Optical UV detection of the glucose content in solution for application in glucose monitoring

doi:10.21203/rs.3.rs-4004823/v1

The present work describes an optical method for glucose determination from frontier equations and predictive mechanisms. A theoretical description of the electronic transitions in glucose molecule treated as a quantum dot and experimental validation were carried out. The calculation relies on the photon absorption between the ground and the first excited state. The results were 263, and 277 nm for experimental and theoretical estimation, respectively. The glucose quantification was done by optical transmittance in a glucose solution. Photonic glucose absorption was recorded in the 5–30 mM range. The method showed a 0.00876%Abs/mM sensibility with linear behavior.

According to the World Health Organization, Diabetes Mellitus (DB) is a chronic, metabolic disease characterized by elevated levels of blood glucose (or blood sugar), which leads over time to serious damage to the heart, blood vessels, eyes, kidneys, and nerves [1]. Worldwide, an estimated 422 million adults were living with diabetes in 2014, an increase from 4.7–8.5% compared to 108 million in 1980 in the adult population.

Currently, numerous methods for the detection of glucose show a high rate of effectiveness. However, the applications are no longer only focused on clinical analysis, but also in the medical, biological, and food areas [2], establishing new parameters. and greater specificity. Therefore, it is necessary to study alternative methods to those already known for the quantification of glucose. For the clinical area, glucose detection has been divided into 2 groups: i) single measurement and ii) continuous measurement. Within this first classification are glucometers and urine test strips; both methods employ amperometric detection methods through glucose oxidation from a biomarker or enzyme. On the other hand, in continuous monitoring methods, there are those that use invasive, non-invasive (NI), or minimally-invasive (MI) techniques that include electrochemical, electrochemiluminescent, optical, and mechanical detection mechanisms [3–7]. The existing optical methods of glucose sensing are based either on the measurement of the refractive index of various liquids of a human body (like ocular aqueous humor [6, 8]) or the infrared absorption of human blood [9]. We studied a different approach based on the UV-Vis optical absorption of glucose in water solution.

Invasive methods are associated with intravenous implantable devices, by microdialysis and subcutaneous sensors, while minimally invasive methods are related to micropore/microneedle techniques. On the other hand, there are the non-invasive (NI) methods, where optical and transdermal methods stand out. Non-invasive technologies (NI) are based solely on some form of radiation without the need to access human body fluid. Thus, technologies for glucose detection using NI methods can be classified into four subgroups: optical, thermal, electrical methods, and nanotechnology [10], with optical technologies being the most relevant because they include all the techniques developed to work in the infrared and optical bands of the spectrum, taking advantage of the properties of reflection, absorption, and scattering of light when passing through biological media. Optical transducers use light at varying frequencies to detect glucose, using different properties of light to interact with glucose molecules in a concentration-dependent manner, spectroscopic measurement of reflected or transmitted light. Unlike electrochemical biosensors, optical sensors rely primarily on the detection of photons rather than electrons [11, 12]. In this way, it has gained a great interest among researchers as a possible option for the continuous monitoring of glucose in real time in patients with DB.

Figure 1 shows some of the non-invasive technologies that use optical methods to detect glucose; we can highlight the fluorescence technique due to its speed, lack of reagents, and extreme sensitivity [7]. This technology is based on the emission of light by a molecule that absorbs energy at a specific wavelength from the incident radiation and is excited from the ground state to a higher energy level, causing a wavelength difference known as Stoke displacement [10, 13, 14]. Fluorescence can be applied to affordable light sources, such as LEDs that generate ultraviolet (UV) or visible light. This has generated significant interest in developing clinical glucose sensor devices based on transdermal detection [11, 15, 16].

The technology makes use of specialized molecules called fluorophores that emit fluorescent light with specific characteristics and proportional to the concentration of the analyte of interest. In the case of glucose, although some of the fluorophores can bind directly to the glucose molecule, problems associated with low selectivity, irreversibility, interference, and analyte depletion necessitate the use of intermediary molecules called receptors as they bind glucose more efficiently and can undergo reversible changes in their local properties [17]. The control of fluorescent light can be measured by detecting intensity or decay time; however, the latter is preferred as the fluorescence lifetime is specific to each analyte, allowing for differentiation between substances, even if they all emit light at the same wavelength [18]. Raman and Infrared spectroscopy have been proven to be adequate to detect glucose through light absorption peaks (absorption due to vibrational modes). However, the absorption peaks at the visible and infrared spectra suffer optical attenuation by other constituents of the blood. A reliable method should solve the problems of attenuation signal and selectivity.

The present work describes an optical method for glucose determination from frontier equations and predictive mechanisms. A theoretical description of the electronic transition of glucose as a quantum dot and experimental validation were carried out. The calculation relies on the glucose molecule C₆H₁₂O₆, which can be considered a quantum dot (QD) with a cylindrical shape. The photon absorption between the ground and the first excited state was calculated for different boundary conditions. The results were 263 nm, and 277 nm for experimental and theoretical estimation, respectively. The glucose quantification was done by optical transmittance in a glucose solution with deionized water. The photonic glucose absorption was recorded in the clinical range of 2–30 mM. The method showed a sensibility of 12 mM*mA/cm² and linear behavior.

The glucose solution was prepared using a Sigma Aldrich reagent with a purity of + 99% (molecular weight of 180.16 g/mol) dissolved in phosphate buffer at pH 7.4. Glucose determination was obtained by UV-visible spectrophotometric techniques using a Perkin Elmer Lambda XLS + model spectrophotometer, which works in a spectral scanning range from 200 to 950 nm. Measurements were made at 5, 10, 15, 20, 25, and 30 mM glucose, and a blank was used as a reference (Buffer without glucose). A quartz cuvette was used for measurements of all concentrations of interest. Subsequently, a calculation was made using Mirror Boundary Condition MBC in solution of the Schrὃdinger equation to relate the characteristic glucose peaks in the UV region with the fundamental analysis developed in this work.

Theoretical description of the electronic transitions in a glucose molecule

The glucose molecule C₆H₁₂O₆ can be considered as a quantum dot (QD) having various geometric shapes (see Fig. 2), one of which is nearly linear, others nearly cylindrical (α and β shapes). Glucose is a molecule characterized by the absence of color, so the main electronic energy transitions that define its optical properties most likely correspond to the UV spectral region (195–400 nm).

For the calculation, we use the approximation developed previously in our group of the Mirror Boundary Condition (MBC) [19, 20], where we equate the function Ψ of the electron near the boundary with that of its reflection in the boundary that acts as a mirror. Since the physical meaning is related to the square of the function module, the MBC has two versions depending on the type of boundary: the non-penetrable boundary-mirror (odd MBC or OMBC) when we equate the real function of the electron and that of its reflection with opposite signs (obviously, it gives function value zero at the boundary) and the boundary with possibility of tunneling when the equalization occurs with the same sign (even MBC or EMBC). In the case of glucose in an aqueous medium, we cannot be sure of the impossibility of electrons crossing the border, so both versions are considered.

One of the approximations of a glucose molecule is a cylinder with a diameter a = 5.2 Å and height c = 7.3 Å. We consider a particle (electron) inside a cylindrical quantum well for the approximation. According to common procedure, we will assume that the longitudinal and transversal motion of the confined particle are independent of each other, allowing us to separate the wave function into:

\(\psi \left(x,y,z\right)=\psi \left(x,y\right)\psi \left(z\right)=\psi (r,\varphi )\psi \left(z\right)\) (1

Under these conditions, the variables can be separated in the time-independent Schrodinger equation. The motion along the z-axis results in the one-dimensional particle in the box problem:

\(\frac{-{\hslash }^{2}}{2m}\frac{{d}^{2}\psi \left(z\right)}{d{z}^{2}}=E\psi \left(z\right)\) (2

The solution for the particle in the box is well-known, resulting in the wave function:

\(\psi \left(z\right)=\sqrt{\frac{2}{c}}\text{sin}\left(\frac{{n}^{2}{\hslash }^{2}}{8m{c}^{2}}\right)\) (3

The quantized energy levels for the z-axis are given by:

\({E}_{n}=\frac{{n}^{2}{\hslash }^{2}}{8m{c}^{2}}\) (4

For the circular cross-section with radius a, the polar wavefunction can be separated into:

\(\psi \left(r,\varphi \right)=AF\left(r\right){e}^{ik\varphi }\) (5

Where \(k\) is the quantized wavenumber associated with the angular momentum \(L=\hslash k\). For the radial component, the time-independent Schrodinger equation satisfies Bessel’s equation:

\({r}^{2}\frac{{d}^{2}F\left(r\right)}{{dr}^{2}}+r\frac{dF\left(r\right)}{dr}+\left({n}^{2}{r}^{2}-{k}^{2}\right)F\left(r\right)=0\) (6

The expression for energy levels in MBC approximation is [19, 20]:

\({E}_{n}=\frac{2{h}^{2}}{{ma}^{2}} {S}_{\lfloor P\rfloor i}^{2}= \frac{{h}^{2}}{{2\pi }^{2}{ma}^{2}} {S}_{\lfloor P\rfloor i}^{2}\) (7

Where \({E}_{n}\) is the quantized energy level, h is Planck’s constant, m is the molecule’s mass, a is the molecular diameter, and c is its height. The parameter s_|p|i takes the q|p|i values for OMBC and t_|p|i for EMBC, which are the nodes and extremes of the Bessel function (See Table 1). Considering quantization along the z-axis, one will obtain the total energy.

\(E=\frac{{h}^{2}}{2m} \left(\frac{{S}_{\lfloor P\rfloor i}^{2}}{{\pi }^{2}{a}^{2}}+\frac{{n}_{z}^{2}}{{4c}^{2}}\right)\) (8

Table 1

Argument values at nodes and extremes of cylindrical Bessel function The Even Mirror Boundary Conditions or EMBC establish that a particle may penetrate the barrier, returning to the confined volume. Meanwhile, the Odd Mirror Boundary Condition establishes strong confinement. The calculated ground state and first state are shown in Table 2. For the OMBC, the ground state is established for q|p|1 = 2.4, and the first excited state is for q_|p|2=3.7. The energy levels for each state are 3.95 and 8.42 eV, respectively. The first transition for the OMBC between the base and first states is 4.47 eV or 277 nm. Meanwhile, the experimental results show an absorption peak at 263 nm, only a 14 nm deviation from the OMBC model. The next excited state corresponds to the value q|p|2 = 5.1, gives E₂ = 15.37 eV, and ΔE = 11.41 eV, wavelength 109 nm. The higher excited states will give transitions in the deep ultraviolet that are out of the limits of our measurements, so we will not consider them. An intertransition between the first and second stages has a ΔE = 6.94 eV, wavelength of 179 nm. For the EMBC, the first transition from the base state to its first level is 3.25 eV or 382 nm. The difference between experimental and theoretical in this model is 119 nm, wider than the OMBC model.
q_\|p\|1	t_\|p\|1	q_\|p\|2	t_\|p\|2	q_\|p\|3	t_\|p\|3	q_\|p\|4	t_\|p\|4
2.4	0	5.5	3.7	8.5	7.1	11.6	10.2
0	1.63	3.7	5.4	6.9	8.6	10.3	11.6
0	2.9	5.1	6.8	8.4	10.0	11.7	13.2
0	4.3	6.4	8.1	9.9	11.4	13.2	14.2

Table 2

Calculated energy levels and transition for the OMBC and EMBC model
OMBC Model				EMBC Model
Ground state q_\|p\|1=2.4		First state q_\|p\|2=3.7		Ground state t_\|p\|1=1.63		First state t_\|p\|1=2.9
E (eV)	3.95	E (eV)	8.42	E (eV)	2.20	E (eV)	5.45
ΔE (eV)		4.47		ΔE (eV)		3.25
λ(nm)		277		λ(nm)		382
Experimental (nm)		263		Experimental (nm)		263