Design and finite element modeling of two–dimensional nanomechanical biosensors for SARS–CoV–2 detection

Abstract

SARS–CoV–2 is the causative agent of COVID–19 disease. The development of different variants has increased the prevalence, pathogenicity, and mortality of the SARS–CoV–2. Prompt diagnosis and timely initiation of therapy can undoubtedly minimize the damage caused by this virus. In this study, a wide range of emerging single layer two–dimensional materials (SL2DMs), including graphene, grapheme oxide (GO), reduced graphene oxide (rGO), hexagonal boron nitride (h–BN), Ti3C2Tx MXene, and MoS2that can be used to fabricate highly sensitive biosensors, are analyzed using the finite element method based on antigen–antibody interaction. Important design parameters including sensor size, sensor aspect ratio, number of viruses, and applying in-plane strain on sensor performance are analyzed using frequency shift technique. In the following, an analytical relationship that can predict the limit of detection (LOD) according to the above parameters is proposed. The results show that all the above materials have a good performance in detecting viruses in the sample range of 10–100 viruses. This range can be reduced significantly by applying strains of less than 0.1. Also, applying strain increases shift frequency index by 2 to 3 times, which is a significant result. The maximum and minimum sensor performance are obtained for GO and Ti3C2Tx, respectively. The results of this paper can be used to build a new generation of two–dimensional biosensors for rapid detection of COVID–19 and other viruses.

1. Introduction

Coronavirus Disease 2019 (COVID–19) was first reported in 2019 in Whan, China. The cause of it is SARS–CoV–2, and today has involved several hundred countries in a critical dilemma [1]. Common treatments include anti–inflammatory and anti–inflammatory drugs. SARS–CoV–2 has undergone several mutations since 2019, which have significantly increased its spread [2]. Multiple variants of the SARS–CoV–2 that cause COVID–19 have been documented. Scientists are working whether currently authorized vaccines will protect people against them. Currently, there are four notable variants in the United States: B.1.1.7 (Alpha), B.1.351 (Beta), P.1 (Gamma), and B.1.617.2 (Delta). Delta variant easily spread, and causes more severe illness [2].

COVID–19 usually affects people of all ages, and the disease is transmitted through respiratory droplets or contact of the virus on the surface with the eyes, nose, and mouth. The most important challenge of fast transfer COVID–19 is long–turn, asymptomatic incubation. Many countries around the world have issued vaccination permits to people in emergencies [3], [4]. Available evidence suggests the COVID–19 vaccines are highly effective against hospitalization and death for a variety of variants [5]. At this time, there are limited data on vaccine effectiveness. Ongoing monitoring of vaccine effectiveness against variants is needed.

Morphologically, SARS–CoV–2 has round shape with approximately 100 nm in diameter [1]. Structurally, SARS–CoV–2 has four major structural proteins, including Spike (S), Nucleocapsid (N), Envelope (E), and Membrane (M) proteins. Spike glycoprotein were divided to the two subunits (S1 and S2 subunits) that is the largest structural protein of SARS–CoV–2. RBD is located on S1 subunit that allows it to dock to receptors on the cells and lead to infection [6]. Spike glycoprotein plays an essential role in the virus's pathogenesis. The mechanism of SARS-CoV-2 infection is through the binding of the RBD to Angiotensin Converted En-zyme 2 (ACE2) receptor on type II alveolar epithelial cells. In this study, we were inspired by this mechanism and simulated a Nanomechanical biosensor based on antigen-to-antibody interaction. Details of this binding mechanism are shown in Fig. 1 . SARS–CoV–2 using RBD bind to Angiotensin Converted Enzyme 2 (ACE2) receptor on type II alveolar epithelial cells. Then, virus enter yours genome to the host cells and infects it [7]. These structural proteins are used for detection of SARS–CoV–2 in both of immunoassay and genome–based diagnosis technique [8], [9].

Fig. 1.

The structure of the SARS–CoV–2. Spike glycoprotein consists of two subunits, S1 and S2. RBD of the S1 subunit is responsible for binding to the ACE2 receptor on the host cells.

Despite the available treatments and vaccines, COVID–19 is still a big challenge globally, and it is definitely necessary to manage this challenge. Prompt and accurate diagnosis of SARS–CoV–2 in people suspected of having the disease can significantly help control the disease. There are many diagnostic tests, including old methods: chest scans (CT) and new methods, including nucleic acid–based methods and antibody–antigen (immunoassay) [9], [10]. Recently, biosensor–based diagnostics and nanotechnology have been developed to detect SARS–CoV–2. Biosensors can detect a wide range of biomarkers, including RNA, DNA, and even the cell or virus [11], [12], [13], [14]. Types of biosensors have been developed, including antibodies based on antibodies (immunosensors), based on nucleic acid (genosensor), and based on the whole–cell to diagnose viral infections. Immunosensors have received more attention due to their higher speed [15], [16].

Owning to nanosensors has many advantages over PCR–based technique, including low cost, specificity, simple structure, higher speed, and the ability to be minimized, which is why they are an excellent option for virus detection. Undoubtedly, limit of detection (LOD) is one of the most important features of analytical processes. LOD of qRT–PCR as gold standard for SARS–CoV–2 detection is 100 copies/test. Despite the advantages of PCR–based techniques, there is a need for a faster and cheaper method that has high sensitivity and specificity [17].

Mechanical nanosensors measure the presence of biomarkers by measuring frequency, pressure, etc. By connecting any external agent to the surface of the mechanical nanosensor, it shifts frequency. Therefore, by recording the frequency changes of the shift and comparing it with the initial state (without external factor connection), the presence of the surface–connected agent is quickly detected. Many studies are using a wide range of two–dimensional materials in simulation or bio–instrumentation [12], [18], [19], [20]. One of the most efficient methods of designing mechanical nanosensors is the use of finite elements method, which has recently received a lot of attention [21], [22], [23]. In the previous study of the our group, a graphene–based mechanical nanobiosensor was simulated that was functionalized with anti–SARS antibody, and the parameters of virus number, antibody concentration, and single layer graphene sheet properties including size, aspect ratio, and boundary conditions were investigated, and the results turned out well. This simulated mechanical nanobiosensor showed that it detects a range of 1–10 viruses in each test with a passable frequency shift. The LOD sensor detects 10 viruses per test [18]. Our simulated graphene–based nanosensor can be used with high sensitivity as a COVID–19 diagnostic tool. Two–dimensional materials (2DMs) are very important in the field of biosensors because of the unique properties, including its superior conductivity, plasmonic property, high elastic modulus, low weight, extremely large surface area, and biocompatibility that are necessary to create accurate and sensitive biosensors [1], [2], [24], [25], [26]. Different single layer two–dimensional materials (SL2DMs) (Listed in Table 1 ) including graphene, graphene oxide (GO), reduced graphene oxide (rGO), hexagonal boron nitride (h–BN), Ti3C2Tx MXene, and MOS2 were selected, which are the most common materials used to manufacture diagnostic tools. For example, MXene has opened a new vision for developing and designing biosensors. The advantage of this material is the possibility of detecting proteins in an oriented way by adding an -OH group to its structure. This possibility is important for oriented immobilization of enzymes and antibodies [27].

Table 1.

Mechanical properties of different SL2DMs used in FEM [28], [29], [30], [31], [32], [33], [34], [35], [36].

Materials	Elastic modulus (TPa)	Poisson's ratio	Density (kg·M−3)	Thickness (nm)
GO	0.21	0.165	260	0.7
rGO	0.25	0.064	1910	1
MOS2	0.27	0.27	5060	0.65
Ti3C2Tx	0.33	0.227	4600	0.98
h–BN	0.87	0.221	2200	0.335
Graphene	1	0.149	2300	0.345

Important design parameters including sensor size, sensor aspect ratio, number of viruses, and applying strain on sensor performance are analyzed using frequency shift technique. In the following, an analytical relationship that can predict the limit of detection (LOD) according to the above parameters is proposed. Since there are many two–dimensional materials, this study aimed to find the better material with higher sensitivity and lower LOD for SARS–CoV–2 detection.

2. Methods & materials

Effective parameters in biosensor design, including material and size of the sensor, number of viruses, and increasing applied strain to increase sensor sensitivity have been investigated. A wide range of emerging SL2DMs that can be used to fabricate highly sensitive biosensors are examined (see Table 1). The main feature of these materials is very high elastic modulus and their very low weight, which makes them have a very high resonance frequency and are suitable for detecting very small objects. Also, their antiviral and bacterial properties significantly increased their use in the manufacture of medical devices [37]. The size of the sensor surface is in the range of 5–100 μm, considering the average diameter of the virus, which is 100 nm. Also, the aspect ratio of the surface is considered between 0.2–5 (M = W/L). This ratio has a significant effect on increasing the sensor's sensitivity due to the increase in system stiffness [18]. Since the purpose of this article is to provide very sensitive sensors, the number of viruses used in sensor surfaces is in the range of 10–1000. It is possible to identify more of them. Applying in-plane strain to the sensor surface before exposing it to the virus is one of the innovations of the present work. Previous studies showed that applying strain to structure changes its natural frequencies [31], [38]. In this method, the strain is done by applying tension to both sides of the surface, causing a significant increase in energy inside the system. As a result, the resonance frequency of the layer is significantly increased. This will eventually increase the sensitivity of the sensor and improve its performance. Of course, in the application of strain, mechanical limitations must also be considered that do not lead to rupture of the material. In the present work, the tensile strain, according to previous articles, is considered to be a maximum of 10% [36], [39].

2.1. Biological consideration

There is now an immunoglobulin G1 (IgG1) monoclonal antibody that neutralizes all currently known variants. This antibody targets the RBD region in spike glycoprotein, and it seems to be a good option for making and designing antigens–antibody–based biosensors. Therefore, we selected anti–SARS–CoV–2 spike RBD antibody as a receptor on nanomaterials surface. The process of the function of the nanobiosensor will be as follows (see Fig. 2a):

• (a)1–pyrenebutyric acid N–hydroxysuccinimide (PBASE), bifunctional linker molecule, is functionalized on the surface of nanomaterials.
• (b)Anti–SARS–CoV–2 antibodies are immobilized to the surface of the nanomaterials. In other words, antibodies binding to PBASE linkers.
• (c)In the second step, the SARS–CoV–2 are randomly distributed on the surfaces using a code written in Python, and shift frequencies are evaluated using FEM approach.

Fig. 2.

(a) Schematic illustration of the nanomechanical biosensor operation; (b) finite element modeling and boundary condition of SL2DM; (c) first mode shape of SL2DM vibration.

The whole sheet has been functionalized with antibodies to attach viruses on the SL2DMs. In order to increase the probability and strength of antibody binding to the SARS–CoV–2 antigen, it is assumed that the antibodies cover the entire surface uniformly. The dimension and molecular weight of the anti–SARS–CoV–2 spike RBD antibody are 15  nm × 2.5  nm × 10  nm, and 147, 400  g ⋅ mol ⁻¹, respectively [40]. Subsequently, it is assumed that each antiSARS–CoV–2 spike S1 antibody has 244.77 zg mass and fills a circular area with a diameter of 15 nm on the SL2DMs surface. The whole sheet has been functionalized with antibodies to attach viruses on the SL2DMs. In order to increase the probability and strength of antibody binding to the SARS–CoV–2 antigen, it is assumed that the antibodies cover the entire surface uniformly. According to the Transmission Electron Microscopy (TEM) observations [1], coronavirus geometry can be considered is spherical shape with diameter 60 and 140 nm [41]. By assuming average diameter and mass density of coronavirus are 100 nm and 1 g/mL [41], respectively, the mass of each virus has been determined as 524 ag (1ag = 10^–18 g).

2.2. Finite element modeling

A single–layer sheet of different candidate materials can be modeled as a plate with the equivalent physical and mechanical properties listed in Table 1. By using high order 8–node shell element, the sheet is meshed with sufficient elements, and a Clamp–Free–Clamp–Free boundary condition is applied to four sides of the plate according to Fig. 2b. Both clamp sides are stretched with a specific in-plane strain before vibration analysis to apply strain to the sheet. The free vibration assumption is considered to solve the problem. When strain is taken into account to vibration analysis of structure, governing equation of FEM is expressed as [29]:

$$\left[m\right]\left\{\ddot{q}\right\}+\left[K+S\right]\left\{q\right\}=0$$ (1)

where [m] is a global mass matrix, [K] is stiffness matrix, {q} is nodes displacement, and {q} is nodes acceleration vector of the system. [S] is a geometric matrix which is determined after applied strain to sheet as below equation:

$$\left[K\right]\left\{q_0\right\}=\left\{F\right\}$$ (2)

where {q ₀} is the displacement vector of nodes and {F} is required force to applied desired strain to the sheet. By identification of the [S] matrix by evolution of stress in SL2DMs surface and estimation of harmonic solution $\left\{q\right\}={\overline{q}}_i{e}^{j{\omega }_{i}t}$ for Eq. (2), the governing equation in converted to conventional eigenvalue problem as follow:

$$\left[K+S\right]\left\{{\overline{q}}_i\right\}={\omega }_i^2\left[m\right]\left\{{\overline{q}}_i\right\}$$ (3)

where ω _i is the angular resonant frequency and $\left\{{\overline{q}}_i\right\}$ is associated with the mode shape of the vibration. The first mode shape of SL2DM vibration is shown in Fig. 2c.

Now, frequency shift can be evaluated as:

$$\mathrm{\Delta }{f}_i=f_{0i}-f_i$$ (4)

Here f _i and f _0i are the resonant frequencies determined by vibration analysis of SL2DMs in the presence and absence of the virus, respectively, which is calculated as:

$$f_i=\frac{{\omega }_i}{2\pi }$$ (5)

The performance criterion of the sensor is parameter f _relative as known relative frequency, With a minimum amount of 5% [30], which is calculated as follows:

$$f_{\mathit{relative}}=\frac{\mathrm{\Delta }{f}_i}{f_{0i}}\times 100$$ (6)

Here we present another design criterion as follows that can help design virus–specific biosensors:

$$\mathit{SS}=\frac{\mathrm{\Delta }{f}_i}{N}$$ (7)

where N is the number of attached virues to SL2DMs surface.

As we know, the spread of viruses on the SL2DMs surface is completely random. In order to design the sensors more accurately, it is necessary to statistically examine the effect of number and distribution of viruses on the SL2DMs vibration behavior. To overcome this problem, Poisson distribution function is used. In this method, a certain number of SL2DMs are generated with different types of virus spreads and frequency analysis is performed. In the present paper, 100 random samples are generated according to Poisson distribution function and subjected to vibrational analysis according to above procedure. Refer to our recently work for more details [18].

2.3. Analytical model for LOD prediction

LOD determination is one of the basic parameters of sensor design. This parameter helps us design other sensor specifications according to the concentration of the virus number and the relative frequency [18]. Payandehpeyman et al. presented the following relation for prediction of relative frequency for graphene–base nanomechanical resonator for detection of COVID–19 as follow:

$$f_{\mathit{relative}}=\alpha N^{\beta }{M}^{\theta }{L}^{\gamma }$$ (8)

where L and M are the sensor length and sensor aspect ratio, respectively. The coefficients α, β, θ, and γ are dimensionless constants that can be calculated by fitting the curve to the simulation results. In Fig. 3 , the effects of different parameters on based on this model are shown for graphene. The acceptable range for relative frequency is f _relative > 5%. As can be seen, the effects of single graphene layer geometry including sensor size and aspect ratio is very crucial.

Fig. 3.

Effect of number of virus, sensor length, and sensor aspect ratio on relative frequency of graphene–base nanomechanical biosensor.

In the current paper, the latter relation can be developed by applying the strain effect on the sensor as follows:

$$f_{\mathit{relative}}=\alpha N^{\beta }{M}^{\theta }{L}^{\gamma }\left({\epsilon }_0+{\epsilon }^{\lambda }\right)$$ (9)

If frelative is assumed desired value, for example f _relative = 5%, LOD can be obtained in terms of the sensor geometry as follow:

$$\mathit{LOD}={\left(\frac{f_{\mathit{relative}}}{\alpha M^{\theta }{L}^{\gamma }\left({\epsilon }_0+{\epsilon }^{\lambda }\right)}\right)}^{\frac{1}{\beta }}$$ (10)

3. Results & discussion

In this section, the effect of the number of viruses, SL2DMs type, SL2DMs geometry, and in-plane strain on the vibration characteristics such as fundamental frequency, frequency shift, sensing index, and sensor sensitivity are investigated. In the caption of each figure, the values of fixed variables in the analysis are mentioned. Totally, more than 10,000 FEA simulations were implemented using a personal computer with a 4–core 2.4 GHz CPU and 8 GB RAM. The simulation run time to solve the problem changed between 20 and 80 seconds, depending on the size and aspect ratio of the SL2DMs sheet. The constant coefficients of the presented model(Eq. (10)) are evaluated for different SL2DMs using curve fitting technique and given in Table 2 .

Table 2.

Constant coefficients of model for different SL2DMs (ε₀ = 10⁻⁵).

Material type	α	β	θ	γ	λ
GO	91.2730	0.5512	−0.6958	−1.2805	0.1096
rGO	41.7476	0.7041	−0.8533	−1.5577	0.1101
MoS2	33.0359	0.7696	−0.9308	−1.6696	0.1248
Ti3C2Tx	20.0817	0.8085	−0.9572	−1.7302	0.1058
h–BN	88.1258	0.6140	−0.7641	−1.3866	0.1352
Graphene	88.5355	0.6163	−0.7641	−1.3949	0.1365

The first frequency, frequency shift, relative frequency shift, and sensor sensitivity of the biosensor versus the number of viruses for different SL2DMs are shown in Fig. 4 . As expected, due to the increase in system inertia [42], the increase in the number of viruses has led to a decrease in the natural frequency (see Fig. 4a). The highest and lowest frequencies belong to rGo and h–BN, respectively. The frequency of values graphene, h–BN, and MoS2 are very close to each other and are significantly lower than other SL2DMs. As shown in the semi–logarithmic diagram in Fig. 4b, contrary to the natural frequency, the frequency shift has increased with the increasing number of viruses and is nearing saturation. In this diagram, the values have changed between 250 Hz and 20 kHz, and GO, and MoS2 have the highest and lowest values.

Fig. 4.

Effect of SARS–CoV–2 copy on the biosensor characteristics: (a) resonant frequency; (b) frequency shift; (c) relative frequency; (d) sensor sensitivity. In the simulation, L = 10 μm, M = 1 and ε = 0.

The effect of increasing the number of viruses on the performance of sensors with different materials is shown in Fig. 4c. Suppose we set the value of 5% to the minimum value of relative frequency for virus detection. In that case, all materials can be used to detect at least 100 viruses in the sample, taking into account the current specifications of the sensor. However, the number of viruses for GO has dropped to 25, indicating the highest susceptibility to the substance. The present model prediction, which is fitted on the simulation results, is shown in Fig. 4c. As can be seen, the model predicts the simulation results well.

The second important design parameter is sensor sensitivity, which is plotted for different materials in Fig. 4d. Sensor sensitivity changes with the number of viruses for Ti3C2Tx and MoS2 substances in the range of 15 to 40 (Hz/number) and are not very noticeable. However, this range is wider for rGo, graphene, and h–BN materials, and there are more changes (about 25–90 (Hz/number)). The highest sensitivity belongs to GO, which has been reduced from about 190 to 50 (Hz/number). The 15–190 (Hz/number) range is a significant value for sensor sensitivity and indicates the excellent ability of these materials to fabricate specific coronavirus biosensors.

The effect of biosensor size on the vibration characteristics for different SL2DMs is illustrated in Fig. 5 . As we know from the vibration principle, increasing the size of the structure due to reducing the system's stiffness leads to a decrease in the natural frequency of the system [42], which is seen in a completely linear logarithmic diagram in Fig. 5a. Increasing the size of the biosensor from 5 μm to 100 μm significantly reduces the natural frequency by an average of about 200 kHz to 650 Hz. This process is the same in the frequency shift. According to the presented model shown in Fig. 5c, the appropriate size of a biosensor to detect less than 100 viruses, by assuming f _relative ≥ 5%, should be <25 μm. However, this number can be increased by increasing the number of viruses in the patient sample. The decrease in sensor sensitivity from about 1000 to 0.01 with increasing length is shown in Fig. 5d.

Fig. 5.

Effect of SL2DMs length on the biosensor characteristics: (a) resonant frequency; (b) frequency shift; (c) relative frequency; (d) sensor sensitivity. In the simulation, N = 100, M = 1and ε = 0.

The effect of the biosensor aspect ratio on the vibration characteristics for different SL2DMs is shown in Fig. 6 . The value of SL2DMs layer aspect ratio is increased from 0.2 to 5, which reduces the system's stiffness and thus reduces its normal frequency as well as shift frequency (Fig. 6a,b). The importance of this parameter in construction can be very high. Because only by changing the bound edges and without changing the sensor size, increasing the number of viruses, applying strain, etc. The efficiency of the sensor can be significantly increased. As shown in Fig. 6c, for M < 1, the relative frequency is greater than 5% and is in a very suitable area for design for all 2DMs. However, it has an acceptable value for GO, graphene, and h–BN in all aspect ratio ranges. Reducing the aspect ratio improves the sensitivity of SL2DMs in the range of 1–10 kHz/number, which again shows the great importance.

Fig. 6.

Effect of SL2DMs aspect ratio on the biosensor characteristics: (a) resonant frequency; (b) frequency shift; (c) relative frequency; (d) sensor sensitivity. In the simulation, SARS – COV – 2 Number = 100, L = 100 μm and ε = 0.

Apply tensile in-plane strain on the vibration characteristics for different SL2DMs are illustrated in Fig. 7 . The effect of applying strain on the performance of the sensor is obvious. As shown in Fig. 7a, applying a small tensile strain of 1% rises multiple orders of frequency magnitude sharply. The reason for this extraordinary improvement is the high elasticity properties of SL2DMs single layer. In other words, by applying strain in the SL2DMs layer, a lot of initial stress is accumulated in the structure, which ultimately causes a significant increase in the system's natural frequency. As the strain increases further, the resonance frequency increase becomes milder and approaches a saturation state. The resonant frequency and shift frequency of biosensors have been improved from about 65 and 8 kHz to 55 and 100 MHz on average, respectively, which is an outstanding achievement (see Fig. 7a,b). Although this process is the same for all SL2DMs, applying strain has the most almost negligible effect on the vibrational properties of graphene and MoS2, respectively. As shown in Fig. 7c, the effect of applying strain on relative frequency, which indicates the sensor's performance, is also very effective. So that after the appearance of an initial jump in relative frequency with a 1% strain, it has caused two to three times its value. The maximum and minimum sensor performance increases are obtained for GO and Ti3C2Tx, respectively. It is also clear that the present model predicts the effect of strain on relative frequency well and can be used in the design of other mass–base biosensors. In the case of sensor sensitivity, we also encounter a jumping trend, so that from a value of about 85 (Hz/number) in the no–strain mode, it jumps to 600 (kHz/number) by applying strain.

Fig. 7.

Effect of applied in-plane strain on the biosensor characteristics: (a) resonant frequency; (b) frequency shift; (c) relative frequency; (d) sensor sensitivity. In the simulation, SARS – COV – 2 Number = 100, L = 100 μm and M = 1.

The fitted curves on the simulation variables are shown in Log–Log Figs. 4c, 5c, 6c and 7c. In the following, put a specific value in the frequency shift and calculate LOD for SL2DMs as a function of in-plane strain and biosensor geometry, shown in the Fig. 8 . As we know, smaller LOD means better sensor performance. Therefore, according to Fig. 8, GO and Ti3C2Tx show the highest and lowest performance. The interesting point that can be seen in the table is that the performance of GO and h–BN is very close to each other. As seen in the previous figures, reducing the aspect ratio and length increases the sensor performance, which is evident in the Fig. 8. Reducing the length and aspect ratio from 100 to 5 and 5 to 0.2, respectively, reduces LOD about three and one order of magnitude. Although reducing the size of the sensor increases its efficiency, due to its number and the average size of 100 nm, care must be taken in choosing sizes smaller than 5 μm. It is also observed that to increase the efficiency of sensor, taking into account the production considerations, geometry characterization can be very suitable and efficient. Increase the gain on the sensor by applying strain to the log–log diagrams linearly. The slope of the LOD changes in all sizes, and the sensor's aspect ratio is almost the same. The essential point about the amount of strain applied to SL2DMs layer is that the mechanical limitations of each material must be considered concerning its strength and yield point. For example, research has shown that graphene maintains its elasticity up to 10% strain. In several studies, the real interaction between anti-spike glycoprotein antibody and spike glycoprotein has been investigated and it has been shown that this antibody has a high affinity to bind spike glycoprotein in a different type of SARS-CoV-2 and form an immune complex [43], [44], [45]. Therefore, it seems that this interaction can be considered in the design of diagnostic biosensors.

Fig. 8.

Prediction of biosensor LOD for SL2DMs as a function of in-plane strain and biosensor geometry in SARS–CoV–2 detection using proposed model (f_relative = 5%, ε₀ = 10⁻⁵).

4. Conclusion

With the development and discovery of a new class of materials, the need to use them in the production of various biosensors is felt. On the other hand, with the spread of new diseases such as COVID–19, the need for rapid detection of patients with inexpensive biosensors is one of the most effective ways to prevent their spread. It is necessary to study effective parameters such as sensor geometry, virus concentrations, and hypersensitivity techniques such as applying strain to design the sensors optimally. This paper investigates the application and efficiency of new 2D materials using the finite element technique in mechanical sensors. The results show that a size of 5 to 100 μm is a good range for detecting the number of viruses less than 1000. Also, choosing the right aspect ratio is a great option to increase the sensitivity and performance of the sensor. By reducing this ratio from 5 to 0.2, you can increase the frequency shift index ten times. This significant effect demonstrates the effectiveness of this parameter in mechanical biosensors without incurring additional costs. Also, Reducing the length and aspect ratio from 100 to 5 and 5 to 0.2, respectively, reduces LOD about three and one order of magnitude. Applying strain can also be very effective in increasing f _relative. So that by applying a small strain of 1%, we will have a 2 to 3 times increase of f _relative. Also, these strain actions reduce the LOD by five times, which indicates a considerable increase in sensor efficiency. The results show that all materials used in this study have good performance for use in sensors. The maximum and minimum sensor performance are obtained for GO and Ti3C2Tx, respectively. Finally, it can be said that using the results of the present article, the rapid detection sensors of the SARS–CoV–2 virus can be designed and manufactured with new materials. This method can be used in the future to identify other existing or new viruses and be calibrated for them.

CRediT authorship contribution statement

Javad Payandehpeyman: Theory, Conceptualization, Methodology and Writing.

Neda Parvini: Conceptualization, Writing, Reviewing and Editing.

Kambiz Moradi: Programming, Simulation and Validation.

Nima Hashemian: Conceptualization, Writing and Editing.

Declaration of competing interest

• •All authors have participated in (a) conception and design, or analysis and interpretation of the data; (b) drafting the article or revising it critically for important intellectual content; and (c) approval of the final version.
• •This manuscript has not been submitted to, nor is under review at, another
• •journal or other publishing venue.
• •The authors have no affiliation with any organization with a direct or indirect financial interest in the subject matter discussed in the manuscript.
• •The following authors have affiliations with organizations with direct or indirect financial interest in the subject matter discussed in the manuscript:

Author's name	Affiliation
Javad Payandehpeyman	Department of Mechanical Engineering, Hamedan University of Technology, Hamedan, Iran
Neda Parvini	Cellular and Molecular Research Center, Research Institute for Health Development, Kurdistan University of Medical Sciences, Sanandaj, Iran
	Department of Stem Cells and Developmental Biology, Cell Science Research Center, Royan Institute for Stem Cell Biology and Technology, ACECR, Tehran, Iran
Kambiz Moradi	Department of Mechanical Engineering, Hamedan University of Technology, Hamedan, Iran
Nima Hashemian	Faculty of Biology and Center of Excellence in Phylogeny of Living Organisms, College of Science, University of Tehran, Tehran, Iran

Data availability

No data was used for the research described in the article.