2.4. Calibration with Cyanmethemoglobin Method

To validate our proposed method of hemoglobin concentration measurement using the modified Beer–Lambert law, we will compare the results with the standard method for laboratory determination of hemoglobin concentration in blood samples, namely the cyanmethemoglobin method [26].

Cyanmethemoglobin is the standard method for laboratory determination of hemoglobin concentration in blood samples. The test is normally performed by dissolving 20 microliters of blood in 5 mL of Drabkin’s solution. In addition, a spectrophotometer and calibration graph are used to estimate the hemoglobin concentration.

For this experiment, several solutions must be prepared, such as Drabkin’s solution, cyanmethemoglobin standard solution and diluted cyanmethemoglobin standard solution. We first prepared the Drabkin’s solution by mixing 1 vial of Drabkin’s reagent with 1 L of distilled water. Then, we added 0.5 mL of the Brij L23 solution. For safety reasons, due to the acidic properties of the solution, this process must be performed in the fume hood, as shown in Figure 6.

Preparation of a liter of Drabkin’s solution in a volumetric flask.

The next step is to prepare the cyanmethemoglobin standard solution. This solution can be prepared by mixing 20 mL of Drabkin’s solution with 14.345 mg of hemoglobin human lyophilized powder, as shown in Figure 7.

20 mL of cyanmethemoglobin standard solution in a volumetric flask.

Lastly, for the diluted cyanmethemoglobin standard solution, the solution can be created by mixing Drabkin’s solution with cyanmethemoglobin standard solution at different concentrations, as shown in Table 1. The decreased concentration of hemoglobin is needed to provide a calibration curve for hemoglobin concentration.

Diluted cyanmethemoglobin standard solution at different concentrations.

After all the diluted cyanmethemoglobin standard solutions have been prepared, next, spectrophotometry must be performed. The spectrophotometer that has been used is a Hitachi u-2910 model, run with the software called UV solutions. In the software, the range of wavelength and type of data must be selected. The wavelength that was chosen between 450 and 650 nm as the interesting wavelength was 540 nm, and the type of data is absorbance. Besides, before measuring the data, the baseline must be adjusted first. Then, after all the samples were measured by the spectrophotometer, to validate the results, the samples were used to measure hemoglobin concentration with our proposed modified Beer–Lambert-based technique using the MAX30100 sensor. This can be carried out by transferring the solution to a small tube and measuring its absorbance in the darkroom.

However, the sensor, the MAX30100 pulse oximeter, is a reflectance sensor, so the received signal from the sensor is the reflectance of the light. Thus, the data must be converted before being used. Therefore, the relationship between absorbance of light and reflectance of light can be expressed as:

Nonetheless, this system contains a light-balancing intensity program and there are 2 different types of light, so the total light intensities are also varied by the amounts of currents that were used. For a 16-bit analog-to-digital converter and the maximum 50 mA current used, the total intensity of light will be equivalent to 65,535. For the current less than 50 mA, the total intensity of red and infrared light can be described by the following equations, respectively:

where the convention factor is 65,535 per 50 mA.

The light absorbance of the MAX30100 sensor can be calculated from Formulae (16) and (17). However, all the data were collected when the current of the red light was equal to 50 mA. By replacing CurrentRed in Equation (17) to 50 mA, total light intensity will be 65,535. Therefore, Equation (16) can be modified to:

All measured data have been tabulated in Table 2, including hemoglobin concentration, MAX30100 sensor shifted light absorbance and light absorbance spectrophotometer. Note that the MAX30100 sensor shifted light absorbance is the shift of the MAX30100 sensor light absorbance such that the minimum is at 0.

Light absorbance values from all devices.

The calibration graph equation is further calculated by using minimized mean square error (MMSE) to estimate the linear equation between spectrophotometer light absorbance and hemoglobin concentration, as shown in Equation (20):

where x is the spectrophotometer light absorbance and y is hemoglobin concentration.

After all the data were collected, 3 statistics tools were used to test the reliability of the data, which are F-test, T-test and linear regression. This process was carried out by using the MATLAB application.

For this test, the result from the shifted MAX30100 absorbance value will be compared to the spectrophotometer absorbance value to test whether the result is coming from a single population or not. The F-test result for N = 3 is shown in Table 3.

F-test result from MATLAB for N = 3.

The result has shown that all data are coming from a single population since all F values are less than the value from the F-table (at n = 1 and d = 4), which is 7.71. Thus, the data can be used interchangeably (p < 0.05).

For this test, the shifted MAX30100 absorbance value and hemoglobin concentration will be used to find the regression line, the 95% confidence interval of the regression line, observation, correlation coefficient and coefficient of determination. Moreover, the T-test will be used to test whether the hemoglobin concentration and light absorbance from the MAX30100 sensor are corelated. The result of the 95% confidence interval of the regression line and observation between Hb concentration and light absorbance from the MAX30100 sensor are shown in Figure 8 and Figure 9, respectively.

The 95% confidence interval of the regression line relating Hb concentration and light absorbance from the MAX30100 sensor.

The 95% confidence interval for an additional observation of light absorbance from the MAX30100 sensor at given Hb concentration.

Results of the T-Test and coefficient of determination from MATLAB are given as:

From the T-test results, it can be seen that the hemoglobin concentration and light absorbance from the MAX30100 sensor are not coming from the same population, since the value of T = 6.1969, which is greater than the value from the T-table (at v = 4), which is 2.776. Thus, the hemoglobin concentration and light absorbance from the MAX30100 sensor are correlated (p < 0.05). Moreover, the coefficient of determination (r²) is equal to 0.910117, which means that around 91% of data can be explained by the graph.

Calibration software will be used by our system to determine the hemoglobin concentration. The hemoglobin concentration will be determined indirectly by creating a calibration curve. To obtain the calibrated data, 9 blood samples have been drawn from the three subjects at different times. We then measured hemoglobin concentration using a calibration graph derived from the cyanmethemoglobin method, i.e., light absorbance is measured using a spectrophotometer and later converted to hemoglobin concentration, as shown in Table 4. At the same time, modified Beer–Lambert data using our system were also collected for the 9 blood samples. Minimized mean square error (MMSE) was then used to fit the liner regression line between hemoglobin concentration and modified Beer–Lambert data. The derived regression line equation is provided in Equation (21), with r² of 0.924431, which demonstrates the linear relation between hemoglobin concentration and modified Beer–Lambert data:

Data measured by the modified Beer–Lambert value and cyanmethemoglobin method.

Using the regression line from Equation (21), we will generate calibration data that will be used in our system. By varying the hemoglobin concentration from 0 to 180 mg/mL and recomputing the corresponding modified Beer–Lambert data, the re-sampling of hemoglobin concentration will be called the calibrated data value. Using the data in Table 2, the shifted MAX30100 absorbance value and spectrophotometer reflectance value are also interpolated. All calibration data are provided in Table 5.

Calibrated data.

Similar to data derived from the cyanmethemoglobin method, we also tested the reliability of the data using the F-test, T-test and linear regression.

The calibrated data value will be used to find the regression line, the 95% confidence interval of the regression line, observation, correlation coefficient and coefficient of determination. Moreover, we used a T-test to test whether the hemoglobin concentration and calibrated data value sensor are correlated. The results of the 95% confidence interval of the regression line and observation between Hb concentration and calibrated data are shown in Figure 10 and Figure 11, respectively.

The 95% confidence interval of the regression line relating spectrophotometer reflectance value at difference Hb concentrations and calibrated value.

The 95% confidence interval for an additional observation of calibrated value at given spectrophotometer reflectance values.

Results of the T-test and coefficient of determination from MATLAB comparing the calibration graph and calibrated values are given as follows:

Spectrophotometer Reflectance Value(X)/Modified Beer–Lambert law Value (Y)

From the T-test result, we can conclude that both hemoglobin concentration and calibrated data are not coming from the same population, since the value of T = 8.5672, which is greater than the value from the T-table (at v = 6), which was 2.447. Thus, the hemoglobin concentration and light absorbance from the MAX30100 sensor correlate (p < 0.05). Moreover, the coefficient of determination (r²) is equal to 0.924431, which means that around 92% of data can be explained by the graph.

After the calibration graph is finished, the calibrating software is developed. The software will provide the status of the tester based on the hemoglobin concentration level, with an error of 15%. The status is as shown below in Table 6.

The anemia diagnosis status *.

* Adapted from [27].