Nonlinear Power Loss During Exercise in Single-Ventricle Patients After the Fontan
Insights From Computational Fluid Dynamics
Background— We previously demonstrated that power loss (PL) through the total cavopulmonary connection (TCPC) in single-ventricle patients undergoing Fontan can be calculated by computational fluid dynamic analysis using 3-dimensional MRI anatomic reconstructions. PL through the TCPC may play a role in single-ventricle physiology and is a function of cardiac output. We hypothesized that PL through the TCPC increases significantly under exercise flow conditions.
Methods and Results— MRI data of 10 patients with a TCPC were analyzed to obtain 3-dimensional geometry and flow rates through the superior vena cava, inferior vena cava, left pulmonary artery, and right pulmonary artery. Steady computational fluid dynamic simulations were performed at baseline conditions using MRI-derived flows. Simulated exercise conditions of twice (2×) and three times (3×) baseline flow were performed by increasing inferior vena cava flow. PL, head loss, and effective resistance through the TCPC were calculated for each condition. Each condition was repeated at left pulmonary artery/right pulmonary artery ratios of 30/70 and 70/30 to determine the effects of pulmonary flow splits on exercise PL. For each patient, PL increases dramatically in a nonlinear fashion with increasing cardiac output, even when normalized to calculate head loss or resistance. Flow splits had a significant effect on PL at exercise, with most geometries favoring right pulmonary artery flow.
Conclusions— The relationship between cardiac output and PL is nonlinear and highly dependent on TCPC geometry and pulmonary flow splits. This study demonstrates the importance of studying the TCPC under exercise conditions, because baseline conditions may not adequately characterize TCPC efficiency.
- blood flow
- computational fluid dynamics
- Fontan procedure
- magnetic resonance imaging
For 30 years, the Fontan procedure and its modifications have been the standard end point for most single-ventricle patients. Despite improvements in surgical strategies and management, these patients still face high mortality and morbidity and decreased quality of life compared with peers,1 including limited exercise capacity compared with age-matched normal subjects.2–5 The etiology of this decreased exercise capacity is unclear. The past few years have seen a focus on characterizing power loss through the total cavopulmonary connection (TCPC).6–10 We hypothesize that TCPC efficiency plays a significant role in the exercise capacity of Fontan patients. Previous work has demonstrated significant effects of TCPC geometry on power loss.10–13 This power loss can be amplified by increasing the flow through the TCPC.14 It follows that a TCPC geometry with greater power loss or whose power loss increases more with exercise may have a decreased ability to increase TCPC flow during exercise. This in turn would result in decreased capacity for oxygen delivery during exercise and thus decreased exercise performance. Likewise, a patient with a more efficient TCPC may have a greater ability to exercise.
Recent studies have focused on the Fontan circulation under resting conditions.8,12,13,15 Some studies have evaluated a range of flow conditions that are not necessarily representative of physiological flows under exercise. The goal of this study was to evaluate power loss in a group of TCPC patients using previously validated computational fluid dynamic techniques under baseline and exercise conditions to gain a better understanding of the effects of exercise on TCPC power loss. A secondary goal was to determine the effect of varying relative flow to each lung on the power loss in the TCPC under exercise conditions. If differences in power loss for different flow splits to the pulmonary arteries are magnified at exercise conditions, this could result in either changes in relative pulmonary blood flow or in additional inefficiencies of the TCPC. If flow splits remain the same with exercise, as suggested by studies from Pedersen et al,16 but the optimal flow split for minimizing power loss is different, this could result in further TCPC inefficiencies.
A multicenter Fontan patient MRI database has been assembled to study the anatomic elements of the TCPC. Informed consent was obtained and all associated studies approved by the Internal Review Boards of the Children’s Hospital of Philadelphia (CHOP) and Georgia Institute of Technology. Ten geometries were selected from the CHOP cohort that had adequate anatomic and velocity data to perform valid simulations. Inclusion criteria included: (1) the anatomic reconstruction had no significant visible artifacts or holes in it, and (2) velocity data were available for all caval veins and left and right pulmonary arteries. The authors had full access to and take full responsibility for the integrity of the data. All authors have read and agree to the article as written.
Anatomic and Flow Data
Previous reconstructions of 3-dimensional patient-specific morphologies from MRI have enabled detailed and realistic flow analyses.17 The anatomic models are obtained from patient MRI contiguous axial stacks of steady-state free-precession data. Typical scans have in-plane resolutions of 1.0 to 1.5 mm and out-of-plane (slice thickness) resolutions of 3 to 5 mm. Electrocardiographic gating was performed to obtain all images in end-diastole. Out-of-plane image resolution is enhanced with an adaptive control grid interpolation technique to produce isotropic voxels.18 Each TCPC is isolated within the enhanced MRI data using a shape-element segmentation technique. Intensity thresholding and edge detection methods are used to create a scaffold around the TCPC, within which the vascular area of interest is defined by the motion of a shape element. Computer-aided design tools are used to produce a 3-dimensional model of the TCPC from the segmented data. The resulting geometry is locally smoothed and gaps filled if required.
Using phase contrast through-plane velocity mapping, flow rates from each vessel supplying and draining the region of cavopulmonary connection are measured. Using these velocity maps, baseline resting flow rates are calculated.
The 3-dimensional anatomic reconstructions are used for grid generation in which vessel volumes are divided into computational elements (meshes). The number of elements varies depending on geometry size and complexity, but ranges from 548 842 to 1 674 440 for the models studied. At each element, the governing Navier-Stokes conservation equations of mass and momentum for laminar fluid flow are solved. All solutions were obtained using second-order solvers assuming a Newtonian fluid with a density of 1060 kg/m3 and viscosity of 3.71e-3 N-s/m2. The patient-specific TCPC computational fluid dynamic analysis methodology and the in vitro validations of these techniques have been described elsewhere19 and are further detailed in the online supplement.
Each patient geometry was simulated at baseline steady-state flow conditions by setting the caval vessel flows at a steady rate derived from the MRI flow data averaged over the cardiac cycle. To satisfy conservation of mass, left pulmonary artery (LPA) and right pulmonary artery (RPA) flows were set to a fraction of total caval flow corresponding to the MRI-measured pulmonary flow splits. Exercise simulations of 2 (2×) and 3 times (3×) baseline total flows were performed to simulate exercise flows. This is partially justified by limited data from Shachar et al, in which Fontan patients had significantly depressed baseline cardiac output compared with normal control subjects but were on average able to increase their cardiac index by 2.1 times baseline.5 RPA/LPA flow splits were assumed to remain the same.16 Our exercise simulations were intended to simulate lower limb exercise and assumed that all increases in caval blood flow are from the inferior vena cava (IVC). This has been shown to be the case in normal subjects.20 Limited studies indicate that the caval blood flow changes in Fontan patients in response to exercise are similar.16,21 In the one patient with interrupted IVC with azygous continuation (CHOP20), increased flow from the lower body was split proportionally, according to the baseline measurements, between the azygous vein and the hepatic vein to the pulmonary artery pathway.
To investigate the effect of pulmonary flow split on exercise hemodynamics, we repeated each condition with 30% and 70% of flow to the LPA. Note that these simulations are not to imply that these are realistic flows for a given geometry. It would be unlikely for 70% of pulmonary blood flow to go through a stenotic vessel. However, these data allow us to calculate equal vascular lung resistance (EVLR) operating points. The method for this has been described elsewhere13 and is detailed in the online supplement.
Power Loss Calculations
To characterize TCPC efficiency under baseline and exercise conditions, power loss through the TCPC was calculated using the control volume method derived from the macroscopic energy balance: equation
This has been described more thoroughly in previous work22 and is detailed in the online supplement. In practical terms, total power for each surface is calculated by summing the inertial and static components. From this, net power loss is calculated by subtracting outlet power from inlet power: equation
where Ėdelta is the net power loss in the control volume.
Patient demographics, pulmonary artery dimensions at the position of flow measurement, measured flows, and MRI-measured and calculated EVLR baseline flow splits are summarized in the Table. Figure 1 summarizes calculated power loss versus exercise condition for all 10 geometries studied. Note power loss increases nonlinearly with increasing flow with an average increase of 10.5 times and 38.9 times baseline to the 2× and 3× exercise conditions, respectively. Power loss normalized to cardiac output (effective head loss) shows a similar trend (Figure 2). Further indexing of head loss by cardiac index (Figure 2) demonstrates that resistance index increases with flow. Although slight inaccuracies may be exaggerated, the calculated increases do not seem unreasonable because hydraulic power loss is proportional to flow times pressure loss, and pressure losses attributable to the dissipation of kinetic energy are themselves related to the square of velocity, a relationship familiar to cardiologists who use the modified Bernoulli equation.
Flow fields from CHOP31 are presented in Figure 3. At baseline, a vortex forms centrally with some penetration of IVC flow into the superior vena cava (SVC). As cardiac output increases, SVC–IVC flow collision is much more striking with significant power loss occurring in this region. In the orthogonal view, one can appreciate an additional source of power loss at exercise conditions from a narrowing in the IVC baffle. Complete flow fields for all 10 patient geometries are presented in the Appendix.
Effect of Pulmonary Flow Splits
Figure 4 summarizes the effect of varying LPA flow from 30% to 70% for 4 representative patient geometries. For most, increasing LPA flow for a given cardiac output leads to increased power loss, an effect magnified at exercise. One geometry (CHOP37) demonstrated marked preference toward the LPA. Not surprisingly, this model had a larger relative LPA size with mild proximal RPA hypoplasia. The power losses of some geometries (CHOP22, CHOP30, CHOP20) are relatively independent of pulmonary flow split. Figure 5 summarizes the effect of pulmonary flow splits on the 3× exercise condition with EVLR points marked by stars.
Effect of Exercise
We demonstrated that power loss in the TCPC increases markedly and in a nonlinear fashion with increasing flow. More importantly, power loss normalized to calculate an effective resistance index still demonstrated flow rate dependence. TCPC resistance at the 3× exercise condition was as high as 3.4 mm Hg/[L/min/m2], which is on the order of magnitude of the pulmonary vascular resistance.
This dramatic increase in resistance index with exercise may cause significant increases in Fontan baffle pressure, limiting TCPC flow during exercise. Head losses in Figure 2 at the 3× MRI flow exercise condition are nonphysiological for many patient geometries corresponding to pressure drops of as high as 52 mm Hg. Although other factors such as pulmonary vascular resistance and ventricular filling are likely important, this may partially explain why most Fontan patients are unable to obtain this level of exercise performance.
Effect of Pulmonary Flow Splits
Another significant phenomenon explored was the effect of pulmonary flow splits on power loss. For most geometries, power loss increased significantly as LPA flow increased, reflecting LPA hypoplasia. Although the penalty for increasing LPA flow was generally small at baseline flows, it was quite significant at exercise. It has been shown that IVC flow is directed toward the LPA and SVC flow toward the RPA.23 Increasing IVC flow to simulate exercise forces more blood through the LPA or forces abnormal streaming of IVC flow into the RPA.
Note in the Table the variability in the EVLR point at baseline flows. Furthermore, the EVLR point changes by as much as 10% from baseline to exercise, suggesting that TCPC geometry plays an important role in pulmonary flow distribution at both rest and exercise.
Flow visualization from our computational simulations (Figure 3; Appendix) demonstrates the importance of collision between the SVC and IVC flow during exercise. In our simulations, many of the geometries demonstrate increased penetrance of IVC flow into the SVC with exercise flow rates attributable to increased IVC flow and momentum. This results in increased power loss and thus decreased efficiency of the TCPC during exercise.
Preliminary Clinical Correlation
The ultimate goal of this research is to establish the clinical importance of power loss through the TCPC. In 7 of the patient geometries studied, we had adequate metabolic exercise studies (as defined by a Respiratory Exchange Ratio of greater than 1.1). Figure 6 shows a plot of the percent of predicted maximum oxygen consumption (V̇o2) versus the resistance index at the 3× flow condition for these 7 patients. Note that the trend is negative but that the sample size is insufficient to be significant. The goal of future research will be to obtain a large enough sample size to determine whether the effects of increased flow rate on power loss demonstrated in this study have a significant clinical impact on exercise performance.
Although TCPC power loss is recognized as a potentially important factor in the long-term outcome of Fontan patients, most studies have focused on resting conditions. Hsia et al studied computational fluid dynamic models reconstructed from angiographic data under resting conditions, showing that idealized extracardiac models had lower power loss than lateral tunnel or intraatrial tube connections.8 Migliavacca et al studied 3-dimensional models derived from MRI data. They again focused on different TCPC types under MRI-measured resting flow conditions, studying 4 intraatrial and 2 extracardiac geometries with variations in the IVC anastomosis, showing that IVC size and anastomosis geometry significantly affect power dissipation.12
Some studies have varied flow rate, but none systematically examined the effect of physiological exercise flow rates on TCPC efficiency. De Zelicourt et al studied a TCPC with bilateral SVCs under varying pulmonary flow splits and flows. Flows were changed by increasing IVC and SVC flows symmetrically as opposed to increasing only the IVC. They concluded that power losses were reduced by moving the IVC anastomosis more centrally.14
Although great care was made to accurately reconstruct the geometry, it is conceivable that some stenoses may be exaggerated, which may in turn exaggerate the effects of exercise for some models. The proportions of flow through the different sections of each model were not necessarily realistic, particularly when flow that could have found an alternative route was forced through a stenosed section. For example, the pulmonary artery stenosis located between the IVC flow path and the entry of a left-sided SVC in CHOP33 carried little flow and caused insignificant power loss at baseline, but appeared to result in a 99-fold increase of power loss in the exercising condition. In a patient, however, increased flow through the right lung or through azygos venous collaterals to the left could bypass the stenosis on exertion. However, because nonlinear effects of exercise were observed in all models, it is unlikely that these exaggerations would affect the overall results.
Another significant limitation is the use of rigid models. This is an area of active investigation, but preliminary studies indicate that compliance effects are on the order of 9% to 15%.24 We would expect these effects to be similar across all models studied, making comparisons between models valid. Ignoring the small pulsatile component of caval flow may cause small overestimations in power loss, which again should be similar across the models.
A third important limitation is the use of laminar simulations. At the highest flow rates, there may be some regional areas of turbulence. In this case, the calculated power loss would underestimate actual power loss, making exercise effects even more important than demonstrated in these simulations.
Power loss increases in a nonlinear fashion with physiological increases in IVC flow simulating lower limb exercise. Small differences in power loss between patients at rest may translate into marked, hemodynamically important differences at exercise. In addition, relative pulmonary blood flow to each lung at exercise has a profound effect on power loss. It may be important to understand the effect of exercise on pulmonary blood flow distribution to adequately characterize TCPC efficiency.
Future studies will be aimed at exploring the differences between the flow characteristics of extracardiac and lateral tunnel Fontans under both resting and exercise conditions. We will continue to explore the clinical relevance of these findings by comparing the hydrodynamic analysis presented in this research with actual patient metabolic exercise data in a larger series of patients. The ultimate goal is to provide guidelines and tools for surgeons to optimize the TCPC pathway.
Sources of Funding
This work was supported by NIH BRP Grant R01 HL 67622 from the National Heart, Lung and Blood Institute. K.K.W. was supported in part by the NIH training grant T32 HL007915–08.
Presented at the American Heart Association Scientific Sessions, Chicago, Ill, November 12–15, 2006.
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