A Novel High-Sensitivity Terahertz Microstructure Fiber Biosensor for Detecting Cancer Cells

Abstract

Cancer is one of the leading causes of mortality worldwide. In recent years, various kinds of biosensors based on optical fiber have been proposed for detection of cancer cells due to their advantages of accurate diagnosis, small size, low cost, and flexible design parameters. In the present study, a microstructure fiber (MSF) biosensor with porous-core structures was designed to detect cancer cells using a terahertz time-domain system (TDS). The fiber characteristics of the proposed MSF were optimized by adopting a finite element numerical technique and perfectly matching layer absorption boundary conditions. The numerical results show that the proposed biosensor presented an ultrahigh sensitivity for detection of cancer cells. Under the optimal condition of 0.9 THz, the relative sensitivity of the proposed structure to breast cancer cells was as high as 99.8%. Moreover, other optical fiber parameters, such as effective material loss (EML), confinement loss (CL), numerical aperture (NA), power fraction, and effective area (A_eff), were optimal according to the reported results. The proposed structure can be easily fabricated by 3D printing and flexibly applied in the fields of biomedicine and biosensing with a terahertz (THz) waveguide.

1. Introduction

Cancer refers to tumors produced by malignant changes in epithelial tissues, which represents the ordinary type of malignant tumors in the biomedical domain. Malignant tumors are characterized by uncontrolled growth, metastasis to other organs, and destruction of bodily functions. An effective method for detecting cancer cells is currently being developed. Traditional cancer sample detection techniques include X-ray and magnetic resonance imaging (MRI) diagnosis technology [1,2,3,4,5,6,7] and microscopic endoscopic diagnosis technology [8,9,10]. X-rays cause radiation damage to the human body, and the cost of an examination is relatively high. An endoscope is a kind of optical instrument that needs to enter the body from the outside through a natural cavity of the human body to examine internal diseases. The process is complicated, and the maintenance cost of the instrument is high. Currently, the emerging diagnostic technologies of circulating tumor cell detection (CTC) diagnosis [11] and free DNA detection of tumor cells [12,13] are relatively mainstream. CTC is a method to directly detect cancer cells in the blood, whereas tumor-cell-free DNA technology is more inclined to detect the DNA of cancer cells. Although these two methods involve no radiation or trauma to the human body, their technical requirements are considerable, and they have not been effectively promoted. Microstructure fiber (MSF) can be combined with THz waves, as its characteristic working frequency band can be tuned according to the transmission wavelength, and THz waves do not damage biomolecules. Therefore, MSF is a biological detection method with considerable development potential.

In recent years, MSF has been extensively used in various applications, including chemical identification [14], THz communication [15], cancer cell detection [16], liquid analyte sensing [17], and harmful gas detection [18]. MSF has emerged as an efficient and versatile platform for biosensing due to its high relative sensitivity, low EML, and low CL. When photonic biosensors are used to detect cancer cells, they not only provide useful information about cells in real time but also have the advantage of being relatively small in size [14]. Some important optical properties of MSF, such as material absorption loss, core power fraction, relative sensitivity, numerical aperture, and effective area, can be optimized by adjusting the core diameter, fill-in factor, arrangement, shape of air holes, etc. Calculation and comparison of these characteristics can be used to judge whether the optical fiber structure performance is outstanding and whether it can be used for biosensing.

THz radiation is widely used in biosensing because it is harmless to the human body. For the application of THz waveguides to biological or chemical sensing fields, a variety of geometric descriptions of MSF have been reported [19,20]. Jakeya Sultana designed a revised hexagonal structure with elliptical-core air holes in 2018 [21]. This revised design shows an inappreciable CL of 7.99 × 10⁻¹² cm⁻¹, with a relative sensitivity of 68.87% at 1 THz. Md. Saiful Islam designed a hollow-core MSF for analysis and detection of chemical samples [22]. In 2019, Md. Ahasan Habib suggested a novel MSF in which the fiber center region is composed of rectangular and circular air holes. The structure exhibits a relative sensitivity of 89% with a CL of 1.15 × 10⁻⁹ dB/cm with optimal parameters [1]. An MSF based on Zeonex (amorphous polyolefin) was demonstrated by Md. Saiful Islam. They obtained a near zero-dispersion of 0.49 ± 0.05 ps/THz/cm with a low EML of 0.05 cm⁻¹ at 1THz. This designed structure achieved satisfactory performance, but the preparation process was very complicated [23]. Similarly, a highly sensitive MSF based on a modified hexagonal structure was designed by Md. Shadidul Islam et al., which showed a sensitivity of 53.22% to ethanol, 48.19% to water, and 55.56% to benzene. However, this structure and involves a complicated preparation process [24]. A late-model multicore MSF was devised by Md. Ahasan Habib, which exhibited near-zero dispersion of 1.1 ± 0.02 ps/THz/cm, a lower EML of 0.07 cm⁻¹, and a higher birefringence of 0.018 in the frequency range of 0.8 to 1.2 THz [25]. Md Toaha Anas et al. proposed late-model design of a hexa-flabellate MSF with a lower CL of 5.78 × 10⁻⁹ dB/m, a numerical aperture of 0.8774, and higher birefringence of 0.259 under optimal conditions [26]. The above-mentioned studies reveal that optimizing the performance of MSF by selecting suitable materials, geometric configuration, and preparation process results in opportunities related to parameter exploration to meet the needs of biosensing applications.

Here, we report a simple and efficient design of a multicore MSF sensor for biosensing applications that is feasible for a 3D printing preparation process. In the proposed structure, six fan-shaped air holes are introduced into the cladding, and the core is composed of two triangles and a rectangle, forming a hexagonal shape. The designed MSF is used to detect cancer cells, with a relative sensitivity of 99.8% at 0.9 THz. Moreover, simulation results of the proposed design reveal that high power fraction, high numerical aperture (NA), and low CL can be simultaneously achieved over a broad THz frequency range, outperforming previously proposed designs in the biomedical domain.

2. Design Principles and Theoretical Model

2.1. MSF Structure and Sensing Mechanism

A 2D intersecting surface schematic diagram of the designed MSF structure is exhibited in Figure 1a, with the fiber core highlighted in orange. As shown in Figure 1b, the wall thickness of the regular hexagonal fiber core and the thickness of the two horizontal support strips in the fiber core are d₁, the distance between two adjacent holes in the cladding region is d₂, and the distance between the cladding holes and the perfect matching layer (PML) is d₃. In our work, d₁, d₂, and d₃ were initially set to 25 μm, 25 μm, and 100 μm, respectively. The distance between the upper and lower vertices of the regular hexagon core was set as the core diameter, which is represented by D_core.

The cladding of the designed MSF consists of six flabellate air holes arranged in a circular ring around the fiber core. The core is a hexagon structure composed of two triangular holes and a rectangular hole. With respect to the substrate material, we chose the commonly used polymer Zeonex (refractive index = 1.5258) for the proposed MSF. Compared with other polymer materials, Zeonex has the unique advantages of low material absorption loss, constant refractive index, excellent optical stability, insensitivity to temperature and humidity, and almost negligible absorption of water [23,27]. Because Zeonex is relatively unaffected by environmental factors, it is suitable for use as a substrate for biosensing applications.

In order to absorb the outgoing wave, a perfect matching layer (PML) was set at the boundary of the computational domain. The total diameter of the fiber is 3000 μm, and the breadth of PML accounts for 10% of the total diameter of the fiber and remains unchanged during the subsequent simulation. Figure 1c shows the propagation direction of the THz wave in the proposed fiber structure and the specific composition of each part of the fiber. The core is made of cancer cells combined with a small amount of Zeonex, and the cladding is made of air mixed with Zeonex. The specific refractive index distribution is shown in Figure 2.

The refractive index distribution and THz wave propagation inside the MSF biosensor are exhibited in Figure 2a. Transmission of THz waves in the fiber core is represented by the total internal reflection (TIR) because the several large air holes introduced into the fiber cladding led to a reduction in refractive index (n₂) compared to the core index (n₁) after injection of the analyte. Figure 2b shows the principles involved in the use of a terahertz time domain system (THz-TDS) to detect cancer cells. The effective refractive index and CL can be extracted from the original data obtained from the output end, the final measurement results are compared with the results of the numerical simulation, and the consistency between the experimental data and the simulated data is judged.

2.2. Theoretical Methods and MSF Characteristics

The revised Lambert–Beer law was used to calculate the sensing capability of the designed MSF structure in the context of the mutual effect between light and analytes. This circumstance can be expressed by the following formula [16]:

$$I(f)=I_0(f)exp\left[-s{a}_{m}lc\right],$$

(1)

where I(f) and I₀(f) represent the incident light intensity and the output light intensity, respectively; s represents relative sensitivity; α_m represents absorption coefficient; l is the length of the designed MSF used for detection; c is the detected analyte density; and f represents the frequency of light.

The absorption of the sample to be tested can be computed by the following formula [16]:

$$A=log\frac{I}{I_0}=-s{a}_{m}lc,$$

(2)

Relative sensitivity is a key optical parameter to measure the sensing capability of chemical or biosensors. It represents the amount of THz waves interacting with the object being measured and can be expressed as follows [14]:

$$s=\frac{n_r}{R_e\left(n_{eff}\right)}\times K,$$

(3)

where n_r is the refractive index of the analyte to be tested, R_e (n_eff) represents the real portion of the effective refractive index of the guide mode, and K is the factor of the interaction degree between light and the substance (expressed in percentage), which can be computed by the following formula [14]:

$$K=\frac{{\displaystyle {\int }_{analyte}{R}_e\left(E_m{H}_n-E_n{H}_m\right)dxdy}}{{\displaystyle {\int }_{total}{R}_e\left(E_m{H}_n-E_n{H}_m\right)dxdy}}\times 100,$$

(4)

where E_m and H_m represent the transverse components of the electric and magnetic fields, and E_n and H_n are the longitudinal components.

Due to the existence of the background substrate material, the interaction of THz waves with background material produces a significant loss value, which is called effective material loss (EML). In order to build up the capability of MSF THz waveguides, the absorption loss of materials can be minimized by selecting suitable substrate materials and a reasonable geometric arrangement. The EML calculation formula of the designed MSF is as follows [18]:

$${\alpha }_{\left(EML\right)}=\sqrt{\frac{{\epsilon }_0}{{\mu }_0}}\frac{{\displaystyle {\int }_{mat}{n}_{mat}{\left|E\right|}^2{L}_{mat}dA}}{\left|{\displaystyle {\int }_{mat}{S}_{z}dA}\right|},$$

(5)

where α_(EML) represents the EML; ε₀ and µ₀ represent the permittivity and permeability in vacuum, respectively; n_mat represents the sum of the refractive index (RI) of Zeonex and the analyte; L_mat represents the sum of the absorption coefficient of Zeonex and the analyte; S_z denotes the z component of the Poynting vector; and E refers to the component of the electric field.

When a THz wave travels through a microstructure fiber, a small amount of energy is leaked to the outside, known as the CL. The α_(CL) calculation formula of the designed MSF is as follows [14]:

$${\alpha }_{\left(CL\right)}=\left(\frac{4\pi }{wl}\right)Im\left(n_{eff}\right),$$

(6)

where wl represents the wavelength, and Im (n_eff) represents the imaginary part of the effective refractive index of the mode.

Effective area refers to the amount of transverse area occupied by a given mode in an optical fiber, which influences how tight in space the light–matter interaction occurs. It can be computed by the following formula [21]:

$$A_{eff}=\frac{{\displaystyle \iint {\left({\left|E\left(x,y\right)\right|}^{2}dxdy\right)}^2}}{{\displaystyle \iint \left({\left|E\left(x,y\right)\right|}^{4}dxdy\right)}},$$

(7)

where E (x, y) is the mode field distribution of x polarization and y polarization.

The numerical aperture of the fiber indicates its ability to receive incoming light. Typically, the numerical aperture (NA) is used to measure the maximum acceptable incidence angle of incident light inside the MSF. For spacious sensing cases, NA can be computed by the following formula [28]:

$$NA=\frac{1}{\sqrt{\left(1+\frac{\pi A_{eff}}{{\lambda }^2}\right)}},$$

(8)

where A_eff represents the effective area, and λ represents the wavelength.

Core power fraction (P) describes how the power distributes in different regions of waveguide when THz wave is transmitted in an MSF, which is given by [29]:

$$P=\frac{{\displaystyle {\int }_x{S}_{z}dA}}{{\displaystyle {\int }_{total}{S}_{z}dA}},$$

(9)

where x represents the area to be investigated, such as the fiber core, cladding, or material; and ‘total’ represents the intersecting surface area of the entire fiber.

3. Numerical Simulations and Analysis

3.1. Optimization of Structural Parameters in MSF

When light passes through an optical fiber, the most intuitive expression of its limiting ability is to observe the mode field distribution. In the fundamental mode state, the mode field can be confined to the core, which proves that there is a strong interaction between light and the target analyte and the fiber has a good limiting ability. Here, the geometric design of MSF is numerically analyzed by the full-vector finite element method (FEM). The results show that the fundamental modes are confined within the tested frequency range. When breast cancer cells were taken as analytes, as shown in Figure 3, (a) and (b) were the fundamental modes of the x and y polarization directions, respectively.

3.1.1. Influence of D_core on Optical Fiber Performance

An important characteristic of the MSF is that the size of the hole is roughly on the same order of magnitude as the transmission wavelength. The frequency range considered in the present study is 0.5~1.5 THz, and the corresponding wavelength range is 0.2~0.6 mm. The limit effect is optimized when the core size is generally two to three times larger than the transmission wavelength. Therefore, we roughly determined a value range for analysis and calculation. Because the size of the fiber core has a considerable influence on the limiting effect, the fiber core should be analyzed and discussed first.

The variation in relative sensitivity, EML, CL, NA, and A_eff with frequency is shown in Figure 4. Here, D_core was used as a variable, and d₁ = 25 μm, d₂ = 25 μm, and d₃ = 100 μm. Figure 4a shows that the relative sensitivity increases gradually with increased frequency in the range of 0.5~1.5 THz because the interaction between the THz wave and the analyte increases with increasing frequency within the tested frequency range, and the energy of the mode field is bound to the fiber core. The correlation of EML with frequency under different MSF diameters is plotted in Figure 4b. According to Formula (5), EML is directly proportional to the absorption coefficient, and the absorption coefficient in reference [30] was reported to increase monotonically with frequency, so EML increases with frequency. The variation of CL with frequency is shown in Figure 4c. CL has a small range of variation within the tested frequency range, and the value is basically maintained at about 10⁻¹², which also proves that the designed structure has a positive effect on THz wave restriction.

Figure 4d displays the variation relationship between power fraction and frequency with different core diameters. The power fraction increases gradually with increased frequency and will also increase gradually increased core diameter, similar to the transformation law of relative sensitivity.

Figure 4e depicts the NA change as a function of frequency. The relationship between NA and frequency presents with a decreasing tendency, as the THz wave is more firmly bound to the core region with increasing frequencies, and the NA ultimately decreases. The increase in core diameter leads to a decrease in NA because the energy of the mode field can be restricted in the porous core when the core is larger, which consequently leads to a lower NA value.

The functional relationship between A_eff and frequency for different core sizes is plotted in Figure 4f. A_eff decreases monotonically with increased frequency. In this case, A_eff decreases with increased core diameter, similar to NA. In order to balance all variables, D_core = 800 μm and 0.9 THz were determined as the optimal parameters according to a comprehensive consideration.

3.1.2. Influence of d₂ and d₃ on Optical Fiber Performance

After determining the optimal core diameter, we fixed D_core = 800 μm, d₁ = 25 μm, and d₃ = 100 μm using the control variable method and numerically simulated the column width (d₂) of the cladding. Figure 5a,b shows the changes in relative sensitivity and EML with frequency when d₂ is a variable. The change in d₂ has a minimal influence on the performance of the optical fiber. From the perspective of structural stability, d₂ = 30 μm was selected as the optimal strut width. Subsequently, the outermost thickness (d₃) was also simulated, as shown in Figure 5c,d. After comprehensive consideration, d₃ was fixed at 100 μm.

3.1.3. Influence of Fill in Factor on Optical Fiber Performance

The fill in factor is another important variable with respect to geometric parameters, which can be defined as the ratio of the area filled with analyte (Area₁) to the total area of the fiber core (Area₂), expressed as the fill-in factor, i.e., Area₁/Area₂. As the fill-in factor increases, the filling volume of the analyte in the fiber core will increase; conversely, the volume of the background material will be compressed, so the EML will be reduced accordingly. We controlled the fill-in factor by adjusting the size of d₁ and judged its influence on fiber performance by keeping other variables unchanged (Figure 6). The fill-in factor is inversely proportional with d₁. A relatively satisfactory fiber performance was achieved with a decreased d₁ value.

The relationship between relative sensitivity and frequency is depicted in Figure 6a. The relative sensitivity increases with decreased d₁ because THz waves can interact with more analytes, so the sensitivity is relatively high [31,32,33,34,35,36,37]. As shown in Figure 6b, the decrease in d₁ has an insignificant impact on EML, which is closely related to the absorption coefficient of the material because the absorption coefficient of the filled cancer cells is much higher than that of the background material. Therefore, changes in porosity have a minimal effect on the total EML. The relationship between CL and frequency is shown in Figure 6c with varying d₁ values. The change in porosity does not have a considerable impact on the CL, which is still around 10⁻¹² and can be ignored. Figure 6d shows the relationship between core power fraction and frequency at different values of d₁. The power fraction increases with a decrease in d₁, exhibiting a similar trend to that of sensitivity. As shown in Figure 6e, the change in d₁ has almost no significant effect on NA. At our optimal frequency of 0.9 THz, an NA value of 0.41 is achieved for the designed MSF, which is comparable in value to that of other existing designs [38,39]. Figure 6f shows the variation in A_eff relative to frequency at different d₁ values. As d₁ decreases, the amount of analyte increases, and the interaction between the analyte and light will also increases, so A_eff will increases slightly. Based on the data comparison in Figure 6, we decided to take d₁ = 25 µm as the optimal fill-in factor for subsequent numerical simulation.

3.2. Exploring a High-Sensitivity MSF Biosensor for Detecting Cancer Cells

After determining the optimal geometric parameters, we simulated a scenario in which cancer cells, including breast, skin, and gastric cancer cells, are added to the core of the designed structure for biosensing. Subsequently, the differences in relative sensitivity, EML, and other parameters between cancer cells and normal cells were analyzed. The cause of cell canceration is mainly due to abnormal cell proliferation, which leads to an increase in the content of organelles in the cell. Therefore, the water content of cancer cells is significantly higher than that of normal cells. THz waves are sensitive to water molecules, and the absorption of THz waves increases with increased water content in cells, so the absorption coefficient of THz waves is relatively high in cancer cells.

Figure 7a shows the relative sensitivity of the three cancer cells as a function of frequency. The refractive index of cancer cells is higher than that of normal cells and proportional to the relative sensitivity. Therefore, the sensitivity of cancer cells with a high refractive index is relatively high, and the simulation results correspond to the data reported in the literature [30,40,41]. Figure 7b shows the relationship between EML and frequency. The absorption coefficient of materials is closely related to EML. According to the calculation formula of EML, the absorption coefficient is also directly proportional to EML. Compared with the data reported in the literature, the variation trend of EML relative to frequency corresponds to the absorption coefficients of the three cancer cells [30,40,41]. Although the calculated EML value is high, the contrast between cancer cells and normal cells is obvious and can be effectively distinguished. Some references did not mention the absorption coefficient of the analyte itself, so the calculated EML was relatively low [18,21,29].

Based on the considerations discussed above, the proposed MSF THz sensor represents a considerable improvement over the previously reported MSF-based biochemical sensors in terms all the considered crucial properties. A comparison is presented in

Table 1. Comparison between the parameters of the sensor in the proposed MSF with reported results.

Reference	Sensitivity (%)	EML (cm−1)	CL (cm−1)	NA	Aeff (μm2)	P (%)
[18]	89	0.028	1.15 × 10−9	0.42	9.38 × 108	_
[21]	68.87	0.05	_	0.356	_	67.05
[29]	90	0.019	_	_	_	_
[31]	70	_	_	0.549	1.37 × 105	68
Proposed	99.8	191	2.62 × 10−11	0.44	1.44 × 107	97.18

. To the best of our knowledge, our proposed structure has the highest relative sensitivity compared with other reported structures.

4. Preparation Possibilities of the Designed MSF

Recently, the development of 3D printing techniques has enabled versatile implementations of MSF structures [42]. The 3D printing method relies on the principle of molten deposition and the thermoplastic extrusion and stretching of TOPAS material to produce thin fiber structures. Compared with traditional technology, 3D printing technology is a subversive preparation technology; its advantage lies in the preparation complex geometric structures, providing flexibility and diversity in the manufacturing process, enabling a high degree of freedom and rapid prototyping. 3D printing technology has positive development prospects and is expected to represent a mainstream technology for optical fiber preparation in the future.

Because errors inevitably occur in the preparation process of optical fiber, we also simulated and analyzed the errors of optical fiber preparation, as shown in Figure 8. We analyzed a fiber structure change of ±5% in the manufacturing process. We found that a 5% increase in D_core from the optimal value increased the relative sensitivity because such an increase enlarged the air holes and allowed for the inclusion of more analytes. Conversely, a 5% decrease in D_core resulted in a slight decrease in relative sensitivity within the allowable tolerance range.

5. Conclusions

In conclusion, we propose a THz-MSF with porous-core structures for the detection of cancer cells using TDS. The FEM was employed to numerically analyze the fiber capabilities and sensing performance of the proposed structure. By adjusting the fiber-core diameter, fill-in factor, and analyte, the designed structure can not only distinguish cancer cells from normal cells but also exhibit an increased sensitivity to cancer cells. The designed structure displays an ultrahigh relative sensitivity of 99.8% at an optimal frequency of 0.9 THz for breast cancer, which is the best result reported to date to the best of our knowledge. Due to its ultra-high sensitivity, the designed MSF structure has considerable potential for the early detection of cancer cells. In addition, the proposed structure is simple in design and can be prepared using 3D printing technology.