^{1}

^{2}

^{3}

^{1}Department of Mechanical Engineering,

^{2}Department of Mechanical Engineering,

^{3}Department of Mechanical Engineering,

The innovation of technology in the field of medical and cardiovascular implantation has increased the demand for metal-free restoration and has led to the growth of innovative alternative materials. Biomaterials are frequently used for clinical applications in cardiovascular implantation, dental implants, heart valves, coated hip implants, surgery and for drug delivery “A biomaterial is a non-viable material used in a medical device proposed to interact with biological systems”^{[1]}.

Cardiovascular artery disease is the most universal cause of death in the globe^{[2]}. Around 2300 Americans die of coronary disease daily, the average of one death for every 38 s. Every year there are more than 17.9 million of deaths, is projected to rise to 23.6 million deaths by 2030. The total direct and indirect clinical costs of cardiovascular disease are likely to increase to 749 billion $ by 2035^{[3]}.

Cardiovascular disease occurs when excess of cholesterol attach to the blood vessels wall, causing coronary artery disease (CAD)^{[4]}. There are different measures are available to revascularise a jammed vessel, including bypass surgery, atherectomy, angioplasty and coronary stenting^{[3]}.

Forty years ago, coronary artery bypass surgery was the trendy revascularization action used to cure blocked CAD. Regular coronary closures occur and thus urgent surgery was essential^{[5,6]}. Compared to other possible treatments stenting shows some advantages, has less complications, less pain and also has faster recovery. Therefore, the use of stents in cardiovascular activities has quickly improved from 10% to over 80% in current practice^{[7]}.

The present problem in cardiovascular field is that, Co-Cr L605 alloy stent implant has higher modulus of elasticity; owing to higher level of stresses developing in stent expansion which affects the coronary artery, hence chances of vessel damage is very high. In addition, the alloy has very poor plasticity and machinability. Further the presence of Nickel in Co-Cr L605 alloy is a risky aspect from the point of view of allergic problems^{[8]}.

Polyether ether ketone (PEEK) boasts of outstanding fatigue resistance and toughness. The Young’s modulus is extremely close to that of the bone. It is available for implantable devices viz cardiovascular, dental, orthopedics and spine applications. In addition, PEEK offers several advantages over metals, were excellent biocompatibility, chemical resistance, and superior in machinability, low co-efficient of friction, lessening of stress shielding.

Ortega-Martínez ^{[9]} have studied and recommended PEEK is an alternative material for medical implants because of several advantages over metals. The drawbacks of metals include high elastic modulus which causes high stress, allergies, and radiopacity. Guo ^{[10]} have investigated and suggested application of PEEK used as medical implants because of high modulus of elasticity (approximately equal to human bone), and high strength. The excellent biocompatibility and chemical resistance makes PEEK an attractive alternative compared to other biomaterials. Pargaonkar ^{[11]} have made comparison between different biomaterials and suggested that PEEK is the excellent biomaterial for medical devices. It has superior biocompatibility, chemically and physically stable, radiolucent and Young’s modulus is similar to bone. Sagomonyants ^{[12]} have conducted cytocompatibility and mineralization

By comparison with costly experiments performed in laboratories and hospitals, numerical simulation performed by computers offer benefits of both cost and flexibility. This research article aims to modeling and finite element analysis of cardiovascular stent implant to evaluate the radial displacement, stress distribution, and plastic strain in the proximal area of PEEK 450G biomaterial under pressure load conditions of 0.8, 1.0, and 1.2 MPa.

At present there are different coronary stent designs available in the market. In modern days the use of stents in vascular procedures has speedily increased. In order to improve outcome of the coronary stent implantation, it is essential to study the biomechanical performance of the stent before manufacturing and utilized. One of the effective methods used is finite element analysis to study the performance of the cardiovascular stent to alter the design of the coronary stent and its presentation.

This section covers modeling of different parts used in the study of biomechanical performance of cardiovascular stents. The modeling of coronary stent, vessel, plaque and balloon are illustrated in

Assemble model of stent, balloon, vessel with plaque

Finite element meshed model of stent, vessel, balloon and plaque

In this research article a balloon expandable coronary stent was modeled. To create prime model of cardiovascular stent, commercially accessible software was used. The modeling of cardiovascular stent produced on source of imagery^{[13]}. The stent length = 15 mm, stent outer diameter = 1.915 mm, and stent thickness = 0.05 mm. The element type used for modeling of stent in ABAQUS as C3D8R (linear 8-noded solid element). The FE model of the coronary stent contains of 40,852 elements 108,080 nodes.

Geometrical illustration of balloon model was formed based on standard reference^{[14]}. The length of the balloon was 25 mm and as a medium to inflate the coronary stent. The balloon thickness and outer diameter were 0.05 mm and 1.79 mm. To signify the balloon a polyurethane rubber form material was used. The balloon was modeled by using Mooney-Rivlin hyper elastic strain energy potential “W” and polyurethane is incompressible. Like coronary stent, the element type used for modeling of balloon in ABAQUS as M3D8R (linear 8-noded membrane element). The FE model of the balloon consisted of 13,750 elements 13,805 nodes.

The model of vessel was created by assuming of isotropic and homogeneous material. The vessel was modeled by using hyper elastic Ogden material behavior and as a one- layer blood vessel. The vessel length was 23 mm, vessel outer diameter was 5 mm, and vessel thickness was 0.5 mm. The element type used for modeling of vessel in ABAQUS was C3D8R (linear 8-noded solid element). The FE model of the vessel consisted of 2352 elements, and 111,692 nodes.

There are two types of plaque generated in coronary artery, viz., hypo-cellular and calcified plaque. The hypo-cellular type was used for the modeling of plaque. Geometrical parameters used for the plaque are as follows. Length of plaque = 10 mm, outer diameter of plaque = 4 mm, and thickness of plaque = 1 mm. Element type used for modeling of plaque in ABAQUS was C3D8R (linear 8-noded solid element). The FE model of the plaque consisted of 21,030 elements and 125,390 nodes

The bending of coronary stent implant has both limitations and advantages. On one side, bending of coronary stent produces elevated stresses on coronary artery; due to these high stresses vessel damage might occur. On other side, the coronary stent bending can facilitate to keep coronary stent steady against the force of pulsate movement of blood. Hence the bending analysis in coronary stent implant can be extremely helpful to alter design of coronary stents. In this article only cardiovascular stent is considered for bending analysis.

In this study, the assumption was made that the PEEK 450G biomaterial was homogenous and isotropic characterized by four material properties, i.e., Modulus of elasticity, Density, Poisson’s ratio and Yield stress. The mechanical properties of PEEK 450G biomaterial are represented in the ^{[15]}.

Mechanical properties of PEEK 450G biomaterial^{[15]}

Material | Material Properties | |||
---|---|---|---|---|

Modulus of Elasticity E in (MPa) | Density ρ in (kg/mm^{3}) |
Poisson’s Ratio υ | Yield Stress σy in (MPa) | |

PEEK 450G | 3700 | 1.30 × 10^{-6} |
0.36 | 100 |

PEEK: polyether ether ketone

Based on numerical data for biomedical stent using PEEK 450G biomaterial the deformation of the stent in terms of bending which is dealt as four different loading cases as shown in ^{[16]} and also the one end of the stent is fixed in all DOF.

Loading cases^{[16]}

Loading cases | Displacement-Y in mm | Displacement-Z in mm |
---|---|---|

Case-1 | 1 | 0 |

Case-2 | 2 | 0.1 radian |

Case-3 | 2 | 0.15 radian |

Case-4 | 2 | 0.25 radian |

Finite element analysis solver ABAQUS V6.10 was used to find out von-mises stresses of PEEK 450G stent at various loading cases, i.e., 1 mm displacement in Y direction, 2 mm displacement in Y direction with 0.1 radian rotation in Z direction, 0.15 radian rotation in Z direction and 0.25 radian rotation in Z direction.

Von-mises stress distribution of PEEK 450G stent when subjected to (A) 1 mm displacement (B) 2 mm displacement with 0.1 radian rotation (C) 0.15 radian rotations, (D) 0.25 radian rotations. PEEK: polyether ether ketone

Here, coronary stent, balloon and vessel with plaque was considered to carry out non-linear pressure analysis by using commercially available ABAQUS 6.10 software, and to determine radial displacement, von mises stresses and plastic strain of coronary stent when it is subjected to different loading conditions i.e., 0.8 MPa, 1 MPa, and 1.2 MPa.

The stress strain performance determine from the Ogden model is shown in ^{[17]} with parameters specified in

Stress-stretch curve for intima vessel^{[13]}

Ogden model parameters of vessel

Material | ρ (kg/mm^{3}) |
µ_{1} |
µ_{2} |
µ_{3} |
α_{1} |
α_{2} |
α_{3} |
D_{1} |
---|---|---|---|---|---|---|---|---|

Intima | 1.07 × 10^{-6} |
-7.04 | 4.23 | 2.85 | 24.48 | 25.00 | 23.54 | 8.95 × 10^{-7} |

Intima vessel wall was modeled as a single homogeneous hyper elastic layer. Intima vessel layer is stiffer than other layers like media and adventitia, and have only intima vessel is considered for the analysis. Isotropic material properties were used and described by third-order Mooney-Revlin hyperelastic model^{[18]}. The third-order strain energy potential for Ogden model is given by the equation:

Where, W = Strain energy density function; I_{1}, I_{2} and I_{3} = the strain energy invariants; C_{ij} = hyperelastic constants.

The stress-strain behaviour of hypo-cellular and calcified plaque show that, hypo-cellular plaque is less resistance to stretch or deformation than calcified plaque as shown in ^{[17]}. Hence, in this work hypo-cellular plaque was considered for simulation.

Stress-stretch curve for hypo-cellular and calcified plaque^{[13]}

Like blood vessel, here also the similar Ogden hyper elastic model was used, but with first order (i.e., i = 1) and the values are specified in ^{[17]}.

Values of the Ogden model parameters for hypo-cellular plaque

Material | ρ (kg/mm^{3}) |
µ_{1} |
α_{1} |
D_{1} |
---|---|---|---|---|

Hypo-cellular Plaque | 1.45 × 10^{-6} |
0.093 | 8.17 | 4.30 × 10^{-7} |

Polyurethane rubber material was used for modelling of balloon, by using Mooney-Revlin hyperelastic strain-energy potential, W and is given by the equations:

Where, C_{10}, C_{01} and D_{1} = model co-efficient; J = volumetric stretch; λ_{1} λ_{2} λ_{3} = stretches in 3 principal directions.

The polyurethane material is incompressible and was defined by a non-linear first order hyper-elastic Mooney Revlin model^{[17]}. The stress strain curve for polyurethane rubber balloon is shown in

Stress-strain curve for polyurethane rubber balloon^{[13]}

Values of the Ogden model parameters for hypo-cellular plaque

Material | ρ (kg/mm^{3}) |
C_{10} |
C_{01} |
D_{1} |
---|---|---|---|---|

Polyurethane | 1.07 × 10^{-6} |
1.03176 | 3.69266 | 0 |

To simulate the inflation process of stent, a pressure was applied to the inner surface of the balloon. The pressure applied was 0.8 MPa, 1.0 Mpa, and 1.2 MPa. In simulation, the balloon has fixed in all degrees of freedom at left end, the balloon were fixed in all degrees of freedom at right end, preventing axial movement of balloon to slide in the artery. Contacts between the balloon and stent, plaque and stent, artery and plaque, were modeled as face-to-face solid contacts, with a frictionless movement under common interaction.

There was no direct contact among any surfaces of the stent model at the beginning of the simulation. When pressure was applied at internal surface of the rubber balloon, first contact between stent and balloon was recognized, then between stent and plaque, and finally between plaque and vessel. In stent expansion, contact between stent and vessel was also noticed.

Explicit solver (ABAQUS 6.10) was used to carry out simulations, which was used to produce to the expansion of the balloon. Considering artery and plaque for the non linear pressure analysis of stent expansion, for the stent inflation balloon was used as a medium for which various pressure load cases was performed to know the mechanical behaviour of artery and stent, such as radial displacement of artery and stent, von-mises stresses sharing of artery and stent and plastic strains at plaque and non-plaque regions.

Many researchers elaborated in their work, Co-Cr L605 alloy stent implant has higher modulus of elasticity; owing to higher level of stresses developing in stent expansion which affects the coronary artery during stent expansion, hence chances of vessel damage is very high. To overcome these problems, the alternate material is essential for the cardiovascular stent implants. The results of PEEK450G stent implant has discussed in following two methods.

The results of non-linear bending analysis of coronary stent by using PEEK 450G as shown in ^{[15]}. The bending of coronary stent causes high stresses on artery may injure the coronary artery^{[14]}. Hence, PEEK 450G has an ideal material in terms of flexibility and stability, also recommended for future coronary stent implants.

Relation among von-mises stresses and different load cases

The results obtained for PEEK 450G stent in terms of radial displacement, when subjected to 0.8 MPa pressure load case as shown in

Radial displacement of PEEK 450G stent (Left) with artery (Right) at non-plaque (A) and plaque (B) regions when subjected to 0.8 MPa pressure load. PEEK: polyether ether ketone

The relation between radial displacement and pressure at non-plaque region

The relation between radial displacement and pressure at plaque region

The results obtained for PEEK 450G stent in terms of von-mises stress, when subjected to 0.8 MPa pressure load case as shown in ^{[14]}. The von-mises stress of PEEK 450G is superior in both plaque and non-plaque regions and also flexible to expand. Thus, PEEK 450G is a better material for coronary stent implants.

Von-mises stress of PEEK 450G stent at (A) non-plaque region (Left) and (B) plaque region (Right) with (C) artery subjected to 0.8 MPa pressure. PEEK: polyether ether ketone

The relation among von-mises stress and pressure at non-plaque region

The relation among von-mises stress and pressure at plaque region

The results obtained for PEEK 450G stent in terms of plastic-strain, when subjected to 0.8 MPa pressure load case as shown in

Plastic strain of PEEK 450G stent at (A) non-plaque region (Left) and (B) plaque region (Right) subjected to 0.8 MPa pressure. PEEK: polyether ether ketone

The relation between plastic strain and pressure at non-plaque region

The relation between plastic strain and pressure at plaque region

In this work, 3D modeling of PEEK 450G stent was done by using CATIA V5 and finite element analysis of cardiovascular stent implant were carried out by using commercially available ABAQUS 6.0 software to evaluate the radial displacement, stress distribution, and plastic strain in the proximal area of PEEK 450G biomaterial under pressure load conditions of 0.8, 1.0, and 1.2 MPa. It was clear from FE simulation, both in non-linear bending analysis and non-linear pressure analysis, that PEEK 450G stent exhibits very good radial expansion and lowest stress concentration and also which is well below the yield level (100 MPa), however plastic strain is high because of softness, the strain rate needs to be minimized by suitably varying its chemical composition. Hence, blood circulation will be appropriate and also chances of vessel damage may be reduced more by using PEEK 450G. The FE analysis results showed that PEEK 450G is a best alternate candidate biomaterial suitable for cardiovascular stent implants.

Formulated the problem, designed model and performed FEM analysis: Kumar V

Wrote the first draft of the manuscript: Kumar V, Ramesha CM, Sharanraj V

Discussed the results and implications as well as commented on the manuscript at all stages: Kumar V, Ramesha CM, Sharanraj V

Read and approved the final manuscript: Kumar V, Ramesha CM, Sharanraj V

Not applicable.

None.

All authors declared that there are no conflicts of interest.

Not applicable.

Not applicable.

© The Author(s) 2019.