WO2006086566A2  Methods and apparatuses for noninvasive determinations of analytes  Google Patents
Methods and apparatuses for noninvasive determinations of analytes Download PDFInfo
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 WO2006086566A2 WO2006086566A2 PCT/US2006/004608 US2006004608W WO2006086566A2 WO 2006086566 A2 WO2006086566 A2 WO 2006086566A2 US 2006004608 W US2006004608 W US 2006004608W WO 2006086566 A2 WO2006086566 A2 WO 2006086566A2
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 G—PHYSICS
 G01—MEASURING; TESTING
 G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
 G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using infrared, visible or ultraviolet light
 G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
 G01N21/47—Scattering, i.e. diffuse reflection
 G01N21/49—Scattering, i.e. diffuse reflection within a body or fluid

 G—PHYSICS
 G01—MEASURING; TESTING
 G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
 G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using infrared, visible or ultraviolet light
 G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
 G01N21/25—Colour; Spectral properties, i.e. comparison of effect of material on the light at two or more different wavelengths or wavelength bands
 G01N21/27—Colour; Spectral properties, i.e. comparison of effect of material on the light at two or more different wavelengths or wavelength bands using photoelectric detection ; circuits for computing concentration
 G01N21/274—Calibration, base line adjustment, drift correction

 G—PHYSICS
 G01—MEASURING; TESTING
 G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
 G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using infrared, visible or ultraviolet light
 G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
 G01N21/25—Colour; Spectral properties, i.e. comparison of effect of material on the light at two or more different wavelengths or wavelength bands
 G01N21/31—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry

 A—HUMAN NECESSITIES
 A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
 A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
 A61B5/00—Detecting, measuring or recording for diagnostic purposes; Identification of persons
 A61B5/145—Measuring characteristics of blood in vivo, e.g. gas concentration, pH value; Measuring characteristics of body fluids or tissues, e.g. interstitial fluid, cerebral tissue
 A61B5/14532—Measuring characteristics of blood in vivo, e.g. gas concentration, pH value; Measuring characteristics of body fluids or tissues, e.g. interstitial fluid, cerebral tissue for measuring glucose, e.g. by tissue impedance measurement
Abstract
Description
METHODS AND APPARATUSES FOR NONINVASIVE DETERMINATIONS OF ANALYTES Technical Field
[0001] This present invention relates generally to determining analyte concentrations by analyzing light that has passed through a material sample. More specifically, the present invention relates to methods for improving the accuracy of analyte determinations in material samples that both scatter and absorb light.
Background Art
[0002] It is well known that absorbance spectra measured in the presence of scattering media differ from spectra of the same chemical species measured in the absence of scattering. It is also well recognized that the paths that light rays travel through a scattering sample are more difficult to characterize than those in nonscattering samples, within which, light rays generally travel a straight line. In nonscattering samples, path length can be calculated from the physical dimensions of the sample and a basic knowledge of beam and sample geometry. Furthermore, path length in an ideal transmission measurement is a common property for all light rays incident on the sample and thus path length can be represented with a scalar value common to all rays and all wavelengths.
[0003] In contrast, light rays traveling through a scattering sample have multiple potential paths and are therefore best described by a path length distribution (PLD). In simple terms, this distribution will have some fraction of rays that traveled the typical path length, as well as a fraction of rays that traveled shorter and longer paths through the sample via the random nature of scattering interactions. The properties of this path length distribution can also be further characterized with statistical properties, such as the distribution's mean and standard deviation. These properties are not necessarily fixed for a measurement system as they depend, in complex ways, on sample properties including both the scattering and absorbance.
[0004] There is great interest in measuring analyte concentrations in samples that both absorb and scatter light, despite the difficulties described above. This is because many important biological systems scatter light due to their heterogeneous composition. One example of these heterogeneous structures is collagen fibers in skin that scatter light because they have a different refractive index than the interstitial fluid that surrounds them. This scattering can complicate noninvasive glucose measurements such as those described in Patent number 4,975,581 , issued December 4, 1990. Another important example is measuring the concentration of urea in suspension of cells, such as those in whole blood. In this example, the red blood cells have a different refractive index than the surrounding serum that causes them to scatter both visible and infrared light. Another important example, is measuring lactate concentration in bioreactor cell cultures. This is an example where structures inside the cells, such as mitochondria, can be strong scattering elements. Determining analyte concentrations in all of these sample types is complicated by intrinsic biological variability in their absorbance and scattering properties. [0005] Known methods for determining an analyte concentration in a sample from optical measurements with variable path length distributions, due to scattering and absorbance changes, typically involve simplifying assumptions that limit their measurement performance in practice or involve methods that seek to estimate the path length distribution.
[0006] One class of methods uses theoretical approaches to estimate absorbance and scattering properties separately by applying Diffusion Theory. For example, Tissue Optics: light scattering methods and instruments for medical diagnosis, Tuchin V., ISBN 0819434590, The Society of PhotoOptical Instrumentation Engineers, 2000 Section 1.1 includes descriptions of optical properties of tissue with multiple scattering including blood and skin. The Diffusion Theory approach requires simplifying approximations that are not valid for all combinations of absorbance and scattering properties. For example, Diffusion Theory is not accurate when the effects of absorbance are greater than scattering or when the number of scattering events is small. Noninvasive tissue measurements in the near infrared spectral region can have one or both of these conditions.
[0007] Another theoretical approach uses Monte Carlo simulations to estimate the path length distribution from explicit knowledge of the system under study, which requires some, if not all, of the following optical properties: absorbance coefficient, scattering coefficient, scattering phase function, and sample geometry. In practice, it is difficult to accurately estimate the optical scattering properties of tissue as the true shapes of collagen fibers or blood cells need to be simplified to geometric forms like spheres or cylinders with known analytical solutions.
[0008] Another class of methods makes assumptions about optical properties of the sample at specific wavelengths. For example, that nonabsorbing wavelengths exists that can be used to correct analyte absorbance at wavelengths with similar scattering properties. Patent number 5,099,123 issued March 24, 1992. This approach is typically limited to spectral regions where water, a major constituent in many biological samples, is a weak absorber. A second example of assumed optical properties is the use of isobestic points. Patent number6,681 ,128, issued January 20, 2004. An isobestic point occurs at a wavelength where there are only two absorbing species, typically an analyte and another major absorber, and both species have the same absorptivity. Again, these approaches are applicable in some biological measurements, like pulse oximeters measurements in the 500 to 1000 nm region, but not throughout the infrared region where there are many more spectrally active biological species.
[0009] Multiplicative Scatter Correction, Multivariate Calibration, Martens and Naes, Section 7.4 and similar publications, estimates the net effect of scattering on path length across spectral wavelength with loworder polynomials, such as a quadratic function. Such functions do not accurately represent scattering over broad spectral range, such as the 4000 to 8000 cm1 region commonly used in noninvasive glucose measurements.
[0010] Another approach to determining analyte concentrations in highly scattering and absorbing samples is to measure the path length distribution explicitly and incorporate the path length estimate in the measurement algorithm. One such technique is to use photon timeofflight measurements to characterize the sample's optical properties at discrete wavelength in combination with absorption measurements, Leonardi, L; Burns, DH Multiwavelength Scatter Correction in Turbid Media using Photon TimeofFlight; Applied Spectroscopy, 50(6), 637646,1999. This approach requires additional measurement apparatus including a pulsatile or frequencymodulated light source, which adds cost and complexity. It also assumes that the path length properties at all wavelengths can be inferred from one or more discrete measurements.
Brief Description of the Drawings
[0011] FIG. 1 shows an idealized absorbance measurement system.
FIG. 2 shows the difference between a pure analyte signal and a net analyte signal.
FIG. 3 shows a net analyte signal with selectivity errors
FIG. 4 shows a net analyte signal with proportional errors
FIG. 5 shows pathlength changes that produce proportional errors
FIG. 6 shows a conceptual framework for understanding prediction errors
FIG. 7 shows a spectroscopic framework for understanding prediction errors
FIG. 8 shows spectra from several application areas
FIG θ.shows glucose measurement results in scattering media
FIG lO.shows ethanol measurement results in scattering media
FIG 11. shows urea measurement results in scattering media
FIG 12. shows the dependence of scatter on wavelength
FIG 13. shows the different in predictor functions for two scatter levels
FIG 14. shows the interaction between interfering substances and the predictor function
FIG 15. a illustration of the fundamental probe of analyte measurement in scattering media
FIG 16. illustrates a system with multiple observations point
FIG 17. illustrates the relationship between path and scattering media
FIG 18. illustrates the relationship of photon travel to scattering media
FIG 19. illustrates the influence of scattering media on glucose predictions
FIG 20. illustrates a conceptual framework for determining media characteristics through multiple observations
FIG 21. shows the ability to classify media based upon the diagnostic metric
FIG 22. illustrates the path characteristics of the calibration samples
FIG 23. illustrates the path characteristics of the validation samples
FIG 24. plots the prediction results for standard single channel processing
FIG. 25 plots the prediction results generated by the submodel approach
FIG. 26 shows the process of generating predictions results from multichannel spectra
FIG. 27 plots the resulting prediction results and error structure
FIG. 28 plots the prediction results generated by the XY model approach using glucose only
FIG. 29 plots the prediction results generated by the XY model approach using multiple analytes
FIG. 30 show different predictor functions developed from different media FIG. 31 shows the relationship between different predictor functions
FIG. 32 shows prediction differences as a function of different predictor functions
FIG. 33 plots the prediction results generated by the adaptive model approach
Disclosure of Invention
[0012] This patent describes a new family of methods to improve the accuracy of analyte concentrations measured in samples that both absorb and scatter light. Light scattering in biological samples, including blood, skin and bioreactor cell cultures, causes light rays to travel different paths through a sample. The paths of these rays violate several assumption of Beer's law because the paths are no longer parallel or of equal lengths. As a result, there is no longer a simple relationship between absorbance and concentration changes because interactions between scattering and absorbance properties across the desired operating spectral range distort the absorbance features of the analyte. The consequences of these distortions, in particular their effect on measurement precision, are not adequately discussed in prior art except for algorithmic approaches that generally compensate for scattering with multiplicative and offset corrections. The following discussion describes a novel family of methods for determining analyte concentrations in a sample from one or more optical measurements. These methods improve the accuracy of analyte determinations in material samples that both scatter and absorb light. One clear benefit of these methods is their improved ability to measure new samples with optical properties that are different from the samples used to calibrate the method. This overcomes a known limitation for applying existing methods in many practical applications where the method appears to perform well on a calibration set but performs poorly on new sample types that require extrapolation or interpolation. These new methods also overcome limitations in applying linear prediction methods based on Beer's law to samples that span a range of optical measurement or sample properties that violates its inherent assumptions.
Absorbance Spectroscopy
[0013] Spectroscopy measures the interaction of light with a sample. In general, light intensity entering and exiting a sample is compared to extract qualitative or quantitative information. The following section outlines the assumptions inherent in spectroscopy for ideal samples before moving on to more complex systems. For illustrative purposes, this section focuses on absorbance spectroscopy in the visible and infrared regions. The visible region includes wavelengths from 380 to 780 nm. The near infrared region includes wavelengths from 780 to 2500 nm and the midinfrared region includes wavelengths from 2500 nm to 50000 nm. This illustrative discussion is not restrictive, as the same fundamental principles apply broadly to absorption measurements outside these regions, including absorbers in the ultraviolet region and Xray region and nuclear magnetic resonance. In the visible and infrared regions, a molecule absorbs light at frequencies characteristic of its chemical structure, which is determined by vibrational and electronic energy levels. In qualitative spectroscopy, the frequency and relative intensities of these characteristic absorbance features are used to identify specific chemical species (such as ethyl alcohol) or a broader class of chemicals (such as alcohols). In quantitative spectroscopy, the magnitude of one or more absorbance features is used to estimate the concentration of an individual chemical species in a sample (such as alcohol levels in blood) or a family of related compounds (such as total proteins in blood). Thus it is understood that the analyte measurement can estimate the concentration of a single species (such as glucose), a composite property (such as octane number of gasoline), a physical property (such as sample temperature), or a subjective sample property (such as fruit ripeness).
[0014] An idealized system for absorbance measurements is shown in Figure 1a where the sample is presented in a cuvette with rectangular crosssection to the incident beam, which has parallel rays of monochromatic radiation. The sample transmittance (T) is the ratio of the intensity of the exiting light (I) to the incident light (I_{0}),
T = 1/I_{0}
[0015] The sample absorbance (A) is calculated from transmission with a logarithmic transform
A = log_{10} (T) = IOg_{10} (I_{0}/!)
[0016] Absorbance spectra are generally used for quantitative and qualitative analysis because, in these ideal systems, their magnitude is linearly related to concentration through Beer's law
A = elc
[0017] Where e is molar absorptivity, I is path length, and c is concentration of the absorbing species. Note that in the measurement example shown in Figure 1a the path lengths of the three illustrated rays are equal and equivalent to the internal dimension of the cuvette. Thus path length is completely described with a scalar value of path length, I. In contrast the scattering systems shown in both a transmission (Figure 1b) and a diffuse reflectance (Figure 1c) measurement modes where three possible light rays are shown that have different path lengths in the sample due to scattering interactions.
[0018] Also note, that the Beer's law notation is easily extend to a spectrum measured at multiple wavelengths using a vector notation,
A_{v} = e_{v}lc
[0019] where A_{v} is a vector containing the absorbance measured at each wavelength (v), e_{v} is a vector containing the molar absorptivity at each wavelength (v) and path length, I, is still a scalar quantities as it is the same for all wavelengths. For a measurement system with a fixed pathlength, the change in absorbance at each wavelength for a unit change in concentration will be called the pure component spectrum, K_{v}
K_{v} = e_{v}l [0020] While this pure component spectrum is often considered to be the absorbance of the analyte, such as absorbance features of the glucose molecule, there are also cases where the signal includes the influence of the analyte on the solvent or other constituents of the sample. Examples of these indirect effects include negative absorbance features of displaced solvent and changes in the hydrogen bonding structure of the solvent due to temperature or dissolved ions, such as the spectral changes associated with adding salts like sodium chloride.
[0021] The Beer's law equation can be similarly extended to describe a sample with multiple absorbing components using a matrix representation,
/Λ_{v} — I C^_{n} U_{n}
[0022] where E_{v},_{n} is matrix with the absorptivity of species 1 to n at each wavelength, v, and C_{n} is a concentration vector of the n constituent concentrations in the sample. Note again, that path length, I, is assumed to be a scalar quantity for this sample.
[0023] Also note, while many methods of determining analyte concentration are described for absorbance measurements, this choice of units is for mathematical convenience and compactness alone, as equivalent computational algorithms can be written by one skilled in the art to operate on other inputs forms including transmission spectra, detector intensities, and interferograms.
A calibration estimates the relationship between measured absorbance and analyte concentration
[0024] In practice, a calibration step can be required to create an accurate relationship between the measured absorbance spectra and analyte concentration for a given measurement system. In this discussion, method calibration refers broadly to using a set of spectral measurements of samples with known properties to calibrate the relationship between the measured spectra and the analyte of interest. Method validation refers to a subsequent step where new samples are used to test the validity of the calibrated measurement method. Ideal validation samples have a distinct composition (absorber concentrations and scattering properties) from the calibration samples.
[0025] If a wavelength exists where only the analyte of interest absorbs then Beer's Law describes a linear relationship between the absorbance at this selective wavelength, A_{1}, and the analyte concentration, c,
A_{1} = CK_{1}
[0026] where K_{1} is the slope of the calibration curve  a plot of measured absorbance versus analyte concentration.
[0027] Estimated concentration, c_{hat>} is determined with the predictor function, b,
Chat = A_{I} b and b=1/Ki [0028] This calibration approach will be called a singlewavelength singlecomponent prediction model, as it requires the one component's (the analyte) spectral properties to be calibrated at one wavelength. This concept can also be extended to a multiplewavelength singlecomponent prediction model,
Chat = A_{v}b_{v}
[0029] Note that the predictor function (also called a regression vector) for a singlecomponent model, b_{v}, is simply a scaled version of the pure component signal of that analyte and, as such, the entire signal is used to predict analyte concentration.
[0030] Biological samples typically contain many constituents, which can potentially interfere with the singlecomponent prediction functions described above. The constituents or conditions that interfere with analyte measurements will collectively be called interferences or interfering species. In some cases, the interference is a chemical component that absorbs at one or more wavelengths common to the absorbance of the analyte. In other cases, the interference is a spectral change resulting from changes in the sample environment, like temperature or pH. As discussed above, scattering can be viewed as an interferent it alters or modifies the measured spectrum. In other cases, the interference results from spectral artifacts due to component aging or alignment changes in the optical measurement system.
[0031] If uncorrected for, such interfering species degrade the measurement performance of the prediction function. Thus, the goal of multicomponent calibrations is to calculate a 'netanalyte' spectrum that responds proportionally to analyte concentration but is selective against interfering species. As the name implies, a multicomponent calibration requires both analyte properties and the interfering species properties to be adequately represented in the calibration set in order to produce an accurate prediction model.
[0032] A simple geometric presentation of a net analyte signal is shown in Figure 2. In this example the net analyte signal is the portion of the pure component signal that is perpendicular (or orthogonal) to the interfering species' signal. There are two classes of linear models that estimate such net analyte signals: forward calibrations and inverse calibrations. One example of a forward calibrations the Classical Least Squares (CLS) solution of the multicomponent Beer's law described previously.
b_{v} = K^{T}(KK^{T})^{"1}
[0033] where K is a matrix of pure component spectra. Solving this leastsquares solution requires pure component spectra to be known for all absorbing components in the calibration set.
[0034] In practice, the knowledge required to solve a CLS model can be difficult to obtain for biological samples due to their potentially large number of constituents. As a result, many biological measurements systems use another class of multicomponent models called inverse models. Inverse models estimate the predictor function b_{v}from b_{v} = (A^{T}A)^{"1}A^{T}c_{n} where c_{n} is a vector of analyte concentrations.
[0035] Inverse models only require concentration values to be known for the analyte of interest in the calibration step. These reference concentrations are often available from standard clinical methods. For example, the glucose reference concentrations used in this disclosure were measured with an electrochemical method on a Yellow Springs Analyzer.
[0036] The class of inverse methods includes many specific computational algorithms including inverse least squares (ILS), multiple linear regression (MLR), partialleast squares (PLS), principal components regression (PCR), canonical correlation, ridge regression, and Tikhonov regression. Multivariate Calibration, Martens and Naes, Section 7.4 The PLS algorithm is used to solve the inverse multicomponent models in this work, unless stated otherwise. The goal of each of these methods is to produce a regression vector for the multiplewavelength prediction model shown above. While the prediction functions (regression vectors) produced by forward and inverse models will look similar for some chemical systems, the two approaches have different optimization functions. Forward models, like those defined in the CLS approach, find solutions with spectral signals that best represent true spectral shapes, in other words, CLS is an optimal estimator of pure component spectra. In contrast, inverse models, like those solved with the PLS approach, find solutions for the predictor function so its output best matches the reference concentrations, in other words, solutions that minimize prediction error. This is an important distinction, as the predictor functions in a the presence of path length changes can be very different from the predictor function that are optimal for a fixed pathlength measurement. For details see Brown C, Discordance between Net Analyte Signal Theory and Practical Multivariate Calibration, Analytical Chemistry, Vol. 76, No. 15, August 1, 2004
Sources of prediction error
[0037] The following discussion focuses on three general classes of prediction errors: measurement noise errors, selectivity errors, and proportional errors.
[0038] Measurement noise errors result from the propagation of random instrument noise through the prediction equation. Random instrument noise arises from a variety of sources including photon counting, dark current noise at the detector and Johnson noise across electronic junctions. While reduced by good instrument design and signal averaging, instrument noise is never eliminated. This noise reduces the precision of the concentration predictions. The relationship between optical signal variance and concentration estimate variance depends on the magnitude of the net analyte signal and the predictor function derived from it. Specifically, for a given measurement error magnitude the concentration variance is proportional to the Euclidean length, (sqrt(v v^{τ})) of the regression vector. Accordingly, the effects of measurement error noise are smallest when the maximum amount of the pure component signal is retained.
[0039] Selectivity errors as diagramed in Figure 3a result when the prediction function (drawn as a regression vector) is not completely selective for the analyte of interest. In this case, concentration changes of the interfering signal will influence the analyte prediction. This influence can bias the sample prediction away from the true analyte concentration in samples containing interfering species. Measuring the same sample repeatedly does not reduce such a bias. Note that the sample can be biased to over or underreport the analyte concentration. The direction and magnitude of the bias depends on spectral differences between the analyte and interfering species and the concentration of the interfering species in a prediction sample relative to the average value in the calibration set.
[0040] Although the effect of a selectivity error on individual sample predictions is a constant bias, the effect of selectivity errors across multiple samples with variable composition can appear random, especially when plotted as analyte prediction versus true concentration. A simple example of this is shown in Figure 3b where variation in an interferent concentration can cause the analyte concentration to be over or under reported. In a controlled setting, the effect of a single interfering species would be clear if the prediction errors (predicted concentration minus true concentration) were plotted as a function of the interfering species concentration. In practice the effect of selectivity error can appear random, particularly if the model has selectivity errors for multiple interfering species. Selectivity errors can occur if the interfering species variation was not well represented in the calibration set or if the shape of the interfering species spectrum (and hence its direction) is different in a new sample as a result of distortions caused by changes in the path length distribution.
[0041] Proportional errors occur when the magnitude of the regression vector is incorrect. The resulting errors are proportional to the analyte concentration as shown in Figure 4. Unlike the prediction error structure observed for selectivity in Figure 3, the predicted concentrations lie on a line. The nature of the proportional error is that this line differs from the line of indentity. Note that the optimal net analyte signal and estimated net analyte signal in this example point in the same direction but differ in magnitude. As such, if the optimal net analyte is orthogonal to the interfering species then the estimated net analytical signal will maintain the same selectivity. This implies that the proportional errors can be distinct from selectivity errors in their origin and observed error structure.
Example of path changes that produce proportional errors
[0042] Figure 5 illustrates a hypothetical system where path length changes are induced by changing the physical dimensions of the cuvette. The effect of these path length changes is equal for all wave lengths of the spectrum. This system was mathematically constructed with knowledge of the pure component spectra of water, glucose, urea, and ethanol, which will be components of tissue phantoms discussed in the following sections. Figure 5a shows the spectral effect of this path length change on one sample. As would be expected from Beer's law, these spectra differ only by a scalar factor. For this example, the prediction function was calibrated using only samples collected at the 1 mm path length. Figure 5b shows prediction results for the 1 mm prediction function on a set of validation samples, also collected with the a 1 mm path length. These predictions lie along the line of identity with little variation as the prediction function is optimal for these data. In contrast, predcitions from the 1 mm predictor function applied to samples with 0.8 and 1.2 mm path lengths show clear proportional errors. It is important to note that the change in path length for each wavelength is the same in this measurement system and this is not the behavior generally seen when scattering and/or absorbance changes in many of the biological systems where the path length is a distribution.
[0043] Figure 6 shows a mathematical framework for assessing prediction errors in a linear prediction model that can be used to assign the origins of the three classes of errors discussed in the previous section: measurement noise errors, selectivity errors, and proportional errors. The glucose value estimated by applying the prediction function to a spectrum is equal to the sum of the glucose prediction values applied to each constituent of the sample as Beer's law describes as linear additive system. This framework is used in Figure 7 for the case of the 1.0 mm model predicting 500 samples measured in a 1.2 mm cuvette. Note that the proportional error in glucose predictions is consistent with that of a net analyte signal calibrated on a system on samples with a shorter path length but that this path length change in a nonscatteing sample does not increase selectivity errors because concentration variation in the two potential interferents (urea and ethanol) have no significant effect on the glucose prediction. Also note that measurement noise errors are not significantly increased.
[0044] Given the proportional nature of these errors, it is reasonable to apply a multiplicative correction using methods described in the prior art section. In general, such approaches assume that path length is constant across small spectral regions or changes smoothly with wavelength. These methods are adequate because the correction does not need to adjust the model to correct for a selectivity error with respect to the ethanol or urea components.
A major limitation in biological samples is path length changes due to scattering elements.
[0045] The cuvette example shown in Figure 1a and discussed in the previous section is not an accurate representation of path length changes that occur in measurements of biological samples. In these systems, the path length distribution results from scattering, which is defined here to broadly include interactions that change the direction of a light ray due to interactions with inhomogeneties in the sample including scattering structures described previously (such as cell structures and collagen fibers) as well as inhomogeneites from concentration gradients, temperature gradients, and diffuse reflecting surfaces (such as airsample boundaries). Figures 1b and 1c show how such scattering events can change the direction of a light ray and influence its total path length within the sample. Many factors can change the scattering of a sample, including changes in the number, size, and geometry of scattering elements.
[0046] In blood samples, scattering changes occur due to hematocrit level differences across a population or changes within a single patient over time, due to factors like dehydration or blood loss during surgery. The shape of red blood cells can also change as a function of blood pH and tonicity. [0047] Noninvasive tissue measurements can also include significant scattering variations due, in part, to physiological variations in collagentowater ratios and collagen fibril diameter changes as a function of age and disease state. It should also be noted, that the very act of placing skin on an optical sampling element can change its scattering properties through compression, tension, temperature, and humidity changes.
[0048] Large scattering changes also occur during bioreactors run where cell density can vary over the course of a single run as cells multiply or are extracted.
[0049] Figure 8 shows examples of spectral variation observed in noninvasive tissue measurements, blood samples, and bioreactor runs. To further understand problems of this nature, a set of tissue phantoms was constructed with wellcharacterized variation in absorbing and scattering constituents. This set of tissue phantoms was then studied to test the effects of changing path length distributions through several mechanisms, including changes in scatter bead concentration, absorber concentration, and optical sampler configuration. These tissue phantoms contained polystyrene beads (0.298 μm diameter sphere supplied by Bang's Beads) as scattering elements with a twofold variation in concentration (4000 to 8000 mg/dL). These scattering beads were suspended in 0.9% saline solutions, phosphate buffered to physiological pH and warmed to a physiological temperature range (varied from 36 to 38 C) consistent with noninvasive tissue sampling. The scattering bead concentrations were clustered around nine discrete levels with steps of 500 mg/dL between 4000 and 8000 mg/dL of polystyrene. For convenience, these will be referred to a scatter levels 1 to 9. Each scattering level included samples with variable analyte and interference concentrations. These scattering samples also contained glucose, urea, and ethanol over a wide, but physiologically representative range. For example, the glucose range of 100 to 600 mg/dL includes values observed in diabetic subjects. These spectra were obtained by [Extract a description and figure from the Noncontact Sampler Patent].
[0050] Figure 9 includes results from a study that essentially repeats the path length investigation shown in Figure 5, now using tissue phantoms instead of variable thickness cuvettes to induce path changes. Figure 9a shows results of using prediction function calibrated for glucose with lowscattering samples (scatter levels 13) performs (versus reference glucose concentration) on a validation set with similar scattering levels. The slope of the glucose predictions is close to unity and the scatter around the line is consistent with the measurement noise errors for this instrument. Panel 9d shows similar behavior for a prediction function calibrated for glucose with high scattering samples (scatter levels 79) and validated on samples with similar scattering levels.
[0051] Figures 9b and 9c illustrate prediction errors that occur when these same prediction functions are applied to validation samples with scattering characteristics outside the calibrated range. Although there are slope errors of about 3 and 7% respectively, the greatest loss in overall measurement performance results from prediction errors that scatter around these lines. Given the measurement noise and prediction functions are the same as those in Figures 9a and 9d, errors of this magnitude and character are more consistent with a selectivity error such as those illustrated in Figure 3b. Figures 10 and 11 illustrate similar behavior for the ethanol and urea predictor functions calibrated and validated in the same way. These examples illustrate a loss of prediction performance with for all three chemical constituents when a prediction function is used on samples with different path length distributions that differ from those used to calibrate the predictor function. This behavior was confirmed by measuring validation samples with both high and lower concentrations of scattering elements than samples included in the calibration.
[0052] The error structure seen in the scattering samples is in contrast to that observed with the nonscattering samples in Figure 5. The differences in the prediction errors are due to the fact that the change in path length is different at each wavelength. In fact the observed pathlength is a function of both scattering and absorbance. This pathlength change as a function of wavelength has been described as a distortion of the glucose signal. Both scattering and absorbance are wavelength dependence. The pathlength change between samples is a complicated vector which changes with every wavelength versus a simple scalar multiplier. The changes in pathlength as a function of wavelength effectively distort the glucose signal. This distortion creates a slightly different PLD at every wavelength which results in the observed glucose prediction errors. This distortion can be conceptualized as a variable degree of blurring across an image. Figure 12 illustrates the change in scattering as a function of wavelength.
[0053] Returning to a more rigorous spectroscopic interpretation of the error, Figure 13 illustrates key geometric properties of glucose predictor functions (specifically the net analyte signals calculated with the PLS algorithm) of glucose estimated from high and low scattering calibrations with an inverse model. It is important to note that the optimal model for low scatter samples is different than the model for high scatter samples, with respect to the length of the regression vector but also the direction of the regression vector. This implies that a single regression vector will underperform a regression vector optimized for a given path length distribution.
[0054] Figure 14 illustrates how scattering changes distorts not only the analyte signal shape (through a nontrivial rotation) but also the spectra of potential glucose interferences, like urea and ethanol. For example, the glucose model calibrated for low scattering samples is orthogonal to the spectral response of urea and ethanol in low scattering measurements, which is consistent with the measurement performance for these samples. This performance is not maintained when these chemical species are distorted by path length changes in a manner that reduces the glucose model selectivity by rotating or distorting the signals in a manner that induce overlaps with the glucose model. This is the origin of selectivity error with path length distribution changes, the behavior of this error is consistent with discussion of Figure 3. This is a key spectroscopic insight into why path variation in scattering media generates both proportional errors and /or selectivity errors when the path length distributions change in a complex manner as a function of wave length. Samples that exhibit these selectivity errors with path length distribution changes require a new class of prediction methods to maintain acceptable performance across samples that have scattering and absorbance changes.
New Approach to Pathlength Determination by Prediction Differences
[0055] As described above, path length distributions can be a complex function of scatter, absorbance and wavelength. The process of determining the effective PLD at each wavelength with information obtained from a single spectral observation (also called a singlechannel measurement) on each sample is extremely difficult. In general, the problem is one where the number of unknown parameters exceeds the number of independent measurements.
[0056] To accurately determine analyte concentrations in material samples that both scatter and absorb light, additional information can be obtained by using an optical system that acquires multiple observations of the sample. These observations can differ in the subsets of light rays they collect from the sample. These subsets of light rays are collected by what are often referred to a as multichannel samplers, or equivalently a multipath samplers or equivalently as multidepth samplers. These samplers have the capability of acquiring spectral data that have differences in their PLDs . These subsets of light rays are filtered out of the set of all rays exiting the tissue through the use of filters. In this discussion, filter has a broad definition that includes optical filters that attenuate light rays based on their linear or elliptical or circular polarization state. The definition of filter also includes spatial filters (also called masks or apertures) that attenuate rays based on the physical location they leave the sample such as described in US patent 5,935,062, Diffuse reflectance monitoring apparatus.. The definition of filter also includes and angular filters such as the intrinsic acceptance angle of a fiber optic, lens, or set of baffles that attenuate rays based on the angle they leave the sample. None, one, or combinations of these filters can be applied to each measurement channel of a multichannel sampler.
[0057] Even with a multiplechannel measurement, determining the effect of scattering on the PLD and the prediction function can remain a complex calculation. A simple approach for determination of the relative pathlength is needed. The approach disclosed below is based upon the fact that Beer's law:
A = elc is unable to distinguish between path length changes and concentration changes. This fundamental characteristic of Beer's law can be exploited to characterize the scattering characteristics of the tissue. As discussed previous, historical approaches have sought to deduce the path length properties directly from the one or more spectral measurement. In contrast the analysis framework disclosed herein uses the net effect of the path length distribution changes on the predicted analyte concentration to characterize the sample.
[0058] In Figure 15, the problem is described in a pictorial representation. Samples of scattering media are represented in Figures 15a and 15b. Both boxes are filled with the same glucose concentration. In Figure 15a the light rays travel a more direct path due to the fact that less scattering occurs, resulting in an average path of 5. In Figure 15b the light rays travels a much less direct path due to the increase scattering and travels a average pathlength of 8. Thus, if the same prediction function is applied to both measurement channels, the glucose prediction for the box in figure 15A will be less than the prediction result for the box in figure 15B despite the fact that both boxes are filled with solution of the same glucose concentration. As the goal of the system is to measure glucose, one has the inability to determine if the boxes have different glucose concentration or different path lengths based upon the information and results generated by this single observation system.
[0059] For description purposes and explanation of the key inventive concept, consider the boxes in Figure 16 to contain nails that are perpendicular to the plane of the paper. If marbles or balls were dropped in the top of these two boxes, the number of nails and resulting bounces (which are considered here to be a type of scattering) would influence the path traveled and the resulting distribution of balls in the collection bins. In the case of fewer nails, the distribution is much more center focused. As the number of nail bounces increase the distribution becomes more dispersed and the relative differences in the number of balls in adjacent bins is reduced. Thus, by examination of the number of balls in each bin or an examination of the ball distribution as a function of bin location, a relative measure of the effect of nail interactions can be determined. The observed ball distribution allows one to assess the density of nails in the box without looking in the box.
[0060] Figure 17 illustrates the same information as Figure 16, but now includes information regarding the pathlength traveled by the balls as they travel from top to bottom. Those balls that effectively drop straight through will have the shortest pathlength, while balls on the outer bins in a case with lots of nail encounters will have the longest pathlength. Thus, if one could obtain a measure of pathlength at each bin location, like counting the number of balls in each bin, a relative determination of the number of nails within the box could be made (e.g. scattering events).
[0061] Figure 18 returns to a spectroscopic illustration. The boxes are now filled with scattering media, the left box with fewer scattering centers then the right box. The glucose concentration in each box is the same. Light rays are launched into the media from a single light source at the top of the box and the light rays reaching the bottom of the box are recorded at two sampler channels or detectors. This is an example where different spatial filters are applied to the two measurement channels. As the light rays travel through the media they are scattered much like the balls of the prior example. As illustrated, the photons travel different distances based upon the scattering characteristics of the media. The relationship between the path lengths traveled is heavily influenced by the amount of scatter. For example, in the left side with more scatter, the difference in pathlengths traveled as observed by the two detectors is less than for the lower scatter situation on the left side.
[0062] The spectral information recorded at each detector channel of this multichannel sampler can be used to generate glucose prediction results. In this application, the same predictor function is applied to the signal or spectrum measured by each channel. The resulting glucose predictions effectively scale with the pathlength the photons have traveled and the actual glucose concentration of the media. As the objective of this process is to characterize the scattering or pathlength of the media, the contribution of the glucose concentration of the media needs to be removed. The media concentration of glucose can be effectively removed by examining the relative difference between the glucose predictions, an simple subtraction creates the relative difference. Thus, the relative prediction difference can be used to classify or characterize the media or tissue under examination. As shown in Figure 19, difference in the glucose prediction results for channel 1 and channel 2 of the sampler can be a diagnostic metric to characterize the scattering or pathlength characteristics of the tissue sample. This method is very powerful as it is a direct measure of the influence that the media is imposing on the prediction result. Stated differently, this analysis framework uses the net effect of the path length distribution changes on the predicted analyte concentration to characterize the sample. In practice, the analysis method determines the characterization of the media by effectively using the same system used for analyte measurement versus a secondary measurement system for media characterization. Specifically, the media characterization method uses the same optical system, similar processing methods, a similar predictor function, and similar level of computational complexity. The observation that relative differences in prediction results can be used for media characterization is extremely valuable and requires only an additional piece of spectral information. This second piece of spectral information should have a different functional dependence on the scatering and absorbing characteristic of the sample than the first piece of spectral information.. The fact that the media is characterized by the relative difference in the prediction results removes any requirements to know the true glucose concentration of the sample.
[0063] The relative prediction difference method can be extended to other analytes in the sample. For example, alcohol diffuses throughout tissue and will be influenced by changes in pathlength. As alcohol absorbs differently than glucose, the influences of path can be slightly different than glucose but the basic concept that the measurement is sensitive to path applies. Thus, the use of relative prediction differences as a diagnostic function to characterize the media can be extended to multiple analytes in the sample. The use of diagnostics metrics from multiple analytes increases the information content available for tissue scattering characterization. Using an image analogy, it transitions the picture from black and white to color.
[0064] Figure 20 is a summary of the concept described above. Historically, most noninvasive glucose measurement systems have used a single source and detector. This results in a single spectra or singular piece of information and can be equated to a monocular vision system with a limited ability to determine pathlength. The expansion of the system to multiple observation points increases the information content and transitions the system to a binocular system with the ability to diagnose and characterize the effects of path length distribution changes that result from variations in absorbance and scattering across a set of samples. The extension of the concept to include multiple analytes adds an additional dimension to the information content and allows for further tissue characterization. In analogy terms, we think of the addition of multiple analytes as adding color to a black and white image, a dramatic increase in information content. [0065] The discussion above describes a general framework where a prediction function optimized for a set of calibration samples is applied to measurements made on a new sample measured at two (or more) channels of a multichannel sampler. The spectral measurements made at these channels differ in the subset of light rays collected from the sample, such that the path length distribution for these subsets of rays have different functional dependences on the underlying absorbance and scattering properties of the sample. Rather than deducing the path length properties directly from these multiple spectral measurement, this analysis framework uses the net effect of the path length distribution changes on the predicted analyte concentration to characterize the sample.
Demonstration of Media Classification by Relative Prediction Difference
[0066] To demonstrate the above concept the tissue phantoms composed of polystyrene beads were sampled on a sampler with different sourcedetector separations. This sampler is an example of a multichannel system that applies a spatial filter to light rays leaving the sample. The four measurement channels correspond to detector fibers spaced 300, 370, 460, and 625 μm (centerto center) from the source fiber. A predictor function was developed using spectral from all four source detector separations but only those samples have from scatter level 5. This single predictor function was then used to generate glucose prediction results on the remaining scatter levels at two different source detector separations (300 and 625 μm). The difference between the glucose predictions was then calculated to generate a diagnostic metric for use in characterizing the media. This diagnostic metric was then plotted versus the scatter level of the sample upon which the diagnostic metric was calculated. Figure 21 demonstrates that the diagnostic metric enables the identification of the correct scatter level of the sample. In summary, the analysis framework using predicted analyte concentration differences does effectively enable characterization of the media.
Prediction function calibrated on a singlechannel.
[0067] For comparison purposes the first method discussed applies single channel calibration and prediction process to a set of validation samples. The predictor function was developed on calibration samples from only a single channel of the multichannel sampler and glucose predictions were generated on validation spectra acquired on the same channel as the calibration spectra..
[0068] In this study the tissue phantoms were measured on multichannel sampler that uses up to four rotational settings of a polarizing filter to define the measurement channels. Figure 22a shows the relationship between polarization angle and pathlength. Examination of the data at a polarization angle of 90 shows the degree of pathlength variation present in the samples. Figure 22b shows a histogram of the number of calibration samples used and their corresponding scatter level.. The scattering levels used were midscattering samples that includes scatter levels 3 to 7.This calibration and subsequent calibration models are developed in this manner to simulate the expected distributions of scattering levels in humans. Estimated path lengths observed for these scattering levels are reported by estimating the effective path length observed at the absorbance peak centered at 6900 cm^{'1} , which is a strong water absorbance feature. The effective path length for this spectral region is estimated by comparing its baselinecorrected absorbance to that of the same peak in a 1 mm cuvette of pure water. This crude metric is used for illustration purposes and it is not used for subsequent glucose predictions,
[0069] In this first method the predictor function was calibrated on a single channel of spectral measurements. In particular, all calibration spectra and validation spectra were collected using a polarizer angle of 90 degrees, which has the longest pathlength through the scattering samples. The glucose predictor function was calibrated with the PLS algorithms using nearinfrared spectral absorbance between 4200 and 7200 cm^{"1}.
[0070] Figure 23 shows characteristics of validation samples data in a similar format to Figure 22. The validation set includes some samples at scatter level 5, which is at the center of the calibration set scattering levels as well as samples from scattering levels 3 and 6. The validation set also included samples with scatter levels lower and higher then the calibration samples, level 1, 2, 8 and 9. These samples were included to test prediction performance at the limits, or outside the scattering range included in the calibration set. Examination of Figure 23B at a polarization angle of 90 shows the pathlength variation present in both the calibration samples and validation samples.
[0071] Figure 24 compares predicted glucose values to their true concentrations and presents the standard error of prediction (SEP) at each scatter level. Consistent with previous discussions, measurement precision deteriorates when the calibration model is forced to extrapolate beyond its calibrated range of path length distributions. One average, the worst predictions are observed for scatter levels 1 ,2, 8 and 9. Thus, an object of the invention is to use the ability to characterize the media for the generation of more accurate glucose results.
Using the relative reference approach with a single prediction function to classify new samples
[0072] In the first demonstration of the relative referencing concept will to use the media characterization capabilities in a classification framework. The application of the concept applies a single prediction function to samples collected on a multichannel sampler to classify new samples for improved glucose predictions. At a high level, the steps are to build a single prediction function on a calibration set the includes and then to apply this prediction function to a new sample observed on the multichannel sampler. This prediction function will produce a diagnostic vector of predicted glucose values for each channel of the sampler
d_{n} =A_{n},v b_{v} where d_{n} is an (number of channels by 1) diagnostic vector containing a glucose prediction for each sampler channel, A_{n},_{v} is an absorbance matrix for a new sample (number of channels by number of wavelengths), and b_{v} is a prediction function (number of wavelengths by 1). [0073] In one embodiment, the diagnostic vector for a new sample is used to build a submodel for this sample by selecting a subset of the calibration samples with similar path length distributions. In practice the steps are: a. Measure the spectra of calibration samples on a multichannel sampler with n channels. b. Estimate a predictor function b_{V}. (where the star indicates all channels are used) using an inverse model and a subset 'A' of the calibration set that includes all or a restricted range of path length variation and spectra acquired on two or more channels of a multichannel sampler. c. Apply the prediction function b_{v},. developed in Step (2) to the all channels of all calibration samples to produce a diagnostic vector for each calibration sample. d. Characterize the samples using one or more diagnostic metrics, m, calculated from the diagnostic vector. One example of a diagnostic metric, based on the relative reference approach is to subtract one element of the diagnostic vector from another,
d_{2}
This diagnostic metric is equivalent to the relative referencing example in Figure 21. e. Save one or more diagnostic metrics for each calibration sample. f. Measure a new sample on a multichannel sampler and calculate its diagnostic metric or metrics g. Select a subset ^{1}B' of calibration samples with similar diagnostic values to the new sample. h. Estimate a predictor functions [b_{v}i, b_{v2}, ■■■ b_{vn}] from subset 'B' of calibration samples by building one model for each of, n, sampler channels. i. Predict the new sample's concentration by applying predictor functions b_{v1}, b_{v2}, b_{v3}, and b_{V4} the appropriate measurement channels of the new sample.
[0074] One example of this approach was applied the set of scattering tissue phantoms discussed previously. For step 1 of this example, the samples were measured on a sampler with different source detector separations. This is a example of a multichannel sampler that applies a spatial filter to light rays leaving the sample. The four measurement channels correspond to detector fibers spaced 300, 370, 460, and 625 μm (centertocenter) from the source fiber.
[0075] In step 2 the predictor function b_{Vι}. was estimated with the PLS algorithm applied to spectra from all four channels of the sampler and the subset ^{1}A' included only calibration samples from scatter level 5. These absorbance spectra included all wavelengths (v) between 4200 and 7200 cm^{"1} in the nearinfrared spectrum.
[0076] In step 3 the predictor function b_{v},. was used estimate glucose concentrations for all channels of the remaining calibration samples. This provided a fourelement diagnostic vector for all sample in the full calibration set.
[0077] In step 4 the diagnostic metric was the difference between between glucose concentrations estimated with predictor function applied to spectra for the shortest sourcereceiver separation (element di of the diagnostic vector) and the longest sourcereceiver separations (element d_{4} of the diagnostic vector).
[0078] In step 5 the diagnostic vector or metric was saved for each calibration sample.
[0079] Figure 21 illustrates the value of this diagnostic method applied to tissue phantoms across the entire range of scattering levels. This diagnostic metric alone can accurately classify the scattering of the tissue phantom into their nine respective levels.
[0080] In step 6 the diagnostic metric was calculate for validation samples using the predictor function b_{v}* calibrated in step 2.
[0081] In step 7 the calibration subset 'B' was selected by finding the 25 calibration samples with the most similar diagnostic metrics.
[0082] In step 8 a set of predictor functions b_{v1}, b_{v2}, b_{v3}, and b_{V4} were calibrated for each of the four channels using calibration samples from subset 'B'.
[0083] In step 9 glucose concentrations estimate at each channel by applying the channel specific prediction functions to the appropriate each model to the corresponding channel of the new sampler were averaged together.
[0084] Figure 25 shows that the predictive ability of a model built on samples chosen with the relative referencing approach described above a significantly better than prediction results from a set of randomly chosen samples. [0085] While the example above uses a diagnostic vector of glucose predictions, steps 1 to 6 could be repeated for other analytes, such that diagnostic vectors computed with urea or ethanol model could be concatenated to make a diagnostic vector with more elements. For example a 12 element diagnostic vector could be for these samples in step 3 by applying three models (calibrated for glucose, ethanol and, and urea) to spectra from each of the four channels of the sampler.
[0086] Note that there are many possible diagnostics metrics that can be calculated from the diagnostic vector that can be applied in step 4 with mathematical combinations of it elements. Note there are similarity metrics other than the absolute value that can be applied to a one or more diagnostic metrics to find calibration samples that are similar to the new sample. Examples calculating the dot product between the two vectors, calculating a Mahalinobis distance, and using the knearest neighbors approach. For many more examples see Handbook of Chemometrics and Qualimetrics: Part B.
Using the relative reference metrics as a prediction model input.
[0087] In the previous section, the concept of relative referencing was used in a classification framework. Analyte prediction functions were applied to spectra collected on a multichannel sampler to produce a diagnostic vector. In the next step, mathematical operations are applied to this diagnostic vector to produce one or more diagnostic metrics. These diagnostic metrics are then collectively used as a classification features to identify samples in the calibration set which have similar path length properties to the new sample.
[0088] Another related approach is to produce a diagnostic vector for a new sample and then use this vector alone, rather than an absorbance spectrum, as an input to a second prediction model. This twomodel approach will be called the XY approach. The first step is to build predictor functions using Xmodels that calibrate the relationships between absorbance spectra measured on each channel of a multichannel sample and the analyte. In this example, the Xmodel step would provide glucose prediction functions for each of the four channels of the polarizer sampler, which will be labeled as b_{Vl0} , b_{Vi50}, b_{Vl63}, and b_{v},_{90}. Next, the diagnostic vector, d, is generated by applying the four prediction function to each of the four measurement channels to produce a 16element diagnostic vector.
[0089] Figure 26 illustrates the framework for generating all 16 possible predictions along with the 16 sets of prediction that result from applying the prediction functions calibrated on five middle scattering levels to a set of samples containing all nine scattering levels. Figure 27 shows that the resulting glucose prediction errors are highly structured with respect to scatter level.
[0090] The second step is to calibrate the Ymodel, which uses the interrelationship of the X model predictions to estimate an implicit correction for changes in the path length distribution. The Y calibration uses diagnostic vectors from the Xmodel step for each calibration sample as the data matrix. In other words, a vector of prediction results for each sample replaces the usual vector of absorbance values for a sample in the calibration procedure. The relationship between this data matrix of estimated concentration (many of which are corrupted by changes in the path length distribution) and the true analyte concentration is established with a linear regression to produce the Ymodel prediction function.
[0091] The determination of analyte concentration in a validation sample is then estimated as a twostep process. In the first step, the set (one for each sampler channel) of Xmodel prediction functions are applied, in all possible combinations, to the multichannel spectra to generate a diagnostic vector of glucose predictions. In the second step, the Ymodel prediction function is applied to this diagnostic vector to produce a single analyte prediction that is corrected for distortions due to changes in the sample's path length distributions. Figure 28 shows results from an XY model for glucose compared to the baseline case of a prediction function estimate with PLS from one channel of spectral data. The result of the XY model and the PLS model are similar for scatter level 3 and 7, which are scatter level present in the calibration set. The XY model has significantly better measurement performance than PLS when applied to samples with scattering properties outside the calibrated space, such as scatter levels 1 and 9.
[0092] In this first example, all the Xmodels were calibrated for glucose. This approach can also be extended to include multiple analytes, such as adding urea and ethanol in the first step (X models). The resulting diagnostic vector will then include concentration values for more than one analytes. The second step (Ymodel) uses then uses predicted concentrations for multiple analytes as the input to a prediction function for a single analyte. For example, this approach can use relative reference error for glucose, urea, and ethanol to collectively predict glucose in scattering samples. The prediction results generated using the other analytes is shown in Figure 29.
[0093] The basic concept of creating diagnostic vectors from one modeling process and using the vectors as inputs into a second model has been disclosed above. The implementation can take many forms and a variety of calibration methods can be used to include neural networks, nonlinear models, and other approximation and estimation techniques.
New Approach to Adaptive Model Selection using Prediction Differences
[0094] The adaptive modeling method is an attempt to overcome some general limitations of submodeling approach described previously or possible limitations associated with the use of a second prediction model as described in the previous section. A general limitation of a submodeling is it requires a set of samples that are reasonably similar to the new sample. This approach can limit the performance of a submodel for samples that require extrapolation beyond the calibration set or interpolation across sparse regions within the calibration set. As was shown in Figure 24, these samples are often the most difficult sample to predict.
[0095] The adaptive model approach starts with the assumption that the optimal prediction function for a sample with one path length distribution is not the optimal model for another sample with a different path length distribution, but the prediction functions share similar attributes. Examination of Figure 13 demonstrates that the general characteristics of these prediction functions are similar but that they have subtle differences as well. Furthermore, that the most important model attributes for interpolation or extrapolation can be derived by examining the set of valid prediction functions (or equivalently net analyte signals or regression vectors) rather than examining the attributes of the raw data from which they were constructed. In this construct, examination of different prediction function obtained from different media or media with different pathlength distributions allows one to understand the influence the media differences are imposing on the prediction function.
[0096] A practical application of this approach involves a. Build a series of discrete calibrations submodels that include a single channel and a relatively narrow ranges of path length properties or scattering conditions. For the example data set, a model was built on each scattering level in the calibration set using samples from adjacent scattering levels if they were available. These individual models have limited performance due to the small number of samples in each submodel but collectively they map the space of valid regression vectors for this system, or equivalently, locallyoptimal net analyte signals. A sequence of these local models is shown in Figure 30. b. The next step is to find a function that smoothly interpolates and extrapolates the geometric properties of these regression models. In the example shown, the geometric properties of length and direction varied linearly with scatter level. See Figure 31. Thus a family of models can be created by progressively changing the contributions of the length vector and the direction vector contributions to tune the central model. In a more complex situation, a series of regression vectors can be decomposed through eigenvector decomposition such that differences in both direction and length can be smoothly modeled.
[0097] The ability to progressively modify the predictor function allows the estimation of predictor function for samples with properties in between scatter levels. For example, a prediction function could be estimated for samples containing a scatter level between calibrated scatter levels 3 and 4 by equally weighting these two models. Similarly, a calibration function could be estimated for samples with higher or lower scattering level than the calibration set. The used of an optimized model minimizes the type of prediction errors seen in Figures 9, 10 and 11.
[0098] The next step is to select the optimal model for a set of validation samples from this larger, continuous family of models. An obvious metric would be to select the most accurate model, but this metric requires glucose reference values. A successful alternative is constructed from the knowledge that models mismatched to the scattering properties of the sample result in degraded prediction precision. Thus the correct family of models should produce similar prediction values across multiple observations. Using the approach of prediction consistency, prediction values generated from different channels can be compared. The prediction difference between two such models are minimized when the correct scattering model is applied. The process of using prediction consistency allows selection of the optimal predictor function by accounting for the net effect of the path length distribution of the media in which the measurement is being made. This ability to select the optimal model for a given media condition is critical as an optimized model can out perform a single unoptimized model. This approach is validated in Figure 32. The xaxis is used to define the data upon which the predictor function was generated. The yaxis is the difference in the prediction results at two channels. As shown in the figure, the sample being predicted contains scatter consistent with scatter level three. The predictor function developed from media or a scattering level most consistent with the media or scattering level of the validation sample should generate the most consistent prediction results, the lowest prediction difference and the most accurate prediction. Examination of the prediction differences demonstrates that the smallest prediction differences are for the predictor function generated from scatter level three calibration data. Adjacent models have the next lowest prediction differences while predictor functions developed from dissimilar scatter levels generate appreciable prediction differences. The results presented demonstrate that the method does enable one to select the best model for subsequent prediction. In practice the two predictions are then averaged together to estimate the analyte concentration. The performance of the adaptive model approach is summarized in Figure 33 for the validation data set. This approach outperforms the PLS calibration in terms of prediction accuracy and extrapolation abilities.
[0099] The method of determining the best prediction function by searching a space of possible prediction function with the subsequent select being driven by prediction consistency across channels can be implemented in many different methodologies. The above example should simply be viewed as one of many possible embodiments of this general method.
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