Dan Loyd

Estimation of volume flow rate by surface integration of velocity vectors from color Doppler images

A new Doppler echocardiographically based method has been developed to quantify volume flow rate by surface integration of velocity vectors (SIVV). Electrocardiographic-gated color Doppler images acquired in two orthogonal planes were used to estimate volume flow rate through a bowl-shaped surface at a given time and distance from the probe. To provide in vitro validation, the method was tested in a hydraulic model representing a pulsatile flow system with a restrictive orifice. Accurate estimates of stroke volume (+/- 10%) were obtained in a window between 1.2 and 1.6 cm proximal to the orifice, just before the region of prestenotic acceleration. By use of the Bernoullis equation, the estimated flows were used to generate pressure gradient waveforms across the orifice, which agreed well with the measured flows. To demonstrate in vivo applicability, the SIVV method was applied retrospectively to the determination of stroke volume and subaortic flow from the apical three-chamber and five-chamber views in two patients. Stroke volume estimates along the left ventricular outflow tract showed a characteristic similar to that in the in vitro study and agreed well with those obtained by the Fick oxygen method. The region where accurate measurements can be obtained is affected by instrumental factors including Nyquist velocity limit, wall motion filter cutoff, and color flow sector angle. The SIVV principle should be useful for quantitative assessment of the severity of valvular abnormalities and noninvasive measurement of pulsatile volume flows in general.

The Shape of the Proximal Isovelocity Surface Area Varies With Regurgitant Orifice Size and Distance From Orifice: Computer Simulation and Model Experiments With Color M-Mode Technique

The hemispheric proximal isovelocity surface area method for quantification of mitral regurgitant flow (i.e., Qc = 2 pi r2v), where 2 pi r2 is the surface area and v is the velocity at radius r, was investigated as distance from the orifice was increased. Computer simulations and steady flow model experiments were performed for orifices of 4, 6, and 8 mm. Flow rates derived from the centerline velocity and hemispheric assumption were compared with true flow rates. Proximal isovelocity surface area shape varied as distance from each orifice was increased and could only be approximated from the hemispheric equation when a certain distance was exceeded: > 7, > 10, and > 12 mm for the 4, 6, and 8 mm orifices, respectively. Prediction of relative error showed that the best radial zone at which to make measurements was 5 to 9, 6 to 14 and 7 to 17 mm for the 4, 6, and 8 mm orifices, respectively. Although effects of a nonhemispheric shape could be compensated for by use of a correction factor, a radius of 8 to 9 mm can be recommended without the use of a correction factor over all orifices studied if a deviation in calculated as compared with true flow of 15% is considered acceptable. These measurements therefore have implications for the technique in clinical practice.

Pressure Half-Time Does Not Always Predict Mitral Valve Area Correctly

A theory is presented elucidating factors that influence the pressure half-time. By combining the Bernoulli and continuity equations and making certain assumptions about the shape of the atrioventricular pressure difference decay, it can be shown that valve area, volume transported across that area, and initial pressure difference influence the pressure half-time according to a formula in which the pressure half-time is related to V/(Ao square root of delta po), where V is the transported volume across the orifice with the area Ao, and delta po is the initial pressure difference across that area. In a subsequent hydraulic model experiment pressure half-time was determined for three different hole areas, with various initial volumes and initial pressure gradients. We did not obtain a unique relation between the pressure half-time and area. Instead the results supported our theory, and we found a close linear relationship between area and V/(T0.5 square root of delta po) (correlation coefficient [r] = 0.998), as predicted in the theory (T0.5 = pressure half-time). Clinical examples in which the pressure half-time may be misleading in the assessment of severity of mitral stenosis are presented.

A hybrid equation for simulation of perfused tissue during thermal treatment

Bio-heat equations (BHEs) are necessary for predicting tissue temperature during thermal treatment. For some applications, however, existing BHEs describe the convective heat transfer by the blood perfusion in an unsatisfactory way. The two most frequently used equations, the BHE of Pennes and the k eff equation, use for instance either a heat sink or an increased thermal conductivity in order to account for the blood perfusion. Both these methods introduce modelling inaccuracies when applied to an ordinary tissue continuum with a variety of vessel sizes. In this study, a hybrid equation that includes both an increased thermal conductivity and a heat sink is proposed. The equation relies on the different thermal characteristics associated with small, intermediate and large sized vessels together with the possibilities of modelling these vessels using an effective thermal conductivity in combination with a heat sink. The relative importance of these two terms is accounted for by a coefficient g . For g = 0 and g = 1, the hybrid equation coincides with the BHE of Pennes and the k eff equation, respectively. The hybrid equation is used here in order to simulate temperature fields for two tissue models. The temperature field is greatly affected by g , and the effect is dependent on, e.g. the boundary conditions and the power supply. Since the BHE of Pennes and the k eff equation are included in the hybrid equation, this equation can also be useful for evaluation of the included equations. Both these heat transfer modes are included in the proposed equation, which enables implementation in standard thermal simulation programmes.Bio-heat equations (BHEs) are necessary for predicting tissue temperature during thermal treatment. For some applications, however, existing BHEs describe the convective heat transfer by the blood perfusion in an unsatisfactory way. The two most frequently used equations, the BHE of Pennes and the k(eff) equation, use for instance either a heat sink or an increased thermal conductivity in order to account for the blood perfusion. Both these methods introduce modelling inaccuracies when applied to an ordinary tissue continuum with a variety of vessel sizes. In this study, a hybrid equation that includes both an increased thermal conductivity and a heat sink is proposed. The equation relies on the different thermal characteristics associated with small, intermediate and large sized vessels together with the possibilities of modelling these vessels using an effective thermal conductivity in combination with a heat sink. The relative importance of these two terms is accounted for by a coefficient beta. For beta = 0 and beta = 1, the hybrid equation coincides with the BHE of Pennes and the k(eff) equation, respectively. The hybrid equation is used here in order to simulate temperature fields for two tissue models. The temperature field is greatly affected by beta, and the effect is dependent on, e.g. the boundary conditions and the power supply. Since the BHE of Pennes and the k(eff) equation are included in the hybrid equation, this equation can also be useful for evaluation of the included equations. Both these heat transfer modes are included in the proposed equation, which enables implementation in standard thermal simulation programmes.

Heat transfer evaluation of the nasal thermistor technique

When analyzing transvalvular and venous flow velocity patterns, it is important to relate them to respiration. An accurate recording of the respiratory phase can be carried out with different methods. One of these methods is the use of a thermistor, which reacts to the variation in air temperature, placed in the nose of the patient. The thermistor used has a diameter of 1.0 mm and is of standard bead type. Although small, it has a considerable long time-constant and a long time-delay. The high time-constant gives a low cutoff frequency, well below the respiratory frequency and thereby causing a large phase difference. The thermistor was analyzed with the lumped heat capacity method, where it was easy to study the influence from design parameters, time-dependent air temperature, and velocity. The analysis was extended using the finite element method and the temperature field in the thermistor and the probe was calculated as a function of space and time. These calculations confirmed the result from the lumped model. The result showed that timing of respiration was not accurately obtained with the thermistor analyzed. To improve the timing, it was necessary either to change the measuring method or to use signal processing in order to achieve faster response.

Problems in Timing of Respiration With the Nasal Thermistor Technique

When one analyzes transvalvular and venous flow velocity patterns, it is important to relate them to respiration. For this reason a nasal thermistor technique is often used, although it is known that this signal is delayed in relation to intrathoracic pressure changes. The magnitude and variation in delay have not been investigated previously and were, therefore, studied in a model experiment in 10 normal subjects, in 10 patients with obstructive, and in 10 patients with restrictive pulmonary disease. Esophageal pressure variations measured with an air-filled balloon served as a gold standard for intrathoracic pressure changes. During basal conditions there was, for both patient groups and normal subjects, a considerable delay of the thermistor signal. The average delay for all subjects was 370 msec with a wide variation (from 120 to 720 msec). At higher breathing frequencies the delay shortened to 310 msec (P < 0.01) but there was still a wide variation (ranging from 200 to 470 msec). Theoretic calculations show that the delay caused by the respiratory system accounts for only a minor portion of the total delay. Model experiments confirmed that the response characteristics of the thermistor probes limit the accuracy in timing of respiration. The total delay with the investigated thermistor technique is too long and variable to fulfil clinical demands.

Analysis of different methods of assessing the stenotic mitral valve area with emphasis on the pressure gradient half-time concept☆

There are 2 different theoretical models that analyze factors influencing the transmitral pressure gradient half-time (T1/2), defined as the time needed for the pressure gradient to reach half its initial value. In this report the models and the assumptions inherent in them were summarized. One model includes left heart chamber compliance, the other does not. Although the models at a superficial glance seem to be contradictory, the conclusions drawn from them are similar: i.e., T1/2 is influenced not only by valve area, but also by initial maximal pressure gradient and by flow. Different clinical situations in which the T1/2 method for valve area estimation has been shown not to work are analyzed in the 2 models. It is concluded that these models have contributed to our understanding of the T1/2 concept and when it should not be used. We also advocate use of the continuity equation in these situations, since no assumptions then need be made.

Bio-acoustic signals from stenotic tube flow: state of the art and perspectives for future methodological development

To study the degree of stenosis from the acoustic signal generated by the turbulent flow in a stenotic vessel, so-called phonoangiography was first suggested over 20 years ago. A reason for the limited use of the technique today may be that, in the early work, the theory of how to relate the spectrum of the acoustic signal to the degree of the stenosis was not clear. However, during the last decade, the theoretical basis for this and other biological tube flow applications has been clarified. Now there is also easy access to computers for frequency analysis. A further explanation for the limited diagnostic use of bio-acoustic techniques for tube flow is the strong competition from ultrasound Doppler techniques. In the future, however, applications may be expected in biological tube flow where the non-invasive, simple and inexpensive bio-acoustic techniques will have a definite role as a diagnostic method.

Subaortic Flow Profiles in Aortic Valve Disease: A Two-dimensional Color Doppler Study

With time-corrected color Doppler echocardiography, the aortic subvalvular spatial flow velocity profile was registered in two perpendicular planes in 10 patients with aortic valve disease and in 5 healthy control subjects. Patients with predominant aortic valve stenosis had a fairly flat profile, and the subvalvular diameter, obtained from left parasternal two-dimensional tissue imaging, provided a good estimate of the mean of the two transverse flow axes. This explains the accuracy in determination of stroke volume and aortic valve area that is reported in studies on patients with aortic valve stenosis when the continuity equation is used. However, the use of apical pulsed Doppler ultrasound registrations from the left ventricular outflow tract and parasternal two-dimensional echocardiography for flow area calculation may introduce large errors in calculated stroke volume in certain patients with aortic regurgitation and in normal subjects, because of a non-flat spatial velocity profile or an inaccurate estimate of flow area.

Feasibility of patient specific aortic blood flow CFD simulation

Patient specific modelling of the blood flow through the human aorta is performed using computational fluid dynamics (CFD) and magnetic resonance imaging (MRI). Velocity patterns are compared between computer simulations and measurements. The workflow includes several steps: MRI measurement to obtain both geometry and velocity, an automatic levelset segmentation followed by meshing of the geometrical model and CFD setup to perform the simulations follwed by the actual simulations. The computational results agree well with the measured data.