Method for increasing accuracy and precision of non-invasive blood glucose measurement apparatus

Abstract

The present invention relates to a method for increasing the accuracy and precision of a non-invasive blood glucose measurement apparatus and, more specifically, to a method for increasing the accuracy and precision of a non-invasive blood glucose measurement apparatus, wherein, in order to increase the accuracy and precision of quantitative analysis of the non-invasive blood glucose measurement apparatus, an algorithm having a qualitative analysis and an algorithm of quantitative analysis are combined to enhance blood glucose prediction values. To this end, the present invention comprises: a step of starting measurement after making contact with the capillary system in the skin of the body by using a selected wavelength band related to blood glucose; a skin irradiation step of sequentially irradiating the blood vessels in the skin with monochromatic light corresponding to each of visible light and near-infrared light; and a detector signal step of a detector receiving signals from the monochromatic light in the skin irradiation step, wherein the detector signal step is completed, and the accuracy and precision of the non-invasive blood glucose measurement apparatus are increased.

Description

Methods for improving the accuracy and precision of noninvasive blood glucose measurement devices

[0001] The present invention relates to a method for improving the accuracy and precision of a non-invasive blood glucose measurement device, and more particularly, to a method for improving the accuracy and precision of a non-invasive blood glucose measurement device by combining an algorithm having a qualitative analysis technique and an algorithm having a quantitative analysis technique to improve the accuracy and precision of quantitative analysis of the non-invasive blood glucose measurement device and thereby enhance blood glucose prediction values.

[0002] 1) The need for blood glucose measurement without blood collection

[0003] According to a 2011 report by the International Diabetes Association, diabetes affects 366 million people worldwide, representing 8.3% of all adults. A recent survey in Korea estimates that approximately 4 million people suffer from diabetes, representing 8% of the total population. Based on a family of four, this means one in four to five households has a diabetic patient. Recently, the number of patients with diabetes, a leading cause of adult disease and a leading chronic disease, is rapidly increasing due to a combination of factors, including an aging population, economic growth, and rising incomes. While numerous personal blood glucose meters have been developed and commercially available, the pain associated with blood sampling often leads to inconsistent blood glucose monitoring, exposing individuals to the risk of diabetic complications. Therefore, painless, blood glucose monitoring devices are essential for diabetes prevention and management, enabling consistent self-monitoring.

[0004]

[0005] 2) Resolving safety issues regarding blood glucose meters without blood collection

[0006] Non-invasive blood glucose meters, when used safely and appropriately, are a highly useful technology that can enhance diagnostic accuracy and therapeutic effectiveness. However, if exposed to patients without ensuring safety and accuracy, they also pose a significant risk of negative impacts on national health and health insurance finances. Therefore, guidelines for safety and appropriate performance evaluation are needed to minimize public health concerns related to non-invasive blood glucose meters. Furthermore, these safety and performance evaluation guidelines should ensure that only medical devices that meet certain criteria are permitted for domestic use before market release, thereby establishing a basic mechanism to protect the public from safety and efficacy issues.

[0007]

[0008] 3) Contributes to rapid permit review

[0009] When medical device manufacturers and importers wish to launch or introduce products into the market, they can prepare for rapid medical device product approval through safety and performance evaluation guidelines, and by establishing safety and efficacy evaluation guidelines, they can promote consistency and efficiency in review and evaluation.

[0010] 4) Optical method

[0011] Spectroscopy is a method used to measure the presence or concentration of a substance by measuring how that substance reacts to light. As light passes through a substance, some of it is reflected, scattered, refracted, absorbed, and transmitted. In some cases, when light collides with a substance, the substance emits a specific energy. The degree of absorption, transmission, and emission can be plotted according to the wavelength of the light, and this is called a spectrum. Optical methods include infrared spectroscopy, Raman spectroscopy, optical coherence tomography (OCT), polarization, fluorescence, occlusion spectroscopy, and photoacoustic spectroscopy.

[0012]

[0013] 4-1) Inlight solution - Near Infrared Technology

[0014] ○ To improve the clinical accuracy of blood glucose measurements, we utilize engineering techniques and multi-variate software algorithms, and Inlight's optical methods and software include special features to distinguish glucose molecules from other similar molecules, such as water, by utilizing the unique vibrational characteristics of each molecule.

[0015] The structure consists of a light source, a light detector, and a spectrometer. The principle is that the light source illuminates the skin, and the small amount of light that returns is analyzed by the spectrometer and detector. Blood sugar levels are measured by analyzing the difference between the irradiated light and the reflected light.

[0016] 4-2) Approach to regression analysis

[0017] The dependent variable in regression analysis uses a continuous variable. The independent variables can be either continuous or categorical. Categorical variables must be converted to dummy variables before use.

[0018] Because each independent variable has multiple dependent variable values, the graph representing the relationship between the independent and dependent variables is a scatterplot. Regression analysis seeks to find a regression line, the optimal line that explains the relationship between variables while minimizing error based on the distribution of variable values.

[0019] A regression line can be defined as a straight line representing all points on a scatter plot. Regression analysis generally refers to linear regression analysis, assuming linearity is the simplest equation. Of course, if a straight line cannot explain the relationship between the dependent and independent variables, a curved relationship can be assumed.

[0020] ① Assumptions of regression analysis

[0021] First, each y, or error term, must be independent and not affect each other. Second, the y value has a normal distribution for each x value. Third, the variance of each error term is the same, i.e., equal variance. Fourth, the relationship between x and y is linear.

[0022] ② Regression analysis model

[0023] Regression analysis is divided into simple and multiple regression analysis based on the number of independent variables. Simple regression analysis has one independent variable, while multiple regression analysis has two or more. However, there is no fundamental difference between the two. Therefore, the regression model for simple regression analysis can be expressed as the equation below.

[0024] Y = + X +

[0025] where is a constant, is the regression coefficient, and is the error term. Slope: the amount by which changes when changes by one unit.

[0026] Error terms can arise for a variety of reasons. Most commonly, they arise from sampling error, which occurs during the sampling process. They can also arise from inaccurate measurement scales for variables.

[0027] The present invention has been devised to solve the problems of the prior art as described above, and the purpose of the present invention is to provide a method for improving the accuracy and precision of a non-invasive blood glucose measurement device with optimal accuracy and precision by sequentially applying qualitative and quantitative analysis techniques to correct for these various variables, since the accuracy and precision of a conventional non-destructive blood glucose measurement device are reduced due to various variables.

[0028] The present invention is a means for achieving the above-mentioned object, comprising: a step of starting measurement after contacting the capillary system in human skin using a selected wavelength band related to blood sugar; a skin injection step of sequentially injecting light into the blood vessels in the skin with each monochromatic light corresponding to visible light and near-infrared light; a detector signal step of receiving a signal from a detector in the monochromatic light in the injection step; and when the detector signal step is completed,

[0029] The monochromatic lights used in the injection stage are a total of 7, including 1 visible light monochromatic light with a heart rate and 6 near-infrared monochromatic lights.

[0030] The seven monochromatic lights are composed of 550 nm, 850 nm, 940 nm, 1200 nm, 1300 nm, 1450 nm, and 1650 nm, respectively.

[0031] The scanning method in the scanning stage uses a total of 7 monochromatic lights by first turning on 1 visible light monochromatic light and 1 of 6 near-infrared monochromatic lights, then measuring them with a detector and then turning off 1 of them, and these receive signals through the detector.

[0032] The blood sugar-related signals measured with seven monochromatic lights are first classified using a qualitative method in which the loading value is calculated using the principal component analysis (PCA) calculation method.

[0033] The first principal component analysis is used to classify the data into groups A, B, and C, and then a qualitative technique is adopted to classify the remaining data into groups A, B, and C, which are not completely separated or excluded from the groups, and a second qualitative technique is used to classify the remaining data into groups A, B, and C using the loading value calculated through the same principal component analysis as the first one, thereby improving the accuracy and precision of the non-invasive blood glucose measurement device.

[0034] The first classification using principal component analysis is to classify into groups A, B, and C using a qualitative description method, and at this time, only groups A, B, and C are used to analyze blood sugar levels using a quantitative analysis model using partial least squares regression analysis (PLSR) for group A, a quantitative analysis model using partial least squares regression analysis (PLSR) for group B, and a quantitative analysis model using partial least squares regression analysis (PLSR) for group C, in order to increase the accuracy and precision of the non-invasive blood sugar measurement device.

[0035] To increase the accuracy and precision of non-invasive blood glucose measurement devices by classification, data composed of 7 wavelengths each are expanded to 21 data by interpolation when calculated using principal component analysis (PCA), and

[0036] Grouping by PCA through principal component analysis (PCA) by interpolation, and the grouped PCA is hierarchically separated into the first PCA 1, the second PCA 2, and the last PCA n, and is finished when all are separated through the first layer.

[0037] When there is data that is not classified through the first layer, if further separation is required in the next layer, the second layer classifies only the data that was not classified in the first layer, and if the data is not classified in the first or second layers, the third layer classifies it, and so on, until the classification is complete. This includes a hierarchical separation method that is a basic feature of the technical configuration.

[0038] As described above, according to the present invention, in order to increase the accuracy and precision of quantitative analysis of a non-destructive blood sugar measurement device, a blood sugar prediction value can be improved by combining an algorithm having an analysis technology and an algorithm having a quantitative analysis technology.

[0039] Figure 1 is a basic hardware configuration diagram to improve the accuracy and precision of quantitative analysis of a non-destructive blood glucose measurement device.

[0040] Figure 2 is a diagram of an analysis algorithm configuration with qualitative techniques among mixed quantitative analysis techniques that apply qualitative techniques to improve the accuracy and precision of quantitative analysis of a non-destructive blood glucose measurement device.

[0041] Figure 3 is an example of an analysis algorithm with qualitative techniques.

[0042] Figure 4 is a diagram of an analysis algorithm configuration having a second qualitative technique among mixed quantitative analysis techniques that apply qualitative techniques to improve the accuracy and precision of quantitative analysis of a non-destructive blood glucose measurement device.

[0043] Figure 5 is an example of an analysis algorithm with a second qualitative technique.

[0044] Figure 6 is a diagram of an analysis algorithm that links qualitative technology and quantitative analysis to improve the accuracy and precision of quantitative analysis of a non-destructive blood glucose measurement device.

[0045] Figure 7 is a blood glucose spectrum diagram interpolated to improve the accuracy and precision of quantitative analysis of a non-destructive blood glucose measurement device.

[0046] Figures 8a and 8b show the modeling results by partial least squares regression analysis (PLSR) after each classification.

[0047] Figure 9 is a diagram of the hierarchical classification method, which is a discrimination method using principal component analysis after the interpolation method.

[0048] The present invention is susceptible to various modifications and embodiments, and thus specific embodiments will be described in detail in the detailed description. This is not intended to limit the present invention to specific embodiments, but rather to encompass all modifications, equivalents, and alternatives falling within the spirit and technical scope of the present invention. In describing the present invention, detailed descriptions of related known technologies will be omitted if they are deemed to obscure the gist of the present invention.

[0049] Figure 1 is a basic hardware configuration diagram to improve the accuracy and precision of quantitative analysis of a non-destructive blood glucose measurement device.

[0050] As shown in Figure 1, the basic configuration includes a step of starting measurement after contacting the capillary system within the human skin using a selected wavelength band related to blood sugar; a skin injection step of sequentially injecting light into the blood vessels within the skin with each monochromatic light corresponding to visible light and near-infrared light; a detector signal step of receiving a signal from the monochromatic light in the injection step by a detector; and the completion of the detector signal step.

[0051] The monochromatic lights used in the above injection step are a total of 7, including 1 visible light monochromatic light with a heart rate and 6 near-infrared monochromatic lights, and the 7 monochromatic lights are composed of 550 nm, 850 nm, 940 nm, 1200 nm, 1300 nm, 1450 nm, and 1650 nm, respectively.

[0052] To explain this in detail, after starting the measurement, the selected wavelength band related to blood sugar is used to make contact with the skin and then the measurement begins.

[0053] Basically, since a light signal for monochromatic light is required, in the present invention, monochromatic light of 550 nm, which is a visible light monochromatic light, and monochromatic light corresponding to near-infrared light of 850 nm, 940 nm, 1200 nm, 1300 nm, 1450 nm, and 1650 nm, a total of 7, is sequentially injected into the skin.

[0054] The main injection area is the area around the fingers where there are capillaries in the skin. The injection method is to first turn on one of the seven and then measure it, then measure it with a detector and then turn off one of them.

[0055] In this way, a total of seven monochromatic lights are used to receive signals from the detector. After the seven are completed, a signal for visible light is received, and this signal is measured to hardware-wise compensate for the flow rate in the blood vessel.

[0056]

[0057] Figure 2 is a diagram of an analysis algorithm configuration with qualitative technology among mixed quantitative analysis technologies that apply qualitative technology to improve the accuracy and precision of quantitative analysis of a non-destructive blood glucose measurement device.

[0058] As shown in Figure 2, as a method for primary classification using a qualitative technique using principal components, data from 1 to 7 are collected, and then classification is performed using a machine learning algorithm for the initial skin-related interference factors and blood vessel interference factors through principal component analysis.

[0059] Similar interference factors are classified for this interference factor, and a method is used to first classify the interference factor with the largest variable among all interference factors. The classification method used at this time is principal component analysis. Principal component analysis (PCA) is one of the multivariate analysis methods that removes the redundancy of the data set by linearly combining existing variables, maintains most of the original information, and generates a small number of new variables that contain most of the spectral information relevant to the analysis (Martin et al., 2005; Shlens, 2014). PCA projects each data onto a new single line that linearly combines the data in the direction of maximum variation, and this newly generated linear combination is called a principal component (PC) or latent variable. The PC matrix T for the nxm-dimensional data matrix X is calculated through the following process.

[0060] t = w1x1+...+ w m x m

[0061] t is a new vector created by a linear combination of existing x variables, which represents the score value, and w is a loading value that explains the influence of existing x variables on the score value.

[0062]

[0063] Figure 3 is an example diagram of an analysis algorithm with qualitative techniques.

[0064] As shown in Figure 3, if the principal component analysis is performed on all 120 samples, the classification can be seen in the 2D score plot. Looking at the 2D plot, it is divided into three groups, and the criterion for dividing into three groups is the discrimination by Euclidean distance. This method is often used to measure the similarity between data, and the proximity of the distance is used when the purpose is classification. In this study, the Euclidean distance was used among several representative methods for measuring distance. Two data X with n variables T = [x1x2...x n ], Y T 2= ​​[x1x2...x n ] The Euclidean distance, that is, the straight-line distance, is as shown in mathematical formula a) of Fig. 10.

[0065]

[0066] And at this time, the X-axis and Y-axis calculation formulas representing the score plot are the Loading values ​​as shown in the figure. This Loading value is displayed in two ways, one is a constant for the X-axis calculation formula and the other is a constant for the Y-axis calculation formula. This constant value can be continuously changed and corresponds to the X-axis and Y-axis calculation formulas of the overall score.

[0067]

[0068] Figure 4 is a diagram of an analysis algorithm configuration having a second qualitative technique among mixed quantitative analysis techniques that apply qualitative techniques to improve the accuracy and precision of quantitative analysis of a non-destructive blood glucose measurement device.

[0069] As shown in Figure 4, the second qualitative descriptive method is to classify the data into groups A, B, and C after using the first qualitative descriptive method, and then perform additional principal component analysis on each group. Each of these three groups is then classified into circles or squares using the Euclidean distance.

[0070]

[0071] Figure 5 is an example diagram for an analysis algorithm with a second qualitative technique.

[0072] As shown in Fig. 5, group A, which was classified through the second qualitative analysis method, is subjected to qualitative analysis again. If principal component analysis is performed in the same way, the data belonging to group A are classified. At this time, the classification is confirmed with a score plot, and it is classified into two by the Euclidean distance method, and the X and Y axes of the score plot are divided into X-Loading and Y-Loading. The two X-Loading and Y-Loading corresponding to the first principal component and the two X-Loading and Y-Loading in the second principal component analysis appear differently.

[0073]

[0074] Figure 6 is a diagram of an analysis algorithm that links qualitative technology and quantitative analysis to improve the accuracy and precision of quantitative analysis of a non-destructive blood sugar measurement device.

[0075] Unlike the method of directly performing principal component analysis after converting a total of seven analog signals to digital as shown in Fig. 6, the interpolation method is used because the wavelength band trend between each analog signal is very important.

[0076] The term interpolation refers to a method of connecting two points. Here, the connection refers to creating a trajectory. Since a line is a collection of points, information about countless points is required to express the line, and the shape of the line is determined by the feature points. The basic interpolation method is linear interpolation, which is the most basic, and the most widely used interpolation method is spline interpolation, which is the most widely used.

[0077] In the present invention, both the basic interpolation method and the most commonly used interpolation method are collectively referred to. Principal component analysis is performed through these interpolation methods, and this principal component analysis is classified into a score plot. At this time, the score plot is in 2D, and each coordinate is determined by the X loading value and the Y loading value.

[0078] And only the data points of the group classified in this way are used for quantitative analysis using partial least squares regression analysis (PLSR). At this time, the partial least squares method, PLS, is a method that can faithfully explain the variance of X while also maximizing the covariance with y, and is expressed as a PLS score obtained by applying PLS to the explanatory variable. And it is a method that uses the response variable as a regression analysis for partial least squares regression analysis. The step of partial least squares method (PLS) first creates a latent variable that is composed of a linear combination of the initial explanatory variables. Unlike the explanatory variables, this latent variable has the correlation between variables removed, and the basic concept of PLS ​​is that the linear combination of the explanatory variables is determined to be proportional to the covariance of the explanatory variable and the response variable.

[0079] Figure 7 is a blood glucose spectrum diagram interpolated to improve the accuracy and precision of quantitative analysis of a non-destructive blood glucose measurement device.

[0080] As illustrated in Figure 7, techniques for estimating values ​​based on location can be broadly divided into interpolation and extrapolation. Interpolation is a technique for estimating unobserved points between observed points, and a representative example is linear interpolation. If the values ​​of two points are known, the first interpolation method that comes to mind is linear interpolation.

[0081] As in b) of Fig. 10, if x1 and x2 are observed values ​​and x is a location to be known, d1 means the distance from x1 to x, and d2 means the distance from x2 to x. If f(x) is the value of the location to be known, it can be simply calculated through internal division.

[0082]

[0083] The most widely used interpolation method is cubic interpolation, which is also widely used in research on increasing image resolution. However, linear interpolation has the disadvantage of producing an angular graph at each intersection of approximation intervals. We want the image to be smoothly resized to high resolution. Therefore, we utilize an interpolation method using a spline curve. A spline is a smooth curve passing through given points. Cubic spline is an interpolation method that uses a spline curve as a 3rd degree polynomial (see Fig. 10 c).

[0084]

[0085] For convenience, let's assume that we know the values ​​of x, 0 and 1. Intuitively, we can know a4 and a3. Since f'(x) is discontinuous, we can find all the coefficients of the polynomial by calculating it as shown below.

[0086] Therefore, spline interpolation is a method to obtain a smooth function with a low-degree polynomial by dividing the entire interval into subintervals. Cubic spline was a method to find the value of the desired location by utilizing the four nearest values. Through the principle of this interpolation method, the data can be increased from 7 points to 21 points through interpolation, and the information missing from 7 points can be checked by using 21 points.

[0087]

[0088] Figures 8a and 8b are modeling results obtained by partial least squares regression analysis (PLSR) after each classification.

[0089] As shown in FIGS. 8a and 8b, in FIG. 8a), the determined PLSR result value is a PC value. This PC value extracts a small number of axes PC (principal components) that are not correlated from multidimensional data with a high correlation between variables, and by projecting the data onto these axes again, the multidimensional data can be interpreted as low-dimensional data such as two or three dimensions.

[0090] The lower the PC value, the better the reproducibility, etc. Looking at these results, the PC was confirmed to be a very low value as it was the third, and the SEC was 0.3 and the coefficient of determination was 0.9990, confirming high linearity. b is the PLSR result before discrimination, and the PC value is the same, but the SEC is 33.09 and the coefficient of determination is 0.447, showing very low linearity.

[0091]

[0092] Figure 9 is a diagram of the hierarchical classification method, which is a discrimination method using principal component analysis after the interpolation method.

[0093] As illustrated in Figure 9, grouping is performed through principal component analysis using interpolation. First, in the three-level classification method using interpolation, the first step is defined as the first layer, and this multiple classification method is generally called hierarchical classification.

[0094] Grouping is done by PCA through principal component analysis (PCA) using the above interpolation method, and the grouped PCAs are hierarchically separated into the first PCA 1, the second PCA 2, and the last PCA n.

[0095] At this time, the first stage of grouping can be divided into two layers, with the first layer being the first layer and the subsequent grouping using PCA. Principal component analysis is used to determine the difference at regular intervals, and this regular interval is then sequentially divided into layers, resulting in a so-called hierarchical separation and determination. This separation method allows for greater accuracy and precision by separating each skin type and various interference factors.

[0096] Determining a single layer involves grouping data using the Euclidean distance method, which is used to separate data using PCA at once. This completes the first layer. If further separation is required in the next layer, the second layer is reclassified using only the data that were not classified in the first layer.

[0097] If classification is not achieved in the first or second layers, classification is then performed in the third layer. All of these methods of continuously separating until a perfect classification is achieved are referred to as hierarchical separation methods.

[0098]

[0099] The above description is merely an example of the technical idea of ​​the present invention, and those skilled in the art will appreciate that various modifications and variations can be made without departing from the essential characteristics of the present invention. Therefore, the embodiments and drawings disclosed in the present invention are not intended to limit the technical idea of ​​the present invention, but rather to explain it, and the scope of the technical idea of ​​the present invention is not limited by these embodiments and drawings. The protection scope of the present invention should be interpreted by the following claims, and all technical ideas within a scope equivalent thereto should be interpreted as being included in the scope of the rights of the present invention.

Claims

1. A step of starting measurement by contacting the capillary system in human skin using a selected wavelength band related to blood sugar; A skin injection step that sequentially injects light into the blood vessels of the skin using monochromatic light corresponding to visible light and near-infrared light; A detector signal stage in which the monochromatic light in the injection stage receives a signal from the detector; The detector signal stage is completed, and a method for improving the accuracy and precision of a non-invasive blood glucose measurement device.

2. In paragraph 1, A method for improving the accuracy and precision of a non-invasive blood glucose measurement device by using a total of seven monochromatic lights, including one visible light monochromatic light with a heart rate and six near-infrared monochromatic lights, in the above injection step.

3. In paragraph 2, A method for improving the accuracy and precision of a non-invasive blood glucose measurement device, wherein the seven monochromatic lights are each composed of 550 nm, 850 nm, 940 nm, 1200 nm, 1300 nm, 1450 nm, and 1650 nm.

4. In paragraph 1, The injection method in the above injection step is to first turn on one visible light monochromatic light and one of six near-infrared monochromatic lights, and then measure it, measure it with a detector, and then turn off one of them, using a total of seven monochromatic lights, and have them receive signals from the detector, a method for improving the accuracy and precision of a non-invasive blood glucose measurement device.

5. In paragraph 4, A method for improving the accuracy and precision of a non-invasive blood glucose measurement device, in which blood glucose-related signals measured with seven monochromatic lights are first classified using a qualitative method in which the loading value by the principal component analysis (PCA) calculation method is used.

6. In paragraph 5, A method for improving the accuracy and precision of a non-invasive blood glucose measurement device by using a qualitative description method to classify data into groups A, B, and C using the first principal component analysis, and then using only the remaining data that is not completely separated or excluded from these groups to further classify each group using a second qualitative technique using the loading value calculated through the same principal component analysis as the first.

7. In paragraph 5, This is a method to improve the accuracy and precision of a noninvasive blood glucose measurement device by adopting blood glucose analysis as a quantitative analysis model by partial least squares regression analysis (PLSR) for group A, a quantitative analysis model by partial least squares regression analysis (PLSR) for group B, and a quantitative analysis model by partial least squares regression analysis (PLSR) for group C, as a classification using the first principal component analysis and a qualitative description method.

8. In paragraph 5, A method for improving the accuracy and precision of a non-invasive blood glucose measurement device by classification through data expanded into 21 data by interpolation from data composed of each of seven wavelengths when calculated using the above principal component analysis (PCA).

9. In paragraph 8, A method for improving the accuracy and precision of a noninvasive blood glucose measurement device, wherein the PCAs are grouped through PCA using the above interpolation method, and the grouped PCAs are hierarchically separated into the first PCA 1, the second PCA 2, and the last PCA n, and are finished when all are separated through the first hierarchy.

10. In paragraph 9, A method for improving the accuracy and precision of a noninvasive blood glucose measurement device, including a hierarchical separation method in which, when there is unclassified data through the first layer, if further separation is required in the next layer, only the unclassified data in the first layer are classified again in the second layer, and if the data is not classified in the first and second layers, the classification is performed in the third layer, and so on until the classification is complete.

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