US20140018651A1 - System and method for probability based determination of estimated oxygen saturation - Google Patents

Abstract

Present embodiments include providing an initial estimate of a value representative of a blood flow characteristic at a current timestep, and determining a probability distribution of transition, wherein the probability distribution of transition includes potential values of the blood flow characteristic at the current timestep with associated probabilities of occurrence based solely on the initial estimate. Present embodiments further include obtaining an initial measurement of the blood flow characteristic, and determining a probability distribution of measured values, wherein the probability distribution of measured values includes potential values of the blood flow characteristic at the current timestep with associated probabilities of occurrence based on the initial measurement. Further, present embodiments include combining the probability of distribution of transition with the probability of distribution of measured values to determine a meaningful blood flow characteristic value, and posting the meaningful blood flow characteristic value.

Description

CROSS-REFERENCE TO RELATED APPLICATION
• This application is a continuation of patent application Ser. No. 11/524,167, entitled “System and Method for Probability Based Determination of Estimated Oxygen Saturation”, filed Sep. 20, 2006, which is herein incorporated by reference in its entirety.
BACKGROUND
• 1. Field of the Invention
• The present invention relates generally to medical devices. More particularly, the present invention relates to estimating blood oxygen saturation in a patient.
• 2. Description of the Related Art
• This section is intended to introduce the reader to various aspects of art that may be related to various aspects of the present invention, which are described and/or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present invention. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of prior art.
• Pulse oximetry may be defined as a non-invasive technique that facilitates monitoring of a patient's blood flow characteristics. For example, pulse oximetry may be used to measure blood oxygen saturation of hemoglobin in a patient's arterial blood and/or the patient's heart rate. Specifically, these blood flow characteristic measurements may be acquired using a non-invasive sensor that passes light through a portion of a patient's blood perfused tissue and photo-electrically senses the absorption and scattering of light through the blood perfused tissue. A typical signal resulting from the sensed light may be referred to as a plethysmographic waveform. Once acquired, this measurement of the absorbed and scattered light may be used with various algorithms to estimate an amount of blood constituent in the tissue. It should be noted that the amount of arterial blood in the tissue is time varying during a cardiac cycle, which is reflected in the plethysmographic waveform.
• The accuracy of blood flow characteristic estimations obtained via pulse oximetry depends on a number of factors. For example, variations in light absorption characteristics can affect accuracy depending on where (e.g., finger, foot, or ear) the sensor is applied on a patient or depending on the physiology of the patient. Additionally, various types of noise and interference can create inaccuracies. For example, electrical noise, physiological noise, and other interference can contribute to inaccurate blood flow characteristic estimates. Some sources of noise are consistent, predictable, and/or minimal, while some sources of noise are erratic and cause major interruptions in the accuracy of blood flow characteristic measurements. Accordingly, it is desirable to provide a system and method that continues to provide substantially accurate blood flow characteristic measurements during interference and noisy periods as well as during periods with little or no noise.
BRIEF DESCRIPTION OF THE DRAWINGS
• Advantages of the invention may become apparent upon reading the following detailed description and upon reference to the drawings in which:
• FIG. 1 shows a perspective view of a basic embodiment of a pulse oximeter system in accordance with an exemplary embodiment of the present invention;
• FIG. 2 is a detailed block diagram of the pulse oximeter system ofFIG. 1;
• FIG. 3 is a graph of an exemplary plethysmographic waveform which may be generated by the system ofFIG. 1;
• FIG. 4 is a graph of an exemplary plethysmographic waveform, wherein the waveform includes interference due to noise;
• FIG. 5 is a diagram representing predictive paths and potential SpO₂values based on a previous SpO₂reading in accordance with an exemplary embodiment of the present invention;
• FIG. 6 is a diagram representing predictive paths and the potential SpO₂values for the related timestep based on an initial SpO₂reading for the current timestep in accordance with an exemplary embodiment of the present invention; and
• FIG. 7 is a flow diagram of an algorithm employing probability density functions in accordance with embodiments of the present disclosure;
• FIG. 8 is a flow diagram of an algorithm for determining an appropriate value to post for a patient's SpO₂level in accordance with an exemplary embodiment of the present disclosure; and
• FIGS. 9,10, and11 are representations of data acquired by implementing and testing present embodiments against synthetic data using Viterbi's algorithm in accordance with an exemplary embodiment of the present invention.
DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS
• One or more specific embodiments of the present invention will be described below. In an effort to provide a concise description of these embodiments, not all features of an actual implementation are described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the developers' specific goals, such as compliance with system-related and business-related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure.
• Embodiments of the present invention relate to providing an estimation of blood oxygen saturation (SpO₂) at a particular time or over a designated time period based on a previous SpO₂estimation, related probability estimations, initial SpO₂measurements, and a noise value associated with the readings. Rather than storing or utilizing numerous historical data points to facilitate reducing the effects of noise, in accordance with present embodiments it may be assumed that the blood oxygen saturation value can be predicted based on an immediately prior value of the blood oxygen saturation. Specifically, in accordance with present embodiments, first and second portions of a determination may be combined to establish a probable actual SpO₂value based on a prior SpO₂value and an initial SpO₂measurement. In other words, present embodiments estimate what the actual SpO₂value should be based on a preceding SpO₂value and the value of an initial SpO₂measurement. Once the probable actual SpO₂value is determined, that value may be posted as the calculated value.
• FIG. 1 shows a perspective view of an exemplary embodiment of apulse oximeter system10. Thesystem10 includes a pulse oximeter ormonitor12 that communicatively couples to asensor14. Thesensor14 may include asensor cable16, aconnector plug18, and abody20 configured to attach to a patient (e.g., patient's finger, ear, forehead, or toe). Pulse oximetry systems such assystem10 may be utilized to observe the oxygenation or oxygen saturation of a patient's arterial blood to estimate the state of oxygen exchange in the patient's body by emitting waves into tissue and detecting the waves after dispersion and/or reflection by the tissue. For example, conventional pulse oximeter systems may emit light from two or more light emitting diodes (LEDs) into pulsatile tissue and then detect the transmitted light with a light detector (e.g., a photodiode or photo-detector) after the light has passed through the pulsatile tissue. The amount of transmitted light that passes through the tissue varies in accordance with the changing amount of blood constituent in the tissue and the related light absorption.
• Specifically, as illustrated inFIG. 2, thesensor14 includes twoLEDs30 and a photo-detector32. TheLEDs30 receive drive signals from themonitor12 that activate theLEDs30 and cause them to emit signals alternatively. Thesensor14 is configured such that light from the activatedLEDs30 can pass into a patient'stissue38. After being transmitted from (or reflected from) thetissue38, the dispersed light is received by the photo-detector32. The photo-detector32 converts the received light into a photocurrent signal, which is then provided to themonitor12. The illustratedsensor14 may also include amemory34 and aninterface36. Thememory34 and/or themonitor12 may store software applications in accordance with present embodiments. Theinterface36 may facilitate communication between thesensor14 and themonitor12.
• To measure the oxygen saturation of the patient's arterial blood, two different wavelengths of light are typically emitted from theLEDs30 and are used to calculate the ratio of oxygenated hemoglobin or oxyhemoglobin (HbO₂) and deoxygenated hemoglobin or deoxyhemoglobin (Hb), which are dominant hemoglobin components. The light passed through the tissue (e.g., tissue38) is typically selected to include two or more wavelengths that are absorbed by the blood in an amount related to the amount of blood constituent present in the blood. Specifically, a first wavelength for one of theLEDs30 is typically selected at a point in the electromagnetic spectrum where the absorption of HbO₂differs from the absorption of reduced Hb. A second wavelength for one of theLEDs30 is typically selected at a different point in the spectrum where the absorption of Hb and HbO₂differs from those at the first wavelength. For example, LED wavelength selections for measuring normal blood oxygenation levels typically include a red light emitted at approximately 660 nm and an infrared light emitted at approximately 900 nm.
• While various techniques may be utilized to estimate oxygen saturation, in one common technique, the first and second light signals detected by the light detector from red and infrared light sources are conditioned and processed (e.g., via the monitor12) to determine AC and DC signal components. For example,FIG. 3 illustrates one method of determining AC and DC components from a plethysmographic waveform, wherein maximum (MAX) and minimum (MIN) measurements of each wavelength are measured and correlated as set forth in the following equations:
• 
  AC=MAX−MIN
• 
  DC=(MAX+MIN)/2.  (Eq. 1)
• It should be noted that in other embodiments the maximum (MAX) and minimum (MIN) measurements are not necessarily employed to determine the AC and DC components. Indeed, the AC and DC components may be obtained by using essentially any pair of points along both the infrared and red light waveforms.
• Once obtained, the AC and DC components may be used to compute a modulation ratio of the red to infrared signals. The modulation ratio is generally referred to as “the ratio of ratios” or Ratrat and may be represented as follows:
• $\begin{array}{cc}\mathrm{Ratrat}=\frac{{\mathrm{AC}}_{\mathrm{RED}}/{\mathrm{DC}}_{\mathrm{RED}}}{{\mathrm{AC}}_{\mathrm{IR}}/{\mathrm{DC}}_{\mathrm{IR}}}.& \left(\mathrm{Eq}.2\right)\end{array}$
• The Ratrat at a particular time K or over a designated timestep K may be represented as follows:
• $\begin{array}{cc}\mathrm{Ratrat}=\frac{v_K}{u_K},& \left(\mathrm{Eq}.3\right)\end{array}$
• wherein the variable v_xis representative of a value for red light optical density over timestep K and the variable u_Kis representative of a value for infrared light optical density over timestep K. A timestep may include multiple optical observations taken over a designated period of time. For example, a timestep of 1 second may include 53 optical observations, which may be used to determine v_Kand u_K.
• The Ratrat has been observed to correlate well to arterial blood oxygen saturation, as represented by the following equation:
• 
  Ratrat=f(s),  (Eq. 4)
• wherein s represents blood oxygen saturation. Pulse oximeters and sensors are typically calibrated empirically by measuring the Ratrat over a range of in vivo measured arterial oxygen saturations (SaO₂) on a set of patients (e.g., healthy volunteers). The observed correlation is used in an inverse manner to estimate SpO₂based on the measured value of modulation ratios. A correlation to blood concentrations may be represented by the following equation:
• $\begin{array}{cc}\left(\begin{array}{c}v\\ u\end{array}\right)=\left(\begin{array}{cc}{c}_1& c_{12}\\ c_{21}& c_{22}\end{array}\right)\left(\begin{array}{c}\mathrm{OXY}\\ \mathrm{DEOXY}\end{array}\right),& \left(\mathrm{Eq}.5\right)\end{array}$
• wherein the variables c₁₁, c₁₂, c₂₁, and c₂₂represent coefficients, the OXY variable represents an actual value of oxygenated blood concentration, and the DEOXY variable represents an actual value of deoxygenated blood concentration. It should be noted that the coefficients are a function of wavelength. It should further be noted that calculating SpO₂based on the Ratrat is one of various methods that can be utilized to calculate the level of SpO₂in a patient. Indeed, the Ratrat is used herein by way of example, and present embodiments are not limited to the use of the Ratrat in determining SpO₂levels.
• The accuracy of blood flow characteristic estimations determined via pulse oximetry can be impacted by various types of noise and interference (e.g., electrical noise, physiological noise, and other interference). In a pulse oximetry system, noise generally manifests as variations in detected light values. Thus, in a noisy system, a “dirty” plethsymographic signal may be obtained. For example, if noise is introduced, the detected light values that define the plethysmographic waveform inFIG. 3 (a “clean” plethysmographic signal) could be extremely skewed, as illustrated by the plethysmographic waveform inFIG. 4 (a “dirty” plethysmographic signal). Such variations in detected light values generally directly impact the calculated value of SpO₂. For example, as is clear from the discussion of Ratrat determination above, the value of the Ratrat is dependent on the detected light values, and the Ratrat directly impacts the calculated values of SpO₂. Thus, when the Ratrat is used to calculate an SpO₂value, errors in determining the Ratrat due to noise directly impact the calculation of the SpO₂value. Similarly, in other calculations of SpO₂, noise can create error in the calculated value of SpO₂.
• Because noise causes errors such as those discussed above, it is desirable to remove or filter out the effects of noise when determining an SpO₂value with pulse oximetry. Traditional methods for estimating a patient's SpO₂level may limit the impact of noise by utilizing historical data. Indeed, traditional methods may store historical values of SpO₂observed in the patient, and the historical values may then be utilized in calculations to limit the effects of noise. For example, historical values may be averaged (e.g., using ensemble averaging) or trended to facilitate detection and/or filtering of noise or noisy data. Specifically, a current value of the patient's SpO₂level may be estimated based on averaging numerous historical data points and the estimate may then be compared with a measured value to determine whether noise is present. If noise is present, the measured value may be filtered or modified based on the historical data.
• Rather than storing or utilizing numerous historical data points to facilitate reducing the effects of noise, in accordance with present embodiments it may be assumed that the value of the SpO₂can be predicted based on an immediately prior value of the SpO₂. This can be discussed in terms of the Ratrat because the Ratrat correlates with the value of SpO₂. Accordingly, the assumption may be summarized by stating that, in theory, in predicting a future value of the Ratrat (i.e., Ratrat_K+1) based on knowledge of the most recent Ratrat (i.e., Ratrat_K), no additional predictive power can be gained from learning the historical values of the Ratrat (i.e., Ratrat₀, Ratrat₁, . . . , Ratrat_K−1). For example, the following system may be considered representative:
• 
  Ratrat=t_K(Ratrat_K−1)
• 
  v_K=u_KRatrat_K+n_K^R,  (Eq. 6)
• wherein Ratrat_Kis a function of saturation at major timestep K, u_Kis a red optical density at major timestep K, v_Kis an infrared optical density at major timestep K, and n_K^Rrepresents observation noise. Observation noise may be defined as noise present in physical observations (e.g., optical or otherwise), and not error in the previous or present estimate of saturation. The function t represents the transition of the Ratrat from one timestep to the next, which includes a random variable. The inclusion of a random variable indicates that given the Ratrat at a previous time interval (i.e., Ratrat_K), the value of the Ratrat at a next time interval (i.e., Ratrat_K+1) can be predicted or estimated, but not necessarily directly calculated.
• Embodiments of the present invention assume that SpO₂(and hence Ratrat) follow a Hidden Markov Model of a given distribution. A Hidden Markov Model is a statistical model wherein the system being modeled is assumed to be a Markov process with unknown parameters. A Markov Model or Markov Chain may be characterized by the following property: P {X_k+1=x|X_k, X_k−1, . . . , X₀}=P{X_k+1=x|X_k}. Only the most recent value of the random variable is relevant for predicting the next value. In some embodiments, the model may be further restricted such that it only takes values in a certain range, or in a certain finite set of numbers. For example, under further restriction the following is representative: P {X_k+1=x|X_k}=0 when x is not a number in that certain range, or in that certain finite set. It should be noted that in some embodiments, there is no need to restrict the Markov process to a finite range. However, it may be assumed that the range is bounded between 0 and 100%, but may take any value in that range. The objective of Viterbi's algorithm is to determine the hidden parameters from observable parameters. The Hidden Markov Model models the underlying process, which is observed with some level of uncertainty (e.g., via optical measurements).
• In accordance with present embodiments, first and second portions of a determination may be combined to establish a probable actual SpO₂value based on a prior SpO₂value and an initial SpO₂measurement. In other words, present embodiments estimate what the actual SpO₂value should be based on a preceding SpO₂value and the value of an initial SpO₂measurement. Once the probable actual SpO₂value is determined, that value may be posted as the calculated value. Specifically, in the first portion of the determination, an immediately prior calculated or measured SpO₂value may be utilized to determine a set of predictive paths and potential SpO₂values. These predictive paths and potential SpO₂values correspond to what will probably be the next actual SpO₂value. For example, there is generally a high probability that the SpO₂value following the immediately preceding value will be equivalent to the immediately preceding value. In the second portion of the determination, a set of predictive paths and potential SpO₂values may be determined based on a current SpO₂measurement value. For example, an initial SpO₂measurement may be utilized to determine probabilities associated with potential SpO₂values for the actual SpO₂value. As suggested above, once probabilities based on the immediately preceding SpO₂value and the initial SpO₂measurement are established, they may be combined to predict the actual current SpO₂value for posting. This procedure is discussed in further detail below.
• FIG. 5 is a block diagram representing an example of predictive paths and potential SpO₂values for a current reading that may be determined based on a previously calculated or measured SpO₂value. It should be noted that the predictive paths are not necessarily explicitly constructed in accordance with present embodiments. In other words, the transition illustrated inFIG. 5 may be described as a continuum that does not utilize a discrete list of values. Essentially, the predictive paths and potential SpO₂values represent a probability distribution (e.g., Markov Model transition probability distribution) of what the next SpO₂value is likely to be based solely on the most recently measured and/or determined SpO₂value. This probability distribution may represent what can be referred to as a probability distribution of transition.
• Calculating these predictive paths and potential SpO₂values represented inFIG. 5 may be considered the first portion of the procedure for determining the SpO₂value to post as the current value. Accordingly,FIG. 5 may be representative of results from the first portion of the procedure. Specifically,FIG. 5 includes a previous SpO₂measurement or determination (block40) having an exemplary value of 93%.Block40 represents the SpO₂value obtained from the Ratrat corresponding to timestep K, wherein K is the most recent previous timestep. Each of thearrows42 extending fromblock40 represents a probability that the value of SpO₂for the current or next timestep (e.g., K+1 or the value of SpO₂for the timestep after that represented by block40) will correspond to one of the values in the correspondingblocks44,46,48,50, and52. In other words, thearrows42 represent predictive paths for the potential SpO₂values in blocks44-52. It should be noted that while blocks44-52 represent a specific range of values, in other embodiments the range and values may be different. Indeed, in some embodiments, the range and values represented by blocks44-52 may be dependent on a selected model of how saturation can change.
• The continuum of probability values is represented by a probability distribution function. As indicated above, blocks44,46,48,50, and52 are representative of potential SpO₂values that could be obtained at the next timestep (i.e., K+1) using the corresponding Ratrat for that timestep (i.e., Ratrat_K+1). These potential values (block44-52) represent a range of potential SpO₂values based on established relationships between the value of the timestep between K and K+1 (e.g., 1 second) and the initial or immediately preceding SpO₂value (e.g., block40). The following equation is representative of the relationship betweenblock40 and blocks44-52:
• 
  p(x)=C Pr{Ratrat_K=Ratrat_K−1+x|Ratrat_K−1},  (Eq. 7)
• wherein C represent a constant that can be ignored and the function Pr{a|b} means “the probability that a occurs conditioned on the fact that b was observed to occur.” It may be assumed that a probability distribution function of the transition function t can be estimated by a particular equation or model. In the case of a continuum, the function p(x) is a probability density, which is integrated to obtain probabilities.
• The most likely value for SpO₂that will be obtained in the imminent timestep (i.e., K+1) based on the known Ratrat (i.e., Ratrat_K) is represented byblock48, which has the same SpO₂value as that of the previous timestep (block40). Values for the SpO₂at K+1 that have lesser probabilities of occurrence are dispersed outwardly according to a probability distribution function used to determine theprobabilities42 for each potential value (blocks44-52). For example, in accordance with some embodiments, a piecewise linear spline, a double exponential function, or Gausian probability density function may be utilized to determine probabilities (e.g., probabilities42).Such probabilities42 may indicate that, for example, if the timestep is approximately one second, it is highly unlikely that during the transition from K to K+1 the SpO₂level will drop by a certain amount (e.g., twenty points) and that it is highly likely that the SpO₂value will remain the same. Accordingly, changes within a certain range will be given a higher probability value. Generally, these probability values are lower the further the corresponding SpO₂value (blocks44-52) is from the initial value (block40) (e.g., the probability of the SpO₂value for timestep K+1 remaining at 93% is greater than that of it changing to 91%) because changes in SpO₂do not typically include large, sudden swings. It should be noted that it may be slightly more likely to have a large increase in the SpO₂value in certain situations (e.g., an oxygen starved patient receiving oxygen).
• In accordance with some embodiments, the mean of the probability distribution function for the saturation transition should be the previous value of SpO₂. In other words, the probability distribution function of the saturation transition may be designed such that saturation is a Martingale. This generally prevents present embodiments from predicting large fluctuations in saturation levels when presented with noiseless optical observations. Moreover, for this reason, it may be desirable to adjust or tune the probability distribution function such that its variance is minimized, or otherwise controlled. In some embodiments, the probability density function of the saturation transition is represented by a spline function (i.e., a function composed of portions of polynomials linked together). For example, a spline function utilized in accordance with present embodiments may include a piecewise linear function.
• FIG. 6 may be representative of results from the second portion of the procedure for determining the SpO₂value to be posted as current. As set forth above, these results may be combined with the results illustrated inFIG. 5 to provide the current SpO₂reading. Specifically,FIG. 6 is a block diagram representing predictive paths and the potential SpO₂values for the related timestep based on an initial SpO₂reading for the current timestep in accordance with embodiments of the present invention. Essentially, the predictive paths and potential SpO₂values represent a probability distribution of what the next SpO₂value is likely to be based on an initial measurement. This probability distribution may represent what can be referred to as a probability distribution of measured values or the probability of observing a given measured value.
• Specifically,FIG. 6 includesblock54, which represents an SpO₂value (e.g., 94%±3%) for the current timestep that takes into account observational information. Additionally,FIG. 6 includes theblocks44,46,48,50, and52, which are representative of potential actual SpO₂values that could be obtained for the current time step within a certain likelihood.Arrows56, which connect the potential SpO₂values (blocks44-52) with the value accounting for observational information (block54), are representative of probabilities that given the SpO₂value is actually a certain value, the (optical) measurements indicate the given SpO₂value. For example, the probability along thearrow56 fromblock46 to block54 represents the probability that, given that the SpO₂is actually 92%, optical observations indicate that the SpO₂is 94%. However, the procedure is more general that this example. Optical measurements include an estimate of noise (e.g., ±3%). This estimate of noise facilitates construction of thearrows56. When the error is small (e.g., ±0.5%), it is likely that SpO₂really is the value indicated by the optical observations (e.g., the probability that the underlying SpO₂is 94% and was observed to be 94% is high, while the probability that the underlying SpO₂value is 92% and was observed to be 94% is low). When the error is larger (e.g., ±6%), the distribution flattens out. In other words, the probabilities associated with thearrows56 become nearly equal when the error is large. Theprobabilities56 may be represented and determined by designated equations, which will be discussed in further detail below.
• As illustrated inFIG. 7, once determined, the probabilities represented byarrows56 may be combined with the probabilities represented byarrows42 to determine which potential SpO₂value should be posted as the meaningful SpO₂value. The algorithm represented byFIG. 7 employs probability density functions. It should be noted that a probability density function may be defined as the function, f(x), such that given a random variable X, the following equations applies:
• $\begin{array}{cc}P\left(a\le x\le b\right)=\underset{a}{\overset{b}{\int }}f\left(x\right)x.& \left(\mathrm{Eq}.8\right)\end{array}$
• Further, it should be noted that, in present embodiments, the probability density function may only need to be known up to a constant.
• Determining the meaningful SpO₂value for posting may include the following procedures: let P(x) be a nonzero constant times the probability density function associated with the Hidden Markov Model (i.e. the transition of SpO₂values), let Q(x) be a nonzero constant times the probability density function associated with the observation, and let W(x)=P(x)Q(x) be some constant times the probability density function of the value of SpO₂at the current state, conditional on the (optical) observations. This may be represented as follows:
• $\begin{array}{cc}P\left(a\le X_{k+1}\le bX_k\mathrm{known},\mathrm{optical}\mathrm{observations}\right)=D\underset{a}{\overset{b}{\int }}W\left(x\right)x,& \left(\mathrm{Eq}.9\right)\end{array}$
• where D is an unknown constant. Viterbi's algorithm, which is a maximum likelihood estimate algorithm, estimates X_k+1by that value x which maximizes W(x). Because P(x) and Q(x) are represented in the algorithm as functions (e.g., P(x) is a linear spline, or the probability distribution function of a Gaussian or normal, double exponential, and so forth, and Q(x) is the probability density function of a Gaussian), this maximum can be found using calculus, and not by checking every value between values (e.g., between 91% and 95%).
• In the exemplary embodiment illustrated inFIG. 7, block60 represents a best estimate of saturation at timestep K based on the previous optical observations. Probabilities62 (13) may be based on the Hidden Markov Model of human physiology. Accordingly, theseprobabilities62 may only depend on the estimate of saturation, and not on current optical observations. The probabilities64 (Q_j) may be based on a model of optical noise and optical observations since timestep K. Theprobabilities64 represent the probability that, if the saturation were j at timestep K+1, the observations would correspond to the observations made. Block66 represents a linear regression of red to infrared optical signals over the major time step. Block68 represents the red to infrared optical signals over one second.
• When the noise in optical observations is assumed to be independent identically distributed normal random variables with zero mean and a given variance, the least squares regression slope is a random variable whose expected value is the underlying Ratrat with a certain variance. In this case, the value of theprobabilities64 may be generated from the probability distribution function of the normal. In a specific example, if the saturation value is assumed to be 90 at timestep K, and optical observations indicate 91.8±0.5 saturation, the probability that saturation is j at timestep K+1 is P_jQ_j, under assumptions of independence. Thus, saturation at K+1 may be estimated by that j and an iterative procedure with future optical observations may be invoked.
• FIG. 8 is a block diagram of an algorithm for determining the best value to post for a patient's SpO₂value based on the value of the Ratrat (i.e., Ratrat_K−1) for the previous timestep, the current measurement or measurements for the SpO₂value, theprobabilities42 and56 relating to the actual occurrence of the SpO₂value, and estimated noise. The algorithm is generally referred to byreference number90. Specifically,algorithm90 includes several steps for determining an appropriate estimate of the Ratrat for timestep K+1 that is substantially accurate during periods of noise and/or interference. The determination ofalgorithm90 is largely based on observations during timestep K+1 and a provided (e.g., measured) value of the Ratrat for timestep K. It should be noted that it is assumed in accordance with present embodiments that the sampling rate of optical observations is higher than the meaningful posting rate. For example, in one embodiment optical observations are made at 53 Hz and saturation values are posted at 1 Hz. Intervals between posts may be referred to as timesteps and intervals between observations may be referred to as minor timesteps.
• Inblock92, an initial estimate of the Ratrat at an initial time or for an initial timestep (i.e., Ratrat₀) is provided. This initial value may simply include the value of the Ratrat assigned to the timestep prior to the timestep for which the Ratrat (or the SpO₂value for posting) is being determined. The initial estimate of the Ratrat may be obtained using various procedures, such as bootstrapping a value from an initial reading. For example, the first estimate of saturation may be the value of the current physical measurement. In other embodiments, an overall probability distribution of the saturation in humans may be determined and utilized as the transition distribution from an unknown saturation in the previous time step. For example, population studies may provide estimates of saturation in groups of people, which may be utilized with safety factors (e.g., lower saturation levels for certain groups and generally lower saturation level estimates) to provide an initial estimate. This universal distribution approach does not require that the previous saturation estimate be known. In another embodiment, an estimate of saturation level and an estimate of confidence in the saturation level may be maintained. For example, information such as “at time step k saturation is in the range of 94.5%-95.499% (posting94) with 75% certainty” may be maintained. In order to boot strap, the information may be initialized as “attime step1, the saturation is in the range 89.5%-90.499% (or values provided in accordance with the physical measurement) with 1% certainty (or a value obtained from the physical measurement.”
• After establishing the initial estimate, inblock94, the optical observations over the previous timestep are correlated and a noise estimate is obtained. Various procedures may be utilized to provide this noise estimate. For example, block94 may include performing a linear regression of all the optical observations over the previous timestep to obtain a best fit slope, which may be referred to by the variable

  

  . Additionally, an estimate of noise may be obtained by determining a sample standard deviation of the residuals, which may be referenced by the variable θ. Under the assumption of normal noise,

  

  is distributed as the true slope plus an unbiased normal random variable with variance. This variance may be represented as θ²/σ_ir², where σ_ir²represents the sample standard deviation of the infrared values over the previous timestep. The following equation is representative:
• $\begin{array}{cc}={\sigma }_k+N\left(o,\frac{{\theta }^2}{{\sigma }_x^2}\right)& \left(\mathrm{Eq}.10\right)\end{array}$
• One component of algorithm90 is the incorporation of a maximum likelihood estimator. That is, the estimate of Ratrat_Kis that which is most likely given the previous estimate and the optical evidence over the previous major timestep K−1. This maximum likelihood estimation is represented by block96, wherein:
• 
  

  

  trat_j←

  

  trat_j−1+ξ  (Eq. 11)
• and wherein ξ maximizes the following function:
• $\begin{array}{cc}p\left(\xi \right)e\left(\frac{-0.5{\left(-{\mathrm{Ratrat}}_{j-1}-\xi \right)}^2}{{\theta }^2/{\sigma }_{\mathrm{ir}}^2}\right)& \left(\mathrm{Eq}.12\right)\end{array}$
• which is proportional to:
• 
  Pr{Ratrat_j−Ratrat_j−1=ξ|Ratrat_j−1=

  

  trat_j−1}Pr{

  

  observed|

  

  ˜N(Ratrat_j−1+ξ,θ²/σ_ir²}  (Eq. 13)
• which represents combining (e.g., essentially multiplying) theprobability42 represented inFIG. 5 with theprobability56 represented inFIG. 6 to determine a posting value based on which of the potential values has the highest probability. Because this is a maximum likelihood calculation, it is unnecessary to compute the cumulative distribution function of the normal, and p(x) can be known only up to a constant. Thus, the value posted as the meaningful SpO₂value is represented by Eq. 13.
• FIGS. 9,10 and11 are representations of data acquired by implementing and testing present embodiments against synthetic data using Viterbi's algorithm. The synthetic data consist of a time signal of saturation with a constant level of noise added. The results are plotted in several graphs in each ofFIGS. 9,10, and11. The different graphs correspond to different levels of noise in the observation, different choices of the variance in the underlying Markov Model, and different choices of the transition limits (up and down) of the Markov Model. Each ofFIGS. 9,10, and11 include a first graph (A) with low noise and low variance, a second graph (B) with low noise and high variance, a third graph (C) with medium noise and low variance, a fourth graph (D) with medium noise and high variance, a fifth graph (E) with high noise and low variance, and a sixth graph (F) with high noise and high variance. Further, each graph shows an actual underlyingsynthetic saturation signal72, observed saturation with noise added74, and a maximum likelihood estimator (i.e., output of the algorithm)76.
• FIGS. 9,10, and11 each illustrate slightly different information. The graphs inFIG. 9 show a model wherein the maximal decrease in saturation transition of the Markov Model is one-third the maximal increase in saturation transition. Specifically, the graphs inFIG. 9 illustrate the results of a maximum likelihood estimation using a Markov Model with a saturation increase allowed at triple the rate of saturation decrease. This approximates physiological reality, as saturation decreases are typically slow, while increases occur quickly with inspiration. The graphs inFIG. 10 show a model wherein the maximal decrease and maximal increase in saturation transition are equal. Specifically, the graphs inFIG. 10 show the results of a maximum likelihood estimation using a Markov Model with saturation increase allowed at the same rate of decrease. The graphs inFIG. 11 show a model wherein the maximal decrease is 4.5 times greater than the maximal increase in saturation transition. Specifically,FIG. 11 shows the results of a maximum likelihood estimation using a Markov Model with the aforementioned ratio between saturation increase and decrease.
• While the invention may be susceptible to various modifications and alternative forms, specific embodiments have been shown by way of example in the drawings and will be described in detail herein. However, it should be understood that the invention is not intended to be limited to the particular forms disclosed. Rather, the invention is to cover all modifications, equivalents and alternatives falling within the spirit and scope of the invention as defined by the following appended claims.

Claims (21)

1.-20. (canceled)

21. A method, comprising:

using a monitor for:

providing an initial estimate of a value representative of blood oxygen saturation at a current timestep;

correlating one or more optical observations obtained during a previous timestep;

obtaining a noise estimate based on the correlation; and

performing a maximum likelihood calculation to determine a value of blood oxygen saturation that is most likely given the initial estimate, the one or more optical observations, and the noise estimate.

22. The method ofclaim 21, wherein correlating the one or more optical observations obtained during the previous timestep comprises performing a linear regression of the one or more optical observations.

23. The method ofclaim 21, wherein obtaining the noise estimate comprises determining a sample standard deviation of residuals.

24. The method ofclaim 21, wherein performing the maximum likelihood calculation comprises combining a first probability distribution and a second probability distribution.

25. The method ofclaim 24, wherein the first probability distribution comprises a probability distribution of potential values of blood oxygen saturation at the current timestep based on the initial estimate.

26. The method ofclaim 24, wherein the second probability distribution comprises a probability distribution of observed blood oxygen saturation values based on an actual value.

27. The method ofclaim 26, wherein the probability distribution of observed values is based at least in part upon the noise estimate.

28. The method ofclaim 24, wherein the first probability distribution comprises a probability distribution of potential values of blood oxygen saturation at the current timestep based on the initial estimate, wherein the second probability distribution comprises a probability distribution of observed blood oxygen saturation values based on an actual value, and wherein performing the maximum likelihood calculation comprises multiplying the first probability distribution by the second probability distribution.

29. The method ofclaim 21, wherein obtaining the initial estimate comprises assigning a previous value of blood oxygen saturation at a previous timestep as the initial estimate.

30. The method ofclaim 21, wherein obtaining the initial estimate comprises obtaining a current physical measurement of blood oxygen saturation at the current timestep.

31. A system for providing a meaningful blood oxygen saturation value at a current timestep, comprising:

a pulse oximetry monitor configured to:

determine a first probability distribution of potential blood oxygen saturation values, based on an initial estimate of a blood oxygen saturation value;

determine a second probability distribution of potential blood oxygen saturation values based on an initial measurement of a blood oxygen saturation value; and

combine the first and second probability distributions to provide a meaningful blood oxygen saturation value,

wherein each probability distribution of potential values includes potential values at a current timestep with associated probabilities of occurrence.

32. The system ofclaim 31, comprising a sensor including an emitter configured to emit first and second wavelengths of light, a detector configured to detect the first and second wavelengths of light, and a transmitter configured to transmit photocurrent signals indicative of the first and second wavelengths of light to the pulse oximetry monitor, and wherein the initial measurement is based on the photocurrent signals.

33. The system ofclaim 31, wherein the initial estimate comprises a previous value representative of blood oxygen saturation at a preceding timestep.

34. The system ofclaim 31, wherein the initial estimate comprises a stored estimate value based on a patient type.

35. The system ofclaim 31, wherein the probability distribution of transition is a Markov Model transition probability.

36. The system ofclaim 31, wherein the probability distribution of measured values is a linear spline measured value distribution.

37. A pulse oximeter, comprising:

a processing device configured to:

provide an initial estimate of a value representative of blood oxygen saturation at a current timestep;

provide an initial measurement of a value representative of blood oxygen saturation at a current timestep;

determine a noise estimate based on a correlation of one or more optical observations during a previous timestep; and

perform a maximum likelihood calculation to determine a value of blood oxygen saturation that is most likely given the initial estimate, the initial measurement, and the noise estimate.

38. The pulse oximeter ofclaim 37, wherein the processing device is configured to perform the maximum likelihood calculation by combining a first probability distribution of potential values based on the initial estimate and a second probability distribution of potential values based on the initial measurement and the noise estimate.

39. The pulse oximeter ofclaim 37, wherein the processing device is configured to perform a linear regression of the one or more optical observations to correlate the one or more optical observations.

40. The pulse oximeter ofclaim 37, wherein the processing device is configured to determine a sample standard deviation of residuals to determine the noise estimate.

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