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Method and apparatus for the automatic calibration of signals employed in oximetry    

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United States Patent4913150   
Link to this pagehttp://www.wikipatents.com/4913150.html
Inventor(s)Cheung; Peter W. (Mercer Island, WA); Gauglitz; Karl F. (Kirkland, WA); Hunsaker; Scott W. (Seattle, WA); Prosser; Stephen J. (Lynnwood, WA); Wagner; Darrell O. (Monroe, WA); Smith; Robert E. (Edmonds, WA)
AbstractUnder the present invention, a method and apparatus are provided for compensating for the effect temperature variations have on the wavelength of light emitted by the oximeter sensor light sources (40, 42). In pulse oximetry, LEDs are typically employed to expose tissue to light at two different wavelengths. The light illuminating the tissue is received by a detector (38) where signals proportional to the intensity of light are produced. These signals are then processed by the oximeter circuitry to produce an indication of oxygen saturation. Because current oximetry techniques are dependent upon the wavelengths of light emitted by the LEDs (40-42), the wavelengths must be known. Even when predetermined combinations of LEDs (40-42) having relatively precise wavelengths are employed, variations in the wavelength of light emitted may result. Because the sensor (12) may be exposed to a significant range of temperatures while in use, the effect of temperature on the wavelengths may be significant. To compensate for this effect, a temperature sensor (50) is included in the sensor (12) to produce a signal indicative of sensor temperature. This signal is interpreted by the oximeter circuitry including, for example, a microcomputer (16), where the effect of temperature on wavelength is compensated for. In a preferred arrangement, this compensation takes the form of a computation of an alternative calibration curve from which the oxygen saturation is indicated, given a particular processing of signals from the detector (38).
   














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Inventor     Cheung; Peter W. (Mercer Island, WA); Gauglitz; Karl F. (Kirkland, WA); Hunsaker; Scott W. (Seattle, WA); Prosser; Stephen J. (Lynnwood, WA); Wagner; Darrell O. (Monroe, WA); Smith; Robert E. (Edmonds, WA)
Owner/Assignee     Physio-Control Corporation (Redmond, WA)
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Publication Date     April 3, 1990
Application Number     06/897,663
PAIR File History     Application Data   Transaction History
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Filing Date     August 18, 1986
US Classification     600/323 600/549
Int'l Classification     A61B 005/00
Examiner     Jaworski; Francis
Assistant Examiner     Hanley; John C.
Attorney/Law Firm     Christensen, O'Connor, Johnson & Kindness
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USPTO Field of Search     128/633 128/634 128/664 128/665 128/666 330/59 330/308 250/214 A
Patent Tags     automatic calibration signals employed oximetry
   
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The embodiments of the invention in which an exclusive property or privilege is claimed are defined as follows:

1. An apparatus for receiving and processing signals produced by light detection means in response to the illumination of tissue having arterial blood flowing therein by light from first and second sources at separate temperature-dependent wavelengths, said signals containing information about the oxygen saturation of said arterial blood, said apparatus comprising:

temperature indication means for producing an indication of the temperature of said first and second light sources; and

processing means, responsive to said detection means signals and said indication of the temperature of said first and second light sources, for producing an indication of the oxygen saturation of said arterial blood flowing in said tissue that is compensated for the effect of temperature on the wavelengths of said first and second sources.

2. An oximeter, comprising:

first and second light sources for illuminating tissue having arterial blood flowing therein, the light produced by each of said first and second sources being at a separate temperature-dependent wavelength;

temperature-indication means for producing an indication of the temperature of said first and second light sources;

light detection means responsive to the illumination of said tissue for producing signals that are proportional to the intensity of light received at each of said temperature-dependent wavelengths;

processing means for analyzing said detection means signals to produce a preliminary indication of the oxygen saturation of said arterial blood flowing in said tissue;

selection means for selecting a set of data indicating the relationship between independently derived oxygen saturations and said preliminary indications of oxygen saturation, said set of data selected in accordance with said indication of temperature; and

output means for converting said preliminary indication into an oxygen saturation determination by referring to said set of data selected.

3. The oximeter of claim 2, further comprising red optical filter means for filtering said light received by said light detection means.

4. The oximeter of claim 2, further comprising a differential current-to-voltage amplifier means for amplifying said signals produced by said light detection means before said signals are analyzed by said processing means.

5. The oximeter of claim 2, further comprising a sensor housing to which said first and second light sources, said temperature indication means, and said light detection means are connected.

6. The oximeter of claim 5, wherein said sensor housing comprises first and second elements, said first and second light sources being attached to said first element and said light detection means being attached to said second element, said first and second elements arranged to allow insertion of said tissue therebetween and to define a lightpath between said first and second sources and said light detection means that includes said tissue.

7. The oximeter of claim 6, further comprising a reflective member positioned between said light detection means and said first and second light sources, said lightpath including a first segment defined between said first and second sources and said reflective member and a second segment defined between said reflective member and said light detection means, said first and second segments of said lightpath being at a predetermined angle to each other.

8. The oximeter of claim 7, wherein said first and second elements of said sensor housing are pivotally connected in a closably biased manner.

9. The oximeter of claim 2, further comprising a substrate, said first and second light sources and said temperature indication means being mounted on said substrate.

10. The oximeter of claim 2, further comprising wavelength-indication means for indicating said separate temperature-dependent wavelengths of light produced by said first and second sources at a reference temperature, said selection means further selecting said set of data in accordance with said indication of said wavelengths at said reference temperature.

11. The oximeter of claim 10, wherein said wavelengths of said light produced by said first and second sources at said reference temperature are within a plurality of predetermined wavelength ranges.

12. The oximeter of claim 11, wherein said plurality of predetermined wavelength ranges includes a first plurality of ranges substantially centered about a visible-red wavelength and a second plurality of ranges substantially centered about a near-infrared wavelength, said wavelength of said first source falling within one of said first plurality of ranges and said wavelength of said second source falling within one of said second plurality of ranges.

13. A method of determining the oxygen saturation of arterial blood flowing in tissue, comprising the steps of:

exposing the tissue to light from two sources at separate temperature-dependent wavelengths;

producing an indication of the temperature of said sources;

producing signals in response to the exposure of the tissue to said light at said temperature-dependent wavelengths; and

producing an indication of said oxygen saturation, from said signals and said indication of the temperature of said sources, that is compensated for the effect of temperature on the wavelengths of said sources.

14. The method of claim 13, further comprising the step of producing an indication of said separate temperature-dependent wavelengths at a reference temperature.

15. The method of claim 14, wherein said indication of said oxygen saturation is further produced from said indication of said separate temperature-dependent wavelengths at said reference temperature.

16. The method of claim 15, wherein said separate temperature-dependent wavelengths of light from said sources at said reference temperature are within a plurality of predetermined wavelength ranges.

17. The method of claim 16, wherein said plurality of predetermined wavelength ranges includes a first plurality of ranges substantially centered about a visible-red wavelength and a second plurality of ranges substantially centered about a near-infrared wavelength, said wavelength of said first source at said reference temperature falling within one of said first plurality of ranges and said wavelength of said second source at said reference temperature falling within one of said second plurality of ranges.
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BACKGROUND OF THE INVENTION

This invention relates to oximetry and, more particularly, to automatic calibration techniques employed in oximetry.

The arterial oxygen saturation and pulse rate of an individual may be of interest for a variety of reasons. For example, in the operating room up-to-date information regarding oxygen saturation can be used to signal changing physiological factors, the malfunction of anaesthesia equipment, or physician error. Similarly, in the intensive care unit, oxygen saturation information can be used to confirm the provision of proper patient ventilation and allow the patient to be withdrawn from a ventilator at an optimal rate.

In many applications, particularly including the operating room and intensive care unit, continual information regarding pulse rate and oxygen saturation is important if the presence of harmful physiological conditions is to be detected before a substantial risk to the patient is presented. A noninvasive technique is also desirable in many applications, for example, when a home health care nurse is performing a routine check-up, because it increases both operator convenience and patient comfort. Pulse transmittance oximetry is addressed to these problems and provides noninvasive, continual information about pulse rate and oxygen saturation. The information produced, however, is only useful when the operator can depend on its accuracy. The method and apparatus of the present invention are, therefore, directed to the improved accuracy of such information without undue cost.

As will be discussed in greater detail below, pulse transmittance oximetry basically involves measurement of the effect arterial blood in tissue has on the intensity of light passing therethrough. More particularly, the volume of blood in the tissue is a function of the arterial pulse, with a greater volume present at systole and a lesser volume present at diastole. Because blood absorbs some of the light passing through the tissue, the intensity of the light emerging from the tissue is inversely proportional to the volume of blood in the tissue. Thus, the emergent light intensity will vary with the arterial pulse and can be used to indicate a patient's pulse rate. In addition, the absorption coefficient of oxyhemoglobin (hemoglobin combined with oxygen, HbO.sub.2) is different from that of unoxygenated hemoglobin (Hb) for most wavelengths of light. For that reason, differences in the amount of light absorbed by the blood at two different wavelengths can be used to indicate the hemoglobin oxygen saturation, % SaO.sub.2 (OS), which equals ([HbO.sub.2 ]/([Hb]+[HbO.sub.2 ])).times.100%. Thus, measurement of the amount of light transmitted through, for example, a finger can be used to determine both the patient's pulse rate and hemoglobin oxygen saturation.

As will be appreciated, the intensity of light transmitted through a finger is a function of the absorption coefficient of both "fixed" components, such as bone, tissue, skin, and hair, as well as "variable" components, such as the volume of blood in the tissue. The intensity of light transmitted through the tissue, when expressed as a function of time, is often said to include a baseline component, which varies slowly with time and represents the effect of the fixed components on the light, as well as a periodic pulsatile component, which varies more rapidly with time and represents the effect that changing tissue blood volume has on the light. Because the attenuation produced by the fixed tissue components does not contain information about pulse rate and arterial oxygen saturation, the pulsatile signal is of primary interest. In that regard, many of the prior art transmittance oximetry techniques eliminate the so-called "DC" baseline component from the signal analyzed.

For example, in U.S. Pat. No. 2,706,927 (Wood) measurements of light absorption at two wavelengths are taken under a "bloodless" condition and a "normal" condition. In the bloodless condition, as much blood as possible is squeezed from the tissue being analyzed. Then, light at both wavelengths is transmitted through the tissue and absorption measurements made. These measurements indicate the effect that all nonblood tissue components have on the light. When normal blood flow has been restored to the tissue, a second set of measurements is made that indicates the influence of both the blood and nonblood components. The difference in light absorption between the two conditions is then used to determine the average oxygen saturation of the tissue, including the effects of both arterial and venous blood. As will be readily apparent, this process basically eliminates the DC, nonblood component from the signal that the oxygen saturation is extracted from.

For a number of reasons, however, the Wood method fails to provide the necessary accuracy. For example, a true bloodless condition is not practical to obtain. In addition, efforts to obtain a bloodless condition, such as by squeezing the tissue, may result in a different light transmission path for the two conditions. In addition to problems with accuracy, the Wood approach is both inconvenient and time consuming.

A more refined approach to pulse transmittance oximetry is disclosed in U.S. Pat. No. 4,167,331 (Nielsen). The disclosed oximeter is based upon the principle that the absorption of light by a material is directly proportional to the logarithm of the light intensity after having been attenuated by the absorber, as derived from the Beer-Lambert law. The oximeter employs light-emitting diodes (LEDs) to produce light at red and infrared wavelengths for transmission through tissue. A photosensitive device responds to the light produced by the LEDs, after it has been attenuated by the tissue, and produces an output current. That output current is amplified by a logarithmic amplifier to produce a signal having AC and DC components and containing information about the intensity of light transmitted at both wavelengths. Sample-and-hold circuits demodulate the red and infrared wavelength signals. The DC components of each signal are then blocked by a series bandpass amplifier and capacitors, eliminating the effect of the fixed absorptive components from the signal. The resultant AC signal components are unaffected by fixed absorption components, such as hair, bone, tissue, skin. An average value of each AC signal is then produced. The ratio of the two averages is then used to determine the oxygen saturation from empirically determined values associated with the ratio. The AC components are also used to determine the pulse rate.

Another reference addressed to pulse transmittance oximetry is U.S. Pat. No. 4,407,290 (Wilber). In that reference, light pulses produced by LEDs at two different wavelengths are applied to, for example, an earlobe. A sensor responds to the light transmitted through the earlobe, producing a signal for each wavelength having a DC and AC component resulting from the presence of constant and pulsatile absorptive components in the earlobe. A normalization circuit employs feedback to scale both signals so that the DC nonpulsatile components of each are equal and the offset voltages removed. Decoders separate the two signals, so controlled, into channels A and B where the DC component is removed from each. The remaining AC components of the signals are amplified and combined at a multiplexer prior to analog-to-digital (A/D) conversion. Oxygen saturation is determined by a digital processor in accordance with the following relationship:

OS=X.sub.1 R(.lambda..sub.1)+X.sub.2 R(.lambda..sub.2)/(X.sub.3 R(.lambda..sub.1)+X.sub.4 R(.lambda.2) (1)

wherein empirically derived data for the constants X.sub.1, X.sub.2, X.sub.3 and X.sub.4 is stored in the processor.

European Patent Application No. 83,304,939.8 (New, Jr. et al.) discloses an additional pulse transmittance oximeter. Two LEDs expose a body member, for example, a finger, to light having red and infrared wavelengths, with each LED having a one-in-four duty cycle. A detector produces a signal in response that is then split into two channels. The one-in-four duty cycle allows negatively amplified noise signals to be integrated with positively amplified signals including the detector response and noise, thereby eliminating the effect of noise on the signal produced. The resultant signals include a substantially constant DC component and an AC component. To improve the accuracy of a subsequent analog-to-digital (A/D) conversion, a fixed DC value is subtracted from the signal prior to the conversion. This level is then added back in by a microprocessor after the conversion. Logarithmic analysis is avoided by the microprocessor in the following manner. For each wavelength of light transmitted through the finger, a quotient of the AC component over the constant component is determined. The ratio of the two quotients is then determined and fitted to a curve of independently derived oxygen saturations. To compensate for the different transmission characteristics of different patient's fingers, an adjustable drive source for the LEDs is provided.

In European Patent Application No. 83,304,940.6 (New et al.) a calibrated oximeter probe is disclosed. That probe includes a coding resistor or coding connector used to identify the particular combination of wavelengths of light emitted by the two LEDs contained thereon. Oximeter circuitry then senses the code of the resistor or connector to determine the wavelengths of light emitted by the LEDs. In this manner, the effect that different wavelengths have on the oxygen saturation computations can be compensated for. The basis upon which oxygen saturation is measured involves the determination of the quotient of the pulsatile component over the constant component of light transmitted at each wavelength. The ratio of the quotients for the two wavelengths is then fitted to a curve of independently derived oxygen saturations. Outputs include pulse rate and oxygen saturation.

Even with the calibration technique of New, Jr. et al. employed, however, the wavelengths of light emitted by the LEDs may change in a manner that the oximeter circuitry is unable to detect. As will be appreciated, such variations can significantly affect the accuracy of the oxygen saturation measurements. The disclosed invention is directed to the provision of more complete information about the actual wavelengths of the light emitted and, hence, the production of more accurate oxygen saturation measurements.

SUMMARY OF THE INVENTION

The present invention discloses a method of determining the oxygen saturation of arterial blood flowing in tissue. The method includes an initial step in which the tissue is exposed to light from two sources at separate temperature-dependent wavelengths. An indication of the temperature of the sources is produced, as are signals produced in response to the exposure of the tissue to the light at the separate temperature-dependent wavelengths. A preliminary indication of the oxygen saturation is then produced from the signals. A comparison of independently derived oxygen saturations with a continuum of such preliminary indications of oxygen saturation is then selected in accordance with the indication of the temperature of the sources earlier produced. From this comparison, the actual oxygen saturation corresponding to the preliminary indication previously obtained is produced.

In accordance with a particular aspect of the invention, an indication of the separate temperature-dependent wavelengths of light emitted by the sources at a reference temperature is produced. This indication is used to further aid in the selection of the appropriate comparison of independently derived oxygen saturations to the preliminary indications of oxygen saturation.

In accordance with a further aspect of the invention, an oximeter is disclosed that employs the foregoing method to determine the oxygen saturation of arterial blood flowing in tissue. The oximeter includes first and second light sources that illuminate the tissue with light at separate temperature-dependent wavelengths. The oximeter also includes a temperature detector that produces an indication of the temperature of the light sources. Signals that are proportional to the intensity of light received from the tissue at each of the temperature-dependent wavelengths are produced by a light detector and a processor analyzes the signals to produce a preliminary indication of the oxygen saturation of the blood. A selection circuit selects a particular comparison of oxygen saturations with the continuum of preliminary indications of the oxygen saturation in accordance with the indication of temperature received. Finally, a converter converts the preliminary indication of oxygen saturation into an oxygen saturation determination by reference to the comparison selected.

In accordance with additional aspects of the invention, a red optical filter filters the light received by the light detector. The signals produced by the light detector can, similarly, be amplified by a differential current-to-voltage amplifier before being analyzed by the processor. A sensor housing, having first and second elements, is employed to receive the tissue being analyzed and to define a light path between the light sources and the detector. A mirror, attached to the housing, is positioned between the light sources and detector and breaks the lightpath up into first and second segments at a predetermined angle with respect to each other. The two elements of the housing may pivot and be closably biased. In another arrangement, an apparatus is constructed in accordance with this invention independently of the light sources and light detector.

In accordance with another aspect of the invention, a sensor is disclosed for use with an oximeter to determine the oxygen saturation of arterial blood flowing in tissue. The sensor includes first and second light sources for illuminating the tissue with light at separate temperature-dependent wavelengths. A temperature indicator is also included to produce an indication of the temperature of the light sources. Signals are produced in response to the illumination of the tissue at each of the temperature-dependent wavelengths by a light detector.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention can best be understood by reference to the following portion of the specification, taken in conjunction with the accompanying drawings in which:

FIG. 1 is a block diagram of an oximeter including a sensor, input/output (I/O) circuit, microcomputer, alarm, displays, power supply, and keyboard;

FIG. 2 is a block diagram illustrating the transmission of light through an absorptive medium;

FIG. 3 is a block diagram illustrating the transmission of light through the absorptive medium of FIG. 2, wherein the medium is broken up into elemental components;

FIG. 4 is a graphical comparison of the incident light intensity to the emergent light intensity as modeled in FIG. 2;

FIG. 5 is a graphical comparison of the specific absorption coefficients for oxygenated hemoglobin and deoxygenated hemoglobin as a function of the wavelength of light transmitted therethrough;

FIG. 6 is a block diagram illustrating the transmission of light through a block model of the components of a finger;

FIG. 7 is a graphical comparison of independently derived oxygen saturation measurements with a variable that is measured by the oximeter;

FIG. 8 is a schematic illustration of the transmission of light at two wavelengths through a finger in accordance with the invention;

FIG. 9 is a graphical plot as a function of time of the transmittance of light at the red wavelength through the finger;

FIG. 10 is a graphical plot as a function of time of the transmission of infrared light through the finger;

FIG. 11 is an exploded view showing the sensor of FIG. 1 in greater detail;

FIG. 12 is a more detailed schematic of the I/O circuit illustrated in the system of FIG. 1;

FIG. 13 is a schematic diagram of a conventional current-to-voltage amplifier circuit;

FIG. 14 is a schematic diagram of a differential current-to-voltage preamplifier circuit included in the I/O circuit of FIG. 1;

FIG. 15 is a graphical representation of the possible ranges of I/O circuit output, showing the desired response of the I/O circuit and microcomputer at each of the various possible ranges;

FIG. 16 is a more complete schematic diagram of the microcomputer illustrated in FIG. 1; and

FIG. 17 is a family of curves similar to the one illustrated in FIG. 7.

DETAILED DESCRIPTION

Referring to the overall system block diagram shown in FIG. 1, a pulse transmittance oximeter 10 employing this invention includes a sensor 12, input/output (I/O) circuit 14, microcomputer 16, power source 18, display 20, keyboard 22 and alarm 24. Before discussing these elements in detail, however, an outline of the theoretical basis of pulse transmittance oximetry as practiced by the oximeter of FIG. 1 is provided.

An understanding of the relevant theory begins with a discussion of the Beer-Lambert law. This law governs the absorption of optical radiation by homogeneous absorbing media and can best be understood with reference to FIGS. 2 and 3 in the following manner.

As shown in FIG. 2, incident light having an intensity I.sub.0 impinges upon an absorptive medium 26. Medium 26 has a characteristic absorbance factor A that indicates the attenuating affect medium 26 has on the incident light. Similarly, a transmission factor T for the medium is defined as the reciprocal of the absorbance factor, I/A. The intensity of the light I.sub.1 emerging from medium 26 is less than I.sub.0 and can be expressed functionally as the product TI.sub.0. With medium 26 divided into a number of identical components, each of unit thickness (in the direction of light transmission) and the same transmission factor T, the effect of medium 26 on the incident light I.sub.0 is as shown in FIG. 3.

There, medium 26 is illustrated as consisting of three components 28, 30, and 32. As will be appreciated, the intensity I.sub.1 of the light emerging from component 28 is equal to the incident light intensity I.sub.0 multiplied by the transmission factor T. Component 30 has a similar effect on light passing therethrough. Thus, because the light incident upon component 30 is equal to the product TI.sub.0, the emergent light intensity I.sub.2 is equal to the product TI.sub.1 or T.sup.2 I.sub.0. Component 32 has the same effect on light and, as shown in FIG. 3, the intensity of the emergent light I.sub.3 for the entire medium 26 so modeled is equal to the product TI.sub.2 or T.sup.3 I.sub.0. If the thickness d of medium 26 is n unit lengths, it can be modeled as including n identical components of unit thickness. It will then be appreciated that the intensity of light emerging from medium 26 can be designated I.sub.n and the product is equal to T.sup.n I.sub.0. Expressed as a function of the absorbance constant A, I.sub.n can also be written as the product (1/A.sup.n) I.sub.0.

From the preceding discussion, it will be readily appreciated that the absorptive effect of medium 26 on the intensity of the incident light I.sub.0 is one of exponential decay. Because A may be an inconvenient base to work with, I.sub.n can be rewritten as a function of a more convenient base, b, by recognizing that A.sup.n is equal to b.sup..alpha.n, where .alpha. is the absorbance of medium 26 per unit length. The term .alpha. is frequently referred to as the extinction coefficient and is equal to log .sub.b A.

Given the preceding discussion, it will be appreciated that the intensity of the light I.sub.n emerging from medium 26 can be expressed in base 10 as I.sub.0 10.sup.-.alpha. 1.sup.n, or in base e as I.sub.0 e.sup.-.alpha. 2.sup.n, where .alpha..sub.1 and .alpha..sub.2 are the appropriate relative extinction coefficients for base 10 and base e respectively. The effect that the thickness of medium 26 has on the emergent light intensity I.sub.n is graphically depicted in FIG. 4. If the light incident upon medium 26 is established as having unit intensity, FIG. 4 also represents the transmission factor T of the entire medium as a function of thickness.

The discussion above can be applied generally to the medium 26 shown in FIG. 2 to produce:

I.sub.1 =I.sub.0 e.sup.-.alpha.d

where I.sub.1 is the emergent light intensity, I.sub.0 is the incident light intensity, .alpha. is the absorbance coefficient of the medium per unit length, d is the thickness of the medium in unit lengths, and the exponential nature of the relationship has arbitrarily been expressed in terms of base e. Equation (1) is commonly referred to as the Beer-Lambert law of exponential light decay through a homogeneous absorbing medium.

With this basic understanding of the Beer-Lambert law, a discussion of its application to the problems of pulse rate and hemoglobin oxygen saturation measurement is now presented. As shown in FIG. 5, the absorption coefficients for oxygenated and deoxygenated hemoglobin are different at every wavelength, except isobestic wavelengths. Thus, it will be appreciated that if a person's finger is exposed to incident light and the emergent light intensity measured, the difference in intensity between the two, which is the amount of light absorbed, contains information relating to the oxygenated hemoglobin content of the blood in the finger. The manner in which this information is extracted from the Beer-Lambert law is discussed below. In addition, it will be appreciated that the volume of blood contained within an individual's finger varies with the individual's arterial pulse. Thus, the thickness of the finger also varies slightly with each pulse, creating a changing path length for light transmitted through the finger. Because a longer lightpath allows additional light to be absorbed, time-dependent information relating to the difference between the incident and emergent light intensities can be used to determine the individual's pulse. The manner in which this information is extracted from the Beer-Lambert law is also discussed below.

As noted in the preceding paragraph, information about the incident and emergent intensities of light transmitted through a finger can be used to determine oxygen saturation and pulse rate. The theoretical basis for extracting the required information, however, is complicated by several problems. For example, the precise intensity of the incident light applied to the finger is not easily determined. Thus, it may be necessary to extract the required information independently of the intensity of the incident light. Further, because the changing volume of blood in the finger and, hence, thickness of the lightpath therethrough, are not exclusively dependent upon the individual's pulse, it is desirable to eliminate the changing path length as a variable from the computations.

The manner in which the Beer-Lambert law is refined to eliminate the incident intensity and path length as variables is as follows. With reference to FIG. 6, a human finger is modeled by two components 34 and 36, in a manner similar to that shown in FIG. 3. Baseline component 34 models the unchanging absorptive elements of the finger. This component includes, for example, bone, tissue, skin, hair, and baseline venous and arterial blood and has a thickness designated d and an absorbance .alpha..

Pulsatile component 36 represents the changing absorptive portion of the finger, the arterial blood volume. As shown, the thickness of this component is designated .DELTA.d, representing the variable nature of the thickness, and the absorbance of this component is designated .alpha..sub.A representing the arterial blood absorbance.

As will be appreciated from the earlier analysis with respect to FIG. 3, the light I.sub.1 emerging from component 34 can be written as a function of the incident light intensity I.sub.0 as follows:

I.sub.1 =I.sub.0 e.sup.-.alpha.d (2)

Likewise, the intensity of light I.sub.2 emerging from component 36 is a function of its incident light intensity I.sub.1, and:

I.sub.2 =I.sub.1 e.sup.-.alpha. A.sup..DELTA.d (3)

Substitution of the expression for I.sub.1 developed in equation (2) for that used in equation (3), when simplified, results in the following expression for the intensity I.sub.2 of light emerging from the finger as a function of the intensity of light I.sub.0 incident upon the finger;

I.sub.2 =I.sub.0 e.sup.-[.alpha.d+.alpha. A.sup..DELTA.d] (4)

Because our interest lies in the effect on the light produced by the arterial blood volume, the relationship between I.sub.2 and I.sub.1 is of particular interest. Defining the change in transmission produced by the arterial component 36 as T.sub..DELTA.A, we have:

T.sub..DELTA.A =I.sub.2 /I.sub.1 (5)

Substituting the expressions for I.sub.1 and I.sub.2 obtained in equations (2) and (3), respectively, equation (5) becomes: ##EQU1## It will be appreciated that the I.sub.0 term can be cancelled from both the numerator and denominator of equation (6), thereby eliminating the input light intensity as a variable in the equation. With equation (6) fully simplified, the change in arterial transmission can be expressed as:

T.sub..DELTA.A =e.sup.-.alpha. A.sup..DELTA.d (7)

A device employing this principle of operation is effectively self-calibrating, being independent of the incident light intensity I.sub.0.

At this point, a consideration of equation (7) reveals that the changing thickness of the finger, .DELTA.d, produced by the changing arterial blood volume still remains as a variable. The .DELTA.d variable is eliminated in the following manner. For convenience of expression, the logarithms of the terms in equation (7) are produced with respect to the same base originally employed in equation (1). Thus, equation (7) becomes:

lnT.sub..DELTA.A =ln(e.sup.-.alpha. A.sup..DELTA.d)=-.alpha..sub.A .DELTA.d(8)

A preferred technique for eliminating the .DELTA.d variable utilizes information drawn from the change in arterial transmission experienced at two wavelengths.

The particular wavelengths selected are determined in part by consideration of a more complete expression of the arterial absorbance .alpha..sub.A :

.alpha..sub.A =(.alpha..sub.OA)(OS)-(.alpha..sub.DA)(1-OS) (9)

where .alpha..sub.OA is the oxygenated arterial absorbance, .alpha..sub.DA is the deoxygenated arterial absorbance, and OS is the hemoglobin oxygen saturation of the arterial blood volume. As will be appreciated from FIG. 5, .alpha..sub.OA and .alpha..sub.DA are su