Non Invasive Estimation of Blood Glucose using Near Infra red Spectroscopy and Double Regression Analysis

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1 Non Invasive Estimation of Blood Glucose using Near Infra red Spectroscopy and Double Regression Analysis Swathi Ramasahayam 1, Sri Haindavi K 2 Center for VLSI and Embedded Systems Technology 1,2,4, IIIT-Hyderabad, India Bharat Kavala 3, Shubhajit Roy Chowdhury 4 Department of EEE, IIT-Guwahati, India 3 Abstract This paper presents a unique technique for noninvasive estimation of blood glucose concentration using near infra red spectroscopy. The spectroscopy has been performed at the second overtone of glucose which falls in the near infra red region. The near infra red spectroscopy has been performed using transmission photoplethsymography (PPG). The analog front end system has been implemented to get the PPG signal at the near infra red wavelengths of 1070nm, 950nm, 935nm. The PPG signal that has been obtained is processed and double regression analysis is carried out with the artificial neural network for estimating the glucose levels. The root mean square error of the prediction was 5.84mg/dL. Keywords- Blood glucose; Non-invasive; Near-infrared;Second overtone. I. INTRODUCTION Millions of people suffer from diabetes Miletus which is caused because of the disturbances in the metabolic activity of pancreas. Long term diabetes is dangerous as it can lead to blindness, damage nerves and kidneys. It also increases the risk of heart stroke and other heart diseases [1]. More frequent blood glucose monitoring is required for diabetic patients as the amount insulin intake has to be decided accordingly. Currently used equipment for the self monitoring of blood glucose is invasive and usually requires pricking of finger tip which is painful. It also involves risk of spreading infectious diseases. In order to overcome the disadvantages of the invasive methods some non invasive methods have been proposed. However they have the disadvantages like lack of selectivity like in scattering method [2], or require heavy, delicate and expensive instruments like Raman spectroscopy [3], and polarimetric method [4]. For the non-invasive measurement of the blood glucose most of the research is done based on Photoplethsymography (PPG) in the mid infrared (2µm-2.5µm) and first overtone regions (1.53µm-1.82µm) [5-7] as the fundamental frequencies and first overtones fall under these regions. The absorbance of the glucose bonds(c-h, O-H) is strong in this region. The major disadvantage in these regions is due to three reasons. Firstly the drastic rise in the price of components and secondly the strong absorption due to other components like water and lastly the scattering in fatty tissue [8,9]. This makes the mid and first overtone regions economically not viable for developing a noninvasive glucose meter. This paper details about the ability to measure the blood glucose levels accurately in relevant to the clinical levels in second overtone region ( µm). Here the cost of the components is less but glucose has weaker absorption and it requires the electronic noise in the analog front end to be suppressed much below the signal from the sensor output. Here we have used artificial neural network for regression analysis to accurately predict the blood glucose levels. II. THEORETICAL ANALYSIS A. Molecular composition and relative absorptivities When a photon is incident on a molecule, there will be bond deformations or bond vibrations at different energy levels related to different bonds, depending on the energy of incident photon [10]. So, only the photon with energy that corresponds to the difference between two of its energy levels can be absorbed. The frequency of the vibration is given by the = 1 2 Where k is the bond strength and m is the reduced mass. (1) For a glucose molecule, the molecular structure is as shown in Fig1. Table 1 shows the frequencies corresponding to different bond vibrations in glucose molecule [6]. Figure 1. Molecular structure of D-glucose /13/$ IEEE 631

2 Table 1. Absorption bands of glucose bonds Wave length bond Wave length bond Fundamental 3377nm vc-h 2817nm vo-h First Second 1688nm 2vC-H 1408nm 2vO-H 1126nm 3vC-H 939nm 3vO-H Where A is the absorbance of glucose over a range of wavelengths and f ( ) is the probability density function of intensity of light emitted. By multiplying the relative intensity of the light emitted by the LED shown in Fig.3 and the absorbance value of glucose taken from the spectrum and averaging it over spectral distribution of LED we calculate the mean value of the absorbance which is shown in Fig.4. At a deeper level absorption of light can be seen as dependent on the probability of absorbance of a photon by the molecule. For nth overtone final energy is (n+1)*e, where E is the fundamental energy. As n increases, probability of absorbance decrease rapidly and hence intensities of absorbance decrease as overtones increase. The absorption at fundamental frequency is calculated and from that the absorption at second overtone is calculated relatively [11]. Table 2 depicts the relative absorptivities of C-H bond at different overtones with respect to the fundamental. It is evident that the absorptivity decreases rapidly as one goes from fundamental to the overtones in sequence. Table 2. Relative absorptivities of C-H bond Wave number(cm -1 ) Relative Absorptivity Fundamental First Second * 10-3 B. Selection of the Wavelength of Peak absorption The absorption spectrum of the glucose has been studied in order to choose the wavelengths for LEDs. For this purpose a IR absorption spectrum of 0.1M aqueous glucose solution has been collected and analyzed in second overtone region of the near-infra red spectra using the Bruker tensor 27 FTIR spectrometer. Fig.2 shows the absorption spectrum of the glucose over the second overtone region where the selected wavelengths are shown. We can observe that the absorption peaks in this region are very narrow typically of the order of the 2nm to 5nm but the LED emits the light over a range of wavelengths. The wavelengths are chosen such that the weighted average of the absorption over the spectral bandwidth of the LED is high. While calculating this weighted average the intensity of light emitted by the LED acts as weight for the absorption at that particular wavelength. The expected value of the absorbance over a range has been calculated as = ( ) (2) Figure 2. Spectrum showing the transmitance of glucose Figure 3. Graph showing the relative senstivity of light emitted by 1070nm LED. Figure 4. Intensity weighted mean absorbances over 920nm to 1100nm /13/$ IEEE 632

3 In order to improve the accuracy of the prediction of blood glucose level, the wavelengths have been chosen such that mean value of the absorbance of glucose over the frequency range of LED is high. For the current research, wavelengths of 935nm, 950nm, and 1070nm have been chosen. III. DESIGN METHODOLOGY A. Photoplethysmography (PPG) Photoplethysmography is an optical technique widely used to measure the pulse rate, arterial blood oxygen saturation and blood volume changes. It uses a clip which contains a light source and a detector on the opposite sides to detect the cardio vascular pulse wave that propagates through the body. The PPG waves can be described as containing a DC component due to venous blood and an AC component due to blood volume changes in the arteries. According to Beer-lambert s law the absorbance of light by a liquid is related to the concentration of the material by = (3) Where the molar absorptivity of solute at a particular wavelength, C is is the concentration of the solute and is the path length. Hence for a specific wavelength i, equation (3) may be written as = (4) In our particular case, i=1 corresponds to a wavelength of 935nm, i=2 corresponds to a wavelength of 950nm and i=3 corresponds to a wavelength of 1070nm. As the concentrations and path lengths are same for a person at a particular time, we can write C 1 = C 2 = C 3 (5) = = (6) B. Analog Sensing Circuit As discussed in the previous section, three different wavelengths have been selected which have peak absorption of glucose in the near infrared region of the spectrum, viz 1070, 950 and 935 nm. The block diagram of the glucose sensing system is shown in the Fig.5. This light is converted in to an equivalent current by the detector and is high pass filtered with a cut off frequency of 0.8Hz. Then it is given to the trans impedance amplifier for amplification of the signal. For this a low noise amplifier LMV796 has been used. The input referred noise of the amplifier is less than 17nv/ Hz. After necessary amplification it has to be low pass filtered in order to get PPG wave. A 4 th order Sallen-key topology has been used to build a low pass filter whose cut off frequency is 10Hz. Fig. 6 shows the experimental setup of the sensing circuit and Fig. 7 shows the PPG waveform. Figure 6. Experimental set up of Sensing circuit Figure 7. PPG waveform for 950 nm Figure 5. Block Diagram of the glucose sensing system. It consists of the finger clip with LED acting as a light sensor and the photodiode as the detector to detect the small changes in the incident light as it passes through the finger. For getting glucose level in blood the absorbance which is mainly due to blood glucose is calculated from AC component of PPG wave as follows = log 1 + ( ) ( ) (7) Where is difference between optical densities at time t i and t i+1, ( ) is the pulsatile component at time t i and ( ) is the intensity of light at time t i /13/$ IEEE 633

4 This difference has the effect of removing the venous and the tissue contributions to yield only the change in intensity due to the pulsating arterial blood compartment. [12,13]. The optical densities have been calculated at three wavelengths for 35 subjects. The actual glucose values have also been determined using standard invasive glucometer. Regression analysis has been done on these values using neural network toolbox in MATLAB. IV. REGRESSION ANALYSIS USING ARTIFICIAL NEURAL NETWORKS Multivariate calibration models have come into wide use in quantitative spectroscopic analyses due to their ability to overcome deviations from the Beer Lambert s law caused by effects such as overlapping spectral bands and interactions between components [14]. PLS and PCR are the most widely used chemo-metric techniques for quantitative analysis of complex multicomponent mixtures. These methods are not optimal when the relationship between the IR absorbance s and the constituent concentration deviates from linearity. The theory and the application of Artificial Neural networks (ANN) in modeling chemical data have been widely presented in the literature [15]. In this current work, ANN has been used for function fitting to develop a model based on the PPG data and invasive glucose measurements. For calculating glucose concentration from beer-lambert s law we can say that, = ( ) Where A i (λ ) is the optical density at wavelength λ, of the i th component, whose concentration is C i, A(λ) the optical density of the mixture. If we have the spectra of all the components {A i (λ)} and measure the spectrum of the mixture {A i (λ)}, we can use a mathematical tool to estimate the {C i }. The three wavelengths have been chosen such that glucose has considerable amount of absorption when compared to other components. So we have given the matrix (8) Initially, the first set of regression coefficients are used to estimate Glucose levels. But, if it falls above 110 mg/dl second set of regression coefficients are used to estimate the glucose concentration accurately. The performance of the regression analysis was evaluated in terms of root mean square error of prediction over the first data set which has glucose concentration below 110mg/dL is given by Eq. (9) = 1 (9) The test samples whose estimated glucose concentration fall above 110mg/dl are taken as second data set and regression analysis is performed whose root mean square error of prediction is given by = 2 The overall root mean square error can be obtained as = (10) 11 Results of regression analysis on the first data set are shown in Fig.8 where the parameter R signifies the correlation between estimated glucose and the actual glucose levels, we can observe that R is nearly equal to 1 for training, validation and test. For this a root mean square error (RMSE 1 ) of 5.61mg/dL is obtained. Results of the second regression analysis performed are shown in Fig.9, the root mean square error (RMSE 2 ) is 6.32mg/dL. as input and as output which are measured using standard invasive method. In this way we have three different optical densities as inputs and one output for a single sample. MATLAB neural network toolbox has been used. A two layer feed forward network with sigmoid hidden neurons and linear output neurons has been chosen. Number of hidden layers have been chosen as 10. V. DOUBLE REGRESSION To minimize the deviations and increase the sensitivity of the device regression has been used twice i.e.., double regression. So we get two sets of regression coefficients for two different datasets. Figure 8. Regression analysis on first data set /13/$ IEEE 634

5 Figure 9. Regression analysis on filtered data set (>110mg/dl). [9] Kevin h. hazen,* mark a. arnold,² and gary w. small, Measurement of Glucose in Water with First- Near-Infrared Spectra. Applied Spectroscopy, Vol. 52, Issue 12, pp (1998). [10] Airat k. amerov, jun chen, and mark a. arnold, Molar Absorptivities of Glucose and Other Biological Molecules in Aqueous Solutions over the First and Combination Regions of the Near- InfraredSpectrum. Appliedspectroscopy, Volume 58, Number 10 (Oct. 2004) Page [11] A. I. Pavlyuchko, E. V. Vasilyev, and L. A. Gribovb, calculations of molecular ir spectra in the overtone and combination frequency regions, Journal of Applied Spectroscopy, November 2011, Volume 78, Issue 5, pp [12] K. Yamakoshi,Ogawa M, Yamakoshi T, Tamura T, Yamakoshi K. Multivariate regression and discreminant calibration models for a novel optical non-invasive blood glucose measurement method named pulse glucometry Conf Proc IEEE Eng Med Biol Soc. 2009;2009: doi: /IEMBS [13] Y. Yamakoshi Pulse Glucometry: A New Approach for Non-invasive Blood Glucose Measurement Using Instantaneous Differential Near InfraredSpectrophotometry, JBiomed Opt Sep-Oct;11(5): [14] Bhandare, P., Mendelson, Y., Peura, R.A.: Multivariate Determination of Glucose in Whole Blood Using Partial Least-Squares and Artificial Neural Networks Based on Mid-Infrared Spectroscopy. J. Applied Spectroscopy 47, (1993). [15] Smits, J.R.M., Malssen, W.J., Buydens, L.M.C., Kateman, G.: Using Artificial Neural Net- works for Solving Chemical Problems. Part 1. Multi-layer Feed-forward Networks. J.Chemometrics and Intelligent Laboratory Systems 22, (1994). VI. CONCLUSION In the current work, we have designed a non invasive, low cost, sensitive and user friendly device for glucose measurement. The device is simple, low cost and is widely available as we have used near infra red spectroscopy at second overtones. Accuracy of the prediction model is found to be 5.84mg/dL. Because of the double regression analysis we used, the equipment has become more sensitive and accurate. REFERENCES [1] H.M. Heise, in: R.A. Meyers (Ed.), Encyclopedia of Analytical Chemistry, vol. 1, John Wiley Press, New york, 2000, pp [2] J.S. Maier, S.A. Walker, S. Fantini, M.A. Franceschini, E. Gratton, Opt. Lett. 19(24) (1994) [3] J.P. Wicksted, R.J. Erckens, M. Motamedi, W.F. March, Appl. Spectrosc. 49(7) (1995) [4] G.L. Cote, M.D. Fox, R.B. Northrop, IEEE Trans. Bio-medical Engrg. 39(7) (1992) [5] S. F.Malin, T. L. Ruchiti, T. B. Blank, S. U. Thennadil, and S. L. Monfre, Noninvasive prediction of glucose by near-infrared diffuse reflectancespectroscopy, Clinical Chemistry, vol. 45, pp , 999.)O. S. Khalil, Spectroscopic and clinical aspects of noninvasive glucosemeasurements," Clinical Chemistry, vol. 45, no. 2, pp , [6] K. J. Jeon, I. D. Hwang, S. Hahn, and G. Yoon, Comparison betweentransmittance and reflectance measurements in glucose determinationusing near infrared spectroscopy, Journal of Biomedical Optics, no. 11,p , [7] A. K. Amerov, J. Chen, G. W. Small, and M. A. Arnold, Scatteringand absorption effects in the determination of glucose in whole blood bynear-infrared spectroscopy, Anal. Chem, no. 77, pp , [8] Y. Yorozu, M. Hirano, K. Oka, and Y. Tagawa, Electron spectroscopy studies on magneto-optical media and plastic substrate interface, IEEE Transl. J. Magn. Japan, vol. 2, pp , August 1987 [Digests 9th Annual Conf. Magnetics Japan, p. 301, 1982] /13/$ IEEE 635