Detection of isoprene traces in exhaled breath by using photonic crystals as a biomarker for chronic liver fibrosis disease

Detection of blood-carried volatile organic compounds (VOCs) existing in the exhaled breath of human is an attractive research point for noninvasive diagnosis of diseases. In this research, we introduce a novel application of photonic crystals (PCs) for the detection of isoprene traces in the exhaled breath as a biomarker for liver fibrosis. This idea is introduced for the first time according to the best of our knowledge. The proposed sensor structure is constructed from a multilayer stack of two dielectric materials covered with an air cavity layer filled with the dry exhaled breath (DEB) and a thin metallic layer of Au is attached on the top surface. Hence, the proposed sensor is configured as, [prism/Au/air cavity/(GaN/SiO 2 ) 10 ]. The transfer matrix method and the Drude model are adopted to calculate the numerical simulations and reflection spectra of the design. The essential key for sensing isoprene levels is the resonant optical Tamm plasmon (TP) states within the photonic bandgap. The obtained numerical results are promising such as high sensitivity (S) of 0.321 nm/ppm or 278720 nm/RIU. This technique can be reducing the risk of infection during the taking of blood samples by syringe. Also, it can prevent the pain of patients. Finally, this work opens the door for the detection of many diseases by analyzing the breaths of patients based on photonic crystals.


Introduction
In recent years, exhaled human breath analysis became an urgent tool for the detection of various diseases and assists clinicians in early diagnose of the impending effects of diseases [1]. The actual beginning for monitoring diseases based on exhaled breath analysis was dedicated by Linus Pauling [2]. However, breath analysis was an ancient diagnosis tool since Hippocrates learned his students to utilize exhaled for identifying many diseases such as failing kidneys and liver disease [3]. From this date, the exhaled breath analysis techniques attracted researchers' attention because they considered as a specific diagnosis of diseases, noninvasive, and inexpensive [1,4].
Previous studies proved that healthy people exhaled about 874 types of volatile organic compounds (VOCs) such as acetone (1.2 -900 ppb), isoprene  ppb), methanol (160 -2,000 ppb), and ethanol (13 1,000 ppb) [2][3][4]. Therefore, any disorder in the levels of exogenous VOCs could reflect the physiological state of the person. For example, increasing the percentages of isoprene molecules in the exhaled breath of a person can be an indicator of liver fibrosis disease [5], acetonitrile level increase in the exhaled breath of smokers, and high concentrations of acetone represent diabetes disease [6]. Consequently, many techniques were presented for the diagnosis of diseases depending on the concentrations and percentages of VOCs in exhaled breath. For example, Popa et al. investigated that high levels of exogenous ammonia and ethylene in human breath is a diagnosis of schizophrenia [7]. Also, lung cancer can be diagnosed based on levels of exogenous toluene as reported by Szulejko et al. [8].
More recently, optical and surface plasmon resonance (SPR)-based sensors have introduced novel results in the applications of biosensors and biomarkers based on levels of VOCs in patient respiration [9][10][11]. Optical biosensors are characterized by high performance, inexpensive, and compact design which can be inserted with a lab-on-a-chip device [12,13]. Photonic crystals (PCs) are considered fascinating optical sensors and biosensors in recent years [14][15][16]. PCs are periodic structures in 1D, 2D, or 3D designs that able to control the propagation of electromagnetic waves (E.M waves) within ranges of frequencies called photonic band gaps (PnBG). The formation of PnBG due to the refractive index contrast between the constituent materials [17][18][19]. Making a cavity inside the periodic design of PCs leads to the generation of local resonance modes that were used in gas or liquid sensor applications. Clevenson et al. reported a 1D PC as a gas sensor with low concentrations (ranging from 600 parts per million (ppm)) [20]. The temperature and concentration of ethylene/air mixture were measured by a 1D PC sensor presented by Chen et al. [21]. A 2D PC gas sensor with a high sensitivity of 575 nm/RIU was introduced by Anamoradi et al. [22].
Another way for producing resonant modes in PCs is achieved based on surface plasmon resonance (SPR) and optical Tamm plasmon (TP) resonance. TP resonance is defined as the quantization of free electrons oscillations at a metaldielectric interface [23]. A theoretical 1D PC sensor was presented based on TP resonance. It provided higher sensitivity than conventional PC sensors that reached to 5018 nm/RIU [13]. Also, the 1D PC sensor was investigated experimentally by Auguie et al., who obtained a sensitivity of 55 mm/RIU [24].
On the other side, about 2 million deaths per year worldwide due to liver disease.
The eleventh most common cause of death worldwide is liver fibrosis. The fibrosis making it hard for the liver to function and it is life-threatening. Liver fibrosis is caused by many forms of liver diseases such as chronic alcoholism and viral hepatitis (hepatitis B, C, and D). Egypt has the highest prevalence of hepatitis C virus infection in the world. The early diagnosis may prevent damage from occurring in the liver. Hence, this present study focuses on the application of exhaled isoprene sensing as a possible and advanced tool to diagnose liver fibrosis disease.
For this purpose, a novel application of 1D PCs as a biomarker or biosensor for sensing the lowest isoprene levels in the dry exhaled breath based on the phenomenon of TP resonance is presented in this work. The 1D PC gas sensor is designed as a multilayer from two dielectric materials with a thin metal layer on its face. Then, the exhaled breath with different levels of isoprene (from 0 ppm to 100 ppm) is proposed to pass through an air cavity between the multilayer stack and the metal layer. The well-known transfer matrix method (TMM) was used to manipulate the propagation of EM waves through the sensor structure and calculate the reflection spectra of each level of exhaled isoprene. Moreover, the most important performance parameters for any sensor such as quality factor, sensitivity, detection limit, the figure of merit, and sensor resolution were calculated for each isoprene level.

Sensor design
The suggested design of the 1D PC gas sensor is shown in the schematic diagram in Fig. 1. Firstly, the sensor structure is a periodic multilayer 1D PC from GaN/SiO 2 . Secondly, a thin metals layer (Au) is attached to the front of the GaN/SiO 2 multilayer stack. Thirdly, the exhaled breath with the different isoprene levels should pass and fill an air cavity between the metal layer and the PC multilayer. The thickness of the multilayer stack is proposed to be a = d 1 where, d 1 and d 2 are the thickness of GaN and SiO 2 , respectively. Also, the thickness of Au and the cavity layer is set to be d m and d c , respectively. Finally, a prism is set on the metal layer to enhance the reflection for the incident EM on the PC design [16]. Consequently, the complete design of the PC gas sensor can be configured as the following, [prism/Au/air cavity /(GaN/SiO 2 ) N ]. Where N is the unit cells (periods) number. The choosing of GaN and SiO 2 due to their excellent optical, chemical stability, and mechanical properties [25,26]. Also, they are used widely in the design of PCs sensors theoretically and experimentally [13,15,16 ,19].

Analysis of the transfer matrix method
Here, we intend to investigate the basic equations implemented to obtain the optical reflectance of the incident EM waves through the proposed sensor design.
The propagation of EM waves through periodic structures is manipulated by using As shown in Fig. 1, the incident EM wave is assumed to propagate through xdirection. Therefore, the two polarization modes (electric and magnetic fields) are oscillating through the (yz) plane. For the transverse electric (TE) mode, the general solution of the incident EM wave through the j th layer can be written as, Where, k y is the wavevector, ω is the angular frequency, E(x) and H(x) are the components of the electric and magnetic fields, respectively. They can be written within a specific layer j th as, Where, k j is the wavenumber in layer j and n j defines its refractive index. S j and P j are the electric and magnetic field amplitudes, respectively. By substituting equation (1) in equation (2), the following matrix form can be obtained as, TMM requires the continuity of the EM wave solution through the boundaries between each two successive layers j and (j +1). Therefore, the elements of the E j (x) and H j (x) elements at these boundaries are given as, Equation (4) can be rewritten in a simple form as, Where, j  is the angle of incidence through the layer jth, χ j and τ j are two coefficients with the values,  ( Similarly, the matrix analysis of the TM mode can be deduced using equations

Materials refractive index
As it well-known, metals have a high absorption for the incident EM waves, so its dielectric constant is a complex function. The complex dielectric constant (ϵ m ) of any metal is given according to Drude model as the following equation [29], Where, ϵ 1 and ϵ 2 represent the real and imaginary parts of the complex dielectric constant, respectively. Also, ω p is the plasma frequency of metal (here is Au) and γ is the damping constant. Then, the refractive index can be written as the square root of the complex dielectric constant, n m = √ ϵ m .
Concerning the refractive index of SiO 2 is a wavelength-dependent as the following equation [30]: . 0.0045 -0.0026 1.4513 ) ( Where, λ (in microns) is the wavelength of the incident E.M wave. Also, the refractive index of GaN is a wavelength-dependent as well and it is given as [31]:

Numerical results and discussions
We propose here the materials parameters and present the numerical investigations concerning the interaction between the incident EM waves and the sensor design at different levels of isoprene.
For this purpose, the GaN layer is set with a thickness d 1 = 200 nm while the SiO 2 layer is set with a thickness d 2 = 900 nm. The number of periods is proposed to be N = 10, the angle of incidence is taken as θ 0 = 50 0 and the prism is assumed with the index n p = 1.3. The metallic layer of Au and air cavity layer are designed with thicknesses d m = 10 nm and d c = 14 μm, respectively. Also, the operating wavelength of the incident EM waves will be in the range of 2000 nm to 4000 nm.
All the aforementioned parameters were taken to achieve a higher sensor performance and a wide bandgap after multi optimization steps.
In the beginning, we will investigate the reflection properties of the PC multilayer stack in the absence of the metal layer and air cavity in order to set the best boundary conditions of the PnBG. Therefore, the reflectance of the 1D PC structure that is arranged as, [prism/(GaN/SiO 2 ) 10 ] is shown in Fig. 2. As shown in this figure, a wide perfect photonic bandgap appears in the wavelength range 2337.5 nm− 3347.7 nm and with a bandwidth of 1010.2 nm. The bandgap is characterized by nearly zero transmission of EM waves. Such a wide bandgap is due to the high mismatch in refractive index between GaN and SiO 2 materials, and it is resulted due to the destructive interference of EM waves at layers boundaries [13,15]. The production of wide band gaps in the refection spectrum of PCs is considered a desired indicator for designing sensor platforms. This is facilities the localization of resonant modes within the band gap without crosstalk with other ripples or reflected dips. By embedding a cavity layer of thickness 14 μm in front of the previous PC GaN/SiO 2 multilayer, the designed structure is considered as prism/air cavity/(GaN/SiO 2 ) 10 /air. As seen in Fig. 3, the reflectance intensity of this structure is increased due to the presence of the air cavity layer. Also, the PnBG width became wider due to the insertion of the air cavity layer, since, the refractive index mismatch becomes higher in that case, prsim, air cavity and GaN layer. The wavelength range of that bandgap extended from 2220.5 to 3398.9 nm with a bandwidth of 1178 nm. Moreover, more ripples with a high reflection intensity are produced outside the bandgap due to the insertion of that defect air cavity layer.

Wavelength (nm)
Where, the large thickness of the air cavity layer (14 μm) is another reason for producing these large number of ripples. In addition to that, the most interesting defect dip here is the ones that localized at the wavelength of 3500 nm. This defect dip is produced exactly according to the well-known quarter wave stack ( = 4 ), where, is the dip wavelength, is the air cavity refractive index ( here = 1.00026 for the dry exhaled breath) and is the thickness of the air cavity layer [17].  50000 ppm), O 2 (6 % or 160000 ppm), and N 2 (78 % or 780000 ppm). In the case of liver fibrosis disease, the levels of isoprene (ppm) are increased in the exhaled breath of unhealthy persons [5]. The effective refractive index (n eff ) of the dry exhaled breath is obtained by the rule of the mixture as [32]: n eff 2 = n 1 2 ϕ 1 + n 2 2 ϕ 2 + n 3 2 ϕ 3 + ⋯, where, n and ϕ represent the index of refraction and volume fraction of each exhaled air gas component. The detailed methods of the refractive index calculation for these gases are described in reference [33,34]. Meanwhile, we plot in Fig   Depending on the results of Fig. 6 we have plotted in Fig. 7  Where, C is the isoprene concentration in ppm. From that figure and the above equation, we could obtain the sensitivity of the proposed 1D PC gas sensor by taking the slope of the relation in Fig.7 [35 -37]. Herein, we could obtain higher sensitivity that reaches the value of 0.321 nm/ppm or 278720 nm/RIU. Consequently, this sensitivity value is considered very high compared with other PC counterparts [13,21]. The results obtained in table (1) show that our 1D PC gas sensor achieved not only high sensitivity but also high performance based on the other performance parameters. The value of the reduced sensitivity or the so-called FoM reached higher than 0.134 /ppm. Besides the stability of the reflection intensity for all isoprene levels, it did not decrease than 18 % in the worst case. In addition to that, the detection accuracy and detection limit of the sensor reached higher than 0.37 and 5.45 ppm, respectively. Moreover, the sharpness of each TP resonance dip is very brilliant represented by the high QF (more than 985) and low FWHM (not more than 2.7 nm for all TP dips).

Funding:-Not applicable
Availability of Data and Material:-The data that support the findings of this study are available from the corresponding author upon reason-able request.

Code availability:-Not applicable
Ethics approval:-I, hereby, the corresponding author declare that the authors have thoroughly read the Journal Policy and admitted all its requirements. Specifically, I declare here that this contribution is original and has not been published anywhere.