Quantitative Analysis of Different Multi-Wavelength PPG Devices and Methods for Noninvasive In-Vivo Estimation of Glycated Hemoglobin

Abstract

Diabetes is a serious disease affecting the insulin cycle in the human body. Thus, monitoring blood glucose levels and the diagnosis of diabetes in the early stages is very important. Noninvasive in vivo diabetes-diagnosis procedures are very new and require thorough studies to be error-resistant and user-friendly. In this study, we compare two noninvasive procedures (two-wavelength- and three-wavelength-based methods) to estimate glycated hemoglobin (HbA1c) levels in different scenarios and evaluate them with error level calculations. The three-wavelength method, which has more model parameters, results in a more accurate estimation of HbA1c even when the blood oxygenation (SpO₂) values change. The HbA1c-estimation error range of the two-wavelength model, due to change in SpO₂, is found to be from −1.306% to 0.047%. On the other hand, the HbA1c estimation error for the three-wavelength model is found to be in the magnitude of 10⁻¹⁴% and independent of SpO₂. The approximation of SpO₂ from the two-wavelength model produces a lower error for the molar concentration based technique (−4% to −1.9% at 70% to 100% of reference SpO₂) as compared to the molar absorption coefficient based technique. Additionally, the two-wavelength model is less susceptible to sensor noise levels (max SD of %error, 0.142%), as compared to the three-wavelength model (max SD of %error, 0.317%). Despite having a higher susceptibility to sensor noise, the three-wavelength model can estimate HbA1c values more accurately; this is because it takes the major components of blood into account and thus becomes a more realistic model.

1. Introduction

Photoplethysmography (PPG) is an optical method of obtaining changes in blood volume in tissue. In the general approach of obtaining PPG signals, the tissue in the region of the digital or radial artery is illuminated with light of multiple wavelengths. The light waves interact with the tissues and blood components and are absorbed or scattered in the medium. As the blood volume changes in a certain location of the human body, due to the pulsatile nature of blood flow, the received light intensity also changes with the change in blood volume.

Historically, PPG signals have been utilized to detect time-domain properties and quantitative properties of the human body. The time-domain properties include—but are not limited to—respiratory rate [1] and heart rate [2]. The most widely used quantitative property of the human body that is measured with PPG signals is the blood oxygenation (SpO₂) parameter [3,4,5]. This parameter indicates the percent amount of oxygenated hemoglobin with respect to total hemoglobin count. Recently, a study was conducted to warn for potential infection by COVID-19 by estimating SpO₂ using PPG signals [3]. The other quantitative properties include blood pressure [4], hypo- and hypervolemia [5], and blood glucose levels [6,7]. The time-domain properties require single-wavelength PPG (SW-PPG) to evaluate. On the other hand, to estimate the quantitative properties, multiple wavelengths of PPG (MW-PPG) signals are required.

Diabetes mellitus is a disease that affects the production and utilization of insulin, which directly modifies the consumption of blood glucose by body cells. A result of diabetes is the presence of an excessive amount of glucose available in the bloodstream. This not only changes the properties of the blood but also causes other serious diseases, including kidney failure [8], heart disease [9], and sudden mortality [10]. For these reasons, the diagnosis of diabetes is very important for reducing the risk of insulin control failure in its early stages. There are several methods available to diagnose diabetes. The main approaches for diagnosis are random, fasting, or oral glucose tests, and glycated hemoglobin test.

Estimating blood glucose levels non-invasively for the diagnosis of diabetes is a fairly new topic within the scope of PPG signals [6]. The current state-of-the-art for non-invasive blood glucose estimation is the utilization of external skin tissues and saliva or tears [11,12]. There are also other non-invasive procedures, with which glucose levels can be estimated [13,14,15,16].

However, the non-invasive glycated hemoglobin (HbA1c) test is the most recent topic of discussion. Since the invasive test of HbA1c requires blood samples, it can be inconvenient for users to perform tests frequently. HbA1c is the non-enzymatic bond of hemoglobin with sugar molecules. The sugar molecules are usually monosaccharides. The more sugar molecules present in the bloodstream of a person, the more the probability of the glycation of hemoglobin increases. Moreover, the final product of glycation (HbA1c) is very stable and does not usually alter within the life cycle of the glycated hemoglobin molecule. Due to these factors, the HbA1c level in a human body is a very slow varying parameter, and is usually considered equivalent to the three-month weighted average of the blood sugar level [17]. Measurement of hyperglycemia-associated conditions was performed on mice models to classify normal, obese, and diabetic groups in a recent study [18]. In another study, the researchers designed a method to estimate HbA1c by measuring breath acetone components [19]. There are only two papers that conducted studies on the estimation of glycated hemoglobin using PPG signals. One of the studies performed an in vitro analysis from the blood sample [20], and the other study was designed to measure the HbA1c by in vivo measurement [21].

Although PPG signals are characterized as an easy-to-acquire optical signal compared to other bodily signals (e.g., EEG (Electroencephalography), ECG (Electrocardiography), ABP (Arterial Blood Pressure)), there are specific methods and wavelength selection procedures that are required to obtain a good quality signal.

Among the wavelength-dependent methods, SW-PPG, MW-PPG, and all-wavelength PPG (AW-PPG) are employed based on the purpose of the signal acquisition. As described previously, time-dependent properties usually require SW-PPG. On the other hand, MW-PPG and AW-PPG are employed in the measurement of quantitative properties. Since glycated hemoglobin is a quantitative property of blood, an MW-PPG or AW-PPG signal is required for estimation.

The most widely used technique for acquiring an MW-PPG signal uses discrete LEDs of different wavelengths and single or multiple photodetectors (PDs) to record the PPG signals. In this method, the specimen or medium is placed between the LEDs and PDs for transmission-mode PPG, and the medium is placed on one side of the LED-PD arrangement for reflection-mode PPG signal acquisition. In the reflection mode PPG system, the LEDs and PDs are placed in a single plane facing at the medium. Figure 1 depicts the different arrangements of LEDs and PDs for PPG signal acquisition.

The advent of wearable and mobile devices has led to an exponential increase in mobile-based healthcare systems. Smartphones with powerful processors, multiple sensors, and large data storage capabilities are well suited for healthcare systems. A smartphone camera can be a great candidate for a PPG signal acquisition device, where the camera sensor is the PD and the white built-in flashlight is the light source. In this case, the light source contains a wide range of wavelengths interacting with the medium, and the camera sensor filters the input light into three distinct wavelengths (red, green, and blue). The different signals from these three wavelengths can be utilized as an MW-PPG signal. Transmission- and reflection-mode PPG signals can also be acquired using smartphone cameras by placing the white LED on the opposite side of the medium or at the same plane of the camera sensor, respectively. Figure 2 illustrates the different modes of PPG signal for a camera-sensor-based PPG system.

In this study, we compare the camera-sensor-based and discrete-LED/PD-based processes of MW-PPG acquisition to estimate in vivo glycated hemoglobin. We also perform comparative analyses on the two PPG-based HbA1c estimation methods described in [20]. In this manuscript, the study of [17] is described as a two-wavelength based method, and the study of [18] is described as a three-wavelength based method for estimating glycated hemoglobin.

2. Methodology

In a recent study [21], we built a finger model based on the hypothesis that when blood enters a tissue the total volume of the tissue expands, increasing the amount of light traversing a path through the tissue medium.

Moreover, the study also hypothesized that the blood constitutes oxyhemoglobin (HbO), deoxyhemoglobin (HHb), and glycated hemoglobin (HbA1c). The HbA1c component of blood is stated to be fixed at a mixture of 98% oxygenated and 2% deoxygenated HbA1c. So, the total absorption coefficient of the blood solution becomes

$$C_a={ϵ}_a^{\mathrm{HbA}1\mathrm{c}}\left(\lambda \right)\times c_{\mathrm{HbA}1\mathrm{c}}+{ϵ}_a^{\mathrm{HbO}}\left(\lambda \right)\times c_{\mathrm{HbO}}+{ϵ}_a^{\mathrm{HHb}}\left(\lambda \right)\times c_{\mathrm{HHb}}$$

(1)

$$C_a={\mu }_a^{\mathrm{HbA}1\mathrm{c}}\left(\lambda \right)+{\mu }_a^{\mathrm{HbO}}\left(\lambda \right)+{\mu }_a^{\mathrm{HHb}}\left(\lambda \right)$$

(2)

In (1) and (2), $C_a$, $ϵ$, and $c$ are the total absorption coefficient of the blood solution, molar absorption coefficient, and molar concentration of the individual component of the solution, respectively.

From another study [20], we can obtain a different blood-solution hypothesis to estimate the amount of glycated hemoglobin in the blood. According to the hypothesis, the blood solution only contains glycated and non-glycated hemoglobin components. So, the blood solution absorption coefficient expression becomes

$$C_a={ϵ}_a^{\mathrm{HbA}1\mathrm{c}}{c}_{\mathrm{HbA}1\mathrm{c}}+{ϵ}_a^{\mathrm{NonHbA}1\mathrm{c}}{c}_{\mathrm{NonHbA}1\mathrm{c} }$$

(3)

$$C_a={\mu }_a^{\mathrm{HbA}1\mathrm{c}}+{\mu }_a^{\mathrm{NonHbA}1\mathrm{c}}$$

(4)

The system from (3) and (4) greatly simplifies the actual finger structure. The non-HbA1c component of (3) and (4) mostly indicates the homogenous mixture of 98% oxyhemoglobin and 2% deoxyhemoglobin compounds. So,

$${ϵ}_a^{\mathrm{NonHbA}1\mathrm{c}}={ϵ}_a^{\mathrm{HbO}}\times 0.98+{ϵ}_a^{\mathrm{HHb}}\times 0.02$$

(5)

Now, from the Beer–Lambert law

$$A=C_{a}d=-\log \left(\frac{I}{I_0}\right)$$

(6)

In (6), $A$, $d$, $I$, and $I_0$ denote the total solution absorbance, light transmission path length, received light, and the incident light, respectively. Applying (6) in (1) and (3) with different wavelengths of light can enable us to calculate the parameters of (1) and (3), respectively.

Now, placing (1) in (6), we get

$$A\left(\lambda \right)=\left({ϵ}_a^{\mathrm{HbA}1\mathrm{c}}\left(\lambda \right)\times c_{\mathrm{HbA}1\mathrm{c}}+{ϵ}_a^{\mathrm{HbO}}\left(\lambda \right)\times c_{\mathrm{HbO}}+{ϵ}_a^{\mathrm{HHb}}\left(\lambda \right)\times c_{\mathrm{HHb}}\right)d=-\log \left(\frac{I\left(\lambda \right)}{I_0\left(\lambda \right)}\right)$$

(7)

Similarly, placing (3) in (6), we get

$$A\left(\lambda \right)=\left({ϵ}_a^{\mathrm{HbA}1\mathrm{c}}{c}_{\mathrm{HbA}1\mathrm{c}}+{ϵ}_a^{\mathrm{NonHbA}1\mathrm{c}}{c}_{\mathrm{NonHbA}1\mathrm{c} }\right)d=-\log \left(\frac{I\left(\lambda \right)}{I_0\left(\lambda \right)}\right)$$

(8)

From the discussion of these models, it can be deduced that the oxyhemoglobin and deoxyhemoglobin are kept fixed in the latter model, which may lead to more errors due to the change of blood oxygenation level (SpO₂) in the bloodstream. The processes of error analysis are described in the following subsections.

A. 

Error analysis between HbA1c estimation models

To analyze the error level of the models, a reference model should be set. As the first model (7) consists of most of the blood parameters (i.e., oxy-, deoxy-, and glycated hemoglobin), it is considered to be the reference model for estimating the error of the second model due to change in SpO₂ levels.

Now, to estimate the error level of the second model, the models are analyzed within a range of HbA1c and SpO₂ levels. The HbA1c range is set to 4–14%, and the SpO₂ is set to 70–100%. For each value of HbA1c and SpO₂, the $c_{\mathrm{HbA}1\mathrm{c}}$, $c_{\mathrm{HbO}}$, and $c_{\mathrm{HHb}}$ parameters are calculated using the following equations and placed in (7) to calculate absorbance values for a certain wavelength.

$$c_{\mathrm{HbA}1\mathrm{c}}=\frac{\%\mathrm{HbA}1\mathrm{c}}{100}\times c_{\mathrm{Wb}}$$

(9)

$$c_{\mathrm{HbO}}=\left(1-\frac{\%\mathrm{HbA}1\mathrm{c}}{100}\right)\times \frac{{\%\mathrm{SpO}}_2}{100}\times c_{\mathrm{Wb}}$$

(10)

$$c_{\mathrm{HHb}}=\left(1-\frac{\%\mathrm{HbA}1\mathrm{c}}{100}\right)\times \left(1-\frac{{\%\mathrm{SpO}}_2}{100}\right)\times c_{\mathrm{Wb}}$$

(11)

$$c_{Wb}=2.2 {\mathrm{mol} \mathrm{L}}^{-1}=2.2\times {10}^{-3}\mathrm{M}$$

(12)

Now from (7), we can define the terms %HbA1c and %SpO₂ as

$$\%\mathrm{HbA}1\mathrm{c}=\frac{c_{\mathrm{HbA}1\mathrm{c}}}{c_{\mathrm{HbA}1\mathrm{c}}+c_{\mathrm{HbO}}+c_{\mathrm{HHb}}}\times 100\%$$

(13)

$${\%\mathrm{SpO}}_2=\frac{c_{\mathrm{HbO}}}{c_{\mathrm{HbO}}+c_{\mathrm{HHb}}}\times 100\%$$

(14)

In (9)–(12), the term $c_{Wb}$ indicates the molar concentration of whole blood.

After calculating the $c_{\mathrm{HbA}1\mathrm{c}}$, $c_{\mathrm{HbO}}$, and $c_{\mathrm{HHb}}$ parameters for a set of HbA1c and SpO₂ values, these are placed in (7) to calculate the absorbance values $A\left({\lambda }_1\right)$, $A\left({\lambda }_2\right)$, and $A\left({\lambda }_3\right)$ for three wavelengths—${\lambda }_1$, ${\lambda }_2$, and ${\lambda }_3$—respectively, considering the value of $d$ as 1 cm. These three absorbance values are then used to reversely calculate the $c_{\mathrm{HbA}1\mathrm{c}}$, $c_{\mathrm{HbO}}$, and $c_{\mathrm{HHb}}$ parameters from (7) and $c_{\mathrm{HbA}1\mathrm{c}}$ and $c_{\mathrm{NonHbA}1\mathrm{c}}$ parameters from (8), using the least square curve fitting algorithm. Due to the differences between the model approximations, the reversely calculated parameters will be different and will result in errors.

B. 

SpO₂ approximation error from model (8)

Though the $c_{\mathrm{HbO}}$ and $c_{\mathrm{HHb}}$ parameters cannot be directly evaluated from (8) to estimate the SpO₂ value, these parameters can be approximated with certain considerations.

For the first consideration from (8), the $c_{\mathrm{NonHbA}1\mathrm{c}}$ parameter can be hypothesized as being very close to $c_{\mathrm{HbO}}$, as the $c_{\mathrm{NonHbA}1\mathrm{c}}$ contains 98% of the $c_{\mathrm{HbO}}$ parameter. So,

$$c_{\mathrm{NonHbA}1\mathrm{c}} \approx c_{\mathrm{HbO}}$$

(15)

Thus, from (9) and (10), we can state that,

$$c_{HbO}=\frac{{\%\mathrm{SpO}}_2}{100}\times c_{\mathrm{Wb}}-c_{\mathrm{HbA}1\mathrm{c}}\times \frac{{\%\mathrm{SpO}}_2}{100}$$

$${\%\mathrm{SpO}}_2=\frac{c_{\mathrm{HbO}}}{c_{\mathrm{Wb}}-c_{\mathrm{HbA}1\mathrm{c}}}\times 100$$

(16)

Now, from (15) and (16) we determine the molar concentration based approximation as below.

$${\%\mathrm{SpO}}_2\approx \frac{c_{\mathrm{NonHbA}1\mathrm{c}}}{c_{\mathrm{Wb}}-c_{\mathrm{HbA}1\mathrm{c}}}\times 100$$

(17)

On the other hand, ${ϵ}_a^{\mathrm{NonHbA}1\mathrm{c}}$ can be considered as a mixture of ${ϵ}_{\mathrm{HbO}}$ and ${ϵ}_{\mathrm{HHb}}$, corresponding to the blood oxygenation level.

$${ϵ}_a^{\mathrm{NonHbA}1\mathrm{c}}={ϵ}_a^{\mathrm{HbO}}\times \frac{{\%\mathrm{SpO}}_2}{100}+{ϵ}_a^{\mathrm{HHb}}\times \left(1-\frac{{\%\mathrm{SpO}}_2}{100}\right)$$

(18)

Now, from (8) it can be said that,

$$\frac{A-c_{\mathrm{HbA}1\mathrm{c}}{ϵ}_a^{\mathrm{HbA}1\mathrm{c}}d}{d c_{\mathrm{NonHbA}1\mathrm{c}}}={ϵ}_a^{\mathrm{NonHbA}1\mathrm{c}}$$

$$\frac{A-c_{\mathrm{HbA}1\mathrm{c}}{ϵ}_a^{\mathrm{HbA}1\mathrm{c}}d}{d c_{\mathrm{NonHbA}1\mathrm{c}}}={ϵ}_a^{\mathrm{HbO}}\times \frac{{\%\mathrm{SpO}}_2}{100}+{ϵ}_a^{\mathrm{HHb}}\times \left(1-\frac{{\%\mathrm{SpO}}_2}{100}\right)$$

So, the molar absorption coefficient based approximation becomes

$${\%\mathrm{SpO}}_2=\frac{\frac{A-c_{\mathrm{HbA}1\mathrm{c}}{ϵ}_a^{\mathrm{HbA}1\mathrm{c}}d}{d c_{\mathrm{NonHbA}1\mathrm{c}}}-{ϵ}_a^{\mathrm{HHb}} }{{ϵ}_a^{\mathrm{HbO}}-{ϵ}_a^{\mathrm{HHb}}}\times 100$$

(19)

Using (17) and (19), SpO₂ values can be approximated for the second model of (8).

C. 

Model error due to sensor-induced noise levels

The PDs used in discrete-LED/PD systems and the color sensor used in the camera-sensor-based PPG signal acquisition system have their own sensitivity, noise level, sampling rate, and quantization limitations. In this study, we perform a noise analysis on the models (7) and (8), which is based on the experimental noise levels obtained from two different sensors. The noise is added to the received light intensity of the sensor and the $c_{HbA1c}$, $c_{HbO}$, and $c_{HHb}$ parameters are reversely calculated using the least square curve fitting method.

To estimate the estimation error due to sensor-induced noise, the HbA1c and SpO₂ levels are taken in a range as previously described. Utilizing (9) to (12), different parameters are evaluated and placed in (7) to calculate the absorbance values $A\left({\lambda }_1\right)$, $A\left({\lambda }_2\right)$, and $A\left({\lambda }_3\right)$ in different wavelengths of light. Two ratio values are also calculated from these absorbance values to cancel out the light traversing path length term, $d$. From the original hypothesis of [21], we can say that the parameter $d$ will change slightly when the blood enters a tissue region. So,

$$\delta d=d_1-d_2 \mathrm{and} \delta A\left(\lambda \right)=A_1\left(\lambda \right)-A_2\left(\lambda \right)$$

Here, $A_1$ and $A_2$ indicate the two absorbance values at $d_1$ and $d_2$, respectively. These two values, $d_1$ and $d_2$, represent the diameter of the blood vessel when blood enters and leaves the vessel, respectively. So, we can define the ratio terms from these equations as (20) and (21).

$$R_1=\frac{\delta A\left({\lambda }_1\right)}{\delta A\left({\lambda }_3\right)}=\frac{{\left[log\frac{I\left(d_2\right)}{I\left(d_1\right)}\right]}_{\lambda 1}}{{\left[log\frac{I\left(d_2\right)}{I\left(d_1\right)}\right]}_{\lambda 3}}$$

(20)

$$R_2=\frac{\delta A\left({\lambda }_2\right)}{\delta A\left({\lambda }_3\right)}=\frac{{\left[log\frac{I\left(d_2\right)}{I\left(d_1\right)}\right]}_{\lambda 2}}{{\left[log\frac{I\left(d_2\right)}{I\left(d_1\right)}\right]}_{\lambda 3}}$$

(21)

At this stage, the received light values are calculated from (6), and a noise parameter is added with the received light for each set of HbA1c and SpO₂ values,

$$I\left(\lambda \right)=I_0{10}^{-A}$$

(22)

$$I^{\prime }\left(\lambda \right)=I\left(\lambda \right)+N$$

(23)

In (23), $I^{\prime }\left(\lambda \right)$ is the noisy received light when a Gaussian noise $N$ is added with the ideal received light, $I\left(\lambda \right)$. The values of the terms $d_1$ and $d_2$ cancel out in the ratio equations.

After adding noise to the received light, the ratio values are calculated using (20) and (21), resulting in $R_1^{\prime }$ and $R_2^{\prime }$. These two ratio values are used to inversely calculate the $c_{\mathrm{HbA}1\mathrm{c}}$, $c_{\mathrm{HbO}}$, and $c_{\mathrm{HHb}}$ parameters from (7) and $c_{\mathrm{HbA}1\mathrm{c}}$ and $c_{\mathrm{NonHbA}1\mathrm{c}}$ parameters from (8), respectively, using the least square curve fitting algorithm. We then calculate the HbA1c estimation error for different models in different sensor-induced noise levels.

3. Results

To quantitatively analyze the errors associated with the analysis methods described in the previous section, we have selected 3 wavelengths of light (${\lambda }_1=465 \mathrm{nm}$, ${\lambda }_2=525 \mathrm{nm}$, and ${\lambda }_3=615 \mathrm{nm}$). The molar absorption coefficients for these selected wavelengths are given in

Table 1. Table of molar absorption coefficients of HbA1c [22], HbO, and HHb [23] for selected wavelengths.

Wavelength (nm)	HbA1c ($M^{-1}c{m}^{-1}$)	HbO ($M^{-1}c{m}^{-1}$)	HHb ($M^{-1}c{m}^{-1}$)
465	549,024.7353	38,440.2	18,701.6
525	455,139.5677	30,882.8	35,170.8
615	170,555.4218	1166.4	7553.4

.

A. 

Error analysis between HbA1c estimation models

Comparing model (7) with the model (8) by the process described in the previous section, taking (7) as a reference, yields two error metrics: HbA1c error and SpO₂ error. Figure 3 illustrates the HbA1c and SpO₂ error for model (7), and the HbA1c error for model (8). The SpO₂ error is not shown in this section as the SpO₂ parameter cannot be directly deduced from the model (8). The SpO₂ approximation results and errors are described in the following sub-section.

In Figure 3, the estimation error associated with the model (7) and (8) based systems with respect to reference values is shown. Figure 3a–b illustrate the estimation error of HbA1c and SpO₂ associated with the model (7), whereas Figure 3c depicts the estimation error of HbA1c with the model (8).

The color bars drawn in Figure 3a–c show the corresponding reference SpO₂ level for each data point. The color bar in Figure 3b shows the reference HbA1c value for each estimation data point of SpO2.

In Figure 3a–b, the model-(7)-based HbA1c and SpO₂ estimation error is in the range of ${10}^{-14}$ and ${10}^{-13}$, respectively. These error values can be associated with floating-point errors in computing algorithms. In Figure 3c, the HbA1c estimation error varies from $-1.306\%$ to $0.047\%$. This large error is due to the lack of parameters for changes in blood oxygenation level.

The mean of the error levels for Figure 3a,c are found to be 8.52⁻¹⁷, −1.60⁻¹⁵, and −0.60, respectively. The standard deviation (SD) values of the error levels are also found to be 2.90⁻¹⁵, 3.31⁻¹⁴, and 0.37, respectively, for the corresponding plots.

B. 

SpO₂ approximation error from model (8)

The blood oxygenation parameter can be approximated from the model (8). Two equations, (17) and (19) were derived to approximate the SpO₂ value. Equation (17) only depends on estimated non-HbA1c and HbA1c molar concentrations, whereas (19) depends on light-wavelength-dependent properties. So, approximating SpO₂ with (19) can render different SpO₂ approximations for different wavelengths of light. Figure 4 shows the SpO₂ approximation error for (17).

The molar concentration based SpO₂ approximation results give an error range of −4% to −1.9% in the range of 70 to 100% reference SpO₂ values. Figure 5 depicts the SpO₂ approximation error of (19) for 465 nm, 525 nm, and 615 nm.

The 3-dimensional plots of Figure 4 and Figure 5a, c illustrate the approximation error of SpO₂ using model (8). The X, Y, and Z axes of the plots are reference HbA1c, reference SpO₂, and SpO₂ approximation error, respectively. The 2-dimensional plot beside the 3-dimensional figure depicts the Y-Z plane, which is the SpO₂ approximation error vs. reference SpO₂ values.

From all these figures (Figure 4 and Figure 5), we can see that the SpO₂ values do not depend on the HbA1c values. Furthermore, for the approximation with (19), the error range changes depend upon the wavelength selection. A reduction in the oxygenation of the blood sample increases the approximation error of SpO₂. As a result, the minimum approximation error can be found for 465 nm (−9 at SpO₂ 70% and about 1 at SpO₂ 100%).

C. 

Model error due to sensor induced noise levels

To examine the sensor-induced noise levels in the HbA1c estimation models, we considered two sensors for PPG acquisition. One of the sensors is the Osram SFH7050 with AFE4404 and the other is the TCS34725 color sensor. The Osram SFH7050 and AFE4404 pair are considered as a discrete-LED/PD-based PPG acquisition system. On the other hand, the TCS34725 is considered to be a camera-sensor-based PPG acquisition system. According to our tests on these sensors, the standard deviation (SD) of error values generated by the AFE4404 front end is $1.820\times {10}^{-4}$ for transmission-mode PPG, and $1.480\times {10}^{-4}$ for reflection mode PPG signals. The TCS34725 sensor has an SD of $3.640\times {10}^{-5}$ and $6.711\times {10}^{-5}$ for transmission and reflection mode PPG signals, respectively.

Considering the method described in subsection C of the Methodology section, the width of the Gaussian function is set using the SD values obtained from the different sensors for different modes, as given previously. Figure 6 shows the HbA1c values estimated from the noise-prone ratio values ($R_1$ and $R_2$) for the AFE4404 based sensor and PPG mode. On the other hand, Figure 7 illustrates the HbA1c estimation error for the TCS34725 sensor.

In Figure 6, the estimation error of HbA1c is illustrated with respect to reference HbA1c values for model (7) (Figure 6a–b) and model (8) (Figure 6c–d), respectively. From all these figures it is evident that the estimation error level increases as the HbA1c level increases. This is due to the high light attenuation property of HbA1c molecules. An increment of HbA1c molecules inside a solution can lead to reduced amplitudes in received light signals, resulting in greater errors in estimation.

The standard deviation (SD) of the erroneous estimation for the AFE4404-based sensor of the model (7) is found to be 0.258 and 0.317 for reflection and transmission modes, respectively. On the other hand, model (8) has an SD of 0.114 and 0.142 for reflection and transmission modes, respectively.

Figure 7 also depicts similar illustrations to Figure 6. However, since the TCS34725 sensor receives less signal noise than the AFE4404, the SD of the estimation error of HbA1c is reduced greatly, which can be seen in Figure 7.

The SD of the erroneous estimation of the model (7) is found to be 0.117 and 0.063 for reflection and transmission modes, respectively. For model (8), SD is found to be 0.052 and 0.028, in reflection and transmission modes, respectively.

4. Discussion

From the above discussions that assess the two models for their different errors in estimating in vivo glycated hemoglobin values, certain important points can be made. Upon comparing the two models (model (7) and model (8)), it can be easily seen that model (8) is a simplified version of model (7). Model (8) combines the oxygenated and deoxygenated hemoglobin parts into one variable. For this reason, a change in the blood oxygenation value (i.e., a change in the ratio of oxygenated and deoxygenated hemoglobin count in the bloodstream) can significantly impair the HbA1c estimation accuracy of model (8).

On the contrary, model (7) is more susceptible to the sensor noise, degrading the estimation accuracy of glycated hemoglobin as compared to model (8). This occurs as model (7) is more complex and more parameters are built into the model equation itself. As a result, any error in the input of the model amplifies the error with the model parameters and gives more erroneous results. From Figure 6 and Figure 7, we can see that the error level of model (7) is almost double when compared to the error level of the model (8) for both modes of PPG signal using the AFE4404-based sensor and TCS34725-based sensor. Though the sensitivity of model (7) to noise is large compared to model (8), model (7) can be made robust against sensor noise by taking multiple sampling processes in the application of the model. The sensors usually exhibit random noise in the signals. Taking the arithmetic mean of several samples of measurement can ensure the reduction of random noise, hence reducing random estimation error.

From Figure 6 and Figure 7, it is also evident that the more the HbA1c components are present in the blood solution, the greater the error level becomes. This is due to the fact that the glycated hemoglobin component of blood has a much higher molar absorption coefficient than that of the other two components of blood considered in this study (HHb and HbO). Thus, an increase in HbA1c decreases the received light intensity, and consequently decreases the signal-to-noise ratio for a fixed amount of added noise, resulting in poor estimation accuracy.

5. Conclusions

In this study, we performed a quantitative analysis on two models for the non-invasive estimation of glycated hemoglobin (HbA1c). Comparing the two models, by taking one as a reference for different parametric states, the two-wavelength model was found to have errors in the range of −1.306% to 0.047% of HbA1c, depending on the amount of oxygenated and deoxygenated hemoglobin compounds present in the blood solution. On the other hand, the three-wavelength model’s HbA1c-estimation error was found to have a magnitude of ${10}^{-14} \%$.

From the approximation of the blood oxygenation (SpO₂) value of the two-wavelength model, it can be seen that a lower error can be attained by using the molar concentration based SpO₂ approximation technique, as compared to the molar absorption coefficient based method. The method based on the molar absorption coefficient depends on the wavelength of the light and, in our experiment, we observed that the light at a wavelength of 465 nm produced the lowest error for the two-wavelength-based SpO₂ approximation.

Finally, from the estimation error of HbA1c due to sensor noise level, it can be seen that the two-wavelength-based model has a higher resistance to sensor noise, and that the three-wavelength-based model is more susceptible to noise due to the higher complexity of the model. Though the two-wavelength based model has a low error level even when the sensor noise is high, the model performs poorly (error range varies between −1.306% and 0.047% with the change in SpO₂ values) when estimating the glycated hemoglobin as compared to the three-wavelength based model. This is because the two-wavelength based model does not consider the two major hemoglobin components of blood.