Hadi Mohammadi^{1,2*}, Mehdi Jahandardoost^{1} and Guy Fradet^{3}

*Correspondence: Hadi Mohammadi hadi.mohammadi@ubc.ca

1. School of Engineering, Faculty of Applied Science, University of British Columbia, Kelowna, BC, Canada.

2. Faculty of Applied Science, University of British Columbia, Vancouver, BC, Canada.

3. Department of Surgery, Faculty of Medicine, University of British Columbia, Vancouver, BC, Canada.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

St. Jude Medical (SJM) bileaflet mechanical valves were approved by the Food and Drug Administration in 1977. The SJM valve design consists of two semicircular leaflets which pivot on hinges. Compared to other mechanical heart valve prostheses such as ball and cage and tilting disk prosthetic valves, it provides good central flow, the leaflets open completely, and the pressure drop across the valve is trivial. However, non-physiological hemodynamics around these valves may lead to red blood cells lysis and therombigenic complications. Also, the regurgitation-flow inSJM valves is almost twice that of the native valves in the aortic position. In this study, we suggest a new design for the stent (housing) of SJM valves in which 15% ovality is applied to the stent whereas its perimeter remains constant. In a pilot study, the hemodynamic performance of the proposed design is analyzed in the closing phaseand compared to that of conventional SJM models. Results show that while the elliptic SJM model offers a shorter closing phase (9.7% shorter), the regurgitation flow remains almost unchanged. In other words, even though the dynamic response of the valve is improved, the regurgitation flow is not decreased. Thus, a more efficient effective orifice area (EOA) is shown to be provided by the proposed model. The preliminary calculations presented in this study justify an improved hemodynamics of elliptic SJM valves compared to conventional models; the proposed design shows promise and merits further development.

**Keywords**: Finite strip method, vascular hemodynamics, bileaflet mechanical heart valves, st, jude medical valve, heart valve prostheses, numerical modeling

Bileaflet mechanical heart valves (MHVs) are used extensively due to their great hemodynamic performance, as indicated by a uniform flow profile, free central flow and considerably higher level of durability. However, thrombogenicity is an issue with the bileaflet MHVs due to a non-physiological hemodynamics around the valve [1-3]. More than 300,000 replacement heart valves are implanted annually worldwide and mechanical heart valves are used to replace diseased human heart valves in approximately 50% of these interventions. In addition, two million patients receive St. Jude Medical (SJM) valves worldwide each year [4,5]. In our previous studies, we extensively assessed the hemodynamic performance of the SJM valve in the opening phase using computational fluid dynamics (CFD). Results suggested that SJM valves may be associated with thrombogenic complications around the hinges, on the leading edge of the leaflets and at the sinuses, possibly because of high blood shear stresses, turbulence, and the overall complexity of the hemodynamics in MHVs [6,7].

In this study, we propose a design modification on SJM valves. We hypothesize that 15% ovality on the housing while its perimeter remains constant may result in an improved hemodynamics around the SJM valves. In a pilot study, we study the hemodynamic performance of the proposed design to evaluate its regurgitation flow and its velocity and the leaflet tip velocity in the closing phase. We apply a quick but novel numerical model which is sufficiently accurate to estimate the overall performance of the new design. The numerical model uses the finite strips method to solve the equations of motion. The computations run on an Intel (R) Core (TM) i7-4500u CPU @1.80 GHz &1.80GHz processors with 16.0 Gb of RAM.

The SJM model considered in this study has an inner diameter of 25 mm as shown in Figures 1a and 1b. In the proposed design, the perimeter of the housing remains constant. The housing is elliptic with a major diameter of 27 mm and a minor diameter of 23 mm as shown in Figures 1c and 1d. Due to the leaflet's rotation, the computational domain is defined as a control volume (CV) with moving boundaries as shown in Figures 2a and 2b. In order to simplify the computational process, flow is assumed to be unidirectional in the direction of the major axis and the projected area between the leaflets and the aortic wall is assumed to be rectangular at various positions during the closing phase [5]. The flow is considered inviscidsuch that velocity is uniform at every cross section in the CVand the inlet [8,9]. The regurgitation flow is divided into two regimes through the minor and major orifices at the entrance of each section. When the valve is fully open, it is assumed that the aortic pressure (P_{ao}) and the ventricular pressure (P_{v}) are both uniform and equal. This is because the valve remains fully open during the systole with almost no forward flow. The control volume is ABCD, where AB is the leaflet, o is the pivot, and EF is an arbitrary section. U_{AD}, U_{BC}, and U_{EF} are the velocities of blood at the entrance (AD), at the outlet (BC) and at the arbitrary section (EF), respectively. The distance from the EF section with respect to the inlet section is denoted as Y. l_{AD}, l_{bc} and l_{EF} are the length of the inlet and the outlet and the arbitrary sections which are time dependent but their width (w) remains constant (Figure 2). Velocities and pressures vary constantly through the sections AD to BC. Mass is conserved within the CV such that the velocity at the EF section (V_{EF}) is calculated with respect to the inlet velocity (V_{AD}) or the outlet velocity (V_{BC}) in the CV. It should be noted that the velocity of blood in the vicinity of the leaflet tips and at the EF section is higher than the axial velocity of the leaflet tip (V_{tAD},V_{tBC}) and the axial velocity of the leaflet at the EF section (V_{tEF}), respectively. The unsteady continuity equation on the CV takes the form:

Figure 1 : **Conventional, Elliptic SJM valves and models.**

Figure 2 : **The Computational domain of the study.**

where A_{AD} (w l_{AD}) and A_{EF} (w _{lEF}) are cross sectional areas at the sections AD and EF, respectively. The axial velocities of the leaflet at A and E are
*ω* is the angular velocity of the leaflet, and *θ* is the angle between the AD and the leaflet. V_{i} is the volume of the CV which is

where A_{BC} (w _{lBC}) is the cross sectional area at the outlet,

Also, the unsteady energy equation between the inlet and the outlet is applied to calculate

The two approaches used to calculate
_{AD}). Using VADthe angular velocity of the leaflets is calculated. The governing equation of motion for the leaflets takes the form:
_{o} is the mass momentum of inertia of the leaflets about the pivot. Tp and Tg are calculated as such:

The hemodynamic performance of proposed design including the velocity of the blood and the velocity of the leaflets and the regurgitation flow volume are calculated with respect to time in the beginning of the diastolic phase, i.e., the closing phase. The time increment δt is chosen to be 0.05 ms. Also, mentioned above,

The velocity of the leaflet tip, the velocity of the blood flow in the vicinity of the leaflet tip and the regurgitation flow volume of the conventional SJM valves obtained in this study and those reported before [5,11] are consistent. Figure 3 shows the velocity of the leaflet tip in the closing phase for both designs. The velocity of the leaflet tip in the elliptic design is higher than that of the conventional design. It also shows that the closing phase in the elliptic design is 9.7% lower. Figure 4 shows the velocity of the regurgitation flow in the vicinity of the leaflet tip for the two elliptic and conventional SJM valves. The velocity of the regurgitation flow in the elliptic model shows an average increase of 11% compared to the conventional SJM valve. The higher velocity of the regurgitation flow in the elliptic SJM model leads to a shorter closing phase. The two effective parameters to calculate the regurgitation flow volume is (1) the closing phase time and (2) the velocity of the blood which is shown in Figure 5. Results show that even though the velocity of the regurgitation flow in the elliptic SJM model is higher than that of the conventional SJM model, the backflow volume in the two models is comparable and equal (<0.05% error).

Figure 3 : **The velocity of the leaflet tip in the closing phase for both elliptic and conventional SJM valves.**

Figure 4 : **The velocity of the regurgitation flow in the vicinity of the leaflet tip in the closing phase for both elliptic and conventional SJM valves.**

Figure 5 : **The regurgitation flow volume in the closing phase for both elliptic and conventional SJM valves.**

In this study, we proposed a design modification to the SJM conventional valves and developed a numerical tool that can quickly assess the hemodynamic performance of bileaflet mechanical heart valves in general and the elliptic SJM valve proposed in this study in particular. Results of the current study suggest a clear improvement in the hemodynamic performance of elliptic SJM valves over the conventional models. A comprehensive set of experimental and computational studies in the opening and closing phases will further address the hemodynamic performance of the proposed elliptic SJM valve.

The authors declare that they have no competing interests.

Authors' contributions |
HM |
MJ |
GF |

Research concept and design | √ | -- | -- |

Collection and/or assembly of data | √ | √ | √ |

Data analysis and interpretation | √ | √ | -- |

Writing the article | √ | √ | -- |

Critical revision of the article | √ | -- | √ |

Final approval of article | √ | -- | √ |

Statistical analysis | √ | √ | -- |

The authors would like to thank the University of British Columbia and the NSERC/DG for financially supporting this study. Start-up Grant, University of British Columbia.

Senior Editor: Shiwei Duan, Ningbo University, China.

Received: 12-Jan-2015 Final Revised: 13-Feb-2015

Accepted: 02-Mar-2015 Published: 09-Mar-2015

- Mohammadi H and Mequanint K.
**Prosthetic aortic heart valves: modeling and design**.*Med Eng Phys*. 2011;**33**:131-47. | Article | PubMed - Mohammadi H, Bahramian F and Wan W.
**Advanced modeling strategy for the analysis of heart valve leaflet tissue mechanics using high-order finite element method**.*Med Eng Phys*. 2009;**31**:1110-7. | Article | PubMed - Mohammadi H, Klassen RJ and Wan WK.
**A finite element model on effects of impact load and cavitation on fatigue crack propagation in mechanical bileaflet aortic heart valve**.*Proc Inst Mech Eng H*. 2008;**222**:1115-25. | Article | PubMed - Mohammadi H,Boughner D,Millon LE and Wan WK.
**Design and simulation of a poly(vinyl alcohol)-bacterial cellulose nanocomposite mechanical aortic heart valve prosthesis**.*Proc Inst Mech Eng H*. 2009;**223**:697-711. | Article | PubMed - Mohammadi H,Ahmadian MT and Wan WK.
**Time-dependent analysis of leaflets in mechanical aortic bileaflet heart valves in closing phase using the finite strip method**.*Med Eng Phys*. 2006;**28**:122-33. | Article | PubMed - Jahandardoost M, Fradet G and Mohammadi H.
**A New Computational Model for the Hemodynamics of Bileaflet Mechanical Valves in the Opening Phase. Proceeding of the institution in mechanical engineering Part H**.*J of Eng. in Medicine*. 2014. - Jahandardoost M, Fradet G and Mohammadi H.
**Effect of Pulsatility Rate on the Hemodynamics of Bileaflet Mechanical Prosthetic Heart Valves (St. Jude Medical Model) for the Aortic Position in the Opening Phase; A Computational Study**.*J of Cardiovascular Engineering and Technology*. 2014. - Reif TH.
**A numerical analysis of the backflow between the leaflets of a St Jude Medical cardiac valve prosthesis**.*J Biomech*. 1991;**24**:733-41. | Article | PubMed - van Steenhoven AA,van Duppen TJ,Cauwenberg JW and van Renterghem RJ.
**In vitro closing behaviour of Bjork-Shiley, St Jude and Hancock heart valve prostheses in relation to the in vivo recorded aortic valve closure**.*J Biomech*. 1982;**15**:841-8. | Article | PubMed - Mohammadi H and Mequanint K.
**An Inverse Numerical Approach for Modeling Aortic Heart Valve Leaflet Tissue Oxygenation**.*Journal of Cardiovascular Engineering and Technology*. 2011;**3**:73-79. | Article - Subramanian A,Mu H,Kadambi JR,Wernet MP,Brendzel AM and Harasaki H.
**Particle image velocimetry investigation of intravalvular flow fields of a bileaflet mechanical heart valve in a pulsatile flow**.*J Heart Valve Dis*. 2000;**9**:721-31. | Article | PubMed

Volume 3

Mohammadi H, Jahandardoost M and Fradet G. **Elliptic st. jude bileaflet mechanical heart valves**. *Cardio Vasc Syst*. 2015; **3**:1. http://dx.doi.org/10.7243/2052-4358-3-1

View Metrics

Copyright © 2015 Herbert Publications Limited. All rights reserved.

Post Comment|View Comments