Extension-Enhanced Wavelet Decomposition: a Noise and Background Resilient Square-Wave Voltammogram Signal-Processing Technique for Electrochemical Aptamer-Based Biosensing In Vivo

Abstract

Electrochemical aptamer-based (E-AB) sensors undergo structure-switching upon target binding, making them well-suited for in vivo continuous monitoring of biomolecules with high sensitivity and selectivity. Although square-wave voltammetry (SWV) is the most widely used analytical technique for probing the states of E-AB sensors, precise signal extraction from SWVs acquired during in vivo measurements remains challenging. The difficulty arises due to additive electronic and chemical noise, as well as varying background currents caused by factors such as the reduction of dissolved oxygen, degradation of self-assembly monolayer on the electrodes, biofouling, and other unforeseen effects. Conventional signal extraction algorithms, which typically assume a constant or a linearly varying background current with respect to the scanning potentials, are therefore error prone. In this work, we present a signal-processing technique termed Extension-enhanced Wavelet Decomposition (EWD) that enables background-resilient and noise-reduced SWV peak extraction while preserving quantitative redox signals. Inspired by the symmetric extension technique used in MRI image processing, EWD introduces pseudo-periodicity to the background signals and improves its spectral separation with redox signals from the process of wavelet transformation. We first validate the proposed EWD using simulated data, followed by its application to the datasets from both in vitro and in vivo experiments using several E-AB sensors. Compared to the conventional SWV signal extraction workflow, EWD demonstrates reduced background susceptibility and achieves 1.75 ~ 3.6-fold improvement in extraction variations from five in vivo datasets measured in whole blood when comparing with conventional SWV signal extraction method.

Graphical Abstract:

Aptamers are synthetic nucleic acids that can serve as high-affinity biosensors for a wide range of biomolecules, including small-molecule metabolites and protein markers. These aptamers can be further engineered into molecular switches that undergo conformational changes upon binding to target molecules.^1,2 When conjugated with a redox reporter, as illustrated in Figure 1, these conformational changes can be read out electrochemically by measuring changes in the electron transfer (ET) rates from the tethered redox labels at the electrode interface. As no additional reagents are required, this positions electrochemical aptamer-based (E-AB) sensors as one of the most promising platforms for continuous in vivo monitoring. E-AB sensors have been developed for detecting various analytes, including chemotherapeutic and antibiotic drugs, stress hormones such as cortisol, neurotransmitters including dopamine and serotonin, as well as serum proteins.^1–10 These sensors can be further integrated with miniaturized electronics fabricated using semiconductor technologies, enabling wearable and implantable systems.^11–13 Such integration highlights their potential for next-generation biomedical applications, including precision drug dosing for personalized medicine and real-time neurochemical monitoring in neuroscience research.

Figure 1.

Aptamers have demonstrated reliable performance in in vivo environments, where sensor surfaces may experience challenging conditions, including oxygen reduction, self-assembled monolayer (SAM) degradation and pinholes, and biofouling. These nonidealities often lead to SWV degradation over time, affecting the accuracy in signal extraction.

Square-wave voltammetry (SWV) is the most widely used electrochemical technique for interrogating E-AB sensors due to its high sensitivity and wide dynamic range (Figure S1).^14–16 In SWV, square waves are superimposed on a stepping potential sweep and the ET rates are probed by sampling at the end of each half-cycle. This approach avoids excessive non-Faradaic currents that overwhelm the desired redox signal. Moreover, due to a wide scan of the electrode potential, it can be relatively insensitive to variations in reference electrode potential, and redox behaviors can be reliably captured. This feature is particularly beneficial for in vivo measurements, where miniaturized yet less stable pseudoreference electrodes, such as silver/silver chloride (Ag/AgCl), are often used. A square-wave voltammogram, or termed SWV trace, is constructed by taking the difference between the forward (oxidation) and reverse (reduction) currents, typically resulting in a pulse-like waveform resembling a Gaussian function (Figure 1, right). The target redox signal is extracted by measuring the difference between the peak current in the SWV trace and the corresponding background current at the same potential. As aptamers undergo conformational switching in response to varying target concentrations, the SWV peak height is modulated due to the associated changes in the ET rate (Figure S1).

The background trace in SWV is typically fitted as a linear line (Figure 2). We term this conventional method linear background fitting (LBF) in the rest of the context. Nevertheless, this simplified extraction introduces potential sources of measurement uncertainty for several reasons.^17–20 In typical E-AB sensors, the electrode surface is passivated with a self-assembled monolayer (SAM) to minimize the electron transfer from nonspecific ions and other redox molecules presented in the biofluids. As a result, freshly prepared E-AB sensors usually exhibit a low and flat background offset. However, the integrity of the SAM can degrade over time due to desorption that occurs naturally or after repeated potential scanning.¹⁷ Additionally, biofouling can interfere with the SAM layer.¹⁸ All of these mechanisms create pinholes that compromise surface passivation. Over time, these effects gradually shift the background profile in the SWV traces.¹⁸ Compounding this issue, reduction of oxygen in biofluids can introduce competing redox reactions near the potential window of interest.¹⁹ As a result, the overall shape of the SWV curve can become increasingly distorted in unpredictable ways, as observed in our in vitro and in vivo measurements. This distortion makes the background offset unclear, causing signal extraction to be error prone. Figure 2a shows an extreme case where background tilting leads to an incorrect peak current extraction. The problem is further exacerbated under high-noise conditions, where fluctuations in the raw SWV trace cause the estimated background to “wiggle,” leading to significant artifacts in extracted peak values. From a signal-processing perspective, these background distortions exhibit low-frequency characteristics and are difficult to separate from the redox signal.²⁰ This inability to reliably decouple background shifts from the target signal limits the accurate interpretation of aptamer responses, impeding both the theoretical understanding of aptamer mechanisms and the development of robust readout platforms. Ultimately, these issues hinder the practical deployment of E-AB sensors in real-world applications.

Figure 2.

(a) Illustration of conventional linear background fitting (LBF). Method 1 fits a linear baseline in situ, but background tilting can cause errors between the extracted and actual peak. Method 2 rotates the SWV trace and extracts the signal as the difference between the local maximum and minimum. When referring to LBF, it is Method 2 that was implemented. (b) Illustration of discrete wavelet transform (DWT). Noise can be fitted using a down-scaled mother wavelet to scan the SWV traces, signal can be fitted with medium-scaled mother wavelet, and background can be fitted using an up-scaled mother wavelet.

Several alternative strategies have been developed to extract signals from voltammograms. In ref (21), first-order differentiation is applied to linear sweep voltammetry (LSV) to suppress background currents through an equivalent high-pass filtering process. However, this approach becomes less effective when the background currents deviate from a linear line. In contrast, Fourier-transformed alternating current voltammetry (FTacV)²² introduces an 80–100 mV sine wave superimposed on the voltage ramp of cyclic voltammetry (CV), effectively modulating redox currents into the frequency spectral domain. This allows separation of the signals from both the low-frequency background and the high-frequency noise. Nonetheless, FTacV is not directly applicable to SWV traces due to the incompatibility of the waveform shapes.

Another class of signal-processing techniques for electrochemical analysis is based on multiresolution analysis (MRA), a mathematical framework that decomposes measured signals by using basis functions with varying temporal resolutions. Unlike Fourier transform (FT), MRA offers greater flexibility in capturing time-varying features such as redox peaks in our case. Since the rising and falling edges of redox peaks can be abrupt, FT tends to spread the signal energy across the entire spectrum, making it difficult to isolate and filter relevant components (Figure S2). In contrast, MRA preserves both time and frequency information, enabling a more effective separation of signal and background. MRA techniques have been successfully applied to chromatographic profiles, biomolecular spectra, and electrochemical measurements.^23–26

Among the most widely used MRA techniques is wavelet transformation (WT), which decomposes signals by translating a “mother wavelet” across the range of the input data repeatedly but at different scales. Small-scale wavelets capture fast-varying, high-frequency components, often including noise, while large-scale wavelets extract slow-changing, low-frequency trends, such as the background currents (Figure 2b). The quality of decomposition strongly depends on the choice of the mother wavelet; better shape matching between the wavelet and the target signal yields more effective separation of meaningful signal components from background interference.^27,28 Previous study²⁸ has demonstrated the effectiveness of the continuous wavelet transform (CWT) in analyzing anodic stripping voltammetry signals. In this work, we apply the discrete wavelet transform (DWT) to SWV traces measured from E-AB biosensors to address the aforementioned challenges in precisely extracting meaningful signal information. Compared to CWT, DWT is more computationally efficient as it represents signals using wavelets at dyadic intervals. In our implementation, the number of decomposition levels is selected based on the signal length.

However, DWT is usually implemented with real, orthonormal wavelet bases, while CWT readily allows for both real and complex-valued wavelets. This decreases its flexibility in choosing mother wavelets that are more comparable to the ideal redox shapes. Therefore, it remains challenging for the DWT to separate low-frequency background currents without interfering with the desired signal. To address this issue, we further introduce a preprocessing step that was inspired by the symmetric signal extension technique used in MRI data analysis.²⁹ Specifically, we create replicas of raw SWV traces and concatenate them all together by appending the start of the next SWV curve to the end of the previous one (Figure 3). Mirror symmetry is subsequently applied after the concatenation. Such a repetition of the SWV curves converts the background signals into a pseudoperiodic component in the wavelet domain and facilitates easier separation between the desired signals and the background currents. In essence, we amplify the differences between the desired redox currents and other lower-frequency components, thus making the signal extraction process less impacted by the drifting background. We term our approach extension-enhanced wavelet decomposition (EWD). Unlike conventional LBF in which a linear background-current shape is assumed, EWD is more adaptive and robust to changing the background while simultaneously suppressing high-frequency noise. The full signal-processing procedure is detailed in the Methods section.

Figure 3.

Signal-processing flowchart of the proposed extension-enhanced wavelet decomposition (EWD) method. (a) The raw SWV trace is first denoised using polynomial fitting and truncated by identifying the most concave point of the waveform. (b) The truncated signal is elongated by concatenating and mirroring N copies to introduce pseudoperiodicity into the background component. (c) Discrete wavelet transform (DWT) is applied to the extended signal using the “fk8” mother wavelet. The resulting coefficients are classified into noise, signal, and background bands based on their energy distribution. (d) Only the signal band coefficients are retained and summed to reconstruct a background-free extended waveform. (e) Selected mirrored periods from the extended signal are averaged, and the peak value of the resulting background-reduced SWV is used as the output signal representing analyte concentration.

We demonstrate the application of the proposed EWD method across a range of scenarios to validate its robustness and performance improvement. We begin with simulated data sets featuring varying noise levels and background currents to assess noise resilience under controlled conditions. Next, we apply EWD to both in vitro and in vivo measurements of E-AB sensors, where background drift and noise are often exacerbated by biofouling and physiological variability. In nearly all cases, EWD reliably extracts the signal with high fidelity, achieving more than a 2× reduction in noise. Finally, we evaluate EWD on SWV signals collected from a custom-designed CMOS-based system-on-a-chip (SoC) electrochemical circuit developed for miniaturized implantable applications. These systems operate under stringent power constraints and thus exhibit elevated noise levels, yet EWD remains effective in isolating the desired signal.

METHODS

Signal Extraction Flow of Extension-Enhanced Wavelet Decomposition (EWD)

Figure 3 illustrates the signal extraction flow of the proposed EWD. EWD is conducted on the basis of a discrete wavelet transformation (DWT) and is designed to more effectively identify and remove noise and background drifts in the measured SWVs. Compared to the continuous wavelet transform (CWT), DWT offers reduced computational complexity. On the other hand, DWT is less shift-invariant and limited to real, orthogonal wavelets, which increases the difficulties to match the SWV traces with wavelets and separate background and redox signals effectively (Supporting Information Appendix F).

To compensate for these trade-offs, we propose EWD. The key idea is to extend the measured SWV traces by introducing pseudoperiodicity into the background component while preserving the target redox waveform. This transformation enhances the spectral separation between the signal and background in the wavelet domain (Figure S2). The signal extraction process consists of five sequential steps: step 1 (Figure 3a): Noise in the raw SWV signal is reduced by using polynomial curve fitting. The rationale for performing polynomial fitting is discussed in the Results section. The filtered square-wave voltammogram, typically 400–500 mV wide, is truncated by removing part of the background current at both ends of the SWV. Truncation boundaries are determined by identifying the most concave points within a user-defined window of 100–200 mV centered around the SWV redox current peak. Changing the window size by ± 50 mV results in only a 2% variation in the final results (Figure S3a). Step 2 (Figure 3b): Inspired by the symmetric extension technique used in magnetic resonance imaging (MRI),²⁹ we concatenate and mirror N copies of the truncated SWV trace to introduce pseudoperiodicity. The spectral separation between the low-frequency background signal and the redox signal is improved by a factor of 2N in the wavelet domain as the extended signal contains 2N redox periods but only one period of background signal. We optimize N = 8 to ensure sufficient spectral separation without incurring an excessive computational load. Increasing N improves background separation in the wavelet spectrum and reduces the deviation of the extracted values from the ideal ground truth. However, it also proportionally increases the computation time. Beyond N = 8, the improvement in accuracy becomes marginal while the computational cost continues to rise (Figure S3b). Step 3 (Figure 3c): The extended signal is decomposed using the eighth-order Fejér-Korovkin wavelet (“fk8”) from MATLAB’s wavelet toolbox. The decomposition depth, defined as the number of levels in the wavelet decomposition, is determined by log₂(M × 2N), where M is the number of data points in the original SWV trace. In our data sets, each SWV traces contain at most 300 data points, and the decomposition depth is limited to 12 levels with N = 8. Several other wavelets, including fourth-order Daubechies (“db4”), fifth-order Symlet (“sym5”), and second-order Coiflet (“coif2”), were also evaluated and yielded similar results due to waveform similarities (Figure S4). Step 4 (Figure 3d): Reconstructed signals from each decomposition level are grouped into three categories: the noise band, signal band, and background band. The signal band typically corresponds to the fifth to seventh levels among the 12 decomposition levels in our data sets. Only waveforms from the signal band are retained and summed for the final reconstruction. Step 5 (Figure 3e): Finally, we remove the first, last, and middle replicas to avoid boundary artifacts and edge effects arising from the DWT. These segments can introduce undesired discontinuities that distort the final SWV trace, especially at the edges and in the center where mirrored sequences meet. The remaining 12 replicas are then averaged to “collapse” them back into a single representative cycle, producing the final background- and noise-reduced SWV trace.

In Vitro and In Vivo E-AB Measurement Setup

The efficacy of the proposed EWD in improving signal integrity is tested by measuring various E-AB biosensors in both in vitro and in vivo setting. In total, we have tested five different aptamers of various sequences for sensing three different targets: kanamycin, ampicillin, and ATP. The sequences are adapted from refs. (12), (5), and (30) and are summarized in Table S1. The in vivo experiments were carried out by implanting aminoglycoside-aptamer-functionalized wire-shaped electrodes into the femoral veins of rats using catheters to perform sensing in whole blood. The sensing surface is coated with polyacrylamide hydrogel as an antibiofouling barrier, similar to our prior works in ref (31). The details of the sensor device preparation, electrochemical measurement schemes, and measurement setups are detailed in the Supporting Information in Appendix A–D.

Electrochemical Measurement

Square-wave voltammetry (SWV) is used to probe the electron transfer kinetics of MB. For in vitro experiments, we utilize both a commercial potentiostat (PalmSens4, PalmSens Inc., GA, Houten) and a low-power CMOS-integrated circuit developed in our previous work, whereas for in vivo studies, only the PalmSens4 is used. The potentials are typically scanned from −0.6 V to −0.1 V with a square-wave amplitude of 36 mV and a voltage step of 1 mV per potential increment. The scanned range is made adjustable to align the SWV peak current potential to the center of the potential window. Design and operation principles of the CMOS platform are detailed in the Supporting Information, Appendix E.

RESULTS

Validation with the Simulated Data

The proposed EWD technique is first validated using simulated data sets created in MATLAB and compared against the conventional LBF workflow, which assumes a linear-shape background current. To generate the simulated SWV voltammograms, we modeled the redox peaks using Gaussian functions with a 100 nA peak amplitude, a 0.3 V pulse width, and a center at −0.3 V. These values were empirically chosen to match those from the measurements from MB-labeled E-AB sensors. The full procedure for generating these simulated voltammograms is described in the Supporting Information, Appendix G. A set of nine SWV traces was created, each corresponding to a different target concentration computed from the Langmuir isotherm (Figure 4a, top), as defined by the equation

$Y\left(C\right)=\frac{S\times \left[C\right]}{\left[C\right]+K_{\text{D}}}$ (1)

where $Y$ is the signal level as a function of the target concentration [$C$], S is a fitted constant, and $K_{\text{D}}$ is the dissociation constant. For this numerical study, we use a $K_{\text{D}}$ of 0.5 mM, a value previously reported for aminoglycoside-binding aptamers used to detect kanamycin.¹¹ The exact $K_{\text{D}}$ value holds no intrinsic significance in this simulation but serves as a reference point to evaluate how background current estimation errors affect the accuracy of extracted $K_{\text{D}}$ values. In the initial simulations, we assume noiseless and zero background current in SWV traces and confirmed that the proposed method could reach the exact answer as the conventional LBF workflow with negligible deviations (Figure 4a, bottom). We then introduced measurement noise and background currents of varying shapes to systematically compare the two methods under nonideal conditions.

Figure 4.

Performance of the proposed EWD method is evaluated using simulated SWV data sets and compared to conventional LBF extraction. (a) Simulated SWV traces with varying concentrations (top) following an ideal Langmuir isotherm; corresponding extraction results show negligible deviation between EWD and LBF in the noise-free case (bottom). (b) Noise resilience is assessed with Monte Carlo simulations against added Gaussian noise from 100 fA_rms to 10 nA_rms. Left: signal extraction variability increases with noise, but the EWD maintains a tighter distribution. Middle: EWD shows 5-fold higher precision than LBF before applying polyfit(). Polynomial fitting improves LBF precision by 31.2%, but only marginally improves EWD. Right: EWD shows 13.2-fold better accuracy than LBF. Polynomial fitting reduces LBF error by 7% while having a marginal effect on EWD, demonstrating its noise-resilient nature. (c) The ideal SWV traces are corrupted with 60 Hz periodic noise (top); EWD significantly reduces extraction error versus LBF, which remains sensitive even with polynomial fitting (bottom). (d) Exponential-shaped background currents are added on the top of the ideal SWV traces (top); EWD maintains higher fidelity to the ideal Langmuir response, achieving 3× better agreement than LBF (bottom). (e) Evaluation under drifting backgrounds created by combining temperature- and H₂O₂-aged waveforms (left); EWD maintains better quantification across a range of background tilts (middle), with 5% improved resilience in peak preservation over LBF (right).

To begin, we examine the impact of trace-level noise on signal extraction (Figure 4b). Random Gaussian noise with varying RMS levels, from 100 fA_rms to 10 nA_rms, is added to the ideal SWV curves, which have target redox peak currents ranging from 100 to 200 nA. To assess robustness against added noise, we perform Monte Carlo simulations by repeating the signal extraction procedure 50 times at a given noise level. For each run, we computed the mean and standard deviation of the extracted peak currents for Langmuir fitting (Figure 4b, left). The standard deviation is used as a measure of the algorithm’s ability to suppress noise. Precision is assessed by averaging the standard deviation across nine concentration points (Figure 4b, middle), and accuracy is evaluated by computing the mean deviation from the ideal values (Figure 4b, right). Our results show that the proposed EWD achieves a 5-fold higher precision and a 13.2-fold better accuracy compared to the conventional LBF extraction when the SWV traces are superimposed by a 10 nA_rms noise. This demonstrates the strong noise-rejection capability of the wavelet-based decomposition, which can effectively separate high-frequency noise components from the low-frequency signal content. In contrast, the conventional LBF suffers from higher noise contributions due to both the signal fluctuations at the redox potential and the inaccuracies in estimating the background currents. Despite significant noise, EWD yields a dissociation constant of 0.48 mM ± 0.078 mM as compared to 3.4 mM ± 18.3 mM from LBF, while the true answer is 0.5 mM, indicating that EWD preserves quantification accuracy under noisy measurements. Deviation is quantified as the root-mean-square difference between the extracted and ideal values across all test cases.

Alternative signal decomposition methods such as the Fourier transform (FT) were also examined (Figure S5). In FT, the localized SWV peak in the time domain is spread over a broad range of frequency components, from the signal band to higher-frequency bands (Figure S5a). As a result, part of the true SWV signal overlaps with high-frequency noise in the FT spectrum. When only the signal band is used for reconstruction, the recovered SWV trace is noticeably distorted because part of the signal energy is missing (Figure S5b). The low-frequency band primarily captures the background as expected, whereas the high-frequency band contains a mixture of signal and noise. Langmuir fitting of the SWV traces reconstructed from these bands (Figure S5c) further shows large deviations from the ideal response, indicating that FT cannot cleanly separate the redox signal from the noise. In summary, we conclude that the Fourier transform (FT) method is effective at rejecting nonlinear baseline components and low-frequency noise but is less effective against high-frequency noise, which cannot be removed without distorting the true square-wave voltammetry (SWV) signal.

It is worth noting that the noise performance in the conventional linear background fitting can be improved through moving averaging or curve fitting with a template, such as a Gaussian function. However, we observed that moving average can lead to waveform distortion, and Gaussian fitting, on the other hand, performs poorly when a nonzero background current is present, as it assumes a symmetric peak with no offset. To address these limitations, we applied polynomial fitting using MATLAB’s polyfit() function, which preserves the SWV shape better and yields moderate noise reduction. As shown in Figure 4(b, middle, and right), polynomial fitting improves the precision by 31.2% and the accuracy by 7% for LBF extraction while it has minimal improvement for EWD (1.72% and 0.23%, respectively), indicating its noise-resilient nature. On the other hand, we observed that the choice of polynomial order significantly impacts the result. A polynomial order that is too low can distort the waveform and fail to capture the redox peak, while an excessively high order may overfit the noise, introducing unwanted artifacts (Figure S6). Nevertheless, even with optimized polynomial fitting (21st-order), the variation remains approximately 1.42-fold higher, and the accuracy is still 5.45-fold worse than that using the proposed EWD, as shown in Figure 4b. In the remainder of this paper, EWD is compared against LBF with high-order polynomial equation fitting for measurement noise rejection.

In some cases, measurements can be corrupted by periodic noise from 50/60 Hz power supply lines if the system is not properly shielded. This type of interference can superimpose onto the SWV curves and causes a high extraction error (Figure 4c, top). We found that the proposed EWD method effectively rejects such periodic noise due to its ability to isolate frequency components through wavelet decomposition, as shown in Figure 4c, bottom. In contrast, conventional LBF extraction is highly susceptible to this interference, resulting in substantial errors in the extracted signals. Even with polyfit() applied, LBF still performs 1.6-fold larger variation than EWD. Without the aid of polyfit(), LBF has 122.5-fold larger variation (Figure S7).

Next, we introduce background currents with an exponential-like shape to the noise-free SWV curves to simulate scenarios where a nearby redox reaction occurs (Figure 4d, top). This situation commonly arises in biological fluids with high oxygen content, where oxygen is reduced with negative voltage applied relative to the reference electrode.¹⁹ Our results show that the presence of such a large background distorts the extracted signal currents in both methods, as the signals are buried under the background. However, when comparing the fitted Langmuir isotherms, the curve obtained using the EWD method is 3-fold closer to the ideal Langmuir response than that obtained using conventional LBF (Figure 4(d), bottom). This demonstrates that the proposed EWD approach is more resilient to complex, nonlinear background currents and provides a more accurate representation of binding behavior under realistic conditions.

Finally, we emulate a scenario involving changing background currents, a phenomenon frequently observed in hours-long in vitro and in vivo experiments. We examine the impact of varying backgrounds at different tilting levels, while maintaining a constant target concentration. The background signal was obtained from a temperature-aged background and an H₂O₂-treated background (Figure 4e, left, Figures S8 and S9). The sum of the two is scaled from 0.2 to 2-fold and superimposed on an ideal Gaussian curve to achieve SWV traces with different tilting levels (Figure 4e, middle). Although the peak values extracted from both methods inevitably degrade,¹⁹ our EWD presents 5% better resilience to such harsh background.

Application of EWD to In Vitro Measurements

Next, EWD was applied to measurements acquired from the in vitro E-AB sensing assay with titrations of target molecules. The tested aptamers included those for ampicillin and ATP, with the results summarized in Figures 5 and S10. When the input signals are lower quality (smaller peaks or a more tilted baseline), EWD shows greater noise resilience, yielding a 2- to 4-fold reduction in standard deviation in the extracted time traces compared with conventional LBF. This directly translates to an improvement in the limit of detection (LOD). As shown in Figure 5a, a 3-fold reduction in extraction deviation improves the LOD from 43 μM to 12 μM (Figure 5d). By contrast, when the redox peaks are larger (Figure 5b,c), the LODs from LBF and EWD are comparable (19.4 vs 15 μM; Figure 5d). This result is consistent with the simulations, where LBF and EWD perform similarly when the data are only mildly distorted. In this paper, “noise” refers to the random Gaussian noise present in the measurements, whereas “extraction deviation” is defined as the variation of the extracted signal at a fixed target concentration under steady-state conditions and is used as a metric for extraction accuracy (Figure S11). Data points collected while diffusion kinetics were still settling were excluded from this calculation. The degree of improvement is highly dependent on the quality of the SWV voltammograms. In cases where the SWV signaling currents are high and the noise levels are low, the conventional LBF performed comparably to EWD in terms of deviation. However, the advantage of EWD became significantly more pronounced when the SWV currents were lower compared with noise levels. These lower signal amplitudes were typically associated with smaller electrode surface areas, lower square-wave frequencies, or aptamers with inherently weaker electron transfer efficiency due to secondary structures.

Figure 5.

EWD and LBF extraction results from measuring the (a) ampicillin aptamer (AMP.P in Table S1) and (b) ATP aptamer (ATP.P in Table S1) when titrated with different target concentrations. EWD achieves 2.88-fold error reduction in (a) and around 1.32-fold in (b). Here, the curves from the two methods are offset for clarity, and the deviation from linear background extraction is denoted as e_LBF and the one from EWD is denoted as e_EWD. (c) Collected SWV traces from the experiments in (a) and (b), showing a smaller, tilted peak for the ampicillin case and a larger, cleaner peak for the ATP case. These results verify that EWD provides greater benefit when the input peak is with lower quality. (d) Summary of error rates and LODs for parts (a) and (b). The lower extraction deviation with EWD directly translates to improved LOD.

It is also worth noting that these in vitro experiments were completed within 3 to 4 h, which is not long enough to induce time-varying background drift. As such, we conducted an accelerated aging test. This involved periodically heating the aptamer-functionalized electrodes to approximately 45 °C and allowing them to cool naturally to room temperature. We found that this thermal cycling induces desorption of the SAMs from the electrode surface, which in turn results in elevated background currents due to the presence of pinholes on the electrode surface. A representative set of SWV curves is shown in Figure S12a,c, summarizing the time traces processed using both methods with two different aptamers. Before accelerated aging, the deviation levels appear similar between the two methods, as the SWVs exhibit relatively high current amplitudes and sufficient signal-to-noise ratio. However, the presence of distorted background currents significantly affects the conventional LBF, as it can wrongly samples the peak current. This leads to sudden signal jumps in the time traces (Figure S12b). In contrast, EWD decomposes the measured SWV traces and reconstructs it after isolating the background components, and thus, it is much less affected by the tilted background current.

Application of EWD to In Vivo Measurements

We subsequently applied EWD to data obtained from in vivo experiments. A bolus of kanamycin was administered through the rat’s femoral vein, and the resulting response was measured by kanamycin aptamers using wire probes in whole blood (Supporting Information, Appendix D). Due to the complex physiological environment of whole blood and the use of thin wire-type electrodes with reduced sensing areas, the resulting SWV traces were often distorted and more susceptible to signal extraction errors.^{2–4,6–8,18} Additionally, to enhance measurement robustness, each aptamer probe was interrogated twice per sensing cycle, once at an SWV frequency of 400 Hz and once at 60 Hz, to implement kinetic differential measurements (KDM) for drift rejection through self-normalization.^{2,3,6,7,11,12} Notably, the 60 Hz SWV traces exhibit approximately 4× lower current amplitudes compared to the 400 Hz measurements, making them more vulnerable to both noise and background distortion. Figure 6 shows the time-domain traces acquired at both frequencies from two different animal models. In the first data set (Figure 6a), tilted SWV traces led the conventional LBF extraction to occasionally misfit the background, resulting in “spiking” artifacts at several data points. These artifacts required manual inspection and correction. In contrast, EWD operated robustly without manual intervention and achieved a near 2-fold improvement in standard deviation after KDM is applied. In the second data set (Figure 6b), where background distortion was less prominent and signal levels were higher, EWD still demonstrated a 1.28-fold reduction in deviation compared to the conventional approach. Additional three in vivo results are provided in the Supporting Information (Figure S13). Across all cases, the EWD method consistently improves signal quality and minimizes sampling errors in physiologically relevant sensing environments.

Figure 6.

EWD and LBF comparisons on in vivo continuous measurements of aminoglycoside E-AB sensors with bolus administration of kanamycin. (a) Extraction results of the first experiment demonstrating a 2-fold deviation reduction in EWD and (b) 1.28-fold deviation reduction. Left column: scans with high-frequency SWV; middle column: scans with low-frequency SWV; right column: results after implementing KDM by taking the difference between high-frequency traces and low-frequency traces. Here, the curves from the two methods are offset for clarity, and the standard deviation from LBF is denoted as e_LBF and the one from EWD is denoted as e_EWD.

Application of EWD to Data Collected from Miniaturized System-on-Chip (SoC)

EWD was also applied to data collected from our recently developed CMOS-based electrochemical readout circuit for implantable and wearable applications.^11,12 Unlike benchtop potentiostats, which leave the electrodes open-circuit between scans, this low-power circuit continuously biases the electrodes at a specific voltage. This difference alters the shape of the background currents, as illustrated in Figure 7a. Such background distortions in the SWV traces make conventional LBF extraction challenging, because there are no obvious local minima for LBF to extract a linear baseline curve. Mis-extraction of these local minima is the main source of the blip-like error seen in Figure 7b. In the past, we corrected these errors by manually examining every blip, adjusting the baseline curve, or replicating the baseline from previous measurements, which is a tedious and error-prone process. A similar result is also observed when employing the software provided by the commercial potentiostat vendor. In contrast, EWD enables more accurate background removal, resulting in reduced deviation in the extracted signal, particularly for low-amplitude signals measured at lower SWV frequencies (Figure 7c).

Figure 7.

Application of EWD and LBF extraction methods to kanamycin-spiked human whole blood data collected using a miniaturized System-on-Chip (SoC) platform. (a) Example of a distorted SWV trace acquired using the SoC system. Due to background distortion from continuous electrode biasing, the right-side local minimum is no longer discernible and requires manual definition in conventional LBF extraction. (b) Signal extraction results from 60 Hz SWV traces. The redox signal is 13× smaller than that at 400 Hz, making it particularly vulnerable to noise and background artifacts. EWD significantly reduces extraction errors, achieving a 4.93-fold reduction in deviation compared to LBF. Upward spikes in LBF arise from background overestimation, while downward spikes result from signal misidentification as zero. (c) Extraction results from 400 Hz SWV traces, where both EWD and LBF yield comparable outcomes due to stronger signal amplitude. Extraction deviations from LBF and EWD are denoted as e_LBF and e_EWD, respectively.

In this experiment, SWV was performed at two frequencies, 60 and 400 Hz, to enable KDM for drift mitigation. Here, we show the results measured from each SWV frequency prior to KDM to highlight the improvement in deviation reduction from EWD. At 60 Hz, the SWV current peaks were 13-fold smaller than at 400 Hz as the sampling of current happened nearly at the end of the redox reaction. This small signal makes conventional LBF extraction ineffective at distinguishing the current peaks from the background. It is also worth noting that the traces in Figure 7b,c are normalized. Because of the smaller amplitude in the 60 Hz SWV traces (on the order of 20–30 nA), even a 10 nA extraction error can appear as an ~50% spike after normalization. In some cases, this led to large downward or upward signal spikes where downward spikes are caused by mistakenly interpreting the signal to be “zero”, i.e., the algorithm fails to identify any signal peaks, and upward spikes are from erroneous background inclusion. On the other hand, EWD significantly reduced the occurrence of these artifacts and lowered the overall time-trace standard deviation by 4.93-fold (Figure 7b).

At 400 Hz, the higher signal amplitudes yielded similar outcomes from both LBF and EWD (Figure 7c). These findings demonstrate the robustness of the EWD for signal extraction across different readout platforms. Notably, while our implantable CMOS electronics are optimized for low power, they inherently suffer from higher noise compared with benchtop systems. Our results show that EWD provides a more reliable signal-processing approach in these resource-constrained, high-noise applications.

CONCLUSION

In this work, we introduce extension-enhanced wavelet decomposition (EWD) as an effective solution for background- and noise-resilient signal extraction techniques in E-AB sensing with SWV measurements. By introducing periodic extension of raw SWV traces, the proposed EWD outperforms the conventional linear background fitting (LBF) signal extraction workflows in overall noise performance, especially in the presence of unpredictable and nonlinear background signals. We validated the EWD technique across simulated data sets, in vitro and in vivo measurements, as well as using CMOS application-specific integrated circuits (ASICs) developed for wearable and implantable biosensing applications. Importantly, EWD consistently achieved a 2–3× improvement in noise reduction in measured time traces, demonstrating that much of the noise attributed to E-AB sensors originates from imperfect background signal removal rather than from the measured electrical or chemical noise. This advantage becomes particularly significant when using small electrodes or E-AB sensors with inherently smaller SWV current peaks, where signal extraction is more sensitive to background interference.

By improving signal robustness in complex biological environments, EWD enables a more accurate interpretation of aptamer behavior under realistic conditions, which in turn supports better sensor design, improved readout platform development, and advances in point-of-care diagnostics. Additionally, a major benefit of the proposed DWT-based approach is its low computational complexity, which makes it well-suited for hardware integration. This is particularly critical for wireless implantable and wearable systems where power and bandwidth constraints limit the feasibility of transmitting full SWV traces. With EWD, on-chip signal processing can be performed at low power, enabling more efficient data handling. Computation time was evaluated using a 1512-point data set. EWD required roughly only twice more computation time (0.0235 s/measurement) than LBF (0.0115 s/measurement) on a 12th Gen Intel Core i5–12500H processor at 16 GB RAM. In general, the aptamer sensors, when measured in vivo, are interrogated every minute at the highest throughput; thus, the processing time required by EWD is well below the practical limits and introduces negligible overhead. It is also worth noting that because EWD explicitly models the SWV peak shape, in principle, it could allow accurate extraction from SWV scans sampled with fewer voltage points per cycle. This could potentially improve temporal resolution by shortening each scan, but a systematic evaluation of the trade-off between sampling density, extraction accuracy, and acquisition speed is left for future work.

Future research directions include further optimization of wavelet basis selection and extension of the EWD framework to multianalyte detection and other electrochemical techniques such as cyclic voltammetry and chronoamperometry. Another promising direction is the parallel decomposition of redox signals and background currents by using separate wavelets tailored to the feature of each component. For example, the background currents are typically slow and at low curvature and require a new wavelet specifically suited for modeling such a signal type. Developing such application-specific wavelets remains an open challenge and will be a key focus of future efforts.

Supplementary Material

ASSOCIATED CONTENT

Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acssensors.5c02906.

Detailed fabrication; functionalization; and protective coatings of E-AB sensors for both in vitro and in vivo experiments; the design and operation of a custom low-power CMOS readout; experimental setups; additional validation results; and aptamer sequences (PDF)

ABBREVIATIONS

E-AB sensor

electrochemical aptamer-based sensor

SWV

square-wave voltammetry

EWD

extension-enhanced wavelet decomposition

LBF

linear baseline fitting

RMS

root-mean-square

ASICs

application-specific integrated circuits

MB

methylene blue

ET

electron transfer

SAM

self-assembled monolayer

MRA

multiresolution analysis

CWT

continuous wavelet transform

DWT

discrete wavelet transform

WT

wavelet transform

PBS

phosphate-buffered saline

SNR

signal-to-noise ratio

FFT

fast Fourier transform

SoC

system-on-chip

WE

working electrode

RE

reference electrode

CE

counter electrode

CV

cyclic voltammetry

TCEP

tris(2-carboxyethyl) phosphine

SSC

saline sodium citrate

MCH

6-mercapto-1-hexanol

ADC

analog-to-digital converter

DAC

digital-to-analog converter

FSM

finite-state machine

mPES

modified poly(ether sulfone)

MRI

magnetic resonance imaging

KDM

kinetic differential measurement