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Highly sensitive quasi-D-shaped photonic crystal fiber biosensor designed for the detection of RBC parasitized by Plasmodium falciparum for the early diagnosis of malaria

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Abstract

A simple quasi-D-shaped photonic crystal fiber (PCF)-based surface plasmon resonance biosensor is proposed for the early diagnosis of malaria that arises as a result of Plasmodium falciparum parasite development in erythrocytes in the human body. The flat surface of the D-shaped PCF is covered with a thin layer of TiO2 along with a gold layer. The finite element method (FEM) is used to numerically investigate the characteristics of the sensor. With the well-optimized set of parameters, the proposed sensor exhibits maximum spectral sensitivities of 42857.14 nm/RIU, 22105.26 nm/RIU, and 16206.90 nm/RIU with resolutions of 2.33 × 10−06 RIU, 4.52 × 10−06 RIU, and 6.17 × 10−06 RIU for ring, trophozoite, and schizont phases, respectively. The obtained amplitude sensitivities are 784.55 RIU−1, 491.02 RIU−1, and 407.99 RIU−1 and FOMs are 596.90 RIU−1, 423.98 RIU−1, and 341.63 RIU−1 for the three phases, respectively. Therefore, with the promising results and simplified practical realization, the proposed sensor can be an excellent candidate for the identification of Plasmodium falciparum phases in RBC for malaria diagnosis.

© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Malaria is an acute febrile disease caused by unicellular hemoparasites of the Plasmodium genus which are transmitted to humans and animals through the bites of infected female Anopheles mosquitoes. Globally, there are estimated to be 241 million cases and 6,27,000 deaths from malaria in 2020, according to the WHO's most recent World Malaria Report, 2021 [1]. When compared to 2019, there would be 69,000 more deaths and around 14 million more cases in 2020. The Covid-19 pandemic caused a significant decrease in the prevention, detection, and treatment of malaria, which contributed 66.67% to an additional 47,000 deaths [1]. Early diagnosis of this illness is the only solution to scale down the morbidity and mortality rate. Plasmodium falciparum, Plasmodium vivax, Plasmodium ovale, Plasmodium malariae, and Plasmodium knowlesi are the five kinds of Plasmodium parasites that are responsible for malaria. Among these, the most deadly form of human malaria is P. falciparum which is the cause of almost all fatalities. The lifecycle of the malaria parasite depends heavily on the RBC or erythrocyte. A healthy RBC's morphology and biophysical characteristics are permanently altered by the invasion and growth of the malaria parasite. Previous research has demonstrated that P. falciparum infection causes RBCs to become gradually less deformable as the intra-erythrocytic parasites mature and the infected cell becomes more spherical [2,3]. With the bite of infected female Anopheles mosquitoes, first, the liver cells are attacked after the parasite enters the human blood in the form of sporozoites. Following the hepatocyte stages, the intra-erythrocytic cycle begins with the attack on the erythrocytes by the parasite in the form of merozoites. Figure 1 illustrates different phases of the intra-erythrocytic cycle of P. falciparum.

 figure: Fig. 1.

Fig. 1. The intraerythrocytic cycle of P. falciparum.

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There are mainly three phases: the ring phase which begins after merozoites intrude into the erythrocyte, the trophozoite phase where mononuclear trophozoites are formed, and finally schizont phase where multinuclear schizonts are produced [4].

One of the most precise and sensitive methods of malaria diagnosis uses the polymerase chain reaction (PCR) technique that employs the amplification of malaria DNA. However, the usefulness of this technique is constrained by complicated methodologies, high costs, and demands skilled technicians [5]. Compared to the PCR technique, loop-mediated isothermal amplification (LAMP) is a simple, quick, and cost-effective molecular diagnostic test for malaria. The LAMP technique relies on the measurement of turbidity with a turbidity meter while amplifying DNA sequences [6]. Giemsa stain microscopy was first used to identify malaria in the laboratory from blood smears of infected patients. For many years, this method had been the standard method for diagnosing malaria. However, it was occasionally used outside of the lab, required a skilled microbiologist, and test reports were obtained at a comparatively slow pace [7]. Later, a rapid detection test (RDT) was developed to detect malarial infection by looking for parasite antigens or enzymes in the host's blood. However, RDT may be costly for poor communities living in malaria outbreak zones. Additionally, the RDT's detection accuracy in low-endemic areas was unsatisfactory and could lead to false-positive or false-negative results [8].

Photonic crystal fiber (PCF)-based biosensors have gained popularity in recent years for malaria diagnosis. An elliptical channel PCF-based biosensor for malaria detection was proposed in [9] where the highest spectral sensitivities were reported to be about 11,428.57 nm/RIU, 9473.68 nm/RIU, and 9655.17 nm/RIU for the ring, trophozoite, and schizont phases of the parasite, respectively. However, fabrication of the elliptical channel and infiltration of the sample in the channel is difficult in reality. Another work of gold-immobilized PCF-based SPR was reported in 2021, where an external sensing scheme was adopted. For the ring phase, trophozoite phase and Schizont phase RBCs calculated spectral sensitivities were 13714.29 nm/RIU, 9789.47 nm/RIU, and 8068.97 nm/RIU, respectively in the x-polarized direction. The spectral sensitivities were found to be 14285.71 nm/RIU, 10000 nm/RIU, and 8206.9 nm/RIU, respectively in the y-polarized direction [10]. However, the obtained spectral sensitivities in both of these works are not remarkable.

The fabrication of PCF-based SPR biosensors is simplified by the deposition of metal films over the PCF's dielectric surface, which allows for the development of novel PCF sensor designs like D-shaped sensors, exposed-core sensors, micro-channel sensors, U-shaped sensors, and others [1113]. Due to a closer distance between the plasmonic layer and the core of the PCF, D-shaped PCF enhances sensing performance by increasing energy transfer from core to plasmonic mode. The first D-shaped SPR-based optical fiber sensor was published in 2011 by G. Lanza et al. [14]. Researchers have recently reported on a variety of D-shaped SPR sensors due to their improved fabrication tolerance and high sensitivity. However, the D-shaped fiber becomes more fragile with a deep polishing depth. To prevent a nonuniform sensing surface and to impair sensing performance, the flat surface of the D-shaped fiber must be perfectly smooth.

In this paper, we proposed and numerically investigated a quasi-D-shaped PCF- based SPR sensor for malaria detection taking into account the critical aspects mentioned above for its practical implementation. With the ultra-short polishing depth and slightly lifted core, the fabrication is simplified and the fragility of the sensor can be avoided. Gold along with TiO2 as an adhesive is coated on the flat surface of the fiber structure. This sensor is more promising because it operates in the visible to near-IR spectrum. In comparison to the visible spectrum, the penetration depth of the evanescent field is higher at near IR wavelengths. As a result, a very sharp depth appears, making sensing and detection easier. Additionally, laser sources in the near-IR region are readily available commercially. The sensor can identify different phases of malaria-infected RBCs employing the significant refractive index (RI) difference between the healthy and infected RBCs.

2. Structure of the sensor

The 2D schematic representation of the proposed quasi-D-shaped sensor is shown in Fig. 2(a). The refractive index n as a function of wavelength λ of silica is evaluated by using the following Sellmeier equation:

$${n^2}(\lambda )= 1 + \frac{{{A_1}{\lambda ^2}}}{{{\lambda ^2} - B_1^{}}} + \frac{{{A_2}{\lambda ^2}}}{{{\lambda ^2} - B_2^{}}} + \frac{{{A_3}{\lambda ^2}}}{{{\lambda ^2} - B_3^{}}}.$$

The values of the Sellmeier coefficients A and B in Equation (1) are taken from [15]. The air holes are organized in three hexagonal rings to reduce leaky modes. The stack preform of the proposed PCF is exhibited in Fig. 2(b) in the transverse plane. Figure 2(b) shows that a selected air hole above the center is replaced by silica’s solid rod to form a single core. Two scaled-up air holes with diameter dl and three scaled-down air holes with diameter ds around the core control the leakage path for light and the core size to create an evanescent electric field that reaches the plasmonic material to stimulate free electrons. All other regular air holes in the proposed structure have a diameter d. The preform structure demonstrates that thick silica tubes are adopted for forming the scaled-down air holes, and thin silica tubes are used for the scaled-up and regular air holes. To create a flat surface for a quasi-D-shaped structure, side polishing process is used and the PCF is polished with a polishing depth of h.

 figure: Fig. 2.

Fig. 2. (a) Schematic view of the proposed quasi-D-shaped PCF -based SPR sensor, and (b) Fiber’s stack preform in the xy plane.

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In our proposed work, we have adopted gold as the plasmonic layer with thickness tg due to its superior characteristics compared to other noble metals, for example, copper, silver, gold, aluminum, niobium, etc. This is because gold is more stable in aqueous environments and has a higher shift of the resonance peak. Also, it is chemically inert, biocompatible, stable throughout time, and simple to structure. Because of these advantages, gold is commonly chosen as the plasmonic material in many SPR sensors [16,17]. The thin film of gold may exhibit discontinuities and this phenomenon is known as island formation. To resolve this problem and attach gold firmly with silica, the implementation of an adhesive layer is required. We used a layer of TiO2 with a thickness of tt as an adhesive layer over the flat surface of the quasi-D-shaped PCF.

The structural parameters used in the proposed quasi-D-shaped model are optimized to attain the best performance and the optimized values are shown in Table 1. Unless otherwise specified, all the parameters mentioned in Table 1 were maintained in all the simulations of performance investigation throughout this work.

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Table 1. Optimized Parameters of the Proposed quasi-D-shaped PCF for Malaria Detection

The permittivity of gold was determined by following the Drude–Lorentz model:

$${\varepsilon _{Au}} = {\varepsilon _\infty } - \frac{{\omega _D^2}}{{\omega ({\omega + j{\gamma_D}} )}} - \frac{{\Delta \varepsilon \Omega _L^2}}{{({{\omega^2} - \Omega _L^2} )+ j{\Gamma _L}\omega }},$$
where ω represents the angular frequency. The other parameters in Eq. (2) were taken from [18]. The RI of the TiO2 layer is found from [19] as follows:
$${n^2}(\lambda )= 5.913 + \frac{{2.441 \times {{10}^7}}}{{{\lambda ^2} - 0.803 \times {{10}^7}}}.$$

To prepare the sensor for malaria parasite detection, monoclonal antibodies specific to the target P. falciparum antigen are immobilized onto the surface of the sensor. The antibodies are attached to the sensor surface through a covalent coupling. Finally, a blocking solution is applied onto the sensor surface, washed in Phosphate Buffer Saline (PBS) and dried for bio-detection application [20].

The prepared sensor surface is exposed to the blood sample, and any malaria parasites present in the sample will bind specifically to the immobilized ligand on the sensor surface. Different antigens are released during the lifecycle of P. falciparum parasite. For example, some of the prominent antigens are ring-infected erythrocyte surface antigen (RESA), Plasmodium falciparum histidine-rich protein 2(PfRH-2), Plasmodium falciparum erythrocyte membrane protein 1 (PfEMP1), and merozoite surface protein 1 (MSP-1). The antigen-antibody binding event causes a change in the refractive index of the sensor surface, which is detected as a shift in the SPR signal [2123].When the healthy RBC of the human body is parasitized by P. falciparum, there is a significant change in the RI of the RBC due to the non-uniform RI distribution. Taking advantage of this major change in RI of RBC, we can detect malaria in the human body in its early stages. Table 2 lists the average RIs of the healthy and malaria-infected RBCs in three phases.

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Table 2. Average RIs of normal and malaria-infected RBCs at three phases

A circular perfectly matched layer was adopted to prevent the reflection of stray energy and absorb the radiant energy that arrives at the boundary. Figure 3 represents an experimental arrangement for the practical malaria diagnosis using the proposed quasi-D-shaped PCF sensor. To launch the light into the SMF, Broadband Light Source Module (BBLSM) is used. SMFs can be adopted as interconnection links and a splicing technique can be implemented for coupling the PCF and the SMFs at both ends. It should be noted that the splicing loss can be maintained with 1 dB for upward-shifted core of D-shaped PCF as shown in [25]. Additionally, to increase coupling efficiency splice-free interfacing technique [26], or objective lens [27] can be implemented. An analyte flow channel is added externally to the PCF to assist the inlet and outlet of the RBC sample which can be maintained by using a pump. Finally, an Optical spectrum analyzer (OSA) can be employed to examine the transmitted light. Additionally, the spectrum response may also be simply sent to a computer for further observation and analysis. Though our study is fully numerical, the realization of the experimental setup can easily be carried out using the devices and technologies used in [28].

 figure: Fig. 3.

Fig. 3. Schematic diagram of the experimental arrangement for the proposed quasi-D-shaped PCF sensor for malaria detection.

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3. Related theory

The PCF's cladding has a limited number of air holes, resulting in light leakage from the PCF's core. The following equation is used to find out the loss of fundamental mode during propagation:

$$\alpha (\textrm{dB/cm}) ={-} 8.686 \times {\kappa _0}\,{\mathop{\rm Im}\nolimits} ({n_{eff}}) \times {10^4},$$
where the imaginary effective mode index of the fundamental core mode is indicated as Im(neff), the wave number is ${\kappa _0} = 2\pi /\lambda $ and the operating wavelength is λ [29].

To evaluate the sensitivity of the proposed quasi-D-shaped sensor, we used wavelength interrogation and amplitude interrogation methods, respectively. Analyte sensing is carried out when the wavelength of bio-targets in the surrounding environment varies slightly. If the RBC is parasitized by P. falciparum, the RI falls from the RI of the healthy RBC which in turn blueshifts the resonant wavelength. Taking advantage of this fluctuation in resonant wavelength, the spectral sensitivity of the sensor can be obtained as follows:

$${\textrm{S}_\lambda }(\textrm{nm/RIU}) = \Delta {\lambda _{\textrm{resonance}}}({n_a})/\Delta {n_a},$$
where Δλresonance is the amount of change of the resonant wavelengths in nm for the normal and infected RBC and Δna is the difference in RI of a normal and malaria-infected RBC [30].

The amplitude interrogation method, unlike the wavelength interrogation approach, requires only a single wavelength to detect a sample, where a difference in propagation loss is used. The amplitude sensitivities for different RBC state was obtained using the following equation:

$${\textrm{S}_A}(\textrm{RI}{\textrm{U}^{ - \textrm{1}}}) ={-} \frac{1}{{\alpha (\lambda ,{n_a})}}\frac{{\partial \alpha (\lambda ,{n_a})}}{{\partial {n_a}}},$$
where $\alpha (\lambda ,{n_a})$ is confinement loss with RI na at a particular wavelength λ. $\partial \alpha (\lambda ,{n_a})$ indicates the change in propagation loss at wavelength λ for the change in the RI of $\partial {n_a}$ [30].

Another significant parameter is sensor resolution through which the sensor’s capability to sense the tiniest fluctuation in the RI of the RBC can be found. To obtain the sensor resolution the following formula is used:

$${R_\lambda }(\textrm{RIU}) = \Delta {n_a} \times \Delta {\lambda _{\min }}/\Delta {\lambda _{\textrm{resonance}}},$$
where minimum spectral resolution is considered as $\Delta {\lambda _{\min }} = 0.1\textrm{ nm}$. The figure of merit (FOM) is another critical indicator for assessing a sensor's quality. FOM should be as high as possible for a high-performing biosensor. It can be obtained by first determining the FWHM of the loss spectra at a particular RI and finding the ratio of the spectral sensitivity to FWHM at that RI [30].

Lastly, due to the asymmetry in the structure of a PCF, a PCF-based biosensor exhibits birefringence. The absolute difference of effective refractive indices of orthogonally polarized fundamental modes is defined as birefringence. The birefringence of a PCF can be determined from the following equation:

$$B = |{{n_x} - {n_y}} |, $$
where ${n_x}$ represents the real part of the effective mode index of x-polarization and ${n_y}$ represents the real part of the effective mode index of y-polarization [31].

4. Optimization of the reference structure

By varying the parameters of the sensor one by one, we optimized the parameters based on maximum spectral sensitivity and maximum amplitude sensitivity to obtain the best performance. While investigating the impact of a single structural parameter other parameters were kept fixed. First, we optimized the air hole diameter ds which is the diameter of the three small air holes surrounding the core. Since it controls the core size and leakage of light, it needs to be tuned with care. Figure 4(a) depicts the impact of ds variation on the maximum Sλ and SA. As we increase ds maximum Sλ keeps on rising. However, maximum SA obtains its highest value at ds = 0.45 Λ and decreases 48.2% for ds = 0.5 Λ. So, we select ds = 0.45 Λ as the optimized value. Next, we optimized dl which is the diameter of the large two air holes on top of the core. This also controls the leakage of light and core size. Figure 4(b) illustrates the impact of dl variation on the maximum Sλ and SA. As we increase dl maximum Sλ will increase and the maximum SA will decrease. If we increase dl from 0.97Λ to 1.02Λ, maximum Sλ increases by 6.67% and maximum SA will decrease by 56.9%. On the other hand, if we decrease dl from 0.97Λ to 0.92Λ, the maximum Sλ decreases by 53.33% and the maximum SA will increase 5.4%. To get best of the both realm and keep the diameter less than pitch Λ for ease of fabrication, we set dl = 0.97 Λ. The diameter of the rest of the air holes is d and the consequence of its change on maximum Sλ and maximum SA is displayed in Fig. 4(c). The maximum Sλ linearly decreases with the increase of d. Maximum SA has its minimum at d = 0.75Λ and then increases with the increase of d. We selected d = 0.8Λ as the optimized value to get a moderate maximum Sλ and maximum SA. It is also vital to investigate the impact of polishing depth h as it is the parameter that controls the distance of the plasmonic layer from the core. Figure 4(d) illustrates the impact of h on the maximum Sλ and SA. If we increase h, the short path between the metal surface and the core leads to a strong mode coupling which results in better wavelength sensitivity. But polishing the fiber after a certain level, there exists a coupling tendency between the fundamental mode and first order SPP mode. Thus, the loss peak of the core mode decreases, and the wavelength sensitivity also decreases [32]. The maximum Sλ is 45714.29 nm/RIU is found at h = 1 Λ. However, the maximum SA = 784.55 RIU−1 is obtained at h = 1.05Λ. If we reduce h from 1.05Λ to 1Λ, the maximum Sλ increases by 6.67% but the maximum SA falls by 11.26%. To keep SA larger, we choose h = 1.05 Λ as the optimized value of the polishing depth.

 figure: Fig. 4.

Fig. 4. Variation of maximum wavelength sensitivity and maximum amplitude sensitivity with the change in (a) ds, (b)dl, (c)d, and (d) h.

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The gold layer's thickness has a significant impact on the sensor performance as the surface plasmon wave (SPW) generates on it. Figure 5(a) illustrates the effect of gold layer thickness tg on the maximum Sλ and SA. Maximum Sλ = 42857.14 nm/RIU is obtained for tg = 50 nm which is the highest and maximum SA is 784.55 RIU−1at this thickness. For tg = 40 nm, Sλ decreases by 36.67%, and SA increases to 60.38% compared with tg = 50 nm. Figure 5(b) shows the peak confinement losses for the ring phase and normal phase RBC for varying tg. Clearly, for 40 nm gold thickness, the peak loss is 349.75 dB/cm and 496.57 dB/cm for ring phase and normal RBC respectively, which are more than three times than in the case of tg = 50 nm. The reason is a thinner layer of gold provides better coupling between the core mode and SPP mode. As the thickness is increased, due to the damping properties of the gold EM wave is obstructed to interact well with the analyte, resulting in suppressed confinement loss. Nevertheless, high confinement loss will lead to reduced sensor length, since the sensor length and confinement loss are inversely proportional [33]. This reduced sensor length can be difficult to achieve. Also, if the loss is sufficiently severe, the input signal would not be able to provide a substantial signal on the output port to detect the unknown sample during the actual implementation. That is why we choose 50 nm gold thickness to get greater Sλ and an achievable sensor length. The TiO2 layer thickness affects confinement loss and thus, alters the sensitivity of the sensor. In Fig. 5(c) the effect of change of tt on the maximum Sλ and SA is illustrated. As we increase tt, the maximum Sλ increases and SA decreases gradually. It is worth mentioning that the TiO2 film generates a large number of free surface electrons which attract the evanescent field from the core. Hence, the fundamental mode interacts well with the gold and improves the sensitivity. However, a thicker layer of TiO2 restricts the interaction of core-guided light from the analyte. Due to the reduced penetration depth of light, it generates broader loss peaks. Thus, thicker tt causes lower SA. So, to trade-off between the maximum Sλ and SA, we set the tt to 10 nm. The pitch (Λ) is another crucial parameter as all the air hole diameters depend on this, and so we optimized it carefully. Figure 5(d) depicts the impact of pitch on the maximum Sλ and SA. The maximum Sλ is found at 2 µm pitch. Increasing pitch to 2.1 µm the maximum Sλ decreases by 53.33% and the maximum SA increases by only 3.17%. If we decrease the pitch to 1.9 µm, maximum SA falls by 54%, and maximum Sλ increases to only 6.67%. Therefore, we chose Λ = 2 µm as the optimum value of pitch.

 figure: Fig. 5.

Fig. 5. (a) Variation of maximum wavelength sensitivity and maximum amplitude sensitivity with the change in tg (b) variation in loss peaks for RI of ring phase and normal RBC with the change in tg. Variation of maximum wavelength sensitivity and maximum amplitude sensitivity with the change in (c) tt, and (d) Λ.

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5. Performance investigation and numerical results

To explore the crucial optical properties of the proposed quasi-D-shaped sensor numerically, we employed the finite element method (FEM)- based commercial software COMSOL Multiphysics. Maximum mesh size is obtained by using λ/6n for the entire geometry of the sensor. Here, n refers to the mesh size parameter that increases up to 1 and λ is the operating wavelength. Figure 6 shows the confinement loss and the maximum number of elements as a function of n. Figure 6 demonstrates that confinement loss is nearly constant for n < 0.6. To make the computation process faster, we used $n = 0.43$.

 figure: Fig. 6.

Fig. 6. Confinement loss and the maximum number of elements as a function of the mesh size parameter.

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Due to the placement of the gold layer over the PCF flat surface, energy transfer in the x-polarization mode is more efficient than in the case of y-polarization. The asymmetrical structure of the quasi-D-shaped PCF is the reason behind the birefringence. Figure 7(a) illustrates the dispersion relation of the fundamental core mode and the SPP mode in the case of x-polarization for trophozoite phase RBC. Resonance is observed at the phase-matching wavelength where the energy transfer from the fundamental modes to the SPP modes is at its highest and confinement loss is at the maximum. For example, the phase-matching is observed for the trophozoite phase at 790 nm where the confinement loss is found to be 86.04 dB/cm for x-polarization. As the wavelength red or blue shifts from the phase-matching wavelength, the confinement loss decreases to the tail. Figure 7(b) displays the confinement loss spectra for the four RBC phases for y polarization. The phase coupling is not strong for y polarization which results in confinement loss under 1 dB/cm in the visible to near operating band. This is why we only consider the x-polarization mode for modal analysis throughout this work. The Fig. 7(c) shows the birefringence response of the proposed sensor for three phases of malaria infected RBC and healthy RBC. The proposed PCF sensor is designed asymmetrically to have high birefringence and to excite the sensing medium using x-polarized light only, rather than y-polarized light, in order to increase sensitivity. Figure 7(d) - 7(f) depicts the corresponding electric field distributions for trophozoite phase RBC at the resonant wavelength.

 figure: Fig. 7.

Fig. 7. (a) Dispersion relation of core mode and SPP mode for trophozoite phase, (b) Confinement loss versus operating wavelength curve for different phases of RBC for y-polarization. (c) Birefringence of different phases of malaria and healthy RBC as a function of wavelength. Electric field distribution of (d) x-polarized core, (e) y-polarized core, and (f) x-polarized SPP mode for trophozoite phase RBC.

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Figure 8 depicts the confinement loss spectra for RI of three infected RBCs during three phases of the parasite where the loss spectra of the normal RBC are taken as reference. When the normal RBC is affected and turns into ring phase RBC the RI changes; therefore, the resonant wavelength blueshifts from 1210 nm to 910 nm (see Fig. 8(a)). The peak loss also falls from 164.08 dB/cm to 102.54 dB/cm. In the case of trophozoite phase RBC, the resonant wavelength blueshifts to 790 nm, and the confinement loss at this condition fall to 86.04 dB/cm as shown in the Fig. 8(b). Finally, for schizont phase RBC, the resonant wavelength blueshifts to 740 nm, and confinement loss decrease to 71.82 dB/cm as shown in the Fig. 8(c). Evidently, the phase-matching wavelengths of healthy and malaria-infected RBCs are very sensitive to the RI change. Employing these blueshifts in the resonant wavelengths and the confinement spectra, different important sensor parameters can be found like as wavelength sensitivity, spectral resolution, FWHM, and FOM which are listed in Table 3. The amplitude sensitivity spectrum for Ring, Trophozoite and Schizont phases of RBC is shown in Fig. 8(d). As can be seen from the figure there are multiple peaks and we only listed the maximum amplitude sensitivity of each phase in Table 3.

 figure: Fig. 8.

Fig. 8. Confinement loss versus wavelength curve of (a) normal RBCs and infected ring phase RBCs, (b) normal RBCs and infected Trophozoite phase RBCs, (c) normal RBCs and infected Schizont phase RBCs, and (d) amplitude sensitivity of different phases of malaria parasite as a function of wavelength.

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Table 3. Performance of sensor for different infected RBC phases

Practically, it is difficult to exactly maintain the design parameters during fabrication. Therefore, ± 1% variation is generally considered. To get an accurate idea about the fabrication tolerance, we investigated the variation of loss spectra for ±5% and ±10% change of the structural parameters at a higher RI of ring phase RBC. Figure 9(a) illustrates the confinement loss spectra for change of pitch size. As the pitch Λ increases the peak loss falls and the resonant wavelength blueshifts slightly. On the other hand, the peak loss increases, and the resonant wavelength redshifts slightly with the decrement of pitch size. The reason is lower pitch size scales down the core size and there is a strong interaction with the plasmonic layer. For example, 10% decrement and 10% increment of the pitch size lead to a 33.07% increase and 24.55% decrease in peak loss, respectively. In the case of polishing depth h, the loss increases at lower polishing depths, and the resonant wavelength redshifts insignificantly, as illustrated in Fig. 9(b). As the h is scaled down to 10%, the loss rises to 42.36% and as h is increased by 10%, the loss decreases by 24.24%.

 figure: Fig. 9.

Fig. 9. Confinement loss spectra within ±10% change in air hole diameter (a) Λ, and (b) h.

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The diameters of the air holes are varied within ±10% and the effect on confinement loss spectra is displayed in Fig. 10. As ds increases the peak loss increases and the resonant wavelength shifts to longer wavelengths to some extent. The opposite scenario is observed in case the diameter ds is decreased, as illustrated in Fig. 10(a). This is mainly because as ds is increased, the core area decreases leading to more leakage of the field to the plasmonic layer and making stronger coupling between the core mode and SPP mode. This is why with a 10% increment of ds, a 32.61% increase in peak loss was found. On contrary, a 24.81% decrease in peak loss was found for a 10% decrement from the optimized ds. Additionally, the situation is the opposite in the case of dl. As depicted in Fig. 10(b), with the increase in dl the peak loss decreases, and the resonant wavelength shifts to a longer wavelength. For example, with a 10% increase in dl, the peak loss decreased by 54.9%. However, as dl decreases, the peak loss raises dramatically. Using dl we can control the leakage path of the field from the core to the plasmonic layer. Higher dl leads to more confined light to the core and generates lower confinement loss. On the other hand, smaller dl gives a broader path to the leakage field leading to more efficient interaction of the core mode and the SPP mode and developing higher loss at resonant wavelength. As shown in Fig. 10(c) there is no discernible impact on the confinement loss spectra despite the variation in d. From Fig. 10(c) it is found that, as d is incremented by 10%, the peak confinement loss rises by 3.4%. In contrast, as d is scaled down 10%, the loss is decreased by 3.9%, while the resonant wavelength is almost unaltered in both cases. Therefore, the proposed sensor has decent tolerance for fabrication error.

 figure: Fig. 10.

Fig. 10. Confinement loss spectra within ±10% change in air hole diameter (a) ds, (b) dl, and (c) d.

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The fabrication of the proposed sensor in real life should be simple as there is a lesser number of air holes arranged in three rings. To build up the hexagonal lattice structure of the quasi-D-shaped sensor, stack-and–draw, sol-gel casting, or injection molding can be adopted. However, with low cost and flexibility standard stack-and-draw method is mostly preferred [34]. Laser drilling [35] and 3D printing techniques [36] can be employed to produce the preform. Capillaries are stacked inside a jacket tube, which is then drawn and passed through a high-temperature furnace to soften. Fresh jacketing undergoes additional modification if the air hole diameters require adjustment. The cane is then made, then pulled through a fiber of fixed diameter, and finally chopped to the required length. Another technique is to apply pressure on the cane to change the size of the chosen air holes [37]. However, providing pressure necessitates a unique pressurizing apparatus, which can add some extra complexity to the manufacturing process. To achieve the flat surface of the d-shape, polishing needs to be performed carefully. For this purpose, the traditional side polishing technique or chemical etching method can be adopted [29,38]. The ultra-short polishing depth simplifies the fabrication method as we need to polish off a tiny portion of the PCF. Also, as the core is lifted to some extent, this type of structure will provide toughness to the PCF and reduce fragility [39]. However, to avoid micro-cracks and surface contamination completely, laser technology can also be implemented [40,41]. After producing the flat surface, the surface needs to be coated with 10 nm TiO2 and then a 50 nm Au layer externally. The deposition can be performed by high-pressure micro fluidic chemical deposition, pulsed laser deposition (PLD), and RF sputtering [4244]. Consequently, the suggested quasi-D-shaped PCF sensor can be manufactured in real life, thanks to these already-available technologies.

In Table 4 we compare the performance of the previously reported sensors for malaria detection in terms of sensitivity. The PCF biosensor's detection limit is determined by the difference between the RI of healthy and infected RBCs at different stages of the malaria parasite. As a result, the detection thresholds for the ring phase, trophozoite phase, and schizont phase of malaria parasites, respectively, are 0.007, 0.019, and 0.029 in this work. The methods for diagnosing malaria that has been previously reported rely mostly on the use of clinical, laboratory, or molecular diagnostic techniques to find antibodies against parasites, malaria pigment, hemozoin, and antigens or enzymes. However, these methods call for an experienced microscopist, knowledgeable staff, pricy diagnosis equipment, quality control improvement, and other viral infections that could result in false positive responses. The SPR-based sensing method of malaria parasites offers higher sensitivity, quick detection, and a low detection limit. Additionally, the sensors have a straightforward design and an affordable malaria detection method. In terms of sensitivity, our proposed work stands out among them. The superior performance with high sensitivity makes the proposed quasi-D-shaped SPR sensor an appropriate candidate for the early diagnosis of malaria.

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Table 4. Comparison of the proposed sensor with some previous works

6. Conclusion

In this work, a highly sensitive quasi-D-shaped PCF-based SPR biosensor is proposed with a simple hexagonal structure for the detection of malaria-affected RBC in the human body. The sensor’s flat surface is coated with TiO2 and Au layer and it works in the visible to near IR range. Ultra-short polishing depth makes fabrication of the sensor easier and the promising structure of the sensor makes it less fragile. The structural parameters of the sensor are well-optimized to ensure the best performance of sensor. The performance of the sensor was investigated by employing FEM. With the optimized parameters, numerical results show maximum wavelength sensitivities of 42857.14 nm/RIU, 22105.26 nm/RIU, and 16206.90 nm/RIU with resolutions of 2.33 × 10−06 RIU, 4.52 × 10−06 RIU, and 6.17 × 10−06 RIU for parasite’s ring, trophozoite and schizont phases, respectively. The obtained amplitude sensitivities are 784.55 RIU−1, 491.02 RIU−1, and 407.99 RIU−1 and FOM are 596.90, 423.98, and 341.63 for the three phases, respectively. We have explored the fabrication tolerance of sensor parameters and the fabrication prospects. Due to the remarkable performance, quick and easy detection process, portability, simple design, environment compatibility, and fabrication feasibility, the proposed sensor can be utilized for early malaria diagnosis in real life.

Acknowledgments

The authors would like to cordially thank anonymous reviewers for their meaningful insights. We also thanks the Research & extension of RUET for its financial assistance (DRE/7/RUET/528(39)/PRO/2021-22/16).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (10)

Fig. 1.
Fig. 1. The intraerythrocytic cycle of P. falciparum.
Fig. 2.
Fig. 2. (a) Schematic view of the proposed quasi-D-shaped PCF -based SPR sensor, and (b) Fiber’s stack preform in the xy plane.
Fig. 3.
Fig. 3. Schematic diagram of the experimental arrangement for the proposed quasi-D-shaped PCF sensor for malaria detection.
Fig. 4.
Fig. 4. Variation of maximum wavelength sensitivity and maximum amplitude sensitivity with the change in (a) ds, (b)dl, (c)d, and (d) h.
Fig. 5.
Fig. 5. (a) Variation of maximum wavelength sensitivity and maximum amplitude sensitivity with the change in tg (b) variation in loss peaks for RI of ring phase and normal RBC with the change in tg. Variation of maximum wavelength sensitivity and maximum amplitude sensitivity with the change in (c) tt, and (d) Λ.
Fig. 6.
Fig. 6. Confinement loss and the maximum number of elements as a function of the mesh size parameter.
Fig. 7.
Fig. 7. (a) Dispersion relation of core mode and SPP mode for trophozoite phase, (b) Confinement loss versus operating wavelength curve for different phases of RBC for y-polarization. (c) Birefringence of different phases of malaria and healthy RBC as a function of wavelength. Electric field distribution of (d) x-polarized core, (e) y-polarized core, and (f) x-polarized SPP mode for trophozoite phase RBC.
Fig. 8.
Fig. 8. Confinement loss versus wavelength curve of (a) normal RBCs and infected ring phase RBCs, (b) normal RBCs and infected Trophozoite phase RBCs, (c) normal RBCs and infected Schizont phase RBCs, and (d) amplitude sensitivity of different phases of malaria parasite as a function of wavelength.
Fig. 9.
Fig. 9. Confinement loss spectra within ±10% change in air hole diameter (a) Λ, and (b) h.
Fig. 10.
Fig. 10. Confinement loss spectra within ±10% change in air hole diameter (a) ds, (b) dl, and (c) d.

Tables (4)

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Table 1. Optimized Parameters of the Proposed quasi-D-shaped PCF for Malaria Detection

Tables Icon

Table 2. Average RIs of normal and malaria-infected RBCs at three phases

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Table 3. Performance of sensor for different infected RBC phases

Tables Icon

Table 4. Comparison of the proposed sensor with some previous works

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

n 2 ( λ ) = 1 + A 1 λ 2 λ 2 B 1 + A 2 λ 2 λ 2 B 2 + A 3 λ 2 λ 2 B 3 .
ε A u = ε ω D 2 ω ( ω + j γ D ) Δ ε Ω L 2 ( ω 2 Ω L 2 ) + j Γ L ω ,
n 2 ( λ ) = 5.913 + 2.441 × 10 7 λ 2 0.803 × 10 7 .
α ( dB/cm ) = 8.686 × κ 0 Im ( n e f f ) × 10 4 ,
S λ ( nm/RIU ) = Δ λ resonance ( n a ) / Δ n a ,
S A ( RI U 1 ) = 1 α ( λ , n a ) α ( λ , n a ) n a ,
R λ ( RIU ) = Δ n a × Δ λ min / Δ λ resonance ,
B = | n x n y | ,
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