Electromagnetic Velocity Probe Research Articles

Adaptive Measurement for Automated Field Reconstruction and Calibration of Magnetic Systems

This paper presents an efficient method to adaptively determine the locations for taking measurements for automated calibration of electromagnetic systems using reconstructed magnetic fields. This coupled measurement- computation method solves the Laplace's equation with measured boundary conditions. Along with the formulation of two selection criteria (chord-height and data-spacing), an adaptive scanning algorithm has been developed, which bases four local measurements to determine the next measurement point. This adaptive method, which relaxes the assumption of approximately known structure, has been illustrated (with experimental verification) with three practical applications; electromagnetic velocity probe, electromagnetic flow-meter (EMF) and spherical motor. Comparisons against published data demonstrate that the adaptive measurement algorithm greatly reduces the number of measurements and shortens the scanning route length of all three applications without sacrificing the accuracy of the computed results. Dry calibration results of an EMF were also experimentally verified against test data obtained from a standard flow-rig confirming that a relative error of 0.2% can be achieved. This finding makes the cost-effective dry calibration a practical alternative to the conventional flow rig calibration. As demonstrated on a spherical motor, the flexibility to include a least-square curve fit offers a practical means to filter measurement noise.

Analytical calculation of the measuring error of an electromagnetic velocity probe caused by a side channel wall

The distribution of virtual current around an electromagnetic velocity probe is distorted as the probe is installed too close to a wall and thus, an additional measuring error is caused. In this paper, an analytical calculation method is introduced to determine the distorted virtual current and the additional measuring error caused for a probe having two line electrodes on its side surface when installed close to the side wall of an open channel. Based on ignoring the end effect of the line electrodes, the problem is discussed in a horizontal section plane of the measuring system. Through conformal mapping of the irregular section plane to an annulus, Laplace’s equation of the virtual current’s potential is analytically solved using Neumann (as the wall is insulated) and Dirichlet–Neumann mixed boundary conditions (as the wall is conductive). The analytical solutions are verified by a comparison with numerically calculated data for a test case and used to calculate the distorted virtual currents for different ratios of the installing distance d (between the probe and the wall) to the probe radius R . The measuring error of an actual probe is calculated and compared with experimental data to validate the analytical calculation method. Possible reasons for the discrepancy between theory and experiment are discussed.

Divisionally analytical reconstruction of the magnetic field around an electromagnetic velocity probe

Determination of the magnetic field around an electromagnetic velocity probe is a key work for the dry calibration of the probe. In the paper, a novel divisionally analytical reconstruction approach to determine the magnetic field is introduced. It is especially suitable to be used in the dry calibration due to following advantages: no numerous measurements needed, unnecessary to know the inner magnetic exciting structure of the probe, high accuracy and convenient for further calculations. It is a measurement and calculation joint approach, in which the magnetic field is calculated from the measured boundary conditions through solving a Laplace’s equation of magnetic scalar potential. To obtain an analytical solution of the Laplace’s equation, the complex calculation geometry around the probe is divided into two simple ones using an auxiliary surface, and then the Laplace’s equation in the each generated geometry is analytically solved through a method of separation of variables. The divisionally analytical solution is pre-requisite since a pure analytical solution can bring convenience for further calculations in the dry calibration and such a solution is still lacked due to the complexity of the calculation geometry. A magnetic scanning device used to measure the distributions of the normal component of magnetic field on the surface of probe and the auxiliary surface is also introduced. The measured data provide the required boundary conditions for the determination of the magnetic field. Finally, the novel approach is validated through reconstructing the magnetic field around an actual electromagnetic velocity probe and comparing the results with the experimentally measured data.

A reconstruction approach to determining the magnetic field around an electromagnetic velocity probe

A novel approach to determining the magnetic field around an electromagnetic velocity probe is introduced. This is a measurement and calculation joint approach. Based on the characteristic that there are no exciting currents in the measuring volume out of the probe, a magnetic scalar potential is introduced to calculate the magnetic field around the probe. The potential obeys Laplace's equation in the volume. A magnetic scanning device is designed to measure the contribution of the normal component of the magnetic field on the surface of the probe, which provides boundary conditions necessary for solving Laplace's equation. Thus, the magnetic field around the probe can be numerically reconstructed by solving Laplace's equation with a finite-element method. Compared with traditional measuring approaches, directly measuring the distribution of the 3D magnetic field in the whole measuring volume out of the probe, the novel approach only needs to measure the distribution of the normal component of the magnetic field on the surface of the probe. Compared with traditional calculating approaches, calculating the magnetic field from the inner exciting unit of the probe based on Maxwell's equations, the novel method has overwhelming advantages of avoiding modeling of the inner complex structure of the probe and solving only one Laplace's equation. All the above advantages together lead to a good, efficient and accurate determination of the magnetic field, which is experimentally verified and is very useful for studying the performance of an electromagnetic velocity probe, especially in dry calibration of the probe.

Divisionally analytical solutions of Laplace’s equations for dry calibration of electromagnetic velocity probes

The potentials of weight function W → and magnetic flux density B → both obey Laplace’s equations in the measuring volume around an electromagnetic velocity probe. Analytical solutions of the Laplace’s equations are pre-requisite for the dry calibration of the probe, in which the sensitivity of the probe is calculated according to a mathematical model. However, the complexity of calculation geometry hindered the directly analytical solution of the equations, and there are still no effective analytical solutions applicable for the dry calibration at present. A method proposed in the paper is dividing the complex calculation geometry into two simple ones by an auxiliary surface, and thus the Laplace’s equations can be analytically solved in the each generated geometry separately. Specifically, two ways of division which can be effectively applied in the dry calibration, and the corresponding analytical solutions of the Laplace’s equations accessed using the method of separation of variables, are represented. Approaches to determine the additionally required boundary conditions on the auxiliary surfaces in dry calibration are also introduced. Finally, the study is validated on a numerical electromagnetic velocity probe.

Theory of a simple electromagnetic velocity probe with prediction of the effect on sensitivity of a nearby wall

A calculation of the sensitivity of a wafer-shaped electromagnetic velocity probe is presented. This takes into account the electric and/or magnetic effect of a plane wall near the probe and thus gives some idea of possible errors due to pipe walls in electromagnetic probe velocity profile scanning. The concepts of surface and vorticity weight vectors are introduced and the potential of the former for electromagnetic probe calculations is indicated.

Calculation of the virtual current around an electromagnetic velocity probe using the alternating method of Schwarz

A semi-analytical method is introduced to solve Laplace's equation in a complex geometry under certain boundary conditions and hence to calculate the virtual current around an electromagnetic flow velocity probe situated near a wall. Contours are given of virtual current potential with insulating and conducting walls with the probe at various distances from the wall.

Measurement of pipe flow by an electromagnetic probe

Electromagnetic (EM) flow velocity probes have some important advantages over normal full scale flow meters when being used in pipe flow measurement. To predict the sensitivity of an electromagnetic probe, with the effect of electrode and magnetic coil arrangement, properties of pipe wall and probe wall, work has been done recently on a mathematical model of an electromagnetic flow velocity probe [1]. This paper gives a brief description of the model. Then the model is used to calculate the pipe wall effect where the pipe wall of different properties is near the sensing head of the probe. The result of the calculation gives a suggested minimum distance between the pipe wall and the electrodes of the probe to keep the error of sensitivity within an accepted degree.

Effects of exercise on aortic input impedance and pressure wave forms in normal humans.

The effects of supine bicycle exercise on the input impedance of the ascending aorta were studied in thirteen male subjects undergoing cardiac catheterization, but in whom no cardiovascular disease was found. Ascending aortic flow velocity and pressure were recorded simultaneously from a multisensor catheter with an electromagnetic flow velocity probe and a pressure sensor mounted at the same location. A second pressure sensor at the catheter tip provided left ventricular pressure. Fick cardiac outputs were used to scale the velocity signal to instantaneous volumetric flow. Input impedance was calculated from 10 harmonics of aortic pressure and flow. For each subject, impedance moduli and phases from a minimum of 15 beats during rest and exercise were averaged. Peripheral resistance decreased from a resting value of 1142 +/- 51 (+/- SE) dynes sec/cm5 to 712 +/- 39 dynes sec/cm5 during exercise. Characteristic impedance remained unchanged with a resting value of 47 +/- 4 dynes sec/cm5 and an exercise value of 45 +/- 4 dynes sec/cm5. These results were associated with an increase in aortic pressure (96 +/- 2 to 111 +/- 2 mm Hg) and pulse wave velocity implying a decrease in aortic compliance. An increase in aortic cross-sectional area apparently offsets the effects of these changes in compliance and pulse wave velocity to result in an unchanged characteristic impedance. The increase in pulse wave velocity caused wave reflections to occur earlier during exercise, but the general characteristics of the pressure wave shapes remained unchanged.

Studies on flow velocity patterns within cardiac chambers and great vessels using a catheter-tip electromagnetic velocity probe

Studies on flow velocity patterns within cardiac chambers and great vessels using a catheter-tip electromagnetic velocity probe

Aortic Input Impedance during Nitroprusside Infusion

Beneficial effects of nitroprusside infusion in heart failure are purportedly a result of decreased afterload through "impedance" reduction. To study the effect of nitroprusside on vascular factors that determine the total load opposing left ventricular ejection, the total aortic input impedance spectrum was examined in 12 patients with heart failure (cardiac index <2.0 liters/min per m(2) and left ventricular end diastolic pressure >20 mm Hg). This input impedance spectrum expresses both mean flow (resistance) and pulsatile flow (compliance and wave reflections) components of vascular load. Aortic root blood flow velocity and pressure were recorded continuously with a catheter-tip electromagnetic velocity probe in addition to left ventricular pressure. Small doses of nitroprusside (9-19 mug/min) altered the total aortic input impedance spectrum as significant (P < 0.05) reductions in both mean and pulsatile components were observed within 60-90 s. With these acute changes in vascular load, left ventricular end diastolic pressure declined (44%) and stroke volume increased (20%, both P < 0.05). Larger nitroprusside doses (20-38 mug/min) caused additional alteration in the aortic input impedance spectrum with further reduction in left ventricular end diastolic pressure and increase in stroke volume but no additional changes in the impedance spectrum or stroke volume occurred with 39-77 mug/min. Improved ventricular function persisted when aortic pressure was restored to control values with simultaneous phenylephrine infusion in three patients. These data indicate that nitroprusside acutely alters both the mean and pulsatile components of vascular load to effect improvement in ventricular function in patients with heart failure. The evidence presented suggests that it may be possible to reduce vascular load and improve ventricular function independent of aortic pressure reduction.

True power dissipation of catheter tip velocity probes.

A recent paper, (Jones and Wyatt, 1970) reports that the catheter tip electromagnetic velocity probe described by Bond and Barefoot (1967) and Warbasse, Hellman, Gillilan, Hawley, and Babitt (1969) is thermally unsafe. We have evaluated the true power dissipation of this probe and have found it to be comparable with the dissipation of the catheter tip probe described by Mills (1966) and Mills and Shillingford (1967), and evaluated thermally by Jones and Wyatt (1970). The temperature rise of a probe is directly related to the power dissipation of the probe. Any statement regarding the thermal safety of the Mills probe applies equally to that of Bond and Barefoot. We conclude that both probes are thermally safe, except possibly for long periods of operation under zero flow conditions.

Use of a catheter tip electromagnetic velocity meter to determine the cardiovascular effects of glucagon.

The cardiovascular effects of glucagon were determined in anaesthetized dogs. Glucagon increased heart rate and myocardial contractility. Aortic, renal, and mesenteric flow increased. Neither the cardiac nor vascular dilating actions of glucagon were prevented by β-adrenergic blockade. Glucagon had a biphasic effect on carotid artery flow; an initial increase followed by a decrease. With femoral flow the initial response was variable, but the late response was usually a decrease in flow. These results were seen with intravenous injection. Intra-arterial injection of glucagon produced an increase in mesenteric, renal, carotid, and femoral flow. Results obtained with the intravascular catheter tip electromagnetic velocity probe were similar to those obtained with the external electromagnetic cuff flowmeter. An important advantage of the catheter tip probe over the cuff probe was that the former could be manipulated into various arteries via a small incision in a peripheral artery, thus avoiding extensive surgical dissection.

Applications of the catheter-tip electromagnetic velocity probe in the study of the central circulation in man

Phasic and mean blood flow velocities and pressures were continuously recorded within the venae cavae, pulmonary artery and ascending aorta with a catheter-tip electromagnetic velocity probe in twenty-three conscious patients. During the Valsalva maneuver, following the initial rise in the aorta, blood flow velocity diminished and, after release, increased above normal in all great vessels. In atrial fibrillation, peak aortic and pulmonary arterial velocities varied directly with the length of the preceding cardiac cycle and ventricular end-diastolic pressure. Peak aortic velocity rose markedly following premature ventricular contraction. Leg exercise, isoproterenol and glucagon caused striking elevations of aortic and pulmonary arterial velocities. Thus, this flowmeter catheter allows accurate, rapid and safe measurement of instantaneous linear blood flow and pressures in great vessels of intact patients in the assessment of cardiovascular function. Phasic and mean blood flow velocities and pressures were continuously recorded within the venae cavae, pulmonary artery and ascending aorta with a catheter-tip electromagnetic velocity probe in twenty-three conscious patients. During the Valsalva maneuver, following the initial rise in the aorta, blood flow velocity diminished and, after release, increased above normal in all great vessels. In atrial fibrillation, peak aortic and pulmonary arterial velocities varied directly with the length of the preceding cardiac cycle and ventricular end-diastolic pressure. Peak aortic velocity rose markedly following premature ventricular contraction. Leg exercise, isoproterenol and glucagon caused striking elevations of aortic and pulmonary arterial velocities. Thus, this flowmeter catheter allows accurate, rapid and safe measurement of instantaneous linear blood flow and pressures in great vessels of intact patients in the assessment of cardiovascular function.

Measurement of Instantaneous Blood Flow Velocity and Pressure in Conscious Man with a Catheter-Tip Velocity Probe

Twenty-three patients were investigated during diagnostic right and left cardiac catheterization with an electromagnetic catheter-tip velocity probe. The catheter contained a pressure lumen for simultaneous measurements of intravascular pressure. Average peak and mean blood velocities were 66 and 11 cm/sec in the ascending aorta, 57 and 10 cm/sec in the pulmonary artery, 28 and 12 cm/sec in the superior vena cava, and 26 and 13 cm/sec in the inferior vena cava. The velocity pattern in the ascending aorta was similar to that obtained by other methods. Positioning of the catheter in the ascending aorta required care; in one patient with aortic stenosis the recorded blood velocity pattern was unsatisfactory. In the pulmonary artery flicking of the catheter often produced artifacts in the records. The effect of deep respiration on blood velocity in the ascending aorta and pulmonary artery was studied. In the ascending aorta the highest velocities and stroke volumes were achieved during late expiration while in the pulmonary artery blood velocity and stroke volume were greatest in inspiration. In nine patients the cardiac outputs calculated from the product of mean velocity and radiologically measured cross-sectional area of the ascending aorta or pulmonary artery were compared with cardiac outputs determined by the indicator-dilution method; the correlation coefficient was 0.73. There were no complications, and the probe proved reliable.

Physiologic evaluation of a catheter tip electromagnetic velocity probe: A new instrument

A miniature catheter electromagnetic velocity probe has been designed and enclosed within the tip of a No. 8 F cardiac catheter, 2.67 mm. in external diameter. Peak systolic blood flow rates from 3 to 338 cm. 3/sec. as measured by the catheter probe agreed closely with simultaneous measurements by the perivascular electromagnetic flowmeter probe, in the ascending, descending thoracic and abdominal aorta of 12 anesthetized dogs ( r = 0.97 to 0.99). Catheter and perivascular probe measurements of blood flow, made every 1 100 of a second throughout the cardiac cycle, correlated well with each other in these 12 experimental animals ( r = 0.94 to 0.99). In vitro studies utilizing measured steady blood flow in the physiologic range, 13 to 473 cm. 3/sec., demonstrated that the electrical output of the catheter probe was linear ( r = 0.998). Therefore, the catheter probe can be utilized to record and measure accurately the instantaneous blood velocity and flow in the systemic arterial circulation. In comparison to the perivascular flow probe, the catheter probe has the advantage of (1) not requiring surgical exposure of the blood vessels; (2) not restricting pulsatile expansion of the blood vessel; (3) readily allowing the recording of blood velocity in the larger arteries and veins of the systemic and pulmonary circulation; and (4) having the velocity sensing electrodes in direct contact with the blood.

Solutions of the electromagnetic flowmeter equation for cylindrical geometries

A solution is given for the potential distribution around an electromagnetic velocity probe, of the type proposed by Mills for insertion into human arteries to measure blood flow, and the design and use of the probe are discussed in the light of this solution. A solution is also given for the potential in a pipe flowmeter with a magnetic field which does not vary in the axial direction.

A Catheter Tip Electromagnetic Velocity Probe and its Evaluation

A catheter tip instrument for measuring blood velocities and based on the principle of electromagnetic induction has been constructed and its performance evaluated. The results have shown it to be capable of reproducing velocity waveforms accurately in various circumstances.

Calibration of an Electromagnetic Velocity Probe for Electrically Conducting Liquids

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