In Vitro Model

The in vitro model has been described elsewhere. The phantom was 3D printed using the plastic material WaterShed (DSM, Elgin, IL; Figure 1 ). It consisted of a “ventricle” and an “atrium” submerged in a commercially available “Doppler test fluid” solution (model 707, ATS Laboratories Inc., Bridgeport, CT). A pulsatile pump (ViVitro Systems Inc., Victoria, British Columbia, Canada), mimicking the cardiac cycle, was connected to the “ventricle,” using four connectors, to assure a symmetrical pressurization of the cavity (pump frequency at 60 beats per minute). Mitral valve models with one or two orifices, different interspaces between the orifices (10 or 20 mm), and different anatomic regurgitant orifice areas (AROA: 15, 30, 50, or 70 mm ² ) were used ( Figure 2 ). All orifices were circular. A flowmeter (transit-time ultrasonic flow probe, Transonic Systems, Inc., Ithaca, NY) was placed on the tube connecting the ventricle to the pump. A second flowmeter was placed on the “outflow tract” of the ventricle, where a safety valve prevented pressure overload in the test bench ( Figure 1 ). The flow measured during one beat was then integrated in order to obtain the volume per beat. The difference between the volume passing through the entry tube and the volume passing through the exit tube gave the Rvol passing through the mitral valve, which served as reference method. Rvols acquired during five consecutive beats were averaged.

(A) Three-dimensional representation of long-axis section of the test bench. (B) Photograph of the experimental apparatus. (C) Schema of the whole in vitro model. I, left ventricle; II, left atria; III, annulus permitting the attachment of different mitral regurgitant orifices; IV, accesses for the piston pump; V, window for the TTE probe; VI, TEE probe holder; VII, outflow tract with unidirectional safety valve; VIII, bath containing a “Doppler test fluid”; IX, vacuum tap; X, piston pump; XI, main flowmeter between piston pump and “ventricle”; XII, auxiliary flowmeter on outflow tract.

(A) Single mitral regurgitant orifice, (B) double regurgitant orifices with 10 mm interspace, and (C) double regurgitant orifices with 20 mm interspace, with their corresponding 2D color Doppler jets ( middle ) and 3D PISA reconstruction ( right ). Note the fused PISAs in (B) .

Echocardiographic Acquisition

TTE (X5-1 transducer, frequency range 1–5 MHz, harmonic imaging mode activated, imaging depth 9 cm, on “ventricular” side) and TEE (X7-2t transducer, frequency range 2–7 MHz, harmonic imaging mode deactivated, imaging depth 6 cm, on “atrial” side) echocardiography (iE33 Phillips Healthcare, Zurich, Switzerland) were performed after setting of the same stroke amplitudes. In order to render the in vitro model similar to the human heart, the distance between the TEE probe and the “mitral” valve was two thirds of the distance between the TTE probe and the valve. After optimization of the depth and narrowing of the image sectors on two perpendicular planes, electrocardiogram-triggered (six beats) 3D volumes focused on MR-PISA were acquired during three cardiac cycles. The peak velocity ( V max) and velocity time integral (VTI) were obtained with continuous wave (CW) Doppler.

Quantification of MR

Color Doppler pyramidal volumes were analyzed on orthogonal planes using QLAB (Koninklijke Philips Electronics, Eindhoven, the Netherlands). Usually, a Nyquist velocity between 20 and 40 cm/sec (range, 11–51 cm/sec) permitted us to obtain an optimal shape of the PISA, and the visually biggest PISA was chosen at midsystole. Three groups were defined according to the presence of one or two MR orifices and according to the presence or absence of a fusion of the PISA shapes: single orifice, double orifices with PISA fusion, and double orifices without PISA fusion. For 2D analysis, the plane was placed across the middle of the regurgitant orifice(s) and manually optimized in order to obtain the visually biggest PISA. The radius ( r ) and the horizontal length ( h ) of each PISA were measured ( Figure 3 A ). To define the base of the PISA, the leading edge on the atrial side of the “mitral valve” was chosen. Once each PISA was characterized with r , h , and Nyquist velocity, several geometric assumptions were tested in order to define the most accurate 2D method for each MR group. We looked for simple formulae, only requiring measurements obtainable on one plane. The PISA surface ( S ) was calculated according to the hemispheric assumption ( S hemisphere = 2π r ² ). EROA was calculated as EROA = ( S hemisphere) × (Nyquist velocity/ V max). The Rvol was calculated as Rvol = EROA × VTI. In the case of double orifices, the whole PISA surface was estimated by taking only the biggest hemispheric PISA (single hemisphere model) or by addition of each separated hemispheric PISAs (double hemisphere model; Figure 3 B). Alternatively, the PISA surface was calculated on the basis of a hemicylindric assumption ( S hemicylinder = π × r × h ), with two bases ( S full hemicylinder = S hemicylinder + π r ² ), or with only one base ( S partial hemicylinder = S hemicylinder + 1/2π r ² ; Figure 3 C). We came to this formula observing the shape of the fused PISAs during the offline analysis. They were not really hemicylindric, given the rounded edges, but this geometrical assumption fitted better than the hemispheric assumption in this particular setting ( Figure 2 B). The horizontal lengths ( h ) of each separated PISAs were added in order to obtain a unique hemicylinder length, and the radii of each observed PISA were averaged to obtain one hemicylinder radius.

(A) Example of offline analysis of 3D CDE data sets: single-plane measurement of the radii ( r ₁ and r ₂ ) and the horizontal length ( h ) of the fused PISAs in the presence of narrow-spaced double regurgitant orifices. (B) Estimation of the PISA with double hemispheric assumption. (C) Estimation of the PISA with partial hemicylindric assumption. S , surface; r _m = mean radius, r _m = ( r ₁ + r ₂ )/2.

The 3D PISA method has been described elsewhere. After suppression of the B-mode components, the PISA was cut into 16 slices from top to base and exported in our customized software (MATLAB, MathWorks Inc., Natick, MA). The first aliasing (red blue shift) border was automatically detected and marked with a red line on each slice. The pixels inside the PISA borders were converted into white-on-black surfaces, and the latter were stacked up to build a 3D object. A triangular mesh was computed onto this object, allowing the measurement of his surface ( Figure 2 ). All PISA shapes visible during the systole were extracted and reconstructed as described. For each PISA _i , the regurgitant flow rate ( Qr _i = PISA _i × Nyquist velocity _i ) and the Rvol (Rvol _i = Qr _i × 1/volume rate) was computed. The integrated Rvol was calculated as integrated 3D PISA Rvol = <SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='∑i=1nRvoli’>∑ni=1Rvoli∑i=1nRvoli
∑ i = 1 n Rvol i
( n = number of PISA extracted).

Statistics

Statistical analysis was performed using SPSS 21 (IBM Corporation, Armonk, NY). Continuous variables were expressed as mean ± SD. Comparisons of mean Rvol (mRvol) between different methods among groups and between groups were performed with paired and unpaired t -test and analysis of variance for repeated measures with Bonferroni post hoc analysis. Linear regression analysis and Bland-Altman bias with limits of agreement (−1.96 SD to +1.96 SD) were performed to estimate the precision of the different imaging modalities. Receiver operating characteristic (ROC) analysis for accuracy analysis was used to determine the cutoff and the biggest area under the ROC curve (AUC).