- Email: [email protected]
Biomechanical comparison between mono-, bi-, and tricuspid valve architectures
Biomechanical comparison between mono-, bi-, and tricuspid valve architectures Henry Y. Chen, PhD,a,b,d Zachary Berwick, PhD,a,d Joshua Krieger, BSME,e Sean Chambers, PhD,e Fedor Lurie, PhD,f and Ghassan S. Kassab, PhD,b,c,d Indianapolis and Bloomington, Ind; and Toledo, Ohio Background: An understanding of the relationship between venous valve architecture and associated fluid and solid mechanical forces will undoubtedly advance prosthesis design and treatments. The objective of the current study was to compare three valve architectures (mono-, bi-, and tricuspid) and the implications of these designs on the fluid and solid mechanics of the valve leaflets. The hypothesis is that the bicuspid valve has the lowest mechanical cost, defined as the ratio of leaflet wall stress and fluid wall shear stress (WSS), for the venous environment as compared with mono- and tricuspid valves. Methods: To address this hypothesis, fully coupled, two-way fluid-structure interaction computational models were developed and simulated for the three types of valves. Results: The numerical simulations showed that the mean fluid WSS of the bicuspid valve was generally higher than the tricuspid valve, which was further higher than the monocuspid valve. The mean leaflet wall stress of the bicuspid valve was lower than the tricuspid valve, which was further lower than
Although the importance of venous valves is wellappreciated given the consequences of valvular dysfunction, current quantification of fluid and solid mechanics of venous valves is limited. In clinical studies, it was found that the venous valves may increase the venous flow resistance. Despite the increase of flow resistance, venous valves improve blood flow to the heart, partly due to prevention of reverse flow.1 The fundamental physiological and pathophysiological issues, as well as interest in venous valve prosthesis to replace insufficient valves, require a full understanding of valve hemodynamics associated with valve anatomy and architecture. Native venous valves are From the Research Engineering, 3DT Holdings, LLC,a the Department of Biomedical Engineering, Indiana University, Purdue University,b and the Departments of Surgeryc and Cellular and Integrative Physiology,d Indiana University School of Medicine, Indianapolis; Research Engineering, Cook Medical, Bloomingtone; and Jobst Vascular Institute, Toledo.f Supported by 3DT Holdings, LLC and Cook Medical. Author conflict of interest: none. Additional material for this article may be found online at www.jvsvenous.org. Reprint requests: Ghassan S. Kassab, PhD, Department of Biomedical Engineering, Indiana University Purdue University Indianapolis, Indianapolis, IN 46202 (e-mail: [email protected]). The editors and reviewers of this article have no relevant financial relationships to disclose per the Journal policy that requires reviewers to decline review of any manuscript for which they may have a conflict of interest. 2213-333X/$36.00 Copyright Ó 2013 by the Society for Vascular Surgery. http://dx.doi.org/10.1016/j.jvsv.2013.08.004
the monocuspid valve. Therefore, the mechanical cost, which was defined as solid wall stress/fluid WSS, of the bicuspid valve was the lowest. Conclusions: The lower mechanical cost may be a reason why the bicuspid valve is the dominant design in the venous system. This knowledge provides guidance for the design of novel venous prosthetic valves and may shed light on venous valve disease when the architecture of the valve is altered. (J Vasc Surg: Venous and Lym Dis 2013;-:1-7.) Clinical Relevance: The physiological and pathophysiological issues as well as interest in venous valve prosthesis to replace insufficient valves require a full understanding of valve hemodynamics associated with valve anatomy and architecture. The current study found that the lower mechanical cost may be a reason why the bileaflet valve is the dominant design in the venous system. This knowledge may provide guidance to the design of novel venous prosthetic valves and shed light on the mechanism of venous valve disease.
predominantly bicuspid valves. Anatomical studies found that venous valves are 80% to 90% bicuspid, 10% to 15% tricuspid, and only approximately 5% monocuspid.2-5 The prevalence of data suggest functional superiority of bicuspid valves followed by tricuspid valves, and inferiority of monocuspid valves. This was confirmed in ex vivo experiments.3 The monocuspid valves were shown to be insufficient and did not prevent retrograde flow. Despite these variations in nature, with the bicuspid venous valve being the most common, it is unclear what dictates the design of the venous valve geometry. Experimental and clinical evidence suggests that alteration of fluid wall shear stress (WSS) contributes to endothelial remodeling and may affect valvular endothelial cell phenotype.6,7 Solid wall stresses also affect the cells and fibers within the wall, such as the vavular interstitial cells, collagen, and elastin fibers. Valvular interstitial cells have characteristics of smooth muscle cells and respond to mechanical stimuli.8 The stretching of these cells and fibers may induce mechanotransduction, resulting in tissue remodeling.9 Therefore, perturbations in the mechanical environment can lead to the pathogenesis of valvular disease. Computational modeling can be a very useful tool for medical device design as well as simulation of cardiovascular surgery procedure and vascular device implants.10-12 The fluid and solid stress analysis can provide valuable insights into tissue injury response and disease 1
2 Chen et al
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mechanisms. Computational and experimental studies on venous valve design and associated biomechanics, however, are very limited. Recently, a novel mechanical cost function was defined as the ratio of computed wall stress and fluid WSS to capture the effects of both fluid and solid mechanics in tissue.10 The solid wall stress is in the numerator since it has a direct relationship with tissue remodeling, while the fluid WSS is in the denominator since the fluid WSS has an inverse relationship with vascular tissue remodeling.11-15 This cost function has been previously shown to significantly correlate with intimal hyperplasia that considers both the effect of fluid shear and solid stress in stented vessels.10 It was shown that lower cost function correlated with less intimal hyperplasia, and hence a lower mechanical cost, thus is more desirable biologically. The objective of the current study was to study the three types of valve designs (mono-, bi-, and tricuspid) and their implications on the fluid and solid mechanics of the valve leaflets. The hypothesis is that the bileaflet valve has the lowest mechanical cost (ratio of leaflet wall stress and fluid WSS) for the venous environment as compared with mono- and trileaflet valves. Accordingly, we performed fully coupled fluid-structure interaction (FSI) simulations on each of the three designs under identical flow conditions to assess the fluid and solid forces on the valve leaflet. Virtual experiments using predictive computational models can produce improved designs, which can then be subjected to experimental validations. METHODS The fluid domain is governed by the Navier-Stokes and Continuity equations (Appendix, online only). Blood was assumed to be incompressible with the density and viscosity of 1050 kg/m3 and 0.004 kg/m∙s, respectively. The blood flow rate was taken as 0.35 liter/min for femoral venous flow based on literature.16 For the wall interface, we assume no slip between fluid and the wall and no permeability of the vessel wall. The solid domain is governed by the Momentum and Equilibrium equations (Appendix, online only). A nonlinear hyperelastic strain energy density function was used for the leaflet material model. A schematic of the three types of valves is shown in Fig 1. Truly coupled two-way FSI models were developed with well-defined FSI interfaces, which are necessary for determination of leaflet fluid WSS during movement. Fluid-structure interfaces were defined at the surfaces of the leaflets and interfaces of the fluid. The Arbitary Lagrange-Eulerian method was used, which allows the fluid mesh to deform with the moving leaflets. The remeshing of fluid domain was done at each time step. Rather than using a single Lagrangian approach or a single Eulerian approach, the Arbitary Lagrange-Eulerian describes the motion of fluid in a moving reference frame with the constraint that the velocity on the fluid-solid boundary must be equal to that of the boundary. The velocity of
Fig 1. Schematic of the A, monoleaflet; B, bileaflet; and C, trileaflet valves.
the reference frame is neither the fluid particle velocity such as in a pure Lagrangian description nor zero in a pure Eulerian description.
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Fig 3. The dynamics of fluid wall shear stress (WSS) at the leaflet base of the three valves during the cycle.
Fig 2. The flow fields of A, monoleaflet; B, bileaflet and c, trileaflet valves. The trileaflet valve opened larger than the bileaflet valve. The velocity color scale is in cm/s.
For evaluation of valve efficiency, we used a mechanical cost function defined as: Cost function ¼ solid wall stress/fluid WSS Both the solid wall stress and fluid WSS were analyzed for the base region of leaflet at the back side, as this is the critical area for valve pathology.17 RESULTS The flow fields of mono-, bi-, and trileaflet valves are shown in Fig 2. The stasis region of monoleaflet valve near the leaflet base at the back side is likely due to the fact that the monoleaflet has to cover the whole lumen and is thus much longer than the bileaflet and trileaflet. Due to the longer leaflet, it is more difficult for flow to reach the back side of the leaflet. The stasis region implies a lower fluid shear stress in the leaflet pocket region. The bileaflet valve opened approximately 40%, while the trileaflet valve opened larger to 60% and would likely open even more if the leaflets were accompanied by sinuses that provide space behind the leaflets for the opening motion. In all three valve cases, jets formed at the exit of the valve, as that is the narrowest region for the flow. The bileaflet jet was the narrowest, while the trileaflet jet was the widest, as the trivalve opened the most.
Fig 3 shows the dynamics of fluid WSS of the three valves at the base of leaflets during the full valve (opening and closing) cycle. The bileaflet valve had the highest WSS during the cycle, while the monovalve had the lowest WSS. In all leaflet configurations, the fluid shear stress on the wall increased during valve opening due to increased flow in the valve pocket. During closing, the fluid WSS reduced as the flow decelerated. After valve closure, the fluid WSS became minimal. The valve or bulk tissue stress concentrations on the leaflets are shown in Fig 4. The stresses were concentrated at the base region or valve pocket during various stages of leaflet motion. The pocket region also experienced the least amount of flow and fluid shear. Thus, this region has the compounded effect of high wall stress and low endothelial shear, which may make it vulnerable for thrombosis and hyperplasia. Fig 5 shows the dynamics of leaflet wall stress of the three valves at the base of the leaflets during the cycle. The bileaflet valve had the lowest stress during the cycle, while the monovalve had the highest stress. The fluid WSS of the bileaflet valve is about three times that of the monoleaflet valve, while the leaflet wall stress is about half that of the monoleaflet valve. As the result, the mechanical cost of the bileaflet valve is only one-sixth of the monoleaflet valve as shown in Fig 6. DISCUSSION The current study showed that the mechanical cost (solid wall stress/fluid WSS) of the bileaflet valve was the lowest compared with mono- and trileaflet valves. This is likely one of the mechanical reasons why the bi-leaflet is the main valve design in the venous system. It was also found that the monovalve had the highest cost function and suggested its predisposition to valve pathology, which is highly consistent with clinical findings. Native venous valves have a predominantly bicuspid architecture. Studies by Diaconu et al and others found that the ratio of native venous valves for mono- vs bi- vs tri- is about 1:15:3.2-5 Furthermore, Silva et al studied
4 Chen et al
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Fig 5. The dynamics of leaflet wall stress at the leaflet base of the three valves during the cycle. The stress of the monovalve was the highest.
Fig 4. The leaflet wall stress distribution (bright region at the base denotes stress concentration), in addition to the flow fields. The stress color scale is in KPa. Top panel, Monoleaflet valve; middle panel, bileaflet valve; bottom panel, trileaflet valve.
the relationship between valve anatomy and function and demonstrated superiority of bicuspid and tricuspid valves as compared with monocuspid. It was concluded that the tricuspid valves are still competent when compared with the normal bicuspid valves. In contrast, they showed that monocuspid valves were insufficient, and did not prevent retrograde flow.3 Although the artifical monodisc mechanical heart valve is a functional design of mechanical valves, they work very differently from tissue valves. The mechanical valves are rigid with no flexibility or compliance. The benefit is that these valves do not calcify. Mechanical valves have problems with thrombosis and cavitation, however, as the rigid material causes lysis of red blood cells and also activates platelets.18,19 A major mechanism of fluid WSS influence on valve biology is that the low shear stress regions at the pockets behind the leaflets may cause flow stagnation and increased adhesion of thrombotic and inflammatory cells.7 This may
enhance the deposition or permeation of these cells onto the vessel wall. WSS act on the surfaces of leaflets and vessel wall where endothelium and glycocolyx is known to sense the WSS and initiate mechanotransduction.7,20 Low shear stress further increases the permeability of the vessel wall, which results in low-density lipoprotein invasion and platelet deposition, which are important contributors to thrombus initiation and progression. Low WSS reduces the endothelium nitric oxide production and nitric oxide synthase, which are atheroprotective and anti-inflammatory.20,21 The phenotype of endothelium is also found to be influenced by fluid shear stress,6 and disturbed flow leads to unfavorable endothelial phenotype. It is known that the back side of the leaflet, especially the base region, is prone to accumulation of inflammatory and thrombotic cells, leading to adhesion of leaflets and valve stenosis.17 This rarely occurs on the front side of the leaflets where the flow is not blocked by the leaflets. It was further found that the back side of valve leaflets has elevated gene expression of inflammatory genes such as CNP and BMP-4.17 Fluid shear stress analysis alone may not fully explain the leaflet remodeling and thrombus formation patterns. It is likely that solid stresses act in synergy with the fluid shear stresses.15,22 Solid wall stresses affect the cells and fibers within the wall, such as the valvular interstitial cells, collagen, and elastin fibers. The interstitial cells express smooth muscle alpha-actin and are considered to respond to mechanical stimuli.8 The stretching of these cells and fibers can induce mechanotrasduction and biological as well as pathological responses.9 Therefore, minimization of solid stresses will promote the longevity of prosthetic venous valves by reduction of fatigue. It should be noted that truly coupled two-way FSI models were developed with well-defined FSI interfaces that are necessary for determination of leaflet fluid WSS during movement. Methods that model a moving solid mesh passing through a static fluid mesh do not have a true FSI interface and associated boundary layer and hence cannot obtain the WSS at the fluid/solid interface reliably.23,24 As the fluid WSS is critical for biological
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Fig 6. Comparisons of stresses (A), wall shear stress (WSS) (B), and cost (C) of mono-, bi-, and trileaflet valves. The cost of bileaflet valve was the lowest compared with mono- and trileaflet valves. The monovalve had the highest mechanical cost.
response, fully coupled FSI models were developed for this study. We have performed sensitivity analysis that changed the various model parameters within 20% of the mean values and have found the conclusions to be robust and representative. Additional simulation runs using higher mesh density resulted in less than a 2% difference in the results. The monocuspid design has been considered as a valve design for pulmonary valve for many years. Yang et al found that the monocuspid valves can prevent pulmonary regurgitation in the early period, but the effects are limited in duration due to progressive degeneration.25 Furthermore, clinical studies by Bortolotti et al found that the monocuspid valves experienced multiple failure modes including leaflet tears at the base and various degrees of collagen disruption.26,27 Silva et al demonstrated functional superiority of bicuspid and tricuspid valves as compared to monocuspid.3 The adverse fluid and solid mechanics issues are likely the culprits for the failure of the mono-cuspid design, since other factors such as the valve tissue and the fixation were similar to bi- and tricuspid bioprosthetic valves. Some limitations of the current simulations warrant discussion. Tricuspid valves are located inside the heart
and accompanied by prominent sinuses behind the cusps to aid larger openings, especially the aortic valve. Without the sinuses, the valve dynamics and extent of opening may be affected. Nevertheless, the effects from the leaflets are demonstrated in the FSI simulations. Additionally, branches near the valves were not considered. The branches divert part of the flow and may further lower the fluid WSS. Finally, the additional technical challenges of producing a tricuspid valve and the potential difficulty of producing complete closure with a monocuspid device may not make these designs desirable. Understanding the mechanism for the preponderance of bicuspid valves in the venous circulation is helpful, however, for elucidating the venous valve structure-function relationship in nature and for designing better prosthetic valves. CONCLUSIONS The mean fluid WSS of the bileaflet valve was generally higher than the tricuspid valve, which was further higher than the monocuspid valve. The mean solid wall stress of the bicuspid valve was generally lower than the tricuspid valve, which was further lower than the mono-cuspid valve. Therefore, the mechanical cost (solid wall stress/fluid WSS) of the bicuspid valve was lower than the tricuspid
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valve, which was further lower than the monocuspid valve. Our findings support that the bicuspid venous valve configuration provides the optimal mechanical cost (ie, minimize solid stress and maximize fluid shear), which is likely the reason why the bicuspid valve is the design of choice in the venous system. The mechanical cost of a monovalve was much higher than bi- and trivalves, which suggests less optimal design for a prosthesis, highly consistent with clinical data. This knowledge can help dictate the design of novel venous prosthetic valves and avoid less optimal designs. AUTHOR CONTRIBUTIONS Conception and design: HC, SC, GK Analysis and interpretation: HC, ZB, SC, FL, GK Data collection: HC Writing the article: HC, GK Critical revision of the article: HC, ZB, JK, SC, FL, GK Final approval of the article: HC, ZB, JK, SC, FL, GK Statistical analysis: HC, GK Obtained funding: HC, JK, SC, GK Overall responsibility: GK REFERENCES 1. Lurie F, Kistner R, Perrin M, Raju S, Neglen P, Maleti O. Invasive treatment of deep venous disease. A UIP consensus. Int J Angiol 2010;29:199-204. 2. Diaconu CI, Staugaitis SM, Fox RJ, Rae-Grant A, Schwanger C, McBride JM. A technical approach to dissecting and assessing cadaveric veins pertinent to chronic cerebrospinal venous insufficiency in multiple sclerosis. Neurol Res 2012;34:810-8. 3. Silva MA, Deen KI, Fernando DJ, Sheriffdeen AH. The internal jugular vein valve may have a significant role in the prevention of venous reflux: evidence from live and cadaveric human subjects. Clin Physiol Funct Imaging 2002;22:202-5. 4. Akkawi NM, Agosti C, Borroni B, Rozzini L, Magoni M, Vignolo LA, et al. Jugular valve incompetence. J Ultrasound Med 2002;21:747-51. 5. Sanchez-Hanke M, Puschel K, Leuwer R. Anatomy of the valve system of the internal jugular vein. Laryngorhinootologie 2000;79:332-6. 6. Butcher JT, Tressel S, Johnson T, Nerem R. Transcriptional profiles of valvular and vascular endothelial cells reveal phenotypic differences: influence of shear stress. Arterioscler Thromb Vasc Biol 2006;26: 69-77. 7. Davies PF. Endothelial mechanisms of flow-mediated athero-protection and sceptibility. Circ Res 2007;101:10-2. 8. Huang HY, Liao J, Sacks MS. In-situ deformation of the aortic valve interstitial cell nucleus under diastolic loading. J Biomech Eng 2007;129:880-9. 9. Fung YC. Biomechanics: motion, flow, stress, and growth. SpringerVerlag: New York; 1998. 10. Chen HY, Sinha AK, Choy JS, Zheng H, Sturek M, Bigelow B, et al. Mis-sizing of stent promotes intimal hyperplasia: impact of endothelial shear and intramural stress. Am J Physiol Heart Circ Physiol 2011;301: H2254-63.
11. Chen HY, Navia JA, Kassab GS. Vessel-clamp interaction: transient closure dynamics. Ann Biomed Eng 2009;37:1772-80. 12. Chen HY, Zhu LD, Huo YL, Liu Y, Kassab GS. Fluid-structure Interaction (FSI) modeling in the cardiovascular system. In: Guccione JM, Kassab GS, Ratcliffe MB, editors. Computational cardiovascular mechanics: modeling and applications in heart failure. New York: Springer; 2010. p. 141-57. 13. Ku DN. Blood flow in arteries. Ann Rev Fluid Mech 1997;29:399. 14. Davies PF, Spaan JA, Krams R. Shear stress biology of the endothelium. Ann Biomed Eng 2005;33:1714-8. 15. Thubrikar MJ, Baker JW, Nolan SP. Inhibition of atherosclerosis associated with reduction of arterial intramural stress in rabbits. Arteriosclerosis 1988;8:410-20. 16. Min RJ, Khilnani NM, Golia P. Duplex ultrasound evaluation of lower extremity venous insufficiency. J Vasc Interv Radiol 2003;14: 1233-41. 17. Simmons CA, Grant GR, Manduchi E, Davies PF. Spatial heterogeneity of endothelial phenotypes correlates with side-specific vulnerability to calcification in normal porcine aortic valves. Circ Res 2005;96: 792-9. 18. Walker PG, Yoganathan AP. In vitro pulsatile flow hemodynamics of five mechanical aortic heart valve prostheses. Eur J Cardiothoracic Surg 1992;6(Suppl 1):S113-23. 19. Murphy DW, Dasi LP, Vukasinovic J, Glezer A, Yoganathan AP. reduction of procoagulant potential of b-datum leakage jet flow in bileaflet mechanical heart valves via application of vortex generator arrays. J Biomech Eng 2010;132:071011. 20. Kassab GS, Navia JA. Biomechanical considerations in the design of graft: the homeostasis hypothesis. Ann Rev Biomed Eng 2006;8: 499-535. 21. Lu X, Kassab GS. Nitric oxide is significantly reduced in ex vivo porcine arteries during reverse flow because of increased superoxide production. J Physiol 2004;561:575-82. 22. Liu Y, Dang C, Garcia M, Gregersen H, Kassab GS. Surrounding tissues affect the passive mechanics of the vessel wall: theory and experiment. Am J Physiol Heart Circ Physiol 2007;293:3290-300. 23. Peskin CS, McQueen DM. Cardiac fluid dynamics. Crit Rev Biomed Eng 1992;20:451-9. 24. Qui Y, Quijano RC, Wang SK, Hwang NH. Fluid dynamics of venous valve closure. Ann Biomed Eng 1995;23:750-9. 25. Yang JH, Jun TG, Park PW, Sung K, Kim WS, Lee YT, et al. Factors related to the durability of a homograft monocusp valve inserted during repair of tetralogy of Fallot as based on the mid- to long-term outcomes. Cardiol Young 2008;18:141-6. 26. Gabbay S, Bortolotti U, Cipolletti G, Wasserman F, Frater RW, Factor SM. The Meadox unicusp pericardial bioprosthetic heart valve: new concept. Ann Thorac Surg 1984;37:448-56. 27. Bortolotti U, Ius P, Thiene G, Minarini M, Milano A, Valfrè C, et al. The Meadox-Gabbay pericardial xenograft: failure of the unicusp principle. Ann Thorac Surg 1992;54:952-7. 28. Merryman WD, Huang HY, Schoen FJ, Sacks MS. The effects of cellular contraction on aortic valve leaflet flexural stiffness. J Biomech 2006;39:88-96.
Submitted Apr 24, 2013; accepted Aug 7, 2013.
Additional material for this article may be found online at www.jvsvenous.org.
JOURNAL OF VASCULAR SURGERY: VENOUS AND LYMPHATIC DISORDERS Volume -, Number -
APPENDIX (online only). Mathematical formulations The governing equations for the fluid domain are the Navier-Stokes and Continuity equations: / ! h/ vV ! / ! V p ! þ V ,V V þ 2 V ,D ¼ 0 (1) r r vt ! V ,V ¼ 0
/
(2)
where V is velocity, p is pressure, r is density, h is /
viscosity, D is the rate of deformation tensor, V is the gradient operator. The governing equations for the solid domain are the Momentum and Equilibrium equations (ie, Newton’s laws of Mechanics):
rai sij ;j rfi ¼ 0 in s Uðt Þ
(3)
sij nj ti ¼ 0 on s Gðt Þ
(4)
where ai is acceleration, fi is force per unit mass, s UðtÞ is the vessel domain at time t, nj is normal vector, ti is surface traction vector, and sij is stress. The following nonlinear hyperelastic strain energy density function was used for the leaflet material model: W ¼ C1 ðI1 3Þ þ D1 ðJ 1Þ2 ;
J ¼ det ðF Þ
(5)
Chen et al 6.e1
where I1 ¼ J 2/3I1 is the first invariant of the deviatoric part of the left Cauchy-Green deformation tensor, and F is the deformation gradient. The material model was assumed to be that of aortic leaflet for all three valve designs.28 C1 was taken as half of the shear modulus (200 KPa) and D1 as half of the bulk modulus (250 MPa) to enforce incompressibility. The fluid density and viscosity were 1050 kg/em3 and 0.004 kg/m∙s, respectively. For the wall interface, we assume no slip between fluid and the wall and no permeability of the vessel wall. The solid and fluid models were coupled by the fluid nodal positions on the fluid-structure interaction (FSI) interfaces, which are determined by the kinematic conditions. The displacements of the other fluid nodes were determined so as to preserve the initial mesh quality. The Arbitary Lagrange-Eulerian modified governing equations for fluid flow were then solved. For the dynamic case, the fluid stresses were integrated along the fluid-solid interface and applied on the corresponding solid nodes. The fully coupled two-way FSI model was solved. The solution process continued until solutions for solid and fluid nodes converge on the FSI interface and a steady solution was achieved. Mathematical formulations: 1) Navier-Stokes equation; 2) Continuity equation; 3) Momentum equation; 4) Equilibrium equation; 5) Nonlinear hyperelastic strain energy density function.
Although the importance of venous valves is wellappreciated given the consequences of valvular dysfunction, current quantification of fluid and solid mechanics of venous valves is limited. In clinical studies, it was found that the venous valves may increase the venous flow resistance. Despite the increase of flow resistance, venous valves improve blood flow to the heart, partly due to prevention of reverse flow.1 The fundamental physiological and pathophysiological issues, as well as interest in venous valve prosthesis to replace insufficient valves, require a full understanding of valve hemodynamics associated with valve anatomy and architecture. Native venous valves are From the Research Engineering, 3DT Holdings, LLC,a the Department of Biomedical Engineering, Indiana University, Purdue University,b and the Departments of Surgeryc and Cellular and Integrative Physiology,d Indiana University School of Medicine, Indianapolis; Research Engineering, Cook Medical, Bloomingtone; and Jobst Vascular Institute, Toledo.f Supported by 3DT Holdings, LLC and Cook Medical. Author conflict of interest: none. Additional material for this article may be found online at www.jvsvenous.org. Reprint requests: Ghassan S. Kassab, PhD, Department of Biomedical Engineering, Indiana University Purdue University Indianapolis, Indianapolis, IN 46202 (e-mail: [email protected]). The editors and reviewers of this article have no relevant financial relationships to disclose per the Journal policy that requires reviewers to decline review of any manuscript for which they may have a conflict of interest. 2213-333X/$36.00 Copyright Ó 2013 by the Society for Vascular Surgery. http://dx.doi.org/10.1016/j.jvsv.2013.08.004
the monocuspid valve. Therefore, the mechanical cost, which was defined as solid wall stress/fluid WSS, of the bicuspid valve was the lowest. Conclusions: The lower mechanical cost may be a reason why the bicuspid valve is the dominant design in the venous system. This knowledge provides guidance for the design of novel venous prosthetic valves and may shed light on venous valve disease when the architecture of the valve is altered. (J Vasc Surg: Venous and Lym Dis 2013;-:1-7.) Clinical Relevance: The physiological and pathophysiological issues as well as interest in venous valve prosthesis to replace insufficient valves require a full understanding of valve hemodynamics associated with valve anatomy and architecture. The current study found that the lower mechanical cost may be a reason why the bileaflet valve is the dominant design in the venous system. This knowledge may provide guidance to the design of novel venous prosthetic valves and shed light on the mechanism of venous valve disease.
predominantly bicuspid valves. Anatomical studies found that venous valves are 80% to 90% bicuspid, 10% to 15% tricuspid, and only approximately 5% monocuspid.2-5 The prevalence of data suggest functional superiority of bicuspid valves followed by tricuspid valves, and inferiority of monocuspid valves. This was confirmed in ex vivo experiments.3 The monocuspid valves were shown to be insufficient and did not prevent retrograde flow. Despite these variations in nature, with the bicuspid venous valve being the most common, it is unclear what dictates the design of the venous valve geometry. Experimental and clinical evidence suggests that alteration of fluid wall shear stress (WSS) contributes to endothelial remodeling and may affect valvular endothelial cell phenotype.6,7 Solid wall stresses also affect the cells and fibers within the wall, such as the vavular interstitial cells, collagen, and elastin fibers. Valvular interstitial cells have characteristics of smooth muscle cells and respond to mechanical stimuli.8 The stretching of these cells and fibers may induce mechanotransduction, resulting in tissue remodeling.9 Therefore, perturbations in the mechanical environment can lead to the pathogenesis of valvular disease. Computational modeling can be a very useful tool for medical device design as well as simulation of cardiovascular surgery procedure and vascular device implants.10-12 The fluid and solid stress analysis can provide valuable insights into tissue injury response and disease 1
2 Chen et al
JOURNAL OF VASCULAR SURGERY: VENOUS AND LYMPHATIC DISORDERS --- 2013
mechanisms. Computational and experimental studies on venous valve design and associated biomechanics, however, are very limited. Recently, a novel mechanical cost function was defined as the ratio of computed wall stress and fluid WSS to capture the effects of both fluid and solid mechanics in tissue.10 The solid wall stress is in the numerator since it has a direct relationship with tissue remodeling, while the fluid WSS is in the denominator since the fluid WSS has an inverse relationship with vascular tissue remodeling.11-15 This cost function has been previously shown to significantly correlate with intimal hyperplasia that considers both the effect of fluid shear and solid stress in stented vessels.10 It was shown that lower cost function correlated with less intimal hyperplasia, and hence a lower mechanical cost, thus is more desirable biologically. The objective of the current study was to study the three types of valve designs (mono-, bi-, and tricuspid) and their implications on the fluid and solid mechanics of the valve leaflets. The hypothesis is that the bileaflet valve has the lowest mechanical cost (ratio of leaflet wall stress and fluid WSS) for the venous environment as compared with mono- and trileaflet valves. Accordingly, we performed fully coupled fluid-structure interaction (FSI) simulations on each of the three designs under identical flow conditions to assess the fluid and solid forces on the valve leaflet. Virtual experiments using predictive computational models can produce improved designs, which can then be subjected to experimental validations. METHODS The fluid domain is governed by the Navier-Stokes and Continuity equations (Appendix, online only). Blood was assumed to be incompressible with the density and viscosity of 1050 kg/m3 and 0.004 kg/m∙s, respectively. The blood flow rate was taken as 0.35 liter/min for femoral venous flow based on literature.16 For the wall interface, we assume no slip between fluid and the wall and no permeability of the vessel wall. The solid domain is governed by the Momentum and Equilibrium equations (Appendix, online only). A nonlinear hyperelastic strain energy density function was used for the leaflet material model. A schematic of the three types of valves is shown in Fig 1. Truly coupled two-way FSI models were developed with well-defined FSI interfaces, which are necessary for determination of leaflet fluid WSS during movement. Fluid-structure interfaces were defined at the surfaces of the leaflets and interfaces of the fluid. The Arbitary Lagrange-Eulerian method was used, which allows the fluid mesh to deform with the moving leaflets. The remeshing of fluid domain was done at each time step. Rather than using a single Lagrangian approach or a single Eulerian approach, the Arbitary Lagrange-Eulerian describes the motion of fluid in a moving reference frame with the constraint that the velocity on the fluid-solid boundary must be equal to that of the boundary. The velocity of
Fig 1. Schematic of the A, monoleaflet; B, bileaflet; and C, trileaflet valves.
the reference frame is neither the fluid particle velocity such as in a pure Lagrangian description nor zero in a pure Eulerian description.
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Fig 3. The dynamics of fluid wall shear stress (WSS) at the leaflet base of the three valves during the cycle.
Fig 2. The flow fields of A, monoleaflet; B, bileaflet and c, trileaflet valves. The trileaflet valve opened larger than the bileaflet valve. The velocity color scale is in cm/s.
For evaluation of valve efficiency, we used a mechanical cost function defined as: Cost function ¼ solid wall stress/fluid WSS Both the solid wall stress and fluid WSS were analyzed for the base region of leaflet at the back side, as this is the critical area for valve pathology.17 RESULTS The flow fields of mono-, bi-, and trileaflet valves are shown in Fig 2. The stasis region of monoleaflet valve near the leaflet base at the back side is likely due to the fact that the monoleaflet has to cover the whole lumen and is thus much longer than the bileaflet and trileaflet. Due to the longer leaflet, it is more difficult for flow to reach the back side of the leaflet. The stasis region implies a lower fluid shear stress in the leaflet pocket region. The bileaflet valve opened approximately 40%, while the trileaflet valve opened larger to 60% and would likely open even more if the leaflets were accompanied by sinuses that provide space behind the leaflets for the opening motion. In all three valve cases, jets formed at the exit of the valve, as that is the narrowest region for the flow. The bileaflet jet was the narrowest, while the trileaflet jet was the widest, as the trivalve opened the most.
Fig 3 shows the dynamics of fluid WSS of the three valves at the base of leaflets during the full valve (opening and closing) cycle. The bileaflet valve had the highest WSS during the cycle, while the monovalve had the lowest WSS. In all leaflet configurations, the fluid shear stress on the wall increased during valve opening due to increased flow in the valve pocket. During closing, the fluid WSS reduced as the flow decelerated. After valve closure, the fluid WSS became minimal. The valve or bulk tissue stress concentrations on the leaflets are shown in Fig 4. The stresses were concentrated at the base region or valve pocket during various stages of leaflet motion. The pocket region also experienced the least amount of flow and fluid shear. Thus, this region has the compounded effect of high wall stress and low endothelial shear, which may make it vulnerable for thrombosis and hyperplasia. Fig 5 shows the dynamics of leaflet wall stress of the three valves at the base of the leaflets during the cycle. The bileaflet valve had the lowest stress during the cycle, while the monovalve had the highest stress. The fluid WSS of the bileaflet valve is about three times that of the monoleaflet valve, while the leaflet wall stress is about half that of the monoleaflet valve. As the result, the mechanical cost of the bileaflet valve is only one-sixth of the monoleaflet valve as shown in Fig 6. DISCUSSION The current study showed that the mechanical cost (solid wall stress/fluid WSS) of the bileaflet valve was the lowest compared with mono- and trileaflet valves. This is likely one of the mechanical reasons why the bi-leaflet is the main valve design in the venous system. It was also found that the monovalve had the highest cost function and suggested its predisposition to valve pathology, which is highly consistent with clinical findings. Native venous valves have a predominantly bicuspid architecture. Studies by Diaconu et al and others found that the ratio of native venous valves for mono- vs bi- vs tri- is about 1:15:3.2-5 Furthermore, Silva et al studied
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Fig 5. The dynamics of leaflet wall stress at the leaflet base of the three valves during the cycle. The stress of the monovalve was the highest.
Fig 4. The leaflet wall stress distribution (bright region at the base denotes stress concentration), in addition to the flow fields. The stress color scale is in KPa. Top panel, Monoleaflet valve; middle panel, bileaflet valve; bottom panel, trileaflet valve.
the relationship between valve anatomy and function and demonstrated superiority of bicuspid and tricuspid valves as compared with monocuspid. It was concluded that the tricuspid valves are still competent when compared with the normal bicuspid valves. In contrast, they showed that monocuspid valves were insufficient, and did not prevent retrograde flow.3 Although the artifical monodisc mechanical heart valve is a functional design of mechanical valves, they work very differently from tissue valves. The mechanical valves are rigid with no flexibility or compliance. The benefit is that these valves do not calcify. Mechanical valves have problems with thrombosis and cavitation, however, as the rigid material causes lysis of red blood cells and also activates platelets.18,19 A major mechanism of fluid WSS influence on valve biology is that the low shear stress regions at the pockets behind the leaflets may cause flow stagnation and increased adhesion of thrombotic and inflammatory cells.7 This may
enhance the deposition or permeation of these cells onto the vessel wall. WSS act on the surfaces of leaflets and vessel wall where endothelium and glycocolyx is known to sense the WSS and initiate mechanotransduction.7,20 Low shear stress further increases the permeability of the vessel wall, which results in low-density lipoprotein invasion and platelet deposition, which are important contributors to thrombus initiation and progression. Low WSS reduces the endothelium nitric oxide production and nitric oxide synthase, which are atheroprotective and anti-inflammatory.20,21 The phenotype of endothelium is also found to be influenced by fluid shear stress,6 and disturbed flow leads to unfavorable endothelial phenotype. It is known that the back side of the leaflet, especially the base region, is prone to accumulation of inflammatory and thrombotic cells, leading to adhesion of leaflets and valve stenosis.17 This rarely occurs on the front side of the leaflets where the flow is not blocked by the leaflets. It was further found that the back side of valve leaflets has elevated gene expression of inflammatory genes such as CNP and BMP-4.17 Fluid shear stress analysis alone may not fully explain the leaflet remodeling and thrombus formation patterns. It is likely that solid stresses act in synergy with the fluid shear stresses.15,22 Solid wall stresses affect the cells and fibers within the wall, such as the valvular interstitial cells, collagen, and elastin fibers. The interstitial cells express smooth muscle alpha-actin and are considered to respond to mechanical stimuli.8 The stretching of these cells and fibers can induce mechanotrasduction and biological as well as pathological responses.9 Therefore, minimization of solid stresses will promote the longevity of prosthetic venous valves by reduction of fatigue. It should be noted that truly coupled two-way FSI models were developed with well-defined FSI interfaces that are necessary for determination of leaflet fluid WSS during movement. Methods that model a moving solid mesh passing through a static fluid mesh do not have a true FSI interface and associated boundary layer and hence cannot obtain the WSS at the fluid/solid interface reliably.23,24 As the fluid WSS is critical for biological
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Chen et al 5
Fig 6. Comparisons of stresses (A), wall shear stress (WSS) (B), and cost (C) of mono-, bi-, and trileaflet valves. The cost of bileaflet valve was the lowest compared with mono- and trileaflet valves. The monovalve had the highest mechanical cost.
response, fully coupled FSI models were developed for this study. We have performed sensitivity analysis that changed the various model parameters within 20% of the mean values and have found the conclusions to be robust and representative. Additional simulation runs using higher mesh density resulted in less than a 2% difference in the results. The monocuspid design has been considered as a valve design for pulmonary valve for many years. Yang et al found that the monocuspid valves can prevent pulmonary regurgitation in the early period, but the effects are limited in duration due to progressive degeneration.25 Furthermore, clinical studies by Bortolotti et al found that the monocuspid valves experienced multiple failure modes including leaflet tears at the base and various degrees of collagen disruption.26,27 Silva et al demonstrated functional superiority of bicuspid and tricuspid valves as compared to monocuspid.3 The adverse fluid and solid mechanics issues are likely the culprits for the failure of the mono-cuspid design, since other factors such as the valve tissue and the fixation were similar to bi- and tricuspid bioprosthetic valves. Some limitations of the current simulations warrant discussion. Tricuspid valves are located inside the heart
and accompanied by prominent sinuses behind the cusps to aid larger openings, especially the aortic valve. Without the sinuses, the valve dynamics and extent of opening may be affected. Nevertheless, the effects from the leaflets are demonstrated in the FSI simulations. Additionally, branches near the valves were not considered. The branches divert part of the flow and may further lower the fluid WSS. Finally, the additional technical challenges of producing a tricuspid valve and the potential difficulty of producing complete closure with a monocuspid device may not make these designs desirable. Understanding the mechanism for the preponderance of bicuspid valves in the venous circulation is helpful, however, for elucidating the venous valve structure-function relationship in nature and for designing better prosthetic valves. CONCLUSIONS The mean fluid WSS of the bileaflet valve was generally higher than the tricuspid valve, which was further higher than the monocuspid valve. The mean solid wall stress of the bicuspid valve was generally lower than the tricuspid valve, which was further lower than the mono-cuspid valve. Therefore, the mechanical cost (solid wall stress/fluid WSS) of the bicuspid valve was lower than the tricuspid
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valve, which was further lower than the monocuspid valve. Our findings support that the bicuspid venous valve configuration provides the optimal mechanical cost (ie, minimize solid stress and maximize fluid shear), which is likely the reason why the bicuspid valve is the design of choice in the venous system. The mechanical cost of a monovalve was much higher than bi- and trivalves, which suggests less optimal design for a prosthesis, highly consistent with clinical data. This knowledge can help dictate the design of novel venous prosthetic valves and avoid less optimal designs. AUTHOR CONTRIBUTIONS Conception and design: HC, SC, GK Analysis and interpretation: HC, ZB, SC, FL, GK Data collection: HC Writing the article: HC, GK Critical revision of the article: HC, ZB, JK, SC, FL, GK Final approval of the article: HC, ZB, JK, SC, FL, GK Statistical analysis: HC, GK Obtained funding: HC, JK, SC, GK Overall responsibility: GK REFERENCES 1. Lurie F, Kistner R, Perrin M, Raju S, Neglen P, Maleti O. Invasive treatment of deep venous disease. A UIP consensus. Int J Angiol 2010;29:199-204. 2. Diaconu CI, Staugaitis SM, Fox RJ, Rae-Grant A, Schwanger C, McBride JM. A technical approach to dissecting and assessing cadaveric veins pertinent to chronic cerebrospinal venous insufficiency in multiple sclerosis. Neurol Res 2012;34:810-8. 3. Silva MA, Deen KI, Fernando DJ, Sheriffdeen AH. The internal jugular vein valve may have a significant role in the prevention of venous reflux: evidence from live and cadaveric human subjects. Clin Physiol Funct Imaging 2002;22:202-5. 4. Akkawi NM, Agosti C, Borroni B, Rozzini L, Magoni M, Vignolo LA, et al. Jugular valve incompetence. J Ultrasound Med 2002;21:747-51. 5. Sanchez-Hanke M, Puschel K, Leuwer R. Anatomy of the valve system of the internal jugular vein. Laryngorhinootologie 2000;79:332-6. 6. Butcher JT, Tressel S, Johnson T, Nerem R. Transcriptional profiles of valvular and vascular endothelial cells reveal phenotypic differences: influence of shear stress. Arterioscler Thromb Vasc Biol 2006;26: 69-77. 7. Davies PF. Endothelial mechanisms of flow-mediated athero-protection and sceptibility. Circ Res 2007;101:10-2. 8. Huang HY, Liao J, Sacks MS. In-situ deformation of the aortic valve interstitial cell nucleus under diastolic loading. J Biomech Eng 2007;129:880-9. 9. Fung YC. Biomechanics: motion, flow, stress, and growth. SpringerVerlag: New York; 1998. 10. Chen HY, Sinha AK, Choy JS, Zheng H, Sturek M, Bigelow B, et al. Mis-sizing of stent promotes intimal hyperplasia: impact of endothelial shear and intramural stress. Am J Physiol Heart Circ Physiol 2011;301: H2254-63.
11. Chen HY, Navia JA, Kassab GS. Vessel-clamp interaction: transient closure dynamics. Ann Biomed Eng 2009;37:1772-80. 12. Chen HY, Zhu LD, Huo YL, Liu Y, Kassab GS. Fluid-structure Interaction (FSI) modeling in the cardiovascular system. In: Guccione JM, Kassab GS, Ratcliffe MB, editors. Computational cardiovascular mechanics: modeling and applications in heart failure. New York: Springer; 2010. p. 141-57. 13. Ku DN. Blood flow in arteries. Ann Rev Fluid Mech 1997;29:399. 14. Davies PF, Spaan JA, Krams R. Shear stress biology of the endothelium. Ann Biomed Eng 2005;33:1714-8. 15. Thubrikar MJ, Baker JW, Nolan SP. Inhibition of atherosclerosis associated with reduction of arterial intramural stress in rabbits. Arteriosclerosis 1988;8:410-20. 16. Min RJ, Khilnani NM, Golia P. Duplex ultrasound evaluation of lower extremity venous insufficiency. J Vasc Interv Radiol 2003;14: 1233-41. 17. Simmons CA, Grant GR, Manduchi E, Davies PF. Spatial heterogeneity of endothelial phenotypes correlates with side-specific vulnerability to calcification in normal porcine aortic valves. Circ Res 2005;96: 792-9. 18. Walker PG, Yoganathan AP. In vitro pulsatile flow hemodynamics of five mechanical aortic heart valve prostheses. Eur J Cardiothoracic Surg 1992;6(Suppl 1):S113-23. 19. Murphy DW, Dasi LP, Vukasinovic J, Glezer A, Yoganathan AP. reduction of procoagulant potential of b-datum leakage jet flow in bileaflet mechanical heart valves via application of vortex generator arrays. J Biomech Eng 2010;132:071011. 20. Kassab GS, Navia JA. Biomechanical considerations in the design of graft: the homeostasis hypothesis. Ann Rev Biomed Eng 2006;8: 499-535. 21. Lu X, Kassab GS. Nitric oxide is significantly reduced in ex vivo porcine arteries during reverse flow because of increased superoxide production. J Physiol 2004;561:575-82. 22. Liu Y, Dang C, Garcia M, Gregersen H, Kassab GS. Surrounding tissues affect the passive mechanics of the vessel wall: theory and experiment. Am J Physiol Heart Circ Physiol 2007;293:3290-300. 23. Peskin CS, McQueen DM. Cardiac fluid dynamics. Crit Rev Biomed Eng 1992;20:451-9. 24. Qui Y, Quijano RC, Wang SK, Hwang NH. Fluid dynamics of venous valve closure. Ann Biomed Eng 1995;23:750-9. 25. Yang JH, Jun TG, Park PW, Sung K, Kim WS, Lee YT, et al. Factors related to the durability of a homograft monocusp valve inserted during repair of tetralogy of Fallot as based on the mid- to long-term outcomes. Cardiol Young 2008;18:141-6. 26. Gabbay S, Bortolotti U, Cipolletti G, Wasserman F, Frater RW, Factor SM. The Meadox unicusp pericardial bioprosthetic heart valve: new concept. Ann Thorac Surg 1984;37:448-56. 27. Bortolotti U, Ius P, Thiene G, Minarini M, Milano A, Valfrè C, et al. The Meadox-Gabbay pericardial xenograft: failure of the unicusp principle. Ann Thorac Surg 1992;54:952-7. 28. Merryman WD, Huang HY, Schoen FJ, Sacks MS. The effects of cellular contraction on aortic valve leaflet flexural stiffness. J Biomech 2006;39:88-96.
Submitted Apr 24, 2013; accepted Aug 7, 2013.
Additional material for this article may be found online at www.jvsvenous.org.
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APPENDIX (online only). Mathematical formulations The governing equations for the fluid domain are the Navier-Stokes and Continuity equations: / ! h/ vV ! / ! V p ! þ V ,V V þ 2 V ,D ¼ 0 (1) r r vt ! V ,V ¼ 0
/
(2)
where V is velocity, p is pressure, r is density, h is /
viscosity, D is the rate of deformation tensor, V is the gradient operator. The governing equations for the solid domain are the Momentum and Equilibrium equations (ie, Newton’s laws of Mechanics):
rai sij ;j rfi ¼ 0 in s Uðt Þ
(3)
sij nj ti ¼ 0 on s Gðt Þ
(4)
where ai is acceleration, fi is force per unit mass, s UðtÞ is the vessel domain at time t, nj is normal vector, ti is surface traction vector, and sij is stress. The following nonlinear hyperelastic strain energy density function was used for the leaflet material model: W ¼ C1 ðI1 3Þ þ D1 ðJ 1Þ2 ;
J ¼ det ðF Þ
(5)
Chen et al 6.e1
where I1 ¼ J 2/3I1 is the first invariant of the deviatoric part of the left Cauchy-Green deformation tensor, and F is the deformation gradient. The material model was assumed to be that of aortic leaflet for all three valve designs.28 C1 was taken as half of the shear modulus (200 KPa) and D1 as half of the bulk modulus (250 MPa) to enforce incompressibility. The fluid density and viscosity were 1050 kg/em3 and 0.004 kg/m∙s, respectively. For the wall interface, we assume no slip between fluid and the wall and no permeability of the vessel wall. The solid and fluid models were coupled by the fluid nodal positions on the fluid-structure interaction (FSI) interfaces, which are determined by the kinematic conditions. The displacements of the other fluid nodes were determined so as to preserve the initial mesh quality. The Arbitary Lagrange-Eulerian modified governing equations for fluid flow were then solved. For the dynamic case, the fluid stresses were integrated along the fluid-solid interface and applied on the corresponding solid nodes. The fully coupled two-way FSI model was solved. The solution process continued until solutions for solid and fluid nodes converge on the FSI interface and a steady solution was achieved. Mathematical formulations: 1) Navier-Stokes equation; 2) Continuity equation; 3) Momentum equation; 4) Equilibrium equation; 5) Nonlinear hyperelastic strain energy density function.