## JACC: Cardiovascular Imaging

# Geometric Characterization of Patient-Specific Total Cavopulmonary Connections and its Relationship to Hemodynamics

## Author + information

- Received May 8, 2013
- Revision received November 27, 2013
- Accepted December 3, 2013
- Published online March 1, 2014.

## Author Information

- Elaine Tang, BEng
^{∗}, - Maria Restrepo, BS
^{†}, - Christopher M. Haggerty, PhD
^{†}, - Lucia Mirabella, PhD
^{†}, - James Bethel, PhD
^{‡}, - Kevin K. Whitehead, MD, PhD
^{§}, - Mark A. Fogel, MD
^{§}and - Ajit P. Yoganathan, PhD
^{†}^{∗}(ajit.yoganathan{at}bme.gatech.edu)

^{∗}School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia^{†}Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, Georgia^{‡}Westat, Rockville, Maryland^{§}Division of Cardiology, Children's Hospital of Philadelphia, Philadelphia, Pennsylvania

- ↵∗
**Reprint requests and correspondence:**

Dr. Ajit P. Yoganathan, Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Technology Enterprise Park, Suite 200, 387 Technology Circle, Atlanta, Georgia 30313-2412.

## Abstract

Total cavopulmonary connection (TCPC) geometries have great variability. Geometric features, such as diameter, connection angle, and distance between vessels, are hypothesized to affect the energetics and flow dynamics within the connection. This study aimed to identify important geometric characteristics that can influence TCPC hemodynamics. Anatomies from 108 consecutive patients were reconstructed from cardiac magnetic resonance (CMR) images and analyzed for their geometric features. Vessel flow rates were computed from phase contrast CMR. Computational fluid dynamics simulations were carried out to quantify the indexed power loss and hepatic flow distribution. TCPC indexed power loss correlated inversely with minimum Fontan pathway (FP), left pulmonary artery, and right pulmonary artery diameters. Cardiac index correlated with minimum FP diameter and superior vena cava (SVC) minimum/maximum diameter ratio. Hepatic flow distribution correlated with caval offset, pulmonary flow distribution, and the angle between FP and SVC. These correlations can have important implications for future connection design and patient follow-up.

The Fontan procedure is a palliative surgical technique for single-ventricle patients. The resulting total cavopulmonary connection (TCPC) is completed by routing superior vena cava (SVC) and inferior vena cava flow directly to the left and right pulmonary arteries (LPA and RPA), bypassing the right heart. This procedure improves life expectancy; however, many patients remain at risk for long-term complications that may be attributed to unfavorable hemodynamics. For example, there is evidence to show a possible link between TCPC energy dissipation and exercise tolerance. As another example, pulmonary arteriovenous malformations can be palliated by avoiding unbalanced distribution of hepatic blood flow between the lungs.

Because of complex native vessel morphology and differences in surgical techniques, a great variability exists in the TCPC geometry. The intra-atrial pathway usually forms a bulge, which promotes flow mixing within the Fontan pathway ([FP] which contains the native inferior vena cava tissue along with intra-atrial pathway or extracardiac conduit), whereas the extracardiac conduit has a more uniform cross-sectional area that results in a more streamlined flow. Such variability can in turn translate to differences in connection flow dynamics.

The hypothesis of this study is that significant correlations exist between certain TCPC geometric features and hemodynamics such as power loss, cardiac index (CI), and flow distributions. This work aims to provide further insight to surgeons and cardiologists regarding the connection geometries to avoid, and also help in the interpretation of suboptimal hemodynamics relative to the post-operative geometries.

One hundred thirty-one consecutive single-ventricle patients with a TCPC were selected from the Georgia Tech–Children's Hospital of Philadelphia Fontan database. Prospective cardiac magnetic resonance (CMR) data were acquired between 2002 and 2012. The study was approved by the institutional review boards of both institutions. Patient data were collected with informed consent. Cases with severe CMR artifacts, diagnosis of Ebstein's anomaly, atriopulmonary connections, left SVC to coronary sinus to systemic venous pathway connection, and bifurcated Fontan Y-graft were excluded. A total of 108 patients were included (Table 1).

Steady-state free precession vectorcardiogram-gated CMR images were acquired in the transverse plane using a Siemens Avanto 1.5-T whole-body magnetic resonance imaging scanner (Siemens Medical Systems, Malvern, Pennsylvania) (Table 2). The CMR images were acquired with 3 excitations every other heartbeat at end-diastole. In general, smaller voxel sizes were chosen for smaller patients to accurately resolve first- and second-order pulmonary arterial branching. To compensate for the signal-to-noise loss, 1 to 2 additional excitations were added, and oversampling was increased to 50%. The images were interpolated and segmented to select the TCPC anatomies using a previously developed and validated methodology from our group.

Phase contrast cardiac magnetic resonance (PC-CMR) was utilized to acquire through-plane velocity profiles across the aortic valve, the vena cavae, LPA, and RPA over the cardiac cycle under breath-hold conditions. Vessel flow rates were time averaged and used to compute CI and pulmonary flow distribution (PFD). They were also used as time-averaged flow boundary conditions for computational fluid dynamics (CFD) simulations to compute connection indexed power loss (iPL) and hepatic flow distribution (HFD) (Fig. 1). The velocity segmentation and CFD methodology have been previously described.

### Geometric analysis

Vascular Modeling ToolKit version 1.0.1 (Orobix, Bergamo, Italy) was used to compute vessel centerlines and bifurcation vectors (which contain the location and direction of the point at which the centerline bifurcates into branches). Each point of the centerline represents the 3-dimensional (3D) coordinates of the center of the maximum sphere inscribed in the vessel lumen at that point, equipped with the radius of such sphere (Fig. 2). Geometric parameters analyzed include vessel diameter, minimum/maximum diameter ratio (to observe any vessel narrowing), relative LPA area (comparing the relative size of LPA and RPA cross sections), vessel offsets, and connection angles (Fig. 3). To account for difference in patient size, vessel diameters were normalized by the square root of the body surface area (√BSA [m]). Vessel offsets were normalized by mean FP diameter of each patient instead of body surface area.

### Statistical analysis

Statistical analysis was performed using IBM SPSS Statistics version 20 (IBM Corporation, Armonk, New York). Paired-samples *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 (normality tested by Shapiro-Wilk test). Pearson's correlation was performed first to identify trends between the geometric and hemodynamic variables. The significant variables were selected, and multiple linear regression (MLR) of the hemodynamic endpoints was performed using forward stepwise procedures. A p value ≤0.05 was considered significant (2-tailed). All models were screened for outliers (standardized residual not within ±2) and influential observations (Cook's distance >0.04). Skewness was quantified using SPSS. Outliers and influential observations were reviewed and all calculations were verified.

### Geometric and hemodynamic characterization

The average geometric features of 108 TCPC are presented in Table 3. FP had the largest average diameter compared with other vessels (p < 0.001). Comparing the pulmonary arteries (PAs), LPA diameters were smaller than the RPA on average (minimum diameters p < 0.001; mean diameters p < 0.001; maximum diameters p = 0.02). Of particular note is the lower minimum/maximum diameter ratio at the LPA (p < 0.001), implying the diameter was less uniform than the RPA and different degrees of vessel narrowing were observed.

For cases without left SVC and azygos vein, (n = 92), the SVC anastomosis was generally more symmetrical with respect to the PAs, demonstrated by similar SVC-LPA and SVC-RPA angles (p = 0.566), whereas the FP-LPA angle was significantly larger than the FP-RPA angle (p < 0.001).

Hemodynamic findings from flow and CFD analysis are presented in Table 3. There were significant correlations between PFD and HFD (r = 0.396, p < 0.001) and between CI and the natural logarithm of iPL (r = −0.366, p < 0.001).

### Correlation between geometry and hemodynamics

Significant correlations between geometric variables and hemodynamic metrics were observed. Because of the skewness of the offset magnitude data (skewness = 3.96 ± 0.23), 4 cases with discrete caval offset magnitude (Fig. 4) were excluded in subsequent statistical correlations, resulting in N = 104 (skewness = 1.17 ± 0.24).

### iPL and CI

By curve fitting, a power law relationship between iPL and normalized vessel diameter was observed (Fig. 5). Therefore, the normalized diameter was transformed to its respective exponent (e.g., normalized minimum FP diameter was powered with −2.274) for MLR. From MLR, only the normalized minimum vessel diameters of FP, LPA, and RPA were identified as independent predictors. The strongest predictor was normalized minimum FP diameter, which was the vessel that carried the majority of TCPC blood (59 ± 15% of total systemic return on average). In addition, the majority of patients with low minimum FP diameter in this cohort had an intra-atrial connection (Fig. 5). Among the PAs, LPA (smaller diameter on average) was a more significant predictor.

Consistent with the trend between iPL and CI, and between iPL and minimum FP diameter, significant positive correlation between CI and normalized minimum FP diameter was observed (standard coefficient 0.347; r = 0.355, p < 0.001). Also, a positive significant correlation between CI and SVC minimum/maximum diameter ratio (standard coefficient 0.215; r = 0.229, p = 0.02) was observed.

### Hepatic and pulmonary flow distribution

To exclude the influence of additional vessels, correlations of %HFD(LPA) were carried out only on cases with the 4 typical TCPC vessels (FP, SVC, LPA, and RPA; n = 90). Normalized caval offset with SVC correlated most significantly with %HFD(LPA) (Fig. 6). When the FP was connected to the left relative to the SVC, higher flow from the FP coursed through the LPA than the RPA as a result of proximity. Significant positive correlation was found between %HFD(LPA) and %PFD(LPA) in this subset of patients (Fig. 6). Also, significant correlations were found between %HFD(LPA) and FP-SVC angle (Fig. 6). An example showing the influence of FP-SVC angle on %HFD(LPA) is illustrated in Figure 7.

For %PFD(LPA), it was found by MLR that relative LPA area was the only independent predictor (Fig. 8).

All MLR findings were further evaluated by including the outliers into the MLR of ranked ordinal dependent variables (ranked iPL, ranked HFD, and so on) and ranked caval offset (with SVC) as a confirmatory analysis using nonparametric methods. Even after including the outliers in the MLR, the same parameters were still identified as significant, which further confirmed the findings.

## Discussion

### Impact of geometry on energy dissipation

Geometric alterations of TCPC to minimize energy dissipation have been widely studied in idealized geometries. Earlier studies have emphasized the benefit of having caval offsets to reduce caval flow collision, hence lower TCPC power loss. Using patient-specific geometry, Dasi et al. (1) have shown that a strong inverse correlation exists between minimum PA area and TCPC energy dissipation (n = 22). Although these findings have provided significant insights, investigations to compare the relative importance of different geometric parameters are still lacking.

In this cohort, the effect of minimum vessel size manifested as the most important geometric parameter. Even when the average LPA diameter was smaller than that of the FP, the correlation between minimum FP diameter and iPL was the most significant. This could be because FP carried higher blood flow, which further elevated energy loss when the diameter was small. On the other hand, caval offset was not significantly correlated to iPL in this cohort, despite previous findings. This indicates that it may not be of critical importance compared with vessel diameter in order to minimize power loss.

Though it was not clear what caused the narrowing of the TCPC vessels, these findings suggest it may be important to dilate the narrowing, or to utilize strategies to promote vessel growth, especially in intra-atrial patients. This is confirmed also by the negative correlation between CI and minimum FP diameter. Long-term post-operative follow-up is essential, and a study evaluating the physiological outcomes after intervention by stent implantation may be warranted, because the pathway narrowing can potentially elevate energy loss during high cardiac flow and lead to exercise intolerance in these patients.

### Factors affecting HFD

Avoiding unbalanced distribution of hepatic flow to both lungs has been shown to be important for palliation of pulmonary arteriovenous malformations in single-ventricle patients. Dasi et al. (2) have shown that %HFD(LPA) is strongly correlated with caval offset in extracardiac patients (n = 5), and with %PFD(LPA) in intra-atrial patients (n = 5). In this cohort as a whole, %HFD(LPA) was most significantly correlated with normalized caval offset (with SVC), which agreed with the previous study. This emphasizes again the need to consider the relative displacement between FP and SVC in the staged procedures.

Another significant variable for HFD is the FP-SVC angle. From the cohort characterization, FP was generally connected towards the left (FP-LPA angle > FP-RPA angle) favoring HFD to the LPA; this was not the case with SVC (SVC-LPA angle ≈ SVC-RPA angle). When the FP-SVC angle was large (close to 180°), the FP and SVC flows were directly opposed and subject to collisions. This likely resulted in more recirculation, negating the preference of the FP flow towards the LPA. As shown in Figure 7, both cases had low caval offset magnitudes and FP pointing towards the left, but the case in Figure 7A was connected anteriorly towards the PAs. On the other hand, the case in Figure 7B had a large FP-SVC angle that almost resembled a straight pipe. Therefore, FP and SVC blood collided and mixed before leaving the PAs, resulting in low %HFD(LPA).

These findings suggest that whereas caval offset remains the most important geometric determinant of HFD, in cases where caval offset is constrained (e.g., by surrounding structures) and PFD is unbalanced, FP should not be angled only towards the desired side of the lungs (left or right, on the basis of the patient-specific circumstances). The relative angle with the SVC should be considered to avoid head-on collisions and reduce caval flow mixing.

Although this cohort included patients with various geometric features, it should be noted that the aforementioned findings are only applicable to typical TCPC (SVC, left SVC, and FP are directly connected to the PAs) with low caval offset. For more complex configurations such as the bifurcated Fontan Y-graft, additional parameters may have to be included. In addition, although this paper has established correlations between TCPC geometric parameters and hemodynamic surrogates such as iPL and HFD, the clinical importance of iPL on patient outcome still warrants further investigations.

### Study limitations

CMR spatial resolution could affect accuracy of the reconstructed vessel sizes. The 3D reconstruction method used for transverse CMR data was previously validated with TCPC geometry, with 0.96% error for PA diameter measurement and 1.77% error on radius curvature as described by previous studies from our group. The in-plane resolution for PC-CMR data ranged from 0.547 to 1.875 mm, which is still sufficient for this analysis, considering the diameter of the right upper lobe PA ranged from 4 to 9 mm. However, in cases with PA stenosis, the sparse transverse slices could potentially lead to inaccuracies in the PA diameter.

Four-dimensional (3D in time) PC-CMR acquisition would have allowed for the assessment of in vivo hemodynamics; because of patient scan time limitations imposed by the institutional review board, this was not performed. CFD assessment was an approximation to the physiology because it applied time-averaged boundary conditions and assumed a rigid vessel wall. PC-CMR data were acquired under breath-hold condition to reduce scan time, which ignored the physiological variability with respiration. Posture, exertion, and so forth can also affect the hemodynamics. Aortopulmonary collateral flow, calculated as the difference between cardiac output and systemic return, was 0.40 ± 0.84 l/min in this cohort (8 ± 20% of cardiac output). Collateral flow and fenestrations, which might have an influence on the hemodynamics, were ignored in the simulations.

## Conclusions

Significant correlations were found between TCPC energy dissipation, cardiac index, and minimum diameters. These findings can have important implications on future connection design and patient follow-up. Hepatic flow distribution is mediated geometrically by both caval offset and connection angles. Understanding the relationship between cavopulmonary connection geometry and hepatic flow distribution should help avoid unfavorable streaming that could leave patients vulnerable to pulmonary arteriovenous malformations.

## Acknowledgments

The authors acknowledge Veronica O'Connor and Ravi Doddasomayajula, from the Children's Hospital of Philadelphia, for their contributions on assisting with patient data collection.

## Footnotes

This study was supported by National Heart, Lung, and Blood Institute (NHLBI) grants R01 HL67622 and BRP HL098252. Dr. Whitehead receives funding from NHLBI grant 5K23HL089647. Dr. Fogel has received grants from Edwards Lifesciences and Siemens Medical Solutions. All other authors have reported that they have no relationships relevant to the contents of this paper to disclose.

- Abbreviations and Acronyms
- 3D
- 3-dimensional
- CFD
- computational fluid dynamics
- CI
- cardiac index
- CMR
- cardiac magnetic resonance
- FP
- Fontan pathway
- HFD
- hepatic flow distribution
- iPL
- indexed power loss
- LPA
- left pulmonary artery
- MLR
- multiple linear regression
- PC-CMR
- phase contrast cardiac magnetic resonance
- PFD
- pulmonary flow distribution
- RPA
- right pulmonary artery
- SVC
- superior vena cava
- TCPC
- total cavopulmonary connection

- Received May 8, 2013.
- Revision received November 27, 2013.
- Accepted December 3, 2013.

- American College of Cardiology Foundation