Pediatr Cardiol (2015) 36:1436–1441 DOI 10.1007/s00246-015-1180-y

ORIGINAL ARTICLE

Total Cavopulmonary Connection is Superior to Atriopulmonary Connection Fontan in Preventing Thrombus Formation: Computer Simulation of Flow-Related Blood Coagulation Koichi Sughimoto1 • Kazuki Okauchi2,3 • Diana Zannino4 • Christian P. Brizard1,4 Fuyou Liang5,6 • Michiko Sugawara2 • Hao Liu2,6 • Ken-ichi Tsubota2



Received: 14 December 2014 / Accepted: 29 April 2015 / Published online: 31 May 2015 Ó Springer Science+Business Media New York 2015

Abstract The classical Fontan route, namely the atriopulmonary connection (APC), continues to be associated with a risk of thrombus formation in the atrium. A conversion to a total cavopulmonary connection (TCPC) from the APC can ameliorate hemodynamics for the failed Fontan; however, the impact of these surgical operations on thrombus formation remains elusive. This study elucidates the underlying mechanism of thrombus formation in the Fontan route by using a two-dimensional computer hemodynamic simulation based on a simple blood coagulation rule. Hemodynamics in the Fontan route was simulated with Navier–Stokes equations. The blood coagulation and the hemodynamics were combined using a particle method. Three models were created: APC with a square atrium, APC with a round atrium, and TCPC. To examine the effects of the venous blood flow velocity, the velocity at rest and during exercise (0.5 and 1.0 W/kg) was measured. The

total area of the thrombi increased over time. The APC square model showed the highest incidence for thrombus formation, followed by the APC round, whereas no thrombus was formed in the TCPC model. Slower blood flow at rest was associated with a higher incidence of thrombus formation. The TCPC was superior to the classical APC in terms of preventing thrombus formation, due to significant blood flow stagnation in the atrium of the APC. Thus, local hemodynamic behavior associated with the complex channel geometry plays a major role in thrombus formation in the Fontan route.

Electronic supplementary material The online version of this article (doi:10.1007/s00246-015-1180-y) contains supplementary material, which is available to authorized users.

Classical Fontan, namely atriopulmonary connection (APC), has been strongly associated with a dilatation of the right atrium (RA) that could occur over time, causing arrhythmia and thickening of the atrial wall, thereby resulting in thrombus formation [1, 3, 11, 21, 22]. A report showed a high incidence (33 %) of thrombus formation in patients who underwent Fontan surgery, which was detected without clinical evidence of thromboembolic complications [1]. The post-Fontan status has also been associated with a low cardiac output, known as a failing Fontan [7, 24]. Converting the venous return flow from the inferior vena cava (IVC) from the APC to a total cavopulmonary connection (TCPC) by placing a conduit has been adopted for a failed Fontan and has gained acceptable outcomes [20, 25, 30]. However, the reason why a TCPC is superior to an APC remains controversial in terms of hemodynamics [8] and

& Ken-ichi Tsubota [email protected] 1

Department of Cardiac Surgery, The Royal Children’s Hospital, Melbourne, Australia

2

Department of Mechanical Engineering, Graduate School of Engineering, Chiba University, Chiba, Japan

3

Hitachi Construction Machinery, Tokyo, Japan

4

Murdoch Childrens Research Institute, Melbourne, Australia

5

School of Naval Architecture, Ocean and Civil Engineering (NAOCE), Shanghai Jiao Tong University, Shanghai, China

6

Shanghai Jiao Tong University and Chiba University International Cooperative Research Centre (SJTU-CU ICRC), Shanghai Jiao Tong University, Shanghai, China

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Keywords Fontan  Thrombus  Congenital heart disease  Computer simulation  Hemodynamics

Introduction

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coagulation [21, 22]. This study aimed to elucidate the underlying theoretical mechanism of thrombus formation in the Fontan route, by using a two-dimensional (2D) computer simulation based on a simple blood coagulation rule combined with hemodynamics models of an APC and a TCPC.

Materials and Methods Blood coagulation was assumed to occur during local flow stagnation. Hemodynamics in the Fontan route was simulated using 2D Navier–Stokes (NS) equations. In a computer simulation of thrombus formation, blood coagulation and its associated hemodynamics were coupled using a particle method. Hemodynamics Model of the Fontan Route Two-dimensional adult-sized Fontan geometries of a blood flow channel were modeled as an APC square, an APC round, and a TCPC. ‘‘Square’’ or ‘‘round’’ in APC models denotes the shape of the right lower corner of the RA. APC models were designed as an adult patient in failing Fontan with dilated RA. To focus on the difference mainly between the failing Fontan patient with dilated RA and the patient with TCPC route, the size of the APC square model was designed as follows: the square RA of 80 mm in length on each side, the vena cavae of 40 mm in length and 20 mm in width, and the pulmonary artery (PA) of 100 mm in length and 14 mm in width. The RA of the APC round model has the rounded lower right corner with a 30-mm curvature radius. With regard to the size of the TCPC model, the length and width of the extracardiac graft were 73 and 20 mm, respectively. The blood flow velocity in the inferior vena cavae, as the inlet boundary condition, was set at 0.1025–0.2083 m/s to express the velocity condition at rest and during exercise (0.5 W/kg and 1.0 W/kg) (Table 1), whereas the flow from the superior vena cava was set from 0.0808 to 0.0814 m/s.

Table 1 Velocity from the SVC and IVC

Here, the velocity values in the two dimensions were determined from published measurements [10]. At the pulmonary arteries as the outlet boundary condition, freeoutflow and zero-pressure conditions were created. A nonslip condition was established at the wall. The density and the kinematic viscosity of the blood were set as 1.06 9 103 kg/m3 and 4.43 9 10-6 m2/s, respectively, giving the Reynolds number an order of a hundred. Thus, the 2D hemodynamics of the Fontan route was determined by the channel geometries of blood flow and velocity values at the vena cavae. Model of Thrombus Formation Under Blood Flow The particle method is generally used for the computer simulation of thrombus formation under blood flow [5, 14]. Here, two types of blood components, normal blood and thrombus, were modeled using computed particles. Incompressible viscous flow of blood, which was based on continuity and the NS equations, was expressed by calculating particle motions using the moving particle semiimplicit method [15]. A simple blood coagulation rule was employed to express more thrombus formation at flow stagnation [5, 26], according to Virchow’s triads. Spring force fcij f c ¼ f c ¼ K c ð rij Þ  r0 Þrij = rij ð1Þ ð rij \r c Þ ij

ji

was applied between two thrombus particles i and j to express blood coagulation, in which rij = rj-ri, ri and rj are the position vectors of particles i and j, respectively; r0 is the natural length of the spring; kc is the spring constant; and rc is the threshold distance for particle interaction. The blood coagulation was combined with the local blood flow by substituting spring force fcij into NS equations as the external force when solving the blood flow using the MPS method [14, 28, 29]. In addition, a normal blood particle was assumed to change to a thrombus when it neighbored any thrombus particle, and its shear rate c_ (as a measure of stagnation) was zero. With respect to the set of simulation

SVC

IVC

3D l/min/m2

2D mean velocity m/s

3D l/min/m2

2D mean velocity m/s

Rest

1.26

0.0808

1.6

0.1025

0.5 W/kg

1.27

0.0814

2.58

0.1654

1.0 W/kg

1.27

0.0814

3.25

0.2083

3D data is referenced from published measurements [10] IVC inferior vena cava; SVC superior vena cava; 2D two dimensional; 3D three dimensional

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parameters, the spatial resolution was d0 = 1 mm in terms of mean particle distance, and the total number of computed particles was 15,925 in the APC square, 15,224 in the APC round, and 11,142 in the TCPC. In Eq. (1) of the coagulation force, kc = 5.0 9 10-2 N/m; r0 = d0; and rc = 1.5 d0. Statistics To compare the area of thrombus burden over time between the three blood flow channel models and the three flow velocities, the area under the curve was used with the jackknife resampling method [4] employed to estimate the variability.

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Effects of Venous Flow Velocity To examine the effects of blood flow velocity at the vena cavae, thrombus formation was compared among three velocity conditions at rest as well as in the presence of light and moderate exercise using the APC square model. The results showed that every condition resulted in thrombus formation at the right lower corner over time (Fig. 2). A lower flow rate caused more thrombus formation. A reduction in thrombus formation was observed during mild exercise (0.5 W/kg), whereas this was more evident during moderate exercise (1.0 W/kg). The comparisons of the area under the curve between two models showed significant differences (rest vs. 0.5 W/kg: p \ 0.0001; rest vs. 1.0 W/ kg: p \ 0.0001; 0.5 W/kg vs. 1.0 W/kg: p \ 0.0001).

Results

Discussion

Effects of Fontan Route Geometry

Initiation of the Fontan procedure has increased the survival rate of patients with single ventricular anatomy [6]. However, the classical Fontan, including the APC route, has been associated with several postoperative issues due to the dilatation of the RA that induces fibrotic change and thickening of the atrial wall, resulting in supraventricular arrhythmia and thrombus formation [7, 24]. Furthermore, these dilated RA may decrease the efficiency of blood delivery to the PA [16]. Conversion from the APC to the TCPC by using a graft may ameliorate venous flow delivery to the lungs [8], ensuring a better quality of life. Although the indication and timing for TCPC conversion is mainly determined through experience-based decisions [12, 25, 31], the underlying mechanism of thrombus formation in the RA and the reason why the TCPC is superior to the classical route in terms of hemodynamics [17, 18] and prevents thrombus formation are not conclusive yet. In this study, we have proven that thrombus formation is largely influenced by the following: (1) the configuration of the Fontan route from the vena cavae to the PA and (2) the speed of the flow in the Fontan pathway. Firstly, with regard to the relationship between the configuration of the Fontan route and thrombus formation, we found that in the dilated atrium, the blood flow rate is reduced once blood enters from the IVC to the RA due to its caliber change. The flow in the atrium is stagnated, which is more evident in the corner or hinge points where the blood clots therefore creating a thrombus. Once a thrombus is created, it grows in size, and all of a sudden, a portion of the thrombus is disengaged and released into the outflow toward the PA. Thrombi embolization into the PA in a Fontan patient is life-threatening; thus, once a thrombus is detected, a TCPC conversion is required immediately [9]. Balling and his colleagues [1] have

Thrombus formation was simulated for the APC and TCPC models with the venous velocity at rest and during exercise. In terms of flow pattern from the vena cavae to the PA, there was a huge difference between the TCPC and the APC. The TCPC route showed a smooth flow from the vena cavae to the pulmonary arteries without significant stagnation in the TCPC route, whereas in the APC the velocity suddenly decreased once the blood entered from the IVC to the dilated atrium due to its caliber change; hence, blood stagnation occurred in the atrium. In the APC square, the particles adjacent to the right lower corner were hardly replaced by the other particles; the blood flow showed more stagnation in the atrium than that in the APC round. Over time, a thrombus was formed and it increased in size in the Fontan pathway (Fig. 1a). The area of summation of the thrombi increased over time (Fig. 1b). The APC square model showed the largest thrombus formation in terms of both total amount and the maximum thrombus size, followed by the APC round model. The TCPC showed the smallest thrombus in the route. The comparisons of the area under the curve between two models showed significant differences (APC square vs. APC round: p \ 0.0001; APC square vs. TCPC: p \ 0.0001; APC round vs. TCPC: p \ 0.0001). Although the APC round reached a plateau in terms of the thrombus area in the middle of the observation period, from this point, the APC square showed a continuous increase in the thrombus area over time until the end of the observation. There were several acute decreases in the thrombus area in the APC models, at which a large block of a thrombus was disengaged from the atrium and subsequently flowed into the pulmonary artery.

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Fig. 1 a Comparison of thrombus formation at 1.0 of total observation time. Atriopulmonary connection (APC) (left); APC round (center); total cavopulmonary connection (TCPC) (right). b Total thrombus area compared among three types of Fontan routes

Fig. 2 Total thrombus area in the route at different velocities

previously reported on the incidence of thrombus formation in Fontan patients, comparing two groups, namely with and without thrombus formation. In 33 % of the patients that underwent the Fontan procedure, thrombus formation was observed in the atrium by echocardiography. Despite no significant differences in the Fontan pathway (p = 0.14), the no-thrombus group consisted of 9 TCPC out of 35 patients (26 %), whereas the thrombus group included 1 TCPC out of 17 patients (5.8 %). This evidence

supports our results. In the current study, we compared three types of Fontan pathways. As we expected, the TCPC showed the lower incidence for thrombus formation, whereas the APC Fontan was more prone to cause thrombus formation. When the atrium has an angled corner, the blood flow showed more stagnation at the corner allowing it to create more thrombus, and the angled corner would stand for the edge of the atrium such as the appendage. These findings explain that the shape of the Fontan route and its complex local blood flow can influence the formation of a thrombus. Therefore, TCPC conversion from the APC Fontan can be a reasonable solution for the prevention of thrombus formation in the route. Further, in terms of the flow rate from the IVC, our results have revealed that a faster flow rate during exercise is less likely to form a thrombus, whereas the slow flow rate at rest is apt to develop thrombus over time. This finding suggests that patients with reduced cardiac output are more likely to form a thrombus and thus should be treated with strict anticoagulation therapies such as warfarin [2]. Virchow’s triad [32] is often used to explain the mechanism of coagulation that consists of the following:

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(1) congestion of blood flow, (2) change in the characteristic of blood, and (3) change in the characteristic of the vessel walls. The first two factors could be explained by the findings of our study, whereas the third factor, which is a characteristic of the vessel wall, was not taken into consideration in this study. However, this factor is also important because an insufficient amount of the intima of the endothelium stimulates thrombus formation [13, 19]. In terms of the coagulation system, previous reports have revealed that patients who underwent the Fontan procedure show abnormalities in blood coagulation, fibrinolysis, and platelet activation [23, 27]. They exhibit enhanced platelet activation and endothelial injury, heightened thrombin formation, and impaired fibrinolysis. Although our coagulation model has revealed that morphological abnormalities and local complex blood flow could influence thrombogenesis in the Fontan route, these complex factors should also be addressed simultaneously using other approaches. This study has limitations because this is a simplified model that focuses on the local blood flow and thrombus formation which resembles biological blood coagulation. In the failing Fontan, the dilated atrium often loses its contractility even maintaining a sinus rhythm. Therefore, we have applied a fixed atrial wall model of the dilated atrium. Simulating blood flow in the contracting atrium is yet to be demonstrated due to technical difficulty of complex calculations. In addition, the fibrinolytic system coexists with the coagulation system in the actual biophysical condition, whereas the fibrinolytic system was not included in this study. Finally, the Fontan route was displayed as a 2D simulation to simplify and focus on the differences in configuration between the APC and TCPC routes. We are currently conducting studies involving a patient-specific 3D thrombus formation model to resolve this issue. Further studies are required to clarify the relationship between our model parameters and the clinical conventional coagulation markers as well as the effect of conventional anticoagulation drugs such as warfarin and aspirin. There is also a need to determine which types of patients require stricter anticoagulation therapy. Assembling the clinical data such as catheterization or cardiac MRI and evidence of thrombus formation can create a robust patient-specific model that may more reliably predict thrombus formation in Fontan circulation and indicate the timing for TCPC conversion.

Conclusions A 2D computer simulation method based on a simple coagulation rule and local complex hemodynamics demonstrated the mechanism of thrombus formation in the Fontan

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route. TCPC is superior to the classical APC in terms of preventing thrombus formation. The flow channel geometry of the APC route stagnates the blood flow, which in turn facilitates thrombus formation. A slower venous flow from the IVC is more likely to form a thrombus. The results of this study suggest that a complex local flow based on the geometry of the blood vessel is a major factor that influences thrombus formation in the Fontan route. The proposed simulation model can contribute to the assessment and prediction of the most efficient surgical approach that would simultaneously minimize the occurrence of local thrombus formation. Acknowledgments This study was partially supported by the Inohana Alumni Association of the Chiba University of Medicine (12046) and a research grant, JSPS (25630046). Conflict of interest

There is no conflict of interest to declare.

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Total Cavopulmonary Connection is Superior to Atriopulmonary Connection Fontan in Preventing Thrombus Formation: Computer Simulation of Flow-Related Blood Coagulation.

The classical Fontan route, namely the atriopulmonary connection (APC), continues to be associated with a risk of thrombus formation in the atrium. A ...
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