Clinical, experimental, and computational validation of a new Doppler-based index for coarctation severity assessment

Structured Abstract

Background:

Long-term morbidity including hypertension often persists in coarctation patients despite current guidelines. Coarctation severity can be invasively assessed via peak-to-peak catheter pressure gradient (PPCG), which is estimated noninvasively via simplified Bernoulli equation and conventionally reported as peak instantaneous Doppler gradient (PIDG). However, underlying simplifications of the equation limit diagnostic accuracy. We studied the diagnostic performance of a new Doppler-based diastolic index called the continuous flow pressure gradient (CFPG) versus conventional indices in assessing coarctation severity.

Methods:

In a rabbit model mimicking human aortic coarctation, temporal blood pressure waveforms revealed diastolic instantaneous pressure gradients and spectral Doppler features impacted by coarctation severity. We therefore hypothesized CFPG provides superior correlation with coarctation gradients measured invasively. PIDG and CFPG were quantified using color flow echocardiography in humans and rabbits with discrete coarctations. Results were compared with PPCG in rabbits (n=34) and arm-leg systolic pressure gradients (ALSG; n=25) in humans via one-way ANOVA, Pearson’s correlation, linear regression, and Bland-Altman analysis.

Results:

A threshold of CFPG ≥4.6 mmHg was identified via Youden index as representative of PPCG ≥20 mmHg (the current guideline value for coarctation intervention) in rabbits, while a CFPG ≥1.0 mmHg represented an ALSG ≥20 mmHg in humans. Accuracy measures revealed superior correlation of CFPG (R² >0.80) and mild ROC improvement (AUC 0.94–0.95) as compared to PIDG (R² <0.63, AUC 0.89–0.95). Inter/intra-observer variability tested by intraclass correlation coefficient revealed measurement reliability with differences ≤8.2 and 10.7%, respectively. Computational simulations of anaesthetized versus conscious hemodynamics showed parameters were minimally impacted by isoflurane inherent in data used to derive CFPG. These results confirm the potential diagnostic accuracy of CFPG in echocardiography-based coarctation severity assessment. We are optimistic that CFPG will be useful for translation of results from pre-clinical studies that revisit current guidelines in order to limit morbidity in humans with aortic coarctation.

Graphical Abstract

Introduction

Coarctation of the aorta (CoA) occurs ~1 in every 2500 live births, is the third most common defect among children with congenital heart disease, and is the fourth most common lesion requiring intervention.^1–3 While surgical repair remains the optimal approach for treatment in most young infants, catheter intervention with either balloon angioplasty or stenting is the standard-of-care in older children and adults.^4,5 Guidelines for intervention include a transcatheter peak-to-peak pressure gradient ≥20 mmHg and many published reports regard this criterion as a hemodynamically significant CoA.⁵ Unfortunately, predicting which patients will meet this criterion remains challenging and complications, such as hypertension and left ventricular hypertrophy, are common despite successful CoA repair referring to this threshold.^6,7

Despite allowing for direct measurement of the peak-to-peak gradient, catheterization is an invasive procedure and can carry unwanted risks among children.⁸ Non-invasive alternatives using continuous wave Doppler are commonly applied in echocardiography to estimate peak instantaneous Doppler pressure gradient (PIDG).⁹ Traditionally, this involves measuring the systolic CoA gradient using peak Doppler velocity (V_pk) readings and applying the simplified Bernoulli equation.¹⁰ Despite widespread use of PIDG clinically, it has poor agreement with the gold-standard of invasive catheterization.¹¹ Factors including simplification of the Bernoulli equation,¹² difficulty obtaining consistent readings through a suboptimal insonation window, and morphological variability¹³ limit the accuracy of PIDG. These errors result in a significant overestimation^14,15 with flow dependency.¹⁶ Even correction for proximal velocity (V_p) in the Bernoulli equation does not substantially improve the estimate when compared to catheter measurements.^14,15

Doppler signal assessment over certain phases of the cardiac cycle has been suggested as a potential diagnostic tool independently correlated with the hemodynamic severity from CoA.¹⁷ While obstructive patterns distal to the CoA region are often accompanied with pronounced diastolic flow¹⁸, few studies have focused on the accuracy of such refined indices. Additionally, there is mounting data to suggest conventional thresholds for CoA intervention may be too high to prevent pathological remodeling associated with morbidity. For example, a recent study using a rabbit model mimicking human CoA¹⁹ showed precursors of persistent vascular remodeling exist with peak-to-peak catheter pressure gradients (PPCG) less than the current intervention threshold, i.e. 20 mmHg.²⁰ With further study, refined Doppler indices may show better agreement with gold standard catheter measurements. Hence, allowing for noninvasive translation of these pre-clinical findings back to the clinic.

The objective of the current study was to identify new Doppler-based indices that have superior diagnostic accuracy over conventional PIDG when assessing CoA severity. Our central hypothesis is that a new diastolic flow continuation index observed in CoA patients reflective of the associated pressure gradient can provide superior correlation with the empirically measured gradient as compared to conventional PIDG. We refer to this new index as the continuous flow pressure gradient (CFPG). CFPG was developed from the generalized Bernoulli equation and then applied through comparative study of catheter and Doppler-based indices in an experimental rabbit model of CoA. To investigate clinical application, CFPG was then compared to the PIDG in human subjects with discrete CoA (similar morphological appearance to the rabbit model) identified from an echocardiographic database at our center. The reliability of the Doppler measurements was then assessed via intra-class correlation coefficient. Finally, to investigate the effect of anesthesia in the rabbit model, a subject-specific computational analysis was performed using a fluid-structure interaction (FSI) approach to model conscious hemodynamics for comparison to those obtained by Doppler measurements under the anaesthetized condition.

Material and methods

Rabbit model of CoA-

All experimental procedures were approved by the Animal Care and Use Committee of the Medical College of Wisconsin and Marquette University. All procedures conformed to the “Guiding Principles in the Care and Use of Animals” of the American Physiological Society and the Guide for the Care and Use of Laboratory Animals as outlined by the National Research Council. After >72 h of acclimation, New Zealand white rabbits ~10 weeks old and weighing ~1.0 kg were anesthetized with ketamine/xylazine IM and maintained with isoflurane (minimum alveolar concentration; MAC ≈ 1%).¹⁹ Rabbits were randomly designated to undergo discrete CoA of varying severity surgically via left thoracotomy in the third intercostal space by tying suture around the aorta and against a wire of known diameter (1.6, 2.0 or 2.7 mm). Removal of the wire resulted in CoA severity dependent on the wire diameter used and resulting in PPCGs within the range observed clinically. Permanent (silk) suture was used to mimic native CoA (diameter reduction: 45–81%) while dissolving suture (Vicryl) was used to mimic residual CoA after suture absorption (diameter reduction: 5–38%).²¹ Non-experimental rabbits were also designated as a control group.

At ~32 weeks of age, rabbits were re-anaesthetized with Isoflurane for magnetic resonance angiography and phase-contrast imaging to be used with FSI simulations (Supplementary materials)¹⁹ as well as Doppler-ultrasound imaging within a 24 hour period. Figure 1A shows morphologic similarity between CoA in rabbits (middle) and humans (bottom). Doppler ultrasound imaging was performed by a trained sonographer using protocols similar to human echocardiography (Figure 1B).²²

Figure 1-. Echocardiography characteristics of CoA in rabbits and humans along with the formulation of the continuous flow pressure gradient (CFPG) index.

Maximum intensity MRI projections for representative rabbit and human aortas comparing control and CoA morphologies (A). Corresponding spectral Doppler images indicating continuous flow over the diastolic phase in CoA (B). B-mode ultrasound images showing discrete narrowing in the proximal descending thoracic aortas of a rabbit and human (C). Formulation of the newly derived CFPG index and the input Doppler measurements (D). dP: diastolic period, dT: time to 50% of diastolic pressure, dPHT: normalized diastolic pressure half-time, V_d: early diastolic velocity, V_pk: peak systolic velocity, V_p: velocity proximal to the CoA. *the diastolic phase was marked from the end of the T wave to the R wave on the ECG readings.

After detailed offline analysis of imaging data, rabbits were re-anesthetized for catheter-based measurement of temporal blood pressure (BP) waveforms proximal and distal to the CoA.¹⁹ Rabbits where then categorized into severe (≥20 mmHg) or mild (<20 mmHg) CoA groups according to the PPCG (Table 1).

Table 1-.

Rabbit and human characteristics.

Rabbits a	PPCG [mmHg]
	≥ 20 (n=14)	< 20 (n=20)	p-value
Weight [kg]	3.16 [0.13b]	3.21 [0.14]	0.58
Age at Ultrasound [weeks]	31.6 [0.80]	32.1 [0.50]	0.61
SBP [mmHg]	82.1 [2.82]	82.0 [2.67]	0.97
DBP [mmHg]	53.9 [2.51]	61.0 [2.84]	0.06
Humans	ALSG [mmHg]
	≥20 (n=13)	< 20 (n=12)
Gender, n (%):
Male	11 (84.6)	11 (91.7)
Female	2 (15.4)	1 (8.3)
Race, n (%):
White non-Hispanic	11 (84.6)	9 (75.0)
White Hispanic	1 (7.7)	1 (8.3)
Black or African American	1 (7.7)	2 (16.7)
Age at echo [month]	28.8 [10.9]	30.3 [16.5]	0.70
Weight at echo [kg]	13.6 [3.85]	12.8 [5.00]	0.89
Height at echo [cm]	79.2 [9.20]	76.8 [14.5]	0.88
BMI [kg/m2]	16.9 [0.7]	17.3 [0.9]	0.68
SBP [mmHg]	115 [4.77]	90.8 [10.8]	0.03
DBP [mmHg]	65.7 [4.03]	51.7 [12.5]	0.18

^aRabbit measurements shown are under Isoflurane at ≈ 1 MAC

^bValues presented as mean [±SEM], ALSG = arm-leg systolic gradient, BMI = body mass index, DBP = diastolic blood pressure, PPCG = peak-to-peak catheter pressure gradient, SBP = systolic blood pressure.

Human echo quantification-

After exempt determination by the IRB Board of Children’s Wisconsin, analysis of CoA patients of either sex identified 25 subjects with discrete juxtaductal CoA and arm-leg systolic pressure gradients (ALSG) measured within 24 hours of echocardiography by sphygmomanometry. Patients with obstructive lesions in series, more than mild aortic insufficiency, hemodynamically significant congenital heart diseases, low cardiac output state, and abnormal ventricular systolic function on echocardiography examination were excluded. Hence, morphologies were comparable to CoA rabbits (Figure 1A and C). Patients were similarly classified into severe or mild CoA groups according to the current 20 mmHg clinical threshold²³ (Table 1).

Echocardiographic measurements included conventional peak instantaneous pressure drop estimation using simplified Bernoulli equation $\left(\text{PIDG}=4V_{pk}^2\right)$ with and without the recommended recovered pressure (RP) term.²⁴ Our new derivation of the generalized Bernoulli equation over the diastolic phase, i.e. CFPG, was also calculated (Eq. 1; see Supplementary materials for derivations) assuming an exponential diastolic decay of the diastolic velocity obtained from spectral Doppler:

$$CFPG=4\frac{dPHT}{ln(2)}\left(1-exp\left(-\frac{ln(2)}{dPHT}\right)\right){(1-DVI)}^2{V}_d^2$$ Eq. 1

where DVI is the Doppler velocity index (DVI = V_p/V_pk; V_p and V_pk are proximal velocity and peak jet velocity)¹³, dPHT is the normalized diastolic pressure half-time (time to 50% of early diastolic pressure normalized by the diastolic period),²² and V_d is the early diastolic velocity. All measurements were quantified from spectral Doppler images with early diastolic velocity identified at the end of the T wave^17,25 as shown in Figure 1B. The derivation resulting in Eq. 1 allows, for the first time, the inclusion of dPHT in a pressure-based index, i.e. CFPG, capturing the coarctation-induced^17,22 gradient over the diastolic phase.

Statistical analysis-

Descriptive statistics are presented for continuous variables as mean ± standard error of the mean (SEM) and for regression coefficients as p-value and 95% confidence interval (CI). Unbalanced one-way ANOVA was used to assess significant differences between groups. Pearson’s correlation and linear regression analysis examined the relationship between Doppler-based estimates and corresponding clinical measurements, i.e., PPCG and ALSG for rabbits and humans, respectively. Agreements between the methods was assessed by Bland-Altman plots with corresponding 95% limits of agreement. Sensitivity, specificity, positive predictive values (PPV), negative predictive value (NPV), diagnostic odds ratio (DOR), overall diagnostic accuracy (DA), and area under the ROC curves (AUC) were quantified for Doppler-derived indices relative to a clinical CoA gradient of ≥20 mmHg. The optimum cutoff value for the CFPG index was computed based on maximizing the sum of the sensitivity and specificity, i.e., the Youden index,²⁶ to find values that best represent a PPCG and ALSG ≥20mmHg according to rabbit and human datasets. The AUCs were then analyzed statistically using the criterion for testing the accuracy in comparative study of multiple diagnostic tests²⁷. MATLAB (MathWorks, Inc.) was used for all the mentioned statistical analysis and a two-tailed p-value of <0.05 was considered significant. Reliability of the echo-based measurements was investigated using intraclass correlation coefficient (ICC) through SPSS software for the standard metrics including, PIDG, CFPG, dPHT, and DVI. Two observers were trained to quantify echo-based indices on a random subgroup of rabbit and human datasets (n=10). Each metric was quantified in triplicate for inter-observer variability with median values used for intra-observer variability analysis²⁸.

Results

Human and rabbit characteristics-

CoA rabbits were classified into mild (n=20) or severe (n=14) groups based on PPCG with severity defined a priori using current putative guidelines for intervention, i.e., gradients ≥20 mmHg. Human patients with discrete CoA were similarly divided into mild (n= 12) and severe (n= 13) groups according to their ALSG after applying the exclusion criteria. Four patients were diagnosed after 1 year of age. Sixteen patients were native CoA, while 9 had mild (n=7) to severe (n=2, underwent second surgical repair) re-coarctation. For the re-coarctation patients, the second diagnostic echocardiography showed discrete narrowing with no significant concomitant anomalies consistent with inclusion criteria for the current study. No significant differences were observed in age, weight, or height of the mild and severe groups.

Rabbit echocardiography and PPCG measurements-

There were several time points during which the temporal catheter gradient was statistically different for severe (≥20 mmHg) versus mild (<20 mmHg) CoA rabbits relative to controls (Figure 2). Importantly, a pronounced change in the shape of the instantaneous pressure gradient waveform was uniquely seen in the diastolic phase according to the severity of CoA (Figure 2, shaded). More specifically, there was a significant increase in temporal catheter gradient at early and mid-diastole. Doppler velocimetry imaging confirmed this shift with pronounced continuous forward flow observed over the diastolic phase (Figure 1B, middle) that was also evident among human CoA cases (Figure 1B, bottom). Consequently, univariate analysis showed a pronounced increase in dPHT in severe CoA rabbits (p-value: 0.009) and humans (p-value: 0.103) vs. corresponding mild groups.

Figure 2-. Diastolic continuation of the pressure gradient for CoA rabbits vs. control.

Temporal catheter pressure gradients from the collection of rabbits in each experimental group (error bars indicate SEM) as quantified by fluid-filled catheters advanced from the right carotid and femoral arteries to measure proximal and distal temporal blood pressure in the thoracic aorta. Significant difference between groups assessed using unbalanced one-way ANOVA: † CoA<20 vs. control, ‡ CoA≥20 vs. control, and * CoA≥20 vs. CoA<20 mmHg.

There was discrepancy between conventional PIDG and PPCG before and after accounting for pressure recovery among rabbits. Figure 3 shows that linear regression yields a moderate relationship (Pearson correlation coefficient = 0.8 and adjusted R² = 0.63) between PIDG and PPCG among studied rabbits. Bland-Altman analysis shows a significant overestimation with a mean bias value of 20–30 mmHg before and after considering the pressure recovery term (Figure 3C &D).

Figure 3-. Doppler regression results for rabbits.

Scatter and Bland-Altman plots for PIDG before (A & C) and after (B & D) accounting for a recommended pressure recovery term. In Bland-Altman plots, the mean bias and 95% CI are represented by solid and dashed lines, respectively.

Human echocardiography and ALSG measurements-

A similar discrepancy between PIDG and ALSG was observed among data from humans with CoA. Figure 4 shows that linear regression yields a moderate to poor relationship (Pearson correlation coefficient = 0.73 and adjusted R² = 0.51) between PIDG and ALSG. Bland-Altman analysis shows a significant overestimation with a mean bias of ~18 mmHg (Figure 4C). This over estimation was also evident after accounting for pressure recovery with mean bias of ~7 mmHg (Figure 4B) resulting in a similarly high degree of scatter (95% CI: −11.52 to 37.87, Figure 4D).

Figure 4-. Doppler regression results for humans.

Scatter and Bland-Altman plots for PIDG before (A & C) and after (B & D) accounting for a recommended pressure recovery term. In Bland-Altman plots, the mean bias and 95% CI are represented by solid and dashed lines, respectively.

CFPG versus PIDG at 20 mmHg-

Conversely, the newly derived CFPG showed a moderate to strong exponential relationship (p-values <0.001) with high degree of scatter among humans and rabbits (i.e., ALSG and PPCG, respectively) resulting in adjusted R²> 0.81 (Figure 5). Measurement of DVI alone (i.e. one input to CFPG) with the severity of the CoA yielded Pearson Correlation coefficients of −0.68 and −0.66 for rabbit and humas, respectably. Similarly, dPHT alone also correlated well to CoA severity with Pearson correlation coefficients of 0.80 and 0.76 among rabbit and human datasets, respectively. This finding aligns with growing evidence that dPHT and DVI themselves may be strong predictors of the CoA severity^13,17. Interestingly, the combination of the DVI and dPHT, as derived in the CFPG formula, provided even stronger correlation coefficients, i.e., 0.82 and 0.79, for rabbit and humans, respectively. Figure 6 shows DVI, dPHT, and CFPG quantified among rabbit and human subjects. The pronounced to significant increase in dPHT and decrease in DVI observed for CoA gradients ≥20 mmHg also emphasizes these correlations. It is also worth mentioning that dPHT alone could not statistically differentiate between mild versus severe CoA for the patients in our study (p-value =0.103).

Figure 5-. Nonlinear regression results of CFPG.

CFPG vs. PPCG and ALSG among rabbits (A) and humans (B). PPCG: peak-to-peak catheter-based CoA gradient, ALSG: Arm-leg peak-to-peak gradient.

Figure 6-. Changes in DVI, dPHT, and CFPG relative to the severity of CoA.

DVI (A), dPHT (B), and CFPG (C) were quantified in mild and severe CoA according to the PPCG and ALSG quantified in rabbit and human cases, respectively. ALSG: arm-leg systolic gradient, CFPG: continuous flow pressure gradient, dPHT: normalized diastolic pressure half-time, DVI: Doppler velocity index, PPCG: peak-to-peak catheter gradient. *significant according to an unbalanced one-way ANOVA with a two-tail 5% significance level. ns: not significant.

ROC curves show overall improved diagnostic performance of CFPG vs. PIDG (Figure 7) in rabbits and humans. Importantly, the AUC for CFPG was either equal or greater than the conventional indices, but improvements were not statistically significant (p-value >0.20). Maximizing the sum of sensitivity and specificity identified the optimum CFPG threshold of 4.6 mmHg that best represents a PPCG ≥20 mmHg among the studied rabbit data set. Similarly, among humans, a CFPG threshold of 1.0 mmHg best represents an ALSG ≥20 mmHg. Using this criterion, the sensitivity, specificity, diagnostic odds ratio (DOR), and DA of CFPG was compared to the conventional PIDG before and after accounting for pressure recovery (Table 2). At the clinical threshold of ≥20 mmHg, pronounced improvement in specificity, PPV, and DA were observed using CFPG vs. PIDG (Table 2). Moreover, the AUC represents up to a 6% improvement when using CFPG vs. PIDG both in rabbits and humans. After accounting for recovered pressure, i.e., PIDG-RP, improvement was still observed as CFPG yielded the highest AUC, 0.94–0.95. The ideal cutoff values of PIDG 63.7 and 39.2 mmHg were identified for rabbit and human datasets according to the Youden index²⁶. Similarly, after accounting for recovered pressure, the ideal cutoff values of 28.5 and 21.8 mmHg were identified for rabbits and humans. ROC analysis according to these values yielded a more balanced sensitivity and specificity for the conventional indices and consequently, improved DORs (Table 3). Overall, the PIDG and CFPG both yielded a diagnostic accuracy of 0.82 in rabbit dataset while 4% improvement was observed for CFPG in humans. Results of the PIDG ROC analysis remained unchanged after correction for proximal kinetic energy as recommended in the literature.²⁴

Figure 7-. ROC curves at 20 mmHg intervention threshold.

ROC curves representing an aggregate measure of the diagnostic performance of Doppler -based indices over the range of sensitivity and specificities considering a 20 mmHg CoA gradient threshold.

Table 2-.

Interpretation of Doppler-based indices relative to the putative 20 mmHg peak-to-peak threshold.

	Rabbit (n=34)			Human (n=25)
	PIDG	PIDG-RP	CFPG	PIDG	PIDG-RP	CFPG
Thresholds [mmHg]	≥20	≥20	≥4.6	≥20	≥20	≥1.0
Sensitivity	1.00	1.00	0.85	1.00	0.85	0.92
Specificity	0.48	0.62	0.81	0.33	0.58	0.83
PPV	0.54	0.62	0.73	0.62	0.69	0.86
NPV	1.00	1.00	0.89	1.00	0.78	0.91
DOR	∞	∞	23.0	∞	8.00	60.0
DA	0.68	0.76	0.82	0.68	0.72	0.88
AUC	0.89	0.94	0.94	0.95	0.92	0.95

AUC: Area under the ROC curve, CFPG: continuous flow pressure gradient, DA: Diagnostic accuracy, DOR: Diagnostic odds ratio, NPV: Negative predictive values, PIDG: Peak instantaneous Doppler gradient, PIDG-RP: Peak instantaneous Doppler gradient corrected for recovered pressure, PPV: Positive predictive values

Table 3-.

Interpretation of Doppler-based indices relative to ideal cutoffs identified from ROC curves.

	Rabbit (n=34)			Human (n=25)
	PIDG	PIDG-RP	CFPG	PIDG	PIDG-RP	CFPG
Thresholds [mmHg]	≥63.7	≥28.5	≥4.6	≥39.2	≥21.8	≥1.0
Sensitivity	0.69	0.85	0.85	0.85	0.85	0.92
Specificity	0.91	0.81	0.81	0.83	0.83	0.83
PPV	0.82	0.73	0.73	0.85	0.85	0.86
NPV	0.83	0.90	0.89	0.83	0.83	0.91
DOR	21.4	23.0	23.0	27.5	27.5	60.0
DA	0.82	0.82	0.82	0.84	0.84	0.88
AUC	0.89	0.94	0.94	0.95	0.92	0.95

AUC: Area under the ROC curve, CFPG: continuous flow pressure gradient, DA: Diagnostic accuracy, DOR: Diagnostic odds ratio, NPV: Negative predictive values, PIDG: Peak instantaneous Doppler gradient, PIDG-RP: Peak instantaneous Doppler gradient corrected for recovered pressure, PPV: Positive predictive values

Reliability of the echo-based measurements used in calculating CFPG as quantified by ICC index revealed ≤8.2 and 10.7% differences among inter and intra-observer measurements, respectively. ICC index also confirmed good to excellent inter and intra-observer agreement in the standard metrics quantified. The 95% confidence interval for ICC was [0.881,0.997] for single subject variability and [0.931,0.999] on average, which is considered excellent reliability according to Cicchetti et al²⁹ and good to excellent according to Koo et al²⁸.

Discussion

Suboptimal agreement between PIDG and PPCG is a major limitation of Doppler-derived indices used for non-invasive CoA assessment.^11,14,30,31 Sources of disagreement include local discrepancy in aortic dynamic distensibility observed among native and treated CoA patients,³² which can increase peak Doppler velocity readings up to 40%.^15,30 This can result in substantial Doppler overestimation even in the absence of a significant PPCG. Therefore, artificial sensitivity, poor specificities, and misclassification of PIDG are extensively reported,^24,30 which can be a significant barrier in translational studies. Animal models of CoA using the gold standard catheter-based PPCG have hinted at intervention using milder severities in hopes of preventing hypertension precursors among treated CoA patients.^19,20 Therefore, a Doppler-based index that provides acceptable accuracy over a range of clinically important CoA severities would be useful to better align Doppler estimates of hemodynamic severity, corresponding mechanical stimuli, catheter measurements, and the potential to translate results from the lab to the clinic for CoA patients.

The clinical application of diastolic indices of CoA severity has been discussed in the literature, including diastolic pressure and velocity half-time showing correlation with obstruction level.^17,22 Antegrade diastolic continuation of flow is a qualitative hallmark of an obstructive flow pattern. Accordingly, diastolic continuation of flow and associated pressure gradient also showed strong correlation with measured gradients among rabbit and human subjects in the current work (adjusted R² >0.81). These findings suggest there may be significant clinical value in diastolic pressure gradient measurements for CoA severity assessment. However, to our knowledge, no index has been derived yet that incorporates the diastolic pressure gradient noninvasively, and there are currently no validated models of diastolic flow parameters that can be used to grade CoA.

In this clinical, experimental, and computational study using human and rabbit CoA data, a moderate overall correlation of the conventional PIDG (R² <0.54) was improved by introducing a new Doppler-derived index that estimates the diastolic pressure gradient by considering an exponential pressure loss over the diastolic phase. We have therefore called the index the continuous diastolic flow pressure gradient index, i.e., CFPG. CFPG showed an improved regression relationship with adjusted R² >0.81 for human and rabbits. Using the current clinical threshold of 20 mmHg for hemodynamics severity, CFPG yielded an overall diagnostic accuracy of at least 6% higher than the conventional PIDG. Improvement was also observed in the AUC that ranged between 0.94 to 0.95 for CFPG as compared to 0.89 to 0.95 for PIDG before and after accounting for recovered pressure. Conventional indices using peak systolic Doppler velocities often overestimate the CoA gradient, which results in bias toward superficial sensitivity of 1.0 or very low specificities (Table 2). This becomes particularly important when a clinical decision is being considered. In other words, deciding whether a CoA is mild enough to delay a surgery, or in need of more invasive diagnostic testing, can be highly affected by Doppler overestimation observed with the conventional PIDG. Interestingly, a stronger balance between sensitivity and specificity was observed for CFPG that was also evident in the reported DORs (Table 2). This is particularly important from translational perspective since superficially increased sensitivity of the conventional indices may result in inaccurate translation of new thresholds back to the clinic. Moreover, the increased AUC suggests better performance of CFPG not only for the current reference standard, i.e. PPCG ≥20 mmHg, but also for any potentially milder intervention threshold (see supplementary materials) as suggested by pre-clinical studies.²⁰

Although the systolic CoA gradient is traditionally used for clinical severity assessment in Doppler-based measurements, other morphological and hemodynamic indices such as DVI and dPHT have also been suggested as predictors of hemodynamic severity in CoA.¹³ However, the role of DVI and dPHT in improving Doppler-based estimates of CoA gradient is debated.¹⁴ Our results confirmed a strong correlation for DVI and dPHT with CoA severity in both rabbits and humans. Importantly, we implemented both non-dimensional parameters of DVI and dPHT in an analytically derived CoA gradient index (i.e. CFPG) for the first time. This new formulation showed improvement in Doppler estimates of PPCG and ALSG in rabbits and pediatric patients, respectively, with relatively larger correlations (adjusted R² > 0.81). The physiologic underpinnings of these observations can be explained by the prolonged recoil (i.e. capacitance) of the proximal aorta in response to the flow-limiting stenosis that leads to diastolic continuation of the flow with a typical sawtooth velocity decay.^33,34 Moreover, in contrast to PIDG which is largely dependent on a single index (i.e. V_pk), CFPG uses several indices that mathematically characterize the profile of continuous flow during diastole as a result CoA severity.

A simulated conscious hemodynamic condition using FSI simulations as detailed in the supplementary materials did not show significant changes in velocity and pressure gradients suggesting that statistical inferences reported here for isoflurane anaesthetized rabbits are expected to remain unchanged under conscious hemodynamic conditions. These findings also suggest that differences of the newly derived CFPG between humans and rabbits are likely due to factors other than those manifesting from the anesthesia used with rabbits in the current study.

A secondary goal of the present investigation was to provide a transfer function to predict PPCG based on Doppler-derived estimates via implementing non-dimensional indices that are compatible with current echocardiography protocols and can be expanded across the sizes, ages, and species. The improved correlation of CFPG in predicting PPCG in rabbits confirmed the superior predictive properties relative to conventional PIDG. This is particularly important when considering translation of milder severity thresholds that can be misleadingly interpreted with the significant Doppler overestimation often observed in conventional systolic indices, i.e. PIDG. Therefore, it is expected that the newly derived CFPG index provides a stronger tool for accurate translation of interventional thresholds from pre-clinical studies with invasive measurements to non-invasive modalities used clinically.

The current study should be interpreted relative to several potential limitations including limited sample sizes in the current data sets. Considering discrete postoperative recurrent CoA cases may help increase the sample size of our human data set and allow for machine learning algorithms to further investigate the diagnostic accuracy of CFPG relative to the conventional PIDG index.

Although strong correlation of CFPG with invasive measurements reported here is promising for translational purposes, it is important to note that echo-based indices are often considered with other clinical symptoms when rendering a clinical diagnosis such as ALSG, left ventricular hypertrophy, left ventricular dysfunction, and others. CoA management is also informed by age at presentation, complexity of the CoA, and whether the CoA represents a native vs. recurrent obstruction. ^32,33,35 Therefore, the diagnostic application of CFPG relative to other criterion requires further investigation in a larger cohort when assessing its utility in minimizing adverse long-term outcomes that have continued to persist for many CoA patients.

It is worth noting that local hemodynamics in acute CoA may be different than chronic CoA, where collateralization helps maintain blood flow beyond the narrowing. Interestingly, catheter measurements from rabbits closely mimic patterns of BP vs. percent area obstruction reported in the setting of collateralization³⁶ (Figure 8). Briefly, although pulse pressure is dampened as a function of CoA severity below a CoA in the absence or presence of collaterals, diastolic pressure is generally preserved when collaterals are present. Preservation of diastolic pressure in our catheter measurements downstream of CoAs was also measured for the rabbits of the current work. These results suggest collateral vessels are present with our rabbit model as a function of CoA severity. Hence, we expect the effect of collateralization to be similar among human and rabbit datasets and accounted for in the results presented.

Figure 8-. The effect of coarctation severity on proximal and distal (shaded) aortic pressures in the absence or presence of collateralization.

Panels A and B show arterial blood pressure in the ascending aorta and femoral arteries under acute conditions (A) and collateralization (B) from prior work (used by permission from McDonald’s blood flow in arteries by Nichols, W. W, and McDonald, D. A., 2011). Dashed lines indicate mean arterial pressure and solid lines indicate systolic and diastolic blood pressures. Panel C shows regression lines for arterial blood pressures in the thoracic aorta proximal and distal to the coarctation from anaesthetized rabbits used in the current study. Although impacted by anesthesia, the similarity in blood pressure measurements with increasing severity of coarctation for panels B and C suggests collateralization may occur with rabbits exposed to our model of CoA.

CFPG showed unique diagnostic power and independent association with CoA severity, but its applicability in patients with concomitant anomalies such as complex CoA (long-segment hypoplasia), previously stented arches, gothic-appearing arches, and aortic valve disease (stenosis, varying degrees of insufficiency, bicuspid, etc.) is yet to be studied. Future work will include alternative approaches to study the application of CFPG in a broader range of hemodynamic and morphological configurations of CoA including reduced order computational fluid dynamics and generalized parametric stenosis models^37,38. The similarity of subject-specific FSI simulations in CoA rabbits under anaesthetized and simulated conscious hemodynamics observed in the current study (supplemental materials) may allow for computational investigation of Doppler-derived indices beyond discrete juxtaductal configuration by providing a computational tool for the investigation of other common CoA configurations such as long-segment CoA and hypoplasia.

Due to the associated risks of invasive cardiac catheterization in native CoA patients, limited clinical data are available to correlate CFPG with PPCG in our small pediatric cohort. Therefore, we used ALSG for comparative study of conventional PIDG vs. CFPG. Literature suggests that arm-leg gradients may not be a strong predictor of invasive gradients in CoA patients.^39,40 Therefore, we expect the cutoffs obtained using two different modalities being different as reported here (i.e., 4.6 mmHg for rabbits vs 1 mmHg for humans). However, in two cases where transcatheter peak CoA gradient was available, good agreement between ALSG and PPCG was observed.

Conclusions

This work provides experimental, computational, and clinical evidence for superior diagnostic performance of CFPG, a newly introduced analytically derived index of CoA severity, relative to conventional PIDG. Results of cutoff-independent AUC showed an aggregate measure of the diagnostic performance over a range of clinically important thresholds. Overall, a stronger correlation with empirical measured CoA gradients was observed for CFPG (adjusted R²>0.81), yielding relatively improved diagnostic performance compared to the conventional Doppler indices studied. According to the data obtained from a rabbit model of the CoA, a CFPG threshold of 4.6 mmHg is suggested to represent the current putative peak-to-peak catheter gradient of ≥20 mmHg.

• Catheterization is preferred for coarctation assessment, but invasive

• Echocardiography provides a non-invasive alternative, but accuracy is limited

• Diastolic run-off pressure gradient provides promising diagnostic performance

• A new Doppler-based index is validated here for coarctation severity assessment

Abbreviations:

ALSG

Arm-leg systolic gradient

BP

Blood pressure

CFPG

Continuous flow pressure gradient

CoA

Coarctation of the aorta

dPHT

Normalized diastolic pressure half-time

DVI

Doppler velocity index

FSI

Fluid-structure interaction

ICC

intraclass correlation coefficient

MAC

Minimum alveolar concentration

PIDG

Peak instantaneous Doppler Gradient

PPCG

Peak-to-peak catheter pressure gradient

RP

Recovered pressure