Ear oximetry process and apparatus - Patent Review 4086915

We claim:

1. A process for determining the value of oxygen saturation of the blood of a subject, comprising:

mounting an earpiece on the ear lobe of the subject, said earpiece comprising light directing means and light intensity detecting means and being arranged such that the light directing means is on one side of said ear lobe and the light detecting means is on the other side of said ear lobe;

directing a first ray of light, from a first light source, at a first frequency at said light directing means;

directing a second ray of light, from a second light source, at a second frequency at said light directing means;

whereby said rays are directed, by said light directing means, to said ear lobe and transmitted through said ear lobe, and the light intensities of the light rays transmitted through the ear lobe at said first and second frequencies are detected, by said light detecting means, and converted, in said light detecting means, to electrical signals representative of said light intensities;

differentiating, with a differentiating means, said electrical signals representative of said light intensities of said first and second frequencies respectively;

providing said differentiated signals to a processor means, said processor means comprising a set of predetermined coefficients;

and processing, in said processor means, said differentiated signals in association with said predetermined coefficients to obtain said value of oxygen saturation.

2. A process as defined in claim 1 wherein said first and second rays of light are directed at said light directing means in alternating sequence under the control of a multiplexer unit;

and wherein said electrical signals are reconstituted under the control of a demultiplexer in synchronism with said multiplexer.

3. A process as defined in claim 1 wherein said electrical signals comprise a low level AC signal superimposed on a slowly varying high level signal, wherein said low level AC signal is separated from said high level signal by the steps of:

taking samples of said electrical signals;

applying said samples to the positive input terminal of a differential amplifier;

simultaneously applying said samples to the input terminal of a low resolution analogue to digital converter and, therefrom, to the input terminal of a digital to analogue converter whereby to obtain a low resolution conversions of said samples;

the output of said digital to analogue converter being applied to the negative input terminal of said differential amplifier;

wherein said low level AC signal is the only signal which is differentiated with said differentiating means.

4. Apparatus for determining the oxygen saturation of the blood of a subject and used in association with an earpiece for mounting on the ear of the subject, the earpiece comprising light directing means and light intensity detecting means and being arranged such that the light detecting means is mounted on one side of the ear lobe and the light directing means is mounted on the other side of the ear lobe, and means for directing rays of light at a first frequency and rays of light at a second frequency at said light directing means whereby said rays are directed at the ear lobe and transmitted through the ear lobe and the light intensity of the light transmitted through the ear lobe at said first and second frequencies is detected to provide electrical signals representative of said light intensities;

said apparatus comprising:

differentiating means for differentiating said electrical signals representative of said light intensities at said first and second frequencies;

processor means, comprising a set of predetermined coefficients and adapted to process said differentiated signals in association with said predetermined coefficients to obtain said value of oxygen saturation.

5. An apparatus as defined in claim 4 wherein said means for directing said rays of light comprises a first light source and a second light source, and further comprising:

multiplexer means for activating said light sources in alternating sequence to thereby provide samples of said electrical signals representative, respectively, of light intensities at said first and second frequencies at the output of said detector means;

and means for reconstituting said samples representative of said first frequency and said samples representative of said second frequency to provide a first reconstituted waveform and a second reconstituted waveform respectively, the aforementioned means for reconstituting said samples being in synchronism with said multiplexer means.

6. An apparatus as defined in claim 5 wherein said means for reconstituting said samples further comprises:

an input buffer amplifier whose input is adapted to be connected to the output of said light intensity detecting means;

a low resolution analogue to digital converter and a differential amplifier, the output of said buffer amplifier being connected, in parallel, to the input terminal of said low resolution analogue to digital convertor and to the positive input terminal of said differential amplifier;

a digital memory device and a digital to analogue converter, the output of said analogue to digital convertor being connected to said digital memory device whose output is connected to the input terminal of said digital to analogue convertor, the output of which is connected to the positive terminal of said differential amplifier;

and timer means connected to said memory device and said digital to analogue convertor;

whereby when a total signal is applied to said buffer amplifier, a resolution portion thereof is subtracted from the totals signal in said differential amplifier.

7. An apparatus as defined in claim 6 wherein said light directing means comprises a fiber optic rod, and wherein said light intensity detecting means comprises a photo transistor.

8. A process for determining the value of oxygen saturation of the blood of a subject, comprising:

mounting a source of light adjacent the subject such that light from the source is directed at an area of skin surface on the subject;

disposing a light detector means relative to said source of light such that light passing from the source to the light means detector will contact said area;

directing a first ray of light, from said source of light, at a first frequency at said area;

directing a second ray of light, from said source of light, at a second frequency at said area;

detecting, with said light detector means, the light intensity of the rays of light after they contact said area to provide electrical signals representative of the light intensities at said first and second frequencies;

differentiating, with a differentiating means; said electrical signals representative of said light intensities of said first and second frequencies respectively;

providing said differentiated signals to a processor means, said processor means comprising a set of predetermined coefficients;

and processing, with said processor means, said differentiated signals in association with said predetermined coefficients to obtain said value of oxygen saturation.

9. A process as defined in claim 8 wherein said first and second rays of light are directed at said area in alternating sequence under the control of a multiplexer unit;

and wherein said electrical signals are reconstituted under the control of a demultiplexer in synchronism with said multiplexer.

10. A process as defined in claim 8 wherein said electrical signals comprise a low level AC signal superimposed on a slowly varying high level signal, wherein said low level AC signal is separated from said high level signal by the steps of:

taking samples of said electrical signals;

applying said samples to the positive input terminal of a differential amplifier;

simultaneously applying said samples to the input terminal of a low resolution analogue to digital converter and, therefrom, to the input terminal of a digital to analogue converter whereby to obtain a low resolution conversions of said samples;

the output of said digital to analogue converter being applied to the negative input terminal of said differential amplifier;

wherein said low level AC signal is the only signal which is differentiated with said differentiating means.

11. A process for determining the value of oxygen saturation of the blood of a subject, comprising:

mounting a source of light such that light from the source is directed at an area of skin surface on the subject to be reflected by said area of skin surface;

disposing a light detector means relative to said area such that light reflected from said area will be directed at said detector means;

directing a first ray of light, from said source of light, at a first frequency at said area and, thereby, by reflectance, at said detector means;

directing a second ray of light, from said source of light, at a second frequency at said area and, thereby, by reflectance, at said detector means;

detecting, with said light detector means, the light intensity of the reflected rays of light to provide electrical signals representative of the light intensities at said first and second frequencies;

differentiating, with a differentiating means, said electrical signals representative of said light intensities at said first and second frequencies respectively;

providing said differentiated signals to a processor means, said processor means comprising a set of predetermined coefficients;

and processing, with said processor means, said differentiated signals in association with said predetermined coefficients to obtain said value of oxygen saturation.

12. A process as defined in claim 11 wherein said first and second rays of light are directed at said area in alternating sequence under the control of a multiplexer unit;

and wherein said electrical signals are reconstituted under the control of a demultiplexer in synchronism with said multiplexer.

13. A process as defined in claim 11 wherein said electrical signals comprise a low level AC signal superimposed on a slowly varying high level signal, wherein said low level AC signal is separated from said high level signal by the steps of:

taking samples of said electrical signals;

applying said samples to the positive input terminal of a differential amplifier;

simultaneously applying said samples to the input terminal of a low resolution analogue to digital converter and, therefrom, to the input terminal of a digital to analogue converter whereby to obtain a low resolution conversions of said samples;

the output of said digital to analogue converter being applied to the negative input terminal of said differential amplifier;

wherein said low level AC signal is the only signal which is differentiated with said differentiating means.

14. A process as defined in claim 11 wherein said area of skin surface comprises the ear lobe of a subject.

15. A process as defined in claim 11 wherein the area of skin surface comprises the forehead of the subject.

16. Apparatus for determining the oxygen saturation of the blood of a subject and used in association with a source of light and light intensity detecting means, the source of light being mounted such that it is directed at an area of skin surface of the subject, the source of light and the light intensity detecting means being arranged relative to each other such that light passing from the source to the detecting means will contact said area, and means in said source of light for transmitting the light at a first frequency and at a second frequency, said detecting means providing electrical signals representative of said light intensities;

said apparatus comprising:

differentiating means for differentiating said electrical signals representative of said light intensities at said first and second frequencies;

processor means, comprising a set of predetermined coefficients and adapted to process said differentiated signals in association with said predetermined coefficients to obtain said value of oxygen saturation.

17. An apparatus as defined in claim 16 wherein said source of light comprises a first light source and a second light source, and further comprising:

multiplexer means for activating said light sources in alternating sequence to thereby provide samples of said electrical signals representative, respectively, of light intensities at said first and second frequencies at the output of said detector means;

and means for reconstituting said samples representative of said first frequency and said samples representative of said second frequency to provide a first reconstituted waveform and a second reconstituted waveform respectively, the aforementioned means for reconstituting said samples being in synchronism with said multiplexer means.

18. An apparatus as defined in claim 17 wherein said means for reconstituting said samples further comprises:

an input buffer amplifier whose input is adapted to be-connected to the output of said light intensity detecting means;

a low resolution analogue to digital converter and a differential amplifier, the output of said buffer amplifier being connected, in parallel, to the input terminal of said low resolution analogue to digital convertor and to the positive input terminal of said differential amplifier;

a digital memory device and a digital to analogue converter, the output of said analogue to digital convertor being connected to said digital memory device whose output is connected to the input terminal of said digital to analogue convertor, the output of which is connected to the positive terminal of said differential amplifier;

and timer means connected to said memory device and said digital to analogue convertor;

whereby when a total signal is applied to said buffer amplifier, a resolution portion thereof is subtracted from the totals signal in said differential amplifier.

19. Apparatus for determining the oxygen saturation of the blood of a subject and used in association with a source of light, which source of light directs rays of light at an area of skin surface of the subject for reflection from the area, light intensity detecting means being disposed such that light rays reflected from said area will be directed at said detecting means, means in said source of light for transmitting rays of light at a first frequency and at a second frequency, whereby the light intensity of the light rays reflected from said area at said first and second frequencies is detected to provide electrical signals representative of said light intensities;

said apparatus comprising:

differentiating means for differentiating said electrical signals representative of said light intensities at said first and second frequencies;

processor means, comprising a set of predetermined coefficients and adapted to process said differentiated signals in association with said predetermined coefficients to obtain said value of oxygen saturation.

20. An apparatus as defined in claim 19 wherein said source of light comprises a first light source and a second light source, and further comprising:

multiplexer means for activating said light sources in alternating sequence to thereby provide samples of said electrical signals representative, respectively, of light intensities at said first and second frequencies at the output of said detector means;

and means for reconstituting said samples representative of said first frequency and said samples representative of said second frequency to provide a first reconstituted waveform and a second reconstituted waveform respectively, the aforementioned means for reconstituting said samples being in synchronism with said multiplexer means.

21. An apparatus as defined in claim 20 wherein said means for reconstituting said samples further comprises:

an input buffer amplifier whose input is adapted to be connected to the output of said light intensity detecting means;

a low resolution analogue to digital converter and a differential amplifier, the output of said buffer amplifier being connected, in parallel, to the input terminal of said low resolution analogue to digital convertor and to the positive input terminal of said differential amplifier;

a digital memory device and a digital to analogue converter, the output of said analogue to digital convertor being connected to said digital memory device whose output is connected to the input terminal of said digital to analogue convertor, the output of which is connected to the positive terminal of said differential amplifier;

and timer means connected to said memory device and said digital to analogue convertor;

whereby when a total signal is applied to said buffer amplifier, a resolution portion thereof is subtracted from the totals signal in said differential amplifier.

Description Submit all comments and votes

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to a non-invasive method of oximetry in which light contacts an area of skin surface of a subject and is then detected to determine oxygen saturation of the patient's blood, and to an apparatus for carrying out the method. The light which contacts the area can either then pass through the skin of the subject before reaching the detector, or can be reflected from the area to be directed at the detector. More specifically, this invention relates to such a method wherein the rate of change of light intensity is determined to thereby determine oxygen saturation, and to an apparatus for carrying out the method.

2. Statement of the Prior Art

Oximetry methods are used to determine oxygen saturation of a subject's blood, i.e., the percentage of oxygenated hemoglobin in the blood. Such methods may be of the invasive or the non-invasive types. The non-invasive type can be further subdivided into a transmittance method, and a reflectance method. With both the transmittance and reflectance method, a source of light is directed at an area of skin surface of the subject. In the transmittance method, the light passes through the skin of the subject and is then detected by the detector. In the reflectance method, the light is reflected by the area and is then directed at the detector.

In presently known methods of ear oximetry, a light source is directed at one side of the ear lobe or pinna (hereinafter referred to as the ear lobe) and a light detector on the opposite side of the ear detects the intensity of light transmitted through the ear lobe or pinna. Oximetry methods are classified a either relative or absolute.

In the relative methods, a reference is necessary, and saturation is determined relative to the reference. As is well known, the amount of light absorbed by the ear as light is transmitted through it is a function of the attenuation due to skin, muscle, fat, cartilage, etc. of the ear as well as the attenuation due to blood in the ear. The attenuation due to blood is itself dependent on the amount of oxygenated hemoglobin in the blood.

In the absolute method, light at two different frequencies is used, and, advantage is taken of the knowledge that the degree of absorption of red light at a certain frequency is different for oxygenated vs. deoxygenated blood. However, as regards infra-red light at a certain frequency, the degree of absorption is the same for both oxygenated and deoxygenated blood. By measuring absorption at red and infra-red light, oxygen saturation can be determined.

One approach of the absolute method is to provide a transducer which can squeeze the ear tightly to provide a "bloodless ear." The amount of light absorbed by the bloodless ear is measured, and the transducer is then adjusted so that the ear is no longer squeezed and blood can once again flow in the ear. Light is again transmitted through the ear lobe under the second condition, and the difference in the amount of light absorbed under the two conditions is used as an indication of the amount of oxygenated hemoglobin in the blood.

This approach has the disadvantages that, no matter how tight the ear lobe is squeezed, there is still some blood left, so that oxygen saturation determined in this fashion may be inaccurate. Further, the approach is clumsy, and therefore not often used, and, in addition, this approach does not take into account the differences of absorption due to differences in the non-blood tissue in the light path.

Other disadvantages of this method are that results may be affected by such variables as the depth of blood in the ear lobe, and differences in total hemoglobin concentration in the blood.

SUMMARY OF THE INVENTION

It is therefore an object of the invention to provide a method of oximetry which overcomes or substantially reduces the above disadvantages.

It is a further object of the invention to provide an apparatus specifically for the purpose of carrying out the invention.

In accordance with the invention, it is the time derivative of the intensity of the transmitted light which is measured to determine oxygen saturation.

More specifically, in accordance with the invention a process for determining the value of oxygen saturation of the blood of a subject comprises: mounting a source of light adjacent the subject such that light from the source is directed at an area of skin surface on the subject; disposing a light detector means relative to said source of light such that light passing from the source to the detector will contact said area; directing a first ray of light at a first frequency at said area; directing a second ray or light at a second frequency at said area; detecting the light intensity of the rays of light after they contact said area to provide electrical signals representative of the light intensities at said first and second frequencies; differentiating said electrical signals representative of the light intensities at said first and second frequencies respectively; providing said differentiated signals to a processor means, said processor means comprising a set of predetermined coefficients; and processing said differentiated signals in association with said predetermined coefficients to obtain said value of oxygen saturation.

Using a reflectance approach, the process consists of:

mounting a source of light such that light from the source is directed at an area of skin surface on the subject to be reflected by said area of skin surface;

disposing a light detector means relative to said area such that light reflected from said area will be directed at said detector;

directing a first ray of light at a first frequency at said area and, thereby, by reflectance, at said detector;

directing a second ray of light at a second frequency at said area and, thereby, by reflectance, at said detector;

detecting the light intensity of the reflected rays of light to provide electrical signals representative of the light intensities at said first and second frequencies;

differentiating said electrical signals representative of the light intensities at said first and second frequencies respectively;

providing said differentiated signals to a processor means, said processor means comprising a set of predetermined coefficients;

and processing said differentiated signals in association with said predetermined coefficients to obtain said value of oxygen saturation.

Using the transmittance approach, the process consists of:

mounting an earpiece on the ear lobe of the subject, the ear piece comprising light directing means and light intensity detecting means and being arranged such that the light directing means is on one side of said ear lobe and the light detecting means is on the other side of said ear lobe. A first ray of light at a first frequency is directed at the light directing means, and a second ray of light at a second frequency is directed at the light directing means, whereby the rays are directed to the ear lobe and transmitted through the ear lobe, and the light intensity of the light transmitted through the ear lobe at the first and second frequency is detected to provide light intensity signals. The light intensity signals of the first and second frequencies respectively are differentiated and provided to a processor means, the processor means comprising a set of predetermined coefficients. The differentiated signals are processed in association with the predetermined coefficients to obtain the value of oxygen saturation.

Preferably, the first and second rays of light are directed at the light directing means in alternating sequence under the control of a multiplexer unit, and the light intensity signals are reconstituted under the control of a demultiplexer in synchronism with the multiplexer.

The light intensity signals will usually comprise a low level AC signal superimposed on a slowly varying high level signal, and the low level AC signal is separated from the high level signal by the steps of: taking samples of the light intensity signals; applying the samples to the positive input terminal of a differential amplifier; simultaneously applying the samples to the input terminal of a low resolution analogue to digital converter and, therefrom, to the input terminal of a digital to analogue converter whereby to obtain a low resolution conversions of said samples; the output of the digital to analogue converter being applied to the negative input terminal of the differential amplifier.

An apparatus in accordance with the invention for determining the oxygen saturation of the blood of a subject and used in association with a source of light and light intensity detecting means the source of light being mounted such that it is directed at an area of skin surface of the subject, the source of light and the light intensity detecting means being arranged relative to each other such that light passing from the source to the detecting means will contact said area, and means in said source of light for transmitting the light at a first frequency and at a second frequency, said detecting means providing electrical signals representative of said light intensitites.

The apparatus comprising:

differentiating means for differentiating said electrical signals representative of said light intensities at said first and second frequencies respectively;

processor means, comprising a set of predetermined coefficients and adapted to process said differentiated signals in association with said predetermined coefficients to obtain said value of oxygen saturation.

The means for directing the rays of light may comprise a first light source and a second light source.

The apparatus further includes multiplexer means for activating the light sources in alternating sequence to thereby provide samples at the first and second frequencies at the output of the detector means, and means for reconstituting the samples at the first frequency and the samples at the second frequency to provide a first reconstituted waveform and a second reconstituted waveform respectively, the aforementioned means being in synchronism with said multiplexer.

The means for reconstituting the waveform may further comprise an input buffer amplifier whose input is connected to the output of the light intensity detecting means. The output of the buffer amplifier is connected, in parallel, to the input terminal of a low resolution analogue to digital convertor and to the positive input terminal of a differential amplifier. The output of the analogue to digital convertor is connected to a digital memory device whose output is connected to the input terminal of a digital to analogue convertor, the output of which is connected to the positive terminal of said differential amplifier, and further including timer means connected to the memory device and the digital to analogue convertor, whereby when a total signal is applied to the buffer amplifier, a resolution portion thereof is subtracted from the totals signal in the differential amplifier.

The light directing means may comprise a fiber optic rod, and said light intensity detecting means may comprise a photo transistor.

The apparatus may be used with the reflectance method wherein the sources of light and the detectors are disposed on the same side of the area, and the detectors are disposed so as to receive light reflected from the area.

When used with the transmittance method, the apparatus includes an ear piece for mounting on the ear of the subject, the ear piece consisting of a light directing means and light intensity detecting means and being arranged such that the light detecting means is mounted on one side of the ear lobe and the light directing means is mounted on the other side of the ear lobe.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be better understood by an examination of the following description, together with the accompanying drawings in which:

FIG. 1 is a schematic diagram of an electronic ear oximetry apparatus in accordance with the invention;

FIG. 2 illustrates typical reconstructed waveforms at the output of the apparatus in FIG. 1;

FIG. 3 illustrates, in schematic form, a processor for the apparatus of FIG. 1; and

FIG. 4 illustrates an embodiment of the shaper demultiplexer circuit of the apparatus of FIG. 1.

THEORETICAL ANALYSIS OF THE INVENTION

In the following analysis, it is assumed that, with proper choice of absorption and scattering coefficients, the Lamber-Beer law will apply.

When light rays of wavelengths .lambda..sub.1 and .lambda..sub.2 are passed through blood containing tissue, such as ear lobes of humans, the following equations apply:

D.sup..lambda..sbsp.1 = .alpha..sub.HbO.sbsb.2.sup..lambda..sbsp.1 .sup.C HbO.sub.2 .chi. + .alpha..sub.Hb.sup..lambda..sbsp.1 .sup.C Hb.chi. - .alpha..sub.T.sup..lambda..sbsp.1 l

D.sup..lambda..sbsp.2 = .alpha..sub.HbO.sbsb.2.sup..lambda..sbsp.2 .sup.C HbO.sub.2 .chi. + .alpha..sub.Hb.sup..lambda..sbsp.2 .sup.C Hb.chi. - .alpha..sub.T.sup..lambda..sbsp.2 l (1)

where

D.sup..lambda..sbsp.1 = optical density of the transmitted light at wavelength .lambda..sub.1

D.sup..lambda..sbsp.2 = optical density of the transmitted light at wavelength .lambda..sub.2

.alpha..sub.HbO.sbsb.2.sup..lambda..sbsp.1 = attenuation coefficient of HbO.sub.2 (oxygenated hemoglobin) at wavelength .lambda..sub.1

.alpha..sub.HbO.sbsb.2.sup..lambda..sbsp.2 = attenuation coefficient of HbO.sub.2 (oxygenated hemoglobin) at wavelength .lambda..sub.2

.alpha..sub.Hb.sup..lambda..sbsp.1 = attenuation coefficient of Hb (hemoglobin) at wavelength .lambda..sub.1

.alpha..sub.Hb.sup..lambda..sbsp.2 = attenuation coefficient of Hb (hemoglobin) at wavelength .lambda..sub.2

.sup.C HbO.sub.2 = concentration of HbO.sub.2 per unit volume of blood in the tissue

.sup.C Hb = concentration of Hb per unit volume of blood in the tissue

.chi. = length of optical path in blood

l = length of optical path in bloodless tissue = constant

.alpha..sub.T.sup..lambda..sbsp.1 = attenuation coefficient in bloodless tissue at wavelength .lambda..sub.1

.alpha..sub.T.sup..lambda..sbsp.2 = attenuation coefficient in bloodless tissue at wavelength .lambda..sub.2

To simplify the following description we will adopt the following conventions:

Write .alpha..sub.HbO.sbsb.2 as .alpha..sub.O and .alpha..sub.Hb as .alpha..sub.H

and let C.chi. = X so that .sup.C HbO.chi. = X.sub.O and .sup.C Hb.chi. = X.sub.H

then equations (1) can be written as

D.sup..lambda..sbsp.1 = .alpha..sub.O.sup..lambda..sbsp.1 X.sub.O + .alpha..sub.H.sup..lambda..sbsp.1 X.sub.H + .alpha..sub.T.sup..lambda..sbsp.1 l

D.sup..lambda..sbsp.2 = .alpha..sub.O.sup..lambda..sbsp.2 X.sub.O = .alpha..sub.H.sup..lambda..sbsp.2 X.sub.H + .alpha..sub.T.sup..lambda..sbsp.2 l (2)

Differentiating equations (2) with respect to time, we get:

D.sup..lambda..sbsp.1 = .alpha..sub.O.sup..lambda..sbsp.1 X.sub.O + .alpha..sub.H.sup..lambda..sbsp.1 X.sub.H

d.sup..lambda..sbsp.2 = .alpha..sub.o.sup..lambda..sbsp.2 x.sub.o + .alpha..sub.h.sup..lambda..sbsp.2 x.sub.h

since l is constant, the third term of each equation (2) on the right hand side disappears. Equation (3) can be solved for X.sub.O and X.sub.H. (See below)

By definition oxygen saturation of the blood =

.sup.C HbO.sub.2 /(.sup.C HbO.sub.2 + .sup.C Hb) (4)

since X = C.chi. ##EQU1## and Since X = C.chi. ##EQU2## Solving for X.sub.O and X.sub.H from equations (3): ##EQU3##

In equation 9, of the terms on the right hand side, D.sup..lambda..sbsp.1 and D.sup..lambda..sbsp.2 are detected as will be described below. In order to solve the equation, it is necessary to find values for the four attenuation coefficients. In this regard, it is convenient to use pseudo-coefficients which can be found from measurements made on the ear of a suitable subject as discussed below in calibrating an apparatus in accordance with the invention.

In the calibration procedure, an earpiece is placed on the ear of a subject who is breathing ordinary air. Light at wavelengths .lambda..sub.1 and .lambda..sub.2 is transmitted through the ear lobe of the subject, and optical density readings D.sup..lambda..sbsp.1 and D.sup..lambda..sbsp.2 are taken at the same time as an arterial blood sample is taken. This sample is analysed for oxygen saturation and total hemoglobin concentration, and C.sub.HbO.sbsb.2.sup.100 and C.sub.Hb.sup.100 are thence calculated.

The subject is then made to breath air of reduced oxygen content to reduce his arterial blood oxygen saturation to 75%. The above procedure is then repeated to obtain values for D.sup..lambda..sbsp.1, D.sup.80 .sbsp.2, C.sub.HbO.sbsb.2.sup.75 and C.sub.Hb.sup.75 at 75% saturation.

The following equations will then apply with respect to .lambda..sub.1

D.sub..phi..sup..lambda..sbsp.1 = C.sub.HbO.sbsb.2.sup.100 .alpha..sub.O.sup..lambda..sbsp.1 .chi..sub.1 + C.sub.Hb.sup.100 .alpha..sub.H.sup..lambda..sbsp.1 .chi..sub.1

d.sub.75.sup..lambda..sbsp.2 = c.sub.hbO.sbsb.2.sup.75 .alpha..sub.O.sup..lambda..sbsp.1 .chi..sub.1 + C.sub.Hb.sup.75 .alpha..sub.H.sup..lambda..sbsp.1 .chi..sub.1 (10)

let us define a pseudo-coefficient

P = .alpha. .chi.

so that

.alpha..sub.O.sup..lambda..sbsp.1 .chi..sub.1 = P.sub.O.sup..lambda..sbsp.1

and

.alpha..sub.H.sup..lambda..sbsp.1 .chi..sub.1 = P.sub.H.sup..lambda..sbsp.1

inserting the pseudo-coefficients in equations (10) gives

D.sub.100.sup..lambda..sbsp.1 = C.sub.HbO.sbsb.2.sup.100 P.sub.O.sup..lambda..sbsp.1 = C.sub.Hb.sup.100 P.sub.H.sup..lambda..sbsp.1

d.sub.75.sup..lambda..sbsp.1 c.sub.hbO.sbsb.2.sup.75 P.sub.O.sup..lambda..sbsp.1 + C.sub.Hb.sup.75 P.sub.H.sup..lambda..sbsp.1 (11)

similarly, for .lambda..sub.2 we obtain:

D.sub.100.sup..lambda..sbsp.2 = C.sub.HbO.sbsb.2.sup.100 P.sub.O.sup..lambda..sbsp.2 + C.sub.Hb.sup.100 P.sub.H.sup..lambda..sbsp.2

d.sub.75.sup..lambda..sbsp.2 = c.sub.hbO.sbsb.2.sup.75 P.sub.O.sup..lambda..sbsp.2 + C.sub.Hb.sup.75 P.sub.H.sup..lambda..sbsp.2 (12)

as the optical densities and th