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ARTICLE

Multiwavelength Pulse Oximetry: Theory for the Future

Takuo Aoyagi, EE, PhD^*, Masayoshi Fuse, EE^*, Naoki Kobayashi, EE^*, Kazuko Machida, MD, PhD, and Katsuyuki Miyasaka, MD, PhD

From the *Ogino Memorial Research Laboratory, Nihon Kohden Corporation; Department of Respirology, National Tokyo Hospital, Tokyo; and Nagano Children’s Hospital, Nagano, Japan.

Address correspondence and reprint requests to: Takuo Aoyagi, PhD, Ogino Memorial Research Laboratory, Nihon Kohden Corporation, 1-31-4 Nishiochiai, Shinjuku-ku, Tokyo 161-8560 Japan. Address e-mail to tyaoyagi{at}s2.ocv.ne.jp.

Abstract

BACKGROUND: As the use of pulse oximeters increases, the needs for higher performance and wider applicability of pulse oximetry have increased. To realize the full potential of pulse oximetry, it is indispensable to increase the number of optical wavelengths. To develop a multiwavelength oximetry system, a physical theory of pulse oximetry must be constructed. In addition, a theory for quantitative measurement of optical absorption in an optical scatterer, such as in living tissue, remains a difficult theoretical and practical aspect of this problem.

METHODS: We adopted Schuster’s theory of radiation through a foggy atmosphere for a basis of theory of pulse oximetry. We considered three factors affecting pulse oximetry: the optics, the tissue, and the venous blood.

RESULTS: We derived a physical theoretical formula of pulse oximetry. The theory was confirmed with a full SO₂ range experiment. Based on the theory, the three-wavelength method eliminated the effect of tissue and improved the accuracy of Spo₂. The five-wavelength method eliminated the effect of venous blood and improved motion artifact elimination.

CONCLUSIONS: Our theory of multiwavelength pulse oximetry can be expected to be useful for solving almost all problems in pulse oximetry such as accuracy, motion artifact, low-pulse amplitude, response delay, and errors using reflection oximetry which will expand the application of pulse oximetry. Our theory is probably a rare case of success in solving the difficult problem of quantifying optical density of a substance embedded in an optically scattering medium.

The principle of pulse oximetry was reported for the first time by Aoyagi and co-workers in 1974 (1,2). Thanks to the subsequent technical improvements by the Minolta and Nellcor Corporations, the use of pulse oximeters has spread worldwide and is contributing to a wide spectrum of medical practice. As the use of pulse oximeters increases, the needs for higher performance and wider applicability of pulse oximetry have increased as well. To realize the full potential of pulse oximetry, we propose that it is necessary to increase the number of optical wavelengths. To develop such a multiwavelength system, a physical theory of pulse oximetry must be constructed. The first physical theory of pulse oximetry was proposed by Shimada et al. (3). Since then many theories have been devised. No theory, however, has succeeded in improving pulse oximetry with an increased number of wavelengths. In this article, will explain our physical theory, how the theory has been experimentally proven, and how it can be practically used for improving the performance of pulse oximetry.

SIMULATORS OF PULSE OXIMETRY

Katsuyuki Miyasaka, the chairperson of the Japanese ISO standards committee for pulse oximeters, proposed establishing a standard method for calibrating pulse oximeters. Minolta had such a pulse oximetry simulator and used it for the basic study of pulse oximetry principles (3). This device had a sample cell with a thickness of 3 mm with pulsation of 0.25 mm given by an external drive. The sample cell had transparent glass windows on both sides. When a pulse oximeter probe was attached to the sample cell filled with purified hemoglobin solution, the hemoglobin–oxygen saturation determined by the oximeter (Spo₂) was consistent with the actual hemoglobin–oxygen saturation (SO₂) of a hemoglobin solution. But when the sample cell was filled with blood, the Spo₂ over-estimated the SO₂ at <90%. Yamanishi of Minolta and Aoyagi of Nihon Kohden together worked to improve the simulator to make the Spo₂ consistent with the blood SO₂. Many simulator modifications were tried, but ultimately the project did not succeed.

Several months later, John Severinghaus in San Francisco gave us data from pulse oximeter tests in human volunteer subjects. Data from one anemic test subject were of particular interest because of the error noted in Spo₂ determination at low saturation; a description of this error was later published by Severinghaus and Koh (4). To model anemia and other clinical issues in pulse oximetry, we constructed a simulator with double layers of blood and milk separated by a transparent elastic diaphragm. With this simulator, the Spo₂ became consistent with the SO₂ of blood (5). From this experimental result, we noticed that tissue (milk in this last simulator) is a source of error in pulse oximetry. Later, we improved the simulator to be able to adjust the amplitude ratio of blood and milk. But when we noticed that venous blood was also a source of error, we gave up on making a pulse oximetry simulator.

OPTICAL ATTENUATION BY BLOOD

To realize the potential of multiwavelength pulse oximetry, we started to build a comprehensive theory of pulse oximetry. The straight incident light into the tissue is gradually scattered. This process is theoretically very complicated. We assumed the optics of pulse oximetry to be a field of completely scattered light. Then we adopted Schuster’s theory of radiation through a foggy atmosphere (6). If we trace the light paths in Schuster’s model in the opposite direction, the optical system is constructed with a small light source and wide light receiver. Therefore, we decided Schuster’s theory could be applied to the theory of pulse oximetry. According to Schuster’s theory, the following formula was obtained for the optical density change A_b caused by the blood thickness change D_b [cm] (7):

where E_h SE_o + (1 – S) E_r; E_o and E_r are the extinction coefficients [dL · g^–1 · cm^–1] of oxyhemoglobin and deoxyhemoglobin, respectively. S is oxygen saturation. Hb is hemoglobin concentration of the blood [g/dL]. F is a scattering coefficient [dL · g^–1 · cm^–1]. We experimentally obtained the following result:

where Z_b [1/cm] is approximated not to depend on the wavelength and becomes zero when the optical receiver is wide enough.

ERROR SOURCES IN PULSE OXIMETRY

There are three factors affecting pulse oximetry: optics, tissue, and venous blood.

1. Optics: A straight incident light to tissue is scattered wavelength-dependently until about 2 mm depth (8). This phenomenon causes an error in Spo₂ when the inner structure of tissue is not uniform. To eliminate this effect, a thin optical scatterer must be attached to the incident side surface of the object.
   
2. Tissue: If the effect of tissue is considered, total optical density is as follows (9):
   

where D_t is the thickness change of the tissue [cm]. Z_t [1/cm] was approximated to be a constant independent of the wavelength. Therefore:

Experimentally E_xj has a little wavelength dependency as follows:

where A_i and B_i were named tissue constants. There are two variables SaO₂ and E_xj in this formula. If three-wavelengths are used, two simultaneous equations are obtained. A solution of the equations gives the Spo₂ without the effect of E_xj.

1. Venous Blood: If the effect of venous blood is considered with the following equation (10):
   

The suffixes "a" and "v" mean arterial blood and venous blood, respectively. There are four variables SaO₂, SvO₂, V, and E_xj in this formula. If five-wavelengths are used, four simultaneous equations are obtained. The solution of the equations gives Spo₂ without the effect of other variables.

THREE-WAVELENGTH PULSE OXIMETRY

To prove our hypothesis on the three-wavelength system, the following study was conducted (11): The wavelengths used were: ₁ = 805 nm, ₂ = 890 nm, ₃ = 660 nm. The LEDs and the photodiode of the probe were attached inside and outside of the external ear, respectively. With informed consent and IRB approval, pairs of A_is and SaO₂ measured with a CO-oximeter OSM3 (Radiometer, Copenhagen, Denmark) were obtained from chronic lung disease patients. Spo₂ was calculated with two methods. The first method was to solve the following simultaneous equations. This was named 3wSpO₂.

Another method was to solve the equation of ₃₂. This was named 2wSpO₂. In the calculation, effective E_oi and E_ri were used for E_oi and E_ri as follows:

where E_o(), E_r(), and L_i() are the spectrums of oxyhemoglobin, deoxyhemoglobin, and LED, respectively. The E_x2 for 2wSpO₂ was selected to be zero. The combinations of tissue constants A_is and B_is for 3wSpO₂ were selected so as to obtain the best correlation between SaO₂ and Spo₂. The result is shown in Figure 1. This result shows that the three-wavelength method improves the accuracy of Spo₂ when the constants A_is and B_is were appropriately selected.

View larger version (15K): [in this window] [in a new window]   Figure 1. Comparison of two-wavelength Spo2 (left) and three-wavelength Spo2 (right) on the relationship between Spo2 and SaO2 determined with hemoximetry. Twenty-one patients with mild chronic lung disease were studied with (both techniques) a three-wavelength probe. Based on the same data two different calculations of Spo2 were tried and compared.

REFLECTANCE PULSE OXIMETRY

A comparison of the transmitting method and reflectance methods was made using a volunteer (12). In the transmitting method, the probe was attached to the thumb, middle finger, index finger, and toe. In the reflectance method, the probe was attached to the forehead, nose, cheek, toe, and thumb. The volunteer was first asked to inspire O₂ gas, then breath-hold and finally to again inspire O₂ gas. The two groups of data were plotted on each plane with x-axis of ₁₂ and y-axis of ₃₂, named ₁₂–₃₂ plane, as shown in Figures 2a and b. The O₂ gas data are the lowest ones for each probe site. The O₂ gas data of the reflectance method makes a straight line. The data on this line are calculated to S = 1 with the three-wavelength calculation. The O₂ gas data of the transmittance method also are on the line. Therefore, with the three-wavelength system, there is no substantial difference between the two methods.

View larger version (27K): [in this window] [in a new window]   Figure 2. Transmittance and reflectance data. Upper graph shows data from the transmittance method (probe attached to thumb, middle finger, index finger, and toe) and the lower graph contains data from the reflectance method (probe located on forehead, nose, cheek, toe, and thumb). For details of experiment see text.

FULL SO₂ RANGE EXPERIMENT

To confirm the reliability of the theoretical formula and to obtain tissue constants A_is and B_is, we conducted an experiment (13) as follows. The wavelengths used were: ₁ = 805 nm, ₂ = 875 nm, ₃ = 660 nm, ₄ = 700 nm, and ₅ = 730 nm. The photodiode size was 6 mm x 6 mm. Figure 3 shows a ₁₂–₃₂ relationship calculated based on the theoretical equations. The equi-SO₂ lines were drawn for each 5% from 100% to 0%. The equi-E_x2 lines were drawn for –0.1, 0, and +0.1. An approximation was made to be A_i = 1 and B_i = 0. The pattern made by these equi-SO₂ lines and equi-E_x2 lines was named "grid." The equi-SO₂ lines are like a Japanese folding fan and all cross at one point named "focus."

View larger version (38K): [in this window] [in a new window]   Figure 3. The relationship between 12 and 32 calculated from theoretical equations. See text for details.

What needed to be proved experimentally was the existence of the focus and location of the focus. For this purpose, SaO₂ must be changed far wider than the limit realizable with a volunteer experiment. Our method was as follows:

1. The LED and PD of a branch type probe were attached to a fingertip.
   
2. The finger was bound by a string to make the blood flow stop and to make the SO₂ of blood in the finger decrease gradually toward zero.
   
3. The finger was wrapped with a small air-cuff and the air pressure was pulsated to make the blood in the finger pulsate.
   
4. The baseline of the pressure was changed to high and low alternately to make the tissue tension change to make E_x2 change.
   
5. The fingertip was massaged between measurements to make the blood SO₂ uniform.
   
6. ₁₂ and ₃₂ were obtained at low pressure, at high pressure, and again at low pressure. The data of the two low pressures were averaged.
   
7. Each pair of points of the high pressure and low pressure on the ₁₂–₃₂ plane was joined with a straight line as an experimental equi-SO₂ line.
   

Another experiment with O₂ gas inspiration was made with young healthy volunteers. ’s values were obtained with the hand in the up, horizontal, and down positions. This data point array on the ₁₂–₃₂ plane does not depend on the person and is an experimental equi-SO₂ line for SO₂ = 1.

The two SO₂ = 1 lines, one theoretical and the other experimental, were not coincident but in parallel. The theoretical grid was moved so as to harmonize the theoretical equi-SO₂ lines with experimental equi-SO₂ lines. The same was done for the ₁₂–₄₂ plane and ₁₂–₅₂ plane. The results are shown in Figure 4. The shift of the focus tells us the values of the tissue constants as follows: A₁ = 1.035, A₂ = A₃ = A₄ = 1, A₅ = 1.01, B₁ = 0.0141, B₃ = B₄ = 0, B₅ = 0.004. The above-mentioned approximations were thus experimentally adjusted.

View larger version (27K): [in this window] [in a new window]   Figure 4. Grids with focus correction. The square symbols indicate oxygen inspiration data. The round symbols indicate low SO2 data.

Since the E_x2 values of the experimental data are not consistent on the three planes, the E_r4 was corrected from 0.2777 to 0.31, and the E_r5 was corrected from 0.20411 to 0.245. The theoretical meaning of these corrections is a problem to be solved in the future. But the theory was confirmed and the tissue constants were obtained. Therefore, we can calculate Spo₂ with multiwavelength pulse oximetry. Figure 5 shows a picture of this deep SO₂ experiment.

View larger version (130K): [in this window] [in a new window]   Figure 5. Apparatus used in deep SO2 experiment.

ELIMINATION OF MOTION ARTIFACT

Motion artifact is conjectured to arise from the movement of tissue and venous blood. The five-wavelength system is supposed to be effective for elimination of motion artifact. Examples of motion artifact elimination are shown in Figures 6 and 7 (14). In both cases, the volunteer was in a supine position and the probe was attached to the right middle finger. The hand was down for Figure 6, and was horizontal for Figure 7. The volunteer was asked to move his hand in a chopping direction and to breath-hold for a short time. Figures 6a–c show 2wSpo₂, 3wSpo₂, and 5wSpo₂, respectively. In Figure 6, there is considerable improvement from a to b. This is probably due to elimination of tissue effect. In Figure 7, there is considerable improvement from b to c. This is probably due to elimination of venous blood effect. The Figures 6d and 7d are running averages of 5wSpo₂ with simple weighting. The patterns of Spo₂ are smooth with little time delay. These are successful examples, but motion artifacts can be difficult to eliminate. The total waveform of the artifact must be considered in order to improve the artifact elimination.

View larger version (31K): [in this window] [in a new window]   Figure 6. Examples of artifact elimination in three- and five-wavelength Spo2 (panels b and c) compared with that in two-wavelength Spo2 determination (panel a). In the lower panel (d) five-wavelength Spo2 determination with smoothing is shown.

View larger version (33K): [in this window] [in a new window]   Figure 7. Another example of artifact elimination with multiwavelength Spo2 determination. See also Figure 6.

HISTORICAL CONSIDERATIONS

The quantitative measurement of optical absorptive substances in an optical scatterer has long been a difficult problem (15). But our theory is probably a rare case of success in solving the problem. A change of the thickness of the object makes the problem easy to solve. This is originally Squire’s idea (2) and is a concept that does not require expelling all of the blood in a body part such as with the approach used in Wood’s ear oximeter (16). The above-mentioned effect of tissue was considered when we made the pulse oximetry simulator. The effect of venous blood on such models was reported by Goldman et al. (17).

Our theory of multiwavelength pulse oximetry may be useful for solving almost all problems in pulse oximetry such as accuracy, motion artifact, low pulse amplitude, quick response, and reflection method, which will expand the application of pulse oximetry.

There was an eight-wavelength ear oximeter [Hewlett-Packard model 47201 Ear Oximeter (Catalog)]. It had excellent accuracy comparable to a modern pulse oximeter. This method measures incident light and transmitted light at the ear lobe for eight-wavelengths and calculates SaO₂ with a rather simple a-priori formula. The constants in the formula were determined empirically from human data. This was an application of Robert Shaw’s patent (18). Shaw says in his patent that the more the number of wavelengths, the more the accuracy will be improved. This may be true, but eventually too many wavelengths make the device impractical.

ACKNOWLEDGMENTS

We must mention our gratitude for the guidance and suggestions of Professor Emeritus Dr. Masao Saito of Tokyo University, Professor Emeritus Dr. John W. Severinghaus of UCSF, San Francisco, and Professor Yukio Yamada of the University of Electro-Communications. We would like to mention our gratitude to Nihon Kohden’s founder, the late Dr. Yoshio Ogino, and President Kazuo Ogino for allowing us to continue research on pulse oximetry.

Appendix 1

Footnotes

Accepted for publication April 19, 2007.

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