A Computational Fluid Dynamic Analysis of Various Heart Valves and Aortic Conduits, on Coronary Filling

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1 A Computational Fluid Dynamic Analysis of Various Heart Valves and Aortic Conduits, on Coronary Filling Joseph A. Knight, B.S. University of South Florida, Chemical Engineering Karl Muffly, PhD University of South Florida, Medical School Department of Anatomy Joel A. Strom, MD University of South Florida, Medical School Division of Cardiovascular Disease Michael D. VanAuker, PhD University of South Florida, Chemical Engineering and Internal Medicine Abstract Introduction: Aortic heart valve replacement/reconstruction may involve alterations of the geometry of the anatomic valve and surrounding tissue (often to the extent of complete excision). Several different types of valves and aortic prosthesis conduits are at the surgeon s disposal to aid in repair, but what are the benefits of each? We sought to create models to investigate the benefits of these different options on the fluid dynamics into the coronary arteries, and hence the flow to the myocardial tissue. Procedure: Valve geometries of tri-leaflet (to represent normal anatomic and bio-prosthetic configuration), bi-leaflet (St. Jude), and single disc (Bjork-Shiley), were compared with a sinus and non-sinus conduit. The coronary arteries were placed at 17mm, based on 30 cadaver measurements (measured from the sinus leaflet junction straight up to the center of the coronary opening). As 85% of resting coronary filling occurs during diastole, the valves were placed in a closed position; a falling backpressure was placed at the aorta, and an outlet pressure at the coronary arteries of 5mmHg to represent coronary backpressure. Simulations were run at one millisecond time steps, for the total 215 milliseconds of the diastolic cycle. Analysis Results & Discussion: Fluid flow patterns and stresses were determined in the models. Mass flow rates where determined from each of the two coronary outlets. Maximum velocity and wall shear were calculated. The data from these models showed little variation in the fluid dynamics, as they relate to coronary filling, of the different valve geometries. There was however significant differences in the sinus and non-sinus geometries, ex. Wall shear for the non-sinus model was almost double that of the sinus model for the trileaflet valve configuration. Conclusion: Computational fluid dynamics can assist in determining the advantages and disadvantages to clinical decisions. The geometries of the prosthesis involved in heart valve surgery, specifically the devices surrounding the chosen valve, can have a significant effect on the overall flow regime into the coronaries, and hence have an impact on the functioning of the myocardial tissue as a whole. Further research with these models is anticipated with the release of ANSYS 8.0 & CFX 5.7, at which time their ability to handle fluid/solid interactions will be used to study the entire cycle of coronary filling. Introduction In 2000 in the United States alone, cardiovascular disease claimed a life every 33 seconds. A relatively small component of these deaths (~20,000) was due to valvular heart disease. This number is minimized by the numerous heart valve procedures performed (~96,000) (2000, American Heart Association Statistics). Though these procedures are effective in limiting the total deaths due to valve failure, a possible issue with these procedures for the aortic valve lies in the lack of conservation for the Sinus of Valsalva (1968, Bellhouse; 2001, Thrubrikar; 2001, Grande-Allen; each published papers showing the significance of these tissues on both the opening and closing the leaflets of the valves and on the blood flow into the coronary arteries).

2 The puzzle is further enhanced by the multiple prosthetic valves available to the surgeon. Numerous studies have been done on the fluid flow of these types of valves, but what of their geometries effect on the flow into the coronary arteries? It seems reasonable that by changing the configuration of the valve or the surrounding aortic conduit, there would also be a corresponding change in the fluid dynamics and hence this would have a resulting effect on fluid flow into the coronaries, and over all coronary filling. This is significant because patients going through such valvular replacement procedures have hearts that are already at a weakened state. Any increased flow that can be provided, or on the opposite side of the coin any flow that is needlessly lost, due to geometry may become a noteworthy factor in the selection of the valve and/or aortic conduit. We sought to explore how these different geometries - sinus, non-sinus and valve (Tri-leaflet, Bi-leaflet, and Single disc) - effect the fluid dynamics and over all coronary filling in the aorta. See Figure 1. Figure 1. Depiction of Heart with a close-up of of the Sinus of Valsalva. The models represent these features of the anatomy in addition to a distal part of the aorta (i.e. Sinus, coronary, aorta). Procedure To test this we created three valve geometries - 1) Tri-leaflet, anatomical valve 2) Bi-leaflet, prosthetic valve & 3) Single disc valve; each of these configurations was paired with a sinus and non-sinus conduit. This gave a total of six models. The majority of resting coronary filling (85%) occurs during diastole, when the valve is in the closed position. As such all valves are placed in the closed position.

3 Tri-leaflet Valve A model to represent the normal anatomic aortic valve was first created. The valve has a diameter of 3 cm, and valve leaflet thickness of.5 mm. See Figure 2. Figure 2. Tri-leaflet Valve Geometry Bi-leaflet Valve The model representing the St. Jude valve (a bi-leaflet configuration) also had a diameter of 3mm, with the thickness of each of its two half circle plates being 2mm. See Figure 3. Figure 3. Bi-Leaflet Valve Geometry Single Disc Valve The model representing the single disc prosthetic valve is 3 cm in diameter, and was set in a flat position (ie perpendicular to the aorta). See Figure 4.

4 Figure 4. Single Disc Valve Geometry Sinus & Cylindrical Non-Sinus Conduits Along with one of the above mentioned valves one of two surrounding aortic configurations was chosen for the geometries - a tri-sinus normal anatomic arrangement and a regular cylinder to represent a possible cylindrical Dacron graft. Measurements for the sinus include a height of 34 mm and arc lengths of 42mm in the horizontal direction and 38 mm in the vertical, both created by splines. See Figure 5. Figure 5. Sinus and Non-Sinus Meshes (displayed with a Tri-leaflet valve configuration). Coronary Attachments The coronary arteries were formed by taking a cylinder 3 mm in diameter and 16 mm in length and attaching each (two) to the aortic conduit. The height chosen for the placement of the coronaries was based upon measurements taken from 30 cadavers. From the bottom of the sinus - at the sinus leaflet junction, straight up to the center of the coronary opening was the measured length. For the 30 cadavers measured this value was 17.1 mm for the right coronary and 17.6 mm for the left. As such, this was approximated to 17 mm (as four of the data points had coronary bypass surgery and the mean measured length of the

5 remaining 26 measurements gave 16 mm and 16.4 mm, for the right and left coronaries, respectively) and used as the height of the coronary attachment sites for all six models. See Figure 6. Figure 6. Coronary Measurements Boundary Conditions Three boundary conditions were set : 1) the inlet at the aorta and two outlets 2) the left coronary artery and 3) the right coronary artery (though all three where initially set as Openings and then the flow regime was allowed to be establish from the initial values). These were run as a transient simulation created by the aortic opening. At the aortic opening the inlet was established by a falling pressure given by the equation P = A * cos ( ω * t ) A = Initial Pressure = 120 mmhg ω = frequency = 2p/.86 based on a heart rate of 70 beats per minute The left and right coronary outlets were set at constant boundary condition of 5 mmhg. All other areas of the model where maintained at a non slip condition. See Figure 7. Figure 7. Falling Inlet Boundary Condition

6 Analysis Results & Discussion Data created from these simulations was used to create streamlines, contours of wall shear, and vector velocity plots. Below are presented depictions of these given from a camera angle from in between the two coronaries. See Figures 8-13 below. Streamlines Figure 8. Tri-Leaflet Sinus Between Coronary Figure 9. Tri-Leaflet Non-Sinus Between Coronary View The maximum flow rate reached at the inlet for the tri-leaflet geometry occurred at 67 and 58 milliseconds for the sinus and non-sinus geometries, respectively. The max flow rate out of the coronaries, occurred at approximately 66 milliseconds for the sinus model and 55 milliseconds for the non-sinus.

7 Figure 10. Bi-Leaflet Sinus Between Coronary View Figure 11. Bi-Leaflet Non-Sinus Between Coronary View The maximum flow rate reached at the inlet for the bi-leaflet geometry occurred at 71 and 59 milliseconds for the sinus and non-sinus geometries, respectively. The max flow rate out of the coronaries, occurred at approximately 71 milliseconds for the sinus model and 56 milliseconds for the non-sinus.

8 Figure 12. Single Disc Sinus Between Coronary View Figure 13. Single Disc Non-Sinus Between Coronary View The maximum flow rate reached at the inlet for the single disc geometry occurred at 71 and 60 milliseconds for the sinus and non-sinus geometries, respectively. The max flow rate out of the coronaries, occurred at approximately 71 milliseconds for the sinus model and 56 milliseconds for the non-sinus Comparison of the streamlines show that the sinuses assist in funneling flow into the coronaries as compared to the non-sinus models which have streamlines that must curve more abruptly into order to allow flow into the arteries. It is also interesting to note that the max flows for the non-sinus models occur more quickly than those of the sinus model. Wall Shear Contour lines representing the wall shear in each model are presented below. The max valve for the wall shear appeared exclusively in all models at a location just distal to the coronary anastomoses. See Figures 14 and 15.

9 Figure 14. Tri-Leaflet Sinus Between Coronary View Figure 15. Tri-Leaflet Non-Sinus Between Coronary View Comparison of the wall shear contours of the tri-leaflet sinus with the non-sinus model show the sinuses' ability to not only lessen the magnitude of the wall shear (max wall shear throughout the 215 millisecond cycle - at 62 milliseconds for the sinus model and 48 milliseconds for the non-sinus; values of 52 Pa and 80 Pa were seen for the sinus and non-sinus models respectively), but also to aid in dissipating of the wall shear over a larger area, there by lessening its overall effect. See Figures 16 and 17.

10 Figure 16. Bi-Leaflet Sinus Between Coronary View Figure 17. Bi-Leaflet Non-Sinus Between Coronary View The max wall shear for the bi-leaflet geometry, again occurring just distal to the coronary attachment site, occurred at 63 milliseconds for the sinus model and 47 milliseconds for the non-sinus. The max values at these time steps is very similar (with a very slight advantage with the sinus, 72 and 74 Pa), but of interest is the fact that the non-sinus model reaches this maximum more quickly than the sinus model. See Figures 18 and 19.

11 Figure 18. Sinus Between Coronary View Figure 19. Single Disc Non-Sinus Between Coronary View Max wall shear for the single disc geometry, occurred at 64 milliseconds for the sinus model and 50 milliseconds for the non-sinus. As in the bi-leaflet models, the max values at these time steps are quite similar to one another (with a very slight advantage with the sinus, 73 and 75 Pa). Again the non-sinus model reaches this maximum more quickly than the sinus model. Conclusion Computational fluid dynamics can assist in determining the advantages and disadvantages to clinical decisions. The geometries of the prosthesis involved in heart valve surgery, specifically the devices surrounding the chosen valve, can have a significant effect on the overall flow regime into the coronaries, and hence have an impact on the functioning of the myocardial tissue as a whole. Further research with these models is anticipated with the release of ANSYS 8.0 & CFX 5.7, at which time their ability to handle fluid/solid interactions will be used to study the entire cycle of coronary filling.

12 References 1. American Heart Association - Fighting Heart Disease and Stroke Heart and Stroke Statistical Update 2. B.J. Bellhouse & L. Talbot, The Fluid Mechanics of the Aortic Valve, J. Fluid Mech. (1969), vol. 35, part 4, pp Mano J. Thrubrikar, Stress Analysis of the Aortic Valve with and without the Sinuses of Valsalva", J. Heart Valve Dis (Jan 2001), Vol. 10. No K. Jane Grande-Allen, Finite Element Analysis of Aortic Valve-Sparing influence of Graft Shape and Stiffness". IEEE Transactions on Biomedical Engineering. (June 2001), Vol. 48, No. 6, 6. L. Henry Edmunds, Jr., Cardiac Surgery in the Adult, The McGraw-Hill Companies, Inc.