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Journal of Engineering Science and Technology EURECA 2013 Special Issue August (2014) 68 - 78 © School of Engineering, Taylor’s University INVESTIGATION OF BLOOD FLOW THROUGH THE MITRAL VALVE YVONNE LIM*, MUSHTAK AL-ATABI School of Engineering, Taylor’s University, Taylor's Lakeside Campus, No. 1 Jalan Taylor's, 47500, Subang Jaya, Selangor DE, Malaysia *Corresponding Author: [email protected] Abstract The mitral valve is a heart valve located in between the left atrium and ventricle. Mitral valve failure occurs due to various reasons resulting in backflow of blood from the ventricle to the atrium. Severe failure requires surgical repair. Medical professionals have different opinions on surgical repair methods. This paper describes the development of an in vitro platform to test effectiveness of a surgical repair method. The study is done experimentally using flow visualisation and numerically using computational fluid dynamics. From the experimental results, it is seen that the flow through an open mitral valve produces two vortices. The set-up can be used as a testing protocol for the testing of surgical repair methods. The numerical results mimic the results from the experimental testing and can be further developed for future testing of the mitral valve failures and repairs. Keywords: Mitral valve, Surgical repair methods, flow visualisation, CFD. 1. Introduction The mitral valve is located in the heart between the left atrium and the left ventricle. It has four basic components, the mitral annulus, the anterior and posterior mitral valve leaflets, and the subvalvular apparatus which consists of the chordae tendineae and the papillary muscles. The mitral annulus is the opening in which the blood flows through; the mitral valve leaflets control the flow of blood into the mitral valve; the chordae tendineae are the fibres which hold the mitral valve leaflets in place and the papillary muscles connect the chordae to the ventricular walls. The mitral valve allows the blood flow from the left atrium to the left ventricle during diastole (when the heart relaxes) and prevents blood from flowing back to 68 Investigation of Blood Flow through the Mitral Valve 69 the atrium during diastole (when the heart contracts). In this way, it mimics the function of a check valve by preventing backflow from the ventricle to the atrium at all times. However, due to various medical reasons, mitral valve failure, either prolapse or stenosis may occur, this reduces the heart’s efficiency as a pump. This causes the heart to work harder as a pump to displace the same amount of blood from the heart to the rest of the body when compared to a healthy heart. There are two major ways to correct mitral valve failure due to mitral prolapse, surgical replacement and surgical repair. Surgical replacement involves replacing the damaged valve with a mechanical valve. Recipients of these mechanical valves have to take anticoagulants to prevent blood clots formed from blood adhering to the walls of the artificial valve. Surgical repair involves repairing the damaged section of the mitral valve without replacement with a mechanical device. In this study, the focus is on the surgical repair of mitral valve prolapse. Surgical repair is considered a better option compared to surgical replacement as there is a better survival rate after the procedure as the patient is not required to take anticoagulants and the mechanical valve used has a limited life-span. There are various types of surgical repair to repair anterior and posterior leaflet prolapse. The most common repair methods are edge-to-edge repair, chordal replacement and chordal transposition [1]. Medical professionals have different opinions of which surgical repair method is the most effective. Surgeons cannot test these methods on patients due to ethical reasons. According to the Hippocratic Oath which states that as medical professionals, they are obliged first and foremost not to do any harm [2]. Furthermore, surgeries are expensive. Mistakes are costly, not just financially; a wrong move might cost the patient his or her life. Therefore, surgeons are not to treat patients with any method that they do not consider the best. Other than that, success rates of various repair methods are not as reliable due to the health condition and general fitness of patients which differ from patient to patient [3]. This paper describes the development of an effective procedure and platform to assess the effectiveness of surgical repair in vitro. This is performed using a designed and fabricated transparent tube model. Computational fluid dynamic, CFD simulations of the flow through the mitral valve at steady state, using 2D simulations was also carried out. 2. Methodology The study of the mitral valve has been carried out experimentally and numerically. Experimental studies can be carried out either in vivo (inside the body) or in vitro (in the lab). Numerical simulations have been carried out using computational fluid dynamics software. Experimental in vitro studies are more commonly carried out as compared to in vivo studies as it is more ethical compared to using a live specimen. Various experimental studies have been carried out in vitro for various purposes. Among which is the study of the effect of formation of vortices in the ventricle [4]; the pressure to cause mitral valve failure and the effect of surgical repair used on pressure to cause mitral valve failure [1,5]; and the flow visualisation of flow through the mitral valve using streak photography [6]. All the mentioned studies except the study carried out by Al-Atabi et al. [6], which uses a plastic model; Journal of Engineering Science and Technology Special Issue 8/2014 70 Y. Lim and M. Al-Atabi utilised a mitral valve specimen obtained from either a porcine or bovine heart. Although in vitro experiments have been widely used to study the mitral valve, there are many challenges associated with in vitro studies. Uncertainties arising from using the real mitral valve are attributed by the variation of size, physical condition and health of the animal which the specimen originated from. These discrepancies may contribute to the uncertainties in the results obtained. Furthermore, the dissection of the heart to obtain the mitral valve specimen is tedious and requires specialised knowledge on the heart anatomy to ensure that the specimen removed is intact. Numerical studies have emerged recently as a tool to study the flow mechanics through the mitral valve. It is also carried out as a means to idealise the structure of the mitral valve to obtain a more accurate result and to reduce discrepancies. Numerical simulations in the form of computational fluid dynamics have been widely used in the study of the mitral valve. Studies have been carried out, for example, to study the filling phase of the ventricle in a 2-dimensional model to detect early heart valve failure [7] and also to study the biomechanics of the left heart chambers using a 2-dimensional idealised structure with fluidstructure interaction using an arbitrary Lagrangian-Eulerian mesh. However, there are challenges associated with the use of numerical studies for mitral valve research as well. The mitral valve structure is difficult to define, as is its motion, therefore assumptions are used in the simulations to simplify the study, which may reduce its accuracy. Hence, both experimental in vitro experimental studies and numerical studies are both carried out in this study. The experimental study was carried out using a porcine mitral valve specimen and a numerical study of the experimental design was carried out. 2.1. Experimental study 2.1.1. Experimental design The experiment was carried out in a closed loop system, Fig. 1. A porcine mitral valve specimen was used; the attachment of the specimen is described in the section below. The mitral valve specimen was set in a fixed open position. The atrial chamber was a PVC pipe of length 1 m and a diameter of 4.5 cm and flow straighteners were positioned inside the tube to produce a fully developed flow. The left ventricular chamber was a transparent tube with the same diameter and a length of 0.3 m. The mitral valve was placed 4 cm from the opening of the chamber to allow the flow visualisation photography. The atrial and ventricular chambers were secured together with nuts and bolts along the flange. The diameter and length of the bolts used were 2 mm and the 1 cm respectively. Water was used as the fluid in the experiment. Due to the non-pulsatile nature of the experiment, the non-Newtonian effect of blood is not considered and therefore water was used as the fluid [3]. The fluid was placed in a 1 L reservoir. A peristaltic pump was used to generate the flow in the system. The Reynolds number of the flowing water was 845. Journal of Engineering Science and Technology Special Issue 8/2014 Investigation of Blood Flow through the Mitral Valve 71 Fig. 1. Experimental Set-up. 2.1.2. Mitral valve specimen The mitral valve specimens were obtained from porcine hearts. Porcine hearts were used as the anatomy is closest to the human heart [8]. The porcine hearts were dissected carefully to remove a circular annulus of the mitral valve and papillary muscles with chordae attached to the valve leaflets removed. The annulus of the specimen was sutured onto a ring. A transparent plastic valve holder was used to hold the mitral valve specimen. The ring holding the specimen annulus was sutured onto the valve holder and the papillary muscles were sutured onto the valve holder approximately 3 cm from the annulus. This is shown in Fig. 2. Fig. 2. Mitral Valve Specimen in Inner Circular Tube. 2.1.3. Flow visualisation The flow was seeded using silver coated hollow glass beads of 1 µm diameter. The glass beads were added to the fluid reservoir after the system was completely filled. The hollow glass beads were illuminated by a scattered laser beam. This was achieved by passing the laser beam through a glass rod place perpendicularly Journal of Engineering Science and Technology Special Issue 8/2014 72 Y. Lim and M. Al-Atabi above the ventricular chamber. The room was blacked out in order to carry out the flow visualisation experiments. A Nikon D7000 DSLR camera with a shutter speed of 1/6 s, an ISO of 100 and an aperture of f/16 was used to capture the flow structure [3]. 2.2. Numerical simulation 2.2.1. Numerical simulation of experimental design A two-dimensional, 2D model of the experimental design was simulated using ANSYS FLUENT ©. A two-dimensional simulation was chosen because from a previous simulation of an experimental study by Hwang et al. [9], the 2D simulation sufficiently mimics the experimental results [10]. Furthermore, 2D simulations are easier and require less computational resources. The geometry of the simulation is shown in Fig. 3. The geometry was generated with a fixed opened valve. The geometry was designed as half of the experimental chamber with the bottom axis as the axis to reflect the geometry. The walls were assumed to be rigid with no-slip condition specified. The valve leaflet is assumed to have uniform thickness of 10 mm. The left wall of the geometry was specified as the inlet, the right wall was specified as the outlet. Water with a density of 1000 kg/m3 and a viscosity of 0.89 mPa.s was used as the fluid. The turbulence model used was the realizable k-ε model. The simulation was done at steady-state. Fig. 3. CFD Geometry of Experimental Chamber. 2.2.2. Numerical simulation of idealised left heart chambers Simulation of idealised left heart chamber was carried out to compare the experimental results to the actual flow within the mitral valve. It also explores the potential of the CFD simulation to be used as a diagnostic tool. The CFD was performed using ANSYS FLUENT ©. Two-dimensional idealised geometries of the left atrium and ventricle with opened and closed mitral valve were generated using echocardiographic measurements of the left heart chambers [11]. The left ventricular quantification data is obtained by measuring the major and minor axis of the left ventricle in the apical four chamber view. The dimension of the left atrium is obtained from the parasternal long axis view (echocardiographic view showing the left atrium and ventricle, the right ventricle, the aortic and mitral valve) and apical two chamber view (echocardiographic view showing the left atrium and ventricle). The mitral valve annulus diameter was obtained from the apical four chamber view. The left ventricular outflow tract is the channel in which the blood exits the left ventricle when the ventricle contracts. It is diameter is obtained from the parasternal long Journal of Engineering Science and Technology Special Issue 8/2014 Investigation of Blood Flow through the Mitral Valve 73 axis view of the left ventricle. Table 1 shows the summary of the quantification data obtained from the echocardiographic measurement as compiled by Anderson [11]. The average values were used to generate the geometries as shown in Fig. 4. Table 1. Left Heart Chamber Measurements. Measured Range (cm) Left Ventricle: Major Axis Minor Axis Left Atrium: Major Axis Minor Axis Mitral Valve Annulus Left Ventricular Outflow Tract Mean Value (cm) 6.9 – 10.3 3.3 – 6.1 8.6 4.7 4.1 – 6.1 2.6 – 4.5 2.6 – 2.9 (Women) 2.9 – 3.2 (Men) 1.8 – 2.5 (Women) 1.9 – 2.7 (Men) 5.1 3.6 2.8 3.1 2.2 2.4 (a) Fixed Open Mitral Valve. (b) Fixed Closed Mitral Valve. Fig. 4. Geometry of Left Heart Chamber. The open valve for the idealized geometry was simulated with the inlet at the left atrium and no outlet. The closed valve for the idealized geometry was simulated with the inlet at the apex and the outlet at the left ventricular outflow tract. The walls were assumed to be rigid. No-slip conditions were used for the walls; this includes the walls of the valves. For the heart chamber geometry simulations, the fluid used was specified to be glycerine. This is because a solution of glycerin has similar properties as blood. The density and viscosity of glycerin used is 1060 kg/m3 and 0.0027 Pa.s respectively [12]. Using glycerine as the blood analogue assumes the blood to be non-Newtonian. The velocity of the fluid flow is 0.5 m/s, representing blood flow through the mitral valve into the left ventricle [13]. The turbulence model used for all simulations was the realizable kε turbulence model. The numerical simulations were performed in steady-state. 2.2.3. Assumptions The fluids used in the simulations are assumed to be Newtonian. Newtonians fluids are incompressible and therefore the flow is governed by the Navier-Stokes equation. This assumption has been made as it is found that for large diameters Journal of Engineering Science and Technology Special Issue 8/2014 74 Y. Lim and M. Al-Atabi and for steady flow, the non-Newtonian effects are not prominent [14,15]. In actual fact, blood is a non-Newtonian fluid. The walls and the leaflets in the simulations were assumed to be rigid. And therefore, the flow for the opened valve only models the flow at a particular instant during diastole and the flow of a closed valve only models the flow at a particular instant during systole. The walls of a real heart are not rigid and their structure changes as the ventricle contracts and relaxes closing and opening the mitral valve. 3. Results 3.1. Experimental results As the water emerges from the mitral valve annulus, two vortices are formed. The vortices appear right after the water emerges from the mitral valve leaflets. Figures 5 and 6 show the vortices formed behind the mitral valve leaflets. Fig. 5. Flow through a Healthy Mitral Valve Producing Two Vortices. Fig. 6. Flow through a Healthy Mitral Valve with Path of Vortices Drawn. Journal of Engineering Science and Technology Special Issue 8/2014 Investigation of Blood Flow through the Mitral Valve 75 3.2. Numerical results 3.2.1. Numerical simulation of experimental design Figure 7 is the generated image of velocity vectors reflected upon its axis of symmetry. The velocity vector shows the formation of two vortices behind the mitral valve leaflets. The numerical simulation of the experimental chamber generated velocity vectors which are comparable with the experimental results (Fig. 5). Fig. 7. Velocity Vector of Simulated Flow through a Mitral Valve in the Experimental Set-up. 3.2.2. Numerical simulation of Idealised Left Heart Chambers Figure 8 shows the idealized left heart chamber with the opened mitral valve simulation generated results. The figure shows two vortices formed behind the mitral valve leaflets. The cardiographic magnetic resonance, CMR image of the left ventricle during diastasis, the mid stage of ventricular relaxation shows two vortices behind the mitral valve leaflets [16]. The numerical simulation of the open mitral valve is similar to the CMR image, and therefore is validated. (a) Velocity Vector of the Simulated Flow through the Opened Mitral Valve. (b) Pathline Visualisation of Blood Flow during Left Ventricular Diastasis [16]. Fig. 8. Flow through Open Mitral Valve. The generated results from the simulation of closed mitral valve shows the flow from the apex of the ventricle and out though the left ventricular outflow tract. There are no vortices formed inside the ventricle during this stage.The Journal of Engineering Science and Technology Special Issue 8/2014 76 Y. Lim and M. Al-Atabi generated velocity vectors of the closed mitral valve simulation closely resembles the CMR image of a ventricle during peak systole as seen in Fig. 9. (a) Velocity Vector of the Simulated Flow through the Closed Mitral Valve. (b) Pathline Visualisation of Blood Flow during Peak Systole [16]. Fig. 9. Flow through Ventricle when Mitral Valve is Closed. 4. Discussion As mentioned above, the porcine valve closely resembles the human heart structure, and therefore the flow obtained may be considered similar to a human mitral valve. In the experimental study, it can be seen that two vortices formed behind the mitral valve leaflets. Vortices are areas where the vorticity of the region is compact and is due to the no-slip condition of the valve walls. The water flowing before the test region flowed in a fully developed velocity profile. When water passes through the mitral valve annulus, the velocity increases because the same amount of water has to pass through the smaller cross-sectional area as compared to the cross-sectional area of the tube. The flow decelerates as the water emerges from the mitral valve annulus, as the cross sectional area increases. As the flow of water pass the leaflets, the boundary layer separates causing flow in opposite directions, causing the formation of a vortex [17]. The formation of vortices is an important aspect in the blood flow in the heart. Vortices are energy containing eddies [18]. The energy generated by the motion of the vortices help propel the flow out of the ventricle when the ventricle contracts. The formation of vortices may be employed as a means of diagnosis of mitral valve failures; a mitral valve with anomalies would present different vortices structures. The structure of the vortices can be used as a baseline for the protocol to determine the optimal mitral valve surgical repair method. The closeness of the resemblance of the vortices of the mitral valve repaired using a particular repair method to a healthy mitral valve will give an indication of how well is a repair method. The experimental set-up can be used to test surgical repair methods. The repaired mitral valve could be placed in the experimental set-up and flow visualisation can be done to compare the baseline and the repaired valve. Journal of Engineering Science and Technology Special Issue 8/2014 Investigation of Blood Flow through the Mitral Valve 77 The computational fluid dynamics simulation of the open mitral valve, both the experimental and the idealized geometry; generated results which show the formation of vortices behind the mitral valve leaflets. This corresponds to the blood flow inside the left heart chambers of a living person as seen in from the CMR images. The simulation for the closed mitral valve in the idealized model also corresponds to the outflow of blood from the left ventricle. This shows that CFD is a powerful tool and the use of CFD to diagnose mitral valve failure and evaluate surgical repair methods can be developed. The accurate assumptions to the structure, dimensions, and physical properties of the mitral valve have to be first defined in order to obtain accurate results. 5. Conclusion and Future Work Flow through a healthy mitral valve produces two vortices. Vortices are important as they help propel the flow from the ventricle. The absence and presence of the vortices and the structure of the vortices can be used to identify possible mitral valve anomalies. This can be used as the baseline for the protocol. The simulated results of the experimental model and the idealised geometry agree with the experimental result obtained as well as the CMR images. The numerical results can therefore be further developed to numerically test surgical repair methods. The set-up can be further developed to test various mitral valve repair methods and implemented for more personalised healthcare. A patient’s mitral valve failure can be evaluated through various medical imaging methods and the data obtained may be used to simulate a physical model which can be used as an analogue to be placed inside the chamber. Various repair methods may be tested on the damaged mitral valve analogue. The method which yields the flow structure closest to a healthy mitral valve will be chosen for the patient. This can lead to personalised health care for each patient, reducing misdiagnosis and surgical errors, hence a tool to provide better healthcare. References 1. 2. 3. 4. 5. Espino, D.M.; Hukins, D.W.L.; Shepherd, D.E.T.; Watson, M.A.; and Buchan, K.G. (2006). Determination of pressure required to cause mitral valve failure. 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