Abstract
Biomarkers in sweat and saliva offer a promising avenue for non-invasive health
monitoring. Electrochemical sensors have the potential to measure such biomarkers
simultaneously. However, they are limited in discriminating individual biomarkers in
mixtures, as redox potentials often overlap, resulting in current signatures that cannot
be deconvoluted.
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This study focuses on differentiating biomarkers using orthogonal sensing mate-
rials combined with machine learning. We introduce a flexible electrochemical sen-
sor array comprising carbon flower electrodes modified with poly(vinylidene fluoride)
(PVDF) or poly(4-vinylpyridine) (P4VP) for the detection of estradiol (E2), ascorbic
acid (AA), serotonin (5-HT), and melatonin (Mel). The two polymers act by alter-
ing the redox potential and current response of each biomarker, thereby enhancing
signal diversity and enabling peak separation. Using multi-output regression models
on 450 single and mixture measurements, the array accurately predicts concentrations
(R2 = 0.95) over a wide dynamic range spanning nanomolar to micromolar levels.
Polymer-resolved analysis reveals that PVDF-modifications enhance E2 and Mel de-
tection, while P4VP-modifications improve AA and 5-HT quantification, highlighting
the benefit of complementary orthogonal sensing electrodes. This finding is further sup-
ported by feature attribution analysis, which shows that the machine learning model
relies on polymer-specific electrochemical signatures, directly linking improved perfor-
mance to distinct polymer-analyte interactions. Overall, these results demonstrate that
combining polymer-modified orthogonal electrodes with machine learning enables accu-
rate, multiplexed sensing in complex mixtures, advancing selective detection strategies
for future sensor platforms.
Keywords
health sensing, carbon flowers, stretchable sensors, selectivity, non-linear re-
gression, sensor array
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Introduction
Human sweat and saliva contain numerous biomarkers that reflect biological processes within
the body. Differences in biomarker concentrations provide insights into healthy and diseased
states, making them attractive for non-invasive disease diagnostics and continuous health
monitoring for personalized and preventive healthcare.1 For example, estradiol (E2) is a hor-
mone essential in female health 2 and affects major organs, including bones 3 and the brain. 4
Serotonin (5-HT) regulates mood and is linked to neurological disorders, such as depres-
sion and post-traumatic stress disorder, 5 while peripheral serotonin is related to metabolic
health. 6 Ascorbic acid (AA) is an essential antioxidant and nutritional indicator.7 Melatonin
(Mel) influences circadian rhythms and sleep patterns. 8
For this reason, wearable sensors have attracted increasing interest. 9–11 Carbon-based
electrochemical sensors are among the most widely studied types, as they are low-cost, have
high potential stability, and are reversible. Various electrochemical neurotransmitter and
hormone sensors have been reported in recent years with high sensitivity using strategies in-
cluding metal (oxide) doping, 12,13 high surface area materials, 14 and conductive polymers. 15
However, accurately detecting and quantifying specific biomarkers remains a significant chal-
lenge due to their co-occurrence and overlapping redox potentials, resulting in overlapping
current signatures that cannot be deconvoluted. In addition, sensors often do not meet
the mechanical requirements for soft, on-skin applications due to their rigidity, for example,
modified glassy carbon electrodes (GCEs), or toxicity (i.e., carbon nanotubes).
Sensor arrays offer a solution towards multiplexed sensing. 16 In principle, each electrode
provides an individual signal pattern, generating diverse and distinguishable signal sets that
enable identification and quantification of individual components. While sensor arrays pro-
vide a viable route towards selectivity, their signal readout, processing, and interpretation re-
main complex, particularly when analyte responses overlap strongly. Machine learning (ML)
has therefore emerged as a powerful complementary tool to extract multivariate informa-
tion from electrochemical signals and enable multiplexed quantification beyond conventional
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peak-based analysis. Recent studies illustrate this trend: overlapping dopamine (DA) and
5-HT signals were distinguished using artificial neural networks (ANNs), achievingR2 > 0.97
and root mean squared error (RM SE ) 0.98
with 4 − 6% error; 18 multiplexed detection was demonstrated on engineered sensor surfaces
with supervised ML models (support vector machine (SVM), ANN) to distinguish tyrosine
and uric acid in sweat and saliva, reaching R2 = 0.85 − 0.95; 19 and SVM, ANN, and GLM-
NET regression were used to detect multiple toxicants in water, reporting RM SE ≈ 0.24
mg L−1 across 23 sensors. 20 Despite these advances, many prior works are constrained by
limited dataset sizes, limited analyte diversity, and a lack of distinctly different electrodes.
Such limitations can hinder model generalization and increase the risk of overfitting when
applied to realistic sensing scenarios. 21 This emphasizes the need for larger, more realistic,
and multiplexed datasets 22,23 alongside improvements in sensor design and electrode speci-
ficity, model robustness, and standardized protocols for deploying ML in practical sensing
applications. 24–26
In one of our recent studies, we demonstrated that introducing polymer modifications
with poly(4-vinylpyridine) (P4VP) and poly(vinylidene fluoride) (PVDF) induces polymer-
specific peak potential shifts due to different adsorption and diffusion characteristics of indi-
vidual biomarkers with these polymers. 27 We further showed that these polymer modifica-
tions work well with nanostructured carbon flowers to achieve high sensitivity.28 In this work,
a sensor array based on polymer-modified carbon flowers is designed to detect the biomarkers
E2, AA, 5-HT, and Mel ( Fig. 1a). Sensor arrays are fabricated by spray-coating carbon
flower inks containing the respective PVDF or P4VP polymers onto stretchable polystyrene-
block-poly(ethylene-ran-butylene)-block-polystyrene (SEBS) substrates. We collected a com-
prehensive dataset of 450 measurements comprising 1-, 2-, 3-, and 4-analyte mixtures to
capture realistic mixed-analyte conditions. This platform is combined with a structured ML
framework to identify analyte concentrations from multiplexed voltammetric signals. The
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framework integrates linear, kernel-based, ensemble, and neural network models to exam-
ine how algorithmic flexibility, preprocessing transformations, and feature representations
affect predictive performance and robustness. Interpretability is ensured through SHapley
Additive exPlanations (SHAP)-based analysis,29 enabling identification of signal regions and
polymer-specific interactions most relevant to prediction. Together, these strategies address
longstanding challenges in selective electrochemical detection of biomarkers in complex mix-
tures and demonstrate the potential of polymer-orthogonal sensing combined with ML for
wearable and point-of-care applications.
Figure 1: — Concept. (a) Target non-invasive biomarkers: estradiol (E2), serotonin (5-
HT), ascorbic acid (AA), and melatonin (Mel). (b) Schematic of sensor design. (c) Dual
sensor array: each sensor consists of 8 electrodes made of conductive carbon flowers coated
with selective polymers — Type 1: PVDF-CF, Type 2: P4VP-CF. (d) Photograph of the
electrochemical sensor. (e-g) SEM image of an electrode and zoomed-in views. (h) Data
acquisition and ML workflow.
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Experimental Section
Sensor Fabrication and Characterization
The sensor fabrication followed the protocols from our previous works. 28,30,31 Carbon flow-
ers were synthesized from acrylonitrile precursors and subsequently carbonized at 1500 ◦C
under nitrogen flow. The as-prepared carbon flowers (45 mg) were dispersed in chloroform
(100 mL) containing the respective polymers (5 mg), poly(4-vinylpyridine) (P4VP, Mw =
60,000 Da, Sigma-Aldrich) or poly(vinylidene fluoride) (PVDF, Mw = 534,000 Da, Sigma
Aldrich), using ultrasonication to obtain a homogeneous ink. The carbon flower inks were
then spray-coated onto stretchable SEBS (Asahi Kasei Tuftec H1052, Tokyo, Japan) sub-
strates featuring pre-defined stretchable silver current collector patterns, using a metal mask
to define the electrode geometry. Electrical connections were established using conductive
z-axis tape to interface the carbon flower electrodes with a flat cable connector. Each sensor
comprised eight working electrodes mixed with the same polymer formulation (PVDF or
P4VP); only one electrode was used for electrochemical testing. In total, 5 P4VP-modified
sensors (ID: MC302, MC312, MC327, MC329, MC330) and 3 PVDF-modified sensors (ID:
MC313, MC320, MC325) were fabricated and included in this study. Scanning electron
microscopy was conducted using an FEI Magellan 400 XHR instrument, operated at an
accelerating voltage of 5 kV and a beam current of 100 pA.
Electrochemical Measurements
Electrochemical measurements were performed using a CH Instruments 760E potentiostat
coupled with a CHI200 picoamp booster and Faraday cage to reduce electrical noise. Square
wave voltammetry (SWV) was used for analyte detection in phosphate-buffered saline (PBS)
using the following parameters: 0.025 V pulse amplitude, 5 Hz frequency, and 0.004 V step
potential across a 0–0.8 V range (resulting in 200 current values per trace). A standard three-
electrode setup was used, consisting of a platinum wire auxiliary electrode, an Ag/AgCl (3 M
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KCl) reference electrode, and the respective carbon flower working electrode modified with
either PVDF or P4VP. The CHI setup enabled simultaneous measurements of two elec-
trodes, resulting in two similar current responses per scan. To avoid redundant information
in subsequent modeling, only the first current trace was used for preprocessing and ML
analysis. Experiments were conducted at ambient temperature in 1 × PBS (pH 7.2). At
least three blank scans were collected at the start of the measurement sequence to capture
the plain baseline PBS response for subsequent data preprocessing. 17β -estradiol (> 0.97,
TCI Chemicals) and melatonin stock solutions were prepared in ethanol, whereas serotonin
hydrochloride (≥ 98, Sigma Aldrich), L-ascorbic acid ( ≥ 0.98, Sigma Aldrich), uric acid
(≥ 98, AmBeed), dopamine hydrochloride (≥ 0.98, Sigma Aldrich), norepinephrine (≥ 0.98,
Sigma Aldrich), and epinephrine (≥ 0.99, Sigma Aldrich) were dissolved directly in PBS.
Analyte solutions were freshly prepared and introduced stepwise into nitrogen-purged
PBS at specified concentrations. Mixing was accomplished through nitrogen bubbling. Typ-
ically, three consecutive measurements were performed at each concentration step, with a
uniform waiting time of 60 s; for later analysis, the average of these scans was used. Prior
to each measurement, sensors were rinsed with deionized water.
Dataset Design and Concentration Ranges
For each polymer coating, the dataset was designed to include a diverse set of mixture com-
plexities: 10 single samples per biomarker (80 total), 15 samples for each of six biomarker
pairs (180 total), 15 samples for each of four triple combinations (120 total), 15 samples for
each quadruple (30 total), and 40 additional random samples. In total, this resulted in 450
samples. Detailed measurement and data parameters are provided in Table S1, and a full
dataset summary across polymer coating and individual sensors is shown in Table S2. The
concentration ranges were selected based on reported physiological concentration levels for
ascorbic acid and serotonin in relevant biofluids (see Table S3); for estradiol and melatonin,
concentration levels higher than physiological levels were chosen due to the sensitivity limi-
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tations of the sensors. For PVDF-modified sensors, concentrations ranged from 10–1000 nM
for E2, 5-HT, and Mel and 1–10 µM for AA. For P4VP-modified sensors, concentrations
ranged from 100–3000 nM for E2, 5-HT, and Mel and 6–20 µM for AA.
Data Preprocessing, Machine Learning, and Performance Evalua-
tion
Raw SWV scans (Fig. S1a, 200 data points per trace) were preprocessed to reduce measure-
ment noise and enhance electrochemical features. First, up to three blank PBS scans were
averaged and subtracted from the analyte signals, followed by Savitzky–Golay (SG) filtering
(polynomial fit of degree 3 over a 9-point window) to suppress high-frequency noise while re-
taining peak shapes and overall signal morphology (Fig. S1b). The potentiostat used in this
study (CHI750E) produces very little noise, with the high-frequency component representing
only ∼3.5% of the total signal variance (SNR ≈ 276). SG smoothing provides approximately
2× noise reduction in the raw signal and 2 .8× in the derivative domain. These steps en-
sured that models were trained on signals reflecting true electrochemical activity rather than
artifacts from instrumentation or baseline drift.
To address baseline variability and overlapping peaks, three signal transformation strate-
gies (Fig. S1c ) were evaluated: min-centering for baseline alignment, linear baseline cor-
rection by fitting and subtracting a first-degree polynomial using the edge regions of the
voltammogram (10 points at the start and end), and first-derivative transformation (dI/dV )
computed via numerical gradient (numpy.gradient), which enhances peak contrast and in-
troduces secondary extrema to improve analyte separability. If not noted explicitly otherwise,
first-derivative transformation was used, as it yielded the best performance.
For ML analysis, the preprocessed scans were used directly, allowing the models to learn
from the complete voltammetric signal without assuming a fixed number or position of
peaks. In addition to the electrochemical features, two categorical variables were included:
the sensor identifier (ID number) and the polymer coating type.
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The modeling task was formulated as supervised multi-output regression to predict con-
centrations of the four biomarkers (E2, AA, Mel, and 5-HT). To prevent data leakage from
repeated measurements, samples were grouped by sample ID during splitting. For each ran-
dom seed (0, 42, 1337, 2023, 9999), an independent held-out test set was generated using
GroupShuffleSplit (90/10). The remaining 90% of the data was used for model development
with 5-fold GroupKFold cross-validation. Training and validation metrics were computed as
the mean across the five cross-validation folds for each seed, while test metrics were evaluated
on the corresponding held-out test set. All reported performance values are given as mean
± standard deviation across the five random seeds. Numerical features were standardized
to zero mean and unit variance using a StandardScaler, fitted exclusively on the training
data, and subsequently applied to the validation and test sets, while categorical features
were one-hot encoded. Six regression algorithms representing diverse learning paradigms
were implemented to explore how model complexity and inductive bias influence prediction
from multiplexed voltammetric signals: Ridge regression (serving as a baseline for linear
modeling with regularization), random forest and XGBoost (tree-based ensembles, suited
for non-linear tabular data), k-nearest neighbours (non-parametric local model), support
vector regression (kernel-based method for non-linear signal relationships), and multilayer
perceptron (MLP, a small neural network capable of capturing complex non-linearities).
Hyperparameters were tuned using grid search cross-validation and were tuned inside the
cross-validation loop; the held-out test set was not used for model selection. Parameter
ranges were guided by prior biosensing ML literature 22,23,32 and refined iteratively.
False non-zero predictions, where the model predicts non-zero concentrations in the ab-
sence of an analyte, were mitigated using a zero-aware two-stage architecture for the repre-
sentative model shown in Fig. 3. In this approach, each analyte was first classified as present
or absent using multi-output binary classification (labels: y > 0), and concentrations were
then predicted using multi-output regression. At inference time, regression outputs were
gated by the classifier decision and set to zero when an analyte was predicted absent. This
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suppresses ”phantom positives” while retaining the regression performance on samples where
the analyte is present. Negative concentration predictions were clipped to zero prior to eval-
uation to enforce physical plausibility, which can yield exact 100% relative errors, when
non-zero ground-truth samples are predicted as zero.
Predictive accuracy was assessed using complementary metrics. The coefficient of de-
termination (R 2) quantified variance explained, while root mean square error (RMSE) em-
phasized large residuals, which are particularly important in biosensing applications where
outliers can represent sensor artifacts. Mean absolute error (MAE) provided a more inter-
pretable measure of average prediction error across analytes. Training and validation scores
were retained to assess potential overfitting, and predicted-versus-true plots were used to vi-
sualize systematic deviations. Residual distributions were additionally inspected to identify
potential systematic biases across concentration ranges.
SHAP feature importance was computed using KernelExplainer with 100 explanation
samples and 100 background samples per fold (randomly sampled from a pool of 200 samples
in the training set). SHAP values were computed for the representative split (seed = 42) and
averaged across the five cross-validation folds. To assess stability, we verified that feature
rankings remain stable across different background sample sizes ( Fig. S2).
Results
and Discussion
Sensor Array
Wearable sensor arrays require skin conformability, low-cost production, simple fabrication,
and high-throughput capability. These requirements are addressed in our fabrication proce-
dure. The sensor design is depicted in Fig. 1b and consists of a stretchable SEBS substrate,
conductive stretchable silver interconnects, orthogonal carbon-based electrodes, an SEBS en-
capsulation layer, and a flat cable connector. The sensing electrodes are fabricated by spray-
coating electrode inks comprising carbon flowers with either PVDF or P4VP (Fig. 1c). This
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simple and robust fabrication technique is well-suited for sensor arrays and can be readily
adapted and scaled up to incorporate additional polymer modifications.
A photograph of the as-prepared PVDF-carbon flower (PVDF-CF) sensing electrodes
before encapsulation and flat cable connection is shown in Fig. 1d . The SEBS substrate
is flexible and skin-conformable, 28 ideal for wearable applications. A representative SEM
image of the sensing electrode is shown in Fig. 1e , with a magnified view in Fig. 1f.
The carbon flowers have a diameter of approximately 1 µm (Fig. 1g) and are connected by
polymer binder. Carbon flowers are used due to their beneficial properties in electrochemical
sensing, which have been attributed to their unique morphology, defect-rich structure, and
high conductivity. 28 Importantly, while the polymer binder does not cover all carbon flowers
homogeneously, we have previously demonstrated that the polymer effect on electrochemical
performance is retained. 27
The data collection and ML workflow are shown in Fig. 1h. A comprehensive dataset of
450 samples was collected, comprising single-analyte, 2-, 3-, and 4-analyte mixtures. Data
preprocessing included blank subtraction, filtering, and derivative transformation (Fig. S1).
ML algorithms, including Ridge regression, multilayer perceptron (MLP), random forest
(RF), XGBoost (XGB), support vector regression (SVR), and k-nearest neighbors (KNN),
were trained on the preprocessed data, and the best-performing algorithm was used to predict
analyte concentrations. Overall, this modular platform architecture combined with widely
available ML methods enables straightforward integration of additional electrode types to
diversify the feature set, thereby facilitating distinction of a broader range of molecules in
complex mixtures.
Electrode-specific Electrochemical Detection
Representative voltammograms illustrating the effect of the polymer modifications are shown
in Fig. 2 (raw data Fig. S3 ). To emphasize the oxidation potential shift, we show the
normalized voltammograms for each biomarker in Fig. 2a. Each polymer–biomarker pair
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exhibits a characteristic oxidation potential, reflecting the polymer-dependent interaction.
For example, E2 shows a clear oxidation peak at 0.50 V on PVDF-CF. In contrast, P4VP-
CF electrodes detect estradiol at 0.64 V. When testing different concentrations, the peak
current varies while the oxidation potential remains unchanged. This significant 140 mV
shift in oxidation potential is characteristic of the polymer coating and crucial for achieving
selective detection. This likely relates to altered diffusion and adsorption characteristics. 27
Similar trends are observed for 5-HT and Mel: oxidation peaks appear at lower potentials
with PVDF-CF, while P4VP-CF shifts them to higher values. Notably, 5-HT exhibits two
oxidation peaks, which may originate from first oxidation to the carbocation, followed by
oxidation to quinone imine, as previously reported. 14 Interestingly, AA exhibits reversed
behavior: P4VP-CF shifts the peak to lower potentials, while PVDF-CF shifts it to higher
values. Note that while all measurements were conducted in PBS, the behaviors for estradiol
detection in artificial saliva and under varying salt levels appear similar as reported in our
previous work. 28
These polymer-induced potential shifts form the basis for quantitative electrochemical
analysis and enable ML models to distinguish and deconvolute overlapping signals in mix-
tures. The relative separation of analyte peak positions differs markedly between the two
polymers, as summarized in Fig. 2b . On PVDF-CF, AA and 5-HT peaks appear closer
together, while E2 and Mel are well separated. Conversely, P4VP-CF provides clear separa-
tion between AA and 5-HT, while E2 and Mel peaks overlap. This complementary behavior
highlights the orthogonal selectivity achieved through polymer modification.
The importance of these findings becomes more evident in analyte mixture measurements.
In 2-analyte mixtures, PVDF-CFs resolve E2 and Mel as two separate peaks, consistent with
single-analyte measurements (Fig. 2c, raw data Fig. S3e). Similarly, P4VP-CFs separate
AA and 5-HT signals. However, in 4-analyte mixtures, PVDF-CFs cannot distinguish AA
and 5-HT, while P4VP-modified electrodes show overlapping signals for E2 and Mel (Fig. 2d,
raw data Fig. S3f ). While basic regression approaches may suffice for the examples shown
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Figure 2: — Selective Detection Principle. (a) Normalized SWV data of PVDF-CF
and P4VP-CF for E2, AA, 5-HT, and Mel as single analytes (three different concentrations
for E2). (b) Oxidation peak potentials, showing better distinction of E2 (green) and Mel
(purple) with PVDF-CF, while P4VP-CF provides better separation of AA (red) and 5-HT
(yellow). Error bars represent three separately fabricated sensors. (c) Pairwise and (d)
four-analyte mixture voltammograms.
in Fig. 2, deconvolution becomes increasingly challenging when analytes are present at vastly
different concentration levels, as commonly occurs in physiological samples (e.g., when vita-
min C is supplemented). This motivates the use of ML models, which can learn and exploit
polymer-dependent peak shifts and signal shapes to enable robust multiplexed biomarker
detection.
Performance and Model Comparison
Fig. 3 summarizes the predictive performance of the proposed ML framework across analytes,
error metrics, and model architectures using the derivative preprocessing on the combined
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data set. Fig. 3a–d show predicted versus experimentally measured concentrations obtained
using the best-performing MLP model on a representative train-test split (linear axis shown
in Fig. S4a–d). To reduce false non-zero predictions, classifier-gated masking was applied in
zero-analyte cases (Fig. S4e). This masking resulted in a modest performance improvement
(i.e., test R2 increased from 0.969 to 0.972 for Mel) and was therefore applied only for the
analysis shown in Fig. 3. For all four analytes, predictions closely follow the identity line,
yielding coefficients of determination ( R2) exceeding 0.91. The slightly lower R2 observed
for AA likely reflects the reduced sensitivity of the sensor towards this biomarker. For this
representative split, the model achieves an overall R2 of 0.947 averaged across biomarkers. A
comprehensive multi-seed comparison across all six regression models and analytes, reporting
mean ± standard deviation across five random seeds, is provided inTable S4and a summary
is shown in Table 1. RF and XGB showed larger train–validation R2 gaps (i.e., higher
training R2 with reduced validation/test R2), consistent with overfitting, whereas the MLP
exhibited a smaller generalization gap while achieving the best overall test metrics.
Table 1: Overall model performance. Test metrics averaged across all four analytes and
five random seeds using derivative preprocessing on the combined dataset. Best split: MLP
seed 42 with classifier-gated masking.
Model R2 MAE (nM) RMSE (nM)
Ridge 0.611 1020 1441
RF 0.828 492 799
KNN 0.828 453 769
XGBoost 0.848 475 751
SVR 0.892 414 696
MLP 0.908 409 644
MLP (best split) 0.947 312 542
Robust prediction accuracy is maintained down to tens to hundreds of nanomolar for
estradiol and serotonin (Fig. S4f-h), demonstrating stable performance across a wide dy-
namic range. While further sensitivity gains would be advantageous for non-invasive mea-
surements in sweat and saliva (sometimes required sensitivity is in the pM range), the current
Results
already indicate strong predictive capability. Importantly, these data were acquired
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Figure 3: — Key ML Performance. Predicted versus true concentrations (log-log) andR2
values for a representative MLP model (seed = 42) for (a) E2, (b) Mel, (c) 5-HT, and (d)
AA. For this representative split, a zero-aware two-stage architecture (classifier→ regressor)
was used and regression outputs were masked to zero when the classifier predicted analyte
absence, to suppress false non-zero predictions. (e) Relative MAE bands (0-10% and 10-
20%) for E2 predictions. (f) Distribution of relative prediction errors across analytes. (g)
Learning curve of the MLP model showing training and validationR2 as a function of training
set size. (h) Comparison of this work with previously reported electrochemical ML sensing
studies; note that reported R2 metrics may refer to calibration, cross-validation, or held-out
test sets depending on the study (see Table S5)
using multiple sensors operated over days to weeks without calibration: As shown inFig. S5,
noticeable inter-sensor variations are observed in absolute peak currents, likely arising from
differing electrochemical surface areas. In contrast, oxidation potentials show only minimal
variation (i.e., 0.532 ± 0.026 V for PVDF-CF and 0.679 ± 0.002 V for P4VP-CF), high-
lighting that the polymer-induced shift is highly reproducible. Over an operation period of
37 days, we observe a reduced E2 peak current (from 2.45 to 0.84 nA) and an increase in
oxidation potential (i.e., from 0.52 to 0.60 V ( Fig. S6). The near-perfect overlap between
electrodes on the same substrate from the same fabrication batch (Fig. S7) supports the use
of a single electrode per sensor substrate for ML training. The capability of the ML model
to accurately predict analyte concentrations despite inter-sensor variabilities and temporal
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drift further underscores the robustness of both the sensor platform and the ML framework.
This is further supported by a noise robustness analysis showing that the model maintains
R2 > 0.79 for all analytes up to 2% additional noise when SG smoothing is applied (Fig. S8).
In addition to R2, prediction accuracy was evaluated using the mean absolute error
(MAE), shown exemplarily for E2 in Fig. 3e for the 0–10% and 10–20% error bands. MAE
provides a complementary, scale-aware measure of absolute prediction error and enables in-
tuitive interpretation of quantitative accuracy. Approximately 30% of predictions fall within
the 0–10% band, with an additional 30% within the 10–20% range. The larger errors are
likely attributed to the complexity of the system (i.e., testing analytes with similar oxida-
tion potentials and varying concentration ranges), as well as the inter-sensor variability and
stability over time. The combination of these factors reduces the accuracy of our sensor but
represents a more realistic protocol. The relative error distributions across all biomarkers are
summarized in Fig. 3f, with corresponding MAE values and standard deviations reported
in Fig. S4i,j . For this representative split, relative errors exceeding 100% were observed
only for E2 (4/71 non-zero samples). For AA, 5-HT, and Mel, the maximum relative error
reached exactly 100%, arising from cases where negative regression outputs were clipped
to zero. Although individual prediction errors can reach several tens of percent, the mod-
els consistently preserve concentration-dependent trends across all biomarkers. This is an
outcome that is hardly achievable using conventional peak-based or univariate analysis for
datasets and biomarkers with such strongly overlapping voltammetric signals. Importantly,
physiological variations in these biomarkers frequently span one to two orders of magnitude
(e.g., day–night melatonin levels vary by up to 100×), indicating that the achieved accuracy
is sufficient to resolve biologically meaningful changes.
Comparing our work to the state of the art is inherently challenging, as previous studies
have applied ML to electrochemical sensors under highly variable conditions, including dif-
ferences in number of biomarkers, sample size, sensor type, and measurement environment.
To enable a meaningful comparison, we focus on four key parameters: sample size, number of
16
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biomarkers, R2, and targeted concentration range (Fig. 3h, details in Table S5). Our work
stands out by introducing a dataset that is both substantially larger (450 samples, nearly
an order of magnitude greater than most prior ML studies) and more diverse, encompassing
a wide concentration range (down to nM) and complex mixtures (up to four biomarkers),
while achieving comparable R2 values. This was accomplished despite deliberately selecting
biomarkers that oxidize within a narrow potential window (0.2–0.8 V), which increases the
challenge of signal deconvolution. It is important to note, however, that some prior studies
were conducted in real human fluids, which introduce additional complexity not addressed
in our current work.
Overall, we attribute the strong performance of our system to the use of polymer-diverse
electrode modifications, which enhance peak separation and enable more effective signal de-
convolution, as shown in Fig. 2. Moreover, rigorous validation, including cross-validation
and evaluation across five random seeds, ensures a robust assessment of model generaliz-
ability. Learning curve analysis (Fig. 3g ) indicates that the MLP model’s test R2 has not
yet plateaued with respect to dataset size, suggesting that additional training data could
further improve predictive accuracy. Potential systematic prediction bias was further as-
sessed using residuals as a function of true concentration for melatonin as a representative
example (Fig. S4l). In summary, our work combines polymer-modified sensors with a large,
mixture-rich dataset and multi-seed validation, enabling a robust evaluation of multiplexed
electrochemical ML performance and providing a foundation for studies in more complex,
physiologically relevant fluids.
Effect of Polymer: Feature Analysis
To explore the importance of polymer modification, we trained the optimized models sepa-
rately on PVDF-CF and P4VP-CF datasets and compared their performance ( Fig. 4 and
Table S6). All models were tuned using identical hyperparameter search spaces and eval-
uated without applying a classification mask, ensuring a fair and consistent comparison.
17
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Note that the goal of Fig. 4 is to illustrate polymer effects rather than focusing on absolute
performance, as evaluating polymers separately halves the dataset, and data splits reduce
absolute R2.
Figure 4: — Feature Importance and Interpretability. (a) R2 values for derivative
preprocessing for the MLP model only and (b) averaged across all six models (R2 > 0.6). (c)
Heatmap of ∆R2 (R2
P V DF −R2
P 4V P ) across all preprocessing transformations (R2 > 0.6). Red
shades indicate better performance for PVDF, while blue shades indicate better performance
for P4VP (d) Top 5 SHAP values of all analytes for the PVDF-CF and (e) P4VP-CF data
using derivative transformed signals. (f) Top 5 SHAP values mapped onto the average
derivative signal of PVDF-CF and (g) P4VP-CF data using the MLP model.
The polymer-specific R2 values obtained using the MLP model are shown in Fig. 4a.
PVDF-CF outperforms P4VP-CF for predicting E2 and Mel, whereas P4VP yields superior
performance for AA and 5-HT, in excellent agreement with the electrochemical observations
in Fig. 2. This polymer-dependent selectivity persists across all ML models ( Fig. 4b). The
heatmap (Fig. 4c ) summarizes the performance difference (∆R 2 = R2
P V DF − R2
P 4V P ) and
reveals the same consistent trend: PVDF-CF is advantageous for the detection of E2 and
Mel (red), while P4VP-CF outperforms PVDF-CF for AA and 5-HT (blue), with only a
few exceptions. Importantly, Table S6 reports the complete set of R2 values without ap-
18
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plying any threshold, ensuring full transparency of model performance. Additionally, the
heatmap represents data averaged across the three preprocessing steps, including derivative
(used in Figs. 3 and 4), min-centering, and polynomial. Min-centering and polynomial per-
form slightly inferiorly to the derivative method, which is why the derivative was chosen
throughout most of our study; however, as shown in the heatmap and supporting table,
the polymer-dependent selectivity trends hold true across all the preprocessing methods,
demonstrating that the preprocessing does not alter the underlying electrochemical informa-
tion. Note that in Fig. 4a-c, only polymer–biomarker combinations exceeding a threshold of
R2 > 0.6 are displayed to emphasize robust and practically relevant predictions. Overall, our
Results
highlight that polymer modification is a key factor in enhancing sensor performance,
with the close agreement between electrochemical observations and ML results confirming
that polymer-induced peak separation directly improves predictive accuracy.
To further investigate polymer-specific selectivity, we applied SHAP to the MLP model to
assess the feature importance of each polymer dataset. SHAP quantifies the contribution of
individual features, 33 in our case current–potential points, enabling direct mapping between
learned model features and regions of the electrochemical signal. Fig. 4d,e show the top
five voltage features ranked by mean absolute SHAP value for all analytes using the P4VP-
CF and PVDF-CF datasets with derivative-transformed traces (additional SHAP values in
Fig. S9 ). The MLP model relies on distinct voltage regions for different analytes, and
changing the polymer coating shifts which regions are deemed informative; specifically, E2
and Mel shift to higher potentials on P4VP-CF and can only be distinguished on PVDF-
CF, whereas AA and 5-HT shift to lower and higher potentials, respectively, on P4VP-CF,
enabling their distinction, again consistent with Fig. 2.
Mapping the most influential features onto average signal traces (Fig. 4f,g ) shows that
key ML features correspond to extrema, zero crossings, and high-slope regions, i.e., regions
of analyte oxidation. Although these results are based on derivative-transformed data and
absolute potentials may appear shifted relative to Fig. 2, the same trends hold for polynomial-
19
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transformed signals (Fig. S10), confirming that the model relies on distinct potential regions
for different analytes depending on the polymer coating.
Overall, the feature analysis and SHAP results underscore the critical role of polymer
modifications in multiplexed sensing, confirming that orthogonal sensor arrays are essential
for effective ML deconvolution of overlapping voltammetric signals; something a single sensor
type cannot achieve. Crucially, our findings provide a mechanistic explanation for how
polymer-induced selectivity enhances multiplexed sensing, rather than applying ML as a
black box—a significant advance, as many studies do not clarify why their models succeed.34
This work demonstrates how interpretability tools can connect electrochemical intuition
with data-driven ML models. It also highlights the potential of a two-electrode array for
four analytes and provides a roadmap for scaling to more complex datasets by incorporating
additional polymer coatings that induce distinct peak shifts.
Limitations
and Outlook: This study demonstrates that a two-electrode sensor array
can effectively distinguish four analytes. However, several limitations must be addressed
for translation to wearable applications. Estradiol and melatonin sensitivity needs to be
enhanced to match physiological levels. Other molecules such as dopamine, epinephrine,
norepinephrine, and most critically uric acid, feature oxidation potentials that overlap with
the current molecules (Fig. S11). Further evaluation under varying conditions (e.g., ionic
strength, pH, artificial and real saliva) and their impact on the ML model is needed to
improve robustness. Finally, our model is a closed-set regression trained on four analytes,
and cannot detect unknown species in its current form, an inherent property of all closed-set
ML sensor systems. We believe that, despite being demonstrated in a simplified system,
the current work provides a viable strategy to address stringent selectivity limitations of
electrochemical sensors and can enhance the robustness and selectivity of next-generation
electrochemical sensors.
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Conclusion
This study presents an electrochemical sensor array capable of selectively detecting 5-HT,
AA, E2, and Mel in mixture conditions. The array consists of carbon flower electrodes
modified with PVDF or P4VP polymers and deposited onto stretchable substrates via a
scalable process, making it well-suited for skin-based applications and readily adaptable to
larger arrays. Polymer modifications shift analyte oxidation potentials, producing distinct,
resolvable electrochemical signatures and generating high-quality datasets optimized for ML
analysis. We evaluated 450 square wave voltammograms from single- and multi-analyte mix-
tures at clinically relevant concentrations. ML-based signal processing achieved an overall
R2 of 0.947, with most MAE values within the 30% error band, sufficient to resolve biologi-
cally meaningful changes. Among six tested ML algorithms, the MLP model performed best,
likely due to its ability to capture complex non-linear relationships in overlapping voltam-
metric signatures, outperforming linear models. Feature importance analysis revealed that
PVDF-CFs are critical for distinguishing E2 and Mel, whereas P4VP-CFs enable discrim-
ination between AA and 5-HT. SHAP analysis further confirmed that the models rely on
oxidation-relevant regions, validating the mechanistic role of polymer-induced selectivity. In
summary, this work demonstrates that polymer-modified carbon electrodes combined with
interpretable ML can robustly discriminate and quantify multiple non-invasive biomarkers
in complex mixtures. The approach offers a clear pathway for expansion to larger electrode
arrays and broader analyte panels.
Supporting Information
Preprocessing and features; SHAP sensitivity analysis; raw voltammograms; prediction accu-
racy and error analysis; inter-sensor variability; temporal drift; linearity and inter-electrode
variability; noise robustness analysis with Savitzky–Golay filtering; SHAP density plot;
SHAP feature importance; dataset; ML parameters; concentration ranges; model-dependent
21
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performance; literature comparison; preprocessing/polymer-dependent performance
Acknowledgments
This project was supported by the Stanford Wearable Electronics Initiative (eWEAR) seed
grant, the Tianqiao and Chrissy Chen Ideation and Prototyping Lab, the Swiss National Sci-
ence Foundation (SNSF, I.C.W.: P500PT-214498), and the Turing Grant Scheme (A.L.M.D.).
Part of this work was performed at the Stanford Nano Shared Facilities (SNSF), supported
by the National Science Foundation under award ECCS-2026822. Z.B. is a Chan Zuckerberg
Biohub San Francisco investigator and an Arc Institute innovation investigator. We thank
L. Mondonico, A. Mahmud, K-J Hsu, and K. Parkatzidis for their scientific advice.
Data and Code Availability
All electrochemical raw data, processed datasets, and analysis notebooks used in this study
are available at the following: https://github.com/esemsc-ald24/ML-Biomarker-Sensing.gitGitHub
repository.35 Further data are available from the corresponding author upon reasonable re-
quest.
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