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

applied
 sciences
Article
Quantitative Analysis of Different Multi-Wavelength PPG
Devices and Methods for Noninvasive In-Vivo Estimation of
Glycated Hemoglobin
Shifat Hossain , Chowdhury Azimul Haque and Ki-Doo Kim *

 Department of Electronics Engineering, Kookmin University, Seoul 02707, Korea;
 shifathosn@kookmin.ac.kr (S.H.); c_azimul@kookmin.ac.kr (C.A.H.)
 * Correspondence: kdk@kookmin.ac.kr

 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
Citation: Hossain, S.; Haque, C.A.;
Kim, K.-D. Quantitative Analysis of
 molar concentration based technique (−4% to −1.9% at 70% to 100% of reference SpO2 ) as compared
Different Multi-Wavelength PPG to the molar absorption coefficient based technique. Additionally, the two-wavelength model is less
Devices and Methods for susceptible to sensor noise levels (max SD of %error, 0.142%), as compared to the three-wavelength
Noninvasive In-Vivo Estimation of model (max SD of %error, 0.317%). Despite having a higher susceptibility to sensor noise, the three-
Glycated Hemoglobin. Appl. Sci. wavelength model can estimate HbA1c values more accurately; this is because it takes the major
2021, 11, 6867. https://doi.org/ components of blood into account and thus becomes a more realistic model.
10.3390/app11156867

 Keywords: glycated hemoglobin; error analysis; sensors; mathematical models; photoplethysmography
Academic Editors: Alberto Belli,
Paola Pierleoni and Sara Raggiunto

Received: 29 June 2021
 1. Introduction
Accepted: 25 July 2021
Published: 26 July 2021
 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
Publisher’s Note: MDPI stays neutral
 or radial artery is illuminated with light of multiple wavelengths. The light waves interact
with regard to jurisdictional claims in
 with the tissues and blood components and are absorbed or scattered in the medium. As the
published maps and institutional affil- blood volume changes in a certain location of the human body, due to the pulsatile nature of
iations. 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
Copyright: © 2021 by the authors.
 property of the human body that is measured with PPG signals is the blood oxygenation
Licensee MDPI, Basel, Switzerland.
 (SpO2 ) parameter [3–5]. This parameter indicates the percent amount of oxygenated
This article is an open access article
 hemoglobin with respect to total hemoglobin count. Recently, a study was conducted to
distributed under the terms and warn for potential infection by COVID-19 by estimating SpO2 using PPG signals [3]. The
conditions of the Creative Commons other quantitative properties include blood pressure [4], hypo- and hypervolemia [5], and
Attribution (CC BY) license (https:// blood glucose levels [6,7]. The time-domain properties require single-wavelength PPG
creativecommons.org/licenses/by/ (SW-PPG) to evaluate. On the other hand, to estimate the quantitative properties, multiple
4.0/). wavelengths of PPG (MW-PPG) signals are required.

Appl. Sci. 2021, 11, 6867. https://doi.org/10.3390/app11156867 https://www.mdpi.com/journal/applsci

Appl. Sci. 2021, 11, 6867 2 of 14

 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 [13–16].
 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 proce-
 dures 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.

Appl. Sci. 2021, 11, 6867 3 of 14

 Transmission- and reflection-mode PPG signals can also be acquired using smartphone
Appl. Sci. 2021, Figure
 11, x FOR cameras by placing the white LED on the opposite side of the medium or at the same 3plane
 1. PEER REVIEW
 Discrete-LED/PD-based transmission- (left) and reflection-mode (right) PPG acquisition devices. of 15
 of the camera sensor, respectively. Figure 2 illustrates the different modes of PPG signal for
 a camera-sensor-based PPG system.
 The advent of wearable and mobile devices has led to an exponential increase in mo-
 bile-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.
 Figure 1. Discrete-LED/PD-based transmission- (left) and reflection-mode (right) PPG acquisition devices.
 Figure 1. Discrete-LED/PD-based transmission- (left) and reflection-mode (right) PPG acquisition devices.

 The advent of wearable and mobile devices has led to an exponential increase in mo-
 bile-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
 Figure 2. Camera-sensor white-LED MW-PPG system. The (left) figure is the transmission mode and the (right) figure is
 Figure 2. Camera-sensor white-LED MW-PPG system. The
 for a camera-sensor-based PPGleftsystem.
 figure is the transmission mode and the right figure is the
 the reflection mode.
 reflection mode.
 In this study, we compare the camera-sensor-based and discrete-LED/PD-based pro-
 In this study, we compare the camera-sensor-based and discrete-LED/PD-based pro-
 cesses of MW-PPG acquisition to estimate in vivo glycated hemoglobin. We also perform
 cesses of MW-PPG
 comparative analysesacquisition
 on the twotoPPG-based
 estimate inHbA1c
 vivo glycated hemoglobin.
 estimation We also perform
 methods described in [20].
 comparative analyses on the two PPG-based HbA1c estimation methods described
 In this manuscript, the study of [17] is described as a two-wavelength based method, in [20].
 In this manuscript, the study of [17] is described as a two-wavelength based
 and the study of [18] is described as a three-wavelength based method for estimatingmethod, and
 the study of [18]
 glycated hemoglobin. is described as a three-wavelength based method for estimating glycated
 hemoglobin.
 2. Methodology
 2. Methodology
 In a recent study [21], we built a finger model based on the hypothesis that when
 bloodIn a recent
 enters study
 a tissue the[21],
 totalwe built of
 volume a finger model
 the tissue basedincreasing
 expands, on the hypothesis
 the amountthat
 of when
 light
 blood enters
 traversing a tissue
 a path the total
 through volume
 the tissue of the tissue expands, increasing the amount of light
 medium.
 traversing a path
 Moreover, thethrough the tissue
 study also medium.that the blood constitutes oxyhemoglobin
 hypothesized
 Figure 2. Camera-sensor white-LED MW-PPG system. The
 (HbO), deoxyhemoglobin left figure
 (HHb), is the transmission
 and glycated hemoglobinmode and the right
 (HbA1c). The figure
 HbA1c is the
 compo-
 reflection mode. nent 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
 In this study, we compare the camera-sensor-based and discrete-LED/PD-based pro-
 HbA1c
 cesses of MW-PPGCa = eacquisition
 a (λ) ×to cHbA1c + eHbO
 estimate ain vivo
 (λ) ×glycated eHHb
 cHbO + hemoglobin.
 a (λ) × cHHbWe also perform (1)
 comparative analyses on the two PPG-based HbA1c estimation methods described in [20].
 HbA1c
 In this manuscript, the study Ca =ofµ[17]
 a is(λ ) + µHbO
 describeda (λ)a +
 as µHHb (λ)
 two-wavelength
 a based method, and (2)
 the study
 In (1)of [18](2),
 and is described
 Ca , e, andas a three-wavelength
 c are the total absorptionbased method for
 coefficient of estimating glycated
 the blood solution,
 hemoglobin.
 molar absorption coefficient, and molar concentration of the individual component of the
 solution, respectively.
 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.

Appl. Sci. 2021, 11, 6867 4 of 14

 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

 Ca = eHbA1c
 a cHbA1c + eNonHbA1c
 a cNonHbA1c (3)

 Ca = µHbA1c
 a + µNonHbA1c
 a (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% oxyhe-
 moglobin and 2% deoxyhemoglobin compounds. So,

 eNonHbA1c
 a = eHbO
 a × 0.98 + eHHb
 a × 0.02 (5)

 Now, from the Beer–Lambert law
  
 I
 A = Ca d = − log (6)
 I0

 In (6), A, d, I, and I0 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
  
 
 HbA1c HbO HHb
  I (λ)
 A(λ) = ea (λ) × cHbA1c + ea (λ) × cHbO + ea (λ) × cHHb d = − log (7)
 I0 (λ)
 Similarly, placing (3) in (6), we get
  
   I (λ)
 A(λ) = eHbA1c
 a cHbA1c + eNonHbA1c
 a cNonHbA1c d = − log (8)
 I0 (λ)

 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 cHbA1c , cHbO , and cHHb parameters are
 calculated using the following equations and placed in (7) to calculate absorbance values
 for a certain wavelength.
 %HbA1c
 cHbA1c = × cWb (9)
 100
  
 %HbA1c %SpO2
 cHbO = 1 − × × cWb (10)
 100 100
    
 %HbA1c %SpO2
 cHHb = 1 − × 1− × cWb (11)
 100 100
 cWb = 2.2 mol L−1 = 2.2 × 10−3 M (12)

Appl. Sci. 2021, 11, 6867 5 of 14

 Now from (7), we can define the terms %HbA1c and %SpO2 as
 cHbA1c
 %HbA1c = × 100% (13)
 cHbA1c + cHbO + cHHb
 cHbO
 %SpO2 = × 100% (14)
 cHbO + cHHb
 In (9)–(12), the term cWb indicates the molar concentration of whole blood.
 After calculating the cHbA1c , cHbO , and cHHb parameters for a set of HbA1c and SpO2
 values, these are placed in (7) to calculate the absorbance values A(λ1 ), A(λ2 ), and A(λ3 )
 for three wavelengths—λ1 , λ2 , and λ3 —respectively, considering the value of d as 1 cm.
 These three absorbance values are then used to reversely calculate the cHbA1c , cHbO , and
 cHHb parameters from (7) and cHbA1c and cNonHbA1c 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 cHbO and cHHb parameters cannot be directly evaluated from (8) to esti-
 mate the SpO2 value, these parameters can be approximated with certain considerations.
 For the first consideration from (8), the cNonHbA1c parameter can be hypothesized as
 being very close to cHbO , as the cNonHbA1c contains 98% of the cHbO parameter. So,

 cNonHbA1c ≈ cHbO (15)

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

 %SpO2 %SpO2
 c HbO = × cWb − cHbA1c ×
 100 100
 cHbO
 %SpO2 = × 100 (16)
 cWb − cHbA1c
 Now, from (15) and (16) we determine the molar concentration based approximation
 as below.
 cNonHbA1c
 %SpO2 ≈ × 100 (17)
 cWb − cHbA1c
 On the other hand, eNonHbA1c
 a can be considered as a mixture of eHbO and eHHb ,
 corresponding to the blood oxygenation level.
  
 %SpO2 %SpO2
 eNonHbA1c
 a = e HbO
 a × + e HHb
 a × 1 − (18)
 100 100

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

 A − cHbA1c eHbA1c
 a d
 = eNonHbA1c
 a
 d cNonHbA1c

 A − cHbA1c eHbA1c
  
 a d HbO %SpO2 HHb %SpO2
 = ea × + ea × 1−
 d cNonHbA1c 100 100
 So, the molar absorption coefficient based approximation becomes

 A−cHbA1c eHbA1c d
 a
 d cNonHbA1c − eHHb
 a
 %SpO2 = HbO HHb
 × 100 (19)
 ea − ea

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

Appl. Sci. 2021, 11, 6867 6 of 14

 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(λ1 ), A(λ2 ), and A(λ3 )
 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,
 δd = d1 − d2 and δA(λ) = A1 (λ) − A2 (λ)
 Here, A1 and A2 indicate the two absorbance values at d1 and d2 , respectively. These
 two values, d1 and d2 , 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). h i
 I ( d2 )
 δA(λ1 ) log I (d1 ) λ1
 R1 = = h i (20)
 δA(λ3 ) I (d )
 log I (d2 )
 1 λ3
 h i
 I ( d2 )
 δA(λ2 ) log I (d )
 1
 R2 = = h iλ2 (21)
 δA(λ3 ) I ( d2 )
 log I (d )
 1 λ3
 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 (λ) = I0 10− A (22)
 0
 I (λ) = I (λ) + N (23)
 In (23), I 0 (λ) is the noisy received light when a Gaussian noise N is added with the
 ideal received light, I (λ). The values of the terms d1 and d2 cancel out in the ratio equations.
 After adding noise to the received light, the ratio values are calculated using (20) and
 (21), resulting in R10 and R20 . These two ratio values are used to inversely calculate the
 cHbA1c , cHbO , and cHHb parameters from (7) and cHbA1c and cNonHbA1c 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 (λ1 = 465 nm, λ2 = 525 nm,
 and λ3 = 615 nm). The molar absorption coefficients for these selected wavelengths are
 given in Table 1.

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

 HbA1c HbO HHb
 Wavelength (nm)
 (M−1 cm−1 ) (M−1 cm−1 ) (M−1 cm−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

HbA1c HbO HHb
 Wavelength (nm)
 ( − − ) ( − )
 − 
 ( − )
 − 

 465 549,024.7353 38,440.2 18,701.6
Appl. Sci. 2021, 11, 6867 525 455,139.5677 30,882.8 35,170.8 7 of 14
 615 170,555.4218 1166.4 7553.4

 A. Error analysis between HbA1c estimation models
 A. Error analysis between HbA1c estimation models
 Comparing model (7) with the model (8) by the process described in the previous
 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.
 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
 Figure 3 illustrates the HbA1c and SpO2 error for model (7), and the HbA1c error for model
 model (8). The SpO2 error is not shown in this section as the SpO2 parameter cannot be
 (8). The SpO2 error is not shown in this section as the SpO2 parameter cannot be directly
 directly deduced from the model (8). The SpO2 approximation results and errors are de-
 deduced from the model (8). The SpO2 approximation results and errors are described in
 scribed in the following sub-section.
 the following sub-section.

Appl. Sci. 2021, 11, x FOR PEER REVIEW 8 of 15

 (a) (b)

 (c)
 Figure 3. Error analysis between HbA1c estimation models: (a) HbA1c error for model (7), (b) SpO SpO22 estimation error for
 (7), and
 model (7), and (c)
 (c) HbA1c
 HbA1cestimation
 estimationerror
 errorfor
 formodel
 model(8).
 (8).For
 For(a,c)
 (a, c),
 thethe color
 color barbar represents
 represents the the reference
 reference SpOSpO 2 values
 2 values andand
 the
 the color bar in (b) represents reference HbA1c
 color bar in (b) represents reference HbA1c values.values.

 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 SpO22 associated
 associated with
 with the
 the model
 model (7),
 (7), whereas Figure 3c depicts the estimation
 error of HbA1c with the model (8).
 color bars
 The color bars drawn
 drawn in in Figures
 Figure 3a–c
 3a–cshow
 show thethe corresponding
 corresponding reference
 reference SpOSpO22 level
 for each data point. The The color
 color bar
 bar in Figure 3b shows the reference HbA1c value for each
 estimation data point of SpO2.
 Figure 3a–b,
 In Figures 3a–b,thethemodel-(7)-based
 model-(7)-basedHbA1c HbA1cand andSpO
 SpO22 estimation
 estimation error
 error is
 is in the range
 of 10 −−14
 14 and 10−13−13, respectively. These error values can be associated with floating-point
 10 and 10 , respectively. These error values can be associated
 errors in computing algorithms. In In Figure
 Figure 3c,3c, the
 the HbA1c estimation
 estimation error varies from
 −1.306% to
 −1.306% to0.047%.
 0.047%.ThisThislarge
 largeerror
 errorisisdue
 duetotothe
 thelack
 lackof
 ofparameters
 parameters for
 for changes
 changes inin blood
 blood
 oxygenation level.
 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

Appl. Sci. 2021, 11, 6867 8 of 14

 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
Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 15
 different SpO2 approximations for different wavelengths of light. Figure 4 shows the SpO2
 approximation error for (17).

 Molarconcentration
 Figure4.4.Molar
 Figure concentrationbased
 basedSpO
 SpO2 2approximation
 approximationerror
 errorfor
 for(17)
 (17)from
 fromthe
 themodel
 model(8).
 (8).

 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 Figures 4 and 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 (Figures 4 and 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(a)
 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 × 10−4 for transmission-mode PPG, and 1.480 × 10−4
 for reflection mode PPG signals. The TCS34725 sensor has an SD of 3.640 × 10−5 and
 6.711 × 10−5 for transmission and reflection mode PPG signals, respectively.

Appl. Sci. 2021, 11, 6867 9 of 14
 Figure 4. Molar concentration based SpO2 approximation error for (17) from the model (8).

 (a)

Appl. Sci. 2021, 11, x FOR PEER REVIEW 10 of 15

 (b)

 (c)
 Figure
 Figure 5.
 5. Molar
 Molar absorption
 absorption coefficient
 coefficient based
 based SpO
 SpO22approximation
 approximationerror
 errorof
 of(19)
 (19)for
 for(a)
 (a)465
 465nm,
 nm,(b)
 (b)525
 525nm,
 nm,and
 and(c)
 (c)615
 615nm.
 nm.
 The
 The color bar represents the reference HbA1c values.

 The 3-dimensional plots of Figures 4 and 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. ref-
 erence SpO2 values.
 From all these figures (Figures 4 and 5), we can see that the SpO2 values do not de-

Appl. Sci. 2021, 11, 6867 10 of 14

 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 (R1 and R2 ) 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.
Appl. Sci. 2021, 11, x FOR PEER REVIEW Figure 7 also depicts similar illustrations to Figure 6. However, since the TCS34725
 11 of 15
 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.

 (a) (b)

 (c) (d)
 Figure 6. HbA1c estimation error due to AFE4404-based sensor-induced
 Figure sensor-induced noise.
 noise. Model-(7)-based HbA1c estimation values
 are illustrated
 are illustrated for
 for (a)
 (a) reflection-mode
 reflection-mode and
 and (b)
 (b) transmission-mode
 transmission-mode PPGPPG signal.
 signal. Model-(8)-based
 Model-(8)-based estimation
 estimation values
 values are
 are given
 given
 for (c) reflection-mode and (d) transmission-mode PPG signals. The color bar represents the reference SpO2
 for (c) reflection-mode and (d) transmission-mode PPG signals. The color bar represents the reference SpO2 values. values.

(c) (d)
 Figure 6. HbA1c estimation error due to AFE4404-based sensor-induced noise. Model-(7)-based HbA1c estimation values
Appl. Sci.
 are2021, 11, 6867for (a) reflection-mode and (b) transmission-mode PPG signal. Model-(8)-based estimation values are given
 illustrated 11 of 14
 for (c) reflection-mode and (d) transmission-mode PPG signals. The color bar represents the reference SpO2 values.

Appl. Sci. 2021, 11, x FOR PEER REVIEW 12 of 15

 (a) (b)

 (c) (d)
 Figure 7. HbA1c estimation error due to TCS34725
 TCS34725 sensor-induced noise. Model-(7)-based
 Model-(7)-based HbA1c estimation
 estimation values
 values are
 illustrated for (a) reflection-mode and (b) transmission-mode PPG signal. Model-(8)-based estimation values are given for
 (c)
 (c) reflection-mode and (d)
 reflection-mode and (d) transmission-mode
 transmission-mode PPG
 PPG signals.
 signals. The
 The color
 color bar
 bar represents
 represents the
 the reference
 reference SpO2
 SpO2 values.
 values.

 In
 TheFigure
 SD of 6, thethe estimation
 erroneous error ofofHbA1c
 estimation the modelis illustrated
 (7) is found with
 to be respect to reference
 0.117 and 0.063 for
 HbA1c
 reflectionvalues for model (7)modes,
 and transmission (Figurerespectively.
 6a–b) and model (8) (Figure
 For model (8), SD6c–d), respectively.
 is found to be 0.052From
 and
 0.028,
 all in figures
 these reflection and
 it is transmission
 evident that themodes, respectively.
 estimation error level increases as the HbA1c level
 increases. This is due to the high light attenuation property of HbA1c molecules. An in-
 4. Discussion
 crement of HbA1c molecules inside a solution can lead to reduced amplitudes in received
 From
 light signals, theresulting
 above discussions
 in greater errors that assess the two models for their different errors in
 in estimation.
 estimating in vivo glycated
 The standard deviationhemoglobin
 (SD) of thevalues, certain
 erroneous important
 estimation forpoints can be made. Upon
 the AFE4404-based sen-
 comparing
 sor of the modelthe two(7)models
 is found (model (7) and
 to be 0.258 model
 and 0.317(8)),
 for itreflection
 can be easily
 and seen that model
 transmission (8) is
 modes,
 a simplified version
 respectively. of model
 On the other hand, (7).model
 Model(8)(8)has
 combines
 an SD ofthe oxygenated
 0.114 and 0.142and for deoxygenated
 reflection and
 hemoglobin parts
 transmission modes, into one variable. For this reason, a change in the blood oxygenation
 respectively.
 valueFigure
 (i.e., a7change in the ratio
 also depicts similar of oxygenated
 illustrationsand deoxygenated
 to Figure hemoglobin
 6. However, since thecount in the
 TCS34725
 bloodstream) can significantly impair the HbA1c estimation accuracy
 sensor receives less signal noise than the AFE4404, the SD of the estimation error of HbA1c of model (8).
 On the
 is reduced contrary,
 greatly, whichmodel can be (7) seen
 is more susceptible
 in Figure 7. to the sensor noise, degrading the
 estimation
 The SDaccuracy of glycated
 of the erroneous hemoglobin
 estimation of the as
 modelcompared to model
 (7) is found to be (8).
 0.117This
 andoccurs as
 0.063 for
 model (7) is more complex and more parameters are built into the
 reflection and transmission modes, respectively. For model (8), SD is found to be 0.052 model equation itself. As
 a result,
 and any
 0.028, in error in theand
 reflection input of the model
 transmission amplifies
 modes, the error with the model parameters
 respectively.
 and gives more erroneous results. From Figures 6 and 7, we can see that the error level
 ofDiscussion
 4. 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
 From the above discussions that assess the two models for their different errors in
 the sensitivity of model (7) to noise is large compared to model (8), model (7) can be made
 estimating in vivo glycated hemoglobin values, certain important points can be made.
 robust against sensor noise by taking multiple sampling processes in the application of
 Upon comparing the two models (model (7) and model (8)), it can be easily seen that
 the model. The sensors usually exhibit random noise in the signals. Taking the arithmetic
 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).

Appl. Sci. 2021, 11, 6867 12 of 14

 mean of several samples of measurement can ensure the reduction of random noise, hence
 reducing random estimation error.
 From Figures 6 and 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 conse-
 quently 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.

 Author Contributions: S.H.: conceptualization, methodology, software, validation, data curation,
 visualization. C.A.H.: software, validation, data curation, investigation. K.-D.K.: conceptualization,
 validation, supervision, formal analysis, funding acquisition. All authors have read and agreed to
 the published version of the manuscript.
 Funding: This research was supported by the Basic Science Research Program through the National
 Research Foundation (NRF) of Korea, funded by the Ministry of Education (NRF-2019R1F1A1062317),
 and was also supported by the National Research Foundation of Korea Grant, funded by the Ministry
 of Science, ICT, and Future Planning [2015R1A5A7037615].
 Conflicts of Interest: The authors hereby declare that they have no conflict of interest. The funders
 had no role in the design of the study; in the collection, analyses, or interpretation of data; in the
 writing of the manuscript; or in the publication of the results.

Appl.
Appl. Sci.
 Sci. 2021, 11, 6867
 2021, 11, x FOR PEER REVIEW 13 14 of 15
 of 14
 Appl. Sci.
 Appl. Sci. 2021,
 2021, 11,
 11, xx FOR
 FOR PEER
 PEER REVIEW
 REVIEW 1414ofof1515

Short
Short Biography ofof Authors
 Authors
 Short Biography
 Biography of Authors
 Short Biography of Authors
 Shifat
 Shifat Hossain
 Hossain waswas was
 born born
 in inBangladesh,
 Dhaka, Bangladesh, on 10HeMay 1994.a He areceived a Bach-
 Shifat Hossain
 Shifat Hossain born
 was born inDhaka,
 in Dhaka,Dhaka, Bangladesh,
 Bangladesh, on
 on 10on 10
 May10May
 May1994.
 1994. He
 Hereceived
 received
 1994. aBach-
 Bachelor
 received of Science
 Bach-
 elorelor
 (B.Sc.) of Science
 degree (B.Sc.)
 in Electrical and degree in Electrical
 Electronic Engineering and Electronic
 from the Khulna Engineering
 University from
 of the
 Engineering
 elor of
 of Science
 Science (B.Sc.)
 (B.Sc.) degree
 degreein inElectrical
 ElectricalandandElectronic
 ElectronicEngineering
 Engineeringfrom fromthethe
 and Khulna
 Technology,
 Khulna University
 Bangladesh, of Engineering
 in 2017. and
 Later he Technology,
 received his Bangladesh,
 Master of Science in 2017.
 (M.Sc.) Later
 degreeheinre-
 Khulna University
 University of ofEngineering
 Engineeringand andTechnology,
 Technology,Bangladesh,
 Bangladesh,inin2017.2017.Later
 Laterhehere-re-
 2021 from
 ceived Department of Electronics Engineering, Kookmin University, Seoul, South Korea. He is
 ceived
 ceived
 currently hishis
 his Master
 Master
 Master
 appointed
 of
 as
 of Science
 ofaScience
 Science
 full-time
 (M.Sc.)
 (M.Sc.)(M.Sc.)
 degree
 degree
 researcher in
 degree
 in
 in2021
 the 2021in 2021
 from
 from
 Department
 from Department
 Department
 Department
 of Electronic
 of Electronics
 ofofElectronics
 Electronics
 Engineering, Kookmin
 Engineering,
 Engineering,
 Engineering, Kookmin
 Kookmin
 Kookmin University, Seoul,
 University, South
 SouthKorea.
 Seoul, South He isiscurrently
 Korea. appointed
 He is currently asas
 appointed as
 University. He worked as aUniversity,
 Lecturer with Seoul, Korea.of
 the Department He currently
 Electrical appointed
 and Electronic Engineering,
 a full-time researcher
 a full-time researcherin the Department
 inDepartment
 the Departmentof Electronic Engineering,
 of Electronic Kookmin
 Engineering, Univer-
 Kookmin Univer-
 a full-time
 Daffodil researcher
 International in the
 University from September of Electronic Engineering,
 2018 to February Kookmin
 2019. His currentUniver-
 fields of study
 sity. HeHe
 sity. worked
 workedas a as
 Lecturer
 a with the
 Lecturer withDepartment
 the of Electrical
 Department of and Electronic
 Electrical and Engi-
 Electronic Engi-
 sity. He worked as a Lecturer with the Department of
 are machine learning algorithms and computational biomedical engineering. Electrical and Electronic Engi-
 neering, Daffodil International University from September 2018 to February 2019.
 neering,
 neering, Daffodil
 Daffodil International
 International University
 University from September
 from September 2018 to 2018 to February
 February 2019. 2019.
 His current fields of study are machine learning algorithms and computational bio-
 His current
 His currentfields of study
 fields are machine
 of study learning
 are machine algorithms
 learning and computational
 algorithms bio-
 and computational bio-
 medical engineering.
 medical
 medical engineering.
 engineering.
 Chowdhury
 Chowdhury Azimul
 Azimul Haque
 Haque received
 received a Bachelor
 a Bachelor of Science
 of Science (B.Sc.)
 (B.Sc.) degreedegree in electrical
 in electrical and electronic
 Chowdhury
 Chowdhury Azimul
 AzimulHaque received
 Haque a Bachelor
 received a of Science
 Bachelor of (B.Sc.)
 Science degree
 (B.Sc.)in electrical
 degree in electrical
 and electronic
 engineering engineering from Khulna University of Engineering and Technology
 and electronic engineering from Khulna University of Engineering and Technology in 2019.
 from Khulna University of Engineering and Technology (KUET), Bangladesh,
 and
 (KUET), electronic engineering
 Bangladesh, in 2019. He from
 is Khulna
 currently University
 pursuing a of
 MasterEngineering
 of Science and
 (M.Sc.)Technology
 He is currently pursuing a Master of Science (M.Sc.) degree in electronics engineering with Kookmin
 (KUET), Bangladesh, in 2019. He is currently pursuing a Master of Science (M.Sc.)
 (KUET),
 degree
 University, Bangladesh,
 inSeoul,
 electronics Hisin 2019.with
 Korea.engineering
 current He Kookmin
 is currently
 research pursuing
 University,
 interests include a Master
 Seoul, Korea.
 biomedical of Science
 His
 signal cur- (M.Sc.)
 processing and
 degree in electronics engineering with Kookmin University, Seoul, Korea. His cur-
 Monte
 rent Carlo
 research
 degree simulations
 in in
 electronics computational
 interests include biomedical
 engineering biomedical
 signal
 with engineering.
 processing
 Kookmin and Monte
 University, CarloKorea.
 Seoul, simula-His cur-
 rent research interests include biomedical signal processing and Monte Carlo simula-
 tions inresearch
 rent computational biomedical
 interests includeengineering.
 biomedical signal processing and Monte Carlo simula-
 tions in computational biomedical engineering.
 tions in computational biomedical engineering.

 Ki-Doo Kim received a B.S. degree in Electronic Engineering from Sogang Univer-
 Ki-Doo Kim received a B.S. degree in Electronic Engineering from Sogang Univer-
 sity, Seoul,
 Ki-Doo South Korea,
 Kim received a B.S. in 1980,inand
 degree the M.S.Engineering
 Electronic and Ph.D. degrees fromUniversity,
 from Sogang Pennsylvania Seoul, South
 sity, Seoul, Kim
 Ki-Doo Southreceived
 Korea, ina1980,B.S. and the in M.S. and Ph.D.Engineering
 degrees fromfromPennsylvania
 State
 Korea, inUniversity,
 1980, and the USA,
 M.S.inand
 1988 anddegree
 Ph.D. degrees Electronic
 1990, respectively.
 from He is currently
 Pennsylvania working
 State University, Sogang Univer-
 as ain 1988
 USA, and
 State
 sity,University,
 Seoul, USA, in 1988 and 1990, respectively. He is currently working as a
 1990,
 Professor with South
 respectively. Korea,
 He School
 the is currently in 1980,Engineering,
 working
 of Electrical and the M.S.Kookmin
 as a Professor and Ph.D.
 with degrees
 the University,
 School from He
 of Electrical
 Seoul. Pennsylvania
 Engineering,
 Professor with theSeoul.
 SchoolHe ofworked
 Kookmin
 StateUniversity,
 worked University,
 as a ResearchUSA,EngineerinElectrical
 1988 as
 withandtheaEngineering,
 Research Kookmin
 Engineer
 1990, respectively.
 Agency for Defense withUniversity,
 HetheisAgency Seoul.
 currently
 Development in
 He Devel-
 forKorea
 Defense
 working as a
 worked
 opment in as a
 Korea Research
 from 1980 Engineer
 to 1985. with
 He the
 joined Agency
 Kookmin for Defense
 University Development
 as an Assistant in Korea
 Professor in 1991.
 from 1980 to 1985.
 Professor with He thejoined
 School Kookmin University
 of Electrical as an Assistant
 Engineering, Kookmin Professor in 1991. Seoul. He
 University,
 from
 HeHe
 also 1980 toas
 served 1985. He joined
 a Visiting Kookmin
 Scholar with University
 the EE EE as an Assistant
 Department, UCSD, Professor
 USA, fromfromin 1991.
 1997 to 1998. His
 also
 worked served
 as aasResearch
 a Visiting Scholar
 Engineer with
 withthe Department,
 the Agency UCSD,
 for Defense USA,
 Development 1997 in Korea
 He also
 current served
 research as a Visiting
 interests include Scholar
 digital with the EE Department,
 communication and signal UCSD, USA, from 1997
 processing.
 to 1998. His current research interests include digital communication and signal pro-
 tofrom
 1998. 1980 to 1985.
 His current He joined
 research Kookmin
 interests includeUniversity as an Assistant
 digital communication and Professor
 signal pro-in 1991.
 cessing.
 He also
 cessing. served as a Visiting Scholar with the EE Department, UCSD, USA, from 1997
 to 1998. His current research interests include digital communication and signal pro-
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