a development on virtual experiments to study matrix-cells

A Development on Virtual Experiments to Study Matrix-Cells Interactions in Aortic Valves

Preliminary Literature Review

Institution: North Carolina State University

Student: John J Cillie, III

Adviser Dr. H. Y. Shadow Huang

Date: May 12, 2010

Aortic Valve Virtual Experiments John J. Cillie Literature Review Dr. H. Shadow Huang

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Table of Contents

1. Introduction ............................................................................................................................. 4

2. Article reviews on AVIC/ECM mechanical properties ........................................................... 5

2.1. Endothelium-Dependent Regulation of the Mechanical Properties of Aortic Valve Cusps, El-Hamamsy et al. 2009 .................................................................................................. 5

2.2. Mechano-potential etiologies of aortic valve disease, Merryman 2010 ........................... 8

2.3. Viscoelastic Properties of the Aortic Valve Interstitial Cell, Merryman et al. 2009 ....... 8

2.4. On the Biaxial Mechanical Properties of the Layers of the Aortic Valve Leaflet, Stella, Sacks 2007 .................................................................................................................................. 9

3. Importance of cellular deformations ...................................................................................... 10

4. Integrin relevance within tissue ............................................................................................. 11

5. Articles covering simulations previously conducted ............................................................. 14

5.1. A unified multiscale mechanical model for soft collagenous tissue with regular fiber arrangement, Maceri et al. 2010 ............................................................................................... 14

5.2. High-order finite element analysis testing HV leaflet tissues ........................................ 18

5.3. Finite element model to simulate effect of collagen remodeling ................................... 21

5.4. Stress analysis on mitral valve using FEM .................................................................... 22

6. Statistics of heart valve disease ............................................................................................. 23

7. Cell deformation and tissue connectivity article reviews ...................................................... 26

7.1. Molecules mediating cell-ECM and cell-cell communication in human heart valves, Latif et al., 2005 ........................................................................................................................ 26

7.2. Quercetin-crosslinked porcine heart valve matrix: Mechanical properties, stability, anticalcification and cytocompatibility, Zhai et al., 2010 ......................................................... 27

8. Summary of literature review ................................................................................................ 28

9. References ............................................................................................................................. 29

Table of Figures

Figure 1: Schematic of heart operation (Aubuchon 2010) .............................................................. 4

Figure 2: Image of experiments conducted and graphical results (El-Hamamsy et al. 2009) ........ 6

Figure 3: Results displayed graphically from article (El-Hamamsy et al. 2009) ............................ 7


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Figure 4: Generic valve properties as a function of age and phenotype (Merryman 2010) ........... 8

Figure 5: Caption shown within image (Liao et al. 2007) ............................................................ 11

Figure 6: Simplified illustration of how integrins connect between cells and ECM (El-Ghannam 2008) ............................................................................................................................................. 12

Figure 7: Caption shown within image (Lodish 2008) ................................................................. 13

Figure 8: Caption shown within image (Lodish 2008) ................................................................. 14

Figure 9: (a) and (b): Captions are shown within image (Maceri, Marino & Vairo 2010) .......... 15

Figure 10: Algorithm of the simulations produced for this article (Maceri, Marino & Vairo 2010)....................................................................................................................................................... 16

Figure 11: Caption shown within image (Maceri, Marino & Vairo 2010) ................................... 17

Figure 12: Caption shown within image (Mohammadi, Bahramian & Wan 2009) ...................... 19

Figure 13: Caption shown within image (Mohammadi, Bahramian & Wan 2009) ...................... 19

Figure 14: Captions shown within image (Mohammadi, Bahramian & Wan 2009) .................... 20

Figure 15: Captions shown within image (Mohammadi, Bahramian & Wan 2009) .................... 20

Figure 16: Caption shown within image (De Hart et al. 2004) ..................................................... 22

Figure 17: Captions shown within image (Kuai et al. 2008) ........................................................ 23

Figure 18: Heart valve disease population statistics, see Table 5 for sources .............................. 25

Figure 19: Captions shown within image (Zhai et al. 2010) ......................................................... 28

Table of Tables

Table 1: Table of collected results from article (El-Hamamsy et al. 2009) .................................... 6

Table 2: Caption shown within image (Merryman et al. 2009) ...................................................... 9

Table 3: Caption shown within image (Merryman et al. 2009) ...................................................... 9

Table 4: Captions shown next to respective tables (Maceri, Marino & Vairo 2010) ................... 17

Table 5: Sources for the information in Figure 17 ........................................................................ 25

Table 6: Caption shown within image (Latif et al. 2005) ............................................................. 26


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1. Introduction

The aortic heart valve is the last portion of the heart that blood sees when being pumped through. A schematic of blood flow through the heart is shown in Figure 1. The red lines are oxygen-rich blood and blue are oxygen-depleted blood. The blood enters the heart through the pulmonary and tricuspid valves to be pumped through to the lungs. The lungs oxygenate the blood and are then pumped through the high pressure portion of the heart through the mitral and aortic valves.

Figure 1: Schematic of heart operation (Aubuchon 2010)

The aortic and mitral valves see the most and second most amount of pressure from the heart, respectively. If the properties of the aortic valve can be found, which cause the most problems in humans, the other valves can also be treated with the knowledge gained from this experiment. In order to pump the blood to the entire body these valves need to be healthy and not damaged. The tissues that make up these valves are extremely important when considering heart valve disease. In order to develop better treatments for these valves, a better understanding of the tissue is required. It is still unclear how exactly this tissue behaves mechanically, although many assumptions have been made (Aubuchon 2010).


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Each portion of the tissue alone creates a non-linear relationship in the stress-strain relationship. There are many layers and parameters that make up this tissue that need to be accounted for. All of these parameters react differently to forces and the connection between them is also unclear. In the combination of all the tissue parameters, the mechanical properties are a series of non-linear relationships that must be further analyzed for better comprehension. This research will attempt to use finite element analysis (FEA) of the tissue at a micro-scale level to better understand the mechanics and properties of the valves.

2. Article reviews on AVIC/ECM mechanical properties

Articles within this section relate to the previously found mechanical properties of tissue within the aortic heart valves. Various layers of the aortic heart valves and sections were measured and tested for actual values. These values will be used and compared within the virtual tests conducted within this research. The mechanical properties of the aortic valve interstitial cells (AVICs) and collagen fiber alignment is important because both combined create the network of tissue to be analyzed. The simulation of collagenous tissues with regular fiber alignment, including but not limited to heart valve material, is important in determining the characteristics of the tissue mechanical properties. This collagenous matrix is referred to as the extra-cellular matrix (ECM). The properties of the materials within the tissue must be known to further examine the behavior virtually.

2.1. Endothelium-Dependent Regulation of the Mechanical Properties of Aortic Valve Cusps, El-Hamamsy et al. 2009

The first article tested the mechanical properties of aortic valve cusps. It is compromised of a group from the United Kingdom, Georgia Tech, and Harvard. The tests were conducted on porcine hearts aged 18 to 24 months. They were harvested from a commercial slaughterhouse. Next, 10 x 10 mm sections of the endothelium were extracted from the “belly,” or center, of the aortic cusp, and treated with L-NAME (N-nitro-L-arginine-methyl-ester) (El-Hamamsy et al. 2009). They were loaded into a biaxial micro-mechanical testing device, using stainless steel springs and attaching to the sample at about 4 points, shown in Figure 2. The baseline aortic valve elastic moduli were found in the radial and circumferential axes. This data is shown to the below in Table 1. Their objective was to determine mechanical properties of aortic valves cusps to further examine their function and durability. The results are shown on the following pages in which they found a non-linear relationship for the tissue (El-Hamamsy et al. 2009).


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Table 1: Table of collected results from article (El-Hamamsy et al. 2009)

Figure 2: Image of experiments conducted and graphical results (El-Hamamsy et al. 2009)


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The elastic modulus shown is in units of kN/m instead of kN/m2. The method they used was derived from Laplace‟s law for cylinders, shown below in equation (1).

T Pr (1)

Where T is the mean valve membrane tension, P is the transvalvular pressure, and r is the radius of the aortic valve. The transvalvular pressure was assumed to be 80 mmHg. The load was plotted versus areal strain, shown in Figure 2. Areal strain is the incorporation of the measured radial and circumferential strain. Equations (2) through (4) are the areal strain equations, shown below.

21 [( ) 1]2A R CE (2)

2 1R RE (3)

2 1C CE (4)

Where R and C are the radial and circumferential stretch ratios and ER and EC are the radial and circumferential Green‟s strain, respectively. The load-strain diagram shows that in the radial direction, strain increases significantly more than the circumferential direction as more load is applied. Their results state that the endothelium, the single layer of cells on the inside of the valve to reduce blood turbulence and resistance, significantly modulates the mechanical properties of the AV cusps. It can be seen that the strains are affected by the different treatments applied shown in Table 1 and in Figure 3 (El-Hamamsy et al. 2009).

Figure 3: Results displayed graphically from article (El-Hamamsy et al. 2009)


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2.2. Mechano-potential etiologies of aortic valve disease, Merryman 2010

An article published January 2010, mentions the stiffness of the extra cellular matrix (ECM) as a function of age and the AVIC phenotype. The quiescent phenotype indicates equilibrium within the tissue whereas the activated are the opposite, as seen in Figure 4. The figure shows many discoveries. It shows that the stiffness of the valves steadily increase with age in a linear fashion. Also, the valves are very unstable in development and degeneration which is understandable, and vaguely explain why most heart valve disease patients are either children or elderly people (Merryman 2010).

Figure 4: Generic valve properties as a function of age and phenotype (Merryman 2010)

2.3. Viscoelastic Properties of the Aortic Valve Interstitial Cell, Merryman et al. 2009

Another article published by Dr. Merryman et al., conducted a study on viscoelastic properties of single aortic valve interstitial cell (AVIC). This article was published in April 2009. The test AVIC was extractive from a leaflet of a young lamb. Time dependent responses were taken from the micropipette aspirations that were conducted. Little viscous effects were noticed when pressure was applied over short period of time (0.5 sec), but pronounced viscous effects were noticed when micropipette pressures were endured for longer times (2.5 and 5.0 sec). (Merryman et al. 2009) The results are shown in Table 2 and Table 3.


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Table 2: Caption shown within image (Merryman et al. 2009)

The standard linear solid (SLS) model is the understood model for the assumption of instantly gathered data. The Boltzmann SLS (BSLS) model is defined as the model which accounts for creep and relaxation. The ceep and stress relaxation results from the simulations by Dr. Merryman et al. are shown below in Table 3.

Table 3: Caption shown within image (Merryman et al. 2009)

It was stated in the same article, “the biomechanical environment of the AVIC remains ill defined. Current evidence suggests that AVICs are tightly attached to the surrounding ECM.” (Merryman et al. 2009) This insinuates there have been limited studies on how strong the AVICs are attached to the ECM. An article was found and will be reviewed later within this report discussing the connectivity between AVICs and ECM.

2.4. On the Biaxial Mechanical Properties of the Layers of the Aortic Valve Leaflet, Stella, Sacks 2007

This article describes the various layers and properties of the aortic valve. The layers of the aortic valve are the fibrosa, ventricularis, and the spongiosa. The interstitial cells within the matrix exhibit characteristics of both fibroblast and smooth muscle cells. The cells can


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communicate between each other, incorporate tissue remodeling, assist in wound healing, and apply contraction when necessary.

The fibrosa layer is predominantly composed of type I collagen fibers well aligned in the circumferential direction. This allows for a more linear type of response as compared to the slightly more random alignment in the radial direction. The direction is very uniform compared to the ventricularis layer. The collagen alignment is random for both at low transvalvular pressures.

The ventricularis layer is composed of elastin and collagen fibers, organized quite randomly in comparison to the fibrosa layer. The elastin is arranged within the layer densely. The elastin has different properties resulting in a more non-linear response in this layer. With increasing transvalvular pressure, the layers seem to become indistinguishable in regards to pressures above 60 mmHg. The degree of collagen fiber alignment in both layers suggests that the ventricularis layer makes significant mechanical contributions to the leaflet stiffness at high pressures. This however, is only assumed and is in part, along with the AVIC properties, what will be found in our simulations.

According to this article, there have been no studies that characterize the multiaxial mechanical properties of the individual leaflet layers. The article also states that current simulations assume uniform transmural wall stress or a membrane tension formulation. This cannot be done if a more correct model is to be developed, each layer‟s properties must be further studied. This article dissected each layer and did mechanical testing (Stella, Sacks 2007).

3. Importance of cellular deformations

This section will cover a discussion on why cell deformations are important for this study. This is for the understanding in preparation for the virtual experiments. Cell deformations and the micromechanical understanding of cells are important for many reasons. It is important not only to develop new types of heart valves, but it also assists in the understanding of how cells react to numerous biological processes. Tissue damage and repair is the main concern of this study, yet when the cell deformation is more completely understood other symptoms and deformations such as: tumor growth, embryogenesis, thrombi formation, and artherogenesis can also be more comprehended. The mechanical deformation characteristics are known to affect the biological and chemical functions of the cells. This means that if the cell micromechanics are better understood, not only will heart valve disease patients benefit from new and improved heart valves, but other sicknesses can be further studied as well (Cleary, Sinnott 2006).

Soft collagenous tissues, such as that within aortic heart valves, exhibit viscoelastic properties including time-dependent creep and stress relaxation, rate-dependence, and hysteresis. (Nguyen 2010) It is important find the underlying mechanisms of these tissues because the viscoelastic properties are not linear and do not follow any one rule such as most inorganic materials.


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Tissues have vast mechanical properties that are changed easily and can vary up to five orders of magnitude. The properties could come from several parts of the tissue including the ECM, interstitial cells, or the connections within and between them. Figure 5 shows an example of the collagen fibers at rest and under an equibiaxial load (Liao et al. 2007).

Figure 5: Caption shown within image (Liao et al. 2007)

Tissues also change properties in relation to temperature, stress, hydration, and other environment and health variables. This is why many tissues are tested with different chemical treatments and preconditioning techniques (Nguyen 2010).

In order to develop new technologies and help advance treatment in the heart valve, better understanding is needed for the mechanical properties of the AV tissue. The tissue has been experimented with many current material tests; however, living tissue is highly anisotropic and cannot be simply compared by the same tests applied to plastic materials. The ECM and cellular interactions must further be studied via their physical mechanical interactions. The key to further comprehension of the relationship between the AVIC deformation, ECM, and the connection between them can be advanced by creating a finite element model, using all the known factors together and explaining why tissue behaves as it does mechanically. A virtual model that will simulate a biaxial loading experiment will help this understanding of the tissue properties encourage further studies on how to help treat heart valve disease.

4. Integrin relevance within tissue

An integrin is a receptor that attaches the cells to the extra cellular matrix (ECM) and transduces signals between the cell and ECM. Within the scope of this review, integrins are the medium of connection and signal transduction between the AVICs and ECM in the aortic valve. Integrins


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work with proteins to mediate cell-cell as well as cell-matrix interactions. The integrins play a major role within the connections between the cell and ECM. Their connectivity could range significantly, which will also overall affect the mechanical properties of the tissue. The integrins also assist in cell signal transduction, which resultantly affect the cell mobility, shape, and cycle. Seen below in Figure 6, integrins are the mediators between the cytoskeleton of the cell and the RGD proteins of the ECM. (El-Ghannam 2008)

Figure 6: Simplified illustration of how integrins connect between cells and ECM (El-Ghannam 2008)

Cell migration occurs in blood vessels within the endothelial tissue. It is assumed that this occurs within the heart valves also because of the direct connection and continuity of the endothelial cells lining the inside diameter. The cell migration occurs constantly and consistently throughout the lifetime of the tissues. Cell migration is the reason for healing and regeneration of damaged or old cells. This can be very important in the study of the heart valve tissue. In order for the heart valve to accept a foreign man-made or bioprosthetic heart valve (BHV), cell migration should be accounted for and possibly compatible in healing the tissue around the outside substance. The cell migration could also affect the mechanical and viscoelastic properties of the heart valve over time. These properties should also be modeled in finite element analysis and conduction of the virtual experiments. The cell migration is directly related with the connection between the ECM and the interstitial cells, more specifically, with the connecting integrins (Lodish 2008) (El-Ghannam 2008).

The integrins are proteins which medicate the linkage between the fibronectin in the ECM and the cytoskeleton. The cytoskeleton varies in shape and is hard to determine the actual connectivity between the AVIC and ECM. The protein, fibronectin, contains sequences of amino acids called peptide sequences. The part of the peptide sequence that the integrin attaches to is the Arginine-Glycine-Aspartic acid (RGD) sequence. As shown in Figure 7, the integrins bind to the tripeptide sequence RGD (Lodish 2008) (El-Ghannam 2008).


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Figure 7: Caption shown within image (Lodish 2008)

The fibronectin regulates the cell-matrix adhesion. This in turn affects the cell-migration, shape, and other aspects in relation to the ECM. The right figures of Figure 7 show the connection between the fibronectin and the ECM. The integrins which connect the fibronectin connections are shown in the top right picture as the green dots, the small cells connecting within the ECM. The connection between the ECM and cells are important to study because diseases are encouraged through abnormalities within the structure. Integrins are essentially a „bridge‟ between the ECM and the fibronectin-containing interstitial cells. This „bridge‟ serves as a mediator to also conduct signal transduction along with its structural duties. As seen in Figure 8, the top example is a non-stressed, low affinity or „inactive‟ conformation. In contrast, the bottom figure is the high affinity or „active‟ version which results from physical pressure applied to the system. When the connections are presented with a conformational change and are deformed, the integrins can become active to change their mechanical properties and signal transduction, therefore complicating their mechanical properties (Lodish 2008).


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Figure 8: Caption shown within image (Lodish 2008)

Since the connection between cells and the ECM within biological tissues are important to prevent damage and disease, further study is necessary to understand these interactions. Many people suffer from aortic heart problems and diseases every year. In order to prevent or treat these diseases, further comprehension of the cell-matrix-tissue interactions is needed. Common mechanical property testers have already been utilized to find corresponding values for tissues and cells. However, due to the unique systems that living tissues contain, these simple tests will not suffice for further study of living tissue mechanical properties. Other tests and simulations have been conducted thus far and will be described in the following section (Lodish 2008).

5. Articles covering simulations previously conducted

The articles in review cover various simulations previously conducted by other groups, interactions between cells and ECM, and bioprosthetic heart valve (BPHV) studies. Simulations include analysis of other collagenous tissues as well as determining the pressure distribution within various heart valves.

5.1. A unified multiscale mechanical model for soft collagenous tissue with regular fiber arrangement, Maceri et al. 2010

This article describes the mechanical response of soft collagenous tissues with regular fiber arrangements (RCSTs). This model used the aorta tissue and not the aortic valve tissue. This tissue is different but the approach to the simulation is still relevant to the current study. They used a nanoscale model and two-step micro-macro homogenization technique. The stress-strain curve of a regular soft collagenous tissue is usually shaped as the one shown in Figure 9b. The stress-strain curve shows the tissue is not linear until the collagen matrix is elongated and stretches linearly (Maceri, Marino & Vairo 2010). As shown in the figure, the fibers are straightened first before they can be tested for actual tissue strength. This information will be useful when conducting the finite element experiments. This information must be accounted for.


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Figure 9: (a) and (b): Captions are shown within image (Maceri, Marino & Vairo 2010)

The collagens straighten and align, then usually exhibit a linear type behavior. This paper uses a unified approach for modeling the regular stranded collagen arrangement for multiscale nano-micro-macro effects. The elastic (reversible) response of a collagenous material is similar to other linear materials. The initial equations are shown here:

cc

FA

(5)

Where c is the along-the-chord nominal stress, F is the force acting along the molecule chord direction, and Ac is the cross sectional area for each molecule.

1c

in

zL

(6)

Where c is the along-the-chord nominal molecule strain, z is the linear length of a contracted collagen molecule, and Lin is the molecule end-to-end reference length. These are standard equations and were utilized this experiment along with other non-linear equations (Maceri, Marino & Vairo 2010).

Shown in Figure 10 the simulations were computed via equations described in the theory and executed with MATLAB. The model depends on very few experimental parameters, yet


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Figure 10: Algorithm of the simulations produced for this article (Maceri, Marino & Vairo 2010)

They calculate parameters on multiscales. The nanomechanics of the collagen are initially described above and continue with non-linear analysis throughout the theory. This calculates individual collagen behaviors and is then analyzed. Micromechanics are also observed and calculated with some assumptions and neglections (such as slippage). (Some calculations used on the micromechanical level I am unfamiliar with, may need to look at in our meeting this Wednesday). Once the fibers have straightened, the material can then be observed on the macromechanical level. They calculate the stiffness and volume fractions (calculations can be found in the article, again not familiar with all of them). The model depends on very few experimental parameters, yet the numerical results are claimed to follow closely with experimental data, they assume Ec is constant. Their data is shown in Table 1, which contains a series of 3 tables. In the top table of Error! Reference source not found., the sensitivity of their simulation was calculated. The sensitivity is a ratio of the change of the variable by the value of the corresponding variable. Tables 2 and 3, within Error! Reference source not found., display parameters affected by each of the three scales, obtained from various sources (Maceri, Marino & Vairo 2010)


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Table 4: Captions shown next to respective tables (Maceri, Marino & Vairo 2010)

Using their simulation, aorta tissue experienced a significant increment of the maximum circumferential stress when the fiber volume fraction is reduced.

Figure 11: Caption shown within image (Maceri, Marino & Vairo 2010)

Figure 11 displays the structural models for the aorta media they used. According to this article, using histological evidences the aortic structure is modeled as a thick-walled cylinder of thickness Sa. The cylinder is compromised of N equally-thick layers (MLU) and is loaded on the inside by a uniform internal pressure. “Each MLU comprises a linearly elastic isotropic elastin-rich layer (Ee,ve) and interlamellar substance (IL), modeled as a composite material reinforced


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with collagen crimped fibers.”(Maceri, Marino & Vairo 2010) This following equation was used to find the multidirectional stiffness matrix [ ]IL of each IL layer.

[ ] [ ( )] ( )IL f f fF d (7)

Where,

( ) 1f fF d (8)

F( f) is a measure of the statistical occurrence of fibers with a wrapping angle, f (angular deflection of the fiber axis with respect to the vessel axis). [ ]IL is the strain-dependent stiffness matrix (Maceri, Marino & Vairo 2010).

5.2. High-order finite element analysis testing HV leaflet tissues

The University of Western Ontario has conducted high-order finite element method tests to heart valve leaflet tissues. The article was published in 2009, these tests are fairly recent in relation to this study and the results should be quite up-to-date with current knowledge. According to the article, “Modeling soft tissue using the finite element method is one of the most challenging areas in the field of biomechanical engineering.” (Mohammadi, Bahramian & Wan 2009)

The article continues to say there is no comprehensive method to modeling soft tissue mechanics because of the following reasons. First, the anisotropy within the material is too high. The collagen fiber density and orientation changes from layer to layer. Second, a material model fully describing all the properties of the tissues within the valve is not currently available. They claim that this experiment is one step closer to using a mesh-less finite element approach to modeling soft tissue in real time (Mohammadi, Bahramian & Wan 2009).

The heart valve leaflet was formed by stacking three layers consisting of varying mechanical properties. The geometry of the valve tissue was based on the Bezier surfaces design procedure, in which they refer to their previous work on the subject. The thickness of each of the leaflets was modeled to not be uniform but come close to real as possible, with the range varying between 0.1mm and 1.4mm. A porcine aortic valve was used in a biaxial machine measuring radial and circumferential stress-strain curves. The stress-strain curve they measured and used for the radial and circumferential directions can be seen below Figure 12.


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Figure 12: Caption shown within image (Mohammadi, Bahramian & Wan 2009)

This finite element experiment was looking for the maximum stresses on the heart valve leaflets. This can useful when modeling the tissue behavior at a smaller level. Shown below in Figure 13, the geometry was meshed into 183 high-order elements.

Figure 13: Caption shown within image (Mohammadi, Bahramian & Wan 2009)

Figure 14 displays where the maximum principle stresses are distributed over the leaflet tissue on the top and bottom layers. The simulations are conclusive in finding the maximum amount of stress and where it is located.


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Figure 14: Captions shown within image (Mohammadi, Bahramian & Wan 2009)

The left figure is the representation of the principle stresses with no connection between the layers. Contrastingly, the right figure is the result when the layers are modeled with a contact between them. This article can be utilized to apply the correct amount of force in relation to where the tissue sample is located and relate it to the thickness of the sample as well.

The deformations of the leaflets are also measured within their finite element method approach. In relation to the finite element model conducted here, it may also prove useful in comparison data. It was found that the surface area of the leaflet valve was initially 6.07 cm2 before deformation and is 6.68 cm2 after. This corresponds to between 5.29% and 10% area expansion. They also noticed „wrinkles‟ down the center of each of the leaflet valves in both their finite element model and the tests, as shown below in Figure 15 (Mohammadi, Bahramian & Wan 2009).

Figure 15: Captions shown within image (Mohammadi, Bahramian & Wan 2009)


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The locations of the wrinkles are said to vary depending on the pressure variety and the thickness of the valve. The wrinkles could be a concentration of force point and may cause extra stresses at that point. It was assumed the pressure was uniform and their calculations used a uniform thickness. Their model claimed to compare relatively close to testing and previous simulations.

5.3. Finite element model to simulate effect of collagen remodeling

The computational analysis of an aortic valve contained in a rigid root was conducted within this experiment, outlined by the article titled: Collagen fibers reduce stresses and stabilize motion of aortic valve leaflets during systole. This research was conducted in 2003 by the Eindhoven University of Technology, in the Netherlands. Their focus was to use a finite element model to simulate the effect of collagen remodeling on the mechanical properties of the aortic valve (De Hart et al. 2004). The flow and pressure forces were assumed to be laminar and used standard methods to calculate the internal pressure and assume that small buoyancy forces were neglected. The methods that were named were the Navier-Stokes, continuity equation, and a Newtonian behavior of blood.

This research was conducted to find the difference between a collagen fiber reinforced and non-reinforced structure within the AHV. In relation to the virtual experiments that will be conducted, this can be a good reference when comparing the pressures and forces used within the system. In this article, it was assumed that the leaflets constitute a fiber reinforced texture in which the matrix structure represents an orthotropic incompressible composite, in which they used a Neo-Hookean material law, shown below in equations (9) and (10).

m m mp I (9)

Where,

( )m G B I (10)

The fibers were then modeled as one-dimensional materials exerting only a tensile stress, fb ,

according to this following relation, in equation (11).

2

2 ( 1)21 ( 1)c

fb c e (11)

Where,

0|| * ||F e (12)

Where c1 and c2 are constants, is the fiber stretch, e0 is the initial local fiber direction, and F is the overall deformation of the fiber stretch. A constitutive law for leaflet composite with N layers was used to find the stress and tensors within the composite. These equations are similar


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to (9) and (10), with the exception of using modified variables to account for the multiple layers, they can be referenced in the article (De Hart et al. 2004).

They also describe an extensive formulation of 3 equations which allow dissimilar and independent discretizations for the fluid and structural domain. This makes the fictitious domain method very appealing for the fluid-structure interaction involving large structural motions. In their experiment, they adopted the Galerkin FEM and used a SEPRAN software package. The key features to this model used 3-dimensions, fully coupled fluid-structure interaction, avoidance of mesh update strategies and fiber-reinforced leaflet composite texture. This model looks into where the most amounts of pressure and stress is applied within the valve, and not in depth into the properties of the heart valve. This information is useful for the FEM model that will be produced. Below in Figure 16, shows the three-dimensional FEM model of the aortic valve their team produced.

Figure 16: Caption shown within image (De Hart et al. 2004)

Their data, when compared to tests in human tissue, resulted in very close values except for one, the commissural height. The article compares a non-reinforced fiber structure with that of a reinforced one. This does not tell us the material properties or the significance in changes with respect to cell-matrix interactions, but can be used as a reference when calculating some of the pressures and forces for the model (De Hart et al. 2004).

5.4. Stress analysis on mitral valve using FEM

This study applied FEM to investigate the mechanical behaviors of a bioprosthetic modified stentless quadrileaflet pericardial mitral valve. The first author is from Hunan University in Changsha, China and the article was written in 2005 and published in 2007. The FE model includes the material non-linearity, large deformations, and the condition of the leaflets. The results are claimed to be reasonable and compare with experimental results (Kuai et al. 2008).


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For the FE model, the FEM software ANSYS (version 8.1) was used. Again, as with the previous two articles, this simulation models the overall stress analysis on the valve, and not the micro material properties of the tissue. In Figure 17, the BP mitral HV is created and meshed with an internal pressure.

Figure 17: Captions shown within image (Kuai et al. 2008)

The model again can be useful in gathering data, but does not establish itself as a prerequisite to the FEA models that will be conducted in this research.

6. Statistics of heart valve disease

This section will cover the current statistics about heart valve disorders and what current technology that is available for treatment. The treatment of HV disease is dependent on many factors including but not limited to: how severe the valve disease is, the age of the patient, and whether other surgeries of the heart are needed simultaneously. Valve disease can lead to sudden death if serious enough. Some types of valve diseases are stenosis, insufficiency/regurgitation, and prolapse. Stenosis is the narrowing of the valve, insufficiency or regurgitation is when the valve does not properly close resulting in back flow, and prolapse is the displacement or irregular shaping of a heart valve preventing normal operation. All types are serious and can be treated with many forms of treatment. The options today include mechanical repair including stitching and replacement with a mechanical valve. Another option includes replacement with a


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biological valve from a donor or animal. The most current form of treatment is the option of tissue-engineered valves, which use the latest technology to make the valve the most biologically compatible and strong as possible. Catheters and minimally invasive techniques are increasingly used in this field since many heart valves can be repaired with minimal invasion (Anonymous).

It is important to find the strength and characteristics of the heart valves so more in-depth information can be gathered when researching heart valve treatment options. The aortic valve withstands the most amounts of stress and pressure from operation. If the information of this valve can be further determined, the other valves will also benefit and can use much of the same information (Anonymous).

When the heart valves need replacement, man-made valves are more durable than biological ones and usually do not have to be replaced. Bio-prosthetic heart valves are made from either pig, cow, or human heart issue and may have parts as well. Since foreign tissue is used, medications must be constantly taken to prevent the body from rejecting the valve. Similarly, man-made valves may last longer, but require the patient to take blood thinning medication for the rest of their life to prevent complications. Biological valves are less strong than man-made valves and are usually recommended to young women and athletes to prevent the use of blood-thinning medications, or elderly since it will probably last the rest of their lives. A new operation method named Ross is a surgical procedure to replace a faulty aortic valve with the patient‟s own pulmonary valve. A pulmonary valve is recovered from a human donor and replaced. This helps ensure that the more important valve doesn‟t get rejected and can heal properly. This operation is still in the experimental phase due to the failing of both valves after a few years (Anonymous).

Shown in Figure 18 are statistics for heart valve disease patients over the past few years. The data has been collected from current statistics variously from trusted internet sources, shown in Table 5. It can be seen from this graph that in every category, the aortic valve has more complications than any other valve. This makes sense since the aortic valve is put under the greatest amount of stress from functioning. Second to the aortic valve in complications and mortality is the mitral valve. This valve similarly goes through more stress than the tricuspid and pulmonary valves. This study is mainly being conducted on the aortic valve because it does have the greatest amount of patients suffering from complications as well as enduring more stress than the other valves. In relativity, if the material properties can be further examined for the aortic valves, the other valves should similarly benefit from this information.


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Figure 18: Heart valve disease population statistics, see Table 5 for sources

Table 5: Sources for the information in Figure 17

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Heart Valve Disease and Treatments by Valve

Mortality Disorder Mortality Any-mention Mortality Hospital Discharges Treatments

http://www.nlm.nih.gov/medlineplus/ency/article/000179.htmhttp://www.nhlbi.nih.gov/health/dci/Diseases/mvp/mvp_whatis.htmlhttp://www.metrohealth.org/body_HV.cfm?id=1534&oTopID=Chttp://my.clevelandclinic.org/heart/disorders/valve/youngvalve.aspxhttp://cardiacsurgery.ctsnetbooks.org/cgi/content/full/2/2003/1017/T22?ck=nckhttp://www.heart-valve-surgery.com/success-story-mortality-ross-recovery.phphttp://www.sjm.com/procedures/procedure.aspx?name=Heart+Valve+Replacementhttp://www.surgery.com/procedure/mitral-valve-replacement/demographics


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7. Cell deformation and tissue connectivity article reviews

7.1. Molecules mediating cell-ECM and cell-cell communication in human heart valves, Latif et al., 2005

The phenotypes of different tissues are dependent on the interactions of the cells between each other and the relation to the ECM. The cells are mediated by receptors that exhibit cell adhesion including integrins as well as immunoglobulin family members, syndecans, and selectins. (Latif et al. 2005) The aim of the study was to investigate the adhesion profile of native human valve interstitial cells (VIC) in situ and in vitro by analyzing these adhesion receptors. The study was conducted at the Imperial College at the Heart Science Centre, Harefield Hospital (Latif et al. 2005).

The reason this article was selected for review is to examine the connection and communication between the AVICs and the ECM. The experiments used immunocytochemistry (ICC) to separate the VICs from the multiple types of integrins and analyze the data. Roughly 92 to 98% of the VICs expressed a fibroblastic nature, and 50 to 100% of all the valve ICs demonstrated smooth muscle -actin. The -actin phenotype indicates that the ICs are of the myofibroblastic and fibroblastic nature.

There are multiple types of integrins, as seen below in Table 6. The cell communication percentage of expression is shown with respect to each type of integrin. The integrins, 5 and were mainly expressed by the VICs in comparison to the endothelial cells, which were strongly expressed by 1-3.

Table 6: Caption shown within image (Latif et al. 2005)

This article states that the valve leaflet ECM is compromised of and the VICs produce mainly collagens I and III. Other connections are mentioned and the article goes into further detail for


May 12, 2010 Page | 27

each type of integrin within the AHV. The only integrin significantly detected was , which happens to function in a dual capacity as adhesion and signaling molecules. They are thought to be important in wound healing and cell migration. Syndecan is absent from the VICs, which suggests that they make stable adhesions through other receptors such as integrins and adhesion molecules (Latif et al. 2005).

This data can prove to be useful when assuming the connectivity rates between the AVICs and the ECM. This article claims to be the first study to report the expression of cell adhesion molecules in all the native human cardiac valve leaflets and in cultured valve ICs (Latif et al. 2005).

7.2. Quercetin-crosslinked porcine heart valve matrix: Mechanical properties, stability, anticalcification and cytocompatibility, Zhai et al., 2010

Bioprosthetic heart valves (BPHV) have been a good solution to the treatment of heart valve repair; however, they also have their limitations. This article aimed to evaluate the cross-linking effect of a natural product, quercetin, on decellularized porcine heart valve ECM. The authors reside at the Chinese Academy of Sciences in Shanghai, China. This article demonstrated that quercetin is able to crosslink with the ECM of porcine heart valves and could possibly be a new reagent for the preparation of the BPHV, and scaffolds for HV tissue engineering (HVTE).

The results from this experiment were promising in relation to BPHVs. This may be used as a new treatment when a patient needs a replacement. BPHVs prepared with glutaraldehyde (GA) have some limitations including poor durability, calcification, and immunogenic reactions. The quercetin prepared sample results were similar to the GA prepared ones in regards to maintaining the valves‟ natural configuration. The samples prepared with GA were similar in ultimate tensile strength as fresh non-prepared samples. The data found that the samples treated with quercetin had substantially higher ultimate tensile strengths, as seen below in Figure 19.


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Figure 19: Captions shown within image (Zhai et al. 2010)

Other properties improved due to the cross-linking with the quercetin include less thermal denaturing with the minimal application. The thermal denaturing of the tissue cross-linked with 1mg/ml quercetin is similar to fresh tissue without cross-linking. This amount also happens to have the second highest tensile strength. Over the period of 30 days, the samples were soaked in D-Hanks solution for an in-vitro test. Only about 11.6% of the quercetin was released and the tensile strength had almost negligible change (Zhai et al. 2010).

Quercetin, when cross-linked with the heart valve tissue, produces similar qualities to that of the GA substance used since the 1960s. The quercetin treated tissue increased the tensile strength significantly and can also stabilize valve materials to resist enzymatic degradation. In addition, the new treatment also showed positive anticalcification effects in the simulated body fluid (SBF) solution as compared to GA, as well as being less toxic to umbilical vein endothelial cells. Some theories include quercetin having positive health effects as a supplement, including that it may help reduce the risk of cancer (Wikipedia, Quercetin). In all, this article was interesting and can be a new method of treating BPHVs (Zhai et al. 2010).

8. Summary of literature review

The aortic valve tissue contains a collagenous tissue matrix in conjunction with interstitial cells. It is known that there is an innumerable amount factors which affect the mechanical properties of collagenous tissue. These factors include but are not limited to the structure and the environmental conditions. The non-linear and unknown mechanical properties for the heart valve tissue are assumed to be described within these main categories:


May 12, 2010 Page | 29

1. Elongation of the collagen fibers within the ECM a. Relaxed state to elongated and straightened state b. Anisotropic viscoelastic properties of the ECM alone

2. Elongation and strength of the integrin connections a. Low affinity to high affinity state in combination with properties of the integrins

themselves b. Affect of connection and integrin properties in relation to environment

3. Integrin cell signal transduction a. Affecting cell behavior, cell size, connectivity, and mobility

4. Cell deformations a. Viscoelastic interstitial cell properties b. Effect depending on order and connection within ECM

5. Different layer characteristics and the connection between them a. Spongiosa, fibrosa, ventricularis, endothelium

In order to better understand the properties of the overall tissue, better understanding of the individual systems must also be acknowledged. Better treatments of heart valve failure and disease will be a result from the improvement on the understanding of cell-matrix-tissue interactions. To improve this understanding, a finite element analysis will be created for the tissue. This will allow the researcher to separate, compare, and integrate all of the various aspects and conditions which affect the properties of collagenous tissue such as the aortic valve. Advancements in treatment will be excelled from this study because understanding of the heart valve tissue is not completely comprehended to date.

9. References

, Treatment of Heart Valve Disease [Homepage of US Dept. of Health and Human Services, National Institutes of Health], [Online] [2010, March 18] .

Aubuchon, V. 2010, April 19-last update, Human Heart Diagram [Homepage of Vaughn's Summaries, www.vaughns-1-pagers.com], [Online]. Available: http://www.vaughns-1-pagers.com/medicine/heart-diagram.htm [2010, May 12] .

Cleary, P. & Sinnott, M. 2006, A micromechanical model for cell deformation in shearing flows using Smoothed Particle Hydrodynamics, Elsevier Ltd.

De Hart, J., Peters, G.W.M., Schreurs, P.J.G. & Baaijens, F.P.T. 2004, "Collagen fibers reduce stresses and stabilize motion of aortic valve leaflets during systole", Journal of Biomechanics, vol. 37, no. 3, pp. 303-311.

El-Ghannam, A. 2008, , MEGR 7090 - Advanced Biomaterials and Tissue Engineering - Course Notes Lecture 6 [Homepage of UNC Charlotte], [Online]. Available:

http://www.vaughns-1-pagers.com/

http://www.vaughns-1-pagers.com/medicine/heart-diagram.htm

http://www.vaughns-1-pagers.com/medicine/heart-diagram.htm


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http://www.coe.uncc.edu/~arelgha/PDF%20lectures%20MEGR7090/lecture%206.pdf [2009, September 15] .

El-Hamamsy, I., Balachandran, K., Yacoub, M.H., Stevens, L.M., Sarathchandra, P., Taylor, P.M., Yoganathan, A.P. & Chester, A.H. 2009, "Endothelium-Dependent Regulation of the Mechanical Properties of Aortic Valve Cusps", Journal of the American College of Cardiology, vol. 53, no. 16, pp. 1448-1455.

Kuai, X., Zhang, J., Ren, B., Liu, F., Gong, G. & Zeng, Y. 2008, "Stress analysis on stentless quadrileaflet pericardial mitral valve", Communications in Numerical Methods in Engineering, vol. 24, no. 9, pp. 785-793.

Latif, N., Sarathchandra, R., Taylor, R.M., Antoniw, J. & Yacoub, M.H. 2005, "Molecules mediating cell-ECM and cell-cell communication in human heart valves", Cell biochemistry and biophysics, vol. 43, no. 2, pp. 275-287.

Liao, J., Yang, L., Grashow, J. & Sacks, M.S. 2007, "The relation between collagen fibril kinematics and mechanical properties in the mitral valve anterior leaflet", Journal of Biomechanical Engineering-Transactions of the Asme, vol. 129, no. 1, pp. 78-87.

Lodish, H.F. 2008, Molecular cell biology, 6th edn, W.H. Freeman, New York.

Maceri, F., Marino, M. & Vairo, G. 2010, "A unified multiscale mechanical model for soft collagenous tissues with regular fiber arrangement", Journal of Biomechanics, vol. 43, no. 2, pp. 355-363.

Merryman, W.D. 2010, "Mechano-potential etiologies of aortic valve disease", Journal of Biomechanics, vol. 43, no. 1, pp. 87-92.

Merryman, W.D., Bieniek, P.D., Guilak, F. & Sacks, M.S. 2009, "Viscoelastic Properties of the Aortic Valve Interstitial Cell", Journal of Biomechanical Engineering-Transactions of the Asme, vol. 131, no. 4.

Mohammadi, H., Bahramian, F. & Wan, W. 2009, "Advanced modeling strategy for the analysis of heart valve leaflet tissue mechanics using high-order finite element method", Medical engineering & physics, vol. 31, no. 9, pp. 1110-1117.

Nguyen, V. 2010, "Viscoelasticity of Soft Tissues", iMechanica, .

Stella, J.A. & Sacks, M.S. 2007, "On the biaxial mechanical properties of the layers of the aortic valve leaflet", Journal of Biomechanical Engineering-Transactions of the Asme, vol. 129, no. 5, pp. 757-766.

Zhai, W., Lue, X., Chang, J., Zhou, Y. & Zhang, H. 2010, "Quercetin-crosslinked porcine heart valve matrix: Mechanical properties, stability, anticalcification and cytocompatibility", Acta Biomaterialia, vol. 6, no. 2, pp. 389-395.

http://www.coe.uncc.edu/~arelgha/PDF%20lectures%20MEGR7090/lecture%206.pdf

a development on virtual experiments to study matrix-cells

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