 ± 2.5 ms for the nonlinear resistance vs. 42.8 ± 3.1 ms for the aperture plate resistance) and was independent on heart rate or stroke volume. Maximum valve opening was reached at approximately 64% of peak flow, then the valves tend to close slowly with a decrease of area of 33% for the nonlinear resistance and 42% for the aperture plate resistance. Early systolic closing motion was smoother, with attenuation of the leaflet oscillations, when the nonlinear resistance device was used.

Frequency domain characteristics of both Windkessel models are depicted in Figure 5. In general, the patterns of input impedance in both models compare well with physiologic data and vary negligible with heart rate and stroke volume. Total peripheral resistance in both models was higher than in vivo14,15 (2.063 ± 0.19 mm Hg·s/ml for the nonlinear resistance and 1.699 ± 0.07 mm Hg·s/ml for the aperture plate resistance). Characteristic impedances of the models were comparable with physiologic values, but with the aperture plate resistance characteristic impedance was higher than for the nonlinear resistance (0.139 ± 0.01 mm Hg vs. 0.076 ± 0.02 mm Hg·s/ml; p = 0.008). Differences between the two models were also found in the phase of input impedance (Figure 5, lower panel); at frequencies below 5 Hz, the phases changed to positive values when the nonlinear resistance device was used, indicating a more inductive characteristic.

Figure 5.:
Frequency domain characteristics of the novel afterload system compared with the classical afterload.


In this study, we demonstrate that the integration of a nonlinear resistance element in the arterial tree of a mock circulation provides arterial pressure tracings in the ascending aorta, more closely simulating natural conditions.

It remains questionable whether the natural conditions of pressure and flow in the arterial tree, which follow extremely sophisticated mechanisms, can be exactly simulated by mechanical properties. However, to come as close as possible to these normal pressure and flow configurations is important for studying the physiology of native heart valves and artificial or biological substitutes. Original pressure tracings of mock circulations published in recent reports show a typical decreasing of pressure after generation of peak pressure during systole, 9–12 probably related to inertial effects, which can hardly be oppressed by linear peripheral resistances as created by restrictor clamps or aperture plates. An improvement could be obtained by the integration of a compressible nonlinear working resistance element in the arterial tree of the mock circulation. This element is compressed by the flow pulse, causing some kind of deceleration of flow velocity and thus pressure retaining between valve and resistance element, ending up in more physiologic pressure tracings as is shown in Figure 4. A possible explanation is the more inductive characteristic of the novel afterload system compared with the aperture plate afterload. Phase angles of input impedance of the novel arterial afterload were positive at low frequencies (Figure 5, lower panel), indicating an inductive resistance, which causes a delay of flow versus pressure. The resulting systolic pressure elevation suitably compensates the nonphysiologic pressure drop caused by inertia; indeed, these phases do not properly represent in vivo characteristics.

The advantage of this nonlinear resistance element can also be demonstrated for leaflet motions of the native aortic valves. Opening and closing characteristics compare with native data, 16–19 showing the distinctive three stage leaflet movement with rapid opening, early slow closing motion during systole, and rapid final closure. Motions of the leaflets were smoother using the novel afterload with attenuation of the oscillations of the leaflets (Figure 4).


A nonlinear resistance element in the arterial tree of a mock circulation has the potential to provide pressure curves more closely simulating physiologic conditions and also normalizing aortic valve motion characteristics. The described afterload system expands the practical and easy to reproduce Windkessel model concerning pressure associated phenomena and may be a helpful tool for in vitro investigations of biological heart valves.


1. O’Rourke MF: Vascular mechanics in the clinic. J Biomech 36: 623–630, 2003.
2. Matonick JP, Li JK-J: Pressure-dependent and frequency domain characteristics of the arterial system. Cardiovasc Eng 1: 21–29, 2001.
3. Latham RD, Westerhof N, Sipkema P, Rubal BJ, Reuderink P, Murgo JP: Regional wave travel and reflections along the human aorta: A study with six simultaneous micromanometric pressures. Circulation 72: 1257–1269, 1985.
4. Matonick JP, Li JK-J: A new nonuniform piecewise viscoelastic model of the aorta with propagation characteristics. Cardiovasc Eng 1: 37–47, 2001.
5. Ferrari G, DeLazzari CD, Kozarski M, et al: A hybrid mock circulatory system: Testing a prototype under physiological and pathological conditions. ASAIO J 48: 487–494, 2002.
6. Sharp MK, Dharmalingam RK: Development of a hydraulic model of the human systemic circulation. ASAIO J 45: 535–540, 1999.
7. Segers P, Dubois F, De Wachter D, Verdonck P: Role and relevancy of a cardiovascular simulator. Cardiovasc Eng 3: 48 –56, 1998.
8. Wu ZJ, Gao BZ, Hwang NHC: Transient pressure at closing of a monoleaflet mechanical heart valve prothesis: Mounting compliance effect. J Heart Valve Dis 4: 553–567, 1995.
9. Jennings LM, Butterfield M, Walker PG, Watterson KG, Fisher J: The influence of ventricular input impedance on the hydrodynamic performance of bioprosthetic aortic roots in vitro. J Heart Valve Dis 10: 269 –275, 2001.
10. Schaub JD, Koenig SC, Schroeder MJ, Ewert DL, Drew GA, Swope RD: Development of a flow feedback pulse duplicator system with rhesus monkey arterial input impedance characteristics. ASAIO J 45: 334 –338, 1999.
11. Schichl K, Affeld K: Computer controlled versatile pulse duplicator for precision testing of artificial heart valves. Int J Artif Organs 16: 722–728, 1993.
12. Fisher J, Jack GR, Wheatley DJ: Design of a function test apparatus for prosthetic heart valves. Initial results in the mitral position. Clin Phys Physiol Meas 7: 63–73, 1986.
13. International Organization for Standardization. ISO 5840: Cardiovascular implants–Cardiac valve protheses. Third Edition 1996.
14. Murgo JP, Westerhof N, Giolma JP, Altobelli SA: Aortic input impedance in normal man: Relationship to pressure waveforms. Circulation 62: 107–116, 1980.
15. Nichols WW, Conti CR, Walker WE, Milnor WR: Input impedance of the arterial circulation in man. Circ Res 40: 451–458, 1977.
16. Higashidate M, Tamiya K, Beppu T, Imai Y: Regulation of the aortic valve opening. In vivo dynamic measurement of aortic valve orifice area. J Thorac Cardiovasc Surg 110: 496–503, 1995.
17. Thubrikar MJ, Heckman JL, Nolan SP: High speed cine-radiographic study of aortic valve leaflet motion. J Heart Valve Dis 2: 653–661, 1993.
18. Van Steenhoven AA, Verlaan CW, Veenstra PC, Reneman RS: In vivo cinematographic analysis of behaviour of the aortic valve. Am J Physiol 240: H286 –292, 1981.
19. Laniado S, Yellin E, Terdiman R, Meytes I, Stadler J: Hemodynamic correlates of the normal aortic valve echogram. Circulation 54: 729 –737, 1979.
Copyright © 2004 by the American Society for Artificial Internal Organs