Figure4 shows the simulation results for a number of variables as a function of simulation time in seconds. These results have already been presented in (Dı´az- Zuccarini et al. 2008). The rate of increase of ventricular pressure is shown in Fig. 4a, the change in ventricular pressure is determined by the definition of the boundary condition model described in Sect. 3.1. The pressure applied at the boundary depends on both the parameters used to define the boundary condition model and the flow calculated in the 3D model.
The angular position of the occluder is shown in Fig.4b. A number of rebounds of the valve leaflet are observed after the initial closure event which is likely to be associated with the numerical implementation of valve closure, where the valve is restricted from rotating beyond an angular position of 0. This leads to a large acceleration of the occluder at the instant when the valve reaches the 0position, in the case of ain vivovalve this effect would be affected by the compliance of the valve mounting. This effect is even more noticeable if we consider the angular
8000 6000 4000 2000 0
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0.01 a
b
c
0.02 time (s)
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0.01 depth (mmHg/s) θ (degree)
200 0 ω (degree) -200
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0.03 0.04 0.05
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time (s)
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Fig. 4 (a) Rate of increase of ventricular pressure vs. time. (b) position history of the occluder vs.
time. (c) Angular velocity of the valve vs. time
velocity of the valve as shown in Fig.4c. There is a significant discontinuity in the angular velocity at the instant of initial valve closure and at each successive time when the valve reaches an angular position of 0.
It is interesting to note that from the implementation point of view, closure is continuous and smooth. The valve closure time predicted by the analysis is 34.4 ms, as measured from the moment when the valve starts to move until the end of the first rebound, which is within the range of experimentally reported values (Hose et al.2006).
To investigate the cavitation potential of the valve, negative pressure values below the vaporization threshold and evidence of vortex formation on the surface of the leaflet were looked for. The pressure field in Fig.5 clearly demonstrates the presence of negative gradients. Negative pressure values alternate on the surface of the leaflet, depending on the direction of movement (Fig. 5). During backward movement (rebound), negative pressure values and vortex flow predominate; whilst during forward movement, vortexes progressively change into swirl flow and negative pressure values decrease. This observation is consistent with experimental observations (Chandran et al.1998) which, in the case of non-overlapping single- disc mechanical heart valves, (the Medtronic-Hall valve, for example) show that fluid vaporization is localized towards the upper (larger) gap.
2 Application 2: An Engineering Approach to Study Percutaneous Valve Implantation Using Structural Simulations
According to the American Heart Association, valvular heart disease is responsible for nearly 20,000 deaths each year in the United States, and is a contributing factor in about 42,000 deaths. Until recently, treatment has required surgical repair or Fig. 5 Left: Pressure fields and vortex formation at the surface of the occluder and the housing, during rebound (at t¼0.0428 s).Right: Pressure fields at the surface of the occluder and the housing, during forward movement (at t¼0.0457 s)
Biomedical Imaging and Computational Modeling in Cardiovascular Disease. . . 181
replacement of the affected valve, usually with cardiopulmonary bypass, and the concomitant complications and serious risks associated with open-heart surgery.
In the late 1990’s, Professor Philipp Bonhoeffer developed a new technique of heart valve replacement that avoided the need for surgery (Bonhoeffer et al.2000).
This was based on the concept that a heart valve sewn inside a stent (Fig.6a) could be reduced in size, by crimping it onto a balloon catheter (Fig. 6b), and then introduced through a peripheral vessel to the desired implantation site in the heart.
Inflation of the balloon deploys the valved stent and anchors it within the old dysfunctional valve (Fig. 6c). Over the last 9 years, this simple technique has shown a marked learning curve with safety and efficacy improvements that have led to the successful, worldwide clinical use of this procedure in over 1,500 implants in the pulmonary position (Lurz et al.2008) and thousands of implants in the aortic position (Chiam and Ruiz2009).
Percutaneous pulmonary valve implantation (PPVI) potentially avoids multiple open-heart surgeries in patients with dysfunctional pulmonary valve both to reduce regurgitation and to treat stenosis. The device is made of a valve from a bovine jugular vein, sewn into a balloon-expandable, platinum-10% iridium stent (Fig.6a).
Bovine jugular venous valves are available only up to 22 mm of diameter, thus limiting the use of this minimally-invasive technique to those patients who have a small implantation site. Selection of patients for PPVI is critical to ensure proce- dural success and to guarantee long-term positive outcome, with no stent fracture occurrence (Khambadkone et al. 2005). Surgical history alone is not enough to decide whether a patient is suitable for the procedure or not; assessment of the implantation site with magnetic resonance (MR) imaging provides important addi- tional information, but a complete understanding of the three-dimensional (3D) anatomy of the implantation site is necessary, not only to guarantee the success of this procedure, but also to study new devices in order to broaden the range of patients who could benefit from this treatment.
The aim of this work was to improve the understanding of the effects of patient specific implantation site morphologies on PPVI device mechanical performances, using a combination of imaging and engineering techniques.
Fig. 6 The PPVI device (a) is mounted onto the catheter for delivery (b). Once in place, the device is inflated: the stent anchors the valve to the RVOT as shown from the post-PPVI angiogram (c)