The present invention relates to the molecular spectroscopy of matter, and more particular the spectroscopy of fluid or tissues in which essentially continuous monitoring can occur without physical sampling, which is removal, of a portion of the fluid or tissue. Even more particularly, the invention relates to the molecular spectroscopy of living tissue for the purpose of determining the concentration of glucose and other small molecules therein.
Prior methods of dielectric or RF spectroscopy have shown correlations between the acquired signals and the blood glucose concentrations.
However, these prior methods suffer a number of recognized deficiencies, in particular electrode polarization, which leads to a loss in signal to noise ratio and other compromises in performance that greatly affect the commercial viability of the methods. Further, such methods appear to measure only the electrolyte imbalances in skin tissue that results from hypo or hyperglycemic events.
Accordingly, it is a first object of the invention to overcome the deficiencies of the prior art methods to provides a non invasive means for blood glucose measurement with a higher signal to noise ratio.
It is a further object of the invention to provide a means for more direct measurement of glucose in tissue that is deeper than the skin and therefore more representative of the availability of glucose at cell membranes.
It is a further object of the invention that the means for direct measurement of glucose in tissue is non-invasive and continuous.
It is a further object of the invention to that this means for more non-invasive and continuous direct measurement of glucose in tissue provides for sufficiently deep penetration to be tissue selective.
It is a further object of the invention that the means for direct measurement of glucose in tissue is not dependent on skin contact reproducibility
6. Higher SNR and wider spectral range for glucose and other molecules of interest
In the present invention, the first object is achieved by providing a process for molecular spectroscopy of a media to determine the concentration of at least one molecular species therein, the process comprising the steps of providing a pair of coiled antennas as electrodes for dielectric spectroscopy measurements, placing the pair of coiled antenna in signal communication through the media, powering at least one of coiled antennas at a first frequency, scanning a frequency range during said step of powering from the first frequency to at least a second frequency, the difference between the first and second frequency representing a first frequency range, acquiring one or more signals from at least one of the coiled antennas during said step of scanning to determine the value thereof, integrating the value of the one or more signals in said step of acquiring, the integration occurring over at least a portion of the first frequency range, calculating the concentration of the molecular species from the integrated value of the one or more signals.
Other objects of the invention are achieved by providing s device for the in-vivo molecular spectroscopy, the device comprising at least one pair of coiled antennas and configured for placement in signal communication with the other antennas in the pair through a first dielectric medium comprising at least a portion of a living organism, a variable frequency power generator in signal communication to each of the antennas in said pair, a signal detector in communication to each of the antennas in said pair for collecting transmitted and reflected signals between each of the antennas over the generated frequency range, a computation means to determine a plurality of signal propagation constants from the detected signals and calculate the concentration of at least one molecular species there from, wherein the pair of coiled antennas have a first resonance below about 100 MHz and the concentration of the molecular species is calculated by integration of one or more of the plurality of signal propagation constants over a frequency range from a first lower frequency to a second upper frequency wherein the second upper frequency is less than about 1 GHz.
Another object of the invention is achieved by providing a process for to calibrate a device for molecular spectroscopy of a media to determine the concentration of at least one molecular species therein, the process comprising the steps of providing at least one sample media through which a plurality of different concentrations of the molecular species is at least one of known and determinable by independent means of the molecular spectroscopy process, providing a pair of coiled antennas as electrodes for dielectric spectroscopy measurements, placing the pair of coiled antennas in signal communication through the sample media, powering at least one of coiled antennas at a first frequency, scanning a frequency range during said step of powering from the first frequency to at least a second frequency, the difference between the first and second frequency representing a first frequency range, repeating said step of scanning of the sample media at plurality of times each corresponding to the different concentrations of the molecular species that is at least one of known and determinable by independent means of the molecular spectroscopy process, acquiring one or more signals from at least one of the coiled antennas during said steps of repeated scanning to determine the value of a plurality of signal propagation parameters, calculating a first correlation product of each of the signal propagation parameters with at least a first subset of the known or determined concentrations of the molecular species, calculating at second correlation product of each of the signal propagation parameters with at least a second subset of the known or determined concentrations of the molecular species, the second subset being larger than the first subset, comparing the first and second correlation products over the first frequency range, identify at least one signal propagation parameter having a selecting regions within the first frequency range wherein the absolute value of the correlation product is greater than about 0.75 over a continuous second frequency range having a width of at least about 50 MHz, calculating the integrated value of each signal propagation parameter identified in the previous step over the continuous second frequency associated therewith provide at least one Q-band parameters, calculating the correlation of the at least one Q-band parameter to the known or determined concentrations of the molecular species to provide a calibration equation.
The above and other objects, effects, features, and advantages of the present invention will become more apparent from the following description of the embodiments thereof taken in conjunction with the accompanying drawings.
Referring to
One embodiment of the inventive apparatus 100 for Coupled Antenna Impedance Spectroscopy is shown in
It should be appreciated that high quality cables and connectors should be used to connect the pair of coiled or patch antennas 111 and 112 to the VNA 120 to minimize signal to noise and variability with subject or sample movement.
In initial experiments, the temperature was controlled by placing the antennas 111 and 112 along with the sample in a temperature controlled box or low temperature oven 150, having a fan and heaters (not shown) in signal communication with a relay box 160. The relay box 160 was connected to a control box 170. The control box 170 was in signal communication with the same computer 130 used for control and data acquisition of the VNA 120 signals, as well the temperature measurements from thermocouple 155, placed at or near the skin of limb or finger 11.
The antenna configuration, shown in part in
Further, in contrast to prior art methods of dielectric spectroscopy, the method disclosed herein is believed to be capable of providing a higher SNR and wider spectral range for glucose and other molecules of interest.
Prior attempts to measure glucose in the human body by non-invasive dielectric spectroscopy are complicated by two factors the inventive method is believed to overcome. First, the conductivity of biological systems creates electrode polarization with capacitive antennas. The electrode polarization effect results from the accumulation of charge on electrode surfaces and the formation of electrical double layers and can overwhelm the characteristic signal. Various methods have been proposed to correct for this effect, such as are described by Feldman et al.: Time Domain Dielectric Spectroscopy of Biological Systems, IEEE Transactions on Dielectrics and Electrical Insulation Vol. 10, No. 5; October 2003, which is incorporated herein by reference.
Further, according to A. Caduff et al. in “Non-invasive glucose monitoring in patients with diabetes: A novel system based on impedance spectroscopy”, Biosensors and Bioelectronics 22 (2006) 598-604, which is incorporated herein by reference, among others, have noted that dielectric spectroscopy does not measure blood glucose directly, but rather the effect of hyper and hypoglycemic excursions that lead to changes in the electrolyte balance in blood, cells and interstitial fluid (ISF), and is thus an indirect measurement. This occurs in part because the electric field of prior art capacitive sensors only penetrates the skin and the closest underlying tissues to a depth of about 1-2 mm.
In contrast, the inventive technique disclosed herein is believed capable of producing more accurate and reproducible results because it not only avoids electrode polarization, but also probes much deeper tissues.
The penetration depth of a patch antenna depends both on frequency and antenna configuration. However, for in vivo application penetration depth is primary limited by absorption of electromagnetic radiation by water molecules, and is thus also frequency dependent. Generally, the losses of any given antenna increases as the frequency exceeds 400 MHz, as has been reported in “A 31.5 GHz Patch Antenna Design for Medical Implants”, Ahmed et al., International Journal of Antennas and Propagation, Volume 2008, which is incorporated herein by reference. It has also been reported by Kim et al. “Implanted Antennas Inside a Human Body: Simulations, Designs, and Characterizations”, IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 52, NO. 8, AUGUST 2004, that for a particular antenna energized at 400 MHz, a transmitted communication signals can penetrate 20 cm. Over the frequency range 30 MHz-800 MHz the penetration range corresponding to a loss of 70 dB was in the range of about 5-10 cm. It should be noted that such losses have been of interest to those designing patch antennas for the wireless communication between implanted medical devices and external monitors or control systems.
The penetration range of the antenna 111 and 112 in
One result of such a simulation of the electromagnetic field penetration within the tissue for the antennas of
Measurement of glucose are then made by the process of first placing the antennas 111 and 112 on skin, the antennas are then sequentially energized in by the VNA 120 in the frequency scanning mode, with both the transmitted and reflected power measured as the frequency range of each antenna is swept. The frequency sweep speed has an impact on the S/N ratio in the measurements, with the higher speed resulting in a lower is S/N ratio. In the current mode of the operation VNA spectrum sampling rate is about 30 sec. of 800 MHz. During this process raw data are acquired to calculate four signal propagation parameters which vary at least somewhat with frequency for determining the concentration of the molecular species of interest.
While the patch antenna structure 111 and 112 have a penetration depth and intensity that is highly dependent on its structure, as well as the signal interaction with the dielectric medium being probed, this depth is much greater than the prior art methods, so it is not necessary to place the antennas directly on the skin. Thus, in a more preferred method of using the inventive antenna structure, a molded carrier or support 301 contains and encases the antennas 111 and 112. As the supporting mold 301 is also sculpted or cast to shape of the finger 11, or other appendage, to reproducibly surround the limb or organ portion being probed the placement of the antennas 111 and 112 provides a reproducible spacing from the subject's skin, as the mold 301 fits snugly around the finger. Variations of such antenna supporting molds 301 are shown in
In such supporting structure each antennas is wound in a common plane so that antennas in the pair can be placed with their respective common planes parallel and spaced apart. However, depending on the portion of the organism that is sampled, the antennas in the at least one pair can be placed adjacent to each other.
In further contrast to the prior art, it was further discovered that it is undesirable to place the antennas in direct contact with the skin. As the tissue areas with higher electric field have more influence on the S-parameters than with the weaker electric field, electric field for antennas placed on skin is maximum at the skin layer. Therefore, the skin layer may have a dominant influence on S-parameters. The outer skin layer is a source of systematic error for VNA data since it is influenced by the varying environmental conditions such as temperature and humidity. Therefore, it is desirable to reduce its influence on the measurement. One way to do it is to separate antennas from skin by some layer of dielectric material. Another, but less desirable approach includes creation of holder that maintains constant environmental conditions (incubator).
Although the current spacing away from the skin (as shown by the thickness of spacer 802 in
Thus, spacing of the antennas away from the skin appears to achieve a better correlation between actual blood glucose, such as measured by the YSI method, and then inventive system for several reasons. This is potentially due to the insensitivity to the skin conditions, that is contact, moisture, pressure and the like, but also may reflect representative sampling of the tissue. It is believed that prior methods of dielectric spectroscopy that place the antenna on the skin sample largely the interstitial tissue, while the inventive method is more capable of sampling a larger portion of the arterial and venous blood of the patient/subject.
In one embodiment, the antenna supporting mold 301 in
It should be appreciated that in addition to the antenna pair being deployed on opposite sides of body portion or appendage, the pair can also be placed adjacent to each other on the same side of the skin or appendage. Accordingly, it is expected that the patch antennas deployed in the inventive method will yield more reproducible and systemic results when properly calibrated for the subject/patient.
Further, alternative positions or appendages for placement of the antenna are optionally the patient's ear lobe, forearm, wrist, head or leg. In additional it may be preferable to place the inventive antenna system either across the abdominal cavity, as for example to more accurately measure blood glucose within an organ such as the pancreas, as well as on adjacent locations or in closer proximity to larger blood veins or arteries. Thus, for example depending on the body portion used, a particular configuration might be more preferred for patient that desires or requires more continuous monitoring. it should be appreciated from the following discussion that the optimum antennas configurations for different portions of the body may be different from what is currently the preferred configuration for making continuous measurement from the hands and finger as illustrated in
In the frequency scan described above with a single antenna pair the vector network analyzer (VNA) 120 yields four main signal propagation parameters: S22, S11 that represent reflection coefficients and S21, S12 that represent transmission coefficients.
In the models that follow, each S-parameter is a function of time and frequency, where
S
ij
=S(ωi,Tj) (1.1) and
T—time
w=2πf
f—frequency
The reflection and transmission coefficients Sij can be transformed to four impedance parameters Y11, Y12, Y21, and Y22 by the following formulas:
Where Z0≈50[Ω] is the reference impedance.
It is possible to model the antennas of
As shown for selected parameters S11 and S12 in
In comparison
Although most of the cross variation in the spectral intensity of any of the Sij parameters is dominated by the antennas resonance pattern, it has been discovered through extensive statistical analysis that small portions of the spectra will correlate very well a patient's blood glucose concentrations.
It has also been discovered that more accurate and reproducible measurements of blood glucose can be obtaining using 4 antennas in a slightly different finger and hand mold, which is now illustrated in
It was also discovered that further improvements were obtained when the antennas had a rectangular shape as shown in
The antennas pairs 111a/112a and 111b/112b in
Not wishing to be bound by theory, it is currently believed that the resonances characteristics of the novel antenna designs have several distinct advantages over prior methods of dielectric spectroscopy to measure or estimate the in-vivo availability glucose in a patient. it is also believed that the antennas designs have distinct advantages in measuring glucose and other molecule in in-vitro.
Deploying antennas that generate deeply penetrating electromagnetic in the most desired range of about 100 to 800 MHz (0.1 to 0.8 GHz) provided more opportunity for the discovery of particular narrow frequency bands that gave good correlations with blood glucose and where also relatively insensitive to sources of error that have hindered the advance of earlier approaches to non-invasive measurements of blood glucose.
This was particularly the case when the resonant characteristics of antennas 111/112 are tuned for the media of interest such that the loss in transmission is generally less than −50 db, but more preferably less than about −30 dB between about 100 MHz and 800 MHz, but more preferably between about 1 MHz to 500 Mhz.
For detecting glucose in living tissue using the inventive method we have discovered it is preferable that the coiled antenna have a first resonance below about 100 MHz, but more preferable below about 50 MHz.
It has also been discovered that it is preferable that the coiled antennas also provide a characteristic zone of flat transmission coefficients in the media of interest over a range of about 200 MHz in which the transmission varies by less than about 30 dB, but more preferably less than about 20 dB, and the loss in transmission also less than −50 db, but more preferably less than about −30 dB. This range is typically up scale, higher wavelength that the first resonant frequency.
As the frequency of the first resonance of microwave antennas is inversely proportion to the antenna length, meeting this requirement posed a particular challenge to a conflicting need to make the antennas as small as possible for patient convenience and obtaining local measurements. However, both these requirements could be met by keeping the antennas width and spacing as narrow as possible and using multiple folds to obtain a long length, as for example the antenna 111 in
The apparatus and method disclosed herein is expected to be more accurate than other methods of dielectric spectroscopy for several reasons. First, the prominent resonance peaks provide a stronger interaction with the dielectric relaxation properties of glucose and are less affected by the absorption from other molecules. This method thus appears to overcome electrode polarization effects noted in the prior art. Further, the inventive method is likely to be more representative of the bio-availability of glucose, as the measurement is more than skin deep.
Further, such deeper sampling of tissue by the inventive method is likely to produce more temporally stable results, being less sensitive to skin temperature and other skin conditions such as dirt, contamination and moisture and the like.
As the dielectric spectra is from a resonant system that will inherently vary with the electrode placement and physiology of each user or patient, it is not possible to precisely define universal lines or ranges of the spectra that are applicable to all patient's or test subjects.
However, it has been discovered that for each user/patient with a particular antenna combination disposed in signal communication across a particular body part or organ it is possible to identify the spectral ranges that correlate well with actual blood glucose concentration.
Accordingly, another aspect of the invention is a process for discovering such portions of the spectrum for each patient for use as a means of continuously and non-invasively accurately determining the blood glucose levels.
Yet another aspect of the invention are methods to develop the most robust means of continuously and non-invasively accurately determining the blood glucose levels.
It should be appreciated that such methods require the collection of data from a patient/subject equipped with the inventive antenna combination over a period that is sufficiently long to record a range actual blood glucose levels that is at least close to those likely to occur in real world conditions.
In the simplest mode of deployment such a device can warn the patient to better control dangerous excursions through the time administration of a source of glucose, generally by eating a healthy meal, or insulin.
In a more advanced mode of deployment such a device is anticipated to guide a patient to better control the blood glucose level within a narrower range to minimize the longer term and generally debilitating effects of diabetes, such as diabetic retinopathy, a proneness to infections and the like.
It is also anticipated that the potential for accurate and continuous measurement will enable integration into an artificial pancreas that in a closed feedback loop to a pump that can continuously provide insulin in response to the blood glucose levels.
According, the currently preferred methods of such embodiments are disclosed in the experimental description in the paragraphs that follow.
Using the antennas and antennas supporting molds of
The acquisition time of sixteen VNA spectra is about 30 sec. The SNR of the VNA in transmission mode is about −120 dB, while the signal level in transmission mode is in the range −30 dB to −70 dB, depending on frequency.
Each of VNA spectra collected in continuous mode with a sample time τ can be organized into the N×M matrix
(2.0)
Where M=1600 is the number of frequency points and N is the number of collected spectra.
Fixing a frequency ωk in we obtain a function of time ƒk(t′)=S(ωk,t) (indexes t,ƒ are omitted); thus we can consider a correlation function
ρ(k,l)=corr(ƒk(t),ƒl(z)), k,l=1, . . . , M (2.1)
As follows from the Equation 2.1, ρ(k,l) is the matrix of size M×M with values of ρ(k,l) from −1 to 1.
Assume that we have a target function g(t) (such as glucose concentration) measured at same set of the sampling times tk, k=1, 2, . . . , K. This set can be a subset of the set of all times tn, n=1, 3, . . . , N.
From two functions g(t) and we can build a correlation product over time.
(2.2)
The correlation product is the correlation function of the measured reflection and transmission coefficients Sij to at least a portion of the measured blood glucose concentration. In the case of determining the concentration of other molecules of interest, the concentration of the other molecules would be used. The function rij(ω) reflects degree of similarity between the data St,ƒ(ω,t) and the target function at given frequency. As definition (2.1) suggests, the module of the functions rij is less than or equal to one.
This correlation product when derived using the glucose values g(t) that vary widely, as can be obtained in an oral glucose tolerance test (OGTT), provides a means to identify spectral ranges in which the measured reflection or transmission coefficient Si,j; correlated highly with the actual glucose concentration.
The example above shows that the behavior of the function r24(ω) is relatively smooth in the high frequency range of approximately from 350 MHz till 800 MHz, while the variation of this function is more considerable at low frequencies (below 200 MHz). By relatively smooth we mean a smaller δγtƒ/δ(ω) than in the region of about 10 MHz to about 200 MHz where the narrow frequency bands corresponds to the antenna radiation pattern. It should now be appreciated that the most preferred antennas though having multiple resonances below 200 MHz frequency range, such that the response above 200 MHz is still relatively flat.
It is more preferable to deploy the frequency range where the behavior of the functions rij is smooth to define the frequency or Q-bands, where the values of |rij| more than some threshold value.
While experiments to date have used antennas of essentially identical sizes and patterns (as is limited by fabrication technology), when using either a total of 2 or 4 antennas, it may also be desirable to deploy 2 different pairs of 2 identical antennas, wherein the resonance characteristics of each antenna pair is different. Three different embodiments of this aspect of the invention are illustrated in
Different pairs of antennas can be arranged in several ways in addition to configuration illustrated in
Alternatively, as shown in
In the embodiment shown in
In addition to expanding the useful spectral range, having such overlapping plural antenna pairs also provide a different penetration depth in the tissue for each pair to permit a continuos comparison of the both glucose in tissue closer to the skin against what might be much deeper venous and arterial tissue. As the glucose in tissue closer to the skin is more likely to represent interstitial tissue, this may provide greater predictability of trends in glucose in the patient/test subject, as well as for greater accuracy of measurement.
Thus, after the acquisition of the different sets of signal propagation parameters Sij, the entire calibration process can be carried out fully automatically by a microprocessor or other computing means by first acquiring the data, that is , then calculating at least 2 sets of rij via the equation below using a complete and partial set of independently measured blood glucose values. Further, the comparison of these at least two sets can be an automated process as described below.
The final predictive equation for blood glucose concentration requires the identification of frequency interval or bands of the spectral response of any Sij parameter in which model function and the measured glucose concentration are well correlated. This can be expressed mathematically as the set of all frequencies bands [ωk, ωl], l>k such that the inequality (2.3) holds are called Q-bands.
(2.3)
Where c is a threshold value. That is, a set of Q-bands are selected where absolute value of rij is greater than or equal to a threshold value, C, from some band width represented by ωk to ωl. This correlation threshold, C, is preferably at least about 0.75. Ideally such Q-bands should not overlap with each other. Thus, within each Q-band the correlation of and the target function g(t) is more than the threshold value.
For each Q-band (indexes here corresponds to the indexes of the one can extract a feature function by averaging St,ƒ over the interval [ωk,ωl].
(2.5)
The definition (2.3) insures that correlation of the and the target function g(t) will be not less that the threshold value c.
The above equations thus provide an algorithm for generating feature functions from the set of Q-bands that are highly correlated with blood glucose concentration of the patient, g(t).
Thus, a preferred mode of using the dual antenna apparatus 100 is to preform the previously described set of calculations on each patient during an initial OGTT, or similar diagnostic processure that provides an opportunity to collect spectral data during a reasonably large excursion in blood glucose concentration when the actual glucose concentration is known very accurately by an independent method. This provides a set of candidate Sij parameters, each at one or more selected Q-bands, to derive a predictive formula for calculating the patient blood glucose concentration continuously. Such sets may range from 10 to 30 potential Q-bands. The analysis to date of about a dozen individuals has revealed a general trend of identifying about 1 to 4 Q-bands for 7 to 10 of the Sij parameters.
A final predictive equation can be derived from the feature functions of equation (2.5) by a wide variety of known regression techniques for each of the feature functions, which are found by integrating the value of the Q-band parameters selected as candidates in the previous set of 10 to 30 Q-bands.
The correlation coefficient for each of the feature function corresponding to specific Sij parameters over the Q-band frequency ranges can then be compared so that only the most highly correlated feature functions are used in the final predictive equation. However, it has also been found preferable to use additional criteria for selecting a limited set of Sij parameters to derive and select the feature functions used in the final predictive formula. Among these criteria it is preferred to compare the temporal stability of the Q-band over a time period when the blood glucose is quite stable. Thus, in this case rather than scanning over the entire band width used to discover Q-bands, just the narrow Q-band would be repeatedly scanned. Such scans can be much faster than 30 seconds, and can be repeated as needed to compare their temporal stability as well as the signal to noise ratio. In this manner, the Q-bands used to derive the final predictive equation can be selected based on their having the highest signal to noise ratio.
It is additionally preferable to also or alternatively select the Sij/Q-band parameters that are relatively insensitive to external effects, for example temperature and well as precise positioning in the antenna holder 301. The exploration of a correlation with temperature is easily performed for each Q-band if there is sufficient temperature excursion either during or after the initial data collection step when the device 100 also includes a thermocouple of non-contact IR thermometer.
As to the sensitivity of candidate Q-band to position of the holder device on the patient/test subject, it has been discovered that more reproducible results are obtained by first acquiring the spectra over the candidate Q-bands repeated times in sequence and then calculating the standard deviation of each Sij value as integrated over the Q-band width to select Q-bands of lower standard deviation.
Ideally, a limited selection of all possible Sij and associated band regions parameters are selected for regression analysis. While various forms of Chemometrics techniques for multivariable regression can be performed on a plurality of Sij parameters, as the objective of the present invention is to provide a diagnostic tool, it is currently preferred that a single Sij parameter be derived by linear regression that provides a good fit to the measured glucose values in the ranges of clinical importance. Thus, another criteria for selecting the most appropriate Q-band is based on the lowest error in the regression analysis.
The flow chart in
Another aspect of the calibration process is to select the optimum Sij parameter that correlates best and most robustly with the measured blood glucose concentration as measured by convention methods in either the hospital or clinical setting, or those routinely used by diabetic patients.
Part of such optimization is insuring that particular parameter is robust with respect to a minimum noise and errors that occur repeated removal and insertion of the hand in the antenna supporting mold 301, or alternatively with respect to any other fixture that holds and support the pair of at least 2 antennas if deployed to measure blood glucose on another organ or part of the body than the hand.
Clinical trials have been conducted using the techniques described above. The predicted blood glucose level from the trial is compared in the Clark grid in
Table 1 refers to tests taken when the subjects were subjected to an OGTT to produce a hyperglycemic state, with the glucose concentration ranging from about 100 to 350 mg/dl. Table 2 refers to tests taken when the subjects were administered a very controlled dose of insulin to lower the insulin levels to the hypoglycemic state, with the blood glucose levels ranging from 50 to 175 mg/dl. The predictive result of the 10 “best” Q-bands in the table were then averaged after linear (uni-variant) regression to provide the final linear predictive equation as described above, and are plotted as the solid line “Regression and Prediction” against the blood glucose measured by YSI, which is the wider partially broken line.
The average of the data from the Q-bands in the above Table 1 is plotted against the actual glucose concentration in
The average of the data from the Q-bands in the above Table 2 is plotted against the actual glucose concentration in
While the invention has been described in connection with a preferred embodiment, it is not intended to limit the scope of the invention to the particular form set forth, but on the contrary, it is intended to cover such alternatives, modifications, and equivalents as may be within the spirit and scope of the invention as defined by the appended claims.
This application claims priority to the U.S. Provisional Patent Application having the title “Non Invasive Glucometry Method and Apparatus”, filed on Nov. 6, 2008, having application Ser. No. 61/111,795, which is incorporated herein by reference.
Number | Date | Country | |
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61111795 | Nov 2008 | US |