Discrimination between COVID-19 Positive and Negative Blood Sera Using an Unmodified Disposable Impedimetric Sensor and Multivariate Analysis

Abstract

The present study introduces a direct approach for classifying blood serum samples as either positive or negative for coronavirus disease (COVID-19) by associating the electrochemical impedance data of the sample with multivariate analysis. The hypothesis is that the systematic alterations in blood composition resulting from a severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection give rise to a distinct impedance spectrum when infected serum is subjected to analysis. A total of 201 serum samples were analyzed using the gold standard method, reverse transcription-polymerase chain reaction (RT-PCR), which served to train and validate the classification models. Two variations of discriminant analysis (partial least squares discriminant analysis (PLS-DA) and principal component analysis-discriminant analysis (PCA-DA)) and a one-class modeling approach (soft independent modeling of class analogies (SIMCA)) were used to classify impedance data in different formats (as complex or real numbers). PCA-DA applied to imaginary impedance spectra was found to be the most effective strategy, achieving sensitivity, specificity, and precision of 94, 94, and 91%, respectively, with classification error rates as low as 6%. These findings are encouraging and could facilitate the development of an inexpensive and reliable screening method for COVID-19.

Keywords:
pattern recognition; SARS-CoV-2; electrochemical impedance; discriminant analysis; one-class modeling

Introduction

The coronavirus disease (COVID-19) pandemic, originating from the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in Wuhan, China in 2019, swiftly engulfed the globe, leaving a profound mark on humanity. Declared a pandemic by the World Health Organization (WHO) in March 2020, it has resulted in over 770 million confirmed cases and more than 7 million deaths worldwide.¹ Despite hallmark symptoms such as coughing, fever, and difficulty breathing, many infected individuals experience mild or no symptoms. This asymptomatic (or minimally symptomatic) group can still transmit the virus, which facilitated silent transmission. Progress in vaccination campaigns and rising population immunity prompted the WHO to declare an end to the pandemic in May 2023.² Despite this, COVID-19 remains a persistent threat. Conventional techniques for detecting SARS-CoV-2 include antigen, antibody, and molecular tests were essential to curb its spread and minimize infection rates. Antigen tests detect virus-specific proteins, while antibody tests assess anti-SARS-CoV-2 levels in the blood, indicating antibody development. Molecular tests analyze different regions of the ribonucleic acid (RNA) genome of the virus, with reverse transcription-polymerase chain reaction (RT-PCR) considered the gold standard and recommended by WHO since the beginning of the pandemic.³ Despite its high sensitivity and specificity, RT-PCR requires specialized laboratories and trained personnel, with results taking several hours to obtain.

Many studies on the diagnosis of COVID-19 using electrochemical biosensors have been published using potentiometry,⁴ amperometry,⁵ voltammetry⁶ and electrochemical impedance spectroscopy (EIS).⁷ EIS is particularly advantageous for biosensing due to its high sensitivity to changes in the electrical properties of the surface of the sensor as it interacts with target biomolecules.⁸ These interactions induce sensitive changes in impedance, mainly the increase of the charge-transfer resistance of a redox probe, that is directly correlated to the presence and concentration of the target.⁹ With its ability to operate with no need for labeling or extensive sample preparation, EIS makes it an appealing choice for rapid, on-site diagnostic applications.

EIS is a sensitive and robust technique but combining it with multivariate analysis and machine learning techniques - referred to as chemometrics when applied to chemical data - can be very advantageous, especially when it comes to improving the efficiency of impedimetric sensors.¹⁰,¹¹ However, scarce examples are found in the context of COVID-19 testing. One such example is the use of a molecularly imprinted polymer for the selective recognition of the SARS-CoV-2 virus in saliva samples aided by principal component analysis (PCA).¹² The developed sensor achieved 75% agreement with the reference method, loop-mediated isothermal amplification (LAMP). It is worth noting that although the test set is limited to 15 positive samples and 9 negative samples, and PCA is an exploratory technique rather than classification one, the findings are interesting. In another study, a label-free impedimetric biosensor was developed based on modifying a glassy carbon electrode with Au nanoparticles that were modified with a low-cost, easy-to-synthesize peptide consisting of five amino acids. The peptide was designed to replicate the N-terminal subunit in the S protein, allowing it to recognize the S protein antibody. Impedance data were used to differentiate between 15 prepandemic individuals and 19 convalescent patients using partial least-squares discriminant analysis (PLS-DA) and sure independence screening and sparsifying operator (SISSO), obtaining 100% accuracy in both cases.¹³

Combining EIS with multivariate analysis or machine learning techniques can also allow for some degree of simplification of the sensor assembly by avoiding complex modifications that use expensive reagents, or even by using unmodified electrodes. This simplification may result in a less selective sensor, which is balanced by the high efficiency of the treatment of the produced multivariate analytical signal (impedance spectrum) with multivariate analysis. Each impedance value in the spectrum is a low-selective and cross-sensitive pseudo-sensor, whose response is related to ionic, redox, or molecular interactions at the sensor/solution interface.¹⁴ The global selectivity resulting from the joint use of such sensors, combined with the chemometric treatment of the signals, produce an “electrochemical fingerprint”¹⁵ that allows both the qualitative recognition of the target biomolecule and its quantification.

There are several successful examples in quantitative and qualitative modeling including the determination of pharmaceuticals¹⁶ and environmental contaminants,¹⁷ as well as electronic tongues.¹⁸ Among the examples of the association between chemometrics and EIS data produced by unmodified electrodes in clinical analysis are the discrimination between normal and cancerous human urothelial cells using random forest¹⁹ and the discrimination between different types of blood thrombi using support vector machines,²⁰ both with an accuracy of over 90%. This study aimed to evaluate the effectiveness of using an unmodified disposable impedimetric sensor to distinguish between blood serum samples infected with COVID-19 and non-infected samples. The samples were analyzed using the gold standard method of reverse transcription-polymerase chain reaction (RT-PCR). The impedance data obtained were used to develop classification models based on discriminant analysis and one-class modeling.

Experimental

All reagents used in this study, including potassium chloride (KCl), disodium hydrogen phosphate (Na₂HPO₄), monopotassium phosphate (KH₂PO₄), sodium chloride (NaCl), sodium hydroxide (NaOH), potassium ferrocyanide (K₄Fe(CN)₆), and potassium ferricyanide (K₃Fe(CN)₆), were of analytical grade and were purchased from LabSynth (São Paulo, Brazil). The study employed a 0.1 mol L^-1 pH 7.4 phosphate buffered saline (PBS) solution, which was prepared with ultrapure water (resistivity > 18 Mil cm^-1, Milli-Q, Millipore, USA).

The blood serum samples were obtained from hospitals in the metropolitan area of João Pessoa and Campina Grande, located in the state of Paraíba, Brazil. The study was approved by the Human Research Ethics Committee of the Lauro Wanderley University Hospital (CAAE:31562720.9.0000.5183). In order to guarantee that the multivariate models obtained are sufficiently robust and have an acceptable chance of correctly discriminating future samples, it is essential that the training and test sets are constructed in such a way as to include samples that represent the greatest possible variability of positive and negative case situations. Consequently, the positive samples represent situations of infection and reinfection. The set of negative samples contained occurrences of patients with symptoms similar to those of the disease, such as a cold or influenza, as well as patients at different stages of immunization (post-infection and post-vaccination), including healthcare workers. However, it is important to note that these differences were not considered in the classification of the samples, which was based solely on the results of the RT-PCR test. To prepare for analysis, all serum samples were diluted in PBS pH 7.4 at a 1:10 ratio.

Impedance measurements were conducted using a potentiostat Autolab PGSTAT 101 (Metrohm, Switzerland) connected to a screen-printed electrode boxed connector (Ref. DSC, Metrohm Dropsens, Spain) and a microcomputer running NOVA 2.1.6 software (Metrohm, Switzerland). Commercially available screen-printed electrodes DRP-220BT (Metrohm Dropsens, Spain) were used, featuring a silver reference electrode, gold working electrode (diameter 4 mm) and gold counter electrode.

For the measurements, a 100 μL aliquot of the background solution (comprising an equimolar mixture of potassium ferricyanide and potassium ferrocyanide at 0.1 mmol L^-1 in PBS pH 7.4) was applied to the electrode. The open circuit potential was recorded for 60 s prior the scan and used as the base potential for the impedance spectrum collection, which was obtained from 100 KHz to 1 Hz, at an amplitude of 10 mV, with ten frequencies per decade, all conducted at ambient temperature (20 ± 1 °C). Subsequently, 10 μL of the prepared blood serum sample were added to the background solution on the electrode and incubated for 30 min to allow for the serum constituents to interact with the electrode surface. A new scan was then carried out. This scan was used in the modeling stage. Samples were analyzed in triplicate. The background solution scan was used to check for electrode reproducibility.

A total of 201 blood serum samples were analyzed using the gold standard method RT-PCR, with 121 testing positive and 80 testing negative for SARS-CoV-2. The spectral data obtained was organized into matrices of size 201 × 51 (samples × frequencies). Five different matrices were obtained considering the following representations of the impedance data as real numbers - real part (Z’), imaginary part (Z"), phase angle (cp) and absolute impedance (IZI) - and complex numbers (Z’ - jZ’’). Each dataset was individually assessed in the model development. First, the samples were divided into training and test sets in a 60:40 ratio by using the Kennard-Stone uniform sampling algorithm.²¹ Thus, the training set included 74 seropositive samples and 47 seronegative samples, while the test set comprised 47 seropositive samples and 33 seronegative samples.

The impedance data was used to develop classification models based on discriminant analysis and one-class modeling. One-class modeling is focused on learning the characteristics of a single class to distinguish typical instances from outliers. This approach was selected because the negative samples (non-infected blood serum) have a high degree of variability and are not well-defined, unlike the positive samples. We employed the Soft Independent Modeling of Class Analogies (SIMCA), a widely used one-class approach based on Principal Component Analysis (PCA). SIMCA builds a PCA model that captures most of the class variance and classifies new samples by measuring their distance to the class model within the reduced-dimensional space. A sample is classified as belonging to the class if its distance to the class centroid is below a predefined threshold; otherwise, it is classified as not belonging to the class.

By contrast, discriminant analysis (DA) is a multiclass technique that distinguishes between two or more predefined classes using linear or nonlinear combinations of features. It can be prone to overfitting in datasets with many variables or multicollinearity, such as EIS data. One approach to mitigate the impact of multicollinearity (and at the same time reducing the number of variables, if necessary) is to transform the original variables into a smaller set of uncorrelated variables through PCA. The obtained scores are used as classification variables in DA, and this technique is referred to as PCA-DA. Similarly, Partial Least Squares (PLS) regression can generate latent variables (LV) that best explain predictor variance and their covariance with the response (class index). The process, referred to as PLS-DA, finds the directions in the predictor variable space that maximize class separation in the response variable. Both PCA-DA and PLS-DA were evaluated in this study.

The chemometric models were developed using the Classification Toolbox 6.0 in the Matlab R2023a environment.²² Leave-one-out cross-validation was used to select the number of PCs (or latent variables, LVs) and validate the model. The models were obtained using between 1 and 20 PCs (or LVs). The number of PCs (or LVs) was chosen based on the lowest classification error rate. Column preprocessing involved data centering and autoscaling, while row preprocessing included the use of spectrum logarithmization in addition to non-preprocessed data. The discriminant function type, linear and quadratic, was also evaluated in the application of PCA-DA. The models developed were then applied to the test set, and their efficiency was assessed based on the figures of merit sensitivity (Sens), specificity (Spec), and error rate (ER), calculated as follows:²³

(1) $\text{Sens}=\frac{\text{TP}}{\text{TP}+\text{FN}}$

(2) $\text{Spec}=\frac{\text{TN}}{\text{TN}+\text{FP}}$

(3) $\text{Prec}=\frac{\text{TP}}{\text{TP}+\text{FP}}$

(4) $\text{ER}=\frac{\text{FP}+\text{FN}}{\text{TP}+\text{TN}+\text{FP}+\text{FN}}$

The terms TP, FP, TN, and FN represent the number of true positives, false positives, true negatives, and false negatives, respectively. Here, true positives (TP) are positive samples correctly identified as positive, false positives (FP) are negative samples incorrectly identified as positive, true negatives (TN) are negative samples correctly identified as negative, and false negatives (FN) are positive samples incorrectly identified as negative. Sensitivity and specificity are metrics that measure the ability of the method to correctly identify positive and negative samples, respectively. Precision, also known as the positive predictive value (PPV), is the proportion of true positive identifications among all samples assigned to the positive class. This metric is also applicable to the negative class, where it is known as the negative predictive value (NPV). The error rate is defined as the ratio of the total number of misclassified samples (errors) to the total number of samples.

Results and Discussion

The hypothesis supporting this study is that COVID-19 infection can be identified indirectly by EIS, from the significant changes in the blood serum chemical composition due to COVID-19.²⁴,²⁵,²⁶ These changes have been evaluated as a basis for the diagnosis of COVID-19 by applying machine learning on blood test results.²⁷,²⁸,²⁹ The serum comprises biomolecules containing thiol, amine, and carboxylic moieties, as well as N-containing heterocycles and ions. These species interact with gold on the surface of the working electrode in various ways. The S-containing groups are the main functional groups that interact with gold, mainly thiols and disulfides, that form some of the strongest known chemisorptive bonds to gold, resulting in stable Au-S bonds.³⁰,³¹ Thiol and disulfide groups are found in small molecules such as glutathione and thiamine, as well as in cysteine-containing peptides and proteins. Other biomolecules can also be directly adsorbed (physiosorption) onto a clean gold electrode via non-covalent interactions.³⁰,³²

It is anticipated that the imbalance resulting from COVID-19 infection will increase the interaction between the biological matrix and the working electrode, impeding the redox process of an electrochemical probe such as the redox pair Fe(CN)₆^3-/4-, altering the impedance spectrum (Figure 1). A classification algorithm can capture the systematic changes in impedance spectra that can be utilized to discriminate COVID-19 positive from negative blood samples.

Figure 1
Hypothesis on the working principle of the sensor. The imbalance in blood composition caused by the COVID-19 infection causes a systematic increase in the impedance of the redox probe reaction, which can be modelled by a multivariate classification algorithm. In the graph on the right, the colors refer to the results provided by the reference method (RT-PCR): blue for positive and red for negative. The symbols represent the predictions obtained in the training (circles) and test (squares) stages.

Figure 2a shows the spectra of independent triplicates for three different seropositive samples (as tested by RT-PCR). The spectra with the same color/symbol in Figure 2a represent the measurements taken before (supporting electrolyte only) and after the serum sample was added to the electrode and incubated for 30 min. The impedance spectra exhibit the benchmark profile of the interaction between the Fe(CN)₆^3-/4- redox couple and a bare electrode surface.³³,³⁴ It features a small semicircle at high to mid-frequency region, representing a low charge transfer resistance (R_ct) and a fast electron exchange, followed by a linear region at lower frequencies, which is the manifestation of the diffusion-controlled process of the redox species to and from the electrode surface. It should be noted that the R_ct (diameter of the semicircle) significantly increases after adding the serum and incubating for 30 min, suggesting that serum components obstruct electron transfer at the electrode surface. It is noteworthy that the spectra obtained in the absence of serum are highly similar, indicating excellent reproducibility of the screen-printed sensors. The inset plot shows an expanded view of the Nyquist plot to highlight the differences among the samples’ spectra.

Figure 2
(a) Each set of spectra with the same color/symbol represents the analysis of a different seropositive sample performed before (supporting electrolyte, smaller semicircle) and after sample incubation on the electrode (larger semicircle). (b) Impedance spectra of the 201 blood samples colored according to the diagnosis obtained by RT-PCR (blue: negative; orange: positive).

Figure 2b presents the Nyquist plot with the impedance spectra of the 201 blood samples colored according to the diagnostic obtained by RT-PCR (blue: negative; orange: positive). The spectra demonstrate the same Fe(CN)₆^3-/4-, redox couple profile, with the positive samples showing a systematically different behavior from the obtained with the negative samples. A systematic increase in R_ct and maximum Z’’ is observed for the seropositive samples (as observed in the inset plot of Figure 2b), indicating an increase in the impedance of the interaction of the redox couple with the electrode caused by the blocking of the surface by the constituents of the serum infected with the SARS-CoV-2 virus. This indirectly indicates that the composition of the COVID-19 positive serum is indeed different.

The work of Pushalkar et al.²⁶ provides an excellent summary of the findings to date relating to the main changes in serum composition due to COVID-19. Proteomics reveal dysregulated pathways in lipid homeostasis, immunoglobulins, cytokines, chemokines, and coagulation. Proinflammatory cytokines (IL-6, IL-1β, TNF-α) trigger a ‘cytokine storm’. Regulatory proteins in coagulation (APOH, FN1, HRG, KNG1, PLG) and lipid homeostasis (APOA1, APOC1, APOC2, APOC3, PON1) increase as the disease progresses. Even asymptomatic COVID-19 patients show altered coagulation and inflammation markers like fibrinogen, von Willebrand factor (VWF), and thrombospondin-1 (TSP1). Regarding small biomolecules, Tristán et al.²⁵ identified specific metabolites such as trimethylamine-N-oxide (TMAO), phenylalanine, N-acetylglycoproteins (NAG), tyrosine, lysine, acetone, mannose, citrate, glycerol, and fatty acids, particularly unsaturated fatty acids (UFA), as the key molecules driving the separation between COVID-19 patients and healthy controls in the serum metabolome.

It is important to note that differential pulse voltammetry (DPV) and square wave voltammetry (SWV) were considered in addition to EIS. The measurement principle remains consistent, comprising the following three steps: (i) obtaining a voltammogram of the supporting electrolyte containing the redox pair; (ii) adding the blood serum and incubating for 30 min; (iii) obtaining a new voltammogram. Figure S1 illustrates the average voltammograms obtained before (step i) and after the addition of three seropositive and three seronegative samples. The voltammogram obtained in the initial step displays a single peak at approximately 0.2 V, which is characteristic of the oxidation of Fe²+ to Fe³+. The peaks obtained in stage iii (following the addition of the sample) occur at a slightly higher potential and with a lower current intensity than that observed for the first peak.

This increase in potential and decrease in current intensity indicates the blocking of the electrode surface by the serum components, as observed for the impedance spectrum. However, as evidenced by Figure S1, the difference between the peak currents produced by the negative and positive samples is minimal. A similar observation was noted in the context of SWV (results not shown). These findings suggest that the voltammetric techniques examined in this study exhibit significantly lower sensitivity compared to EIS and are not indicated for distinguishing between positive and negative samples within the context of this method.

Figure 3 shows the Bode plots obtained from the EIS measurements of the serum samples. Figures 3a, 3b and 3c show the Bode plots of the real component (Z’), the imaginary component (Z") and the phase angle (φ), respectively. The Bode plot for the absolute impedance (IZI) is very similar to the one obtained for the real impedance and has therefore not been shown. The inset plots show the average spectra of each class according to the impedance component used. The spectral profiles in all impedance representations are similar throughout the whole set of measurements, although differences are observed in the low frequency region (<100 Hz) for the spectra of the seropositive samples. At this range, they exhibit higher real impedance values than seronegative samples (Figure 3a), as well as significantly higher imaginary impedance values and lower resonant frequencies (Figure 3b). On the other hand, the phase angle spectra are more similar to each other, although there is a tendency for the spectra from each class to have a different span of time constants (Figure 3c).

Figure 3
Bode plots of the serum samples considering the real (a) and imaginary (b) impedances, and the phase angle (c). Blue: negative samples; orange: positive samples. Inset: average spectra.

The higher Z’ values indicate the emergence of additional resistive phenomena to the main electrochemical process (redox couple reaction), possibly caused by formation of an “insulating layer” by adsorption of inhibitory species on the electrode surface after electrode incubation with serum.³⁵,³⁶ This reflects the increase in R_ct previously discussed. The higher Z’’ values suggest an increase in the capacitive component of the system, which could be related to an increase in double-layer capacitance (C_dl) or introduction of additional capacitive elements. Adsorption of ions or molecules can increase the effective thickness of the double layer.³⁵

Both increases in R_ct and C_dl for seropositive samples produce an increase in the overall time constant of the system, shifting the resonant frequency to a lower value. A lower characteristic frequency means that the dominant electrochemical process has become slower. These distinctions, especially notable when comparing average spectra of each class, suggest that electrode surface blockage is more pronounced in samples from the positive serum class, as hypothesized. Figure S2 (SI section) shows the spectra after row preprocessing by applying the logarithm. The logarithmization produces a reduction in the measurement dispersion, which may favor the production of models based on fewer PCs (or LVs).³⁷

Tables S1 to S15 (SI section) demonstrate the optimal classification results using Z’, Z’’, Φ, |Z| and complex impedance (Z’ - jZ’’) data in PCA-DA, PLS-DA, and SIMCA models across different row preprocessing (none and logarithmization), column preprocessing (mean-centering and autoscaling), PCA-DA discriminant function types (linear and quadratic), and the selection of 1 to 20 PCs/LVs. Results are displayed in a contingence table format, detailing the number of samples classified in each class (type I and type II errors), and the figures of merit resulting from such classifications. The best-performing models, highlighted in grey in Tables S1-S15, showcase the lowest combined error rates (validation and test sets) and highest sensitivity, specificity, and precision. These top models are summarized in Tables 1, 2, and 3 for an easier comparison of the best scenarios for PCA-DA, PLS-DA, and SIMCA, respectively.

Table 1
Best-performing PCA-DA models based on real (Z’), imaginary (Z’’), phase angle (Φ), absolute impedance (IZI), and complex (Z’ - jZ’’) impedance data

Data	RP	CP	Func.	N	Valid.	Class	Pos	Neg	Sens	Spec	Prec	ER
Z'	log(x)	auto	Quad.	13	CV	Pos Neg	65 6	9 41	0.88 0.87	0.87 0.88	0.92 0.82	0.12
					Test	Pos Neg	42 3	5 30	0.89 0.91	0.91 0.89	0.93 0.86	0.10
Z’	none	mean	Lin.	12	CV	Pos Neg	67 4	7 43	0.91 0.91	0.91 0.91	0.94 0.86	0.09
					Test	Pos Neg	44 2	3 31	0.94 0.94	0.94 0.94	0.96 0.91	0.06
Φ	log(x)	auto	Quad.	9	CV	Pos Neg	65 6	9 41	0.88 0.87	0.87 0.88	0.92 0.82	0.12
					Test	Pos Neg	45 2	2 31	0.96 0.94	0.94 0.96	0.96 0.94	0.05
[Z]	none	mean	Lin.	12	CV	Pos Neg	70 7	4 40	0.95 0.85	0.85 0.95	0.91 0.91	0.10
					Test	Pos Neg	41 3	6 30	0.87 0.91	0.91 0.87	0.93 0.83	0.11
Z' - jZ''	none	mean	Lin.	6	CV	Pos Neg	44 9	30 38	0.59 0.81	0.81 0.59	0.83 0.56	0.29
					Test	Pos Neg	41 4	6 29	0.87 0.88	0.88 0.87	0.91 0.77	0.13

• RP: row preprocessing; CP: column preprocessing; Func.: type of discriminant function; N: number of PCs; Valid.: validation; Sens: sensitivity; Spec: specificity; Prec: precision; ER: error rate; Auto: autoscaling; Quad.: quadratic; CV: cross-validation; Pos: positive; Neg: negative; Mean: mean-center; Lin.: linear.

Table 2
Best-performing PLS-DA models based on real (Z’), imaginary (Z’’), phase angle (Φ), absolute impedance (|Z|), and complex (Z’ -jZ’’) impedance data

Data	RP	CP	N	Validation	Class	Pos	Neg	Sens	Spec	Prec	ER
Z'	log(x)	mean	11	CV	Pos Neg	61 6	13 41	0.82 0.87	0.87 0.82	0.91 0.76	0.15
				Test	Pos Neg	42 2	5 31	0.89 0.94	0.94 0.89	0.95 0.86	0.08
Z''	log(x)	auto	8	CV	Pos Neg	64 7	10 40	0.86 0.85	0.85 0.86	0.90 0.80	0.14
				Test	Pos Neg	43 1	4 32	0.91 0.97	0.97 0.91	0.98 0.90	0.06
Φ	log(x)	auto	16	CV	Pos Neg	63 6	11 41	0.85 0.87	0.87 0.85	0.91 0.79	0.14
				Test	Pos Neg	42 6	5 27	0.89 0.82	0.82 0.89	0.88 0.84	0.14
[Z]	none	auto	17	CV	Pos Neg	65 5	9 42	0.88 0.89	0.89 0.88	0.93 0.82	0.11
				Test	Pos Neg	40 2	7 31	0.85 0.94	0.94 0.85	0.95 0.82	0.10
Z' - jZ''	none	mean	11	CV	Pos Neg	62 4	12 43	0.84 0.91	0.91 0.84	0.94 0.78	0.13
				Test	Pos Neg	40 2	7 31	0.85 0.94	0.94 0.85	0.95 0.82	0.10

• RP: row preprocessing; CP: column preprocessing; N: number of PCs; Sens: sensitivity; Spec: specificity; Prec: precision; ER: error rate; Mean: mean-center; CV; cross-validation; Pos: positive; Neg: negative; Auto: autoscaling.

Table 3
Best-performing SIMCA models based on real (Z’), imaginary (Z’’), phase angle (Φ), absolute impedance (IZI), and complex (Z’ - jZ’’) impedance data

Data	RP	CP	N	Validation	Class	Pos	Neg	Sens	Spec	Prec	ER
Z'	log(x)	mean	4	CV	Pos Neg	60 10	14 37	0.81	0.79	0.86	0.20
				Test	Pos Neg	39 6	8 27	0.83	0.82	0.87	0.18
Z''	log(x)	mean	11	CV	Pos Neg	56 14	18 33	0.76	0.70	0.80	0.27
				Test	Pos Neg	44 8	3 25	0.94	0.76	0.85	0.15
Φ	log(x)	mean	10	CV	Pos Neg	57 10	17 37	0.77	0.79	0.85	0.22
				Test	Pos Neg	39 7	8 26	0.83	0.79	0.85	0.19
[Z]	none	mean	4	CV	Pos Neg	52 14	22 33	0.70	0.70	0.79	0.30
				Test	Pos Neg	35 2	12 31	0.74	0.94	0.95	0.16
Z' - jZ''	none	auto	8	CV	Pos Neg	60 10	14 37	0.81	0.79	0.86	0.20
				Test	Pos Neg	43 4	4 29	0.91	0.88	0.91	0.10

• RP: row preprocessing; CP: column preprocessing; N: number of PCs; Sens: sensitivity; Spec: specificity; Prec: precision; ER: error rate; Mean: mean-center; CV: cross-validation; Pos: positive; Neg: negative; Auto: autoscaling.

Table 1 reveals that excellent classification results were obtained with PCA-DA applied to imaginary impedance data, not requiring row preprocessing, and using a linear discriminant function. Sensitivity, specificity, PPV, and NPV values obtained for predicting samples from the test set are 94, 94, 96, and 91%, respectively, with error rate as low as 6%. Although real impedance, phase angle and absolute impedance data also delivered strong outcomes, they incurred slightly more errors than those with the imaginary component and required different row and column preprocessing methods to effectively distinguish between classes. The imaginary impedance was also the best choice for producing a PLS-DA model with excellent prediction power, as seen in Table 2. However, in this case, spectra preprocessing by applying the logarithm is required, as well as data autoscaling. Prediction results are remarkable, mainly for the test set, where all figures of merit also present values at least equal to 90%.

The literature describes impedimetric sensors for COVID-19 diagnostics with performance comparable to those in this study, all relying on electrode modification to detect changes in the R_ct of the redox probe [Fe(CN)₆]^3-/4-arising from interactions between the modifier and a viral component. For example, Huang et al.³⁸ used a nanoporous gold electrode modified with single-stranded DNA oligonucleotides (ss-DNA) to capture SARS-CoV-2 RNA (30-min incubation), achieving 100% sensitivity and 93% specificity. Torres et al.³⁹ functionalized a carbon electrode with angiotensin-converting enzyme 2 (ACE2) to bind the SARS-CoV-2 spike protein (4-min analysis), yielding 80.6% sensitivity and 89.0% specificity. Gevaerd et al.⁴⁰ developed a gold-conjugate-modified carbon screen-printed electrode for detecting the SARS-CoV-2 N protein, reporting 83.0% sensitivity and 96.2% specificity. With a similar approach to this work, Khayamian et al.⁴¹ employed a label-free graphene monolayer on copper to measure the cytokine storm, observing Rct increases of about 65% and 138% in moderate and severe cases, respectively. Applying the same principle for COVID-19 diagnosis resulted in 92% sensitivity and 50% specificity compared to RT-PCR.

The findings in Tables 1 and 2 align with those presented in Figure 3, which illustrates that the variation in imaginary impedance is more pronounced between classes than that observed for the other impedance representations, being the most sensitive property to the adsorption of serum components on the electrode surface. The application of complex impedance in both PCA-DA and PLS-DA did not result in the development of a superior classification model when compared to the optimal DA model (PCA-DA applied to imaginary impedance data). This is due to the fact that the complex number introduces non-discriminating information into the models produced, in contrast to the model based on the most discriminating information (imaginary impedance). A comparison of the best DA models revealed that the application of PLS resulted in a reduction in the number of factors, from 12 PCs in PCA-DA to 8 LVs with PLS-DA. This is attributed to the distinct approach employed in constructing the LVs, which is oriented towards maximizing covariance with the class indices (0 and 1 in this case).²²,⁴²

Figure 4 displays the prediction results for training (circles) and the test (stars) sets using the PCA-DA model based on the imaginary impedance data. One can see the seven false negatives (orange circles with probability < 0.5) and four false positive results (blue circles with probability > 0.5) in the training stage, as well as the two false positives and three false negatives in the test stage. The model exhibits excellent discrimination between classes in both the training and testing stages. The chosen set of PCs effectively captured the information underlying the impedance spectra, which provides the discrimination and adequately describes most of the seropositive samples (orange circles and stars). These samples are highly similar with a probability > 0.9, indicating a strong association with COVID-19 infection. The remaining samples in this class exhibit dispersion, which is expected for a complex matrix such as blood serum during a pandemic. Seronegative samples (blue circles and stars) display more variability, reflecting the broader range of conditions within uninfected individuals, where non-infection does not necessarily mean that the patient is healthy.

Figure 4
Predictions obtained by the PCA-DA model for positive (orange) and negative (blue) in the training (circles) and test (stars) stages. The horizontal dotted line corresponds to the class boundary.

The SIMCA models (Table 3) performed approximately the same considering the different types of data and preprocessing methods, and this performance was below that obtained with the best DA models. These models refer to modeling the seropositive class and showed a satisfactory prediction power, with sensitivity and specificity close to 90% for the test samples in the best scenario. Logarithmic transformation of spectra significantly improved SIMCA’s predictive performance for impedance data as real numbers, likely due to reduced intra-class variability. However, the best model was the one based on complex impedance data, with the lowest prediction errors both when training and analyzing the test samples.

SIMCA defines independent multivariate spaces for each class, which may even overlap, thereby creating a risk of incorrect classification. The definition of these spaces depends on the information available in the training set. In this case, using all the information contained in the complex impedance data resulted in a synergistic effect that provided a slightly better model than models based on each impedance representation as real numbers. In contrast, an alternative phenomenon was observed when employing DA, whose discriminating property was the imaginary impedance rather than its association with the real impedance in the complex number. The objective of DA is to identify a mathematical function that maximizes the separation between the classes involved, based on the combination of the measured properties. Consequently, the utilization of complex numbers, which encompass non-discriminating information in this case, hindered the success of models employing this type of data.

Of the classification models obtained, the most successful ones yielded excellent classification results, although they did not achieve maximum sensitivity and selectivity. Therefore, the use of data fusion was considered to ascertain whether the predictive capacity of the models generated could be improved. The real and imaginary impedance components, as well as the phase angle and absolute impedance representations, were utilized in the low-level fusion, as they are deemed to be representations of complementary electrochemical phenomena. Consequently, the real and imaginary impedance spectra (or the phase angle and absolute impedance spectra) were concatenated to formulate a vector of 102 variables per sample. The resulting matrices (201 × 102) were then submitted to the Kennard-Stone algorithm to generate the training and test sets, as well as to produce and validate the models. The results obtained are included in the Supplementary Information section (Tables S16, S17 and S18). In summary, the fusion did not improve the predictive capacity of the models, with figures of merit similar to those obtained with the best models using the impedance representations separately.

Conclusions

The obtained results confirm the initial hypothesis of a systematic differentiated interaction between the constituents of blood serum and the surface of an unmodified disposable gold electrode for samples that tested positive for COVID-19 with the reference diagnostic method. Supervised pattern recognition methods were applied to the electrochemical impedance data to exploit such differential interaction as a source of information for screening patients infected with SARS-CoV-2. The analysis of the spectra of the imaginary component of the impedance using discriminant analysis based on PCA or PLS was found to be more efficient, producing classification error rates as low as 6%. The sensitivity of the imaginary component to the adsorption of serum constituents on the working electrode surface and to the blocking of the interface to the redox process of the electrochemical probe makes it the most discriminating information. SIMCA-based one-class modeling showed higher error rates in the training stage (around 20%), but acceptable performance for prediction of test samples (a 10% error rate) using the complex form of EIS. The potential of low-level data fusion was investigated, encompassing the concatenation of real and imaginary impedance, or phase angle and absolute impedance. However, no enhancement in performance was observed when compared with the superior models utilizing the impedance representations individually.

The proposed method allows for the differentiation of blood serum samples from patients with and without SARS-CoV-2, making it a viable option for COVID-19 screening, identifying positive cases so that they can be directed to confirmation by RT-PCR, thus reducing the impact of a high demand for the more expensive and more time-consuming method. The assay is straightforward and can be easily administered by non-specialists in ‘black box’ mode, i.e., the analyst only needs to connect the electrode and take the measurements before and after adding the serum sample. All the settings for obtaining the impedance spectrum of a sample, as well as those related to data processing and machine learning, can be set by default. This feature enables the analysis to be performed after very simple training, which could involve switching the equipment on and off, taking the measurements and reporting the result, requiring no specific understanding of the underlying processes. Finally, the approach is cost-effective and produces a negligible amount of waste.

Supplementary Information

Supplementary information is available free of charge at http://jbcs.sbq.org.br as PDF file.

Acknowledgments

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001 and by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (grant No. 313738/2018-1). This study is supported by the Fundação de Apoio à Pesquisa do Estado da Paraíba (FAPESQ), grant No. 071/20; by Public Call No. 03 Produtividade em Pesquisa PROPESQ/PRPG/UFPB PVA13304-2020; and by the National Institute of Science and Technology on Molecular Sciences (INCT-CiMol), grant CNPq 406804/2022-2.

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Edited by

• Editor handled this article:
  Rodrigo A. A. Muñoz (Associate)

Publication Dates

• Publication in this collection
  21 Mar 2025
• Date of issue
  2025

History

• Received
  22 Nov 2024
• Accepted
  14 Feb 2025