Instantaneous Viral Detection of SARS‐CoV‐2 and Beyond using Electromagnetic Sensing

This study proposes a highly sensitive portable device that utilizes electromagnetic waves and data analytics for instantaneous Severe Acute Respiratory Syndrome CoronaVirus 2 (SARS‐CoV‐2) detection. The device consists of a Radio Frequency (RF) circuit that interprets reflected and transmitted electromagnetic waves to identify virus signatures in physiologically significant matrices, including human saliva and diluted nasopharyngeal swabs. The sensor's accuracy is validated in both pre‐clinical and clinical settings, where clinical measurements demonstrate an instantaneous detection accuracy of 94%, sensitivity of 95%, and specificity of 97.5% between the sensor's physical parameters and SARS‐CoV‐2 detection. The sensor's accurate real‐time response is due to its unique design and precise modeling techniques. In addition, the same sensing system is tested across different viruses and its ability to differentiate between influenza A, respiratory syncytial, and SARS‐CoV‐2 viruses is proven. Hence this work presents a holistic system that can predict the viral concentration of SARS‐CoV‐2, as well as differentiate between different viruses instantaneously and without adding any amplifying agent.


Introduction
COVID-19, an acute respiratory viral infection, is caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). [1]Even though the World Health Organization (WHO) declared that COVID-19 is no longer a global health emergency, COVID-19 continues to cause a significant public health burden worldwide due to ongoing outbreaks. [2]Effective clinical management mitigates the disease burden but requires rapid and accurate diagnosis.These procedures emphasize the importance of resorting to sensors for quick clinical diagnosis, especially in limited healthcare infrastructures. [3,4]rimarily, molecular nucleic acid amplification tests (NAATs) were developed to detect SARS-CoV-2 RNA in patient samples.Moreover, reverse transcriptasepolymerase chain reaction (RT-PCR) has been the gold standard for the diagnosis of SARS-CoV-2, due to its high sensitivity and specificity. [5]However, the emergence of variants of concern (VOCs) such as Delta and Omicron increase the rate of false negative results, due to mutations in one or more genetic targets detected by these assays. [6]Loopmediated isothermal amplification (LAMP) gained popularity as an alternative amplification-based test for COVID-19, as it provides rapid results and does not need sophisticated equipment or a skilled workforce, making it suitable for home-based selftesting. [7]Molecular diagnostics have several limitations, including sample delivery logistics, the requirement for specialized equipment and reagents, as well as a technically trained workforce.
Most techniques discussed in the literature rely on electrochemical or pure chemical sensing for virus detection of SAR-CoV-2. [8,9]On the other hand, radio frequency (RF) waves were proposed first as a method to identify breathing rates anomaly as discussed in, ref. [8] or by leveraging blood infused RF resonators with continuous pumping for viral detection. [10,11]However, there is still a need for an accurate diagnostic test that requires minimal sample preparation with a faster turnaround time.Using radio frequency (RF) sensors in the diagnosis of SARS-CoV-2 or any other respiratory virus is based on two key facts: i) the dielectric properties characterizing a certain sample under test (SUT), which control the behavior of the electromagnetic (EM) waves in that medium, and ii) the presence of the viral particles, which alters the dielectric properties of the SUT, in which they are present.Hence, EM waves emitted from an RF sensor and transmitted into a specific SUT undergo modifications due to the particles constituting the SUT, which hold important information about their properties.Hence, by monitoring the change in the scattering parameters (S-parameters) of an RF sensor (Note S1, Supporting Information), viral concentrations of the SUT loading the sensor can be determined.
In this work, we introduce a highly efficient device for the detection of different respiratory viruses such as SARS-CoV-2, H3N2, and RSV.The proposed sensor is specifically designed to identify the concentration of the SARS-CoV-2 virus, as well as to differentiate between different viruses.The proposed sensor is composed of planar microstrip resonators with triple-band variants.It leverages the ability of electromagnetic waves to respond differently to the surrounding particles with distinct electrical identities at different resonant frequencies, and hence it provides a qualitative characterization of a SUT.This sensor enables rapid detection of viruses in a low-cost and low-power manner and has the potential to be used on physiologically important matrices, such as human saliva or diluted nasopharyngeal swabs.Moreover, the design is fabricated, tested, and clinically validated.

Concept and Design of the Proposed Sensing System
The proposed sensing system, shown in Figure 1A, is based on a multi-frequency resonator that modifies its frequency response based on the composition of its loading medium.The designed resonator operates at three distinct frequencies, which are tailored to be 3, 4, and 5.26 GHz.The resonating sensor is designed to operate at these frequencies due to the sensitivity that such operation offers in detecting viral load in a liquid medium.The sensing principle leverages the transmission and reflection behaviors of electromagnetic waves propagating through the SUT.The resonators performing the sensing functionality are one-port narrowband resonators composed of half-wavelength (g/2) resonant elements, where g is the guided wavelength of the frequency used (Note S2, Supporting Information).
The sensor is controlled by a back-end circuitry that enables the generation of EM waves that interact with an SUT positioned facing the resonating components.The reflected EM waves from the sensor are monitored and correlated to the sample viral concentration and ideally, the patient should be able to read the results through a digital display as shown in Figure 1B.
The three half-wavelength resonating elements are designed such that each one of them corresponds to a frequency band of interest.They are all capacitively edge-fed, using a single feeding point as shown in Figure 1C.These resonant elements must simultaneously exhibit high-quality factors indicating extreme sensitivity to minor concentration differences in the SUT loading the sensor. [12]The sensor is designed on a Rogers RT/Duroid 5880 substrate with a dielectric constant of 2.2, a thickness of 0.79 mm, and a loss tangent of 0.0009.The sensor is composed of three half-wavelength microstrip line-based resonators and the design of these resonating elements is strongly dependent on the dielectric material of the substrate between the ground plane and the copper trace. [13]The choice of the Rogers RT/Duroid 5880 substrate has a significant role in determining the performance of the sensor that is based on microstrip-line resonators, and employing any other substrate will result in a different operation.In fact, the choice of a substrate is based on its dielectric constant and loss tangent that contribute positively to confining the sensing area to its desired locations while enhancing the electric field distribution.Moreover, Rogers RT/Duroid 5880 is one of the most popular substrates used for microstrip line-based resonator design due to its low dielectric constant and high-performance fidelity.The sensor is fabricated using milling techniques and the fabricated prototype is shown in Figure 1C.
The ability of the sensor to differentiate between the various concentrations of the SARS-CoV-2 virus within the SUT is demonstrated by monitoring three parameters: the shift in the resonant frequency, the change in the magnitude of the reflection coefficient and the variation in the phase of the reflection coefficient.[14][15][16][17] The data resulting from the variation in the reflection coefficient characteristics is then fed into a regression model, which identifies the different concentrations of the SARS-CoV-2 viral load as depicted in Figure 1D.Furthermore, it is important to note that the multi-layered sensor structure topology, shown in Figure 1E, enables a more engaging interaction between the sensing elements and the SUT, which amplifies the sensitive nature of the proposed resonating structure.
The three resonating elements, shown in Figure 2A, (right to left) have a length of 34.6, 27, and 20 mm, respectively.The widths of the resonant elements in the multi-band sensor are chosen to be 2.43, 2, and 2.43 mm, corresponding to the characteristic impedances of 50 Ω, 57 Ω, and 50 Ω for the three elements respectively.][20][21] Driving the electric current to the various resonating elements is achieved by a 0.8 mm wide microstrip line with a characteristic impedance of 94 Ω, which is connected to a shunt open-circuited 8 mm wide stub with a 20 Ω characteristic impedance.The short stub is modified to enable the simultaneous feeding of all elements and ensures proper impedance matching between the 50 Ω input and the sensor across all bands.The gap between the feeding line and the 3 GHz element is 0.1 mm, whereas the gap between the 4 and 5.26 GHz elements is 0.2 mm.
The proper current flow across the resonating elements is demonstrated through the Electric field (E-field) distribution, which is visualized across the sensor in Figure 2A.A typical E-field distribution of half-wavelength resonators is observed.Hence, proving that the designed sensing elements meet their designated targets.The high-intensity E-field zones are the regions of the sensor, which exhibit the highest sensitivity to variations in the SARS-CoV-2 particles.
The suitable operation of the resonating elements is demonstrated through the magnitude of the reflection coefficient that indicates acceptable impedance matching across all bands of resonance.This is achieved due to the optimized sensor design that accounts for the dimensions of the feeding stub, resonant elements, and the separation between them to achieve the required impedance matching.The multi-band sensor is 41 mm x 14 mm, and the unloaded Q-factors are 117, 212, and 214 for the three resonating frequency bands, respectively.The measured reflection coefficient is compared with the simulated data as shown in Figure 2B where an excellent agreement is observed between them.

Performance Validation: Response to Different Samples Under Test (SUTs)
To assess the sensitivity of the proposed sensor, or in other words the degree to which our device responds to the change in the viral concentration of a loading sample, the sensor is loaded with customized SUTs in Ansys Electronics Desktop as shown in Figure 1E.The SUTs are characterized by distinct dielectric constants varying from 1 to 10, and a fixed loss tangent of 0.002 at a substrate thickness of 1.27 mm.After loading the sensor with each individual SUT, the corresponding reflection coefficient is obtained and recorded.Figure 2C shows the response of the three resonant elements to the SUTs with varying dielectric constants.The response is divided into three groups based on the frequency of operation: Group 1 corresponds to shifts in the frequency response at 3GHz.Similarly, groups 2 and 3 correspond to shifts at the 4 and 5.26 GHz reference frequencies.In Figure 2D, it is observed that all three bands exhibit a similar trend of increased Δf versus the dielectric constant.At the largest dielectric constant of ten, the frequency shifts Δf are 1.73, 1.389, and 860 MHz for the 5 GHz, 4 GHz, and 3 GHz bands respectively.As for the smallest dielectric constant of 2, the frequency shifts are 368, 336, and 174 MHz for the 5, 4, and 3 GHz bands, respectively.Finally, the Equations ( 1)-(3) below represent the 3rd-order polynomial models obtained using the simulated data that best captures the trend: where Δf is normalized to 1 GHz.Moreover, the sensor's reflection coefficient (S 11 ) response upon loading with distinct SUTs was recorded using a portable vector network analyzer VNA [22] to characterize the shift in the resonant frequency due to a change in the dielectric properties of the SUT (Figure S1, Supporting Information).

SARS-CoV-2 Heat-Inactivated Virus Measurements
In this experiment, we assess the proposed sensor sensitivity in measuring variabilities in viral concentrations suspended in Phosphate Buffered Saline Solution (PBS).The SARS-CoV-2 heat-inactivated virus was obtained from Bei resources (catalog number: NR-52286) [23] and then we prepared 25 dilutions using PBS.These dilutions covered a wide range of concentrations, spanning from 10400 PFU/ml to 130 PFU/ml, where PFU stands for plaque forming unit, which is the estimated unit of quantification for the viral particles (Table S2, Supporting Information).
The objective is to demonstrate the proposed sensor's capability of detecting very small variations in the SARS-CoV-2 concentrations.For each SUT, the magnitudes of the S parameters of the proposed sensor are acquired, sampled, and normalized over a range of frequencies, and then joined through a Gaussian process (GP) [24] non-parametric regression model to obtain an estimation of the Viral concentration (Note S4, Supporting Information).The experimental setup is shown in Figure 3A where the sensor is connected to a calibrated portable VNA. [22]Then, the sensor is shielded from any external electromagnetic interference using conductive shielding.Each sample is added into a cuvette that is placed 10 mm away from the sensor as shown in Figure 3A. Figure 3B displays the sensor's response in terms of S 11 magnitude versus the reference viral concentration value.It is evident from Figure 3B that the sensor's S parameters measured using the setup in Figure 3A, closely follow the trend of the reference virus concentration level with R 2 = 0.95.The recorded magnitudes of the reflection coefficients of the sensor loaded with samples that have distinct viral concentration levels are shown in Figure 3C.
The performance metrics used as a measure of the accuracy of predictions are the standard error of prediction (SEP) and mean absolute relative difference (MARD).Figure 3D shows the matching between the trends followed by the predicted SARS-CoV-2 virus concentration using the proposed resonating sensor, and that are followed by the reference concentration.For viral concentrations ranging from 130.82 PFU/ml to 10400 PFU/ml, the proposed sensor is found to exhibit a SEP of 0.76% and a MARD of 1.92%.

Measurements on Clinical Samples
We evaluated the proposed sensor on SARS-CoV-2-positive (n=30) and negative (n=30) clinical nasopharyngeal specimens that were frozen in the lab.The positive specimens had Ct values ranging from 17.5 to 38.4 (Table S1, Supporting Information) and the negative specimens were collected before the pandemic.The reflection coefficient magnitudes of the sensor, due to load-ing with each diluted nasopharyngeal swab are recorded using a portable vector network analyzer (VNA).We perform these measurements by placing the sample over the sensing area of the proposed sensor.The recording of the S 11 magnitude is critical for understanding the nature of the SUT since the viral composition of a sample dictates its complex permittivity.All sixty samples were tested for influenza A/B, RSV, and SARS-CoV-2 using a realtime PCR method to obtain a measurement reference (Note S3, Supporting Information).
To detect whether a specimen is positive for SARS-CoV-2, we use the sensor data acquired at various frequencies, as shown in Figure 4A.Figures 4B,C, show the monotonicity between the S 11 magnitude and the SARS-CoV-2 viral concentration around 4 and 5.26 GHz resonance points, respectively.The sensor data undergoes a pre-processing step for filtering, sampling, and normalization, and is then fed to a forward feature selection wrapper algorithm [25] to select magnitudes of the reflection coefficient at specific frequencies that ensure an accurate representation.Furthermore, all the selected features are then used in developing an appropriate learning model, using a two-class classification model that expects two classes, SARS-CoV2-positive and -negative.Under this scenario, we adopt a two-class support vector machine (SVM) classifier (Note S13, Supporting Information) that produces a model capable of predicting suspected SARS-CoV2-positive cases.Among the sixty data points, five positive and five negative observations are randomly selected and removed from the data set.We refer henceforth to these as blind samples.The remaining 50 samples undergo classification, where only 90% are used for training and validation; hence identifying the best features for classification, and the remaining 10% are used for testing to evaluate if the classifier (that was built due to the training points) can accurately classify positive samples from negative samples.As such, 45 sample points are used for training and validation and five sample points are used for testing.The error is assessed for this set.The procedure is then repeated ten times, each time with 45 different training sample points and five different test sample points.The average test error for the ten repetitions is reported.1]26,27] This is mainly because of the limited number of available observations in the dataset and it allows for the testing/training to cover different viral concentration levels in the different iterations.
Hence, for each iteration, we have five samples that are used to test the built classifier.This results in a total of 5×10 testing samples after the completion of the tenth iteration.For each it-eration, after testing the built SVM classification model on the testing samples, true positive (TP), true negative (TN), false positive (FP), and false negative (FN) cases are identified (Note S14, Supporting Information).These cases allow us to calculate the accuracy, sensitivity, and specificity of our model [28] as per Equations ( 4)-( 6), respectively: The average of the ten executed iterations demonstrates an accuracy of 94%, a sensitivity of 95%, and a specificity of 97.5%.This shows that the proposed system possesses high accuracy within the tested samples that we incorporated.Such accuracy is comparable to that obtained using commercial COVID diagnostic kits.Moreover, among the 50 testing data points used throughout the ten iterations, the classifier detects two false negatives out of 29 positive sample points and two false positives out of 21 negative samples.To assess the sensor's accuracy further, we feed the ten samples (five positive and five negative), removed from the initial dataset to the classifier, as blinded samples, on which the built classifier using the other 50 points is tested to evaluate the detection rate.The classifier was able to detect these samples whether positive or negative with a 100% detection rate.

Beyond COVID-19: Detecting and Differentiating Between Different Viruses
To further assess the proposed sensing system's efficiency and specificity, an experiment was conducted on different viral samples from different viruses.In detail, the experiment was performed on samples of BSA (negative control), influenza A/H3N2 virus, and RSV.For each virus, 25 different concentrations, varying from 130.82 PFU/ml to 10400 PFU/ml for H3N2 (Table S3, Supporting Information) and RSV (Table S4, Supporting Information) and from 125.79 ug/ml to 10000 ug/ml for BSA (Table S5, Supporting Information), were measured using the proposed sensor.The magnitude and phase of the reflection coefficient response of the sensor loaded with each sample were recorded.It is worth noting that H3N2, RSV, and BSA were tested using the same setup and the same concentration levels for the sake of comparison and classification.All the measurements follow the same experimental setup as shown in Figure 3A.Each viral dilution is measured separately, and the sensing system can generate a distinct response for each specific sample.Figure 5A shows the sensor's reflection coefficient's magnitude response for each viral sample.The sensor's response is different for each virus.In fact, the plots in Figure 5B-D demonstrate that the sensor can predict various viral concentrations using the proposed resonating system.This prediction closely follows the trend of the reference sample concentration levels for the BSA, H3N2, and RSV, respectively.As a result, this sensing device can not only track the SARS-CoV-2 concentrations and identify their presence, but it can also differentiate between different respiratory viruses based on the experiments described in this section.

Conclusion
We introduce a highly sensitive portable sensing component that leverages electromagnetic waves' transmission and reflection to identify and predict various SARS-CoV-2 viral concentrations.Moreover, the sensor is unique due to its ability to identify the virus in question without adding any amplifying chemicals.In addition, when loaded with different viral concentrations, this sensor can generate a distinctive response for each viral load.As a result, this device can differentiate between different respiratory viruses in an instantaneous manner.Testing the sensor on SARS-CoV-2 heat-inactivated viral samples suspended in PBS, and applying data analytics and regression techniques demonstrates an accuracy of 98.08%.On the other hand, testing the sensor on 60 nasopharyngeal clinical samples, 30 of which were SARS-CoV-2-negative and 30 were SARS-CoV-2-positive, accompanied by data analytics and classification techniques revealed an accuracy of 94%, a sensitivity of 95%, and a specificity of 97.5%.
Both pre-clinical and clinical testing results are highly promising and manifest the potential of our sensor to accurately recognize different respiratory viruses' signatures in physiologically significant matrices like diluted nasopharyngeal swabs.Future work will include conducting these experiments on additional infection samples to validate the capability of the sensor in selectively detecting SARS-CoV-2 even when mixed with other respiratory viruses.Nevertheless, this sensor has shown an outstanding ability to instantaneously identify the various respiratory viruses from SARS-CoV-2 and beyond without any chemical agent rendering it a one-of-a-kind point-of-care device.

Experimental Section
Sensor Simulation and Fabrication Process: A prototype of the proposed sensing element was designed using Rogers RT/Duroid 5880 substrate material [29] of 0.79-mm thickness with a dielectric constant of 2.2 and a loss tangent of 0.0009.The three incorporated resonant elements were designed to operate in the lower microwave frequency band ranging from 2.5 to 6.5 GHz.Moreover, the pivot of a sensing system to be able to fit point-of-care settings was high sensitivity, which was an essential metric that evaluated the performance of the sensor.To attain high levels of sensitivity, the widths of the resonant elements were optimized to be very narrow for the sake of achieving a narrow bandwidth response, and thus a high-quality factor.The sensor was designed and simulated using the High-frequency structure simulator by ANSYS Electronics Desktop simulator. [30]It was composed of three layers.The top sensing layer comprises the resonant elements that were one-port narrow band capacitively edge-fed half-wavelength (g/2) resonators; the middle layer was itself the dielectric layer made from an RT/Duroid 5880 substrate with a thickness of 0.79mm, and the bottom layer was the ground plane.The fabrication of the design was handled using a computer numerical controlled milling machine.
Sensitivity and Different Viral Samples Experiments: Influenza strain: A(H3N2)/Texas/26/2008 and RSV strain: RSVA 2001/2-20, IRR were used to test the specificity of the sensor.The samples were lysed as follows: the initial volume of the virus was mixed with an equal volume of lysis buffer (PureLink RNA Mini Kit) [31] and heated for 15 min at 56°C.Then each sample was and further diluted using a 1.2 dilution factor using PBS as the diluent.SARS-Related Coronavirus 2, Isolate USA-WA1/2020, Heat-Inactivated was used for the initial validation and optimization of the sensor.The sample was obtained from BEI resources and diluted as described above.BSA was prepared in water and diluted and measured from (10000 μgml -1 ) till (125 μgml -1 ).The dilution factor was also 1.2.
Measurements on Clinical Specimens: A total of sixty nasopharyngeal swabs were used in this study, consisting of 30 samples confirmed as SARS-CoV-2 negative and 30 samples confirmed as positive through PCR testing.
Statistical Analysis: In this section, data collection, processing, and presentation were discussed along with the statistical analysis, regression, and classification techniques used to build the model.
Data Collection: The sensor was connected to a portable VNA.The sensor was then loaded with sample concentrations C∈[130-10400]PFU/ml of SARS-CoV-2 heat-inactivated virus.For each concentration, the sensor measurements provide a reflection coefficient (S 11 ) curve as a function of frequency.The acquired data consists of the magnitude and phase of S 11 , which correspond to the distinct frequencies obtained from the VNA over the range from 2.5 to 6.5 GHz.We note that each VNA measurement was comprised of the average of ten consecutive readings for a given sample to avoid the VNA's inherent random noise as would be discussed later.It was highly probable that the S 11 response trends to varying the SARS-CoV-2 concentration would be very similar for operation within neighboring frequencies.Hence, to minimize redundancy between recorded features, the frequency range was sampled with a 0.0625 GHz frequency step within the operating frequency range from 2.5 to 6.5 GHz.Accordingly, the following were defined: • C j is the viral concentration for sample j, where j∈ [1:N] and N is the total number of samples Hence, each column X j in matrix X in (7) represents the feature vector at C j .
Data Processing and Presentation: As discussed, each VNA measurement was comprised as the average of 10 readings to avoid the VNA's inherent random noise.As such, The feature i is dropped, if max(X i )-min(X i ) ⩽ threshold.Thresholds for S 11 magnitude and phase were set to 0.1 and 1, respectively.Following that, for each feature, the value of S 11 magnitude or phase was normalized to a value between 0 and 1, as per the following equation: Statistical Analysis and Regression Techniques: This work had two main objectives: 1) estimation of the viral concentration of SARS-CoV-2, H 3 N 2 , and RSV and 2) Viral detection of SARS-CoV-2.The first task was fulfilled using a Gaussian process (GP) non-parametric regression model.For each distinct virus, a total of 25 different samples, with concentrations varying from 130.82 PFU/ml to 10400 PFU/ml were used.The performance of the sensor was tested against each of these 25 concentrations for each of the viruses and recordings of the S 11 magnitudes for these different concentrations were taken.Figure 6 shows the S 11 magnitudes for the different 25 SARS-CoV-2 dilutions.The second task was accomplished using a two-class support vector machine (SVM) classifier applied for a total of sixty (SARS-CoV-2-positive (n=30) and negative (n=30)) clinical diluted nasopharyngeal specimens.The data analysis, regression, and classification were carried out using MATLAB software. [32]The work presented herein is based on the performance metrics that are presented in Supporting Information (Notes S7 and S14, Supporting Information).
Gaussian Process Regression: A Gaussian Process (GP) [24] is used since it can be considered as an efficient technique to handle 1) the dataset's small sample size due to the restricted number of reference CT values, and 2) the high dimensionality of the feature set (Note S10, Supporting Information).The dependence between the function values at different input points x and x' was modeled by a covariance function k(x,x') that reaches its maximum whenever f(x) and f(x') were highly correlated; that was, the query x' was close to the sample point x. [33]On the other hand, k(x,x') approached zero for sample points that were distant from the query x', and thus have a negligible role in estimating the query x'.In addition to the point estimated, GP also delivered a measure of the forecast's uncertainty. [34]Hence, GP reported confidence intervals for the estimates as opposed to p-values for linear regression coefficients.In this analysis, the error of the predicted mean of the interval compared to the golden reference was reported.
Classification using Support Vector Machines: Classification using support vector machine (SVM) was used in this application as a binary classifier where the output of the function it learns was either positive or negative. [35]Binary SVMs were classifiers that map an input space to a higher dimensional vector (feature space) to separate data points into two categories.This was achieved by determining a hyperplane that separated the training data belonging to two classes. [36]The hyperplane separates the data linearly; however, SVMs were also "applicable to non-linear problems, thanks to mapping the data into higher-dimensional spaces, in which they were linearly separable-this mapping was achieved using kernel functions". [37]The sensor used SVM along with the wrapper feature selection technique [25] to detect whether a sample under test was SARS-CoV-2-positive or SARS-CoV-2-negative.The dataset was divided into training and testing sets.The training set comprises 90% of the original dataset and was used to determine the hyperplane that separated between two classes.On the other hand, the testing set comprised 10% of the original dataset and was needed to evaluate the performance of the built classifier.Training and testing sets were chosen randomly from the original dataset and the procedure was repeated ten times to compensate for the small size of the datasets.
Feature Selection and Cross-Validation: To find the best model (GP for regression or SVM for classification) and feature set, the forward feature selection (FFS) wrapper method [25] (discussed in Note S8, Supporting Information) was applied to the data sets using tenfold cross-validation.The data sets were randomly divided into ten equal subsets of which one was used as a testing set and nine were used for training and validation.The cross-validation error was then calculated.The training and validation procedure was repeated as the next best features were added iteratively (and test other kernel types for GP), and the best feature set (and kernel combination) providing the lowest cross-validation error was selected.Once the best set of features was identified, a model was built using the training and validation data, and then the performance of the built model was evaluated using the testing data.Due to the limited number of observations in the datasets, this process was repeated ten times by randomly dividing the data each time into training and testing sets. [18,19,26]easurements.R.K., F.A., and R.A.A. realized the data analysis in terms of preprocessing, feature selection, regression, and classification modeling.R.A.A. wrote the paper.All authors edited the paper, reviewed the results, and approved the final version of the paper.

Figure 1 .
Figure 1.Resonator-based Radio Frequency sensor.A) Principle of the sensing approach.B) Targeted patient samples to provide information about the dielectric properties.The reflected EM waves are monitored and correlated to the sample viral concentration through a back-end circuitry.C) Top sensing layer of the sensor prototype.D) Methodology of the proposed sensor design.E) The layer-by-layer layout of the proposed sensor where the bottom layer is composed of copper, the middle layer is a dielectric substrate, and the top layer is a copper layer comprising the three resonant components that hold the SUT.

Figure 2 .
Figure 2. Surface current distribution and flexibility of the proposed sensor.A) E-field concentration for both sensors at their respective resonant frequencies.B) The simulated and measured reflection coefficient (dB).C) The sensor's response upon loading it with a selection of MUTs.D) The simulated frequency shift of the three frequency bands as a function of increasing dielectric constant.

Figure 3 .
Figure 3. Measurement Data.A) Schematic of the experimental setup.B) The sensor's response S 11 magnitude versus the reference SARS-CoV-2 virus concentration.The S 11 fitted curve (cyan line) shows the trend of the sensor's response versus virus concentration.C) S 11 magnitude of the sensor for 25 different SARS-CoV-2 dilutions.D) Predicted versus reference values for SARS-CoV-2 concentration for ten randomly shuffled test/train datasets used in Gaussian Process regression resulting in a SEP of 0.76% and a MARD of 1.92%.

Figure 5 .
Figure 5. Response to Different Viral Samples.A) The proposed sensor's response S 11 magnitude for 25 viral samples (of each virus) and concentrations around 6.1 GHz.B) Predicted versus reference values for BSA concentrations (log scale) ten randomly shuffled test/train datasets used in Gaussian Process regression resulting in a MARD of 0.87%.C) Predicted versus reference values for H3N2 viral concentrations (log scale) for ten randomly shuffled test/train datasets used in Gaussian Process regression resulting in a MARD of 0.69%.D) Predicted vs reference values for RSV viral concentrations (log scale) for ten randomly shuffled test/train datasets used in Gaussian Process regression resulting in a MARD of 4.78%.
5-6.5] GHz with steps of 0.0625 GHz for a total of 64 frequencies • x ij m is the s 11 -parameter magnitude at frequency f i and concentration C j • x ij p is the s 11 -parameter phase at frequency f i and concentration C j This results in X j = [X each reference viral concentration C j (observations).