Biomimetic Design of a Heart Valve

Nash Anderson

Cal Polytechnic State University

Spring 2011

Abstract

In order to test the theory of modifying the material of bio-prosthetic heart valves, an experiment

was conducted to determine whether elastomer films could be used as replacements for the

porcine tissue in bio-prosthetic heart valves. The elastic moduli and fatigue resistance of the

elastomers were tested to determine if they would be acceptable mechanically. The results were

found to be inconclusive due to improper testing methods and small sample size.

Background/Project Overview

Valvular heart disease (VHD) is characterized by the presence of a defect or damage to one of

the four heart valves. The defect or damage may be congenital or acquired. The damaged valve

either becomes too narrow to open fully, preventing normal blood flow; or unable to close,

completely resulting in back flow. About 5 million Americans are diagnosed with valvular heart

disease each year[1]. In mild cases valvular heart disease can be treated with medication, but in

most cases the valve must be replaced or repaired.

Valvular repair is the best possible solution to VHD, but when a patient’s heart valve is severely

damaged, repair is not an option. In these cases the patient’s valve must be replaced with a

either a mechanical or a bio-prosthetic valve.

Mechanical heart valves are made out of pyrolitic carbon and can last an entire lifetime if the

patient takes anticoagulant medication such as Warfarin on a daily basis. Without a frequent

regimen of anticoagulant medication the valve will clot at the mechanical hinges of the valve

resulting in failure. The valve hinges tend to clot due to their shape which causes turbidity of

flow.

Bio-prosthetic valves are the most common valvular replacement, being used in about 80% of

patients today[2]. These valves are made out of pericardium tissue (often from a pig), and closely

mimic the shape of actual heart valves. Because of their unique shape bio-prosthetic valves do

not require anticoagulant medication, which is why they are so popular amongst patients. The

drawback to these valves is that they need to be replaced every 10-15 years due to degradation

and calcification of the pericardium tissue. The pericardium tissue degrades and calcifies

because it is foreign tissue to the body, even though it is treated with chemicals to decrease this

effect.

Problem Statement

All replacement heart valves either have a limited lifespan or require the patient to take

anticoagulant medication for the remainder of their lives. The patient must choose which type of

valve is less inconvenient for them.

User Needs/ Current Solutions

User needs a prosthetic heart valve that will not require long term medication regimens and that

will have a lifespan longer than 25 years. The valve must last long enough so that it never has

to be replaced in the majority of patients.

Design Requirements

● Bio Compatible - not incurring a toxic or detrimental immunological response.

● Resist blood coagulation without use of anticoagulant medication

● Undergo elastic shear deformation

● Maintain a seal that does not permit back flow

● Maintain elastic properties under cyclic shear load (>1.05 billion cycles)

Proposed Solution

Theory Behind Solution

The design of the bio-prosthetic valve has preferred flow characteristics in comparison to

all mechanical valves. The only problem with the bio-prosthetic valve is the tendency of

the pericardium tissue leaflets to degrade and calcify over time. A synthetic material

would not degrade, therefore if a synthetic material can be found which replicates the

mechanical behavior of the pericardium tissue, a valve could be designed with the flow

characteristics of a bio-prosthetic valve and the durability and lifetime of a mechanical

valve.

How Solution Meets Design Requirements and user needs

The proposed heart valve will not require the patient to be put on an anti-coagulant

regimen, and will out last bio-prosthetic heart valves.

Explanation of design

The pericardium tissue used in bio-prosthetic heart valves will be replaced with an

artificial elastomer. The proposed heart valve will maintain the design and function of the

bio-prosthetic valve, but will last longer because the elastomer will not break down and

calcify over time.

Materials Science

Hypothesis

Elastomers closely resemble the mechanical properties of pericardial tissue. They

should therefore be a suitable material to mimic the function of a healthy heart valve.

Elastomers are chemical compounds whose molecules consist of several thousand

smaller molecules called monomers linked together by covalent bonds. These

monomers repeat and are linked together to form long chains. These chains have a

backbone most often made up of carbon bonds, either (C-C) or (C=C). These long

carbon chains are highly flexible, disordered and intertwined. The chains are flexible

because rotation around (C-C) bonds allows the molecules to take up many different

configurations. [3]

In elastomers normal state they are highly disordered with a high entropy. This is the

preferred state of the elastomer. When elastomers are put under tensile stress, the

molecular chains are pulled into alignment and often take on aspects of a crystalline

arrangement. When the chains are lined up under a load, they are at a lower disorder

with a lower entropy. Upon release they spontaneously return to their naturally

disordered, entangled state allowing the polymer to maintain its shape.[3] Both the

deformation and the subsequent recovery are time-dependent, suggesting that some

part of their behaviour is viscous. Elastomers show a combination of elastic and viscous

behavior known as viscoelasticity. The degree of viscoelasticity is strongly dependent

upon temperature and the rate of deformation, as well as such structural variables as

degree of crystallinity, crosslinking, and molecular weight.

In order to be useful for various applications, elastomers

must be strengthened by cross-linking the polymer chains.

With a low frequency of the branching cross links, a soft

rubbery material is produced. Silicones and polyurethanes

can be cast this way, using low-viscosity liquid precursors

with reactive end groups.

If an elastomer is stretched, as shown in Figure 1, energy

is stored in it. Just as in the application of a slingshot, the

elastomer used in the propulsion mechanism will snap

back into place after being stretched. The energy stored

per unit volume in an elastically strained material:

Materials

To pick the materials for testing a CES plot from the biomaterials database was created

looking for low Young’s Modulus (.8-12MPa) and high Fatigue Strength. Fatigue

Strength will be one of the most important factors in the decision because the material

will have to withstand over 1 billion cycles. Young’s Modulus was chosen because it is

closely related to Shear Modulus through the equation:

Shear Modulus: G = E / [2(1+v)]

v = poisson’s ratio = - εt / ε = (lateral or transverse strain) / (axial strain)

For elastomers v = ~ ½ ( G = ~ .333333E)

After research on availability of materials and consideration of the CES plot (Figure 2),

Thermo Polyurethane and PDMS were chosen for testing.

Figure 1. Elastomer molecular chain representation of an unloaded elastomer (A) and loaded elastomer (B).1

Thermo Polyurethane:

(B)

Thermo Polyurethane (Figure 3) polymers are formed through step-growth

polymerization.

Step-growth polymerization refers to a type of polymerization mechanism in which bi-

functional or multifunctional monomers react to form first dimers, then trimers, longer

oligomers and eventually long chain polymers. Many of these are naturally occurring

polymers but some synthetic polymers exist such as polyesters, polyamides,

polyurethanes, and many more. Due to the nature of the polymerization mechanism, a

high extent of reaction is required to achieve high molecular weight.

Figure 2. Biomaterials database CES plot comparing Fatigue Strength v. Young’s Modulus.

Figure 3. Monomer of a polyurethane molecule. 5

The polyurethane chains are complex structures. Due to the presence of benzene rings,

the structure has areas of hard and soft areas within the chains. This results in a

structure that will organize into stronger, less flexible areas and areas that are weak and

elastic. The stiffer areas are the result of the benzene rings from multiple chains lining up

and stacking on top of each other. The weaker areas in the material are the the areas

where the benzene rings have not lined up, and they form a regular disordered

elastomer structure. These softer areas will stretch and result in the elastic properties of

polyurethane, where the benzene alignment is the result in the material’s strength. When

stretched, the soft areas that contain a double bonded oxygen molecule form hydrogen

bonds with methyl’s from other chains within the structure.

Polydimethylsiloxane (PDMS):

(C)

Silicones are inert synthetic compounds, formed through chain growth polymerization.

Chain growth polymerization is when unsaturated monomer molecules add onto a

growing polymer chain one at a time. The structure consists of an -O-Si-O-Si-

“backbone” replacing the common -C-C-C-C- in carbon-based elastomers. This results

in a linear polymer with lower bond angles than the common carbon backbone. This

structure results in a viscous polymer that requires the polymer chains to be crosslink in

order to form silicone rubber and useful in engineering applications. In crosslinking,

methyl groups are substituted by vinyl groups to form crosslinking sites between

entangled chains. They have good stability of rubber properties over large temperature

range of -50C to 200C. Silicones are chemically resistant and have good sealing

capability. They are commonly used in biomedical applications for seals and o-rings.

Figure 4. Monomer of PDMS. 6

Silicone chains have a simple structure with low bond angularity and evenly bonded

methyl-groups that surround the chains. These molecular properties result linear

molecules. Silicone molecules will thus slide past each other very easily when for

example a tensile load is applied. This is why the material results in a lower elastic

modulus than that of polyurethane.

Testing

Objective

The goal of our testing procedures was to obtain values of elastic modulus for

elastomers PDMS and TPU and compare these values to those recommended for

elastomers being used in this application. For elastomers, the shear modulus can be

approximated to be one third of the elastic modulus. It was also an objective to observe

if these values for elastic modulus would be changed after putting the samples through

multiple cycles of fatigue.

Design of Experiment

Values for elastic modulus would be obtained using an Instron Tester. An instron tester

that was more sensitive to strain would have been ideal but was unavailable. The

variables in the experiment were chosen to be materials, amount of cyclic fatigue, and

thickness of elastomer film. Controls included shape of the sample, temperature, and

rate of deformation. These values can be seen in:

Input Variables

Factors: Levels

Materials: PDMS and TPU

Thickness: .01 in and .02 in

Fatigue: 0 cycles and 8,000 cycles

Fatigued Samples

Samples subjected to shear bending for 8,000 cycles, a cycle being one shear

bend to 90 degrees and back to 0 degrees.

Controls

Rate of deformation: 500mm/min

Geometry of sample: Gage length: 1 inch Width: 1 inch

Temperature: 25 C

Response Variable

Elastic modulus

Expected Results

For a material to be considered for the heart valve application, it must have no

difference in elastic modulus between fatigued and unfatigued samples. It is

expected that the PDMS elastomer will have no significant change in elastic

modulus due to its ease of chains sliding past one another at low stresses, and

that it will out-perform the TPU samples..

Results of Test

A statistical analysis of our results in terms of main effects and interactions of variables

can be seen below.

Both of these plots show that the only factor that had a significant effect on our data was

the material of the samples. When the values we obtained were compared to the

recommended values for elastomers in this application, both of our materials fell short.

Obtained E Values:

PDMS = 0.003 MPa

TPU = 0.15 MPa

Recommended elastic modulus values[F] for heart valve leaflet:

> .8 MPa

< 12 MPa

Discussion

Our results did show, as expected, that PDMS has a lower modulus than TPU, but that

is as far as we can go with our own conlusions due to lack of power in our experiment.

The obtained values for the elastic modulus of the polymers did not compare closely to

the recommended values for elastomeric elastic modulus[F], nor the pericardial tissue

values. This result is likely due to the location of the obtained slope on the stress strain

diagram. Figure X depics one of our obtained stress strain diagrams for TPU. As shown

in the figure, the difference the location of the line results in a very different slope. This

difference results in our obtained values of elastic modulus being much lower than the

recommended. There are few to little experiments on elastomers that depict an elastic

modulus from the initial slope (approx. <25% strain) which is the area in question for our

application.

Figure The figure above depicts one of the trials of tensile testing TPU. Line A portrays the slope that was used to

obtain our value of the elastic modulus. Line B is the line that was likely used to obtain the recommended values for

elastic modulus, as well as the E values found in CES.

Because of this uncertainty and our low sample size in testing, there is considerable

room for improvement in our methods and results. A promising place to begin improving

would be to establish a better foundational knowledge of he high-cycle fatigue behavior

of elastomers. There is very little information in this area however because the vast

majority of elastomers are not used in applications where cyclic fatigue is a factor.

It is also possible that we could have obtained more valid results by changing our test

method. This would include testing more samples of each material and testing them

differently. As opposed to simple tensile tests, generation of hysterisis curves for the

elastomers would yield useful information concerning cyclic elastic loading.

Conclusions

Neither PDMS nor TPU can be accepted for use as heart valve leaflets based on our

findings. However, these materials should not necessarily be ruled out either. With more

accurate testing tools and methods, valid elastic modulus values could have been

attained, which could yield a definitive answer as to whether our samples of PDMS and

TPU would exhibit acceptable mechanical properties for use in heart valves.

We suggest further mechanical testing, and once a material is found with sufficient

mechanical properties we suggest testing on coagulation properties.

Sources

1Chemical Composition and Structure of Elastomers." Elastomer Chemistry. 19 Feb. 2011.

<http://www.standard-gasket.com/tech_specs/elastomer_chemistry.htm>.

2“Elastomeric Sheet Materials for Heart Valve and Other Prosthetic Implants.” US Patent, July

20, 1982.

3"Heart Disease: Heart Valve Disease." MedicineNet. 22 Feb. 2011.

<http://www.medicinenet.com/heart_valve_disease/article.htm>.

4 Interview with Dr. Luke Faber on February 3, 2011

5"Polyurethane." Wikipedia The Free Encyclopedia. 3 Mar. 2011. Wikipedia.

<http://en.wikipedia.org/wiki/Polyurethane>.

6"Silicone Rubber." Caojunbang. 11 Feb. 2011. <http://caojunbang.centerblog.net/5-107-rtv-

silicone-rubber>.