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Ann Thorac Surg 2009;88:565-573. doi:10.1016/j.athoracsur.2009.04.109
© 2009 The Society of Thoracic Surgeons
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Original Articles: Pediatric Cardiac

Optimal Conduit Size of the Extracardiac Fontan Operation Based on Energy Loss and Flow Stagnation

Keiichi Itatani, MDa, Kagami Miyaji, MD, PhDa,*, Takahiro Tomoyasu, MDa, Yayoi Nakahata, MDb, Kuniyoshi Ohara, MD, PhDa, Shinichi Takamoto, MD, PhDc, Masahiro Ishii, MD, PhDb

a Department of Cardiovascular Surgery, Kitasato University School of Medicine, Sagamihara, Japan
b Department of Pediatrics, Kitasato University School of Medicine, Sagamihara, Japan
c Department of Cardiac Surgery, The University of Tokyo, Graduate School of Medicine, Tokyo, Japan

Accepted for publication April 28, 2009.

* Address correspondence to Dr Miyaji, Kitasato University School of Medicine, 1-15-1 Kitasato, Sagamihara, Kanagawa, 225-8555, Japan (Email: kagami111{at}aol.com).

Presented at the Forty-fifth Annual Meeting of The Society of Thoracic Surgeons, San Francisco, CA, Jan 26–28, 2009.


   Abstract
Top
 Abstract
Introduction
 Patients and Methods
 Results
 Comment
 Discussion
 References
 
Background: In the extracardiac Fontan operation, larger conduits are used when considering the patients' growth rate. However, larger conduits may cause inefficient flow due to turbulence or stagnation, resulting in late problems such as thrombosis or stenosis. Our objective was to reveal the physiologic effects of respiration and exercise using numerical models, based on the energy loss and flow stagnation, and to determine optimal conduit size.

Methods: For the Fontan operation, a conduit from 14 to 22 mm was created based on angiographic data from 17 Fontan patients (mean age, 36.0 months; mean body surface area, 0.53 m2). Respiratory-driven flow of the superior and inferior vena cava was determined at rest and during exercise on two levels (0.5 and 1.0 W/kg) by magnetic resonance imaging flow studies. Flow stagnation was defined as the volume of the region where flow velocity was less than 0.01 m/second at both the expiratory and inspiratory phases.

Results: In larger conduits, backward flow at the expiratory phase was prominent. Energy loss was small even during exercise, but the change was slightly larger between 14 and 16 mm than other conduit sizes (14 mm, 5.759 mW; 16 mm, 4.881 mW; and 22 mm, 4.199 mW during 1.0 W/kg exercise). Stagnation volume at the expiratory phase increased with an increase of conduit size (14 mm, 9.20% vs 22 mm, 33.9% conduit volume at rest).

Conclusions: Fontan circulation is a low-energy system even during exercise. Larger conduits were proven to have redundant spaces, thus 16 and 18 mm conduits were optimal.


   Introduction
Top
 Abstract
 Introduction
Patients and Methods
 Results
 Comment
 Discussion
 References
 
The Fontan operation is the definitive procedure for patients with univentricular hearts. Since its first description in 1971, many modifications have been introduced including the intraatrial tunnel or the fenestrated Fontan operation [1–5]. The extracardiac Fontan operation has some theoretical advantages over other types of Fontan procedures or total cavopulmonary connection (TCPC) such as a lower frequency of atrial arrhythmias and technical ease of the procedure [5]. Many previous studies have proved that the extracardiac Fontan operation has also flow dynamical advantages [2, 5]. In the extracardiac Fontan operation, larger conduits according to the body size at the time of the operation are used considering the patients growth rate. However, a larger size conduit causes inefficient flow due to turbulence or stagnation and might cause late problems such as thrombosis or stenosis [6]. Despite the improvements in surgical strategies and techniques, the optimal conduit size in the extracardiac Fontan operation has not yet been determined [5–7].

There are a number of reports regarding Fontan hemodynamics based on computational flow dynamic (CFD) models [8–20]. As the fundamental Fontan physiology is a dissociation of the venous return from a ventricular power source, all of the previous numeric models have assumed that pulmonary blood flow is steady and continuous [3, 8–19] except the numeric study by Marsden and colleagues [20] that simulates the effects of exercise and respiration in two cases. However, clinical observations have proved that the pulmonary blood flow in the Fontan physiology is mostly dependent on the respiratory motion [2–4] and often referred to as a "respiratory pump" [2, 4], indicating that pulmonary blood flow is sucked into the lung during inspiration. In Fontan circulation, the decreased exercise capacity is one of the significant morbidities and detailed studies have been reported in regard to flow dynamics of the superior vena cava (SVC) and the inferior vena cava (IVC) of Fontan patients at rest, and during exercise in relation to respiratory flow fluctuation [3, 4, 21–24]. These studies demonstrated that augmentation of pulmonary blood flow with inspiration has important physiologic effects [2]. Therefore, we created respiratory-driven transient flow models using these flow study data.

Previous reports of CFD Fontan models have discussed, mainly, energy expenditure at the anastomosis site and pulmonary blood flow distribution on various types of the Fontan procedure [12, 14–20]. Because the Fontan circulation is supposed to be a low-energy system without ventricular power source, we assumed that the flow stagnation in addition to flow energy expenditure plays an essential role on evaluating flow dynamic efficiency. We schemed to evaluate flow stagnation and defined stagnation volume as the volume of the region where flow velocity was extremely low on the respiratory cycle in the conduit.


   Patients and Methods
Top
 Abstract
 Introduction
 Patients and Methods
Results
 Comment
 Discussion
 References
 
Anatomic Data
The Institutional Review Board approved this study and also waived the need for patient consent. The angiographic data of 17 patients who underwent the extracardiac Fontan operation in our hospital were used to create the ideal extracardiac Fontan geometry. We performed routine cardiac catheterization at 1 year after the Fontan operation. We excluded patients who were diagnosed with apical-caval juxtaposition and those who underwent a bilateral bidirectional Glenn shunt before the Fontan operation. The mean age of these patients was 36.0 ± 32.0 months, and the mean body surface area of these patients was 0.53 ± 0.16 mm2. The following were determined from their angiographic data: SVC diameter, IVC diameter, right and left pulmonary artery (rPA, lPA) diameter, length of the rPA (distance from the center of the SVC anastomosis to the first branch of the rPA), length of the lPA (distance from the center of the SVC anastomosis to the first branch of the lPA), length of conduit, and the conduit axis deviation between the level of center of the conduit and the level of the IVC (Fig 1). The diameter of the IVC was evaluated at the level above the hepatic venous connection. We defined the diameter of the bilateral pulmonary arteries as being identical, and the 9.6 mm diameter (ie, the mean value of the right and left pulmonary artery sizes of 17 patients) is equivalent to the pulmonary artery index (PA index, Nakata's index); 273.0 mm2/m2. We hypothesized that conduits are anastomosed to the pulmonary artery at the site at one-SVC-radius distant from the center of the Glenn anastomosis. The center of the conduit was the length of one-SVC radius from the center of the Glenn anastomosis site. This design is optimal in regard to energy dissipation and right and left pulmonary flow split according to the previous numeric study by de Leval and colleagues [9]. We hypothesized that the anterioposterior axes of the SVC and IVC were identical, as they were of the typical shape as in the extracardiac Fontan operation detected by the lateral views of the angiographic studies. The conduit size was varied from 14, 16, 18, 20, and 22 mm, and connected smoothly to the IVC and pulmonary artery.


Figure 1
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  		Fig 1. (A) Geometry of the extracardiac Fontan computational flow dynamic model. Mean values of 17 patients are used to create the geometry. The right and left pulmonary arteries (PA) are assumed to be the same diameter, and the mean values of the bilateral pulmonary artery diameters are used. A 9.6 mm diameter is equivalent to the pulmonary artery index (PA index, Nakata's index) 273. The radius of conduits varied from 14 to 22 mm. Conduits were anastomosed to the pulmonary artery at a distance equal to one superior vena cava (SVC) radius from the center of the Glenn anastomosis site. The conduit curve was determined as though the middle level of the conduit deviated 6.6 mm from the axis of the inferior vena cava (IVC). (B) Time varying function of boundary conditions. The SVC and IVC flow were given by the previously reported MRI flow study [12]. The pressures of the bilateral pulmonary arteries were given as 11 mm Hg, which dropped to 20% in the inspiratory phase.

 
Boundary Conditions
Respiratory driven, time-varying functions were given for boundary conditions. Inflow boundary conditions for the SVC and IVC were given as flow velocity conditions. Mean flow rate in the SVC and IVC at rest and at two levels of exercise (0.5 W/kg and 1 W/kg) from magnetic resonance imaging (MRI) measurements were given by Hjortdal and colleagues [4] and are listed in Table 1. We created time-varying functions in such a way that the mean respiratory flow values were used as baseline values and defined triangular-shape functions up to and down to inspiration and expiration, respectively (Fig 1B).


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  		Table 1 Mean SVC and IVC Flow Rates at Rest and at Two Levels of Exercise From the Phase-Contrast Magnetic Resonance Imaging Measurements of Hjortdal and Colleagues [4]
 
Outflow boundary conditions for bilateral pulmonary arteries were assumed as pressure condition of 11 mm Hg, which dropped down to 20% only at the inspiratory phase. That was a typical value and physiologic fluctuation of pulmonary artery pressure after the Fontan operation. The wall condition of the fluid was a nonslip boundary condition of zero velocity.

Computational Simulation
Three-dimensional geometries were divided into computational meshes (nodal points and elements). Nodal points ranged from 10,903 to 16,736, and the number of elements ranged from 61,007 to 95,170. Tetrahedral meshes were created using grid generator code GAMBIT 2.3.16 (Fluent Asia Pacific, Tokyo, Japan), which automatically checked the mesh quality. We took note to adopt identical mesh-interval lengths between the geometries in order to equalize the analytic accuracy. The finite element solver package FIDAP8.7.4 (Fluent Asia Pacific, Tokyo, Japan) was used to solve the Navier-Stokes equation of incompressible transient Newtonian fluid. The parameters were the following: density {rho} = 1,060 kg/m3 and viscosity µ = 4.0 x 10–3 kg/m/s.

Energy Loss and Flow Stagnation
The formula of energy loss was justified by previous papers [8–19].


Formula 1

(1)
where Q is the total flow of the cross sections of each vessel. The mean value of one respiratory cycle was calculated. We also calculated the rate of energy loss to the total inlet energy,


Formula 2

(2)
Stagnation volume was defined as volume of the region where the absolute flow velocity was sufficiently low. In this study we integrated the volume of the regions where the flow velocity was under 0.01 m/second.


Formula 3

(3)
The volume was calculated at the time of the middle points of both the expiratory and inspiratory phases, and the percentage of the total conduit volume was also calculated.


   Results
Top
 Abstract
 Introduction
 Patients and Methods
 Results
Comment
 Discussion
 References
 
Hemodynamics
Simulations of hemodynamics at rest and during exercise of two levels were performed for each conduit size models. The results are presented in the form of color pictures in Figure 2, which illustrate the flow velocity fields and the stagnated region in each model. The indicators show the flow direction and the color indicates the flow velocity.


Figure 2
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  		Fig 2. Flow features and stagnation areas at rest. Flow features of inspiratory and expiratory phases for each conduit size are shown. The color contours represent the velocity magnitude, and the indicators (arrowhead) represent the flow directions. Penetration of the superior vena cava flow into conduits is detected in conduits larger than 20 mm. Backflow in the expiratory phase at the lateral portion of the conduits is detected in conduits larger than 18 mm.

 
At rest, there was some backflow from the SVC into the conduit during the expiratory phase in the conduits larger than 20 mm (Fig 2). This penetration flow from the SVC into the conduit is clinically observed on a postoperative angiographic study of the Fontan patients (Fig 3). Some backflow was detected in the expiratory phase at the lateral portion of the conduits (Fig 2). This result revealed that the conduit acted as a flow reservoir during the expiratory phase and ejected flow during the inspiratory phase in larger conduits. The backflow was observed not only at rest but also at all levels of exercise in spite of the fact that the IVC flow became much higher with the increase of exercise level [3].


Figure 3
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  		Fig 3. Clinical manifestations of Fontan flow. Angiographic study (superior vena cava [SVC]) of a patient after the extracardiac Fontan operation in the expiratory phase. Iopamidol was injected in the SVC above the bifurcation site of innominate vein and right carotid vein using a 4 Fr. pigtail catheter at the velocity 6 mL/second. Flow from the SVC penetrates into the conduit, as if the conduit were something like a flow reservoir.

 
In the inspiratory phase, differences of flow velocity between the lateral side and midline or medial portion of the conduit increased as the conduit size became larger (Fig 2). This dilatory flow of the lateral portion became more prominent during exercise than at rest, causing flow stagnation even in the inspiratory phase.

Energy Loss
The results of the mean energy loss of each graft are listed in Table 2. Energy loss tended to increase as the conduit size decreased. The change was slightly larger between 14 mm (1.549 mW at rest, 3.529 mW during 0.5 W/kg exercise, 5.759 mW during 1.0 W/kg exercise) and 16 mm (1.423 mW at rest, 3.077 mW during 0.5 W/kg exercise, 4.881 mW during 1.0 W/kg exercise) than other conduit size intervals. Although energy loss became larger with the increase of the exercise level, we found these absolute values were significantly small even during strenuous exercise. The energy loss (5.759 mW) calculated during 1 W/kg exercise with the 14 mm graft was only equivalent to 0.118 kcal/day, which is trivial compared with the total energy intake or cardiac energy expenditure of young children 2 to 3 years old.


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  		Table 2 Mean Energy Loss (mW) and Rate of Energy Loss to Total Inlet Energy (%) at Rest and on Two Exercise Levels
 
Energy loss rate per inlet energy also tended to increase as the conduit size became smaller and as the exercise levels increased. The greatest energy-expanding model was the 14 mm conduit during 1.0 W/kg exercise, for which the percentage of energy loss was 12.46%.

Stagnation Volume
Calculated results of stagnation volume of any conduit size in the expiratory and inspiratory phase of all exercise levels are listed in Table 3, and the stagnated regions in the conduits are dark blue in Figures 2, 4, and 5.Go Go The stagnation volume tended to be larger in the expiratory phase than in the inspiratory phase according to the decrease of total flow conditions. With the increase of the exercise level, stagnation decreased (Fig 6). Differences of the stagnation volume between the conduit sizes were prominent. At rest, the 22 mm conduit had 33.9% of the stagnation volume in the expiratory phase (Table 3; Fig 6), whereas the 14 mm conduit had only 9.20% of the stagnation volume under the same conditions. Flow stagnation occurred at the lateral portion of the large size conduit (Figs 2; 4), where backflow at the expiratory phase and dilatory flow at the inspiratory phase occurred on the flow dynamics.


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  		Table 3 Stagnation Volume (mL) and Percentage of Total Conduit Volume (%) at Rest and on Two Exercise Levels
 

Figure 4
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  		Fig 4. Change in flow features during the 0.5 W/kg exercise. The upper half indicates flow features on the expiratory phase and the lower half on the inspiratory phase. The 14, 18, and 22 mm conduits are compared on two exercise levels.

 

Figure 5
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  		Fig 5. Change in flow features during the 1.0 W/kg exercise. The upper half indicates flow features in the expiratory phase and the lower half in the inspiratory phase. The 14, 18 and 22 mm conduits are compared on two exercise levels.

 

Figure 6
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  		Fig 6. Graphs of energy loss and stagnation volume at rest and during exercise. (A) Energy loss at rest and on two exercise levels. (B) The rate of energy loss per inlet energy. (C) Stagnation volume at rest. (D) Stagnation volume during 0.5 W/kg exercise. (E) Stagnation volume during 1.0 W/kg exercise.

 

   Comment
Top
 Abstract
 Introduction
 Patients and Methods
 Results
 Comment
Discussion
 References
 
The optimal conduit size of the Fontan operation has not yet been determined [5–7], but determining such size will become important with the popularity of the Fontan operation among younger patients.

The flow collision between the SVC and IVC has been considered to be problematic, such as early circulatory failure after the Fontan operation [19, 25]. In the present study, nonsteady transient simulation with the respiration revealed the new findings: a penetrating flow from the SVC to the conduit, and the backflow in the lateral portion of the curved conduit in the expiratory phase. The results revealed that the larger conduit had larger flow penetration and larger backflow in the lateral portion of the conduit. This may be attributed not only to the conduit size itself but also to the geometric features of the extracardiac Fontan using large conduits. Although we set the offset between the center of the conduit and the center of the Glenn anastomosis site to be the length of one SVC-radius, the larger conduit had a larger facing area with the Glenn anastomosis site and smaller conduit curvatures. This may be the cause of the flow penetration. Because the previous Fontan simulation studies performed under the steady and continuous flow conditions did not reveal the flow penetration or the stagnated backflow at the lateral portion of the conduits, we thought this result revealed the mechanism of the "respiratory pump" (ie, the conduit acted as a reservoir in the expiratory phase and disgorged the reserved blood in the inspiratory phase). Also from this result, and from the fact that the backflow in the lateral portion of the conduit coincided well with the stagnation regions, we conclude that the penetrating flow and the backflow were the causes of the stagnation.

Efficiency of energy of the "respiratory pump" in the Fontan circulation during exercise has been discussed on clinical studies [3] and on numerical models [19, 20]. Our concern is the amount of energy dissipation due to flow collision of the SVC and IVC. Our results indicated that although energy dissipation at the anastomosis site increased during exercise, its hemodynamic attribution was sufficiently low compared with the value of the energy expenditure calculated by the previous CFD models [8–20]. Considering the form of equation (3) and the fact that Fontan circulation is a low-pressure and slow-flow system, energy loss could depend on pressure more than flow velocity. Pressure relaxation occurs in a large conduit space resulting in calculating low-energy loss. This idea may be supported by the previous numeric studies by de Leval and colleagues [9] and Bove and colleagues [13] that proved patch augmentation in the Fontan anastomosis site reduced the energy loss. On the contrary, the stenotic site where a pressure drop occurs might dissipate a large amount of energy, as evidenced in this calculation method that was first reported by Pekkan and colleagues [17]. The stenotic vessel may have a relatively large amount of wall friction in this low Reynolds number system. The difference between 14 mm and 16 mm was slightly larger than other conduit size intervals. The 14 mm conduit might not always seem to be optimal because it might soon become stenotic with the growth in body size and result in much more energy loss.

In order to evaluate stagnation, we defined an index "stagnation volume": the volume of the region where the absolute value of the velocity vector was small enough, less than the threshold value; 0.01 m/second. The stagnated region could be thought to mean high-risk area of thrombosis formation. This method of evaluation of thrombosis formation risk using a slow velocity region has been adopted in other CFD models such as thrombosis formation of coil-embolized cerebral arterial aneurysm [26, 27].

We adopted the threshold of 0.01 m/second for convenience. Because the hemodynamic mechanism of thrombosis formation has not yet fully been revealed, there is little evidence to determine the stagnation threshold.

Our results showed that a larger conduit had a larger stagnation volume. The stagnation region and flow pattern analysis discussed above revealed that a larger conduit had larger redundant volume on the lateral side. According to our results, grafts of less than 18 mm are thought to be optimal from the viewpoint of flow stagnation. However, the 14 mm conduit may be predicted to increase energy loss with body growth as it already has slightly higher energy loss than other conduits at this body size. The 16 mm and 18 mm conduits proved to be optimal for children of these ages.

Recent CFD models reconstruct patient-specific three-dimensional geometry from MRI or computed tomography to increase simulation accuracy [15, 18–20]. The present study is not a patient-specific one but is the idealized model. An idealized model has advantages for obtaining the essential or practical knowledge such as the indication or the strategies of the operation [17]. Our idealized geometry is based on the averaged data and has better agreement with the clinical observation compared with the previously reported idealized geometries [8–12, 17].

For giving the boundary conditions we adopted the previously reported MRI flow study data [3]. The patients studied in that report were older than those in the present study and older than the mean age of patients undergoing the Fontan operation in many institutions. Flow data during exercise of young patients (2- or 3- year-old patients) after having undergone the Fontan operation are not available. However, in the present study the given flow boundary data were corrected with the body surface area, and the flow ratio of the SVC and IVC (Table 1) were in good agreement with the clinical studies in the patients of these ages [28] and with the inlet boundary flow ratio of the previous CFD models [8–20].

In numeric models, several assumptions may oversimplify the multifactor system and become the study limitations. We did not consider the effect of fenestration, which would naturally change the flow fields. In the boundary conditions only respiratory fluctuations were considered, but actual flow patterns of the Fontan circulation contain pulsatile fluctuations which would make the flow character more complex. We also assumed the vessel wall to be rigid. We did not know the effect of compliances of the pulmonary arteries or the compressive effects of the conduit during the respiratory cycle. However, to confirm that these simplifications are acceptable, further studies are warranted.

We did not simulate adult Fontan cases. At the time of the operation, 20 mm or larger conduits could be considered too large; however, these sizes might become optimal after the patient grows larger. Simulation of adult size geometry, based on adult Fontan patient body-size data, should be performed using the same method.

According to our results with the Fontan operation, relative to body size, larger conduits proved to have redundant space. The 16 mm and 18 mm conduits proved to be optimal for children 2 to 3 years old. However, the optimal size considering the body growth warrants further study.


   Discussion
Top
 Abstract
 Introduction
 Patients and Methods
 Results
 Comment
 Discussion
References
 
DR TAIN-YEN HSIA (Charleston, SC): This is a great presentation. I think this is a very interesting subject and it's a subject that we looked at as well in London about five years ago (Hsia TY, Migliavacca F, Pittaccio S, et al. Computational fluid dynamic study of flow optimization in realistic models of the total cavopulmonary connections. J Surg Res 2004 Feb;116:305–13.) And in our modeling study, we found that for each geometry that one models, there is an optimal conduit size, although our energy loss differences among the various conduit sized are more than yours.

For all the simulation you performed, you purposely built in flow competition between the SVC [superior vena cava] and the IVC [inferior vena cava] pathways. Do you think that this might have resulted majority of the energy loss within the TCPC [total cavopulmonary connection], and therefore hide the energy losses differences between various conduit sizes?

And my second question is, what are the Fontan pressures that you obtain in your simulations with exercise? This is a particularly important point because exercise modeling is not just increasing the flow at the boundaries from MRI [magnetic resonance imaging], as you have done. It is important to know what the corresponding pressure conditions are. With exercise, there are hormonal and neural influences that will change pulmonary and venous vascular elasticity and vascular compliance, which are not accounted for in your modeling. So I would be very interested to see what your pressure conditions are in your modeling as well.

DR ITATANI: I'll answer at first the second question. And actually pressure conditions during exercise were not available, so we defined the pressure condition of 11 mm Hg also during exercise. And we assumed that RP, resistance of pulmonary arteries, were not changed at rest or during exercise. So we assumed 11 mm Hg is the same pressure condition for convenience. And please repeat the first question.

DR HSIA: The first question is that your model's built in competitive flow between the SVC and IVC pathway. And we know that this generally results in the greatest energy loss. Therefore, if you have the majority of your energy loss occurring there, could that have artificially minimized the conduit size effects on energy loss?

DR ITATANI: Actually, in this study, SVC/IVC flow conflict is difficult to evaluate. But I think Fontan system is a low pressure and slow velocity system, and by the definition of the energy loss, which is also called Bernoulli's energy, dependent on pressure plus square of the velocity, energy loss depends much more on pressure gradient than flow conflict. So, in stenosis energy loss becomes drastically increased, so in our model only SVC/IVC flow conflict caused smaller energy loss.

DR JOHN HAWKINS (Salt Lake City, UT): I'd like to ask one quick question. Have these findings impacted your clinical care? Do you now place slightly smaller conduits than you would have four years ago or before you knew this data.

DR ITATANI: We had a case of small children operated Fontan operation, to whom we inserted a relatively large conduit. And after the Fontan operation, CT [computed tomographic] exam was taken and in this case thrombosis was found only at the lateral portion in the conduit.

DR CHRISTOPHER CALDARONE (Toronto, Ontario, Canada): Do you know, is there a relationship between 0.1 m/s blood flow speed and thrombosis.

DR ITATANI: I think this is a very good question. We define the threshold of 0.01 m/s for convenience because the fluid dynamic or hemodynamic mechanism of thrombosis formation was not revealed yet. So we wish to study further about the threshold. In this study we define the threshold for convenience.

DR CALDARONE: Just because we do have another minute, could we just have an informal survey of the audience. If you have, let's say, a 14 kg, 1-1/2 to 2-year old who is going to undergo an extracardiac Fontan, how many would use a 16-mm conduit? 18? 20? 22? (Show of hands.) It sounds like mostly 18s. It looked like a bell curve. All right. Thanks.


   References
Top
 Abstract
 Introduction
 Patients and Methods
 Results
 Comment
 Discussion
 References
 

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