A Novel Design and Simulation of a Nano Prosthetic Artificial Heart Valves

Heart valve replacement is a major health burden and is required by millions of people worldwide, which invites the continuous need to discover and manufacture more effective and permanent artificial replacements. In the present work, unique models of eight artificial heart valves were designed and examined using seven synthetic and nanocomposite materials. The designed valves were examined to determine the best designs and materials in terms of durability, flexibility, and energy consumption, and to improve the biomechanical performance by using the Response Surface Methodology (RSM) and the Design Expert System 13. The highest values of the equivalent stress due to the applied blood pressure on the moving parts on each type of manufactured heart valve occur in valves with three dimensions moving parts, reached in the mitral tri-leaflet valve 14.13 MPa, followed by the tricuspid aortic valve. The equivalent stresses for other types of valves produced with simple surface action were lower than 2 MPa. The strain energy that is expended during the process of diastole and systole was found to be directly proportional to the strength and flexibility of the materials used. The energy consumption rates decrease when using highly elastic materials such as TPE and PSN4. The values of this energy also increase with an increase in the area of the moving parts of the valve, especially when faced with the process of closing blood flow, as with the use of the tricuspid aortic


INTRODUCTION
Congenital and rheumatic valvular heart disease (VHD) is the most important cause of heart failure around the world (1-3), which can cause arrhythmias, stroke, heart failure, and potentially life-threatening complications and need continuous clinical attention.More than 30 million people suffer from it.In the United States alone, approximately 90,000 heart valve replacements and more than 300,000 worldwide are performed annually with biomechanical or prosthetic valves (4).
Each human heart has four valves: the mitral, the tricuspid, the aortic, and the pulmonary valve (1,5).There are various forms of aortic valve disease, namely aortic regurgitation, aortic stenosis, congenital aortic valve disease, and atrial septal defect (6).Artificial heart valves are used to replace heart valves that have been damaged by disease or wear and tear for time duration (7).
Mechanical heart valves are made of materials of much higher strength than those found in human soft tissues.There are basic types of mechanical heart valve designs including, the gaged ball, single leaflet, bicuspid, and tricuspid valves (8).The main advantages of the mechanical valve are their durability, and they are wellsuited for patients of all ages.These Artificial heart valves rarely need replacement and often last for the rest of the patient's life.The main drawback of a mechanical valve is its tendency to form blood clots on its surfaces, so patients need lifelong blood-thinning medications and lifestyle modifications (9).
The use of prosthetic artificial heart valves and continuous improvements in valve designs have reduced the death rate of heart patients (9).The selection of a prosthetic valve that is appropriate in shape and size is a key factor for the success of surgery (10).However, the ability of the valve geometry to provide adequate mechanical function immediately after implantation is critical to patient survival.Therefore, the successful application of tissue engineering in the development of heart valves will require that they maintain similar mechanical properties to that of the original valves, and the ability to repair, remodel, and regenerate heart tissue (11,12).So far, no satisfactory mechanism has been found to achieve a dynamically stable and durable implantable heart valve (13).The latest designs of mechanical heart valves provide relatively superior hemodynamics, but high-shear platelets and blood cells still pose significant challenges (14).
Composite materials are one of the most well-known materials for various functions that reduce the structure's weight without reducing its strength.Polymer composites exploit a wide range of applications due to their excellent performance in mechanical, electrical, and thermal properties (such as medical, electronic, automobile, and aerospace) (15).
The current work aims to design and simulate a unique model of eight artificial heart valves using seven synthetic and nanocomposite materials.The designed valves will be examined to determine the best designs and materials in terms of durability, flexibility, and energy consumption performances by using the Response Surface Methodology (RSM) and Expert Design 13 system.

1. Design of a Human Artificial Heart Valves
The mechanical prosthetic heart valves are an effective engineering device used to replace the damaged or diseased natural valves of the heart and are characterized by long performance and high reliability, but they may lead to possible complications such as hemolysis and thrombosis (16).Durability is the most important factor in choosing the right materials for polymeric heart valves to ensure strong mechanical properties that give the valve low creep, high rigidity with self-healing, and the ability to maintain structural integrity at repeated periodic loading and unloading of blood to prevent life-long blood clotting, and it is less prone to calcification and failure compared to bio-prosthetic valves (5).
The most important factors that must be considered when choosing a valve are the patient's age, comorbidities, and life expectancy (8).The process of designing an artificial heart valve needs to evaluate its mechanical performance and blood flow pattern and study both leaflet deformation/stress.As the leaflet is subjected to fluctuating stress, the large lifetime of the stress requires flexibility to open and close the blood flow path as a major function of the heart valve (17).The most important design requirements for valves are those that cause minimal shock to the elements of the structure surrounding the valve, blood vessels, and endothelial tissues of the heart, with good resistance to mechanical and structural abrasion.It works to reduce the chances of deposition of platelets and thrombus, to be nondissolving materials, to be stable and not absorb blood components, and to be sterilizable with high surface quality (18).
In this work, eight artificial heart valves were designed and analyzed.Table 1 lists the main physical and mechanical properties of the designed materials.
Figure 1 illustrates the designing steps for the artificial caged ball heart prosthetic valve.The caged ball valve is the first artificial heart valve designed and implanted in the human body.The valve was initially made of stainless steel (12).The introduction of granulated ball valves is a major advance in the treatment of patients.Now, there are several thousand patients who have such valves implanted (8,19).The caged ball valve design is still the valve of choice for some surgeons (18,20).It consists of a celestial ball with a circular stitching ring and a cage of three or four plastic or metal brackets (usually of titanium rods) that determines the path of movement of the ball (21).
The ball blocks the valve opening to prevent the reverse flow of blood.Its diameter is greater than the inner diameter of a circular ring.These valves were designed to allow blood to flow in only one direction, and act to cause blood to flow from the heart to the aorta when the pressure of the heart exerts on the blood (and the valve ball) exceeds the pressure in the aorta.After the blood leaves the heart, the pressure inside the heart drops drastically, then the negative pressure sucks the ball of the valve back, which will prevent the blood from returning to the heart.
Figure 2a shows the artificial conical caged ball heart valve.This valve works with the same principle as the previous valve, except that the cage that holds the ball takes a conical shape instead of a cylindrical one to Figure 2b shows the designed single hemispherical caged ball artificial valve, Which works in the same way as the single-leaflet disc valve, but with better peripheral blood flow dynamics, ease, and rapid closing of the valve when the blood flow stops.Figure 2c shows the designed artificial single-leaflet prosthetic valve.
It consists of four perpendicular metallic or polymeric stents to hold a disc inward above the orifice for blood flow from the heart, and the opening angle of the disc concerning the valve ring ranges from 60 to 80 degrees.This type may show a complex dynamic flow, where the kinetic energy of the blood flow must first move the disc and then centralize the circumferential flow direction around it (8).These valves are similar to caged ball valves, except that the valve shutter is a disc (22)(23)(24)(25)(26)(27)(28)(29).This valve allows a reduction in the annulus dimensions.The thickness of the disc valve ring is about 0.13D and thus its total length is reduced to 0.82D.It works rapidly and smoothly in the velocity field in the aorta (30).
The single-disc valve has been shown to operate at a much lower rate of clots than the bileaflet valve, and the open rate is greater (31).The structures of the pulmonary and aortic valves are similar, and both are made of three semilunar leaflets within the valve roots (5).Following the great success of interest treatments have grown in treatments to include the mitral valve.The first therapeutic mitral valve implanted in humans was approved by the Food and Drug Administration in 2013.Since then, several technologies have been developed and are currently being investigated (32).The structures of the pulmonary and aortic valves are similar, and both are made of three semilunar leaflets within the valve roots (5).
Figure 3 shows the designing steps of an artificial mitral tri-leaflet heart valve.This valve has been designed to work on the same principles as the previous valve, except that it allows the oxygen-rich blood to flow from the heart into the aorta.The prototype of this valve was produced from a short silicone rubber tube and a metal ring (33).
Then the design was improved by making it without a metal ring.Tricuspid valve disease is an unmet clinical need.Tricuspid valve disease is a common valvular with high patient and mortality rates.Yet tricuspid valve surgery remains the most dangerous of all valvular surgeries with an estimated inpatient mortality rate of 8.8%.
Due to the novelty of these techniques and the complex and variable anatomy of the tricuspid valve, procedural planning, and research based on 3D printing are of great value (32).Increased interest in tricuspid valve replacement has led to the advancement of 3D printing models of this valve (34)(35)(36).Tricuspid polymeric valves were developed that better resemble the original valve geometries and are more dynamically efficient.Figure 4 shows the designed tricuspid prosthetic aortic valve (TAV).It consists of three leaflets of equal shape and size (37).
This valve allows blood to flow from the aorta into the heart.It is a replacement for the bicuspid aortic valve which is a congenital defect since it is not able to completely stop the blood from leaking back into the heart.This can harden and not-open the valve, causing the heart to pump harder to bypass the aortic valve stenosis.

Mathematical Modeling of the Blood Flow
The blood in the human body contains liquid and solid parts.The liquid part of the blood is called plasma, generally made of water, protein, and salts, and over 50% of blood is plasma.For developing the Cardiovascular system equation, the artery material is assumed to be nondeformable, isotropic, tapered, without longitudinal movements, and incompressible with circular sections (38).To derive the equations governing the blood fluid flow, let us assume that the blood fluid flow is assumed to be axisymmetric and incompressible (39).However, under conditions of high blood flow, particularly in the ascending aorta, the laminar flow can be turbulent and disrupted and can be described as chaotic.Turbulence flow generates heat and is dissipated, as the increases the energy required to drive blood flow because turbulence increases the loss of energy as friction.Turbulence occurs when the velocity of flow becomes high enough that the flow lamina separates and when a critical Reynolds number (Re) is exceeded.Reynolds number is a way to predict, under ideal conditions, when turbulence will occur (40).
It's important to recognize that the Navier-Stokes equations are used based on the assumption of Newtonian fluid behavior, where the viscosity is constant regardless of the shear rate.However, in microcirculatory systems such as small branches and capillaries or regions with disturbed flow patterns like the blood flow through the mechanical artificial heart valves, blood exhibits non-Newtonian flow patterns as treated in the current work (39).The equations that describe the geometry of the artificial heart stenosis models in a bell shape can be expressed as in Equation 1: where The blood flow model in an arterial segment is considered to be steady, incompressible, laminar, axisymmetric, and two-dimensional.The Boussinesq approximation is used to approximate the turbulent stresses existing by the turbulent dynamic viscosity (41).Then neglecting the orientation of gravity inside the body, the continuity and momentum equations for a non-Newtonian behavior, for the current blood flow study through the heart valve stenosis when the shear rate is less than 100 s-1.The equation of continuity can be written in the cylindrical coordinates system (r, θ, z) as follows (39,42,43): The equation of momentum is: where, τrz, τrr, and τzz are the shear stress of the model; vz is the axial velocity, p is the pressure of the fluid, vr is the radial velocity, and ρ is the density of the fluid, and: where k is the flow consistency index = 0.02 and: On the arterial wall, the axial velocity gradient is assumed to be zero, which means there is no shear rate of blood fluid along the axis and also there is no radial flow along the axis of the artery.Then the boundary conditions can be expressed as follow: ( , ) 0, 0, 0, ( , ) 0, ( , ) 0, ( ). ( , ) 0, To immobilize the arterial wall, the radial coordinate transformation of governing equations can be used, where y=r/R(z).Then Equations 2 to 7 can be written as follow: where, The transformation initial and boundary conditions are (43): ( , ) 0, 0, 0, ( , ) 0, ( , ) 0, 1. ( , ) 0, = = = z r v y z on y v y z (17) The radial velocity can be solved by multiplication of yR in Equation 11 and then integrated concerning y from 0 to 1, then: By using the boundary condition (of Equation 16), Equation 18will take the form: Since R = R(z), Equation 19can be re-written as: By comparing both sides of the Equation 20, will give: Substituting Equation 21into Equation 11 and multiplying by yR, then: Equation 22 can be re-written as follows: 2 ) Finally, the radial velocity is obtained with the form: .= r z dR v y v dz (24) To obtain the blood radial velocity (vr), it is required to plug vr in Equation 12, then equations of axial momentum can be reduced to: The volumetric blood flow rate (Q) is given by the following equation: And, using the radial coordinate transformation, r = yR, then: Then, the radial velocity can be solved by discretization of Equation 24 as follows: . .(28) The volumetric flow rate can be approximated by discretizing Equation 27:

( ) ( )
1,2,... 1 2 , ( The resistance to the blood flow (λ) can be obtained as: To develop the mathematical model of blood pressure, Poiseuille's equation is considered to determine the relation between blood flow rate and pressure which is: Equation 25 is the mathematical model of the blood pressure in the human body.The required boundary condition and the values of the other parameters to solve these equations are; the pressure gradient, ∂ P /∂z = 40-100 mmHg, the Initial blood flow rate value of Q = 1 to 5.4 liter/minute, the Kinematic viscosity of blood, v = 0.035 cm 2 /s and the density of blood ρ = 1.043 to 1.057 g/cm 3 , the radius of a normal artery R0 = 0.1 cm, the constant dynamic viscosity (μ) of 3.71×10-3 Pa s, the blood density, initial value of S0 = 2.0 to 3.0 cm 3 , and Q0 = 16.7 cm 3 /s.For simplicity, the length of the artery model L = 14 cm, L0 = 3-8 cm, The mean Reynold number = 300, the artery systole duration for 0.3 seconds and diastole 0.5 seconds, and the period is 0.2 seconds (40,(44)(45)(46).Reynolds number and Re = of the blood flow is: Re = V * D * ρ/μ.

RESULTS AND DISCUSSIONS
The equation of the mathematical model of blood flow rate can be solved using the Computational fluid dynamics (CFD) which is a branch of fluid mechanics that uses numerical analysis system, while the finite volume method (FVM) was used for discretization of flow governing equations.Some general settings were set for the CFD analysis in the navigation pane to perform mesh-related activities including setting up the models for the CFD simulation's viscosity by activating a multiphase and viscose model; enabling the volume and viscosity of the fluid as laminar; and enabling the Energy Equation option from the Model list, the k-epsilon and K-equation turbulence model to expand the Viscous Model (45).In CFD analysis system, the Y+ value represents the distance from the first grid cell to the surface wall is an important parameter for determining the accuracy of the boundary layer thickness (46)(47)(48).
Figure 5 represents CFD solution and simulation of the of blood flow in the atria with a tricuspid mitral valve (1mm), using the high-strength and flexible PSN4 nanomaterial.
To determine the mechanical properties of the designed artificial valves, the response surface method (RSM), the finite element method (FEM) and the Design-Expert 13 were applied (49,50).They were first modeled with the static structures analysis system.Then the meshing process was carried out with the additional refinement fragmentation for the moving parts of the valves, which are exposed to variable loads, as shown in Figure 6a.The structure mesh has been used for gridding of each designed artificial heart valve with the number of different cells and the mesh study performed according to the required number of cells were created for gridding (51).
Then the boundary conditions for each valve were determined, where a pressure equal to the blood flowing pressure from the heart, which mmHg, was subjected on the surface of the valve moving parts, while the base area in the assembly completion with the heart was simply supported, as shown in the Figure 6b.Table 2 illustrates the mechanical properties of the designed artificial heart valves.
Figure 7 shows The strain energy simulations for selected types and the used materials of the designed artificial heart valves.Figures 8 to 10 show the simulations models of the strain energies, the total deformations, the equivalent stresses, the stress safety factor for selected types, and the used materials of the designed artificial heart valves.
To simulate of diastolic and systolic of the natural heart at each pulse cycle, the Goodman loading ratio criteria was used for the transient continuously and repeated applied blood pressure of +200 Pa for 0.5 second followed by an absorption pressure -50 Pa for the duration for 0.3 second (47).To analyze the results, the statistical Expert Systems 13.0 program was used.
Figure 11 shows the equivalent stress values resulting and calculated from applying blood pressure on the moving parts of these valves of each type of manufactured heart valve by using the Von Mises method.
From the figure, it is clear that the highest values of the equivalent stresses were found in valves with moving parts in a large range and three dimensions.
The highest values were produced in the mitral trileaflet valve (tri-leaflet Thick.= 0.5 mm) reached 14.13 MPa, followed by the tricuspid Aortic valve (TAV), (tricuspid thick.= 0.5 mm and 1 mm, respectively), while the equivalent stresses for the other types of the produced valves with the simple surface movement were less than 2 MPa, and the lowest value of stress was produced in the single-leaflet type valve, which reached 0.87 MPa. Figure 12 shows the relationship between the produced artificial heart valve type and the filament material with the strain energy expended when blood pressures of 120 mmHg are applied on the moving parts of the manufactured heart valves from the heart to the arteries or from the veins to the heart to open or close the blood flow during the process of diastole and contraction of the heart.
This figure shows that the energy expended is directly proportional to the strength and flexibility of the used material, and the energy expenditure rates decrease when using highly flexible materials such as TPE and PSN4.The values of this energy also increase when the area of the moving parts of the valve increases, especially when the closure process is facing the blood flow, as is the case with the use of a tricuspid Aortic valve (TAV), (tricuspid thick.= 0.5 mm and 1 mm, respectively).The amount of energy increased when using the mitral tri-leaflet valve (tri-leaflet Thick.= 0.5 mm and 1 mm, respectively).The least energy was spent when using simple movement valves in one direction, which are the conical caged ball, the single hemispherical leaflet, the caged ball, and then the single leaflet valves, respectively.In general, the highest calculated strain energy does not exceed 0.049 mJ.

PLA (TPU) PSN4
Caged ball Figure 13 shows the relationship between the produced heart valve type and the used material with the total deformation produced in the valve structure under the influence of applying the same blood pressure above.The figure shows that the highest total deformation in (mm), occurs when using thermoplastic polyurethane (TPU), followed by thermoplastic polyurethane  Also, the lowest rates of deformation under the influence of blood pressure were observed when using materials of superior flexibility and strength, such as the used nanocomposite polyetherimide/silicone rubber with nano silica (PSN4), reaching from 5x10-5 to 0.1 mm, followed by the polystyrene-isobutylene-b-styrene (SIBSTAR103T) nanostructured rubber linear triblock.

Single
Figure 14 shows the relationship between the material and type of the produced artificial heart valve with the stress safety factor, where the obtained values of this factor decrease with the complexity of the movement of the moving parts of the valve.
The highest rates were recorded when using the mitral tri-leaflet valve (tri-leaflet thick.= 1.0 mm) and reached 2.45 when using the high-strength and flexible PSN4 nanocomposite material.This value decreases to 1.27 when using the same material and type of valve but with a tri-leaflet thick.= 0.5 mm.
It is noted here that the PSN4 material is the only suitable for the manufacture of this artificial valve type, as well as the tricuspid aortic valve (TAV), where the other six tested materials failed because the stress safety factors are less than 1 .
For the other types of manufactured valves, it was noted that the highest safety factor reached 15 was obtained when using the single-leaflet type valve, where all materials used in this work are suitable for the production of this type of valve because its movement is simple, flat, and in one direction.The principle of action of the tri-leaflet mechanical heart valve (BMHV) is that it has three semicircular leaflets prisms connected by small hinges with a solid, semi-circular valve ring instead of a single disc, and patients using this valve require anticoagulants for life (18).It has a much lower opening rate than the single-disc leaflet (33).It has a long service life and reliable performance and is of great importance in the treatment of valvular heart patients, but it still has defects such as thrombocytopenia, hemolysis, and thromboembolism (16,20).The thickness of the leaflets is about 0.04D, and each leaflet can be opened up to 85 Figure 14.The stress safety factor for all the designed artificial heart valve types degrees to obtain a rapid distribution of the flow velocity field of blood in the direction of the valve with less thrombosis (13,21,52).
The highest safety factor rates were observed after that when using the single hemispherical leaflet type valve, then the conical caged ball and the caged ball type, respectively.It can be concluded that the best materials for manufacturing these four types of valves are the PSN4, followed by the SIBSTAR103T, TPU, and TPE.
It is not recommended to use PETG, PLA, and nylon materials in the manufacture of any artificial heart valves, due to their lack of strength, flexibility, and high brittleness, especially PETG and PLA materials.SIBS material reinforced with woven polyester fabric or carbon nanotubes is also a promising material for the production of artificial heart valves.It has good mechanical properties, high thermal properties, and oxidative stability is stable, biocompatible, and hematologically compatible making it an ideal candidate for medical applications (53,54).

CONCLUSIONS
• It can be concluded that the best materials for manufacturing these four types of valves are the PSN4, followed by SIBSTAR103T, TPU, and TPE.The use of PETG, PLA, and nylon materials is not recommended in the manufacture of any prosthetic heart valves, due to their lack of strength, flexibility, and high brittleness, especially for PETG and PLA materials.• It was also noted here that PSN4 is the only material suitable for the manufacture of mitral tri-leaflet and tricuspid mitral valve artificial valves.For other types of valves manufactured with a single leaflet, high safety stress factors were obtained because their movement is simple, flat, and in one direction, where the highest values were observed when testing a single hemispherical leaflet type valve, then the conical caged ball and the caged ball type, respectively .• The highest values of the equivalent stress due to the applied blood pressure on the moving parts on each type of manufactured heart valve occur in valves with three dimensions moving parts, reached in the mitral tri-leaflet valve reached 14.13 MPa, followed by the tricuspid aortic valve.The equivalent stresses for other types of valves produced with simple surface action were lower than 2 MPa .• The strain energy that is expended during the process of diastole and systole was found to be directly proportional to the strength and flexibility of the materials used.The energy consumption rates decrease when using highly elastic materials such as TPE and PSN4.The values of this energy also increase with an increase in the area of the moving parts of the valve, especially when faced with the process of closing blood flow, as with the use of the tricuspid aortic valve (TAV).The least values of energies were expended when using simple movement valves in one direction, including the single hemispherical leaflet, the caged ball, and then the single leaflet valves, respectively.• The highest total deformation resulted in the valve body when using TPU, followed by TPE, nylon, PETG, and PLA, while the lowest deformation rates were observed when using PSN4, which ranged from 5x105 to 0.1 mm, followed by SIBSTAR103 nanostructured rubber .
• The obtained values of stress safety factors were decreased with the complexity of the movement for the moving parts of the valve.The highest rates were recorded when using the tricuspid mitral valve, reaching 2.45 when using the high-strength and flexible PSN4 nanomaterial .• Additional future work is required to do mathematical modeling with numerical simulation of pressure distribution, blood flow velocity, and variable viscosity for all types of artificial heart valves presented in this paper.• Working on the production of these types of artificial heart valves using the 3D bioprinting method, based on the successful application of tissue engineering in the development of heart valves to produce valves with mechanical properties similar to the original valves.

Figure 1 .
Figure 1.The designed steps of the artificial caged ball mechanical heart valve

Figure 2 .
The designed prosthetic artificial mechanical heart valve; (a) the designed conical caged ball valve; (b); the single hemispherical caged ball valve (c) the single-leaflet valve increase control over the alignment of the central movement of the ball when the blood is flowing or when the valve is closed.

Figure 3 .
Figure 3.The designing steps mitral tri-leaflet heart artificial valve

Figure 4 .
Figure 4.The designed tricuspid prosthetic aortic valve (TAV) a and b are the dimensionless parameters; a = δ/R0 is the ratio of stenosed depth = 0.03-0.08cm and the radius of a normal artery and b =(m/L0)2 is the square of the ratio of constant value m =1.4-1.8, and the halflength of the stenosis.Let the common parameters such as the radius of a normal artery (R0); R(z) is the radius of a stenosed artery; (L0) is the half-length of the stenosis; (L) is the half-length of an artery, and δ is the highest depth of the stenosis.

Figure 5 .Figure 6 .
Simulation of blood flow in the atria; (a) The initial state of the artery; (b) Boundary Conditions; (c ) Static pressure; (d);Turbulent viscosity (e) Eddy viscosity; (f); Turbulent kinetic energy (g) Molecular viscosity; (h) Total deformation; (iModeling of the designed artificial valves; (a) The meshing process; (b) The determined boundary conditions for the applied heart blood pressure from the hear

Figure 7 .Figure 8 .Figure 9 .Figure 10 .
Figure 7.The strain energy simulations for selected types and the used materials of the designed artificial heart valves

Figure 11 .Figure 12 .
Figure 11.The equivalent stress for each produced artificial heart valve type

Figure 13 .
Figure 13.The total deformation produced in each artificial heart valve structure under the influence of applying the blood pressure

TABLE 2 .
The fatigue properties of the designed artificial heart valves