Design a Heart Valve Model

In this project, we were tasked with designing a model heart valve — namely, a model aortic valve — for a client who wished to conduct experiments to test the properties of heart valves.  Effectively, this required us to identify materials and structure which could accurately mimic a real heart valve.  In addition, we were constrained to using household materials for easy availability.

We began by conducting research into the usage of Young's Modulus to identify key elasticity characteristics of a given material.  We then conducted actual tests on a variety of household materials to determine their Young's Moduli and through background research on the Young's Moduli of real heart valve components we were able to determine suitable materials for our model.  Next, we researched the structure of aortic valves and drew up a design for our valve model which mimicked both the structure and function of the real aortic valve.  We then constructed this model along with a test rig setup that allowed us to apply fluid pressure forwards and backwards on the valve.  Finally, we conducted tests with colored fluid to observe forward flow and backflow (hoping to maximize the former and minimize the latter), which determined with reasonable accuracy that the model was effective.

The Report

Core Concepts

Stress and Strain

Two important concepts in tensile analysis are stress and strain.

• Stress, frequently denoted σ, is a measure of force applied during a deformation.  It is defined to be the force applied divided by the cross-sectional area.  Therefore, the stress is a sort of "scaled ratio" which normalizes the force applied relative to how large the object is.

• Strain, frequently denoted ε, is a measure of the amount of deformation incurred.  It is defined to be the ratio of the change in length to the initial length.  This is effectively a normalized "deformation percentage".

These definitions can be summed by the simple equations:

σ = F / A
ε = ∆L / L₀

Young's Modulus

A crucial aspect of this project was the determination of the Young's Modulus of our materials and of a real heart valve leaflet's layers.  Put simply, Young's Modulus is a measurement of how compliant a material is; a material with a greater Young's Modulus will require more force to deform, while a material with a lower Young's Modulus will deform further with less force.

The Young's Modulus is defined to be the stress divided by the strain.  From this, it becomes apparent why the Young's Modulus carries the relationship which it does; a greater stress (i.e. more force applied for the same deformation) means a greater Young's Modulus, while a greater strain (i.e. more deformation with the same amount of force) means a lower Young's Modulus.

Heart Valves

The valves of the heart are critical to its functioning.  The heart pumps blood in two phases: diastole, when the ventricles expand and fill with blood, and systole, when the ventricles contract and eject blood.  During diastole, it is important that no blood is drawn into the ventricles backwards — that is, in from the aorta, where blood exits the heart — and during systole, it is important that no blood is ejected backwards — that is, out through the vena cava, where blood enters the heart.  To do this, a group of one-way valves are utilized which ensure that blood always moves forwards through the heart and never undergoes retrograde flow.  These valves are the heart valves.

There are four heart valves:

• The tricuspid and mitral valves regulate blood flow from the atria into the ventricles within the heart.

• The pulmonary and aortic valves regulate blood flow from the ventricles into the pulmonary and aortic arteries out of the heart.

Each of these valves have a different structure.  The tricuspid and mitral valves are larger; the tricuspid valve has three "leaflets" (radially-mounted tissues which open and close to allow or prevent flow) while the mitral valve has only two; the pulmonary and aortic valves have three leaflets but are more symmetrical than the tricuspid valve, which is closer to a bicuspid mitral valve with one leaflet split in two.  Since in this project we were tasked with the creation of an aortic valve model, we aimed to create a relatively symmetrical, tri-leaflet design.

Valve Leaflets

The leaflets are the core of any heart valve, and the aortic valve is no exception.  The leaflets of the aortic valve are passive — when pressure is applied, they naturally open to allow blood through, and when backpressure is applied, they naturally close to prevent blood backflow.  This greatly simplifies the mechanism of the heart and improves reliability.

The shape of the heart's leaflets are semilunar (like that of a crescent moon).  This shape serves to correctly respond to applied pressure.  Additionally, each valve leaflet is comprised of three layers:

• Collagen-rich Fibrosa, providing strength to the leaflet

• Spongiosa, which acts as cushioning

• Ventricularis, which complies readily due to its high elastin content

In our model, we did not provide an analog of the spongiosa layer since its purpose is merely that of cushioning (which is less important when using stronger, synthetic materials).  However, we accurately mimicked the other layers in each of our model's leaflets.

Mechanical Anisotropy

A notable property of valve leaflets is that they comply in one direction but remain stiff in another.  This property is known as mechanical anisotropy.  In heart valves, this is achieved through circumferentially-wrapped collagen fibers which provide strength in one direction but freely deform in others.  Mechanical anisotropy ensures that heart valves can properly resist the pressure applied during backflow while still being capable of providing very low resistance to forward flow.

Reflection

This project was a tremendous success.  Despite the incredibly tight deadline (having under a week to move from design to finished product), we were able to deliver a highly effective final product.  For this reason, I believe my group's and my personal conscientious learning was a strong point of this project.  This project required very effective planning of tasks in order to complete everything on time, and I feel confident that each day was utilized to its full extent.  Creating a plan at the start of each section of work helped tremendously, and the plan was followed effectively.  Additionally, I believe that the critical thinking involved in this project was excellent.  The tools at our disposal were less than ideal, but we were able to come up with creative solutions to our problems.  For example, we struggled to find an adhesive that was flexible enough to adhere the multiple layers of our valve model.  However, we realized that we could obviate this by using the existing structure of the latex gloves which comprised the outer layer, placing the interior layers inside sections of the already-shaped finger of the glove to secure the multiple layers together without requiring full application of adhesive.  This solution worked perfectly and allowed us to continue making progress despite shortcomings in resources.

In truth, it is difficult for me to recall faults in this project's completion process.  I can relate only what subtle flaws present themselves to me in recollection.  For one, the communication could have potentially been further polished.  The format of our report remains somewhat unsatisfactory to me for it feels vaguely clumsy in the way it handles the two experiments (the tests regarding Young's Modulus and the test of our heart valve model itself).  While I am not truly certain how I would go about remedying this, I do feel that there is some area for improvement in the presentation of these experiments so as to improve the flow of the paper.  Additionally, I believe that the collaboration could have been slightly improved.  While we did all share the burden, we did not share the work equally within each aspect of the project (within the report, for example); more clearly delegating sections of work to each member could have even further balanced this collaboration.

In total, this project was a clear and resounding triumph.  Despite the uncertainty and pressure we faced, the final result was exceptional.