Wei's Equation Research Articles

Measurement of left ventricular volume with admittance incorporated onto percutaneous ventricular assist device.

Percutaneous ventricular assist devices (pVADs) incorporated with admittance electrodes have been validated in animal studies for accurate instantaneous volumetric measurements. Since miniaturization of the pVAD profile is a priority to reduce vascular complications in patients, our study aimed to validate admittance measurements using three electrodes instead of the standard four. Complex admittance was measured between an electrode pair and a pVAD metallic blood-intake tip, both with finite element analysis and on the benchtop. The catheter and electrode arrays were first simulated inside prolate ellipsoid models of the left ventricle (LV) demonstrating current flow throughout all parts of the LV as well as minimal influence of off-center catheter placement in the recorded signal. Admittance measurements were validated in 3D-printed models of healthy and dilated hearts (100-400mL end-diastolic volumes). Minimal interference between a pVAD motor and the current signal of our admittance system was demonstrated. A modified Wei's equation focused on three electrodes was developed to be compatible with reduced profile pVADs occurring clinically, incorporated with admittance electrodes and wires. The modified equation was compared against Wei's original equation showing improved accuracy of calculated volumes. Reducing electrode footprint can simplify the incorporation of Admittance technology on any pVAD, allowing for instantaneous recognition of native heart recovery and assistance with pVAD weaning.

Validation of admittance computed left ventricular volumes against real‐time three‐dimensional echocardiography in the porcine heart

The admittance and Wei's equation is a new technique for ventricular volumetry to determine pressure-volume relations that addresses traditional conductance-related issues of parallel conductance and field correction factor. These issues with conductance have prevented researchers from obtaining real-time absolute ventricular volumes. Moreover, the time-consuming steps involved in processing conductance catheter data warrant the need for a better catheter-based technique for ventricular volumetry. We aimed to compare the accuracy of left ventricular (LV) volumetry between the new admittance catheterization technique and transoesophageal real-time three-dimensional echocardiography (RT3DE) in a large-animal model. Eight anaesthetized pigs were used. A 7 French admittance catheter was positioned in the LV via the right carotid artery. The catheter was connected to an admittance control unit (ADVantage; Transonic Scisense Inc.), and data were recorded on a four-channel acquisition system (FA404; iWorx Systems). Admittance catheterization data and transoesophageal RT3DE (X7-2; Philips) data were simultaneously obtained with the animal ventilated, under neuromuscular blockade and monitored in baseline conditions and during dobutamine infusion. Left ventricular volumes measured from admittance catheterization (Labscribe; iWorx Systems) and RT3DE (Qlab; Philips) were compared. In a subset of four animals, admittance volumes were compared with those obtained from traditional conductance catheterization (MPVS Ultra; Millar Instruments). Of 37 sets of measurements compared, admittance- and RT3DE-derived LV volumes and ejection fractions at baseline and in the presence of dobutamine exhibited general agreement, with mean percentage intermethod differences of 10% for end-diastolic volumes, 14% for end-systolic volumes and 9% for ejection fraction; the respective intermethod differences between admittance and conductance in eight data sets compared were 11, 11 and 12%. Admittance volumes were generally higher than those obtained by RT3DE, especially among the larger ventricles. It is concluded that it is feasible to derive pressure-volume relations using admittance catheterization in large animals. This study demonstrated agreements between admittance and RT3DE to within 10-14% mean intermethod difference in the estimation of LV volumes. Further investigation will be required to examine the accuracy of volumes in largest ventricles, where intermethod divergence is greatest.

Analysis of the Spatial Sensitivity of Conductance/Admittance Catheter Ventricular Volume Estimation

Conductance catheters are known to have a nonuniform spatial sensitivity due to the distribution of the electric field. The Geselowitz relation is applied to murine and multisegment conductance catheters using finite element models to determine the spatial sensitivity in a uniform medium and simplified left ventricle models. A new formulation is proposed that allows determination of the spatial sensitivity to admittance. Analysis of FEM numerical modeling results using the Geselowitz relation provides a true measure of parallel conductance in simplified left ventricle models for assessment of the admittance method and hypertonic saline techniques. The spatial sensitivity of blood conductance (Gb) is determined throughout the cardiac cycle. Gb is converted to volume using Wei's equation to determine if the presence of myocardium alters the nonlinear relationship through changes to the electric field. Results show that muscle conductance (Gm) from the admittance method matches results from the Geselowitz relation and that the relationship between Gb and volume is accurately fit using Wei's equation. Single-segment admittance measurements in large animals result in a more evenly distributed sensitivity to the LV blood pool. The hypertonic saline method overestimates parallel conductance throughout the cardiac cycle in both murine and multisegment conductance catheters.

Dynamic correction for parallel conductance, GP, and gain factor, α, in invasive murine left ventricular volume measurements

The conductance catheter technique could be improved by determining instantaneous parallel conductance (G(P)), which is known to be time varying, and by including a time-varying calibration factor in Baan's equation [alpha(t)]. We have recently proposed solutions to the problems of both time-varying G(P) and time-varying alpha, which we term "admittance" and "Wei's equation," respectively. We validate both our solutions in mice, compared with the currently accepted methods of hypertonic saline (HS) to determine G(P) and Baan's equation calibrated with both stroke volume (SV) and cuvette. We performed simultaneous echocardiography in closed-chest mice (n = 8) as a reference for left ventricular (LV) volume and demonstrate that an off-center position for the miniaturized pressure-volume (PV) catheter in the LV generates end-systolic and diastolic volumes calculated by admittance with less error (P < 0.03) (-2.49 +/- 15.33 microl error) compared with those same parameters calculated by SV calibrated conductance (35.89 +/- 73.22 microl error) and by cuvette calibrated conductance (-7.53 +/- 16.23 microl ES and -29.10 +/- 31.53 microl ED error). To utilize the admittance approach, myocardial permittivity (epsilon(m)) and conductivity (sigma(m)) were calculated in additional mice (n = 7), and those results are used in this calculation. In aortic banded mice (n = 6), increased myocardial permittivity was measured (11,844 +/- 2,700 control, 21,267 +/- 8,005 banded, P < 0.05), demonstrating that muscle properties vary with disease state. Volume error calculated with respect to echo did not significantly change in aortic banded mice (6.74 +/- 13.06 microl, P = not significant). Increased inotropy in response to intravenous dobutamine was detected with greater sensitivity with the admittance technique compared with traditional conductance [4.9 +/- 1.4 to 12.5 +/- 6.6 mmHg/microl Wei's equation (P < 0.05), 3.3 +/- 1.2 to 8.8 +/- 5.1 mmHg/microl using Baan's equation (P = not significant)]. New theory and method for instantaneous G(P) removal, as well as application of Wei's equation, are presented and validated in vivo in mice. We conclude that, for closed-chest mice, admittance (dynamic G(P)) and Wei's equation (dynamic alpha) provide more accurate volumes than traditional conductance, are more sensitive to inotropic changes, eliminate the need for hypertonic saline, and can be accurately extended to aortic banded mice.

Enhancement of miscibility in blends of poly (vinyl methyl ether) and poly (α-methylstyrene)s modified by incorporation of hydrogen-bonding sites

Poly (α-methylstyrene) and poly (vinyl methyl ether) do not form one-phase blends when mixed together. This situation can be changed if the poly (α-methylstyrene) is modified by introducing hydrogen-bond donor groups into the phenyl ring. Two groups of differing donor strength, methylcarbinol and trifluoromethylcarbinol, were selected, and modified poly (α-methylstyrene) samples, with varying degrees of substitution of these groups, were prepared. If the amount of the modifying group incorporated exceeded 4 mol% then one-phase blends of these copolymers with poly (vinyl methyl ether) could be prepared. The effect of the number and strength of these hydrogen-bonding sites on the phase stability of the blends was measured by locating the lower critical phase separation temperature in each blend. The glass transitions of the blends were found to be normally higher than those predicted from a simple rule of mixtures and reflect the extent of hydrogen-bond formation in the blends. This behaviour could, in part, be described by the K wei equation.