fig1 illustrates a problem addressed by the present invention . a fetal sensor probe 110 is shown having light emitters 114 and detector 118 mounted in housing 122 . three different light paths , 1 , 2 and 3 illustrate different possible penetration depths for light of different wavelengths . the light paths pass through different layers , including a blood - perfused layer 130 , a bloodless layer 132 , and surface layer 138 which can include such things as hair , mucus , etc . between the probe and skin 134 . although the sensor shown in fig1 is a reflectance oximeter sensor , a transmissive sensor would be subject to a similar effect , with the light spreading or scattering different amounts during transmission depending upon wavelength . under certain circumstances , and particularly at low saturation levels , the non - invasive pulse oximetry arterial oxygen saturation estimate , i . e . spo 2 , may be strongly affected by parameters other than the actual saturation level ( i . e ., sao 2 ). such effects are likely due , at least in part , to the fact that the penetration of light in living tissue is related to the wavelength - dependent absorption and scattering characteristics of the tissue , and that therefore two different wavelengths of light in the ranges typically employed for pulse oximetry penetrate such tissue to different extents . at high blood oxygen saturation levels the difference in extent of light penetration is relatively small and there is little effect on spo 2 . however , as saturation levels decrease , the difference in penetration can become great enough so that these other parameters have a significant and undesirable effect on the accuracy of spo 2 . for example , in oximetry systems which employ leds having wavelengths of 660 and 900 nm with the sensor configured in a &# 34 ; reflectance &# 34 ; geometry , as the saturation level drops , light from the red led ( 660 nm ) is detected from relatively shallow tissue depths , while light from the infrared led ( 900 nm ) typically penetrates the tissue more deeply . this phenomenon may be understood with reference to fig1 . as the penetration depths diverge it becomes apparent that the different wavelengths will encounter increasingly different transmission medium characteristics . as a result , the detected signals are affected differently by perturbations in tissue parameters caused by , for example , vasoconstriction or exsanguination in the superficial layers . because the detected signals encounter different perturbations , the effects of these perturbations in the two signals do not &# 34 ; cancel &# 34 ; each other out to the same extent as in circumstances in which the penetration depths are well matched . consequently , the accuracy of spo 2 may be negatively affected . fig2 illustrates a sensor 200 with a fulcrum point 202 biasing sensor 200 against the head of a fetus 204 by pressing against a uterine wall 206 . the need to press the sensor against the fetus to hold it in place may also exsanguinate the tissue , potentially causing a portion of it to be bloodless , adding a different variation in the tissue through which the light must scatter . fig3 illustrates in more detail how an alternate fetal sensor may be placed against a fetus 204 . as shown here , a fetal sensor 300 is attached to a stiff cable 302 which allows it to be inserted and placed against the fetus 204 . rather than using a fulcrum , sensor 300 may use a balloon to bias the sensor against the fetus . fig4 illustrates in more detail emitter 114 of fig1 . the emitter actually contains three separate emitters 402 , 404 and 406 . these are each connected between a ground line 408 and three activating lines 410 ( shown as one line in the diagram .) fig5 is a block diagram of an oximeter probe and monitor which can be used with the present invention . a complete description is set forth in u . s . pat . no . 5 , 348 , 004 . leds 14 transmit light through patient tissue 18 to a photosensor 16 in a sensor 10 . signals are provided to and from an oximeter monitor 34 which include an led drive 32 for alternately driving the leds in multiplexed fashion , either time multiplexed or frequency multiplexed . the received signals are provided through an input amplifier 20 to three different oversampling demodulators 36 which each include an analog switch 40 , low pass filter 42 and a / d converter 38 . a processing unit 44 includes a queue input module 46 , ram memory 52 and cpu 50 . a readout display 30 is also provided , along with control lines 68 . the memory may alternately be rom or a disk , which may contain a program for performing the calculations of the present invention . a calibration resistor ( or other active or passive element ) 17 encodes the mean wavelength of at least one led , and provides it to a calibration reader circuit 19 , which provides it to cpu 50 . the wavelength indicated is used to select coefficients stored in monitor 34 . such a calibration technique is described in more detail in u . s . pat . no . 4 , 621 , 643 , the disclosure of which is incorporated herein by reference . in order to compensate for errors resulting from a single estimate of spo 2 , a second measurement is conducted at substantially the same time and location in a different manner which has a different , but correlated , susceptibility to the perturbing influence . a first measurement of saturation is performed using a first group of components of the sensor . the value obtained , m 1 is equal to the true saturation sao 2 plus some error referred to here as δ : the error δ can come from a number of different causes but is considered here to describe the sensitivities of the measurement to parameters other than sao 2 . at substantially the same time as the first measurement , and at the same location , a second measurement m 2 is performed using a second group of components of the sensor . the second group of components is selected so that the second measurement has a different sensitivity to the perturbing factors than the first measurement , but nonetheless is still sensitive to the cause of the perturbation . as a result , the value m 2 can be written : where k represents the ratio of error in the spo 2 measurement present in m 2 to that present in m 1 , and may be approximated by a constant . k is , to a useful approximation , only a function of the physical sensor design ( constraints on k are that k ≠ 0 and k ≠ 1 .) the variation in error , as the sensor is used on different tissue sites , on different patients , or at different times , or as other physiological parameters vary , appears primarily in variations in the magnitude of δ , and only to a significantly smaller extent in the value of k . accordingly , an improved estimate of oxygen saturation ( m 3 ) is attained by solving equations ( 1 ) and ( 2 ) for sao 2 : notice that m 3 is not subject to the perturbation δ . realistically m 3 will have residual sensitivity to δ , but will nonetheless be less sensitive to the perturbation than either m 1 or m 2 because of their correlated sensitivities . the functional relationship of the perturbation - free value m 3 to the measured values m 1 and m 2 , and the coefficients used , would be empirically determined in a calibration process during instrument design . one cause of limited spo 2 accuracy is an imbalance in penetration depths of the detected light at two wavelengths . accordingly , a three - wavelength sensor can compensate for the resulting errors . the degree of error in a two - wavelength ( 2 - λ ) oximeter will relate to the degree of mismatch in detected light penetration . at low saturation , an error in spo 2 observed with , for example , a 660 / 900 nm light sensor is worse than the error that comes from a 735 / 900 nm light sensor under the same conditions , as described above . such errors , however , can be expected to be correlated since light penetration is smoothly distributed over a broad range , with significant overlap even when each different wavelength has a different average penetration depth . following the methodology described above , the correlation of the spo 2 &# 34 ; errors &# 34 ; can be used to compute a revised ( or &# 34 ; corrected &# 34 ;) estimate of spo 2 based on the difference of the two 2 - λ sensors &# 39 ; values : here , spo 2 ! 735 / 900 and spo 2 ! 660 / 900 refer to the conventionally computed saturations using 735 nm and 900 nm , or 660 nm and 900 nm wavelength pairs , respectively , while k is a proportionality constant . it should be recognized that equation ( 4 ) can be mathematically transformed in a variety of ways that result in fundamentally the same calculations . for example , the improved estimate of spo 2 corrected can be equivalently determined without specific intermediate calculations or determinations of the two 2 - λ estimates of spo 2 by replacing these values with their respective formulations based on their measured signal intensities . this will become more clear as the invention is further described below . in a preferred embodiment , the sensor is fabricated with three light emitting diodes and a spaced photodetector . the three leds are located as close to one another as possible so as best to illuminate the same region of tissue . spo 2 is calculated for each of the two red / ir combinations independently , following normal pulse oximetry protocols as known to those skilled in the art . the revised estimate of spo 2 is made based on the difference between the two initial estimates according to equation ( 4 ) or its equivalent . fig6 is a flowchart illustrating the steps of the present invention . first , radiation of three different wavelengths is emitted towards the tissue sample ( step a .) in step b , the radiation scattered by the tissue sample is detected . in step c , a first estimate of a blood parameter ( e . g ., arterial oxygen saturation ) corresponding to a first pair of wavelengths is determined . in step d , a second estimate of the blood parameter is determined according to a second pair of wavelengths . finally , a corrected estimate is calculated based in part on the difference between the first and second estimates ( step e .) alternately , the same result can be achieved by combining steps c , d and e to eliminate the intermediate calculations . although the three wavelengths 660 nm , 735 nm , and 900 nm are utilized in the described preferred embodiment , other wavelengths may be selected , preferably according to the following table . preferably , two wavelength pairs result in measurements of spo 2 that have at least a minimum sensitivity to changes in sao 2 ( e . g ., at least two wavelengths are chosen to be substantially different from the isosbestic wavelengths of oxygenated and deoxygenated hemoglobin ). simultaneously , two of the wavelengths should result in tissue penetrations of the detected light that are similar but not equivalent . the third wavelength is preferably chosen so that the degree of detected light penetration is not significantly different or substantially equivalent to either of the other two over the span of the saturation range of interest . it should be understood that typical light sources , such as leds , have relatively broad distributions of wavelengths in their output , and the ranges of wavelengths indicated in table i below are ranges from which the peak wavelengths of the distributions should preferably be selected . accordingly , preferred wavelength combinations are chosen to meet the following two criteria evaluated at 40 % sao 2 : 1 ) sufficient overlap in penetration of detected light between wavelengths 1 & amp ; 2 and wavelengths 2 & amp ; 3 ( difference in upper , as well as lower , half standard deviation penetration depths less than 2 mm and not less than 0 . 2 mm ), and 2 ) sufficient measurement sensitivity to changes in sao 2 for wavelength pairs 1 & amp ; 3 and 2 & amp ; 3 ( sufficient sensitivity determined by r 0 % sao 2 !& gt ; 2 · r 100 % sao 2 !, where r = β . sub . λi / β . sub . λj and β . sub . λ refers to the extinction coefficient at wavelength λ .) table i below was calculated utilizing the formulations for the average and standard deviation in detected light penetration found in weiss et al ., &# 34 ; statistics of penetration depth of photons re - emitted from irradiated tissue ,&# 34 ; journal of modern optics , vol . 36 , no . 3 , 1989 . for convenience , wavelength 1 is listed in 25 nm increments , and it should be noted that according to the above selection criteria , wavelengths 1 and 2 ( and in some cases all three wavelengths ) are interchangeable . in the table below , each row represents combinations of peak emitter wavelengths that satisfy the preferred selection criteria ( all wavelengths given in nanometers ): table i______________________________________wavelength 1 (± 12 . 5 nm ) wavelength 2 * wavelength 3 * ______________________________________450 450 - 525 600 - 700475 525 - 675 500 - 825500 525 - 675 575 - 775525 575 - 675 575 - 775550 475 - 525 600 - 675 575 - 650 450 - 775575 475 - 500 600 - 675 550 - 675 600 - 775600 450 - 600 625 - 675 600 - 675 450 - 600 600 - 675 775 - 950625 650 - 800 725 - 950 775 - 925 725 - 775650 600 - 625 450 - 600 675 - 800 775 - 950 775 - 950 700 - 775675 600 - 650 450 - 600 600 - 650 725 - 950 700 - 800 775 - 950 775 - 950 700 - 800700 600 - 675 450 - 600 600 - 675 725 - 950 775 - 950 725 - 775725 , 750 600 - 700 450 - 600 600 - 700 775 - 950 775 - 950 625 - 700775 600 - 700 450 - 600 600 - 700 800 - 950 800 - 950 625 - 725800 , 825 , 850 , 900 625 - 700 600 - 775 700 - 775 625 - 700______________________________________ * wavelengths chosen from overlapping ranges should be separated by at least 10 nm , preferably at least 30 nm , from one another . for a system designed to be practical in a clinical setting , other considerations will also affect the choice of emitter wavelengths such as emitter output efficiency , detector responsivity , and the optical density of blood perfused tissues at the given wavelengths . table i optimizes only the overlap criterion and the measurement sensitivity for a three wavelength system which considers a common ratiometric denominator ( wavelengths 1 and 3 are used for one spo 2 estimation and wavelengths 2 and 3 are used for a second .) similar optimizations can also be accomplished for variations of the spo 2 formulations . for example , wavelengths 1 and 2 can be used for one spo 2 estimation and 2 and 3 can be used for a second . in such a case , the sensitivity optimization would pair wavelengths 1 & amp ; 2 and 2 & amp ; 3 , instead of the pairings considered in generating table i . alternative light penetration overlapping schemes may be considered as well . described more fully , the following algorithm is used in the preferred embodiment . light at three wavelengths is provided at the emitter location using three leds or other suitable source ( for example delivered with an optical fiber ). in order to optimize sensitivity and overlap according to the above wavelength selection criteria , as well as detected signal strength ( affected by , for example , emitter output and the optical density of blood perfused tissue ), three emitter wavelengths are chosen with two coming from the range 625 - 800 nm , preferably 650 - 750 nm , and the third from 775 - 1000 nm . the peak of each emitter wavelength should be separated by at least 10 nm , preferably at least 30 nm , from the other wavelengths ; however , other combinations , ranges , and separations may be used while still conforming to the spirit of the invention . three emitters may be sequentially energized in a time multiplexed manner as described in u . s . pat . no . 4 , 653 , 498 ( new & amp ; corenman ), or in a frequency multiplexed manner as in u . s . pat . no . 4 , 807 , 630 ( malinouskas ). alternatively , either three continuously operating sources or white light may be used , with the different wavelength ranges being separated at the photodetector with filters or a dispersive element . in this latter case , separate photodetector cells will be needed for each of the three different wavelength ranges of light . for the time multiplexed systems , the cycle frequency should be chosen to permit cycling through all of the three or more wavelengths before significant physiological variation occurs over the cardiac - cycle period . for example , it would usually be sufficient for each complete wavelength cycle to occur within 5 % of a cardiac period , or about 50 ms for adult patients . a more preferred time multiplexing period would be 2 % or less of a cardiac period , which is to say 20 ms or less for adult patients and 10 ms or less for neonatal patients . detected signals at the three wavelengths are processed to obtain three signal modulation levels : where i ( t ) and i ( t &# 39 ;) are the detected light intensities at two points in time during the cardiac cycle ( e . g ., systolic and diastolic ). the logarithmic calculations above , which fundamentally define the signal modulations m 1 through m 3 , may be approximated for sufficiently small modulations by the ratio of the ac signal amplitude divided by the dc signal amplitude , since this approximates the first term of a taylor expansion of log ( 1 + x ), when x is small . two of the signal modulation values m 1 , m 2 are divided by the third modulation value m 3 to obtain two ratios . two spo 2 values are calculated according to prior art methods ( a linear formula is shown here and is used in the preferred embodiment , but other formulae may be alternatively used ): ## equ1 ## where a 1 , a 2 , b 1 and b 2 are empirically determined calibration coefficients selected by the usual methods of pulse oximetry calibration . alternative calculations to create two ratios using these or other chosen wavelengths are also possible , e . g ., m 1 / m 2 and m 1 / m 3 or m 1 / m 2 and m 2 / m 3 . calculations of the two ratios or spo 2 values that do not specifically utilize signals at only two specific points in the cardiac cycle can alternatively be used , for example as described in u . s . pat . no . 5 , 533 , 507 . once the two spo 2 values have been calculated , an improved estimate of spo 2 is made according to the difference in the initial estimates : the correlation factor ` k ` can be estimated theoretically , but is preferably determined empirically . by way of example , each of the following equations is mathematically equivalent to equation ( 8a ), yet not all of them necessarily require intermediate calculations of spo 2 ( 1 ) and spo 2 ( 2 ): ## equ2 ## where a = a 1 ( 1 + k ); b =- ka 2 ; c = b 1 ( 1 + k )- b 2 k !. equation ( 8e ) could also be rewritten by substituting log ( i ( t )/ i ( t &# 39 ;)) for the ac / dc terms , in accordance with equations ( 5a ), ( 5b ), and ( 5c ). it is also possible to establish general equations for solutions of this type , which can be written as follows , for n wavelengths ( n ≧ 3 ): ## equ3 ## the alternative ( but not mathematically equivalent ) calculations of the modulation ratios mentioned above can be written in general form for n wavelengths ( n ≧ 3 ) as ## equ4 ## for n & gt ; 3 wavelengths , various combinations of ( 9c ), ( 10a ), and ( 10b ) are also possible and are considered to be within the scope of the invention to the extent that they mathematically relate to combining multiple determinations of spo 2 . the different embodiments of the method of the invention outlined here are specifically different from prior art pulse oximeter techniques in one or more of the following ways : 1 ) the errors from many potential causes ( more than two ) are compensated for by the use of as few as three wavelengths , as opposed to supplying the same or more numbers of wavelengths as causes ( e . g ., one each wavelength for the number of functional and dysfunctional hemoglobins potentially present ). 2 ) tissues are not assumed to be homogeneous in the percentage of tissue volume which is blood , distribution of pulsatile vessels or of other non - absorbing and absorbing media , and resulting spo 2 readings are less affected by such heterogeneity than they would be in a standard two - wavelength pulse oximeter . 3 ) the specific perturbations to which the system will be exposed during use do not need to be present during the calibration . 4 ) no information other than spo 2 is determined during the calculations , such as whether a given sample is within certain boundaries defined by the calibration data set , or the concentration or saturation of any additional absorbers in the tissue . 5 ) arterial oxygen saturation is estimated with improved accuracy under conditions when light penetration into the tissues cannot be sufficiently matched for adequate accuracy with conventional two wavelength oximeters . 6 ) for the multiple calculations of saturation , all of the light is directed into the tissue at one emitter area and all of the detected light is collected in one detector area . numerical modeling numerical modeling has been performed to evaluate theoretically the relative behavior of two conventional 2 - λ and the new 3 - λ approaches . reflectance pulse oximetry was considered and various one - and two - layer tissue bed systems were modeled with the emitter and detector separated by 14 mm . varying tissue blood volumes , pulsatility , and layer thickness were considered . shown in fig7 a and 7b are the relative performances of two 2 - λ systems ( 660 / 900 nm and 735 / 900 nm ), and the revised 3 - λ estimate using a linear proportionality and fixed ` k ` value as in equation ( 4 ). data from six types of tissue beds are shown : homogenous distributions of low , moderate and high tissue blood content ; 3 mm layer of low pulsatility tissue over large pulsatility tissue ; 3 mm layer of large pulsatility over low pulsatility tissue ; and 3 mm layer of completely bloodless tissue over moderately perfused tissue . all three approaches were optimized ( calibrated ) to yield the minimum least - squares error in the saturation range 0 %- 60 %. in the example shown here , the heterogeneous perturbations were present during calibration . similar results are obtained for the improved algorithm when the calibration is performed using only the homogeneous conditions . as can be seen in the fig7 a graph of spo 2 versus sao 2 , the improved algorithm results in significantly less sensitivity to the modeled homogenous and heterogeneous perturbations at low saturation . the table shows the standard deviation of the errors in the low saturation range for the three systems , as well as the range of readings at 20 % sao 2 . although not shown , similar results are observed in the improved algorithm when a 690 nm emitter is used instead of 735 nm emitter . variations in equation ( 4 ) can also be utilized , e . g ., incorporating the difference term in a non - linear relationship such as a higher order polynomial or power - law : further improvements may be realized by varying the value of ` k ` according to a predetermined set of rules . for example , the value of ` k ` may depend on the calculated spo 2 difference δ : ## equ5 ## the values of &# 39 ; k j &# 34 ; and of the thresholds δ 0 and δ 1 may be empirically determined . alternatively , the value of ` k ` may be varied based on an estimate of saturation . for example , ` k ` need not be as large at high saturations as it is at low saturations : ## equ6 ## where spo 2est may be the improved spo 2 previously calculated , or one of the intermediate values determined from one or both of the wavelength pairs . ( as was shown above , algebraic equivalence to each of these variations is possible when the individual signals or intermediate calculations are substituted into the above equations . thus , in the spirit of these examples showing the use of variable k , it is also possible to write variants of the formulae of equations ( 8 ) and ( 9 ), in which the coefficients utilized are given different values depending on the values of an initial estimate of spo 2 .) any three wavelengths may be utilized with this algorithm while still following the spirit of the present invention . the concept exploits the correlated errors based on any two wavelengths &# 39 ; mismatched penetration depths and / or breadths . ( for example , comparable improvement was also modeled using 660 / 690 / 900 nm wavelengths using a different value of ` k ` in equation ( 4 ).) alternatively , four or more wavelengths could be utilized according to the present invention with the two intermediate estimates of spo 2 each made with two unique subsets of the four or more wavelengths ( 3 - λ spo 2 estimates could be made according to the present invention , or any of the prior - art techniques ). the use of more than a minimum of three wavelengths can be utilized for calculations isolating more than sao 2 . constituents other than arterial blood oxygen saturation ( e . g ., hemoglobin , dysfunctional hemoglobin , or glucose ) may be analyzed using the present invention . similarly , non - pulsatile signals may be used to initially estimate a variable , and a subsequent improved estimate may be obtained using the described algorithm . to the extent that any multiple wavelength system is limited in its accuracy ( due to , e . g ., mismatching light penetration ), making an additional estimate based on a different set of wavelengths with different interaction with tissue properties yields a different value with a correlated error . this error may be corrected , as described above , by utilizing further the difference of the estimates , or an algebraically equivalent calculation . as will be understood by those of skill in the art , the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof . accordingly , the foregoing description is intended to be illustrative , but not limiting , of the scope of the invention which is set forth in the following claims .
the present invention utilizes at least three wavelengths of electromagnetic radiation for determining a blood constituent , such as arterial oxygen saturation , in a patient . the detected radiation scattered by the tissue of the patient is analyzed in a manner that compensates for variations in the detected radiation caused by differences in the scattering of the radiation at different wavelengths . in particular , a result is determined which is equivalent to the sum of a first blood constituent estimate using a first pair of the detected signals , and the difference between the first blood constituent estimate and a second blood constituent estimate , using a different pair of wavelengths , with the difference being multiplied by a multiplicative factor .