Temperature Effect on Near Infrared Spectrum of Glucose Monitoring

Transcription

1 206 International Conference on Electronic Information Technology and Intellectualization (ICEITI 206) ISBN: Temperature Effect on Near Infrared Spectrum of Glucose Monitoring Renjie Xu, Mengning Yang, Xin He and Xiaobin Li ABSTRACT This paper used a regression model to describe temperature effect on nearinfrared spectrum for glucose monitoring. By using high-precision instruments, experiments measured near-infrared transmitted light intensity (reflected by voltage values) of glucose solutions whose concentrations were 278 mmol/l, 556 mmol/l, and 2780 mmol/l. Temperature values were accurately controlled, and a regression model using least square method fitting temperature values and voltage values was established. The temperature values and the voltage values were negatively correlated and a t-test showed that results had statistically significant, thus, the model was meaningful. The coefficients of determination of models for three concentrations were 0.928, 0.94, and 0.99 respectively, which showed that majority of voltage could be influenced by temperature, and the fitting performance was well. The significance of this study was to make a contribution to a non-trauma and non-pollution technology, and hope to potentially improve the accuracy of nearinfrared non-invasive blood glucose monitoring. INTRODUCTION Diabetes is a common endocrine disease with a high incidence, which is one of four hazards to human health. With improvement of living standard, the incidence of diabetes is rising. According to the International Diabetes Federation (IDF, headquartered in Brussels) released data, it shows that the number of global diabetes is more than 45 million in 205. So diagnosis and treatment of diabetes are having a great significance. At present, almost all the commercial successes of blood Renjie Xu, Mengning Yang, Xin He, Xiaobin Li, School of Software Engineering, Chongqing University, Chongqing, China 445

2 glucose monitoring devices are invasive, none of a non-invasive monitoring technology can achieve the accuracy of the invasive monitoring []. So there is a great necessity to study the non-invasive blood glucose monitoring technology, which can alleviate the pain of patient on account of frequently piercing skins to obtain samples. In recent years, there are some common methods of non-invasive blood glucose monitoring such as Reverse iontophoresis, Bio impedance spectroscopy, Raman spectroscopy, etc. Anke Sieg et al. studied the use of Reverse iontophoresis method in non-invasive monitoring [2]. Animas Technologies company in California, USA researched a NGM Watch device whose name was GlucoWatch G2. This device used the Reverse iontophoresis method, but it was not a really non-invasive device [3]. For the first time, Caduff s group introduced the Bio impedance spectroscopy to a non-invasive blood glucose monitoring system [4]. Based on this research, Pendragon Medical Ltd in Switzerland researched another NGM device (Pendra ). But it was only suitable for some specific conditions of a special population [5]. Berger AJ et al. studied an application of Raman spectroscopy in blood glucose monitoring [6]. C8 MediSensors in California, USA, was continuing to study the NGM device based on the Raman spectroscopy. But due to the object to be measured was too vivo, the measured signal was quite weak, and also some related problems involved some complicated subjects. So up to now, non-invasive blood glucose concentration monitoring is still a challenge to research. Near-infrared spectroscopy (NIRS) uses the light in nm region, which interrogates the tissue with low energy radiation [7]. Because of its high penetration, high sensitivity, high energy signal and low cost [8], NIRS has broad prospects and research significance in measurement of blood glucose [9-3]. But Environmental variations such as changes in temperature, humidity, skin hydration, carbon dioxide, and atmospheric pressure also interfere with measurement [8]. This research was a basic experimental study, focusing on the temperature effect on near-infrared while monitoring glucose concentration. Because near-infrared spectrum is energy spectrum of molecules, any change in temperature will influence the shape of spectrum, which affects accuracy of the results of near-infrared spectral analysis. Therefore, based on the principle of near-infrared spectroscopy, our experiments researched the influence of temperature on near-infrared spectroscopy glucose concentration monitoring with three different concentrations of glucose samples. We collected spectral information as the form of voltage from three samples with a professional InGaAs detector, and strictly controlled the temperature of each experiment in the range of Cusing a high precision temperature controlling unit. A regression model was also established which determined the relationship between temperature and voltage. In addition, hypotheses testing was proceed on the model in order to ensure accuracy of results. This paper was divided into five parts. Section mainly introduced the research status and significance of non-invasive blood glucose monitoring. The principle of experiments, the choice of wavelength, the experimental environment and the steps 446

3 of data collection were described in Section 2. Section 3 established a regression model which used the least square method to solve. Section 4 described the data preprocessing and hypothesis testing, and the results showed that the negative correlation of temperature and voltage was conducted. Section 5 made a summary and an outlook for this study. METHODOLOGY Around the world, the incidence of diabetes has increased gradually, so accurate diagnosis can suppress the occurrence of diabetes to a certain extent. The nearinfrared non-invasive glucose monitoring opens a new door for the diagnosis of diabetes, whose high efficiency, non-invasive, and non-polluting make it become a direction for a large number of scholars. In this study, effect of temperature on measurement was researched. In this chapter, a detailed process about the experimental apparatus and near-infrared spectral acquisition process was described, which provided reliable data for the model. Basic Principle The basic principle of experiments is based on Lambert-Beer law: A lg I / I kcd () 0 Where A is light absorbency, I0 and I are incident light intensity and transmitted light intensity crossing sample respectively, c is glucose concentration of sample, d is optical path, and k is molar absorption coefficient. When the factor k and the optical path d are fixed, glucose concentration c can be calculated from light absorbency A. In our experiments, we chose an InGaAs detector to monitor light signals. The InGaAs detector transforms light intensity to voltage as the output. And for each sample s glucose concentration, transmitted light intensity I could be replaced by voltage V. So when incident light intensity I0 of the controlled group is fixed, voltage V0 of the controlled group is fixed. Our experimental study focused on the temperature effect on near-infrared monitoring. When glucose concentration c is fixed, voltage V as the InGaAs detector output would be changed through different temperatures. So we will discuss the relationship between temperature and voltage. Wavelength Selection NIR spectroscopy uses a beam of light with wavelength in the range of nm, which is focused on the body to estimate glucose concentration in the tissues ( 00 mm deep) by measuring variations in the light intensity due to 447

4 transmission and reflectance in the tissue [4]. For analysis and prediction of glucose, TABLE I. INFRARED ABSORPTION PEAK OF GLUCOSE AND WATER. Species Glucose Water Wavelength (nm) the wavelength of NIR light between nm in the first overtone region and nm in the combination overtone band are more suitable [2,5-7]. In order to avoid the interference of water molecules (See TABLEI), it is suitable to choose the 550nm as the wavelength of glucose monitoring [8]. Experimental Environment Experimental equipment included a 550nm wavelength laser whose optical fiber output power was between 0 and 200nw, a fiber collimator(4mm collimation spot and 2mm outer diameter), a professional InGaAs detector whose detectable wavelength was between 850nm and 600nm, an Altai acquisition card, a cuvette with 5mm optical path, a high-precision temperature control instrument(±0. C) in the range of C. Three glucose solution samples whose concentrations respectively were 278mmol/L, 556mmol/L, and 2780mmol/L. In our experiments, we used the high-precision temperature control instrument to change the experimental temperature in the range of C for each group of three glucose solution samples. Near-infrared light was emitted by the wavelength laser, and transferred through different glucose solution samples. Spectrum signals collected by the InGaAs detector were converted into voltage signals, and were reserved reliably in a compute. Experimental data was collected every five minutes for each group. 448

5 MODEL In previous section, the InGaAs detector was used to measure the near-infrared spectroscopy of three concentrations of glucose solution in different temperatures. Voltage values were recorded in five minutes for each group. Then a linear regression model was established in this section. This research studied voltage trends of three concentrations in the range of C. For each experiment in temperature T, there were m (about 20 million) voltage values v could be recorded to each concentration. The random error of each voltage value was recorded as ε. All the ε were assumed independent of each other, and were normally distributed with mean zero. Under this assumption, least square estimation β had a clear sampling distribution, which was a normal distribution. Denote the mean of v as V, the expectation as μ, the standard deviation as S, so mv / S obeyed the distribution with the m- degrees of freedom. When the confidence level was -α, the confidence interval forμ was S S V t m V t m m 2 m 2, (2) For the data collected in experiments, S approximately was, t /2m approximately was between and 3, and approximately was 450.Therefore,the confidence interval of μ was in a small range of the mean V. So the expected voltage value μ of each temperature could be replaced by the mean V. The temperature was regarded as a predictor variable T, and the voltage value was regarded as a response variable V. Expression (3) was a linear model, which was assumed to represent the relationship between voltage and temperature. Where β0 and β were constants called model regression coefficients or parameters, and ε was a random disturbance or error. To validate the rationality of this assumption, the scatter lot of voltage and temperature was examined. The graph described the relationship of temperature and voltage in the range of C. As shown in Figure, experimental data showed that the linear relationship model was a reasonable assumption. V T (3) 0 449

6 Figure. Mean of voltage for three concentrations in each temperature. For each concentration, the parameters β0 and β, which were estimated according to the existing data, were used to fit the points of voltage value and temperature value in scatter lot. In accordance with (4), corresponding to the temperature value, each voltage value was expressed as: Vi 0 Tii, i,2,..., n, (4) Where Vi was the ith value of the response variable V, Ti was the ith value of the predictor variable T, and εi was the error in the approximation of Vi. The sum of squares of these errors were expressed as (5), n 2, 2 S V T 0 i i 0 i i i n (5) S The values of β0 and β that minimized 0, respectively, V VT T Ti T ˆ i i 2 were given by (6) and (7), (6) 450

7 ˆ V ˆ T (7) 0 VERIFICATION In previous section, temperature was regarded as the predictor variable, voltage was regarded as the response variable, and a linear regression model was established. This section firstly performed the raw data preprocessing. Then for each concentration, the processed data and the least square method were used to calculate three models. And a hypothesis test was used for testing the reasonability. (a) raw data (b) de-noised data Figure 2. Stages of data preprocessing: (a) raw data (b) de-noised data. Date Preprocessing As shown in Figure 2, the original data was illustrated in (a). The data had noise because of external environmental interference. In this paper, removing outliers and smoothing were executed for the raw data, and the wavelet transform principle was used effectively in reducing signal noise. De-noised data was shown in (b). Least Square Regression In different temperature monitoring environment, the number of the data groups was 24 in total, and each group recorded the data in a 5 minutes period. In each group, the mean value and the standard deviation value were calculated for each one of three concentrations respectively. According to Lambert-Beer law, with the increasing concentrations in the same group, three mean values of voltage should show a trend of decline. Some groups which did not conform to the law should be 45

8 excluded from the whole groups. For this reason above, 77 groups were retained, which were used to determine the model. According to the expression (5)-(7), least square regression lines for three concentrations were accurately calculated as: V T (8) V T (9) 2 2 V 0.69 T (0) 3 3 Expression (8)-(0) were the model of temperature and voltage, whose concentrations orderly were 278mmol/L, 556mmol / L, and 2780mmol/L. Temperature and voltage values from the model showed a negative growth trend. Hypothesis Testing and Confidence Intervals When models were calculated, temperature of model whether it had the ability to predict voltage were measured by the temperature values and voltage values scatter lot. But this was not accurate, just a visual intuitive method for determining. This section used a more rigorous quantitative method, to conduct a test of hypothesis about the regression parameter β. In this model, note that the hypothesis 0 meant that there was no linear relationship between voltage and temperature, the hypothesis 0 meant that there was a linear relationship between voltage and temperature. In order to determine whether the temperature had the ability to predict the voltage value, the hypothesis = 0 was tested in the regression. A monitoring voltage value distribution was shown in Figure 3. For every fixed value of temperature, the ε was independent random quantities normally distributed 2 2 i N with mean zero and a common variance σ2, which meant 0,, 0. With these assumptions, least square estimation ˆ had a clear sampling distribution, which was a normal distribution. With the sampling distributions of ˆ, it was in position to perform statistical analysis concerning the ability of temperature T as a predictor on voltage V. Under the normal distribution assumption, an appropriate test statistic for testing the null hypothesis H0 : =0 against the alternative H: 0 was the t-test, when H0: = 0 was true, the t obeyed the n-2 degrees of freedom of the student-t distribution. The statistic was defined as (), t ˆ se.. ˆ () 452

9 Figure 3. Voltage values distribution, the data came from the group in 25. C and the concentration is 278mmol/L. Where the standard error(s.e) was given by (2), se.. ˆ ˆ T T i 2 (2) The variances of β depended on the unknown parameter α 2, so the unbiased estimate of α 2 was expressed as (3), 2 ˆ V ˆ 2 i Vi 2 ei (3) n2 n2 Where the number n-2 in the denominator of expression (3) was called the degrees of freedom. In order to construct confidence intervals for the regression parameters, 2 2 N experimental assumed random disturbance 0,, 0 to ensure that the estimated amount of and was a normal distribution. Setα=0.05, β0 with 95% confidence interval was defined as (4), se.. 2, /2 ˆ n ˆ t (4)

10 tn 2, /2 Where was a /2 quantile of t-distribution whose degrees of freedom was n-2. Similarly, βwith the 95% confidence interval was given by (5), ˆ t s.. e 2, /2 ˆ n This experiment used R2 (Goodness of Fit Index, GFI) to evaluate the fitting degree. It was equal to the square of the correlation coefficient between the response variable and the predictor: (5) TABLE II. THE COEFFICIENT FITTING RESULTS, ITS 95% CONFIDENCE INTERVAL. mmol/l β 0 β 0 confidence interval β β confidence interval [337.87, ] [-0.62, ] [ , ] [-0.67, -0.68] [ , ] [-0.644, ] TABLE III. THE COEFFICIENT FITTING RESULTS, ITS 95% GOODNESS OF FIT INDEX. mmol/l t n 2, / t R Vˆ ˆ i V Vi Vi V V V V i 2 2 i (6) Results could be calculated as shown in TABLEII and TABLEIII, As can be seen from the calculation results, statistics t of each concentration were satisfied as (7): t t (7) n2, /2 H0 was rejected at the significance level α=0.05. This meant that β most likely was not 0, thus, the predicted effect of temperature T on voltage V was statistically significant, experimental regression model was pregnant. The R2 of three expressions with different concentrations were as high as in sequence. Therefore, most of the change in voltage of the model could be explained by temperature, indicating a good fitting of the experiment. 454

11 DISCUSSION AND CONCLUSION The foregoing paper described the entire experiment process, the establishment and verification of the model. This section discusses the related work which has been done by other researchers in the same field, summarizes the experience with comparison, and looks forward to the future works. Before this study, some scholars have researched temperature effect in this field. Venyaminov used 3.5μm transmittance cuvette to measure the effect of temperature changed from 25 C to 50 C on water spectrum [9]. In the mid-ir and near-infrared region, Jensen discussed the effect of temperature on absorption spectrum of water and glucose when the optical path was 0.4μm and 50μm [20]. Zhao Bo studied the accidental correlation of temperature in blood glucose detection, but did not yet draw a referable conclusion about the impact of glucose monitoring on the continuous temperature [2]. In this experiment, through the voltage data acquired of three concentrations (278 mmol/l, 556 mmol/l, 2780 mmol/l) in a range of C, a trend of voltage was researched at the temperature range. The impact of temperature will further influence the glucose monitoring using near-infrared light. At the initial stage of the experiment, voltage data was processed by noise reduction. Then least square regression was used to obtain a trend that voltage was slowly lowered while temperature raised. For stringency, hypothesis testing was used to calculate a statistical magnitude t which refused β=0 at the significance level of 0.05, the results showed that the regression model had statistically significant. Meanwhile, the R2 of each concentration were 0.928, 0.94, and 0.99, so that temperature and voltage had a probable correlation. This showed that temperature was indeed one of the factors affecting near-infrared spectroscopy. It will help to improve the measurement accuracy for the detection of glucose solution concentration, which has a great significance for prevention and treatment of diabetes. However, due to lack of real blood samples, the data could not be collected in actual monitoring environment to achieve better measurement results. This will be planned to industriously compensate in the future works. Further on, the research will be realized in a variety of wavelengths environment and a wider range of temperature, and will reduce the impact of environmental factors on experimental results. An early realization of a low-cost, high speed, high precision, simple operation clinical application of non-invasive blood glucose monitoring is worth waiting. ACKNOWLEDGMENT This work is sponsored by the National Natural Science Foundation of China (nos ), the Chongqing science and technology talent training project (no. cstc203kjrc-tdjs0062). 455

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