A novel echocardiographic estimate of pulmonary vascular resistance employing the hydraulic analogy to Ohm’s law

Graphical abstract


Background
Pulmonary hypertension (PH) is a chronic, progressive disease common in multiple clinical disorders and associated with poor longterm outcomes. Hemodynamic classification of patients with PH necessitates estimation of pulmonary vascular resistance (PVR), a static index of impedance that reflects pathological remodeling of the distal arterioles and alterations to the pulmonary vascular bed. Accurate quantification of PVR is important for a number of reasons. As a hemodynamic diagnostic indicator, PVR is integral to classifying PH subjects as having isolated post-capillary or combined post-and pre-capillary PH. [1] Further, PVR is an independent risk factor in the setting of heart failure (HF) and a strong predictor for reduced exercise capacity. [2] In multiple randomized clinical trials, reduction in PVR is associated with improvements of traditional risk stratification indices such as 6-minute walk test, WHO functional class and NT-proBNP. [3,4] Reference-standard PVR is assessed using invasive right heart catheterization (RHC). Doppler-based approaches have been proposed [5][6][7][8][9], and present distinct advantages of being non-invasive, low-cost and highly accessible. However, their accuracy has been debated [10] and clinical utility may be limited by method complexity. [9] We have previously presented a novel, Doppler-based approach to assess PVR in a ☆ All authors take responsibility for all aspects of the reliability and freedom from bias of the data presented and their discussed interpretation.
pre-capillary PH cohort based on the hydraulic analogy to Ohm's relationship. In that study, we employed a fixed, non-elevated PCWP estimate in all patients considering their pre-capillary PH status. [11] In the current study, we hypothesized that incorporation of a reliable, clinically relevant and simplified estimate of PCWP would allow wider application of this approach to the general PH population. We aimed to evaluate the accuracy of a Doppler-derived algorithm based on Ohm's law to evaluate PVR using routinely-assessed echocardiographic variables in a general population of symptomatic patients referred for PH evaluation.

Study population
Consecutive patients with unexplained breathlessness referred for clinically-indicated RHC to Norrlands University Hospital between 2010 and 2015 were retrospectively analyzed. Patients with intracardiac or extracardiac shunts and severe valvular disorders were excluded prior to enrollment. Patients with atrial fibrillation or significant arrhythmia and no tricuspid regurgitation (TR) signals on echocardiography were excluded from the final cohort. Ethics committee approval was obtained prior to study enrollment (DNR 07-092M) and all patients provided written informed consent.

Right heart catheterization
RHC was performed by experienced operators blinded to echocardiographic data. Venous access was obtained by inserting an introducer in a medial cubital vein or in the femoral vein. A retrograde, right-heart catheterization was then performed using a Swan-Ganz pulmonary artery catheter (Edwards Lifesciences). Mean right atrial pressure (RAP), systolic and right ventricular end-diastolic pressures, pulmonary artery systolic, mean and diastolic pressures (PASP RHC , PAMP RHC and PADP RHC respectively), and mean pulmonary capillary wedge pressure (PCWP RHC ) were measured. Blood samples for estimation of oxygen saturation were drawn from the superior and inferior vena cava, as well as right atrium, and samples from the pulmonary and femoral arteries were used for screening for intra-cardiac shunts. Cardiac output (CO RHC ) was determined by thermodilution. Pulmonary vascular resistance was calculated using the equation PAMP RHC − PCWP RHC (trans-pulmonary gradient) divided by CO RHC .

Echocardiography
Doppler Echocardiographic examination was performed by an experienced echocardiographer (PL) with > 15 years' experience ontable, during RHC using a Vivid 7 system (GE Ultrasound, Horten, Norway) equipped with an adult 1.5-4.3 MHz phased array transducer. Standard views from the parasternal long and short axis and apical views were used in keeping with current recommendations. [12] Gray-scale images were obtained at 50 -80 frames/sec and Doppler acquisitions at a sweep speed of 100 mm/sec. PASP using echocardiography (PAS-P echo ) was estimated using Continuous-Wave (CW) Doppler from the tricuspid regurgitation (TR) jet considering the most optimal of signals across multiple acoustic windows. Stroke volume (SV) was measured using Pulse-Wave (PW) Doppler at the level of the LV outflow tract, and CO echo calculated by multiplying SV with heart rate. Mitral flow interrogation was performed in the 4-chamber view with the PW samplevolume placed between the mitral leaflets tips and measurements taken at end expiration. Early transmitral (E) and late diastolic (A) velocities were obtained after optimal sample alignment and E/A ratio was subsequently computed. Off-line analysis was performed using a commercially available software system (General Electric, EchoPAC PC version 11.0.0, GE Ultrasound, Waukesha, Wisconsin). Mean of three consecutive tracings were used to estimate a representative measurement.
Assessment of PVR using echocardiography (PVR echo ) was estimated using the hydraulic analogy to the Ohm's relationship, i.e., PVR = (PAMP − PCWP)/CO employing echocardiographic surrogates for each of the variables employed in conventional equation, i.e transpulmonary gradient and ventricular output . PAMP echo was calculated using the formula PASP echo × 0.61 + 2 mmHg according to Chemla et al. [13] PASP echo was estimated employing the peak trans-tricuspid retrograde pressure drop adding a fixed right atrial pressure (RAP) of 7 mmHg. [14] Additional analysis was performed to estimate PASP echo employing current recommendations considering inferior vena cava size and respiratory dynamics. [12] PCWP echo was estimated based on combination of interpretation of Mitral E/A ratio and age. PCWP echo was assigned a simplified estimate of 20 mmHg in younger patients (<50 years) if E/A Fig. 1. Illustration of PVR assessment using routinely acquired variables employing the Ohm's relationship (PVR echo ) and corresponding PVR obtained using right heart catheterization (PVR RHC ). ratio was > 2, and older patients (≥50 years) if E/A was > 1.4. In all other cases PCWP echo was estimated as 10 mmHg. An illustration of PVR echo assessment employing this novel approach has been provided in Fig. 1.

Statistical analysis
Continuous variables were expressed as mean ± SD for parametric variables or median (interquartile range) for non-parametric variables. Categorical variables were expressed as numbers and percentage. PAMP echo and PCWP echo were computed as described earlier. Correlations between reference standard invasive measurements and novel echocardiographic estimates were tested using Pearson's 2-tailed test. Inter-technique agreement between echocardiographic and invasive measurements was tested using Bland-Altman analysis and calculated ĸ coefficients, where 0 to 0.2 was judged as slight; 0.21 to 0.4 as fair; 0.41 to 0.6 as moderate; 0.61 to 0.80 as good and > 0.8 as excellent. Receiver operating characteristics (ROC) analysis was performed to evaluate the diagnostic performance of PVR echo to identify PVR RHC > 3WU. Delong's method was used to compare area under the curve using the novel PVR echo algorithm and conventional echocardiographic assessment. Sensitivity and specificity were calculated. IBM SPSS statistics version 23.0 was employed for analysis. A p-value < 0.05 was considered statistically significant.

Results
Of 145 patients referred for RHC in the derivation cohort, 32 patients with AF or significant arrythmia and 2 with no TR signals were excluded. In effect, 111 (mean age 61 ± 14 years; 36 male) with sinus rhythm were included in the analysis. In the analyzed patient cohort, trivial or mild TR was seen in 88 patients (79%), moderate in 20 (18%) and moderate to severe in 3 (3% Baseline characteristics of the derivation cohort are presented in Table 1, stratified by PVR RHC subgroups. Patients with elevated PVR RHC demonstrated significantly smaller LV volumes and higher EF, larger right atrial (RA) and RV size, and lower RV longitudinal function seen both in lower TAPSE and RV free wall strain (p < 0.05 for all group comparisons).

Feasibility and diagnostic accuracy of PAMP echo to represent PAMP RHC
TR velocity could be adequately assessed in 96 (86%), and echocardiographic estimates of RAP from inferior vena cava size and collapse in 92 (83%) of patients in the derivation cohort. Applying ASE/EACVI recommended estimates of RAP (12), PAMP echo using the Chemla's equation demonstrated strong correlation (r = 0.82, r 2 = 0.67; p < 0.001 for both) and minimal bias (Bias = 0.66; SD 9.22 mmHg) with PAMP RHC . Employing a simplified approach using a fixed, mean RAP echo (7 mmHg), strong correlation (r = 0.80, r 2 = 0.64; p < 0.001 for both) (Fig. 2a) and excellent agreement with PAMP RHC was preserved with a relatively higher spread of data points (Bias = 0.83; SD 9.56 mmHg) (Fig. 2b).
Simplified estimation of PCWP echo as being non-elevated (10 mmHg) or elevated (20 mmHg) considering age in addition to mitral E/A as described in our methods demonstrated excellent diagnostic ability to identify PCWP RHC (AUC = 0.84; CI 0.70 to 0.94; p < 0.001) in addition to good agreement with PCWP RHC (Kappa coefficient = 0.69). When compared with the current 2016 ASE/EACVI algorithm to determine elevated LV filling pressure, age-dependent mitral E/A demonstrated higher feasibility (95 vs 87%), specificity (97 vs 93%) PPV (91 vs. 32%) and modestly higher accuracy (89 vs 87%) ( Table 3). An illustration displaying age-dependent mitral E/A ratio and corresponding PCWP RHC in addition to PVR echo and corresponding PVR RHC is provided in Fig. 4 .

Diagnostic accuracy of PVR echo
PVR echo could be estimated in 88 of 111 patients (79%) employing PAMP echo and PCWP echo in the Ohm's relationship. When compared with those in whom PVR echo could not be assessed (n = 23; 21%), patients with quantifiable PVR echo demonstrated higher PA pressures and PVR on RHC, and lower TAPSE on echocardiography (p < 0.05 for all comparisons).

External validation of PVR echo
We then validated the novel PVR echo in an independent database of 238 symptomatic patients with normal sinus rhythm referred for clinically-indicated RHC to the PH referral center at the Karolinska   Table 2. This population demonstrated a higher proportion of patients with PH (n = 192; 81% vs. 68% in the Umeå cohort) and elevated PVR (61% vs. 48% respectively). Among those with PH, 121 (63%) demonstrated pre-capillary PH and 71(37%), post-capillary PH. Among postcapillary PH patients, 44 (62%) showed isolated post-capillary PH and 27 (38%) demonstrated combined post-and pre-capillary PH.

Discussion
We propose a novel echocardiographic approach to assess PVR employing variables routinely obtained in daily clinical practice using the hydraulic analogy to Ohm's law. Simplified Doppler-based estimates of PCWP and PAMP employed in this equation demonstrated negligible bias and excellent agreement with corresponding invasive measurements. PVR echo obtained using this approach was highly feasible, demonstrated strong diagnostic performance and outperformed traditional echocardiographic algorithms to assess PVR RHC . When validated in an independent hemodynamic database of patients referred for PH evaluation, PVR echo preserved strong agreement with RHC measurements, showed excellent ability to identify elevated PVR RHC and strong diagnostic capability to differentiate isolated post-capillary from combined post-and pre-capillary PH. Our findings showcase PVR echo as a promising, non-invasive surrogate of reference-standard PVR that may be useful in diagnosis and regulating PH therapy.

Age-dependent mitral E/A ratio to represent PCWP
While the mitral E/A ratio is highly feasible and integral to the assessment of diastolic dysfunction, it demonstrates well-recognized limitations that prevent its use as an independent surrogate of elevated LV filling pressures as per current recommendations [16] First, the E/A ratio showcases a U-shaped relation with LV diastolic function. In the specific setting of normal LV function, both subjects with normal and elevated PCWP RHC can demonstrate E/A ratio between 1 and 2. However, for values over 2, a sensitivity of 43% and specificity of 99% for identifying elevated PCWP RHC has been reported. [17] Further, both age and gender are known to significantly affect mitral doppler indices of diastolic dysfunction and age has been earlier shown to be the strongest independent predictor of mitral E/A. [18] An observed shift from a normal transmitral filling pattern to an 'abnormal' relaxation pattern is not unusual with aging, suggesting that absolute cut-offs may not be suited to the diagnosis of diastolic dysfunction. More complex algorithms have been recently proposed to evaluate PCWP RHC . Recently, a model combining TR velocity. E/e', LV EF, RV fractional area change, IVC diameter and LA volume demonstrated a sensitivity of 92%, specificity of 93% and area under the curve of 0.97 to estimate elevated PCWP RHC . [9] However, such an algorithm necessitates acquisition of several measures incorporating considerable inter-and intra-observer variability in the approach. Our data suggests that considering age in addition to mitral E/A (which demonstrated strongest correlation with PCWP RHC ) offers a simple, pragmatic measure with strong diagnostic performance.

Echocardiographic evaluation of PAMP
In this study, PAMP echo was assessed using the validated relationship proposed by Aduen et al. [19] and Chemla et al. [13] Assessment of pulmonary artery systolic pressure has traditionally been performed by adding an RAP estimate derived from IVC size and respiratory dynamics to the trans-tricuspid gradient. [12] Recent studies, however, suggest that these RAP estimates are frequently inaccurate and do not improve agreement with invasive reference. [14] Application of a fixed, Table 2 Clinical Characteristics, right heart catheterization and echocardiographic data of patient population in the validation cohort. Data presented as mean ± SD/ median (Q1; Q3) or number (%).   representative value maintained strong association and minimal bias with invasive PA pressures in the aforementioned study. Our cohort demonstrated a limited spread of invasive RAP (Median 6 mmHg, IQR 4 to 10 mmHg) measurements and no significant differences when patients with elevated and normal PVR RHC were compared. In this context, a fixed RAP estimate simplifies assessment of PAMP echo using the Chemla approach [13], retains strong agreement with invasive measurements, and overcomes inherent technical limitations associated with IVC assessment. [20] One can argue that the assessment of PVR echo as employed in this study requires assessment of PAMP echo , PCWP echo and CO echo , and each variable introduces a margin of error. However, we have chosen a pragmatic, simplified approach to assess highly reproducible variables routinely assessed in echocardiography labs worldwide. The variables chosen demonstrate higher feasibility and our approach demonstrates lower complexity when compared with more recently proposed models.
[9] Advanced speckle-tracking has shown promise in estimation of RAP [21] and potentially improve estimation of PA pressures but this approach demonstrates relatively lower reproducibility and is rarely utilized in clinical practice.

Comparison with other Doppler-based PVR assessment
Our novel approach to assess PVR echo outperformed the conventional Doppler-based algorithm postulated by Abbas and colleagues. [5] The Abbas algorithm was originally tested in a pre-capillary PH population with preserved EF, and one can speculate that this approach may generate false-positives and showcase lower accuracy in a population that includes HF patients with post-capillary PH. However, comparison with other echocardiographic methods to estimate PVR [6][7][8] needs to be explored in further studies. Another strength of the current approach is its reasonable ability to distinguish isolated post-capillary PH from combined post-and pre-capillary PH in the validation cohort, although this may need to be further investigated in larger populations.
Beyond PVR, the Ohm's law relationship considering surrogates of pressure and flow has also been utilized to evaluate systemic vascular resistance in the setting of heart failure [22] and cardiogenic shock. [23] Novel non-invasive approaches such as these may be valuable in monitoring therapeutic interventions [24] and need to be further validated in larger databases.

Clinical implications
Accurate, non-invasive estimation of PVR employing commonly available echocardiographic variables taking age into consideration may improve patient screening and triaging for invasive catheterization in addition to regulating therapy during follow-up. In addition, this approach may be useful to distinguish PH hemodynamic subgroups where PVR evaluation determines therapeutic management.

Limitations
Although micromanometer-tipped catheters offer high-fidelity pressure recordings and are considered the invasive standard, we employed standard fluid-filled catheters that are routinely utilized in clinical practice. Analysis of echocardiographic images in the validation and derivation sites were performed by two experienced operators employing standard international recommendations, thereby minimizing inter-evaluator variability.

Conclusions
PVR echo estimated employing the hydraulic analogy to Ohm's Law is highly feasible, demonstrates excellent agreement with invasive measurements and identifies elevated PVR echo with high accuracy. This novel, pragmatic approach to non-invasive PVR assessment may be of value in patient screening, diagnosis and PH therapy regulation. Fig. 6. (a) Bland-Altman analysis demonstrating excellent agreement between PVR echo and PVR RHC in the validation cohort (b) diagnostic performance of PVR echo to identify PVR RHC > 3WU in the validation cohort.