# Rapid viral detection in milk using near infrared spectroscopy combined with Swiss knife partial least squares (SKPLS) 3-way multiblock

Samy de Oliveira, Stéphane Guyot, Laurence Dujourdy, Emmanuel Denimal, Laurent Gal, Caera O'Neill, Philippe Cayot, Alexis de Rougemont, Elias Bou-Maroun

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Samy de Oliveira, Stéphane Guyot, Laurence Dujourdy, Emmanuel Denimal, Laurent Gal, et al.. Rapid viral detection in milk using near infrared spectroscopy combined with Swiss knife partial least squares (SKPLS) 3-way multiblock. Food Chemistry: X, 2026, 499, pp.147336. 10.1016/j.foodchem.2025.147336. hal-05394400

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# Rapid viral detection in milk using near infrared spectroscopy combined with Swiss knife partial least squares (SKPLS) 3-way multiblock

Samy De Oliveira<sup>a</sup>, Stéphane Guyot<sup>a, *, 1</sup>, Laurence Dujourdy<sup>b, c</sup>, Emmanuel Denimal<sup>b</sup>, Laurent Gal<sup>d</sup>, Caera O'Neill<sup>a</sup>, Philippe Cayot<sup>a</sup>, Alexis de Rougemont<sup>a, e</sup>, Elias Bou-Maroun<sup>a, 2, *</sup>

## ARTICLE INFO

Keywords:

Viral detection
NIRS
Milk
Food safety
Rapid detection
Chemometrics
Neural network

## ABSTRACT

Human norovirus is the leading cause of foodborne illnesses, necessitating rapid, reliable, and cost-effective quantification methods. Near InfraRed Spectroscopy (NIRS) offers real-time analysis with minimal sample preparation. Two independent experiments, conducted 8 months apart in quadruplicate, produced 360 semiskimmed milk measurement spiked with nine MS2 bacteriophage concentrations, a surrogate of human norovirus. Virus concentrations were modeled by 3-way partial least squares (PLS) regression correlating NIRS spectra with plaque-forming unit (PFU) measurements. A group-aware 5-fold cross-validation was applied to 72 sample groups using spectral pretreatments. The best performance was achieved with the extended multiplicative scatter correction (EMSC) and first derivative, yielding an R<fnref n="2" /> of 0.77 and 0.80 for validation. The limit of quantification (LOQ) was estimated at 4.9 × 10³ PFU/mL, close to literature values for virus quantification in complex matrices. These results highlight the feasibility of NIRS as a rapid, non-destructive, and reagent-free approach for viral quantification in food systems.

## 1. Introduction

Food safety is a major global concern, with 1 in 10 people affected by foodborne illnesses annually and 420,000 deaths worldwide (World Health Organization, 2022). Various microorganisms cause these illnesses, including bacteria, viruses, fungi, and prions. Among them, noroviruses (NoVs) from the Caliciviridae family are highly contagious and lead most nonbacterial gastroenteritis outbreaks in humans. Transmission occurs via the fecal-oral route through direct contact, aerosols from vomiting, or contaminated food and water (de Graaf et al., 2016). NoVs are the primary cause of water- and foodborne outbreaks in Europe (Authority, E. F. S, and European Centre for Disease Prevention and Control, 2022; Anses, 2022), partly due to their resistance to thermal and non-thermal antiviral treatments. They account for 60 % of foodborne diseases in the U.S. and Europe, causing nearly 5 million cases annually (Zhu et al., 2020). While NoV contamination often stems

from water, milk spoilage is rare and mainly bacterial (Campylobacter spp., Salmonella spp., Brucella spp., *Escherichia coli*) or associated with other viruses like Coxsackie, tick-borne encephalitis, and hepatitis viruses (Dhanashekar et al., 2012). Norovirus presence in raw milk, possibly linked to *E. coli* contamination as a coliphage, indicates poor hygiene practices and deficient sanitation (Yavarmanesh et al., 2015). Milk serves as a model matrix for studying virus survival due to its complex composition: protein suspension (casein micelles ~200 nm), pseudo-solution (whey proteins), solution (lactose, minerals), and oil-in-water emulsion (fat globules ~3–7 µm in raw milk, ~0.1 µm in homogenized milk) (Horm & D'Souza, 2011).

Monitoring and reporting NoV cases are essential to prevent outbreaks. Detection relies mainly on reverse transcription polymerase chain reaction (RT-PCR) for amplifying the NoV genome in stools, food, or water samples, while antigen screening using immunochromatographic assays is limited to fecal samples (Berthulom, 2022; de Graaf

<footnote><sup>a</sup> UMR PAM, Institut Agro, Université Bourgogne Europe, INRAE, F-21000 Dijon, France</footnote>

<footnote><sup>b</sup> Institut Agro Dijon, Direction Scientifique, Cellule d'Appui à la Recherche en Sciences des Données, F-21000 Dijon, France</footnote>

<footnote><sup>c</sup> Laboratoire d'Informatique de Bourgogne (LIB), Data Science, Université Bourgogne Europe, F-21000 Dijon, France</footnote>

<footnote><sup>d</sup> UMR Agroécologie, INRAE, Institut Agro, Université Bourgogne Europe, F-21000 Dijon, France</footnote>

<footnote><sup>e</sup> National Reference Centre for Viral Gastroenteritis, Laboratory of Virology, University Hospital of Dijon, F-21000 Dijon, France</footnote>

<footnote>* Corresponding authors.</footnote>

<footnote>E-mail addresses: stephane.guyot@institut-agro.fr (S. Guyot), elias.bou-maroun@institut-agro.fr (E. Bou-Maroun).</footnote>

<footnote n="1">¹ 0000–0002-2316-234×.</footnote>

<footnote n="2">² 0000–0003-0208-858×.</footnote>
et al., 2016; Kaplon et al., 2020; Norovirus Laboratory Diagnosis, 2023). Standard molecular methods, though specific and sensitive, are slow, requiring hours, trained personnel, and limited to diagnosing disease or monitoring food and water. Rapid NoV detection in food could significantly aid infection prevention.

Advanced detection methods also exist but have limitations. Next-Generation Sequencing (NGS), which sequences millions of genome fragments in parallel, is reliable but costly, mainly used for environmental metagenomics rather than specific food virus detection (Cantalupo & Pipas, 2019). Immunoassays are employed for diagnostics but face challenges in food matrices, where components like bacteria can interfere with specific antibody binding. NGS and immunoassays are often combined with RT-PCR to enhance reliability.

Innovative techniques like biosensors are also beginning to emerge. They are based on a device that integrates a biological or a biomimetic sensitive material coupled with a transduction element to generate a measurable signal. Depending on the type of bioreceptors (molecularly imprinted polymers (MIPs), nanoparticles, aptamers...), and transducers (electrochemical, optical, piezoelectric, thermal...), virus detection can also be performed without any extraction process (Naresh & Lee, 2021). However, it is still evolving and very few experiments have been conducted on food matrices. The droplet-based digital PCR is also an interesting technique that increases both the specificity and selectivity of traditional PCR methods thanks to the controlled generation of sub microliter droplets before DNA/RNA amplification. Despite this, the initial cost of instruments and the unavailability of microfluidic technology reagents in underdeveloped countries is a serious drawback for now (Kojabad et al., 2021).

Near-Infrared Spectroscopy (NIRS; 780-2500 nm) is a vibrational spectroscopic technique based on the absorption of electromagnetic radiation by overtone and combination bands of fundamental vibrations, mainly involving C—H, O—H, and N—H bonds (Banwell, 1994). In this spectral region, water exhibits strong and well-defined absorption features, which can dominate the spectral response of aqueous and semi-solid food matrices. Nevertheless, NIRS remains highly effective for such systems because it captures subtle variations arising from both chemical composition and physical structure (Rinnan & Engelsen, 2009). When coupled with chemometric tools, NIRS enables rapid, non-destructive, and reagent-free characterization of complex samples, and has been widely used to assess food composition. Although its use for detecting microbial contamination remains more limited, several studies have demonstrated its potential to indirectly monitor microbial activity or spoilage through associated spectral changes (Alexandrakis et al., 2008; Jr & Mark, 2020). Compared with Fourier Transform Infrared (FTIR; 2.5-15 µm) spectroscopy, NIRS provides deeper light penetration and broader screening capacity for heterogeneous materials, making it particularly relevant for food analysis.

Beyond compositional analysis, NIRS has also shown potential for virus detection in diverse biological and environmental samples. Fernandes et al., 2018 demonstrated the rapid, non-invasive identification of Zika virus infection in *Aedes aegypti* mosquitoes with accuracies above 95 %. Other studies have achieved comparable results for several arboviruses and respiratory viruses when combined with chemometric or deep-learning models. In plant systems, NIRS has detected virus-induced spectral variations (Jinendra et al., 2010; Lee et al., 2016). These findings highlight the ability of NIRS to capture direct viral signatures or associated biochemical changes. Owing to its speed, low cost, and reagent-free nature, NIRS represents a promising alternative to molecular assays for rapid viral screening in complex food matrices.

Direct investigation of NoVs is challenging due to their virulence, the absence of efficient continuous cell culture systems, and the need for biosafety level 2-3 containment (de Graaf et al., 2016). Using a surrogate virus circumvents safety concerns, provided the surrogate closely resembles NoVs. MS2, an F-specific RNA phage (FRNAPH), is a suitable surrogate, having been evaluated for fresh produce (Dawson et al., 2005). MS2 is widely used to study viral replication, translation,

infection, and assembly due to its simple composition, ease of growth, purification, and human safety.

This study explored the use of NIRS combined with chemometrics as a cost-effective, repeatable method for rapid MS2 phage detection, with the objective of assessing its feasibility for direct viral quantification in a complex food matrix. Semi-skimmed milk was chosen to assess NIRS's ability to detect viruses in a realistic liquid medium representative of food systems. Two independent experiments, conducted 8 months apart in quadruplicate, produced 88 milk samples spiked with varying MS2 concentrations. Multivariate analysis was applied to interpret the complex NIRS spectra. Predictive models were developed to compare NIRS-estimated viral concentrations with those obtained by the reference method. The process involved evaluating signal pretreatments and constructing a partial least squares regression model. Additionally, a neural network was designed to create a predictive model for viral quantification and determine the achievable detection limit.

## 2. Methods

### 2.1. Experimental methodology

The whole experimental methodology, from virus production/ quantification to the establishment of multivariate models, was performed twice by two different experimenters in the same laboratory 8 months apart. The first will now be referenced as “E1”, and the second “E2”. “Pooled” data indicates E1 and E2 data pooled together. An abstract of a single experiment is shown in Fig. 1. The experimental methodology has been described in detail in the following paragraphs.

### 2.2. MS2 production

Escherichia coli K-12 Hfr and its host bacteriophage MS2 were kindly provided by the Virology Department of CHU Dijon (France). The MS2 phage was propagated by infecting *E. coli* K-12 Hfr in tryptic soy yeast extract (TSY) medium (10 g/L tryptone, 1 g/L yeast extract, 8 g/L NaCl) under aerobic shaking at 37 °C until reaching the exponential growth phase, as described in the standard NF EN ISO 10705-1. After 5 h of incubation, the infected culture was purified by chloroform extraction (1:2, v/v) and centrifugation (900 ×g, 10 min) to remove bacterial debris. The aqueous phase containing the viral suspension was then sterilized through a 0.22 µm nylon filter. All procedures were carried out in a class I biosafety cabinet. The detailed protocol is described in the Supplementary Material.

### 2.3. MS2 quantification

Another *E. coli* preculture was required for viral quantification. 7 mL of TSY was inoculated overnight with 1–2 colonies of *E. coli* at 37 °C under aerobic shaking. 5 mL of this preculture was subsequently regenerated for one and a half hours at 37 °C until reaching an Optical Density (OD) of 0.6–0.7. Before the end of incubation, semi-solid TSY was supercooled at 70 °C. Serial dilutions were also prepared with this culture in liquid TSY, reaching a factor $10^{10}$, the idea being to titer between 30 and 300 units. Upon reaching the correct OD, 1 mL of a dilution, 2.5 mL of semi-solid TSY and 1 mL of *E. coli* were mixed, then poured into a Petri dish containing solid TSY. This process was repeated for each selected dilution (for instance $10^{-8}$, $10^{-9}$ et $10^{-10}$). Once the medium was dry, Petri dishes were incubated overnight at 37 °C. PFU counts were finally determined the next day, and the final concentration were deduced from the chosen dilution between 30 and 300 units.

### 2.4. Reference method (plaque forming unit)

Plaque Forming Units (PFUs) corresponds to a cell-based assays: the method consists in numbering lysed cells infected by the virus (viral plaque). This viral quantification was performed on the selected aliquot
<figure><img src="image_4.png" /><figcaption>Fig. 1. Sample preparation & NIRS chemometrics. The NIRS spectra are provided for illustrative purposes only and do not correspond to experimental data.</figcaption></figure>

for confirmation using the standard NF EN ISO 10705-1.

This reference method determined both E1 and E2 viral titration: $5.63 \times 10^{10}$ PFU/mL and $4.20 \times 10^{10}$ PFU/mL respectively.

## 2.5. NIRS sample preparation

Semi-skimmed Ultra Heat Treated (UHT) milk (Lactel, Mayenne, France) was chosen to perform measurements with the MS2 virus. Commercial milk is a great blend which is standardized in protein and fat content, homogenized to stabilized dispersed fat globules. It can be considered a constant study material to ensure repeatability.

To remove the TSY medium, a dialysis was performed following the approach described by Dika et al. (2013). Dialysis offers a safe medium removal at the cost of time compared to ultracentrifugation. The dialysis membrane used had a cutoff of 100 kDa. Approximately 50 mL of the previously produced MS2 virus was poured inside each membrane and the whole content was dialyzed for three full days in a beaker containing 5 L of distilled water (water was replaced each day at 4 °C). Then the membrane content was filtered with 0.22 µm nylon filter (Dutscher), and several aliquots were obtained this way. One of these aliquots was selected to perform NIRS measurement, and it corresponds to the MS2 samples in distilled water (dialyzed MS2).

To carry out these measurements in milk, some of the previously selected MS2 aliquot was diluted in milk: 10 µL of MS2 aliquot for 990 µL of semi-skimmed milk (MS2 in milk). PFU quantification was done on the aliquot to determine its concentration.

Four serial dilutions of dialyzed MS2 (batches noted A, B, C and D from the same aliquot) were done from $10^{-1}$ to $10^{-10}$ in semi-skimmed milk in tests tube for a final volume of 1 mL. However, the dialyzed MS2 is contained in a volume of water. To carry out the serial dilutions of MS2 in milk, and to keep the same proportion of distilled water and milk, each dilution was done using the previous one in distilled water. Each dilution was stored at 4 °C. Each serial dilution consisted of 9 viral concentrations, ranging from a logQ of 0.6 to 8.5, where Q represents the virus concentration. A total of 36 samples (9 dilutions × 4 batches) were prepared for NIRS measurements and was considered as experiment 1 (E1). After 8 months, the same experiment was repeated by a second experimenter and was considered as experiment 2 (E2). A total of 72 samples were analyzed by NIRS.

## 2.6. NIRS measurement

NIRS measurements were performed with a Metrohm SPELEC NIR instrument (Metrohm DropSens S.L.U., Llanera, Asturias, Spain).

DropView SPELEC was used for the spectra acquisition. A transflection probe (ASD Inc., Malvern Panalytical, Longmont, CO, USA), equipped with a 1 mm optical path tip (Bonsai Advanced Technologies S.L., Alcobendas, Madrid, Spain), was directly immerged for the liquid measurements, making sure to cover the full optical path. The optical parameters were optimized as follows: number of averaged scans: 20; integration time: 1 ms; time of analysis: 1 s and no boxcar average. A light attenuator (from Malvern Panalytical, ref.: A131321) coupled to an SMA adapter was placed between the light source and the probe to avoid signal saturation. The dark and the reference were both set in air. The temperature of each sample was measured with an infrared thermometer Raytech Raynger MX during the experiment. The pH of samples was also measured at the beginning and the end of the experiment. Absorbance was measured between 902 nm and 2120 nm with a resolution of 5 nm. At least 350 µL of sample was required for a good measurement. Finally, for each sample, 5 spectra were collected. The data structure for each experiment is shown in Fig. S1.

## 2.7. Spectra preprocessing and PLS regression

For each NIRS measurement, five raw spectra were acquired for each sample (for a total of 72 × 5 = 360 spectra). One pretreatment or a combination of several pretreatments was applied (using wavelengths between 1107 and 2115 nm to avoid noisy regions): a standard normal variate (SNV) transformation, a multiplicative scattering correction (MSC), a first derivative (SG1), the combination of SNV + MSC, the combination of MSC and SNV (MSC + SNV). SNV and MSC are two widely used normalization techniques in NIR spectroscopy to reduce scattering-related distortions and baseline variations. MSC corrects each spectrum relative to a reference (typically the mean spectrum of the dataset), thereby compensating for additive and multiplicative effects due to optical path or particle size differences. SNV, on the other hand, is applied individually to each spectrum by centering it to zero mean and scaling to unit variance, effectively minimizing intensity-related fluctuations. In this study, both methods were tested independently and in sequence (MSC followed by SNV, and vice versa) to evaluate whether combined normalization could further stabilize spectral variability. All preprocessing methods were done using MATLAB R2024a version of Mathworks.

The Extended Multiplicative Signal Correction (EMSC) is an advanced scatter-correction method that extends the classical MSC by fitting each spectrum to a reference through a polynomial model. It separates additive and multiplicative effects while allowing the inclusion of additional terms (e.g., linear and quadratic trends) to correct for
baseline drifts and curvature. This approach not only normalizes intensity and offset variations but also provides interpretable coefficients ($a_0, a_1, b_1, b_2$) that describe the main sources of spectral variability (Rinnan & Engelsen, 2009). The EMSC was also further used to better understand the spectral variability of our datasets, with the visualization of 4 coefficients:

* $a_0$, an additive offset reflecting baseline shifts.

* $a_1$, a multiplicative scaling factor.

* $b_1$, the first-order polynomial term describing linear slope effects.

* $b_2$, the second-order term reflecting curvature, often linked to light scattering or instrumental drift.

In parallel, Principal Component Analyses (PCA) were also conducted to explore the main sources of spectral variance and to visualize potential inter-experimental differences prior to regression modeling.

A first multivariate regression was performed by a 3-way multiblock PLSR using MATLAB, with a “PLS Swiss Knife” program made by Mishra and Liland (2022). To measure the correlation of a high number of both independent and dependent variables, PLSR is used making it a popular

quantification results (one for each dilution, within a single experiment) referenced later as “measured viral concentration” or “true response”. From the 360 combined spectral samples (E1 + E2), all data were used to develop the model through a group-aware 5-fold cross-validation implemented within the 3-way PLS framework. Technical replicates belonging to the same biological replicate were kept together within the same fold to preserve data hierarchy and prevent leakage between calibration and validation sets. The loadings of the first LV for each pretreatment were also displayed. In this configuration, 72 groups were formed for the entire experiment. As the data were organized in a 3D structure, with biological replicates arranged along the depth dimension, the cross-validation was therefore performed across the 18 dilution levels (9 per experiment per block). Consequently, the cross-validation followed a 2/2/2/2/1 dilution distribution across the five folds, ensuring that all dilution levels were represented while maintaining the experimental balance between E1 and E2. The loadings of the first latent variable (LV) for each preprocessing method were also displayed.

The relative error (%) between measured and predicted viral concentrations by the model was calculated as such:

$$ \text{Relative error} = \sqrt{\left( \frac{\log(\text{predicted viral concentration}) - \log(\text{real viral concentration})}{\log(\text{real viral concentration})} \right)^2} \times 100 \quad (1) $$

method in chemometrics. It is based on the simultaneous modeling of variability in the matrices, X, and the dependent one, Y, by calculating Latent Variables (LVs) that maximize the variance extracted from the two matrices at the same time as their correlation (De Jong, 1990; Wold et al., 2001). The 3-way multiblock data arrangement is displayed in Fig. 2.

Two to twenty LVs were chosen when analysing the two milk data sets. This range was explored to evaluate model performance as a function of LV number (Fig. 5c–f). To select the number of LVs, we used the geometric “knee” (kneedle) criterion on the cross-validated root mean square errors (RMSE) curve as a function of LV. Practically, we normalize RMSE and LV axes, draw the chord between the first and last points, and pick the LV with the largest perpendicular distance to this chord (maximum curvature). This identifies the parsimonious LV where further components provide marginal error reduction, thereby limiting overfitting. When a shallow plateau occurs, we retain the smallest LV within the knee neighborhood to favor model simplicity (Martino et al., 2023). The dependent variable Y was determined from the PFU

This metric was used to assess the precision of the regression models across all dilutions.

The quantification limit threshold was fixed at 25 % to consider the numerous sources of errors that may have happened throughout both E1 and E2.

## 3. Results

The aim of this study was to explore the potential of NIRS for the detection of the MS2 phage in a complex liquid matrix and repeatedly evaluate the limit of quantification (LOQ) of the method coupled with the use of chemometrics and a reference method (PFU method). First, data was collected and preprocessed.

### 3.1. Data collection and preprocessing

For both experiments, the temperature and pH of milk samples were assessed. In E1, the temperature was at 23.1 ± 0.3 °C and the pH of the semi-skimmed milk at 6.8 ± 0.1. In E2, it was 21.5 ± 0.4 °C and 6.9 ± 0.1 respectively.

The raw spectra and the associated preprocessed spectra of E1 and E2 are shown in Fig. 3. Spectra have a water signature, with a large peak between 1350 nm and 1600 nm and convoluted peaks after 1900 nm. Some interferences could be observed at the edges. It is impossible to visually interpret preprocessed spectra as microvariations cannot be perceived in NIRS. However, it can be noted that, except the SG1 and the combination of SNV + MSC, all preprocessed methods contributed to attenuate the spectral differences between E1 and E2.

In addition, trimmed datasets were also considered to investigate the influence of the 1800–2115 nm spectral region, which corresponds to water and fat combination bands. All spectra are presented in Fig. 4, showing no new visual difference compared to Fig. 3.

### 3.2. EMSC visualization & PCA analysis

The EMSC results obtained on the pooled dataset (E1 + E2) are

<figure><img src="image_5.png" /><figcaption>Fig. 2. Data arrangement for 3-way multiblock PLS. Block 1 and 2 contain E1 and E2 data respectively. 212 variables in x-axis correspond to wavelengths, 9 viral dilutions in y-axis and 4 batches in z-axis. NIRS device recorded data in the range of 902 to 2120 nm with a resolution of approximately 5 nm. The initial portion of the spectrum (902–1102 nm) and the final wavelength 2120 nm were excluded for a final selected region of 1107–2115 nm.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Fig. 3. a) Raw spectra of pooled milk data from 1107 nm to 2115 nm. 9 dilutions × 5 extracted spectra × 4 batches × 2 experimenters = 360 spectra. Scan to average: 20. Integration time: 1 ms. Experiment time: 1 s. b) c) d) e) f) & g) Preprocessed spectra of pooled milk data from 1107 to 2115 nm. In order, pretreatments are: Standard normal variate transformation (SNV), multiplicative scatter correction (MSC), first derivative (SG1), EMSC, combination of SNV + MSC and combination of MSC + SNV. All pretreatments were performed on MATLAB.</figcaption></figure>

presented in Fig. 5 with the mean value of each coefficients. The same visualization restricted to E1 is shown in Fig. S2. In the pooled dataset, the coefficients $a_0$ and $a_1$ display opposite mean values between E1 and E2, while $b_1$ and $b_2$ show symmetrical trends of opposite sign. When considering E1 alone, all coefficients are centered around their reference values ($a_0 \approx 0$, $a_1 \approx 1$, $b_1 \approx 0$, $b_2 \approx 0$) with low variability, indicating consistent measurements within this experiment.

All the exploratory PCAs and related loadings of the first and second components are displayed in Fig. S3 and S4. The PCA performed on the raw pooled dataset (Fig. S3a) revealed a clear separation between E1 and E2 along the first principal component (explaining 88.3 % of the total variance), and a much weaker separation along the second component. The two loading plots appeared symmetrical, reflecting the overall shape and trends of the raw spectral data. After applying EMSC preprocessing, the PCA on the pooled dataset still displayed a separation between E1 and E2, but the two experiments were closer to each other along the first component (explaining 89.8 % of the variance), confirming a reduction in inter-experimental variability.

Other PCAs were performed on E1 alone (Fig. S5b). This analysis

showed a compact yet heterogeneous clustering of the different dilutions on the scatter plot, with distinct groupings according to dilution level.

### 3.3. MS2 multivariate regression: 3-way multiblock PLS

Following spectral correction and visualization, Partial Least Squares regression using the Swiss-Knife approach (PLS-SK) was performed to quantify the viral concentration from the preprocessed spectra. A five-fold group-aware cross-validation strategy was implemented to preserve the structure of the dataset and ensure that all technical replicates from a given biological sample were kept within the same fold (see Section 2.7).

The overall performance of the models obtained on the pooled dataset (E1 + E2) is summarized in Table 1, while detailed validation results across the five cross-validation folds are provided in Table S1. In addition, PLS SK Table S2 compiles the main outcomes obtained when models were independently developed on the pooled dataset and on each experiment separately (E1 and E2).

The PLS-SK results obtained on the pooled data are illustrated in
<figure><img src="image_7.png" /><figcaption>Fig. 4. a) Raw spectra of pooled milk data from 1107 nm to 1798 nm. 9 dilutions × 5 extracted spectra × 4 batches × 2 experimenters = 360 spectra. Scan to average: 20. Integration time: 1 ms. Experiment time: 1 s. b) c) d) e) f) & g) Preprocessed spectra of pooled milk data from 1107 to 1798 nm. In order, pretreatments are: Standard normal variate transformation (SNV), multiplicative scatter correction (MSC), first derivative (SG1), EMSC, combination of SNV + MSC and combination of MSC + SNV. All pretreatments were performed on MATLAB.</figcaption></figure>

Fig. 6, showing the relationship between the measured and predicted viral concentrations for the best-performing preprocessing. The corresponding model built on a single experiment (E1) is shown in Fig. S6, allowing direct comparison between intra- and inter-experimental model behaviors.

Among all preprocessing techniques, the SG1 and the EMSC yielded the highest predictive performances. The number of latent variables (LVs) selected for each model was determined using the geometric “knee” criterion (see Section 2.7). Notably, Table 1 shows that models built from untrimmed spectral data (1107–2115 nm) performed slightly better than those using the trimmed range, confirming the relevance of retaining the full NIR region. Across the validation folds (Table S1), the PLS-SK approach showed generally stable performance, although one fold (fold 2) exhibited noticeably lower R² values, sometimes negative and occasionally below −1.

The loadings of the first latent variable (LV1) are displayed in Fig. 6a for the EMSC-preprocessed data and in Fig. S7a for the SG1. The EMSC loadings exhibit meaningful contributions distributed across the entire spectral range, suggesting that information relevant to viral

quantification is not restricted to specific wavelength regions but rather spread throughout the milk spectra. Conversely, the first-derivative loadings closely mirror the general shape of the raw spectral profiles, with alternating positive and negative bands corresponding to the derivative transformation, indicating that this preprocessing mainly enhances local absorptive features already present in the original spectra.

Based on the LOQ criterion defined in section 2.7 and the results obtained in Fig. 6d, the LOQ was established at 4915 viral particles per mL for both the SG1 and EMSC models, which achieved validation R²/ RMSE values of 0.77/1.21 and 0.80/1.12, respectively. The limit of detection (LOD) was empirically estimated at 1.5 × 10³ viral particles per mL, following IUPAC guidelines (LOD ≈ LOQ / 3.3).

## 4. Discussion

The main challenge in this work was to demonstrate that NIRS could serve as a new viral detection method, in a complex liquid food matrix such as milk, and at low concentration (below 100 viral particles per mL). The NIRS experiment started with the optimization of some key
<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Visualization of EMSC coefficients ($a_0$, $a_1$, $b_1$, $b_2$) for pooled E1 and E2 data, including mean values for each parameter. $a_0$ = offset correction, $a_1$ = multiplicative scaling, $b_1$ = linear trend, and $b_2$ = quadratic curvature describing baseline variations.</figcaption></figure>

<caption>**Table 1**</caption>

3-way PLS “Swiss Knife” performances on calibration and validation of the pooled milk data set of E1 and E2 after various pretreatments.

<table><thead><tr><th>Dataset</th><th>LVs</th><th>R<sup>2</sup> cal (mean)</th><th>RMSE cal (mean)</th><th>R<sup>2</sup> val (mean)</th><th>RMSE val (mean)</th></tr></thead><tbody><tr><td>Raw data</td><td>6</td><td>0.99</td><td>0.07</td><td>0.28</td><td>2.54</td></tr><tr><td>SNV</td><td>8</td><td>0.99</td><td>0.11</td><td>0.38</td><td>2.02</td></tr><tr><td>MSC</td><td>8</td><td>0.99</td><td>0.11</td><td>0.38</td><td>2.03</td></tr><tr><td>SG1</td><td>4</td><td>0.96</td><td>0.49</td><td>0.80</td><td>1.12</td></tr><tr><td>SNV + MSC</td><td>8</td><td>0.99</td><td>0.11</td><td>0.38</td><td>2.03</td></tr><tr><td>MSC + SNV</td><td>8</td><td>0.99</td><td>0.11</td><td>0.38</td><td>2.02</td></tr><tr><td>EMSC</td><td>4</td><td>0.96</td><td>0.46</td><td>0.77</td><td>1.21</td></tr><tr><td>Raw data cut</td><td>6</td><td>0.99</td><td>0.08</td><td>- 0.24</td><td>3.45</td></tr><tr><td>SNV cut</td><td>8</td><td>0.99</td><td>0.07</td><td>0.44</td><td>1.97</td></tr><tr><td>MSC cut</td><td>8</td><td>0.99</td><td>0.07</td><td>0.41</td><td>2.00</td></tr><tr><td>SG1 cut</td><td>6</td><td>0.99</td><td>0.19</td><td>0.68</td><td>1.52</td></tr><tr><td>SNV + MSC cut</td><td>16</td><td>0.99</td><td>0.07</td><td>0.41</td><td>2.00</td></tr><tr><td>MSC + SNV cut</td><td>8</td><td>0.99</td><td>0.07</td><td>0.44</td><td>1.97</td></tr><tr><td>EMSC cut</td><td>6</td><td>0.99</td><td>0.14</td><td>0.44</td><td>1.78</td></tr></tbody></table>

LVs refers to the number of latent variables retained for each model, determined by the knee point (Kneedle) method applied to the validation RMSE curve.

Full-spectrum data sets (“Raw”, “SNV”, etc.) include the NIR spectral range of 212 wavelengths (1107–2115 nm).

“Cut” data sets correspond to spectroscopic data trimmed to 145 wavelengths (1107–1798 nm).

parameters. Temperature for instance, was indicated as a source of variability in NIRS measurements (Blanco & Valdés, 2004), and it has been verified prior to the development of any models. Along with the temperature, the following parameters were prone to increase variability if not checked: sample storage duration, bubble presence in the optical path or low scan to average values.

The raw data shown in Fig. 3a exhibit a spectral profile typical of milk, a matrix largely composed of water and characterized by broad absorption bands around 1450 nm and 1950 nm, corresponding to the first overtone and combination bands of O–H vibrations. These water features, together with the overlapping signals of proteins, lipids, and carbohydrates, define the overall shape of the spectra. At this visual level, the signal mainly reflects the physicochemical properties of the milk matrix itself. However, the subtle spectral variations potentially associated with viral presence remain hidden within this complex background and can only be revealed through chemometric modeling and data decomposition rather than direct spectral observation. The

comparison between experiments E1 and E2 nevertheless revealed clear differences in baseline level and intensity, suggesting inter-experimental variability that will be further discussed in the EMSC visualization section.

The raw spectra translated some form of multiplicative effects with a baseline shift. Thus, treatments such as SNV (Fig. 3b), MSC (Fig. 3c) or the SG1 (Fig. 3d), which are particularly suited to correct these alterations, were supposed to have beneficial effects. The SNV allowed visually to mix E1 and E2 spectra, but not MSC and SG1. The latter corrected the baseline as intended. The combinations SNV + MSC and MSC + SNV (Fig. 3f and g) were also evaluated, as sequential preprocessing can occasionally improve spectral consistency in heterogeneous matrices such as milk, where both multiplicative and additive scatter effects coexist (Arianti et al., 2023; Rinnan & Engelsen, 2009). However, as widely discussed in the literature, SNV and MSC address similar variance sources, and their successive application does not necessarily enhance model performance. In our case, the SNV + MSC spectra appeared less homogeneous, whereas the MSC + SNV spectra closely resembled those obtained after SNV alone, confirming that the combined treatments introduced no real added value. Finally, the EMSC preprocessing (Fig. 3e) provided the most refined appearance, further aligning the spectra of E1 and E2 and minimizing residual baseline differences between experiments.

A PCA was first performed on the raw pooled data (E1 + E2), and the corresponding score and loading plots are presented in Fig. S3a and S3b, respectively. This analysis revealed a clear separation between E1 and E2 along the first principal component, which explained most of the variance (88.3 %), while the second component contributed only marginally. The loadings of both components closely followed the overall appearance of the raw spectral profiles. The observed separation justified the use of an Extended Multiplicative Signal Correction (EMSC) to both reduce and better understand the origin of these inter-experimental variations.

After EMSC preprocessing, the resulting PCA (Fig. S4a) showed that the two experiments became closer along the first component, while the corresponding loadings (Fig. S4b) retained the general spectral shape but with reduced amplitude, indicating that some variance sources were efficiently normalized. The full visualization of the four EMSC coefficients is displayed in Fig. 5, showing that $a_0$ and $a_1$ exhibited opposite mean values between E1 and E2, while $b_1$ and $b_2$ presented symmetrical trends of opposite sign. This symmetry between $a_0$ and $a_1$ indicates an inverse relationship between baseline offset and global intensity: spectra
<figure><img src="image_9.png" /><figcaption>**Fig. 6.** a) Loadings of the first latent variable for blocks 1 and 2 (corresponding to the two experiments) during the calibration of the 3-way multiblock PLS "Swiss Knife" model applied to full data (1107–2115 nm) preprocessed by EMSC. b) Coefficient of determination (R²) and root mean square error (RMSE) for the calibration and validation datasets (5-fold cross-validation). R² and RMSE values were determined using the 3-way multiblock PLS "Swiss Knife" on EMSC-preprocessed data. The dashed line indicates the number of selected latent variables using the geometric "knee" (kneedle) method. c) Regression model comparing predicted viral concentrations with reference titration values (PFU) using the 3-way multiblock PLS "Swiss Knife" on pooled milk data preprocessed by EMSC, with four latent variables selected. d) Relative errors of the 3-way multiblock PLS "Swiss Knife" model after prediction, computed using Eq. (1). The quantification limit was set at 25 %. Relative errors are averaged across samples corresponding to the same measured viral concentration.</figcaption></figure>

from one experiment tended to exhibit a higher overall absorbance but a lower baseline, and vice versa in the other. This behavior highlights subtle differences in baseline and curvature related to light scattering and instrumental drift, likely explaining why MSC failed to fully reduce the separation between E1 and E2 for instance.

PLS regressions allow the extraction and quantitative interpretation of this signal. Most PLSR are performed with classic 2D data arrangement, but the use of a complex 3-way PLS becomes relevant to integrate a second experiment performed later in the same conditions, and further study NIRS' repeatability. Many sources of variation can exist between two identical experiments, especially when performed by two experimenters. These variations may alter the regression of a single model considering both results. Multidimensional data arrangement considers these variations. A "PLS Swiss Knife" program was designed for an easier use of such a complex approach (Mishra & Liland, 2022; Sørensen et al., 2021; Zhang et al., 2022).

A brief context about data arrangement is now necessary to better contextualize model performance. Performing a second experiment really allowed further investigations on NIRS repeatability. What motivated this study was a preliminary trial of MS2 in water, using basic preprocessing and PLS, which demonstrated the feasibility of the approach and served as a benchmark for subsequent tests in milk (see for instance Fig. S5, displaying the PCAs of raw data in water and milk). When performing models on the data of a single experiment in water or milk, 2D PLS was able to correlate prediction results with the reference method. When combining both data into a single PLS, the question of data arrangement became a serious concern, especially considering that there were also 4 batches per dilution. Meaning values or splitting data both have their interest when using replicate spectra (Fearn, 2015), but what about two experiments, with a significant time gap and different experimenters. 2D PLS combined model for E1 and E2 performed poorly when compared to very good single data models. Arranging data as displayed in Fig. 2 had a huge impact on the chemometrics.

The prediction was performed using a multiblock Partial Least Squares (PLS) approach, which allows the model to extract latent variables from each block (E1 and E2) successively. This strategy enables the

integration of complementary information from both datasets into a unified predictive model. A model that can be used by multiple laboratories: an all-purpose model.

It is indeed possible to apply the PLS 3-way algorithm to each dataset independently, treating them as single blocks. We have performed this analysis as well, and the results obtained from the single-block PLS models (for E1 and E2 separately) are provided as supplementary material (Fig. S6a + S6b and Table S1). When performing a PLS on a single experiment (E1 or E2), the resulting models are efficient but less robust and not transferable from one laboratory to another. The model established based on the E1 experiment is not able to predict the viral loads in the samples measured during the E2 experiment. For this reason, a 3-way PLS was subsequently performed on the pooled data in order to obtain a single universal model.

The group-aware five-fold cross-validation implemented in the 3-way PLS-SK was designed to preserve the hierarchical structure of the experiment by ensuring that all technical replicates of a given biological sample remained within the same fold. This strategy prevents data leakage and maintains independence between calibration and validation subsets, which is essential for fair model assessment in multi-block or multiway frameworks. However, this structural integrity imposed a fixed 2/2/2/2/1 dilution distribution across folds due to the limited number of available biological replicates and dilutions. This uneven partitioning inevitably reduces the statistical representativity of certain validation subsets, a known challenge in multi-block calibration, where maintaining the internal data hierarchy often conflicts with optimal fold balance (Cattaldo et al., 2024).

The irregular behavior observed in fold 2, with negative or subminus-one R² values, therefore reflects the sensitivity of the validation process to this fold composition rather than a modeling flaw. Similar effects have been discussed in recent work on Sequential Multiblock-PLS, where unbalanced fold structures amplify variance in the validation error despite the underlying model remaining stable (Borràs-Ferrís et al., 2024). In our case, the 3-way PLS-SK approach still provided interpretable results across most folds, demonstrating that it effectively captured the spectral concentration relationships while respecting the
intrinsic organization of the data (samples × wavelengths × biological replicates). Thus, despite the inherent limitations of this constrained k-fold configuration, the validation remains meaningful for evaluating model robustness under realistic experimental constraints.

The interpretation of NIR variability in virus-spiked milk is not straightforward, as several physical phenomena may contribute to the observed signal. Given the small size of MS2 (≈ 27 nm), Rayleigh scattering is likely dominant, leading to wavelength-dependent intensity changes that are particularly visible in the short-wavelength region. The baseline and curvature effects modeled by the EMSC coefficients (a₀–b₂) suggest that light scattering, rather than chemical absorption, accounts for a substantial portion of the variance captured by the first latent variable. Variations in fat-globule dispersion, milk opacity, and refractive index could further modulate the spectral response. Therefore, the PLS models probably rely in part on structural differences induced by viral dilution that alter the optical path or the homogeneity of the medium.

Despite these dominant physical effects, a chemical contribution cannot be excluded. Even at low viral concentrations, MS2 capsid proteins and nucleic acids possess distinctive vibrational signatures (amide,

CH, and phosphate-related overtones) that may weakly influence the near-infrared spectrum through water–macromolecule interactions. The distributed loadings observed with EMSC preprocessing (Fig. 6a) support this interpretation, as relevant information appears spread across the entire spectral range rather than confined to isolated wavelengths. This diffuse pattern is consistent with indirect chemical coupling between viral particles and the surrounding matrix, mediated by changes in local hydrogen bonding and solvation structure. Consequently, the measured NIRS signal likely arises from a combination of physical (scattering) and chemical (interaction-based) effects, whose relative contributions depend on both matrix composition and viral concentration.

To better understand the origin of the variance captured by the 3-way PLS, the loadings were examined to identify the spectral regions contributing most to the global variability, both for the EMSC-preprocessed data and for the SG1 (Figs. 6a and S5a). The loadings obtained from the SG1 completely mirrored the shape of the raw spectra, whereas those from EMSC shared similarities but also revealed distinct features. The explained variance for each block remained consistently high. The most relevant regions were located mainly around 1370–1650

<figure><img src="image_10.png" /><figcaption>Fig. 6. (continued).</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Fig. 6. (continued).</figcaption></figure>

nm and 1850–1930 nm, corresponding to the well-known absorption bands of water and, to a lesser extent, to the overtones and combination bands of various milk biomolecules such as proteins, carbohydrates, and lipids (Daoud et al., 2020; Tsenkova et al., 2000). However, the signal recorded in milk results from complex interactions among these multiple constituents, making it difficult to attribute the observed differences to a single component.

At such low viral concentrations, the mass fraction of MS2 is negligible compared to that of milk proteins and sugars, meaning that a large part of the observed variance likely originates from the matrix itself. Nevertheless, a chemical contribution from the virus cannot be ruled out. The MS2 virion, a compact 27 nm non-enveloped particle composed of densely packed proteins and nucleic acids, possesses a high local molecular density and polarizability. Such dense nanostructures can locally enhance light-matter interactions, producing a disproportionately strong vibrational response relative to their bulk concentration. In addition, viral particles may indirectly influence the surrounding matrix through electrostatic or hydration-shell effects, subtly modifying hydrogen-bonding networks and protein-water interactions. These local matrix rearrangements could generate secondary spectral changes, producing a measurable chemical signature associated with the viral presence.

Taken together, these observations suggest that the NIR signal captured by the model likely arises from a combination of chemical and physical effects, a matrix-driven response modulated by local viral contributions. This dual nature could explain the weak yet reproducible spectral differences observed between samples with varying viral concentrations.

It was not initially clear whether retaining the 1800–2115 nm spectral region was beneficial for modeling, as noise was visually perceived in it. Therefore, an additional 3-way PLS analysis was performed on trimmed data, excluding this region. Instrumental checks confirmed that no detector saturation occurred within this range. The corresponding results, reported in Table 1, show a slight decrease in model performance compared to the full-range data (Fig. S8 showing results on trimmed data preprocessed by EMSC), suggesting that these wavelengths still carry relevant information despite their higher noise contribution.

The quantification limit threshold in Fig. 6b was fixed at 25 % as this experiment cumulates multiple error sources from the MS2 production and its quantification, to the analytical chemistry core of its research. With this threshold, 3-way PLS model provides an acceptable

quantification (4915 PFU/mL) competing with the usual standards for virus concentrations. The theoretical LOD was estimated at 1.5 × 10³ PFU/mL, which is consistent with the high relative error (~ 125 %) observed at the next lower dilution (≈ 5 × 10² PFU/mL). Using RT-PCR standardized assays for COVID-19 which is very targeted, best results are often close to 100 copies of RNA per mL (Arnaout et al., 2020) and sometimes get under 10 copies (Fung et al., 2020; Tastanova et al., 2021). The minimum infective dose of Norovirus is thought to be around 1–100 particles, a study of 2008 estimating that 18 virus particles induce the infection of 50 % of the human population (Yezli & Otter, 2011). Also, non-genomic methods like biosensors-based techniques are emerging. Detection limits reported in similar studies range from as low as 0.1 ng/mL for viral capsid proteins in complex media to detection capabilities as low as 1.7 copies/mL using advanced electrochemical biosensors. While these reference methods and infection thresholds operate at different analytical levels, the present detection/quantification performance in milk remains within the same order of magnitude as values reported in the literature for virus quantification in complex matrices, confirming the feasibility and robustness of the proposed NIRS-based approach under realistic experimental conditions (Baek et al., 2019; Heo et al., 2019; Hwang et al., 2017).

It should be noted that there is little homogeneity for units across the literature for detection limits. Depending on the principle of the method used, involved units may differ and it is perfectly understandable, but it raises one question: how should different techniques be compared? One answer may lie in the use of the reference method. In this study, 3 different approaches were used to titrate MS2: a cell-based one and 2 different spectroscopic/chemometric methods.

Beyond its quantification capability, one major strength of the NIRS approach lies in its real-time detection potential. The method enables on-site monitoring of viral contamination, offering a rapid and continuous alternative to conventional molecular assays. Lastly, the high sustainability and durability of NIRS need to be mentioned. Among all the viral detection methods, the lack of genetic material extraction or any kind of heavy sample preparation favours NIRS as it doesn't use high environmental risk solvents. For instance, RT-PCR requires a lot of consumables in comparison, from primers to PCR enhancers... Moreover, from an economic standpoint, NIRS cost-effectiveness and low maintenance requirements make it very durable. The qualification to perform a NIRS experiment is also less demanding than to perform RT-PCRs, once a statistical model is established. NIRS then appears more durable and accessible.
## 5. Conclusion

This study explored the feasibility of using NIRS combined with chemometric modeling for the detection and quantification of MS2 phage in milk. Despite the complexity of the food matrix, 3-way PLS regression enabled reliable prediction of phage concentration at very low level, with R² values reaching up to 0.81. Among the spectral pre-processing methods, the EMSC and SG1 significantly improved model performance. The use of 3-way multiblock PLS allowed us to incorporate data from repeated experimental replicates, enhancing the robustness and generalizability of the model.

The system achieved a quantification limit of 4915 PFU/mL, a value that remains within the same order of magnitude as those reported in the literature for viral quantification in complex matrices. Although the cross-validation strategy used in this study involved structural constraints to preserve the experimental hierarchy, the model demonstrated consistent and interpretable results across most validation folds. This suggests that further optimization of the validation design and data arrangement could enhance predictive accuracy. Overall, the performance achieved is encouraging and supports the feasibility of applying NIRS for reliable viral quantification in challenging food matrices.

In addition to performance, NIRS presents several practical advantages: it is rapid, non-destructive, environmentally friendly (solvent-free), and cost-efficient. These features make NIRS a valuable candidate for high-throughput, real-time virus screening in dairy processing and other food safety contexts. Future work should include evaluation across different milk types (e.g., skimmed, plant-based) and in the presence of other viral species to further assess the method's robustness.

### CRediT authorship contribution statement

**Samy De Oliveira:** Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Conceptualization. **Stéphane Guyot:** Writing – review & editing, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Conceptualization. **Laurence Dujoury:** Writing – review & editing, Software, Methodology, Formal analysis, Data curation. **Emmanuel Denimal:** Writing – review & editing, Methodology, Formal analysis, Data curation. **Laurent Gal:** Writing – review & editing. **Caera O'Neill:** Writing – review & editing, Validation, Methodology, Investigation, Formal analysis. **Philippe Cayot:** Writing – review & editing. **Alexis de Rougemont:** Writing – review & editing, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Conceptualization. **Elias Bou-Maroun:** Writing – review & editing, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.foodchem.2025.147336.

### Data availability

Data will be made available on request.

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