Non-Invasive Determination of Left Ventricular Workload in Patients with Aortic Stenosis Using Magnetic Resonance Imaging and Doppler Echocardiography

Early detection and accurate estimation of aortic stenosis (AS) severity are the most important predictors of successful long-term outcomes in patients. Current clinical parameters used for evaluation of the AS severity have several limitations including flow dependency. Estimation of AS severity is specifically challenging in patients with low-flow and low transvalvular pressure gradient conditions. A proper diagnosis in these patients needs a comprehensive evaluation of the left ventricle (LV) hemodynamic loads. This study has two objectives: (1) developing a lumped-parameter model to describe the ventricular-valvular-arterial interaction and to estimate the LV stroke work (SW); (2) introducing and validating a new index, the normalized stroke work (N-SW), to assess the global hemodynamic load imposed on the LV. N-SW represents the global hemodynamic load that the LV faces for each unit volume of blood ejected. The model uses a limited number of parameters which all can be measured non-invasively using current clinical imaging modalities. The model was first validated by comparing its calculated flow waveforms with the ones measured using Cardiovascular Magnetic Resonance (CMR) in 49 patients and 8 controls. A very good correlation and concordance were found throughout the cycle (median root mean square: 12.21 mL/s) and between the peak values (r = 0.98; SEE = 0.001, p<0.001). The model was then used to determine SW using the parameters measured with transthoracic Doppler-echocardiography (TTE) and CMR. N-SW showed very good correlations with a previously-validated index of global hemodynamic load, the valvular arterial impedance (), using data from both imaging modalities (TTE: r = 0.82, SEE = 0.01, p<0.001; CMR: r = 0.74, SEE = 0.01, p<0.001). Furthermore, unlike , N-SW was almost independent from variations in the flow rate. This study suggests that considering N-SW may provide incremental diagnostic and prognostic information, beyond what standard indices of stenosis severity and provide, particularly in patients with low LV outflow.


Introduction
Aortic stenosis (AS) is a complex ''systemic'' disease. There are compelling epidemiological and histopathological data suggesting that ''degenerative'' calcified AS is, in fact, an active and multifaceted disease that involves atherosclerotic-like and elastocalcinosis-like processes [1,2,3].
The degenerative process is not limited to the aortic valve; it involves the vascular system distal to the valve as well, which in turn can further contribute to deteriorating of left ventricle (LV) function [4].
Moreover, in patients with severe AS, ''paradoxical'' low flow (stroke volume index (SVi) ,35 mL/m 2 ) and consequently low transvalvular pressure gradients (,40 mmHg) despite the presence of preserved LV ejection fractions (.50%), is a challenging clinical entity [5,6,7]. This mode of presentation of severe AS is relatively frequent (up to 35% of cases) and has been shown to be associated with a more advanced stage of the disease [5,6,7]. Yet, a majority of these patients do not undergo surgery due to inadequate diagnosis. In these patients, the presence of low pressure gradient in conjunction with a normal LV ejection fraction may easily lead to an underestimation of AS severity [5,6,7]. Prognosis in such patients is usually poor (survival rates ,50% at 3-year follow-up) if treated medically and operative risk is high (up to 33%) if treated surgically [5,8]. Early detection and accurate estimation of AS severity are therefore of primary importance. For proper diagnosis of these patients, a comprehensive evaluation of LV hemodynamic loads is crucial. Such a comprehensive evaluation helps to identify needs for closer follow-ups, and to improve risk stratification and clinical decision making [8].
Recently, Briand et al. (2005) proposed the valvulo-arterial impedance (Z VA ) (equation 8) which represents the valvular and arterial factors that oppose ventricular ejection by absorbing the mechanical energy developed by the LV. This index has been shown to be a strong predictor of clinical outcomes in asymptomatic AS patients and is superior to the standard indices of AS severity in predicting LV dysfunctions [9,10]. However, Z VA is flow-dependent and therefore has limited use specifically in AS patients with low flow and low pressure gradient conditions [8].
The LV stroke work has been shown to be effective in characterizing the LV loads and consequently in characterizing patient's outcome and in assessing the inotropic state in patients with AS [11,12,13]. LV stroke work is the energy that the ventricle delivers to the blood at ejection, and potential energy, necessary to overcome the viscoelastic properties of the myocardium itself. Therefore, A method that would allow simple, non-invasive, and accurate estimation of the LV stroke work would contribute towards improving the clinical management of patients with AS and especially the ones with paradoxical low flow. However, estimation of this parameter requires the knowledge of instantaneous LV pressure and volume. Cardiac catheterization with conductance catheters can provide this information but this method is invasive, expensive and may cause cerebral embolisms [14]. A non-invasive alternative to estimate LV stroke work is to model the cardiovascular system using a lumped parameter model based on non-invasive recorded inputs.
The first objective of this study was therefore to develop and to introduce a simple lumped parameter model, solely based on noninvasive parameters, to describe the ventricular-valvular-arterial coupling and to investigate the impact of AS and vascular diseases on LV workload. The second objective was to introduce and validate a new index easily measurable in the clinical setting, i.e., the normalized LV stroke work (N-SW). This index in J/mL, representing the energy required to eject 1 mL of blood through the valvulo-arterial system, is calculated by dividing the estimated LV stroke work by the stroke volume (SV).  Table 1 for all other parameters used in the lumped parameter model). doi:10.1371/journal.pone.0086793.g001

Lumped Parameter Modeling
A schematic diagram of the lumped parameter model is presented in Fig. 1 [15]. This model includes three different submodels: 1) LV model; 2) AS model; 3) systemic circulation model. The effect of AS on LV workload was investigated under several numerical conditions using datasets obtained non-invasively by transthoracic echocardiography (TTE) and cardiovascular magnetic resonance (CMR) in healthy subjects and in AS patients. All other parameters used in the lumped parameter model are listed in Table 1.
Heart-arterial model. Heart function was described by time varying elastance as following where P LV (t), V(t) and V 0 are the left ventricular pressure, the left ventricular volume and the unloaded volume [15], respectively. The amplitude of E(t) was normalized with respect to maximal elastance E max , i.e., the slope of the end-systolic pressure-volume relation, giving E N (t N ) = E(t)/E max . Time then was normalized with respect to the time to attain peak elastance, T Emax (t N = t/T Emax ). Normalized time-varying elastance curves E N (t N ) have similar shapes in the normal human hearts with various inotropic situations or for diseased human hearts despite the existence of differences with regard to etiology of cardiovascular diseases [16,17]. More details can be found elsewhere [15] Modeling aortic stenosis. Aortic stenosis was modeled using the semi-analytical formulation for the net pressure gradient (TPG net ) across the stenotic valve during LV ejection introduced by Garcia et al. [18]. This formulation expresses the instantaneous net pressure gradient across the stenotic valve (after pressure recovery) as a function of the instantaneous flow rate and the energy loss coefficient and links the LV pressure to the ascending aorta pressure (P LV (t){P A (t)) and where E L Co, EOA, A, r and Q are the valvular energy loss coefficient, the effective orifice area, the aortic cross sectional area, the fluid density and the transvalvular flow rate, respectively. Computational algorithm. The lumped model illustrated in figure 1 was analyzed numerically by creating and solving a system of ordinary differential equations in Matlab Simscape (Math-Works, Inc). Capabilities of this program were enhanced by adding additional codes to meet demands of cardiac circuit. Fourier series representation of experimental normalized elastance curve for human adults was used to generate a signal to be fed into the main program. Equation 3, representing the transvalvular pressure gradient across the aortic valve, was represented by an inductance and a variable resistor as depicted in figure 1. Simulation started at the onset of isovolumic contraction and the elastance signal drives the program by feeding elastance value related to each time step in the cycle to the equation 1. The left ventricle volume V (t) was calculated using the left ventricle pressure P LV and elastance values by equation 1. The P LV used at the beginning of calculation was the initial value assumed across the variable capacitor and was automatically adjusted later by the system of equations as solution advances. The left ventricle flow rate subsequently was calculated as the time derivative of the left ventricle volume. After few initial cycles, solution converged. A diode with very low on resistance and off conductance was used in the aortic valve to prevent backflow from the valve. Matlab's ''ode23t'' trapezoidal rule variable-step solver was used to solve system of differential equations with initial time step of 0.1 milliseconds. The Convergence residual criterion was set to 10 25 and initial voltages and currents of capacitors and inductors set to zero.
Determining arterial compliance and peripheral resistance. The total systemic resistance was computed as the average brachial pressure over the cardiac output (assuming a negligible peripheral venous pressure (mean ,5 mmHg) compared to aortic pressure (mean ,100 mmHg)). This total systemic resistance represents the electrical equivalent resistance for all resistances in the current model. Because what the left ventricle faces is the total systemic resistance and not the individual resistances, for the sake of simplicity, we elected then to consider the aortic resistance, R ao , and systemic vein resistance, R SV , as constants and to adjust the systemic artery resistance, R SA , according to the obtained total systemic resistance.
Physiologically, arterial hypertension is determined by two factors [19]: (1) a reduction in the caliber of small arteries or arterioles with an ensuing increase in systemic vascular resistance and mean blood pressure, and (2) a reduction in the arterial compliance with a resulting increase in pulse pressure (systolic minus diastolic blood pressure). In this study, we fitted the predicted pulse pressure to the actual pulse pressure (known by arm cuff sphygmomanometer) by adjusting the systemic compliance (C SAC ). Therefore, C SAC adjustment was done by a simple trial and error for each degree of hypertension [20].

In vivo Measurements
Ethics statement. This study was approved by the Ethics Committee of Research of Laval Hospital affiliated to Laval University. Informed consents were obtained from all patients.
Study population. Forty-nine patients with mild to severe AS (63% men, age 63616 years) and eight healthy subjects (75% men, age 3468 years were included in this study (Table 2). Exclusion criteria were: (1) age ,21 years old. Patients with AS are often older than 21 years, also younger patients are treated as pediatric population according to the American Heart Association guideline; (2) LV ejection fraction ,50%. SV measurements in patients with reduced LV ejection fraction may show inconsistencies; (3) moderate or severe mitral or aortic regurgitation. SV measurements in these patients may show inconsistencies; (4) poor TTE data quality and standard contra-indications to CMR data. To demonstrate the feasibility of our method, only patients with useable data were considered in our study. In 33% of AS patients, the valve morphology was bicuspid. Other measured characteristics of patients were: height (16669 cm), weight (76613 kg), waist circumference (95611 cm), blood pressure (128622 mmHg/71611 mmHg), body surface area (1.8260.23 m 2 ), diabetes (16%) and metabolic syndrome (35%). The summary of performed measurements is presented in Table 2. All patients provided written informed consent under the supervision of the Institutional Review Board. The initial AS severity classification at study entry was based on TTE-derived effective orifice area (EOA): normal (EOA.2.0 cm 2 ), mild (1.5,EOA#2 cm 2 ), moderate (1.0 cm 2 ,EOA#1.5 cm 2 ) and severe (EOA#1.0 cm 2 ).
Transthoracic Doppler-echocardiography (TTE). TTE exams were performed and analyzed by two experienced echocardiographers, and conducted according to the American Society of Echocardiography guidelines [21]. They included: .
where SV i , PP, MAP, and CO are stroke volume indexed by the body surface area, pulse pressure, mean arterial pressure and cardiac output, respectively.
Cardiovascular Magnetic Resonance (CMR). The CMR study was performed 2 to 4 weeks after the TTE study with the use of a 1.5 Tesla scanner and a dedicated cardiac phase-array receiver coil (Achieva, Philips Medical Systems, Best, The Netherlands). CMR image acquisitions and analyses were performed by investigators blinded to clinical and TTE results, as previously described [25,26,27].
A custom-made research application was developed using Matlab software (Mathworks, Natick, Ma) to process and analyze CMR images [24,25,26]. The valve EOA from CMR (EOA CMR ) was then calculated as follow: where SV CMR is the stroke volume using 1/3 Simpson's rule to integrate the systolic flow and VTI AO is the velocity-time integral of the peak aortic flow velocity measured at 10 mm downstream of the valve during systole [25,27,28,29]. Computed normalized stroke work index (N-SW). We have introduced a lumped-parameter method for clinical practice that accurately investigates the impact of AS and concomitant vascular diseases on the LV function. This method only needs few non-invasively measured quantities described as follows. TTE and CMR can both provide the effective orifice area (E L Co) and aortic cross sectional area (A). Equation 4 uses these quantities to calculate the valvular energy loss coefficient (E L Co). Subsequently R av ( r 2E L Co 2 ) and L av ( 2pr ffiffiffiffiffiffiffiffiffiffiffiffi E L Co p ) in Equation 3 and Fig. 1 are calculated. The total systemic resistance is computed as the average brachial pressure over the cardiac output and is used to calculate R SA assuming constant values for other resistances in the circuit. The systemic compliance (C SAC ) was adjusted by fitting the predicted pulse pressure to the measured pulse pressure. The LV stroke work, representing the work of the left ventricle during each heart beat ( Ð P LV dV LV ), was then computed using the left ventricle volume, V (t), and the left ventricle pressure, P LV . Normalized LV stroke work (N-SW) is calculated by dividing the estimated LV stroke work by the SV (see Figure 2 for schematic diagram).
Statistical analysis. Results were expressed as mean 6 SD. CMR and TTE measurements were compared by 2-tailed paired Student t-tests or one-way ANOVA when appropriate. Association and agreement between variables were assessed by Pearson's correlation and Bland-Altman analyses, respectively. Statistical analysis was performed with SPSS 17 (SPSS, Chicago, IL).

Validation of the Lumped Parameter Model using in vivo CMR Flow Wave Forms
Using the above mentioned protocol, data obtained noninvasively in forty-nine patients with mild to severe AS and eight healthy subjects (Table 2) were incorporated in the model and the LVOT flow waveforms resulted from the lumped parameter model were compared with in vivo CMR flow waveforms with an average root mean square error of 12.21 mL/s. There was a very good correlation between the peak values of flow waveforms obtained from simulations and CMR measurements (r = 0.98; SEE = 0.001, p,0.001). Figure 3 presents few examples of comparison between the simulated and CMR flow waveforms. Figure 4 shows a strong correlation between the results calculated using lumped parameter model based on TTE and CMR imaging datasets. Fig. 4a shows the correlation for the computed N-SW (r = 0.9, SEE = 0.005, p,0.001) and Fig. 4b shows the correlation for the Z VA (r = 0.78, SEE = 0.05, p,0.001).     Figure 6 demonstrates that Z VA is significantly influenced by variations in flow rates: Z VA decreased when the stroke volume was reduced from 90 to 30 mL. In contrast, as Figure 7 shows, the flow rate had minimal effects on N-SW.

Advantages of Normalized Stroke Work
Patients with AS often have concomitant arterial diseases. This should alert clinicians that the degenerative process is not only limited to the aortic valve, but also involves the arterial system distal to the valve. The latter can further contribute to deteriorating LV function [2,30]. Under this condition, the LV faces an increased double load: a valvular load imposed by the AS plus an arterial load. Therefore, it is important to assess the hemodynamic load imposed on the LV. To this effect, Z VA representing the valvular and arterial impedances opposing ventricular ejection, was recently proposed [4].
N-SW represents the global hemodynamic load that the LV faces for ejecting a unit volume of the blood. It has a very good correlation with Z VA . However, using N-SW to assess the AS has privilege to Z VA for two main reasons: 1) N-SW is not flow dependent while, by nature, Z VA is. This may limit the utility of Z VA in patients with low-flow and low-gradient AS [8], 2) N-SW determines the actual total mechanical load imposed to the LV, while Z VA gives an estimate of that load.

Estimation of Normalized Stroke Work and Valvuloarterial Impedance by TTE versus CMR
This study demonstrates a very good correlation between the N-SWs computed based on the data from TTE and CMR methods. Similarly Z VA computed based on the data from TTE and CMR methods exhibit a very good correlation. TTE is the primary imaging technique for the assessment of AS severity and its progression. When TTE measurements are inconclusive or show discordances, AS severity should be confirmed with other techniques either invasively using cardiac catheterization or noninvasively using CMR [26,31]. Results of this study suggest that there is a good agreement between TTE and CMR for the calculation of N-SW.

Clinical Implications
Since the management of patients with AS remains a source of debate [3,5,6,7], supplementing currently available indices with the N-SW could be useful in identifying patients who are at high risks and are in need of closer follow-ups and further investigations.
More specifically, as already reported in [6], a significant number of patients with severe AS have low transvalvular flow rates (SVi ,35 ml/m 2 ), low transvalvular pressure gradients (,40 mmHg) and preserved LV ejection fractions (.50%). Clinically, this highly insidious situation represents a challenging clinical entity because the AS may appear less severe on the basis of low transvalvular pressure gradients. This situation may lead clinicians to erroneously conclude that no surgery is required because the stenosis is not considered to be severe. Indeed, these patients are at a more advanced stage of the disease. When compared with patients with severe AS but normal LV output, thus high pressure gradients, these patients are characterized by higher degrees of LV concentric remodeling, lower LVEFs and reduced mid-wall shortenings. It was found that these patients have poor prognoses and outcomes [6,7]. Therefore, it can be conceived that a longstanding increase in the LV load may result  (Table 2) were considered. In these patients, AS was either moderate (EOA = 1.48 cm 2 , n = 4) or severe (EOA = 0.85 cm 2 , n = 5). In both groups, the stroke volume index (SVi) was less than 35 ml/m 2 and the transvalvular pressure gradient was less than 20 mmHg. Both Z VA and N-SW were computed using the lumped parameter model based on the parameters measured by CMR. doi:10.1371/journal.pone.0086793.g008 in a more pronounced LV concentric remodeling, a smaller LV cavity size, and a decrease in intrinsic myocardial function. Early detection and accurate estimation of AS severity are, therefore, of primary importance. In this regard, for a comprehensive evaluation of the valvular and vascular loads, calculation of Z VA appears to be particularly useful for patients with AS. However, in low-flow low-gradient AS patients, Z VA would likely be less precise in the assessment of the LV global hemodynamic load, due to its high flow-dependency (Figure 8a) [8]. In these patients, N-SW which is less flow-dependent, may be useful to better quantify the LV hemodynamic load and to better identify the actual disease severity that is masked by this paradoxical low flow phenomenon (Figure 8b).

Conclusions
Patients with AS often have concomitant arterial diseases. Under this condition, the LV faces a double load: a valvular load imposed by the AS plus an arterial load. The double load results in increasing of the LV stroke work. We, therefore, introduced a lumped parameter method, capable of accurately assessing the impact of AS and concomitant vascular diseases on the LV workload using the data obtained non-invasively by TTE or CMR. The proposed method was then validated by comparing its estimated flow rates with in vivo CMR measurements.
We introduced a new index of LV hemodynamic load, the N-SW, representing the energy required to eject 1 mL of blood through the valvulo-arterial load. N-SW is less flow dependent than Z VA . Findings of this study suggest that beyond standard indexes of stenosis severity and LV geometry and function, N-SW may be useful in order to improve risk stratification and clinical decision making in patients with AS, specifically in a subset of patients with low flow and low gradient conditions.