Fluid Mechanics Of Artificial Heart Valves

Artificial Heart Valves: An Important Choice

Karl Reisig, Shipra Sharma, John Lando Team: Reynold’s Transporters MEM 220: Project Proposal 2 Dr. Alisa Morss

Project Description The human heart is the biological pump that moves blood throughout the circulatory system. It is essential to live and therefore is important that it functions correctly throughout a person’s lifetime. Components of the heart include the four main compartments and the heart valves. For various reasons such as heart valve diseases including valvular stenosis and insufficiency, valve failure can occur leading to the need for valve replacement. This most often occurs in the aortic and mitral valves, making up 95% of replaced valves. Our objective is to characterize the fluid mechanics of the blood due to the single leaflet disk valve and the ball valve and determine any possible physiological effects. Finally we will make a recommendation of which valve is better suited to be implanted. We will focus on the Starr-Edwards ball and Björk-Shiley monostrut tilting disk valves in the aortic position. The Starr-Edwards ball valve was first implanted in 1960 and is the only caged-ball valve approved for use in the United States (appendix D). It is composed of a “floating” ball occluder held in place by three metal segments, forming a cage. The cage loosely constrains the ball, allowing it to move with very little resistance while still confining it, preventing dislocation. The cage is attached to a suture ring for attachment. The valve is positioned in place with the cage facing outward into the aorta. The Björk-Shiley tilting disk valve was initially implanted in 1971 as the first successful implementation of the tilting-disk valve design. The Björk-Shiley valve is composed of a carbon-coated disk occluder held in place by two struts, the inflow and outflow struts (appendix E). The disk is separated into two sections which divide the valve into major and minor orifices. When the necessary pressure is reached the valve opens with the major occluder opening into the aorta and the small occluder tilting towards the left ventricle.

The Natural System To analyze the hemodynamics due to the artificial aortic valves one must first understand the cardiac cycle. During systole the pressure in the left ventricle starts to rise as the R peak of the PQRST wave triggers isovolumetric filling. When the pressure in the left ventricle equals the aortic pressure, the aortic valve opens, at which time the left ventricle contracts, allowing the blood to flow into the aorta and throughout the circulatory system. As the blood ejects, the pressure in the ventricle decreases, causing the valve to close. The ventricle then isovolumetrically relaxes and begins to fill again (diastole). Appendices A, B, and C show the electrical and mechanical events of the heart, the cardiac cycle PV diagram and typical pressure and flow curves for the aortic valve. To design and replace a natural aortic valve knowledge of how it works is necessary. The aortic valve is composed of three semilunar leaflets within a connective tissue sleeve. These attach to the annular ring of the aortic valve, separating the aorta from the left ventricle. During systole, blood accelerates through the valve and reaches a peak velocity once the leaflets have fully opened. The flow then decelerates rapidly creating a pressure gradient, which causes reverse flow in the sinus (base of the valve) region. The pressure difference needed to drive blood flow through the aortic valve is only a few mm Hg, but the pressure difference reaches 80 mm Hg in normal individuals. The valve closes near the end of the deceleration phase of systole with little reverse flow through the valve. Vortices develop behind the leaflets, helping to close the aortic valve quickly and efficiently. At the end of systole, there

is a short period of reverse flow, likely due to the small closing volume or the velocity of the valve leaflets as they move toward their closed position. The velocity profile on the valve orifice plane is almost flat, with the flow skewed slightly toward the septal wall.

Analytical Solution When designing an artificial valve design constraints and criteria must be established. These criteria include the design considerations many hemodynamic factors including: -

Show minimal resistance to flow

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Valve orifice to anatomical orifice ratio

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Minimal leakage/regurgitation

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Trans-valvular pressure gradient

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Show minimal reverse flow necessary to close

Based on these criteria we will answer the following questions when analyzing the valves:

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What is the pressure drop across each valve?

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How does it relate to the orifice diameter?

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Is the flow around each valve turbulent?

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What physiological effects are there?

To compare the valves within the scope of the fluid mechanics curriculum certain simplifications must be made. First we simplify the blood flow to be steady and incompressible. It is safe to assume that blood is incompressible, as fluids at small velocities, such as those seen in the heart and arteries, are reasonably approximated to be incompressible. Also, while blood is a non-Newtonian fluid, it can be assumed to be Newtonian when flowing in large diameter vessels such as the aorta. The pressure field acting on the valves will also be considered as uniform, with the assumption that blood is inviscid. Lastly, in the case where we wish to find the pressure gradient, we will assume that points on each side of the valve are connected by a streamline. While this allows for simplification, it does not rule out the possibly of turbulent flow due to the artificial valve occluder. Pressure drop (Δp) is a measure of flow potential energy losses that occur when blood flows through the heart valve and is a measure of heart valve efficiency. The larger the pressure drop across a prosthetic aortic valve, the larger the systolic pressure in the left ventricle must be to drive flow. Pressure drop should be minimized when dealing with prosthetic valves because left ventricular pressure is the primary determinant of myocardial oxygen consumption. Drawing a diagram of the valve in the aortic position we apply Bernoulli’s equation across points 1 and 2, which reside on the same streamline and the valve is open (where d1= vessel diameter and d2= valve orifice diameter):

p1 + ½ρ1(V1)2+γz1= p2 + ½ ρ2(V2)2+γz2

(1)

While height z changes with an individuals physical orientation, the effect is negligible and can be ignored giving:

p1 + ½ρ1(V1)2= p2 + ½ ρ2(V2)2

(2)

where ρ1=ρ2= density of blood. Assuming no losses and a uniform laminar flow profile we can apply the conservation of mass equation:

Q = ρ1A1V1= ρ2A2V2

(3)

Because we assume blood to be incompressible and the aorta and all valve components to be circular and normal to V1(d1)2=V2(d2)2

the flow (3) simplifies to:

(4)

Combining equations (2) and (4) and rearranging: Δp = ½ ρ(V1)2[(d1/d2)4 -1]

(5)

To minimize pressure drop the orifice diameter must be maximized, as for a set velocity pressure drop increases as the ratio d1/d2 (aortic diameter to orifice diameter) increases. Because d1 is constant this ratio depends only on the orifice diameter. Therefore, the prosthetic valve with the largest orifice diameter will have the smallest pressure drop. Assuming a velocity of 1.35 m/s and a blood density of 1,050 kg/m 3 we can make pressure drop calculations for each valve. The following table shows the pressure drop for both the Starr-Edwards and Björk-Shiley valves, with dimensions taken from . Table 1: Pressure Drop Comparison of the Starr-Edwards and Björk-Shiley Valves*

Valve

Björk-Shiley

Outer

Orifice

Diameter

Diameter

Δp

Δp

(mm)

(mm)

(kPa) 1.4360

(mmHg)

25

19.88

7 1.2217

10.7975

27

21.98

6 1.3289

9.18613

1 4.5857

9.99183

Average 24

15.47

5 5.7075

34.4793

27

16.62

4 5.1466

42.9138

Starr-Edwards 1260

Average 4 38.6966 * In our calculations we assumed valve outer diameter ~ aortic diameter d1 It is clear that the Björk-Shiley valve has less pressure drop than the Starr-Edwards valve. According to these values the Björk-Shiley has insignificant risk of stenosis and valve incompetence with the Starr-Edwards valve having mild risk (appendix F). Another parameter used to determine the hemodynamics of each valve is the Reynolds number, Re= ρVl/μ a dimensionless number used to determine when a flow becomes turbulent. When Re exceeds 4,000 in a pipe flow becomes turbulent. In order to find V, Poiseuille’s law, which is a solution to the Navier-Stokes equations, can be applied where V=R2Δp/8μl. Combining these equations: Re = ρR2Δp/8μ2 Solving for Re for each valve:

(6)

Table 2: Reynolds Numbers of the Starr-Edwards and Björk-Shiley Valves* Valve

R

Björk-Shiley

(mm) 12.5 13.5 12

Starr-Edwards

Δp (Pa)

ρ

1,436.07 1,221.18 4,585.75

(kg/m3) 1050 1050 1050

l (m)

μ (Pa s)

1 1 1

0.004 0.004 0.004

Re 46,016.65 49,293.41 130,006.01

1260 13.5 5,707.54 1050 1 0.004 230,387.86 * In our calculations R= orifice radius, Δp = our calculated pressure drop for each valve size, l= unit length, and ρ and μ are the blood density and viscosity, where the viscosity of blood is .004 Pa s The calculated Re values exceed 4,000, therefore showing turbulence. However these numbers do not incorporate the ball and disk obstructing the flow. As a result, the likelihood of turbulent flow occurring due to both valves increases. Despite the fact that these Re values may be inaccurate, we feel that they show an accurate relationship between the valves, in that the Starr-Edwards valve creates turbulent flow more easily than does the Björk-Shiley valve. This is because the ball is unable to dislocate from the flow path, blocking flow, whereas the disk obstructs much less of the aorta as it tilts to 60°. Because the ball exposes more surface area normal to the flow, we feel that it would create more damaging flow patterns.

Physiological Effects of Valve Hemodynamics Artificial valves have advantages including durability and disadvantages including risk of anti-coagulant related hemorrhage, valve failure, and thrombosis. Many of the negative effects of prosthetic valves can be attributed to their specific design, while others occur in all cases.

Effect of turbulence 407.pdf Thrombus formation fludmechanicsofheartvalves.pdf page 26 The rate of growth of a thrombus depends on the hemodynamic environment, particularly shear rate and shear stress. Shear rate causes diffusion-like platelet motion that is orders of magnitude larger than Brownian diffusion. The shear rate also determines the rate at which plasma proteins and coagulation cascade enzymes are transported to the growing thrombus, and the composition (relative proportion of platelets, fibrin, and trapped red blood cells) of the thrombus. Shear stress modulates the adhesion and aggregation reaction rates of platelets, as well as the rate of embolism of the thrombus Patients with artificial valves have a clot formation of .1-5.7% per patient-year.. A host of biological factors are also involved in thrombosis, including atherosclerotic plaque composition, hematocrit, and platelet count. http://www.me.gatech.edu/david.ku/thrombosis.html hemolysis (cavitation, abrasion against parts), stenosis

How Solved in the Real World Due to our limited knowledge we had to make many invalid assumptions to solve the artificial valve system. When biomedical and mechanical engineers work on developing artificial heart valves, they have a plethora of tools available to them. The previous assumptions of laminar flow and that blood is inviscid are technically invalid when making a real model of flow. Flow can still be assumed to be steady, and that blood is an

incompressible Newtonian fluid. The Navier-Stokes equations with the continuity equation can be applied as shown in appendix G. These equations could be solved with a computer to produce a plot of flow lines through the valve. Additionally, Inaccuracy of our Reynolds Number calculation

EFFECTIVE ORIFICE AREA –fludmechanicsofheartvalves.pdf page 9 MODELING- Real world fluid mechanics problems are most often solved using computational fluid mechanics. It is believed that blood flow experimentation by computer can be useful in designing an optimal heart valve. To reduce or eliminate eddies, a heart valve may be designed such that the flow is directed into areas which would otherwise contain or produce large eddies. The intensity of stress concentrations in the flow field may be reduced by streamlining the heart valve components. The use of computer simulation in such a design process would complement laboratory experimentation and might prove to be both less costly and less time consuming. In order to vary the shape of the heart valve components, however, the irregular boundary problems discussed in this report must be overcome. The finite element approach could be the solution to this problem, and is presently a topic of research. (computer.pdf page 17)

fludmechanicsofheartvalves.pdf page 23 on In vitro testing versus in vivo performance-hard to bioengineer devices to perfectly mimic a natural system (natural systems are complex, difficult to fully understand, hard to recreate. As a result designs are often not perfect. For example, the the Björk-Shiley valve has gone through many design iterations, including the development of the convex-concave occluding disk design. This design performed catastrophicly in vivo. In many patients the occulding disk dislocated, leading to sudden cardiac failure and patient death. This failure led to its withdrawal from the US market.. Despite its failures, the Björk-Shiley valve’s groundbreaking design makes it a valuable device to study for further valve development. Overall, the development of artificial heart valves is like any other engineering design process, it must go through many design iterations and tests before being implemented, and even after extensive in vitro testing and in vivo clinical trials, failures may occur.

Conclusion What We Learned Having completed research for the project, we as a group learned a great deal about the fluid mechanics of biological and artificial heart valves. We learned about the characteristics of 2 different artificial heart valves, how they function if implanted within the human body, and compared the two to see which had the least risk for failure. Throughout our research, we learned how to apply the course material towards a modern application. It is one thing to be told to make assumptions such as steady and incompressible flow when solving the Bernoulli or Navier-Stokes equations, however it was not until we were able to apply these assumptions towards a real system, that their purpose became clear to us as a group. Through our research, we also learned about the Reynolds number, and how it can be an indicator as to whether fluid flow is more steady or turbulent. For the heart valves, we learned that anything above Re = 4000 means that the blood flow is turbulent, leading to an increased risk for valve failure. The lower the Reynolds number, the less turbulent the flow is. Seeing as the Reynolds number for the Björk-Shiley heart

valve was much lower than the Starr-Edwards valve, the Björk-Shiley valve creates less of a turbulent flow, and thus a much less risk of causing any harmful physiological effects. After learning about the heart valves, and applying certain assumptions to the Navier-Stokes equation for the blood flow, we then researched how the heart valves are actually created and tested. Seeing as the Navier-Stokes equations are too complex to be solved by hand without making many invalid, simplifying assumptions, real scientists and engineers use computational fluid dynamics software to calculate as accurately as possible the properties of the blood flow through the heart valve.

Team Chemistry Overall team chemistry was good. We were each able to add something to the group, and to the project. We all feel as if we learned a great deal from working together, not only from the research, but from each other. Our collaboration and communication was very good. We split the proposal up into sections for each of us to write, and then proof read and made changes to each section together.

Works Cited

Appendix B

A

Typical Pressure and Flow Curves in the Aortic and Electrical and Mechanical Events in the Heart C

PV Diagram of the Cardiac Cycle

Mitral Valves

D

E

Starr-Edwards Ball Valve Björk-Shiley Tilting Disk Valve F

Fluid Dynamic Classification of Aortic Valve Disease G

Application of the Navier-Stokes and Continuity Equation to model two dimensional flow through a valve