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Original research article
Effect of Fontan geometry on exercise haemodynamics and its potential implications
  1. Elaine Tang1,
  2. Zhenglun (Alan) Wei2,
  3. Kevin K Whitehead3,
  4. Reza H Khiabani2,
  5. Maria Restrepo2,
  6. Lucia Mirabella2,
  7. James Bethel4,
  8. Stephen M Paridon3,
  9. Bradley S Marino5,
  10. Mark A Fogel3,
  11. Ajit P Yoganathan1,2
  1. 1 School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA
  2. 2 Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology, Emory University, Atlanta, Georgia, USA
  3. 3 Division of Cardiology, Children’s Hospital of Philadelphia, Philadelphia, Pennsylvania, USA
  4. 4 Westat Inc, Rockville, Maryland, USA
  5. 5 Division of Cardiology, Ann and Robert H. Lurie Children’s Hospital of Chicago, Chicago, Illinois, USA
  1. Correspondence to Dr Ajit P Yoganathan, Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology, Emory University, Technology Enterprise Park, Suite 200, 387 Technology Circle, Atlanta, GA 30313-2412, USA; ajit.yoganathan{at}


Objective Exercise intolerance afflicts Fontan patients with total cavopulmonary connections (TCPCs) causing a reduction in quality of life. Optimising TCPC design is hypothesised to have a beneficial effect on exercise capacity. This study investigates relationships between TCPC geometries and exercise haemodynamics and performance.

Methods This study included 47 patients who completed metabolic exercise stress test with cardiac magnetic resonance (CMR). Phase-contrast CMR images were acquired immediately following supine lower limb exercise. Both anatomies and exercise vessel flow rates at ventilatory anaerobic threshold (VAT) were extracted. The vascular modelling toolkits were used to analyse TCPC geometries. Computational simulations were performed to quantify TCPC indexed power loss (iPL) at VAT.

Results A highly significant inverse correlation was found between the TCPC diameter index, which factors in the narrowing of TCPC vessels, with iPL at VAT (r=−0.723, p<0.001) but positive correlations with exercise performance variables, including minute oxygen consumption (VO2) at VAT (r=0.373, p=0.01), VO2 at peak exercise (r=0.485, p=0.001) and work at VAT/weight (r=0.368, p=0.01). iPL at VAT was negatively correlated with VO2 at VAT (r=−0.337, p=0.02), VO2 at peak exercise (r=−0.394, p=0.007) and work at VAT/weight (r=−0.208, p=0.17).

Conclusions Eliminating vessel narrowing in TCPCs and reducing elevated iPL at VAT could enhance exercise tolerance for patients with TCPCs. These findings could help plan surgical or catheter-based strategies to improve patients’ exercise capacity.

  • congenital heart disease; Fontan procedure; exercise hemodynamics; computational fluid dynamics

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The Fontan surgery is a common palliative technique for children born with single ventricle heart defects. The surgery is completed in a series of staged procedures which culminate in the total cavopulmonary connection (TCPC). The TCPC connects both the superior vena cava (SVC) and inferior vena cava (IVC) to the left and right pulmonary arteries (LPA and RPA), bypassing the right heart.1 The Fontan pathway (FP), the final staged procedure, is most often completed by anastomosing the IVC to the SVC and pulmonary arteries (PAs) in the form of either intra-atrial or extracardiac conduits. Even though the completion of the TCPC results in favourable short-term outcomes, long-term complications are still prevalent in Fontan patients,2 3 including limited exercise tolerance years after the TCPC completion.4–8

Primary measurements of exercise performance are peak oxygen consumption, oxygen consumption at ventilatory anaerobic threshold (VAT), peak exercise heart rate (HR), arterial oxygen saturation and cardiac output. Fontan patients show poor exercise capacity indicated by decreased exercise performance variables compared with healthy subjects.4 9 In the past decade, growing evidence suggests the relevance of Fontan haemodynamics and patient’s exercise performance.7 8 10–12 In particular, patient’s exercise performance is associated with TCPC power loss during exercise.13 Moreover, it was found that Fontan haemodynamics are affected by TCPC geometry during resting conditions;14 however, it is still unknown if there is a direct connection between TCPC geometry, its associated haemodynamics and exercise performance. This study hypothesised that TCPC geometry, TCPC haemodynamics and patient exercise performance are all interconnected which may provide insight into TCPC anatomical optimisation for improving patient exercise performance.


Patient cohort

Single ventricle patients with TCPC palliation were prospectively enrolled at The Children’s Hospital of Philadelphia. Patients with a pacemaker or implanted metal that precluded CMR imaging were excluded. This study included 52 consecutive patients. Inclusion criteria comprised of patients with a minimum age of 12 years, the TCPC as the sole source of pulmonary blood flow (besides aortic to pulmonary collateral flow) and the ability to perform a metabolic exercise stress test using a stationary cycle ergometer. The ability to perform and exercise test was determined by age and either prior adequate completion of a metabolic exercise test or discussions with the primary cardiologist regarding patient suitability. Data in which the patient could not reach anaerobic threshold (determined by V-slope method) were deemed inadequate, and the patient was excluded from further participation. Two patients did not complete the entire metabolic exercise stress test; therefore, they were disqualified. Additionally, two patients with CMR artefacts and one patient with a large baffle leak were excluded from this study. As a consequence, a total of 47 consecutive patients were involved in the analysis. A subset of the patients (n=30) was also studied by Khiabani et al. 13 The study was approved by the Institutional Review Boards at both institutions, and all patients signed informed consent.

Exercise stress test

Subjects first completed a routine maximal metabolic exercise stress test using a ramp cycle protocol. Maximal minute oxygen consumption (VO2 at peak exercise), HR, work rate and VO2 at VAT were obtained using a metabolic cart (SensorBiomedics V29, Yorba Linda, California, USA). VAT was measured using the V-slope method.

CMR imaging

After the metabolic stress test, resting and exercise CMR studies were performed. Steady-state free precession electrocardiographically gated contiguous CMR images under the resting condition were acquired in the transverse plane from the diaphragm to thoracic inlet using a Siemens Avanto 1.5 Tesla whole-body MRI scanner (Siemens Medical Systems, Malvern, Pennsylvania, USA) to acquire anatomy and TCPC geometry. Through-plane phase-contrast MRI (PC-MRI) was used to acquire velocity profiles across the venae cavae, branch PAs, the aortic valve and descending aorta (DAO) over the cardiac cycle under the resting breath-held condition.

After the resting CMR acquisition, the patients were slid partially out of the bore of the MRI scanner. Lower limb exercise using an MRI-compatible supine bicycle ergometer (Lode BV, Groningen, the Netherlands) was performed which allowed revolutions per minute(RPM)-independent workload ranging from 10 to 250 W. The workload was set initially at 20 W and then increased at a rate of 20 W/min progressively to develop acquire HR. Immediately afterwards, the subject was returned to isocenter for imaging within 10 s. HR was monitored continuously. PC-MRI across the SVC, ascending aorta and DAO at the level of the diaphragm was acquired as three separate PC-MRI maps. For each acquisition, the patients repeatedly exercised to the target HR (at VAT), which was determined during the exercise stress test. Images were acquired with free breathing. The velocity maps from PC-MRI were averaged. The study lasted approximately 90 min with the subject supine.

Patient-specific anatomy was obtained from resting CMR. The CMR slices were interpolated with adaptive control grid interpolation and segmented with a bouncing ball algorithm.6 The three-dimensional (3D) geometry was then reconstructed using the level-set method. Surface fitting was performed with Geomagic Studio (3D Systems, Rock Hill, South Carolina, USA). While the transverse slice thicknesses of the images acquired for this study were 3–5 mm, the data were interpolated to achieve a nearly isotropic resolution (voxel size: 1.055–1.719 mm). The adaptive control grid interpolation and 3D reconstruction methods used to perform this upsampling were validated for use with the total cavopulmonary connection (TCPC) geometry, demonstrating 0.96% error for PA diameter measurement and 1.77% error on radius curvature.15 Additionally, we assessed the signal-to-noise ratio (SNR) after the data acquisition. The SNR ranged from 50% to 160% (78.9±49%), which is in line with the previous literature.16 Through-plane PC-MRI at both resting and exercise conditions was segmented by using the in-house code,15 and integrated to calculate the associated flow rates.

Geometric analysis

Vascular Modeling ToolKit V. 1.0.1 (Orobix, Bergamo, Italy) was used in this study to compute vessel centerlines, radii and bifurcation vectors. Minimum, mean and maximum vessel diameters; minimum/maximum diameter ratio; vessel offsets; and connection angles were computed as in our previous work.17 To account for variation in patient size, vessel diameters were normalised by the square root of patient body surface area (BSA).11 Normalised minimum PAdiameter was defined as the overall minimum of LPA and RPA diameters. To include the influence of minimum diameter of all vessels, a TCPC ‘diameter index’ was computed by averaging the normalised minimum diameter of all vessels entering into or leading out of the TCPC:

Embedded Image

where n is the number of vessels present at the TCPC, and BSA is the body surface area (m2).

In this way, the influence of narrowing/stenosis at different vessels can be captured with one variable. The magnitude of caval offset (distance between FP and SVC) was normalised by mean FP diameter, given previous conventions.18–21

Haemodynamic assessment

Patient-specific haemodynamics were evaluated using a previously validated in-house computational fluid dynamics (CFD) solver,11 22 23 with cardiac cycle-averaged flow boundary conditions obtained from PC-MRI. Diaphragm motion during exercise made positioning the FP flow plane unreliable (ie, FP immediately above the hepatic veins); therefore, exercise DAO flow rate was substituted for exercise FP flow rate as a boundary condition in the CFD models.24 The in vivo LPA/RPA flow splits obtained from PC-MRI were used as outflow boundary conditions to ensure mass conservation. Vessel extensions of 10 and 50 mm were added to the inlets and outlets, respectively, normal to the cross sections, to ensure flow stability. The flow extensions also minimised boundary flow recirculation and reduced the effect of the prescribed inlet velocity profile on TCPC haemodynamics. The TCPC domain was postprocessed to obtain the fluid domain without the flow extensions. TCPC power loss (Embedded Image ) was defined as

Embedded Image

where p is the static pressure relative to the FP measured from CFD, A is the area of the inlet/outlet and v the velocity. Embedded Image was normalised  to calculate the indexed power loss25 Embedded Image , where Q is the total systemic return and ρ is the blood density (1060 kg/m3).

Statistical analysis

Statistical analysis was performed using IBM SPSS Statistics (V. 22, IBM, Armonk, New York, USA). Normality was tested with the Shapiro-Wilk test. Pearson’s chi-square (or Spearman’s rank correlation for variables that are not normally distributed) test was used to discover the relationship between categorical variables. Paired t-test (or Wilcoxon signed-rank test) and repeated-measures analysis of variance (or Friedman test) were used to compare geometric parameters among vessel types in the entire cohort. Student’s t-test (or Mann-Whitney test) was used to compare geometric parameters, iPL at VAT and exercise parameters between intra-atrial and extracardiac groups. Bivariate correlation was carried out to assess correlations between geometric variables and iPL at VAT. TCPC geometric variables were found to be significantly associated with iPL at VAT; multiple variate regression was therefore performed using forward stepwise procedures to identify the best geometric predictors of iPL at VAT. The best geometric predictor and iPL at VAT were then correlated with exercise stress test parameters using Pearson’s correlation (or Spearman’s rank correlation for data that are not normally distributed). Statistical models were screened for outliers based on the IQR. Outliers are defined as data points that are below (lower quartile−1.5×IQR) or above (upper quartile+1.5× IQR). For all analyses, p value ≤0.05 (two-tailed) was considered significant.


Cohort averages

Patient demographic and anatomic data are summarised in table 1. The computed geometric parameters for the cohort are summarised in table 2. The FP on average had the largest normalised minimum diameter compared with other vessels (p<0.001). LPA (31 out of 47 subjects) was the vessel that most frequently had the smallest normalised minimum diameter (p=0.029). iPL at VAT and exercise performance parameters are presented in table 3. There are no significant differences between intra-atrial and extracardiac patients in iPL at VAT, TCPC diameter index and exercise performance variables.

Table 1

Patient demographic and anatomic information (n=47)

Table 2

Summary of geometric parameters, represented as mean±SD (n=47)

Table 3

Summary of TCPC haemodynamics and exercise performance parameter (n=47)

The patient-specific geometries and streamtraces (coloured by velocity magnitude of all patients), along with the iPL at VAT values, are shown in figure 1. Vessel narrowing was often evident in the FP (eg, patient (xlvii) in figure 1) and the LPA (eg, patient (xxxvii) in figure 1). Regions with vessel narrowing corresponded to regions of relatively high velocity and thus relatively high energy loss.11

Figure 1

Patient anatomies with streamtraces colour-coded by velocity magnitude. The number underneath each figure presents TCPC power loss. The patient is ordered with an ascending TCPC power loss. TCPC, total cavapulmonary connections.

Correlations between TCPC geometry, TCPC haemodynamics and exercise performance

For statistical correlations, two patients were excluded based on age (33 and 42, greater than (upper quartile +1.5×IQR]). The significant correlations between iPL at VAT and geometric variables for the 45 patients are summarised in table 4. Multivariate regression showed that the TCPC diameter index (which included the influence of vessel narrowing of all vessels present) was the strongest geometric predictor of iPL at VAT (r=−0.819, p<0.001).

Table 4

Significant correlations between iPL at VAT and geometric parameters (n=45)

Correlations between exercise stress test parameters, iPL at VAT and TCPC diameter index are summarised in table 5 and illustrated in figure 2. As observed from the correlation coefficients (r values), the negative correlation between iPL at VAT and TCPC diameter index is strong (r=−0.819). There are weak-to-moderate negative correlations between iPL at VAT and exercise performance parameters (r=−0.465 for VO2 VAT and r=−0.510 at peak exercise). Moderate positive correlations between TCPC diameter index and exercise performance parameters are observed (r values range from 0.368 to 0.485). All correlations were further evaluated by including the two age outliers in the correlations presented in table 5 as a confirmatory analysis using a non-parametric method (Spearman’s rank correlation). After including the outliers, all except one correlation were identified as significant (p value≤0.05). The exception was for the correlation between work at VAT/weight and TCPC diameter index (r value=0.284, p value=0.053).

Table 5

Bivariate correlations between iPL at VAT, TCPC diameter index and exercise performance (n=45)

Figure 2

Schematic of significant correlations between TCPC haemodynamic, geometry and exercise performance. iPL, indexed power loss; TCPC, total cavapulmonary connections; VAT, ventilatory anaerobic threshold.


In Fontan patients, normalised FP diameters were negatively correlated with iPL at VAT. The FP, on average, carries the bulk of the total systemic venous return (73%±14%) during the exercise condition. Therefore, it is reasonable that vessel narrowing of the FP was associated with high iPL at VAT. Additionally, the LPA was the vessel with smallest minimum vessel diameter in the TCPC for more than half of the patients. It has been shown previously that obstruction of cavopulmonary flow was mainly observed in the FP and the LPA in extracardiac Fontan patients.26 The presence of FP and LPA narrowing are prevalent, resulting in higher iPL at VAT (figure 1). Therefore, the TCPC diameter index, a compound index which accounts for vessel narrowing at all the TCPC vessels, was defined and found to be the significant predictor of iPL at VAT among the parameters in this study. This highlights that vessel diameter is the primary geometric determinant of iPL at VAT which has been inversely correlated with exercise performance,13 and the relative placement of the inferior and superior vessels (caval offset magnitude and connection angle) was of lesser importance for iPL at VAT. The major reason is the dominant effect of vessel stenosis on TCPC power loss. This does not necessarily mean that caval offset is not important. A previous study with an idealised TCPC model demonstrated that a caval offset of one FP diameter reduced power loss by half when compared with a model without any caval offset.27 Considering 39 out of 45 patients included in this study had caval offset magnitudes less than half of one FP diameter, the lack of negative correlation between caval offset and iPL at VAT could be due to the small caval offset of this patient cohort (0.26±0.36 mm/mm).

Given the significant association between TCPC diameter index and iPL at VAT, it is important to investigate the connection with patient exercise performance. In single ventricle circulation, a low pulmonary vascular resistance (PVR) is essential to achieve the cardiac output increase required during exercise and is, therefore, important for exercise performance.20 The use of oral pulmonary vasodilators has been suggested to improve exercise capacity in Fontan patients.28 29 In a previous study with six Fontan patients, PVR was reported as 2.8±0.9 mm Hg/(L/min/m2) during peak exercise.30 In this same cohort, it was found that TCPC resistance at VAT was on average 0.58±0.49 mm Hg/(L/min/m2), and could be as high as 2.23 mm Hg/(L/min/m2) (for the patient with the lowest TCPC diameter index of 10.8 mm/m). These data imply that TCPC resistance and PVR can be the same order of magnitude, and thus TCPC resistance is not negligible in Fontan patients and can contribute, or even become the dominant factor, in the ability to increase pulmonary blood flow required for effective exercise. Given vasodilators target only reducing PVR and that TCPC resistance can exceed PVR in some patients at exercise, these results highlight the impact of TCPC geometry on exercise performance, by reducing TCPC resistance and minimising power loss, decreasing the overall impediment to flow of systemic venous return.

Khiabani et al,13 was the first to establish negative correlations between iPL at VAT with patient minute oxygen consumption at VAT with a subset of the patients (n=30) included in this study. The current study extends these findings by investigating the most important geometric characteristic that could be relevant to this correlation. Based on the correlations between the TCPC diameter index, iPL at VAT and exercise performance, we provide further evidence that TCPC geometry and haemodynamics are important to exercise performance. The negative correlations between iPL at VAT with exercise performance, as well as the positive correlations between TCPC diameter index with exercise performance (figure 2), suggest that eliminating vessel stenosis by surgical intervention or stimulating vessel growth within the TCPC may minimise TCPC energy dissipation, thereby allowing patients to have improved exercise capacity.

There are several limitations in this study. iPL at VAT computed from this study was an approximation of the physiology due to the assumptions made in the numerical simulations. Moreover, time-averaged boundary conditions (over both respiratory and cardiac cycles) and rigid wall assumptions were applied. Time-averaged boundary conditions may affect the resulting iPL values. However, the effect of geometry remains dominant compared with the effect of instantaneous flow. Additionally, the flow measurement of FP is unreliable because of the drastic motion of the FP during exercise. Therefore, patient-specific DAO flow had to be used as the surrogate for the FP. According to Wei et al,26 it is a reasonable assumption and should not affect the conclusion of this study. Furthermore, the use of a single velocity component at the boundary condition is indeed a limitation of the study. The study is retrospective and does not include a 4D flow MRI protocol. 4D flow MRI is not a standard of care practice at most institutions, and currently, requires a prospective study for use. This limitation was mitigated through the use of inlet flow extensions in an attempt to introduce more accurate flow physics at the physiological IVC location. Moreover, the effect of collateral flow and fenestrations were ignored in the simulations, which may influence the haemodynamics. Another limitation is that the metabolic exercise stress test was performed in the upright position, whereas the exercise CMR was acquired in the supine position. Certainly, there are physiological differences between these two positions. In general, it requires 10–20 W more work to achieve the target HR, hence higher work at VAT, in the supine compared with the upright position. Because we targeted the HR rather than the work rate associated with VAT at upright exercise for the supine CMR study, the haemodynamics should be as similar as possible. Given there were strong correlations between VO2 at VAT and work at VAT observed in these patients, the relationship of elevated iPL and lower exercise performance in the supine position should be similar in the upright position.

Ongoing research is being carried out to evaluate the impact of these assumptions. To further understand the major limiting factor(s) of Fontan patient exercise capacity, the influence of patient ventricular function should also be considered in future studies.

Despite these limitations, this study establishes the relevance of local TCPC geometry and haemodynamics to exercise performance of Fontan patients. Understanding these relationships can potentially help surgeons and clinicians derive novel strategies to improve patient exercise performance, as well as predicting patient outcome and identify patients prone to exercise intolerance.


This study investigated correlations between TCPC geometric characteristics, iPL at VAT and exercise performance variables. We demonstrated a clear relationship between smaller TCPC diameter index, elevated iPL at VAT and worse exercise performance. These findings suggested that eliminating vessel narrowing in TCPCs and reducing elevated iPL at VAT could improve Fontan patient exercise tolerance.

Key messages

What is already known on this subject?

Exercise intolerance is one of the long-term complications for Fontan patients with total cavapulmonary connections (TCPCs). It was shown that TCPC power loss during exercise is significantly negatively correlated with a patient’s exercise performance. Moreover, significant correlations were found between TCPC geometrical characteristics and TCPC power loss under resting conditions.

What might this study add?

This study presents associations between TCPC geometrical characteristics, TCPC haemodynamics at the ventilatory anaerobic threshold and patient’s exercise performance. Since the TCPC geometry is modifiable by surgeries, this paper lays the groundwork for designing better surgical strategies to achieve better patient’s quality of life.

How might this impact on clinical practice?

Fontan patients suffer from many complications. Limited exercise universally exists and hinders the patient’s quality of life. This study reveals the relationship between TCPC geometrical characteristics and patient exercise performance, suggesting that better designed TCPC anatomies can potentially mitigate the exercise intolerance of Fontan patients. This has a great impact on congenital heart disease treatment strategies.


This study was supported by the National Heart, Lung, and Blood Institute Grants HL67622, HL089647 and HL098252, and Pre-Doctoral Fellowship Awards (13PRE14580005 for Maria Restrepo) from the American Heart Association. The authors would like to acknowledge Veronica O’Connor and Ravi Doddasomayajula from The Children’s Hospital of Philadelphia, for assistance with patient data collection; Luyu Zhang from Emory University for assistance in statistical analysis; Phillip Trusty, Michael Clay, Alex Shao and Feiran Li from Georgia Institute of Technology for assistance in data processing.


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  • Contributors All authors were fully involved in the study design, data analysis and interpretation of results, preparation of the manuscript and final approval of the manuscript. All authors have approved the submitted manuscript.

  • Competing interests None declared.

  • Patient consent Obtained.

  • Ethics approval The Institutional Review Boards at Georgia Institute of Technology and Children’s Hospital of Philadelphia.

  • Provenance and peer review Not commissioned; externally peer reviewed.