# The freezing duration and the number of freeze-thaw cycles influence the near infrared spectra of ageing beef muscles

Julien Soulat, Valérie Monteils, Donato Andueza

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Julien Soulat, Valérie Monteils, Donato Andueza. The freezing duration and the number of freeze-thaw cycles influence the near infrared spectra of ageing beef muscles. LWT - Food Science and Technology, 2024, 214, pp.117147. 10.1016/j.lwt.2024.117147. hal-04920495

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# The freezing duration and the number of freeze-thaw cycles influence the near infrared spectra of ageing beef muscles

Julien Soulat, Valérie Monteils, Donato Andueza * ,<fnref n="1" />

Université Clermont Auvergne, INRAE, VetAgro Sup, UMR Herbivores, F-63122, Saint-Genès-Champanelle, France

<figure><img src="image_2.png" /></figure>

ARTICLE INFO

Keywords:

NIRS

Cattle

Meat

ANOVA simultaneous component analysis

A B S T R A C T

The aim of this study was to investigate the effect of the freezing duration and the number of freeze-thaw cycles on the near infrared (NIR) spectra of ageing beef. Freezing duration was tested on the *Serratus ventralis* muscle with durations of 3, 6, and 12 months. The effect of four freeze-thaw cycles was tested on the *Infraspinatus* and *Rhomboïdeus* muscles. Our results obtained by the Analysis of Variance Simultaneous Component Analysis (ASCA) show that the NIR spectra of muscle were impacted by the freezing duration and the number of freeze-thaw cycles. However, these effects were non-linear and varied slightly according to the muscle studied. ASCA analyses showed that the freezing duration and the number of freeze-thaw cycles affect NIR wavelengths mainly related to C-H, O-H, and N-H bonds, which are known to be associated with proteins, lipids, and water. This study showed that the NIR spectra of ageing beef were sensitive to the freezing duration and the number of freeze-thaw cycles.

1. Introduction

Freezing and the cold storage affect the characteristics of the fresh meat, causing deterioration in both its properties and chemical constituents (Zhang, Zhang, & Mujumdar, 2023). Many studies show that the freezing duration and/or the number of freeze-thaw cycles have impacts on the moisture content and distribution in meat tissue (Leygonie, Britz, & Hoffman, 2012), water holding capacity, the color, the lipid and protein oxidations, the microstructure (e.g. muscle fiber diameter, cross-section area, and perimysium thickness), the tenderness evaluated by shear force of the meat in pork (Teuteberg, Kluth, Ploetz, & Krischek, 2021; Tippala, Koomkrong, & Kayan, 2020; Xia, Kong, Liu, & Liu, 2009), poultry (Ali et al., 2015, 2022; Chen et al., 2017), lamb (Daszkiewicz et al., 2018; Muela, Monge, Sañudo, Campo, & Beltrán, 2015; Qi et al., 2012), and cattle (Cheng et al., 2019; Grayson, King, Shackelford, Koohmaraie, & Wheeler, 2014; Wang et al., 2020). These studies were performed from meat without ageing. However, other results established from ageing meat did not observe an effect of the freezing (duration and/or number of freeze-thaw cycles) on the tenderness evaluated by shear force or by a sensory panel (Lagerstedt, Enfält, Johansson, & Lundström, 2008; Muela, Sañudo, Campo, Medel, & Beltrán, 2012; Vieira, Diaz, Martínez, & García-Cachán, 2009).

Contrary to the reference methods used in these different studies, the spectroscopic techniques as near-infrared (NIR) spectroscopy are fast, economical, and nondestructive (Zhang et al., 2023). In addition, NIR spectroscopy can be used to evaluate adulteration, quality and safety of meat (Grassi, Jiménez, Ruiz, & González-Mohino, 2024). Several models have been developed from NIR spectra to indirectly predict some compounds or properties of meat (Andueza et al., 2019; Andueza, Picard, Hocquette, & Listrat, 2021; Cafferky et al., 2020; Zhang et al., 2023). However, it is generally not possible to collect and/or analyze all meat samples on the same d, during an experiment. Meat samples may therefore be frozen for different freezing durations and with different numbers of freeze-thaw cycles, depending on the organization of the laboratory analyses. As a consequence, NIR spectra of meat samples can be usually obtained with different freezing durations or freezing cycles than the reference assessments. These different conditions could affect the NIR spectra and consequently the quality of the prediction or classification models obtained. However, few works have studied the effect of the number of freeze-thaw cycles and the freezing duration on the NIR spectra of beef (Downey & Beauchêne, 1997). These authors concluded that visible-near infrared reflectance technology has the potential to discriminate between fresh and frozen-then-thawed samples of meat. According to the moment of the NIR measurement on uncooked aged

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: donato.andueza@inrae.fr (D. Andueza).</footnote>

<footnote n="1">¹ Postal address: INRAE, Centre Clermont-Auvergne-Rhône-Alpes, Site de Theirix, 63,122 Saint-Genès-Champanelle, France.</footnote>
meat, it is important to improve our knowledge of the effects of the freezing duration and/or the number of freeze-thaw cycles on spectra. These effects could affect the prediction quality of some meat compounds if the NIR measurements are not performed at the same time as the reference analysis. Our hypothesis is that the length of the freezing period and/or the number of freezing cycles have an effect on the NIR spectra of ageing beef samples. Consequently, the aim of this study was to investigate the effect of the number of freeze-thaw cycles or the effect of the freezing duration on the spectra of ageing beef and to identify the wavelengths affected. Two experiments were performed using the *Serratus ventralis* (SV) muscle to test the effect of the number of freeze-thaw cycles and using the *Infraspinatus* (IF) and *Rhomboïdeus* (RH) muscles to test the effect of the freezing duration.

## 2. Materials and methods

### 2.1. Beef sampling

At 24h post-mortem, two rib samples (4th and 5th ribs) were taken from three Charolais heifers. The heifers were slaughtered in an industrial slaughterhouse (SICABA, Bourbon l'Archambault, France). Each rib sample was deboned, individually vacuum-packed, and aged at +4 °C for 14 d. Then, the SV, IF and RH muscles were collected by a professional butcher (INRAE Unité Expérimentale Herbipôle, Theix, France, https://doi.org/10.15454/1.5572318050509348E12). These 3 muscles were studied because they are postural muscles localized in the chuck of cattle and have different fiber type compositions (Totland & Kryvi, 1991). According to the literature after ageing for 14 d, the raw IF muscle was tougher than the raw RH and SV muscles, in heifers. The raw RH and SV muscles also had similar toughness to the *Longissimus thoracis* muscle (Soulat, Monteils, Ellies-Oury, Papillon, & Picard, 2021). Moreover, their quantities are large enough to test different numbers of freeze-thaw cycles and freezing duration.

Two experiments were performed on these muscle samples. The first one tested the number of freeze-thaw cycles using the SV muscle. The second tested the freezing duration using the RH and IF muscles.

### 2.2. Experiment 1: effect of freeze-thaw cycle number

To study the effect of freeze-thaw cycle number, the SV muscle samples were used. After ageing a sub-sample was cut from each SV muscle, and ground directly in liquid nitrogen using a M20 mill (IKA-Werke, Staufen, Germany) to produce a fine homogeneous powder (N0) in order to minimize the sampling error due to the sample heterogeneity (Isaksson, Nilsen, Tøgersen, Hammond, & Hildrum, 1996; Tøgersen, Isaksson, Nilsen, Bakker, & Hildrum, 1999). The remainder of each sample was individually vacuum-packed and frozen at -20 °C.

One wk later, the SV samples were thawed at +4 °C for approximately 24h. A sub-sample was cut from each SV sample, and ground directly in liquid nitrogen (N1). The remainder of each sample was individually vacuum-packed and frozen at -20 °C. This step was repeated each wk to obtain samples N2, N3, and N4 samples.

After grinding, N0, N1, N2, N3, and N4 samples (approximately 100 g per sample) were stored in a tube at -80 °C prior to NIR analysis. Freeze storage of meat powder at -80 °C allows to delay undesirable biochemical reactions in meat such as protein and lipid oxidation (Aubourg, Piñeiro, & González, 2004; Estévez, 2011) which could influence the infrared spectra of samples. There are few variations in meat composition with a storage at -80 °C (Soyer, Özalp, Dalmış, & Bilgin, 2010).

### 2.3. Experiment 2: freezing duration effect

To study the effect of freezing duration, the IF and RH samples were used. The smallest amount of these muscles available was appropriate for this experiment. Each muscle sample was divided into 4 sub-samples.

The first sub-sample of each muscle was cut and ground directly in liquid nitrogen using an M20 mill (IKA-Werke, Staufen, Germany) to produce a fine homogeneous powder (T0). The T0 samples approximately 100 g per sample) were stored in a tube at -80 °C prior to NIR spectroscopic analysis.

The other 3 sub-samples of each muscle were individually vacuum-packed and frozen at -20 °C. After 3 months at -20 °C, one sub-sample per muscle (IF and RH) was thawed for around 24h at +4 °C. These samples were then ground in liquid nitrogen to produce a fine homogeneous powder (T1). Then the T1 samples (approximately 100 g per sample) were stored in a tube at -80 °C. This step was repeated at 6 months and 12 months from the other sub-samples at -20 °C to obtain T2 and T3 samples.

The T0 and T1 samples were analyzed by NIR spectroscopy at the same time as the samples from the experiment 1. The T2 and T3 samples were analyzed by NIR spectroscopy, 1 or 2 d after the grinding step.

### 2.4. Near infrared spectroscopy analyses

For the NIR analysis of each meat sample, approximately 10 g of powder was placed in a 50 mm diameter ring cup (approximately 10 mm deep; part number IH-0307, NIRSystems, Infrasoft International, South Atherton St. State College, PA 16801, USA). After thawing of the powder (approximately 30 min), the ring cup was sealed with a disposable paper-backed wrap. Two ring cup powder sub-samples were taken for each sample. The ring cups were scanned in reflectance mode at 2 nm intervals from 400 to 2500 nm using a FOSS NIRSystems model 6500 NIR scanning spectrometer (FOSS, NIRSystems Hillerod, Denmark) equipped with an autocup module and controlled using ISIScan software v.2.21 (FOSS, Hillerod, Denmark). The reflectance values (R) were converted into absorbance values (A) using formula $A = \log(1/R)$.

### 2.5. Statistical analyses

First, the data underwent a second derivative treatment according to the methodology of Savitzky and Golay (1964). It was applied to the segment between 1100 and 2500 nm. The purpose of this mathematical pre-treatment was to correct the light scattering effect of the spectra due to uncontrollable physical variations. To study the effect of freeze-thaw cycles and freezing duration on the NIR spectra, the Analysis of Variance Simultaneous Component Analysis (ASCA) method was used on the pretreated spectra. ASCA is a multivariate extension of analysis of variance (ANOVA) that can deal with complex multivariate data sets with an underlying experimental design (Jansen et al., 2005; Smilde et al., 2005). It combines the variance factorization and inference capabilities of ANOVA with the exploratory power of principal component analysis (PCA).

#### 2.5.1. Experiment 1: effect of freeze-thaw cycle number

According to de Figueiredo, Giannoukos, Wüthrich, Zenobi, and Rutledge (2023), the spectral matrix X was decomposed into the different sources of variation $X = X_μ + X_α + X_S + X_ε$.

In the ASCA analysis, the first step was to perform a two-way repeated measures ANOVA on each variable described above individually. Equation (1) represents a series of ANOVAs:

$$X_{ijk} = \mu + \alpha_{i} + S_{j} + \varepsilon_{ijk} \quad (1)$$

where $X_{ijk}$ is the measured response. For a given variable, μ is an overall offset, $\alpha_i$ represents the effect number of freezing-thaw cycles which varies between N0 and N4, $S_j$ is the effect of the heifer and $\varepsilon_{ijk}$ is the error.

$\alpha_i$ was considered as a fixed repeated measured effect and S was considered as a random effect.
### 2.5.2. Experiment 2: freezing duration effect

Since not all samples were not analyzed at the same d by NIR, standardization of the spectra was performed to control for possible instrument drift over time. The standardization procedure developed by Shenk and Westerhaus (1991) was used to correct NIR spectra taken on different dates. Thirty sealed samples representing different agricultural products were used at each d of NIR analysis to calculate the wavelength and photometric corrections. Statistical analyses were performed on both total and standardized spectra.

As in the experiment 1, for each muscle, the spectral matrix X was decomposed into the different sources of variation $X = X_μ + X_γ + X_S + X_ε$.

In the ASCA analysis, the first step was to perform a two-way repeated measures ANOVA on each of the variables described above individually. For each muscle (IF and RH), equation (2) represents a series of ANOVAs:

$$X_{ijk} = μ + γ_i + S_j + ε_{ijk} \quad (2)$$

where $X_{ijk}$ is the measured response. For a given variable, μ is an overall offset, γ_i represents the effect freezing duration which varies between T0 and T3, S_j is the effect of the heifer and ε_{ijk} is the error.

γ was considered as a fixed repeated measured effect and S was considered as a random effect.

Then for each model, a principal component analysis (PCA) is applied to each ASCA and PCA sub-model is obtained for each factor. The scores for each PCA sub-model are scores for each factor-level average to determine the contribution of each factor and interaction to the total variation in the data.

To estimate the significance effect of each factor, the p-values were calculated based on a permutation test of the factor's levels with the permutation number of 1000.

The ASCA analyses were performed using the ALASCA package (Jarmund, Madssen, & Giskeødegård, 2022) of the R 4.3.1. Software (R core Team, 2023).

## 3. Results and discussion

According to our results, for raw aged beef, the number of freeze-thaw cycles for the SV muscle and the freezing duration for the IF and RH muscles had an effect on the second derivative of their NIR spectra (Figs. 1–3). Visual differences were observed in the spectra. The number of freeze-thaw cycles affected several NIR second derivative spectra at 1214 nm, 1736 nm, 1744 nm, 1854 nm, 1892 nm, 2308 nm, and 2326 nm (Fig. 1). The freezing duration affected for the IF and RH the NIR second derivative spectra at 1132 nm, 1162 nm, 1308 nm, near 1400 nm, near 1864 nm, near 1894 nm, 2310 nm, 2326 nm, near 2346 nm (Figs. 2 and 3). The freezing duration had a specific impact on the NIR second derivative spectra at 1730 nm and 1382 nm in the IF and RH muscles, respectively (Figs. 2 and 3).

Fig. 4 shows the results of the ASCA model related to with the effect of the number of freeze-thaw cycles on the NIR spectra of SV muscle. This model was represented by the first (PC1) and the second (PC2) principal components, which explained 56.3% and 27.5% of the variability in the data set, respectively. The two principal components represent a non-linear evolution. For PC1, a decrease in score value was observed after one and two freezing (N1 and N2) compared to no freezing (N0). A peak was reached after three freezing (N3). At four freezing (N4), a decrease was observed compared to N3, reaching a score lower than N0, N1 and N2. For PC2, a decrease in score value was observed after N0, then an increase was observed to reach a peak at N2. A new decrease in score value was observed at N3, followed by a slight increase at N4. A slight difference in score value was observed between N1 and N3. In accordance with our results, Downey and Beauchêne (1997) and Atanassova, Yorgov, Stratev, Veleva, and Stoyanchev (2024) using visible and/or NIR observed an effect of the number of freeze-thaw cycles on the spectra in beef and carp, respectively. In pork, Pu, Sun, Ma, and Cheng (2015) also observed this effect using visible and near-infrared hyperspectral images.

Figs. 5 and 6 presented the results of the ASCA models associated with the freezing duration effect on the NIR spectra of IF and RH muscles, respectively.

<figure><img src="image_3.png" /><figcaption>Fig. 1. Second derivative of average near infrared spectra as a function of the number of freeze-thaw cycles, for the *Serratus ventralis* muscle.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Fig. 2. Second derivative of average non-standardized near infrared spectra as a function of the freezing duration, for the *Infraspinatus* muscle.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 3. Second derivative of average non-standardized near infrared spectra as a function of the freezing duration, for the *Rhomboïdeus* muscle.</figcaption></figure>

For the IF muscle, the results of the ASCA model related to the freezing duration without standardization were represented by PC1 and PC2, which explained 76.6% and 18.7%, respectively, of the variability in the data set (Fig. 5). PC1 and PC2 showed a non-linear trend. For PC1, an increase in score value was observed after 3 months of freezing (between T0 and T1). The score values after 3 and 6 months of freezing (between T1 and T2) were similar. A decrease in the score value was

observed between T2 and T3. For PC2, a decrease in score value was observed between T0 and T1. Then, a peak was reached after 6 months of freezing (T2) and a new decrease in score value was observed after 12 months of freezing (T3). The variation of the curves was different between the results obtained with and without standardization (Fig. 5). After standardization of the NIR spectra, PC1 and PC2 explained, 74.6% and 19.4% of the variability, respectively (Fig. 5). For PC1, the score
a) First principal component (PC1)

<figure><img src="image_6.png" /></figure>

N0 = no freezing; N1 = 1 freeze-thaw cycle; N2 = 2 freeze-thaw cycles; N3 = 3 freeze-thaw cycles; N4 = 4 freeze-thaw cycles.

The gray area represents the confidence intervals of the score values.

b) Second principal component (PC2)

<figure><img src="image_7.png" /></figure>

**Fig. 4.** Effect of the number of freeze-thaw cycles on the 2nd derivative near infrared spectra of *Serratus ventralis* muscle by analysis of variance simultaneous component analysis (A, scores; B, loadings). The figure a) results obtained on the first principal component. The figure b) correspond to the results obtained on the second principal component.

value increased between T0 and T1, then a decrease was observed as the freezing duration increased (between T1 and T3). For PC2, a decrease in score value was observed between T1 and T2. Then the score value increased between T2 and T3. For the IF muscle, the unstandardized scores (in which the time drift of the instruments is present; Fig. 5) and the standardized scores (in which the spectral changes due to this drift are corrected; Fig. 5) were practically similar, showing significant changes in the muscle spectra due to the freezing duration that the samples have undergone.

For the RH muscle, the results of the ASCA model related to the freezing duration without or with standardization were mainly represented by PC1 (>75%, Fig. 6). The results obtained on the non-standardized spectra showed no effect of the freezing duration on the NIR spectra (Fig. 6). However, the results obtained on the standardized spectra showed differences according to the freezing duration in PC1 and PC2. For the standardized spectra in PC1, the score value was slightly higher at T1 than at T0. A decrease in the score value was observed between T1 and T3.

Other authors also observed an effect of the freezing duration on the NIR spectra of fish (Reis et al., 2017), chicken (Grunert, Stephan, Ehling-Schulz, & Johler, 2016), and pork (Caceres-Nevado, Garrido-Varo, De Predro-Sanz, Tejerina-Barrado, & Pérez-Marin, 2021). Many studies have found that the freezing (number of freeze-thaw cycles or duration) has an effect on the muscle structure (e.g. sarcomere length and fiber diameter), the fatty acid profile, the thawing loss, the water holding capacity and/or the protein and lipid oxidations, in ovine, pork and beef (Cheng et al., 2019; Qi et al., 2012; Tippala et al., 2020; Xia et al., 2009). As the structure and composition of the meat sample is altered by freezing, this explains some of the variability observed in the NIR spectra (Figs. 1–3). In addition, according to our results, the freezing duration had not the same effect on the IF and RH muscles' spectra. According to Leygonie et al. (2012), the length of the freezing period could affect the chemical composition of muscle due to the unfrozen residual water remaining in the sample at freezing temperatures below –40 °C. Therefore, this phenomenon might explain the differences

between muscles. On the spectra without standardization, the freezing duration had no effect on RH muscle's spectra, whereas, an effect was observed for IF muscle. Alomar, Gallo, Castañeda, and Fuchslocher (2003) also observed a muscle effect on the NIR spectra in beef. The NIR spectra difference between these two muscles can be explained by their different physicochemical properties (Totland & Kryvi, 1991). However, there is heterogeneity according to the muscle area and may also help explain the difference observed between the muscles studied, which is confounded with the effect of the number of freeze-thaw cycles or the freezing duration. Senaratne, Calkins, de Mello, Pokharel, and Hinkle (2010) observed a significant intramuscular heterogeneity of tenderness assessed by shear force. Dissociating these two effects (intramuscular heterogeneity and freezing duration or number of freeze-thaw cycles) is very difficult for studying the sole influence of the freezing effect on muscle samples. Moreover, the standardized spectra of the RH muscle showed that there was also an effect of the NIR spectrometer shift that confused with the freezing effect tested in our study. The variability of the NIR spectra is multifactorial.

For the two freezing effects tested in our study, the ASCA model results allowed the identification of wavelengths that were positively or negatively related to the principal components (PC1 and PC2). wavelengths with positive loadings have higher absorbances in the time points with higher score values, and vice versa for wavelengths with negatives loading values (Figs. 4–6). According to Fig. 4, the wavelengths in the 1520–1532 nm, 1876–1878 nm regions had a positive loading associated to N0 and N3 freeze-thaw cycles. The wavelengths in the 2392–2394 nm regions had a positive loading associated to N0 and N2 freeze-thaw cycles. However, the wavelengths in the 1816–1818 nm, 2018–2020 nm, and 2240–2268 nm regions had a negative loading associated to N1, N2, and N4 freeze-thaw cycles. The wavelengths in the 1100–1142 nm, 2102–2104 nm, and 2404–2498 nm regions had a negative loading associated to N1, N3, and N4.

According to the ASCA results, the freezing duration did not affect the same regions of the unstandardized NIR spectra for IF and RH muscles (Figs. 5 and 6). For the IF muscle, the wavelengths in the
## I) Without standardization of spectra

a) First principal component (PC1)

<figure><img src="image_8.png" /></figure>

b) Second principal component (PC2)

<figure><img src="image_9.png" /></figure>

## II) With standardization of spectra

a) First principal component (PC1)

<figure><img src="image_10.png" /></figure>

b) Second principal component (PC2)

<figure><img src="image_11.png" /></figure>

T0 = no freezing; T1 = 3 months of freezing; T2 = 6 months of freezing; T3 = 12 months of freezing.

The gray area represents the confidence intervals of the score values.

**Fig. 5.** Effect of freezing duration on the Near infrared spectra of *Infraspinatus* muscle by analysis of variance simultaneous component analysis (ASCA) (A, scores; B, loadings). I) ASCA performed on the near infrared (NIR) spectra without standardization; II) ASCA performed on the NIR spectra standardized by the procedure developed by Shenk and Westerhaus, (1991). The figure a) correspond to the results obtained on the first principal component. The figure b) correspond to the results obtained on the second principal component.
## I) Without standardization of spectra

<figure><img src="image_12.png" /><figcaption>b) Second principal component (PC2)</figcaption></figure>

<figure><img src="image_13.png" /></figure>

## II) With standardization of spectra

<figure><img src="image_14.png" /><figcaption>b) Second principal component (PC2)</figcaption></figure>

<figure><img src="image_15.png" /></figure>

T0 = no freezing; T1 = 3 months of freezing; T2 = 6 months of freezing; T3 = 12 months of freezing.

The gray area represents the confidence intervals of the score values.

**Fig. 6.** Effect of freezing duration on the near infrared (NIR) spectra of *Rhomboïdeus* muscle by analysis of variance simultaneous component analysis (ASCA) (A, scores; B, loadings). I) ASCA performed on the NIR spectra without standardization; II) ASCA performed on the NIR spectra standardized by the procedure developed by Shenk and Westerhaus, (1991). The figure a) correspond to the results obtained on the first principal component. The figure b) correspond to the results obtained on the second principal component.
1332–1336 nm, 2274–2298 nm, and 2442–2462 nm regions had a positive loading associated to T2 and T3 freezing duration (Fig. 5). The wavelengths in the 2168–2178 nm had a positive loading associated to T1 and T2. However, the wavelengths in the 1522–1528 nm and 1772–1792 nm regions had a negative loading associated to T0 and T1. The wavelengths in the 2200–2262 regions had a negative loading associated to T0 and T3 freezing duration (Fig. 5). For the RH muscle, the score values are similar (close to 0) but the wavelengths in the 1260–1270 nm and 2010–2042 nm regions had a positive loading associated to T0 et T1, whereas, the wavelengths in the 1984–1994 nm and 2148–2152 nm regions had a positive loading associated to T3 (Fig. 6). However, the wavelengths in the 1396–1398 nm and 1518–1526 nm regions had a negative loading associated to T3. The wavelengths in the 2008–2024 nm, 2160–2164 nm, and 2424–2432 nm regions had a negative loading associated to T0 and T1 (Fig. 6).

Our results showed that the freezing (number of freeze-thaw cycles or duration) had an effect on some similar NIR spectral regions as 1518–1532 nm for the 3 muscles or 2010–2164 nm and 2404–2498 nm for SV and RH muscles. In addition, the freezing can have an effect on specific spectral regions according to the muscle. Nevertheless, the wavelengths identified by the ASCA analysis were mainly related to C-H bonds (regions 1100–1142 nm, 1330–1398 nm, 1816–1878 nm, 2100–2198 nm, 2242–2298 nm, 2342–2394 nm, and 2404–2498 nm), O-H bonds (regions 1106 nm, 1402 nm, 1200–1268 nm, 1520–1592 nm, 1736–1794 nm, 1816–1878 nm, 1946 nm, 2016–2020 nm, 2100–2198 nm, and 2230–2268 nm), and N-H bonds (regions 1520–1592 nm, 1986–1994 nm, 2004–2078 nm and 2102–2186 nm) (FOSS, 2012; Workman Jr & Weyer, 2007). These chemical bonds are known to be associated with proteins, lipids, and water. In accordance with our results, Alomar et al. (2003) identified wavelengths of the NIR spectra associated with proteins (1510, 1980, 2050, and 2180 nm) and lipids (1760 and 2310 nm) affected by freezing in beef. Caceres-Nevado et al. (2021) also observed an effect of the freezing on regions of NIR spectra around 1100, 1200, 1400, in pork. Changes in the C-H absorbance regions were influenced by proteolysis and lipid hydrolysis during thawing (Caceres-Nevado et al., 2021). The O-H absorbance was related to the water content in muscle tissue and it could be influenced by the water losses during the thawing.

Therefore, it is difficult to distinguish whether the different wavelengths associated with the freezing duration and the number of freeze-thaw cycles studied are due to these effects themselves or to the fact that different muscles were used in each study.

Near infrared analysis can be used to predict meat properties. However, some meat traits such as sensory properties (tenderness, flavor, juiciness) and texture (hardness, springiness, cohesiveness, chewiness), in chicken, beef, and sheep may or may not be affected by freezing (duration or number of freeze-thaw cycles), and the effects were not linear (Chen et al., 2017; Cheng et al., 2019; Daszkiewicz et al., 2018). NIR spectra may be more sensitive to the freezing effects than the sensory and rheological methods.

## 4. Conclusions

The ASCA method enables the statistical analysis of spectral databases derived from an experimental design. This method facilitates the identification of the most significant wavelengths associated with the factors under investigation (in this case, the number of freeze-thaw cycles and the freezing duration) from a statistical perspective.

Our results confirm the fact that freezing duration and the number of freeze-thaw cycles has an impact on the NIR spectra of beef, even if it is ageing. However, the results of ASCA analyses showed that these 2 effects were not linear. In addition, these results allowed the identifications of wavelengths affected (positively or negatively) by the number of freeze-thaw cycles or the freezing duration. These wavelengths were mainly related to C-H, O-H, and N-H bonds independent of the freezing effect tested (duration or number of freeze-thaw cycles), but they may be

located in different regions of the NIR spectra (1st and 2nd overtones and combination bands). On the non-standardized NIR spectra, our results showed that the effect of freezing duration on the spectra also depends on the muscle studied. However, this muscle effect remains residual once the spectra have been standardized. To confirm our results, it will be necessary to increase the number of beef samples and probably consider other muscles than those used in the current study. To facilitate the simultaneous NIR evaluation and reference analyses, the reduction of sample preparation (grinding in nitrogen) is necessary using laboratory or portable instruments.

### CRediT authorship contribution statement

**Julien Soulat:** Writing – review & editing, Writing – original draft, Resources, Methodology, Investigation, Formal analysis, Conceptualization. **Valérie Monteils:** Writing – review & editing, Resources, Investigation, Funding acquisition, Conceptualization. **Donato Andueza:** Writing – review & editing, Validation, Software, Resources, Methodology, Investigation, Formal analysis, Data curation, 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.

### Acknowledgment

The authors would like to thank the INRAE staff for the meat samples preparation and NIR analyses, in particular Cédric Coustet, Quentin Delahaye, Cyril Labonne. The authors would also thank Brigitte Picard for her contribution to the support project used, and Fabienne Picard for her contribution to statistical analyses.

This study was financed by the French government IDEX-ISITE initiative 16-IDEX-001 (CAP 20–25), the Auvergne-Rhône-Alpes region (convention Massif central), and the French Ministry of Agricultural and Food.

### Data availability

Data will be made available on request.

### References

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