Fluid flow sensing apparatus for in vivo and industrial applications employing novel differential optical fiber pressure sensors

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INTRODUCTION

This invention is directed to means for measuring fluid flow in arteries and veins of mammals wherein the measurements are provided by differential pressure sensing means positioned in the fluid conduit. With the differential pressure and the knowledge of the cross-sectional area of the conduit, flow rates can be determined. In in vivo flow rate measurements, the diameter of the artery is determined using one of several techniques, such as direct measurement with a probe, two differential pressure measurements, by dye or thermal dilution methods, and by means of x-rays. The invention also has industrial application.

BACKGROUND OF THE PRIOR ART

Means to measure pressure in the human blood stream by a number of techniques are known. However, blood pressure alone fails to provide answers to many questions, such as: whether sufficient volume of blood to satisfy body needs is flowing, the condition of arteries and veins, and the existence of partial blockages that reduce blood flow to critical areas of the body. It is only by determining actual rate and volume of flow that the medical practitioner is provided with greater insight into the actual condition of the circulatory system.

The present invention provides means whereby fluid flow in vivo may be readily determined and in general, the invention comprises one or more fiber optic differential fluid-pressure measuring devices each comprising a first optical fiber sensor and means for positioning the first optical fiber sensor in the flow path at the measurement point. If the devices further consist of several optical fiber sensors, each includes a means for positioning the sensor relative to the measuring position and to each other. In each case, a means for forming a fixed or variable constriction in the flow path of the fluid may be employed. Means are associated with the constriction for positioning the associated optical fiber sensor in the flow path of the fluid at the constriction. The device further includes one or more fiber optic interferometers having either a single leg or a pair of legs with means connecting each of the optical fiber sensors in a leg of an interferometer. Radiant energy is directed into the legs of the interferometers and through each of the sensors; and radiant energy detecting means are connected to the interferometers. The fiber optic probe described may be used in a wide range of veins and arteries (large and small). One specific example chosen for illustration will be the measurement of total cardiac output.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be more particularly described in reference to the accompanying drawings wherein:

FIG. 1 is a chart illustrating cardiac indices at different ages of a human being;

FIG. 2 is a chart illustrating events of a cardiac cycle showing changes in the left arterial pressure, left ventricular pressure, aortic pressure, ventricular volume, the electrocardiogram and the phonocardiogram;

FIG. 3 illustrates diagramatically a Mach-Zehnder interferometer and associated demodulation electronics;

FIG. 4 is a schematic view like FIG. 3 of a Michelson interferometer and associated demodulation electronics;

FIG. 5 is a diagramatic showing of a fiber optic Michelson interferometer with phase-locked-loop homodyne detection;

FIG. 6 is a schematic showing of a fiber optic Fabry-Perot interferometer and associated electronics for a pressure measuring device;

FIG. 6A is a view like FIG. 6 showing a pair of Fabry-Perot interferometers with one sensor in each of the pair of interferometers for measuring differential pressure and measuring fluid flow;

FIGS. 7A and 7B graphically illustrate photo detector output current and its derivative resulting from light wave phase-change fiber optic sensor output;

FIG. 8 schematically illustrates a phase-locked-loop homodyne detection circuit;

FIG. 9 graphically illustrates the sensitivity of fiber optic homodyne sensor at 0.degree. and 90.degree. bias angle;

FIG. 10 schematically illustrates a technique for reducing optical feedback in a laser-supplied interferometer;

FIGS. 11-14 illustrate various fiber optic fluid flow catheter configurations;

FIG. 15 illustrates a pressure measurement probe configuration for use with a Fabry-Perot interferometer;

FIG. 16 is a view like FIG. 15 for use with a Michelson configured interferometer;

FIG. 17 is a view like FIGS. 15 and 16 of a probe associated with a Mach-Zehnder interferometer configuration;

FIG. 18 illustrates diagramatically an industrial application of the present invention;

FIG. 19 is a diagramatic view of another form of the present invention useful for industrial applications;

FIG. 20 is a diagramatic illustration of a modified form of fiber-optic flow catheter;

FIG. 21 is a graph showing discharge coefficient C versus the pipe Reynolds number R.sub.D for square edged orifice 21/2 D and 8 D pipe taps;

FIG. 22 illustrates elements of a differential-producer flowmeter;

FIG. 23 diagramatically illustrates a variable constriction type fiber-optic flow catheter; and

FIG. 24 diagramatically illustrates a fiber-optic catheter designed to measure blood flow past a stenosis.

CHARACTERISTICS OF PULSATILE FLOW

The cardiovascular system consists of the heart, arteries, capillaries, and veins. All metabolic processes begin and end in this system. These include the exchange of gases in the lungs and in the tissues, the intake of food from the gastrointestinal tract and distribution throughout the body, the transport of nongaseous metabolites from the tissues for elimination in the kidneys, and the dissipation of heat through the lungs and body surface. One of the most important parameters for judging the proper functioning of this system is the quantity of blood transported per unit time (the cardiac output). The output of the ventricles for an adult is approximately 70 ml per pulse and the average pulse rate is 72 beats/min. Thus, the average adult cardiac output is 5040 ml/min. This output may increase significantly upon demand. In the case of athletes during intense exercise, the cardiac output can rise as high as 35 l/min. The specific cardiac output varies with age, sex and body size. The cardiac index is defined as the cardiac output per m.sup.2 of surface area. For a normal human being weighing 70 kg, the surface area is approximately 1.7 m.sup.2. The cardiac index is shown in FIG. 1 as a function of age. A reduction of the cardiac index to approximately 1.5 (corresponding to .about.2.5 l/min.) will lead to cardiac shock. About 10% of the patients who experience severe acute myocarditis infarction cardiac shock will die.

The various events which occur during the cardiac cycle are shown in FIG. 2. The upper three curves illustrate the aortic, atrial, and ventricular pressures, respectively. The fourth curve from the top shows the ventricular volume and the lower two curves are typical traces from an electrocardiogram and a phonocardiogram. Referring to the electrocardiogram, the QRS wave indicates the onset of ventricular contraction. This causes the ventricular pressure to rise and the blood contained to be pumped out as evidenced by the decrease in ventricular volume. The ventricular contraction ends just after the T wave in the electrocardiogram trace. At that time, the ventricle begins to be refilled by the left atrium. Blood is pumped into the main pulmonary artery during the time the ventricle is contracting. The area above the ventricular volume curve during contraction, shown shaded, corresponds to the volume of blood ejected from the ventricle during a single pulse. The derivative of this portion of the ventricular volume curve corresponds to the time rate of change of flow volume. At the point nearest the ventricle, the actual pulse width of the ejected pulse is approximately 1/5 the pulse period, thus, the average pulse height is approximately 25 l/min.

CHARACTERISTICS OF THE ARTERIAL SYSTEM

The total cross-sectional area, blood velocity, and pressure of the main pulmonary artery, aorta, arteries, arterioles, and capillaries are shown in Table I. The velocity of the pressure pulse is approximately ten times the velocity of the blood flow pulse given in this table. As can be seen, the total cross-sectional area of the capillaries is approximately 10.sup.3 times that of the main pulmonary artery and the aorta and the blood velocity is approximately 10.sup.-3 that in the main pulmonary artery and the aorta. The aorta itself decreases in diameter with distance from the heart. The taper measured by D. J. Patel in large mongrel dogs corresponded to approximately 3% decrease in cross-sectional area per cm. The ascending aorta and main pulmonary artery are relatively elastic. During the pressure pulse Patel et al. have reported that the ascending aorta and pulmonary artery change their diameters by .+-.6% and .+-.11%, respectively.

TABLE I ______________________________________ AREA VELOCITY PRESSURE PART cm.sup.2 cm/sec mmHg ______________________________________ Main Pulmonary 6.0 30.00 20-30 Artery Aorta 4.5 40.00 80-120 Arteries 20.0 9.00 75-130 Arterioles 400.0 0.45 50-90 Capillaries 4500.0 0.04 0-30 ______________________________________

TECHNIQUE FOR FLOW MEASUREMENT

Fluid-flow measurements have a large variety of applications including the measurement of flowing liquids, gases, and slurries for transportation of goods, chemical materials, and vehicle fuel flow. In general, flow sensors consist of a primary element that is in contact with the flowing fluid and a secondary device that measures the action of the fluid stream on the primary element. In the differential pressure technique of the present invention, the primary element is a constriction or section of tube into which is introduced a variation in cross-sectional area. This produces a differential pressure proportional to the flow rate. The secondary element is a differential pressure cell which is the device that measures this differential pressure.

Conventional Techniques for Measuring Cardiac Output

A variety of techniques are presently employed for measuring cardiac output. These include the Fick procedure which involves measuring the ratio of the oxygen absorbed per minute by the lungs to the difference in the oxygen content of the arterial and venous blood. The thermal dilution technique involves injecting a fixed amount of cold solution into the right atrium and measuring the temperature change down stream in a pulmonary artery. The dye dilution method unlike the two above methods, does not involve cardiac catheterization. In this case, a known quantity of dye is injected into a vein and the output of an artery is passed through a photospectrometer which measures the concentration versus time determined. The thermal dilution technique is most often used today. The thermal dilution and an alternate hybrid approach will be discussed in some detail below.

Differential Pressure Technique for Measuring Flow

One method commonly used for determining flow requires the measurement of the differential pressure associated with a change in the cross-sectional area of a flowing liquid. The relevant equation, known as Bernoulli's equation, applies to an incompressible fluid that flows through a tube of varying cross sections. It can be obtained directly from Newton's second law. The Expression can be written in the form

P.sub.1 +.rho.gy.sub.1 +1/2.rho.V.sub.1.sup.2 =P.sub.2 +.rho.gy.sub.2 +1/2V.sub.2.sup.2 (1)

The subscripts refer to the two points where the measurements are made. P is the absolute pressure in N /m.sup.2, .rho. is the density of the fluid in kg/m.sup.3, g is the gravitational constant, y is the elevation at the location of the measurement, and V is the velocity in m/s. Furthermore, from the equation of continuity

Q=A.sub.1 V.sub.1 .rho.=A.sub.2 V.sub.2 .rho. (2)

one obtains ##EQU1## where Q is the quantity of fluid in kg/s and A is the cross-sectional area in m.sup.2. Assuming Y1=Y2 (in the present application where the orientation will be changing due to movements of the patient, a correction for the elevation may be necessary but for this analysis, will be ignored), and solving for P.sub.12 =P.sub.1 -P.sub.2 from Eqs. (1), (2) and (3) yields

P.sub.12 =(Q.sup.2 /2.rho.) (1/A.sub.2.sup.2 -1/A.sub.1.sup.2)(4)

A square root relation between Q and P.sub.12 follows from this expression. The units of P.sub.12 are n/m.sup.2 or pa. This can be converted to mm Hg by using the fact that 13.3 pa=0.1 mm Hg. In the present device, the values of Q expected are from 1.0 l/min to 15 l/min (3.0.times.10.sup.-4 kg/ s to 4.5.times.10.sup.-3 kg/s). In order to attain 0.5% accuracy at the lower limit, it will be necessary to measure cardiac output over 2 orders of magnitude. This requires that the dynamic range of the pressure measurement be 4 orders of magnitude. Conventional catheter pressure measuring devices fail to satisy this requirement by at least 1 order of magnitude. The fiber optic sensors of the invention exhibit the required dynamic range.

Eq. (4) can be solved for Q in terms of the differential pressure and the cross-sectional areas. However, in order to determine the cross-sectional areas, the inside dimensions of the artery must be known. If the artery being measured has a constant cross-sectional area, then the differential pressure can be measured at two adjacent positions and the cross-sectional area of the artery, as well as Q, can be determined.

Two differential pressure measurements P.sub.12 and P.sub.13 expressed by equations in the form of Eq. (4) are made. The ratio of these expressions is given by Eq. (5) where Q has been cancelled:

P.sub.12 /P.sub.13 =(1/A.sub.2.sup.2 -1/A.sub.1.sup.2)/1/A.sub.3.sup.2 -1/A.sub.1.sup.2) (5)

where A.sub.1, A.sub.2 and A.sub.3 can be expressed in terms of the unknown radius of the artery and the radius of the respective probes in the form

A.sub.i =.pi.r.sub.a.sup.2 -.pi..delta..sub.i.sup.2 r.sub.a.sup.2 =.pi.r.sub.a.sup.2 (1-.delta..sub.i.sup.2) (6)

and r.sub.i =.delta..sub.i r.sub.a is the radius of the ith probe. The relation between the values of the various .delta..sub.i 's are known for the individual probes, thus letting

.delta..sub.i =.delta., .delta..sub.2 =a.delta., .delta..sub.3 =b.delta.(7)

where a and b are known. Substituting Eq. (6) and Eq. (7) into Eq. (5) yields

P.sub.12 /P.sub.13 =[1/(1-a.sup.2 .delta..sup.2).sup.2 -1/1-.delta..sup.2).sup.2 ]/[1/1-b.sup.2 .delta..sup.2).sup.2 -1/(1-.delta..sup.2).sup.2 ] (8)

After some algebraic manipulation it can be shown that Eq. (8) becomes ##EQU2## which is a cubic equation in .delta..sup.2, having at least one real root. Thus, using the measured values of P.sub.12 and P.sub.13, .delta. can be calculated and used in Eqs. (7) and (6) to obtain the values of A.sub.1.sup.2 and A.sub.2.sup.2 required in Eq. (4). Thus, with two differential pressure measurements the diameter of and flow through a tube can be continuously monitored.

Alternate techniques of directly measuring the inside dimensions of the artery by an independent technique may be used. These include thermal and dye dilution, ultrasonics, x-rays, etc. In this case only, one differential pressure measurement would be required.

Consideration must be given to measurements made in a tapered region of an artery. In this case, the probes can all be of equal diameter. The differential pressures will be produced as a result of the naturally occurring taper. At the upstream location (i.e., nearest to the ventricle), a variable probe diameter will permit the taper to be measured. This can be accomplished by expanding the diameter of the probe until the value of P.sub.12 measured between the first two sensing regions is zero and repeating the process until the value of P.sub.13 between the first and third locations is reduced to zero. The values of Q and the arterial dimensions can then be determined as a function of time from the subsequent measurements of P.sub.12 and P.sub.13. In addition to the rate of flow and the dimensions of the vein or artery, the elastic coefficients of the vessel walls can also be determined. This coefficient can be defined by the relation

Ep=R.DELTA.P/.DELTA.R (10)

where R is the mean radius, .DELTA.P is the pulse pressure, and .DELTA.R is the change in radius during the cardiac cycle. Values of E.sub.p reported by Patel et al. for various blood vessels are given in Table II.

TABLE II ______________________________________ Blood Vessel E.sub.p (g/cm.sup.2) ______________________________________ Main Pulmonary Artery 163 Ascending Aorta 779 Femoral Artery 4414 Carotoid Artery 6197 ______________________________________

The vessels become stiffer (larger E.sub.p) with distance from the heart. The value of E.sub.p for the main pulmonary artery is significantly less than that of the ascending aorta except in the case of patients exhibiting pulmonary hypertension. Patel et al. reported on three such patients where the value of E.sub.p corresponding to the main pulmonary artery was observed to be approximately five times the corresponding value given in Table II. Finally the presence and location of stenosis can be determined by the use of such a sensor.

FIBER OPTIC SENSORS

Fiber optic differential pressure sensors have the advantages of no moving parts, applicable to the measurement of flow in most fluids, and well-established performance; however, because of their great sensitivity and large dynamic range, they do not suffer from the disadvantages of conventional differential pressure cells (i.e., limited usable flow range due to the square root relation between flow and differential pressure shown in Eq. (4) and an unrecoverable pressure drop). Thus, both the variation in cross-sectional area introduced by the constriction and the resulting unrecoverable pressure drop may be minimized due to the great sensitivity of fiber optic sensors. Furthermore, the large dynamic range yields a wide usable flow range (>3 orders of magnitude). In addition, fiber optic differential pressure sensors have a number of additional features such as immunity to EMI (electromagnetic interference), ability to operate at high temperatures, small size, high reliability, and low power operation.

A fiber optic pressure sensor consists of at least one optical fiber and a means for enabling the pressure to modulate some property (i.e., phase, intensity, polarization, color, etc.) o