Considerations of the application of indicator dilution methods to the measurement of the flow rates of fluids

Cottrall, M. F.

doi:10.1088/0031-9155/22/4/004

Cited by 6 publications

(6 citation statements)

References 7 publications

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“…Introducing now the mean cross-sectional concentration into the equation (34) by substitution of equation (6), leads to where V = AL is the volume of fluid in the tube between the points of injection and observation. A similar expression for determination of fluid volume has been derived by Cottrall (1977) in the case of power-law fluid, and has been presented by Felder and Gardner (1972) in the case of general laminar fluid flow and impulse-type injection of indicator. The relation in equation (35) has now been generalised in this paper as X-1 = T-l, which relation applies to cases of general laminar fluid flow, and with arbitrary functions of the initial distribution m i ( x ) of indicator and of the line resolution s ( x ) of the detector.…”

Section: Moreover This Total Sum Of Areas Is Equal To the Area Undermentioning

confidence: 63%

“…Note that the output of a density-type detector depends on the mass of indicator, while the output of a flow-rate-type detector depends on the momentum of indicator in the system. On the basis of this difference, density-type and flow-rate-type detection have been characterised as static or dynamic methods respectively (Cottrall 1977). Under conditions of good cross-sectional mixing at the detection site, the mean cross-sectional concentration 2 at that site is equal to the mean flow concentration C: It then follows from equations ( 6 ) and ( 7 ) that f ( x , t ) = ( F / A ) m ( x , t ) .…”

Section: Mass Line Density and Mass Flow Rate Of Indicatormentioning

confidence: 99%

See 1 more Smart Citation

High-T_c (95 K) As-Grown Superconducting Bi-Sr-Ca-Cu-O Thin Films

Ohbayashi

Anma

Takai

et al. 1990

Jpn. J. Appl. Phys.

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From an analysis of the dispersion of indicator in steady laminar fluid flow, expressions are derived for the determination of flow in a straight tube in circumstances in which the familiar Stewart-Hamilton relations for indicator dilution do not generally apply, namely when the method of detection of the tagged blood flow depends on the density of the indicator in the system, as with x-ray videodensitometry. The analysis assumes no diffusion of indicator, and is carried out for arbitrary profiles of fluid flow velocity and tube cross-section. Injections of finite width and finite duration are considered, whereby the indicator is distributed over the tube cross-section either uniformly or in proportion to velocity. Spatial resolution of the detector is considered. A new method is proposed to utilise a priori information when the type of flow is known beforehand. The application of the results is illustrated by several examples for cases with laminar flow. The study is theoretical and is intended only as a first step towards the measurement of blood flow in the human circulation.

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Section: Moreover This Total Sum Of Areas Is Equal To the Area Undermentioning

confidence: 63%

Section: Mass Line Density and Mass Flow Rate Of Indicatormentioning

confidence: 99%

High-T_c (95 K) As-Grown Superconducting Bi-Sr-Ca-Cu-O Thin Films

Ohbayashi

Anma

Takai

et al. 1990

Jpn. J. Appl. Phys.

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“…7 Some other authors have also discussed problematic aspects, mostly by use of flow pipe models. [8][9][10][11][12][13][14] The IDT has also been formulated by use of concepts borrowed from the theory of linear ͑stable͒ systems. 2,3,7,15 The use of such a formulation does not, however, demonstrate the validity of the IDT, especially not for all kinds of detectors and labeling processes.…”

Section: Discussionmentioning

confidence: 99%

Is the indicator dilution theory really the adequate base of many blood flow measurement techniques?

Doriot

Dorsaz

et al. 1997

Medical Physics

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The indicator dilution theory is the underlying model of many blood flow measurement techniques used daily in hospitals, for instance in cardiac catheterization laboratories. The basic version of this theory applies to a "stationary" flow system with one inlet and one outlet, into which a small amount M of indicator is injected "suddenly" at time t = 0 at the inlet. The quintessence of the theory consists in three equations, which themselves result from some apparently simple assumptions about the considered flow systems. The first equation states that the (constant) flow Q through the system can be calculated by use of the known amount of indicator, M, and of the indicator concentration-time curve c(t) recorded at the outlet. The second one allows the calculation of the "mean transit time" t* of fluid and indicator particles through the system from the curve c(t). The third equation, V = Qt*, yields the system volume V. It is generally believed that these three equations would be absolutely valid if the assumptions of the theory could be perfectly fulfilled. We show, by considering a simple model, that all three equations are actually incorrect for most flow systems when the detector used to record the curve c(t) is of the "trans-illumination" type, as is the case for instance in dye dilution methods and in many angiographic or CT techniques. A further consequence is that t*, which is truly the "center of mass" of the concentration-time curve c(t), does not have the well known property of being the adequate parameter for flow determinations. Many flow measurement techniques thus appear to have no theoretical base.

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“…The projection of the flow bolus along the direction of flow can be expressed as the ratio of the area encompassing the tagged spins to the total tube cross-sectional area at a location z. If the slice thickness is given by zO and the leading edge of the bolus is at z = 0 at time t = 0, the projection at t = TE can be written as ( 17)…”

Section: Fig 4 Plot Of Measured Peak Flow Velocity As a Function Ofmentioning

confidence: 99%

Projection flow imaging by bolus tracking using stimulated echoes

Foo

Perman

Poon

et al. 1989

Magnetic Resonance in Med

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Previous investigators have employed the concept of bolus tracking using either spin echoes or gradient echoes. In this paper we introduce two methods of bolus tracking using planar- and volume-selective stimulated echoes. The planar method employs a selective 90 degrees rf pulse which tags all spins in a particular plane. At a time tau 1 later, a nonselective 90 degrees rf pulse is employed, followed after a time tau 2, by another nonselective rf pulse. Only spins which experience all three rf pulses form a stimulated echo at time tau 1 after the third rf pulse. A balanced pair of flow-compensated dephasing (crusher) gradients further ensures that the stimulated echo is due only to the effect of all three rf pulses while minimizing flow dephasing. The first part of this gradient pair is applied after the initial rf pulse in the first tau 1 period to dephase the tagged spins. The second part of this gradient pair is applied after the third rf pulse to rephase the spins. Since the plane of the excited slice is orthogonal to the readout direction, flowing spins are imaged in an angiographic manner as they move away from the excited slice. A modification to this basic sequence excites only a small volume. In this manner, the suppression of stationary spins is effected by volume-selective excitation. In both the planar- and the volume-selective techniques, the excited spins undergo T1 and T2 relaxation during the tau 1 period but only T1 relaxation in the tau 2 period. In blood, where T1 is much greater than T2, keeping tau 1 as short as possible minimizes signal loss due to T2 dephasing. These methods demonstrate increased sensitivity compared to similar bolus tracking methods using either spin echoes or gradient echoes.

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Considerations of the application of indicator dilution methods to the measurement of the flow rates of fluids

Cited by 6 publications

References 7 publications

High-T_c (95 K) As-Grown Superconducting Bi-Sr-Ca-Cu-O Thin Films

High-T_c (95 K) As-Grown Superconducting Bi-Sr-Ca-Cu-O Thin Films

Is the indicator dilution theory really the adequate base of many blood flow measurement techniques?

Projection flow imaging by bolus tracking using stimulated echoes

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Considerations of the application of indicator dilution methods to the measurement of the flow rates of fluids

Cited by 6 publications

References 7 publications

High-Tc (95 K) As-Grown Superconducting Bi-Sr-Ca-Cu-O Thin Films

High-Tc (95 K) As-Grown Superconducting Bi-Sr-Ca-Cu-O Thin Films

Is the indicator dilution theory really the adequate base of many blood flow measurement techniques?

Projection flow imaging by bolus tracking using stimulated echoes

Contact Info

Product

Resources

About

High-T_c (95 K) As-Grown Superconducting Bi-Sr-Ca-Cu-O Thin Films

High-T_c (95 K) As-Grown Superconducting Bi-Sr-Ca-Cu-O Thin Films