The Design of Heart Valves

Abstract

Our cardiovascular system transports important substances, such as oxygen and nutrients, between tissues and organs. It also helps transport and eliminates waste products. Our heart, blood vessels, and blood form a sophisticated network that transports materials around our body. These materials are carried by the blood through the blood vessels and are kept in motion by the pumping action of the heart. The blood vessels of the cardiovascular system are divided into two main pathways. The blood vessels in the pulmonary circuit carry blood from the heart to the lungs and back to the heart. The systemic circuit consists of the pathways between the heart and all other areas of the body.

Appendices

Problems

• 1. Show in a schematic diagram the mechanical equivalent of the human heart, indicating the approximate volume of each chamber and the location of valves and their features. What conditions of the heart valve necessitate its replacement?

• 2. How do you propose to design a mechanical heart valve for replacement of the mitral valve? What materials are to be used for each part, and how will you fix it with the heart tissue? What tests are necessary to predict the life expectancy of such a valve? Could you suggest the manufacturing aspect of the product?

• 3. Discuss the differences between different types of mechanical valves and tissue valves. Indicate their advantages and disadvantages, life expectancy, blood coagulation, complications, and other relevant aspects.

Example from the Literature for Valve Area Calculation

17.2.1 Aortic Valve Area Calculation

Aortic valve area calculation is an indirect method of determining the area of the aortic valve. The calculated aortic valve orifice area is currently one of the measures for evaluating the severity of aortic stenosis. A valve area of less than 0.8 cm² is considered to be severe aortic stenosis [1, 2]. There are many ways to calculate the valve area of aortic stenosis. The most commonly used methods involve measurements taken during echocardiography. For interpretation of these values, the area is generally divided by the body surface area, to arrive at the patient’s optimal aortic valve orifice area.

Planimetry is the tracing of the opening of the aortic valve in a still image obtained during echocardiographic acquisition during ventricular systole, when the valve is supposed to be open. While this method directly measures the valve area, the image may be difficult to obtain due to artifacts during echocardiography, and the measurements are dependent on the technician, who has to manually trace the perimeter of the open aortic valve. Because of these reasons, planimetry of the aortic valve is not routinely performed.

The continuity equation states that the flow in one area must equal the flow in a second area if there are no shunts in between the two areas. In practical terms, the flow from the left ventricular outflow tract (LVOT) is compared to the flow at the level of the aortic valve. Using echocardiography, the aortic valve area is calculated using the time–velocity integral, which is the most accurate and preferred method.

The Gorlin equation states that the aortic valve area is equal to the flow through the aortic valve during ventricular systole divided by the systolic pressure gradient across the valve times a constant. The flow across the aortic valve is calculated by taking the cardiac output (measured in ml/min) and dividing it by the heart rate (to give output per cardiac cycle) and then dividing it by the systolic ejection period measured in seconds per beat (to give the flow per ventricular contraction):

$$ \text{Valve}\text{area}({\text{cm}}^{2})=\frac{\text{Cardiac}\text{output}\left(\frac{\text{ml}}{\mathrm{min}}\right)}{\text{Heart}\text{rate}\left(\frac{\text{beats}}{\mathrm{min}}\right)·\text{Systolic}\text{ejection}\text{period}(\text{s})·44.3·\sqrt{\text{mean}\text{gradient}(\text{mmHg})}}.$$

The Gorlin equation is related to flow across the valve. Because of this, the valve area may be erroneously calculated as stenotic if the flow across the valve is low (i.e., if the cardiac output is low). The measurement of the true gradient is accomplished by temporarily increasing the cardiac output by the infusion of positive inotropic agents, such as dobutamine.

Example:

An individual undergoes left and right heart cardiac catheterization as part of the evaluation of aortic stenosis. The following hemodynamic parameters were measured. With a heart rate of 80 beats/min and a systolic ejection period of 0.33 s, the cardiac output was 5 l/min. During simultaneous measurement of pressures in the left ventricle and aorta (with the use of one catheter in the left ventricle and a second in the ascending aorta), the mean systolic pressure gradient was measured at 50 mmHg. What is the valve area as measured by the Gorlin equation?

Answer:

$$ \text{Aortic}\text{valve}\text{area}=\frac{5,000\frac{\text{ml}}{\mathrm{min}}}{80\frac{\text{beats}}{\mathrm{min}}\bullet0.33\text{s}·44.3\bullet\sqrt{50\text{mmHg}}}\approx 0.6{\text{cm}}^{2}$$

The Hakki equation given below is a simplification of the Gorlin equation, relying on the observation that in most cases the numerical value of $\text{heart rate (bpm)}$ •systolic ejection period (s)•i44.3 1,000.

The resulting simplified formula is

$$ \text{Aortic}\text{valve}\text{area}({\text{cm}}^{2})\approx \frac{\text{Cardiac}\text{output}\left(\frac{\text{l}}{\mathrm{min}}\right)}{\sqrt{\text{mean}\text{gradient}X(\text{mmHg})}}.$$

Example:

An individual undergoes left and right cardiac catheterization for the evaluation of aortic stenosis. Measurements include an aortic pressure of 120/60, an LV pressure of 170/15, and a cardiac output of 3.5 l/min. What is the aortic valve area?

Answer: The peak gradient between the LV and aorta is (170–120) 50 mmHg. This gives

$$ \text{Aortic}\,\text{valve}\,\text{area}\approx \frac{3.5}{\sqrt{50}}\approx 0.5{\text{cm}}^{2}.$$

Some relevant references for further study on this methodolgy:

• 1. Varadarajan P, Kapoor N, Bansal RC, Pai RG (2006) Survival in elderly patients with severe aortic stenosis is dramatically improved by aortic valve replacement: results from a cohort of 277 patients aged >/=80 years. Eur J Cardiothorac Surg 30(5): 722–728

• 2. Hakki A, Iskandrian A, Bemis C, Kimbiris D, Mintz G, Segal B, Brice C (1981) A simplified valve formula for the calculation of stenotic cardiac valve areas. Circulation 63(5): 1050–1055.