EP1855586A2 - Procedes et appareils de determination non invasive d'analyte - Google Patents

Procedes et appareils de determination non invasive d'analyte

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Publication number
EP1855586A2
EP1855586A2 EP06734668A EP06734668A EP1855586A2 EP 1855586 A2 EP1855586 A2 EP 1855586A2 EP 06734668 A EP06734668 A EP 06734668A EP 06734668 A EP06734668 A EP 06734668A EP 1855586 A2 EP1855586 A2 EP 1855586A2
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European Patent Office
Prior art keywords
analyte
prediction
spectra
samples
scattering
Prior art date
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EP06734668A
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German (de)
English (en)
Inventor
M. Ries Robinson
Stephen J. Vanslyke
Christopher D. Brown
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Rio Grande Medical Technologies Inc
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Rio Grande Medical Technologies Inc
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Publication of EP1855586A2 publication Critical patent/EP1855586A2/fr
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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 sub-millimetre waves, 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 sub-millimetre waves, 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 photo-electric 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 sub-millimetre waves, 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—Measuring 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

Definitions

  • 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.
  • PLD path length distribution
  • 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.
  • One class of methods uses theoretical approaches to estimate absorbance and scattering properties separately by applying Diffusion Theory.
  • Tissue Optics light scattering methods and instruments for medical diagnosis, Tuchin V., ISBN 0-8194-3459-0, The Society of Photo-Optical 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.
  • Multiplicative Scatter Correction estimates the net effect of scattering on path length across spectral wavelength with low-order polynomials, such as a quadratic function. Such functions do not accurately represent scattering over broad spectral range, such as the 4000 to 8000 cm-1 region commonly used in noninvasive glucose measurements.
  • 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 time-of-flight 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 Time-of-Flight; Applied Spectroscopy, 50(6), 637-646,1999.
  • This approach requires additional measurement apparatus including a pulsatile or frequency-modulated 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.
  • 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 ⁇ 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. 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. 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 sub-model approach
  • FIG. 26 shows the process of generating predictions results from multi-channel spectra
  • FIG. 27 plots the resulting prediction results and error structure
  • FIG. 28 plots the prediction results generated by the X-Y model approach using glucose only
  • FIG. 29 plots the prediction results generated by the X-Y 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
  • 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.
  • 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.
  • 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 mid-infrared region includes wavelengths from 2500 nm to 50000 nm.
  • 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).
  • a single species such as glucose
  • a composite property such as octane number of gasoline
  • a physical property such as sample temperature
  • a subjective sample property such as fruit ripeness
  • FIG. 1a An idealized system for absorbance measurements is shown in Figure 1a where the sample is presented in a cuvette with rectangular cross-section 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 ),
  • sample absorbance (A) is calculated from transmission with a logarithmic transform
  • 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 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)
  • path length, I is still a scalar quantities as it is the same for all wavelengths.
  • the change in absorbance at each wavelength for a unit change in concentration will be called the pure component spectrum, K v
  • Beer's law equation can be similarly extended to describe a sample with multiple absorbing components using a matrix representation
  • 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.
  • path length, I is assumed to be a scalar quantity for this sample.
  • a calibration estimates the relationship between measured absorbance and analyte concentration
  • a calibration step can be required to create an accurate relationship between the measured absorbance spectra and analyte concentration for a given measurement system.
  • 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.
  • Beer's Law describes a linear relationship between the absorbance at this selective wavelength, A 1 , and the analyte concentration, c,
  • K 1 is the slope of the calibration curve - a plot of measured absorbance versus analyte concentration.
  • the predictor function (also called a regression vector) for a single-component 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.
  • Biological samples typically contain many constituents, which can potentially interfere with the single-component prediction functions described above.
  • the constituents or conditions that interfere with analyte measurements will collectively be called interferences or interfering species.
  • the interference is a chemical component that absorbs at one or more wavelengths common to the absorbance of the analyte.
  • 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.
  • the goal of multi-component calibrations is to calculate a 'net-analyte' spectrum that responds proportionally to analyte concentration but is selective against interfering species.
  • a multi-component 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.
  • FIG. 2 A simple geometric presentation of a net analyte signal is shown in Figure 2.
  • the net analyte signal is the portion of the pure component signal that is perpendicular (or orthogonal) to the interfering species' signal.
  • a forward calibration the Classical Least Squares (CLS) solution of the multi-component Beer's law described previously.
  • K is a matrix of pure component spectra. Solving this least-squares solution requires pure component spectra to be known for all absorbing components in the calibration set.
  • 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.
  • the class of inverse methods includes many specific computational algorithms including inverse least squares (ILS), multiple linear regression (MLR), partial-least squares (PLS), principal components regression (PCR), canonical correlation, ridge regression, and Tikhonov regression.
  • ILS inverse least squares
  • MLR multiple linear regression
  • PLS partial-least squares
  • PCR principal components regression
  • canonical correlation ridge regression
  • Tikhonov regression Tikhonov regression.
  • the PLS algorithm is used to solve the inverse multi-component models in this work, unless stated otherwise.
  • the goal of each of these methods is to produce a regression vector for the multiple-wavelength 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.
  • 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 ⁇ )) of the regression vector. Accordingly, the effects of measurement error noise are smallest when the maximum amount of the pure component signal is retained.
  • 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.
  • the predicted concentrations lie on a line.
  • the nature of the proportional error is that this line differs from the line of indentity.
  • 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.
  • 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.
  • 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.
  • 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.
  • a major limitation in biological samples is path length changes due to scattering elements.
  • 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.
  • 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 air-sample 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.
  • Noninvasive tissue measurements can also include significant scattering variations due, in part, to physiological variations in collagen-to-water 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.
  • Figure 8 shows examples of spectral variation observed in noninvasive tissue measurements, blood samples, and bioreactor runs.
  • a set of tissue phantoms was constructed with well-characterized 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 ⁇ m diameter sphere supplied by Bang's Beads) as scattering elements with a two-fold variation in concentration (4000 to 8000 mg/dL).
  • 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].
  • 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 low-scattering samples (scatter levels 1-3) 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 7-9) and validated on samples with similar scattering levels.
  • 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.
  • the error structure seen in the scattering samples is in contrast to that observed with the non-scattering 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.
  • 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.
  • 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 under-perform a regression vector optimized for a given path length distribution.
  • 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.
  • 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.
  • 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 single-channel 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.
  • 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 multi-path samplers or equivalently as multi-depth 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.
  • 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 multi-channel sampler.
  • 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.
  • 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).
  • 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.
  • the spectral information recorded at each detector channel of this multi-channel sampler can be used to generate glucose prediction results.
  • 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.
  • 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.
  • the relative prediction difference can be used to classify or characterize the media or tissue under examination.
  • 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.
  • this analysis framework uses the net effect of the path length distribution changes on the predicted analyte concentration to characterize the sample.
  • 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.
  • the media characterization method uses the same optical system, similar processing methods, a similar predictor function, and similar level of computational complexity.
  • the relative prediction difference method can be extended to other analytes in the sample.
  • 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.
  • the use of relative prediction differences as a diagnostic function to characterize the media can be extended to multiple analytes in the sample.
  • 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.
  • 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.
  • tissue phantoms composed of polystyrene beads were sampled on a sampler with different source-detector separations.
  • This sampler is an example of a multi-channel 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 ⁇ m (center-to- 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 ⁇ m).
  • 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.
  • the analysis framework using predicted analyte concentration differences does effectively enable characterization of the media.
  • Prediction function calibrated on a single-channel.
  • 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 multi-channel sampler and glucose predictions were generated on validation spectra acquired on the same channel as the calibration spectra..
  • FIG. 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 mid-scattering 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 baseline-corrected 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,
  • the predictor function was calibrated on a single channel of spectral measurements.
  • 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 near-infrared spectral absorbance between 4200 and 7200 cm "1 .
  • 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.
  • 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.
  • SEP standard error of prediction
  • d n A n ,v b v
  • 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)
  • b v is a prediction function (number of wavelengths by 1).
  • 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 multi-channel sampler with n channels. b. Estimate a predictor function b V
  • 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 multi-channel 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.
  • step 1 of this example the samples were measured on a sampler with different source -detector separations.
  • This is a example of a multi-channel 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 ⁇ m (center-to-center) from the source fiber.
  • step 2 the predictor function b V ⁇ . 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 near-infrared spectrum.
  • step 3 the predictor function b v ,. was used estimate glucose concentrations for all channels of the remaining calibration samples. This provided a four-element diagnostic vector for all sample in the full calibration set.
  • step 4 the diagnostic metric was the difference between between glucose concentrations estimated with predictor function applied to spectra for the shortest source-receiver separation (element d-i of the diagnostic vector) and the longest source-receiver separations (element d 4 of the diagnostic vector).
  • step 5 the diagnostic vector or metric was saved for each calibration sample.
  • 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.
  • step 6 the diagnostic metric was calculate for validation samples using the predictor function b v * calibrated in step 2.
  • step 7 the calibration subset 'B' was selected by finding the 25 calibration samples with the most similar diagnostic metrics.
  • 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'.
  • 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.
  • 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.
  • 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.
  • 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.
  • diagnostics metrics that can be calculated from the diagnostic vector that can be applied in step 4 with mathematical combinations of it elements.
  • 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 k-nearest neighbors approach. For many more examples see Handbook of Chemometrics and Qualimetrics: Part B.
  • 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 two-model approach will be called the X-Y approach.
  • the first step is to build predictor functions using X-models that calibrate the relationships between absorbance spectra measured on each channel of a multi-channel sample and the analyte.
  • the X-model 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 .
  • the diagnostic vector, d is generated by applying the four prediction function to each of the four measurement channels to produce a 16-element diagnostic vector.
  • 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.
  • the second step is to calibrate the Y-model, 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 X-model 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 Y-model prediction function.
  • the determination of analyte concentration in a validation sample is then estimated as a two-step process.
  • the set (one for each sampler channel) of X-model prediction functions are applied, in all possible combinations, to the multi-channel spectra to generate a diagnostic vector of glucose predictions.
  • the Y-model 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 X-Y 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 X-Y model and the PLS model are similar for scatter level 3 and 7, which are scatter level present in the calibration set.
  • the X-Y 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.
  • 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 sub-modeling 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.
  • 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.
  • 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.
  • 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, locally-optimal 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.
  • 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.
  • 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.
  • 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.
  • the x-axis is used to define the data upon which the predictor function was generated.
  • the y-axis is the difference in the prediction results at two channels.
  • 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.

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Abstract

L'invention concerne une nouvelle série de procédés destinés à améliorer la précision de concentrations d'analyte mesurées dans des échantillons qui en même temps absorbent et diffusent la lumière. L'invention concerne également une nouvelle série de procédés de détermination de concentrations d'analyte dans un échantillon à partir d'au moins une mesure optique. Ces procédés améliorent la précision de déterminations d'analyte dans des échantillons de matériau qui en même temps diffusent et absorbent la lumière. Ces procédés permettent de mesurer de nouveaux échantillons possédant des propriétés optiques et qui sont différents des échantillons utilisés pour étalonner le procédé. Ceci permet de vaincre une difficulté connue d'application de procédés existants dans de nombreuses applications pratiques où le procédé semble efficace en matière d'étalonnage mais peu efficace sur de nouveaux types d'échantillons nécessitant une extrapolation ou une interpolation. Ces nouveaux procédés permettent également de vaincre une d'application des procédés de prédiction linéaires basés sur la loi de Beer pour des échantillons qui s'étendent sur une plage de mesure optique ou de propriétés d'échantillons qui enfreignent leurs acceptations intrinsèques.
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