# New insights in the 3-D rheological properties and collagen fibers orientation in murine periodontal ligaments

Mahmoud Sedky Adly, Richard Younes, Marta Martin, Thierry Cloitre, Afnan Sedky Adly, Ivan Panayotov, Philippe Bousquet, Csilla Gergely, Frédéric Cuisinier, Delphine Carayon, et al.

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Mahmoud Sedky Adly, Richard Younes, Marta Martin, Thierry Cloitre, Afnan Sedky Adly, et al. New insights in the 3-D rheological properties and collagen fibers orientation in murine periodontal ligaments. Journal of the Mechanics and Physics of Solids, 2024, 189, pp.105715. 10.1016/j.jmps.2024.105715. hal-04679276

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# New insights in the 3-D rheological properties and collagen fibers orientation in murine periodontal ligaments

Mahmoud Sedky Adly<sup>a</sup>, Richard Younes<sup>a</sup>, Marta Martin<sup>b</sup>, Thierry Cloitre<sup>b</sup>, Afnan Sedky Adly<sup>a</sup>, Ivan Panayotov<sup>a,c,d</sup>, Philippe Bousquet<sup>a,c,d</sup>, Csilla Gergely<sup>b</sup>, Frederic J.G. Cuisinier<sup>a,c,d</sup>, Delphine Carayon<sup>a,c,d,#,*</sup>, Elias Estephan<sup>a,e,#,*</sup>

## ARTICLE INFO

### Keywords:

Periodontal ligament

Atomic force microscopy

Multiphoton microscopy

Young's modulus

Collagen fibers

Second harmonic generation

## ABSTRACT

The rheological properties of the periodontal ligament are key parameters to understand the homeostatic stability of the tooth supporting apparatus. The objective of this study is to lay new insights on the rheological properties and structural information of different regions in murine periodontal ligament by using atomic force (AFM) and multi-photon microscopy (MPM). A significant variation in elasticity of different regions was measured. The elasticity of periodontal ligament showed a significant tendency to become softer towards the furcation, the nearest area to the center of resistance of the tooth. This can open a new prospective for connecting the rheological adaptation of periodontal ligament to the tooth geometry that defines the center of resistance. Another important finding revealed by the second harmonic generation (SHG) signal exhibited by collagen fibers and measured by MPM is that the orientation of fibers in the furcation region can both provide space for tooth vertical movement with high compressive loads and prevent horizontal tooth movement. Additionally, it was found that the dispersion of the angles at different levels of cutting indicates homogeneity in the directionality of fibers across different regions. These results provide an accurate description of the rheological properties and structural information of periodontal ligament, which can serve as a base for comparison with other local and systemic diseases that may influence the periodontal ligament.

## 1. Introduction

The rheological properties of the periodontal ligament are essential parameters to understand the biomechanical behavior of the tooth as well as its surrounding tissues (Limjeerajarus et al., 2023). Periodontal ligament is an essential component of the tooth which has many important functions. These include: (i) supportive function as it provides an attachment for the root of the tooth to the alveolar bone, allows the teeth to withstand the forces of mastication, prevents the tooth from moving too far by non-elastic fibers and

<footnote><sup>a</sup> Bioengineering Nanoscience Laboratory UR_UM104, LBN, Univ Montpellier, 545 Avenue prof. Viala, Montpellier Cedex 34193, France</footnote>

<footnote><sup>b</sup> L2C, Univ Montpellier, CNRS, Montpellier, France</footnote>

<footnote><sup>c</sup> CSERD, CHU Montpellier, Montpellier, France</footnote>

<footnote><sup>d</sup> UFR odontologie, Univ. Montpellier, Montpellier, France</footnote>

<footnote><sup>e</sup> Neuroscience Research Center, Faculty of Medical Sciences, Lebanese University, Beirut, Lebanon</footnote>

<footnote>* Corresponding authors.</footnote>

<footnote>E-mail addresses: delphine.carayon@umontpellier.fr (D. Carayon), elias.estephan@umontpellier.fr (E. Estephan).</footnote>

<footnote># These authors contributed equally to this work as co-last authors</footnote>
the components of the ligament which act together as shock absorber or hydraulic damper; (ii) nutritive function, as blood vessels of the ligament provide nutrition for cells of the ligament, cementum, and alveolar bone; (iii) homeostatic function because cells of the periodontal ligament have the capacity to synthesize and resorb the extracellular substances of the ligament, cementum and alveolar bone; (iv) sensory function by inclusion of mechanoreceptors for touch and pressure sensations, hereby protecting the tooth in case of sudden overload; (v) finally, a protective function which is achieved by collagen fibers arranged in bundles running in different directions so they counteract the forces applied to the tooth whatever is their direction. Also, blood capillaries that are arranged in the form of coils act as shock absorber and nerves protect the tooth in case of sudden overload (Faroog et al., 2021; Buduneli et al., 2020).

Moreover, the periodontal ligament (PDL) is considered the most deformable dental component having the ability to transmit both orthodontic and functional forces to the alveolar bone (Dong-Xu et al., 2011). The ligament is composed mainly of collagen fibers running in several directions between alveolar bone and root surfaces. In addition, the fibers density was found to be different along the various sites of the periodontal ligament (Connizzo and Naveh, 2020). The unique architecture of the PDL collagen fibers, their perpendicular or oblique alignment along the length of the tooth is essential for maintaining proper tooth functioning as well as facilitating development of alveolar bone during childhood (Huri et al., 2015).

Reviewing the literature, it appears that numerous imaging techniques are used to study the biomechanical behavior of periodontal ligament related biomechanics, which include photo-elasticity (Asundi and Kishen, 2000), Moire interferometry (Wood et al., 2003), electronic speckle pattern interferometry (Zaslansky et al., 2006), strain gauges (Popowics et al., 2009), digital image correlation (Zhang et al., 2009), and a micro CT scanner with a loading system (Naveh et al., 2012).

Nanoindentation techniques, powerful technologies to explore mechanical aspects of biological matter at the nanoscale, open generating significant contributions in the comprehension of various human diseases. Atomic force microscopy (AFM) is a nano-sensing device that provides accurate measurements of elastic modulus and determines cellular strain distribution (Saab et al., 2013). AFM is also a label-free imaging technique providing high resolution images of cell morphology. AFM has the potential to spatially resolve the sample's elasticity by nanoindentation, and to map sample properties that are directly correlated to the topography. (Shi et al., 2010).

A number of recent studies proposed multi-photon microscopy (MPM) as a valuable label-free imaging technique to characterize different aspects of the periodontal ligament (Martínez-Ojeda et al., 2020). MPM is a non-linear optical technique enabling deep imaging of a biological sample when scanned by an IR pulsed-laser. The spatial localization of the excitation in the focusing volume of the objective allows a significant reduction of photobleaching. Therefore, MPM can provide high resolution sectioning images without the need of histological approaches or staining (Chen et al., 2007). The multiphoton excitation process will produce a second harmonic generation (SHG) signal, providing useful information on the structure and optical properties of a non-centrosymmetric specimen like the fibrillar collagen.

The minimal invasiveness of AFM and MPM imaging modalities and the valuable complementary information they can provide renders these approaches highly suitable to monitor dental tissues (Chen et al., 2007). Towards diagnostic applications, experimental animal models have been used to enable the study of periodontal ligament and oral structures (Marchesan et al., 2018).

In orthodontic applications, the movement of teeth within the alveolar bone is based mainly on the ability of the surrounding periodontal ligaments to react to mechanical stimulation with remodeling processes (Kawarizadeh et al., 2003; Adly et al., 2024). Furthermore, the emerging dental implant applications aim for using bioengineered PDL around the osseointegrated dental implants to improve efficiency of the biological function (Mathew et al., 2020).

Evaluation of the rheological properties of periodontal ligaments is considered a great challenge for guiding orthodontic applications. This study aims to investigate the rheological properties in relation with the structural information of different regions in murine periodontal ligament by a combined AFM and MPM study.

## 2. Materials and methods

### 2.1. Animals and ethics statements

Animal experiments were approved by the national ethics committee on animal experimentation and were conducted in compliance with the European Community and national directives for the care and use of laboratory animals. C57BL/6 J mice were purchased from Jackson laboratory (Bar Harbor, MA (USA)) and maintained under specific-pathogen free conditions. In our experiments, mice were used at 140 days of age. They were housed in cages with light/dark cycle with 12 h each. Mice were feed ad libitum in the animal facilities of Institute for Neurosciences of Montpellier (INM), UMR 1298 Inserm, University of Montpellier, France accredited by the French Ministry of Food, Agriculture and Fisheries (B34 172 36-11 March 2010). In addition, all the experiments were done in accordance with the Directives of the Council of the European Communities of November 24, 1986 (86/609/EEC) and the French Ethics Committee (approval number D3417236).

### 2.2. Samples preparation

This study was conducted on 3 mice that were sacrificed and their mandibles were dissected then cleaned from soft tissue and finally sectioned. According to the method recommended by Kawamoto (Kawamoto and Kawamoto, 2021), the samples were immediately embedded in SCEM followed by snap freezing in 2 methyl-butane cooled with liquid nitrogen, then were stored at -80 °C until testing. The mandibles were then mounted on a cryostat (Epredia cryostar NX50 (Kalamazoo, Michigan, USA)) and sectioned every 20µm in the transverse plane from the apical region till the furcation region. Finally, samples were mounted on an adhesive film
<figure><img src="image_5.png" /><figcaption>**Fig. 1.** Samples definition A) the different examination levels of mandibular roots and the Furcation (FF) area. B) schema explaining the labelling of different surfaces of the root. C) histological section illustrating the different surfaces. Mesial (MM), Mesial Buccal (MB), Mesial Lingual (ML), Mesial Furcation (MF), Distal Furcation (DF), Distal Buccal (DB), Distal Lingual (DL), Distal (DD).</figcaption></figure>
for study by AFM and MPM.

Sectioning of mandibular roots were performed at three different levels of the second molar and every level was examined with at least 7 sections. These include the furcation level (NF) having a thickness of ~140µm, level 2 (N2) having a thickness of ~220µm and level 1 (N1) having a thickness of ~260µm (Fig. 1A). Measurements were made on eight regions on every section. The examined sites were named according to Fig. 1B and Fig. 1C.

## 2.3. Atomic force microscopy (AFM)

AFM force spectroscopy (FS) experiments were performed using an Asylum MFP-3D head coupled to a Molecular Force Probe 3D controller (Asylum Research, Santa Barbara, CA, USA). Borosilicate glass spherical colloid probe cantilevers with a nominal spring constant of 0.1 N/m, radius of 10 µm, length 125 µm, width 35 µm and resonance frequency 30 kHz (CP-qp-CONT-BSG-B-5, Nano-AndMore GmbH) were used. The spring constant of the cantilevers was determined using the thermal noise method available within the MFP-3D software. Force measurements were performed in phosphate buffred saline (PBS) buffer, at room temperature and with a maximum loading force of 25 nN. Force-volume experiments were performed on a grid of 15 × 15 points over a region of 5 × 5 µm² in the different areas, with at least 3 measurements per area type. The recorded AFM-FS data were used to determine the Young's modulus (E) of the tissue using a modified Hertz model based on the work of Sneddon (Sneddon, 1965). Histograms of the Young's moduli distribution were fitted with a Gaussian function to obtain the mean E value of the probed area in the different locations.

## 2.4. Multiphoton microscopy (MPM)

MPM images were acquired with a custom-made multiphoton microscope build on an upright SliceScope microscope (MPSS-1000P, Scientifica, Uckfield, UK) equipped with a galvanometer scan head and a Nikon 16x water immersion objective (CFI75 LWD-16x-W, Tokyo, Japan). Samples were excited at 780 nm by a femtosecond Ti:Sapphire laser with ~100 fs pulse duration at 80 MHz (Tsunami, Spectra Physics, Milpitas, CA, USA). The polarization of the beam was controlled by a combination of achromatic half wave and quarter wave plates mounted on rotary stages. SHG signal was detected in transmission by a high sensitivity GaAsP photomultiplier (H7422P, Hamamatsu, Hamamatsu-city, Japan), through a 1.4-NA water-immersion condenser (U-AAC, Olympus, Tokyo, Japan), filtered by a 482 nm long pass dichroic mirror (86–331, Edmund Optics, Barrington, NJ, USA), a 550 nm short pass filter (84–708 Edmund Optics, USA) and a 447 nm high-performance band-pass filter (NT 48–074, Edmund Optics, USA). In depth, Z-stack images were recorded in a window of 410 × 410 µm², at 1024 × 1024 pixels resolution, with a 6 µm Z-step.

<figure><img src="image_6.png" /><figcaption>**Fig. 2.** Steps to measure the directionality of collagen fibers in the MPM images. A) view of furcation area; B) zooming of A; C) after tubeness filter used to enhance the filamentous structures of the specified thickness (Sato et al., 1998); D) directionality histogram (Diagram for directionality is in the range of blue); E) landmark for the measured angles.</figcaption></figure>
## 2.5. FIJI-Image J

MPM images were analyzed using ImageJ 1.54f (NIH (New York, USA)). First of all, images were stacked and grouped in Z, enhancing the contrast of the resultant image in order to delineate our region of interest (Fig. 2A). This latter was extracted from the original images (Fig. 2B) and treated with the tubeness filter in order to enhance the structure as shown in Fig. 2C. Finally, the plugin directionality was used and histograms were built (Fig. 2D) following the landmark in Fig. 2E. The average of the orientation angle of fibers and its dispersion were extracted from the histograms.

## 2.6. Statistics

One-way ANOVA was assessed for comparison of Young's modulus values. Tukey's multiple comparisons were employed after performing normality tests for comparison of mean values. Three mice were studied, analyzing for each 3 different height sections (at N1, N2 and NF levels), 8 different areas of acquisitions (MM, MB, MF, ML, DD, DB, DF and DL) for N1 and N2 and 7 different areas of acquisitions (MM, MB, ML, DD, DB, DL and FF) for NF. Statistical significance was set at *p* ≤ 0.05. Data were analyzed via the GraphPad PRISM (ver.8.4.2) software.

## 3. Results

The main challenge to perform combined AFM and MPM studies on the murine second molars periodontal ligaments was to obtain

<figure><img src="image_7.png" /><figcaption>**Fig. 3.** A) High resolution combined 3D height - Young's modulus map images recorded by AFM at the furcation level (80µm² x 80µm² [top image] and 5µm² x 5µm² [lower left image], color bars 2.5 kPa). B) Histogram of the associated Young's modulus (E) of the highlighted furcation level showing one Gaussian distribution with a mean value of 440 Pa.</figcaption></figure>
high quality cryostat sections from the apical region till the furcation region on non-demineralized mandibles. Using the adhesive films proposed by KAWAMOTO method we succeeded to obtain net mandible sections at all levels. Fig. 1C clearly shows the mesial and the distal roots in addition to the bone and the ligament at all regions in the N2 level.

## 3.1. Biomechanics of periodontal ligaments by AFM

High resolution combined 3D height-force map images were recorded in the FF region (Fig. 3). Elasticity maps reveal that the ligament in the middle of the region is softer (blue color in the Figure), becoming harder when closer to the dentine part. Fig. 3A highlights the contrast in Young modulus, this latter is in the order of 0.5 kPa for the ligament and higher than 2.5 kPa at the border of the dentine. A zoomed image was recorded in the middle of the furcation region, revealing a Young's modulus histogram with an average of 440 Pa (Fig. 3B).

At least three force maps were performed on every region of each section. The results of the calculated Young's modulus (E) are illustrated in Fig. 4. No significant differences between sections were found at the first level (N1) and the second level (N2), as shown in Figs. 4A and B. However, significant differences were found at the furcation levels (NF) between MM and DD (P = 0.0028), ML and DD (P < 0.0001), and finally DD and FF (P = 0.0003) sections, as shown in Fig. 4C. This latter Figure indicates that the MM, ML and FF (where MF and DF are in contact at the furcation level) regions are softer than the DD one.

Additionally, a comparison between N2 and NF, as well as N1 and N2, revealed no significant differences for all the regions (see supporting information Figures 1 and 2). On the other hand, comparison between N1 and NF levels revealed significant differences between N1-MM and NF-FF (p = 0.0425), N1-MM and NF-ML (p = 0.0125), N1-MB and NF-FF (p = 0.0405), N1-MB and NF-ML (p = 0.0118), and finally N1-MF and NF-ML (p = 0.0181). These results are shown in Fig. 5: Young's modulus is softer when we are close to

<figure><img src="image_8.png" /><figcaption>**Fig. 4.** Violin plot of the Young's modulus values for A) N1 level, B) N2 level and C) NF level of mandible. This chart, a combination of a box plot and a density plot, was used to display the distribution shape of the data, also including markers for the medians of the data and boxes indicating the interquartile ranges. NF, Furcation level; N2, Level 2; N1, Level 1; FF, Furcation; MM, Mesial; MB, Mesial Buccal; ML, Mesial Lingual; MF, Mesial Furcation; DF, Distal Furcation; DB, Distal Buccal; DL, Distal Lingual; DD, Distal.</figcaption></figure>
the furcation level (higher level).

## 3.2. Collagen fibers orientation in the periodontal ligaments by MPM

Eight images (one image per region) were recorded on every section using the MPM. Examples of the acquired images are shown in Fig. 6. The second harmonic generation of the collagen fibers are evident in the MF region of the mesial root at the N1 level (Fig. 6A). We can clearly differentiate between dentine, ligament and bone. Also, in the FF region between the mesial and the distal roots at the furcation level, the orientation of the fibers is noteworthy (Fig. 6B).

Using the Directionality Plugin of Image J, the orientation of collagen fibers was investigated. After evaluating the mean and the dispersion of the angle for each region and each section, circular statistics has been used to calculate the mean and the standard deviation of the θ angles according to the following equations (Mardia and Jupp, 2009):

$$avr = \arg(\langle e^{i2\theta} \rangle) / 2$$

$$Var = \langle 1 - \cos(2\theta - 2\theta_{avr}) \rangle$$

$$STD = (-2\log(1 - Var))^{1/2}$$

The fibers' orientation results are gathered in Fig. 7. Knowing that a very large error on the orientation can be obtained when positive and negative angles (blue-red or green-red respectively on the landmark (Fig. 2E)) are calculated in the same region of a level, we remained careful to make some statistics on our results. Significant differences in angles were found in the N1 level between DB and MB, ML, DL (P = 0.0039, P = 0.0280, P = 0.0120 respectively) as shown in Fig. 7A. Additionally, comparisons between angles in the N2 level revealed significant differences between DB and MB, MF, ML, DL (P = 0.0011, P = 0.0446, P < 0.0001, P = 0.0009 respectively) as well as between ML and DF (P = 0.0409) as shown in Fig. 7B. Finally, comparisons between angles in the NF level revealed significant differences for MM when compared to MB, ML, DB (P < 0.0001, P = 0.0165, P = 0.0003 respectively), MB when compared to DD, DL, FF (P < 0.0001, P < 0.0001, P < 0.0001 respectively), ML when compared to DD, DL, FF (P = 0.0069, P = 0.0001, P = 0.0090 respectively), and DB when compared to DD, DL, FF (P < 0.0001, P < 0.0001, P < 0.0001 respectively) as shown in Fig. 7C. However, no significant differences were found between the other regions. It should be pointed out that at all levels when we are localized in MM, MF, DF, DD and FF we are parallel to the x axis with angles ranging between 0° and rarely 20°. Contrariwise, when we are in MB, ML, DB and DL we are not perpendicular to the x axis with angles ranging between 35° and rarely 85.0°.

Comparisons between levels were also performed. When comparing N1 level with N2 level, significant differences in angles were found between N2-DB and N1-DL, MB, ML as well as between N1-DB and N2-ML (See supporting information Figure 3 and Table 1).

When comparing N1 level with NF level, significant differences in angles were found between NF-DB and N1-DF, DL, MB, MF, ML, MM. In the same manner, significant differences in angles were found between NF-MB and N1-DF, DL, MB, MF, ML, MM in addition to DD. Moreover, significant differences were found between NF-ML and N1-DL, MB, ML. There was also significant difference between NF-FF and N1-MB as well as between NF-DL and N1-DB (See supporting information Figure 4 and Table 2).

When comparing N2 level with NF level, significant differences in angles were found between NF-DB and N2-DD, DL, MB, MF, ML.

<figure><img src="image_9.png" /><figcaption>Fig. 5. Comparison of the Young's modulus (E) between different levels and regions of mice mandible; NF, Furcation level; N2, Level 2; N1, Level 1; FF, Furcation; MM, Mesial; MB, Mesial Buccal; ML, Mesial Lingual; MF, Mesial Furcation; DF, Distal Furcation; DB, Distal Buccal; DL, Distal Lingual; DD, Distal.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>**Fig. 6.** Second Harmonic Generation – MPM image of: A) MF region of the mesial root. B) FF region between the mesial and the distal roots in the furcation level. MF, Mesial Furcation; FF, Furcation.</figcaption></figure>

In the same manner, significant differences in angles were found between NF-MB and N2-DD, DL, MB, MF, ML in addition to DF and MM. Moreover, significant differences were found between NF-ML and N2-DL, MB, ML. There was also significant difference between NF-FF and N2-DB, ML as well as between NF-DL and N2-DB and between NF-DD and N2-DB (See supporting information Figure 5 and Table 3). However, no significant differences were found between the remaining sections.

When comparing all angles at all levels we observe that the average of the orientation angle in MB is positive in N1 and N2 and it becomes negative at NF. While in DB and DL it is always negative and positive respectively (Fig. 7A, B, C).

There was no change in the dispersion of the angles extracted from the original histograms on the ImageJ plugin at different levels and different regions (Figure not shown).

## 4. Discussion

The periodontal ligaments have been investigated mainly in terms of their histological properties and the biochemical nature of its fibers (Motoji et al., 2020). However, linking rheological properties to the ability of these fibers to stretch at any functional loads is an important item also as it is responsible for the maintenance of the root at nearly elastically fixed state (Muslov et al., 2023). Our study was able to perform mechanical and structural assessment of the murine periodontal ligaments in several multiple regions of mice mandible through measuring the Young's modulus at these sites. These findings support previous studies that assume different Young's moduli in different regions (Connizzo and Naveh, 2020; Fill et al., 2011). Analysis for the values of different moduli showed inhomogeneity in tissue properties based on the anatomical locations (Connizzo and Naveh, 2020). Compared to these reports our study explore and discuss the elastic modulus at different levels and heights of the periodontal ligament.

The rheological properties of periodontal ligament have an essential role in controlling the deformation of these ligaments (Dorow et al., 2003). The application of external forces can result in major changes of the response of alveolar bone to the remodeling process (Ho et al., 2013). Thus, differences in Young's modulus at several levels of the periodontal ligament can significantly affect the process of remodeling inside the alveolar bone (Lin et al., 2017).

Indeed our AFM results revealed significant variations in tissue elasticity in different regions of the periodontal ligament. Elasticity of periodontal ligament showed a significant softening towards the furcation. A possible explanation for this finding can be attributed to the location of the center of resistance in molar teeth. The softening can be an important property that causes the center of resistance to be considered the point of greatest resistance to tooth movement. The center of resistance in the molar teeth was predicted to be positioned between the roots and just below the furcation (Oh et al., 2019). The center of resistance is considered an analogous to the center of mass because the tooth is not a free object as it is held by periodontal ligament (Gandhi et al., 2021), therefore it can be regarded as a balancing point for restrained bodies. This is because if a force is applied to this point, the tooth will produce pure bodily movement without any tipping (Nanda et al., 2010; Kuruthukulam and Patil, 2023). The position of the center of resistance of a tooth is dependent on various morphological or compositional factors. Morphological factors include length, number and shape of the roots in addition to the level of alveolar bone height surrounding the tooth. Unlike morphological factors, compositional factors such as periodontal ligament, elasticity of desmodontal structures and density of surrounding alveolar bone can be affected by more systemic rather than local factors such as age and nutrition (Nanda, 2014; Winning et al., 2021). Thus, elasticity of periodontal ligament can be significantly influenced by the position of the center of resistance. A study conducted by Kawarizadeh et al., found that strain at furcation area of molars was significantly higher than any other area indicating lower elastic modulus, in accordance with our findings (Kawarizadeh et al., 2003). This was confirmed by another AFM study that indicated that a low Young's modulus at the furcation area serves as a cushion that absorb vertical loading (Connizzo and Naveh, 2020). Another study on living periodontal ligament using AFM showed that generally the periodontal ligament exhibited a high elastic modulus value at the cell's nuclear sites, while most of the
<figure><img src="image_11.png" /><figcaption>**Fig. 7.** Angles of collagen fibers orientation for A) N1 level, B) N2 level and C) NF level of the periodontal ligaments. NF, Furcation level; N2, Level 2; N1, Level 1; FF, Furcation; MM, Mesial; MB, Mesial Buccal; ML, Mesial Lingual; MF, Mesial Furcation; DF, Distal Furcation; DB, Distal Buccal; DL, Distal Lingual; DD, Distal.</figcaption></figure>

lower elastic modulus were found within the peripheral regions of the periodontal ligament cell. The heterogeneity in elasticity was assumed to be related to the distribution of stress fibers (Shi et al., 2010). Therefore, as demonstrated in Fig. 3, we suggest that the blue region is softer than the neighboring regions because the collagen fibers are more concentrated near the bone and/or the dentine (37). In addition to that, the longest collagen fibers inside the PDL are in the furcation region. They are attached from one side to the dentine and from the other side to the bone, rendering softer the middle region.

Liao et al., demonstrated that the computational characterization of dynamic dental structures can be conducted in the context of a predetermined or presumed PDL stiffness range. The PDL stiffness varies if an external load or orthodontic force is applied, therefore the non-linearity of the PDL Young's modulus should be considered (Liao et al., 2015).

MPM has been proven a powerful method for analysis of the morphology and directionality of collagen fibers in dental tissues. Although, using MPM in vivo can be unreliable because of the inability to control intrinsic tissue movement (Martínez-Ojeda et al., 2020) studies on excised tissues can provide valuable information on tissue organization.

Our MPM results revealed that the angle of the distal buccal surface was always negative and became more negative at the furcation level. On the other hand, the angle of the distal lingual surface was always positive and became less positive at the furcation level. We hypothesized that by the different orientation of collagen fibers in the furcation region periodontal ligaments can both provide space for tooth vertical movement with high compressive loads and prevent tooth movement in the other direction via its particular
orientation. However, no change was found in the dispersion of the angles at different levels and different regions which indicate homogeneity in the directionality of fibers across different regions. When comparing directionality of fibers on level N1 and N2, where the oblique fibers of periodontal ligament is usually found, no-significant difference between the orientation angles have been revealed (De Jong et al., 2017). On the other hand, significant differences in fibers orientation were found when comparing N1 and N2 to NF. This can be explained with the fact that the type of fibers in NF are inter-radicular between the two roots and horizontal in other areas (Gilani et al., 2021). Finally, we can hypothesize that fiber orientations can be correlated to periodontal tissue elasticity by allowing cushioning properties against both vertical and horizontal masticatory forces with a predominance of resistance to the vertical force type. This was confirmed by MPM, which revealed different orientations of collagen fibers in the furcation region in addition to the softer Young's modulus revealed by AFM. The main limitation of our study was the small sample size; therefore, future work should aim at comparing some pathologies to a control group but with a larger sample size.

**5. Conclusion**

The combination of atomic force microscope and multiphoton microscopy is a promising approach to investigate in a label-free manner the nanomechanical and structural properties of the periodontal ligament. The main highlight of our study is that the collected and sectioned mice mandibles, without any further preparation, were investigated in their whole, enabling to compare the tissue elasticity and fibers collagen orientation in the periodontal ligament at different locations, levels and to correlate these with their functional and physiological role.

The main insights revealed by this study are the following:

* The elasticity of the periodontal ligament showed a significant tendency to become softer towards the furcation, which is the nearest area to the center of resistance of the tooth. Additionally, it was found that there were no significant differences between N2-sections (level 2) and NF-sections (furcation level), as well as between the N1 and N2 sections (level 1 and 2) for all the regions.

* The orientation of fibers in the furcation region can both provide space for tooth vertical movement with high compressive loads and prevent horizontal tooth movement.

* The dispersion of the angles at different levels of cutting indicates homogeneity in the directionality of fibers across different regions.

**CRediT authorship contribution statement**

**Mahmoud Sedky Adly:** Writing – review & editing, Writing – original draft, Visualization, Methodology, Investigation, Conceptualization. **Richard Younes:** Methodology. **Marta Martin:** Methodology, Conceptualization. **Thierry Cloitre:** Methodology, Conceptualization. **Afnan Sedky Adly:** Writing – review & editing. **Ivan Panayotov:** Methodology, Conceptualization. **Philippe Bousquet:** Writing – review & editing, Visualization, Supervision, Methodology, Investigation, Conceptualization. **Csilla Gergely:** Writing – review & editing, Visualization, Supervision, Methodology, Investigation, Conceptualization. **Frederic J.G. Cuisinier:** Writing – review & editing, Visualization, Supervision, Methodology, Investigation, Conceptualization. **Delphine Carayon:** Writing – review & editing, Visualization, Supervision, Methodology, Investigation, Conceptualization. **Elias Estephan:** Writing – review & editing, Visualization, Supervision, Methodology, Investigation, 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.

**Data availability**

Data will be made available on request.

**Acknowledgments**

We gratefully acknowledge Dr. Vasiliki Kalatzis for her help concerning the microcryostat experiments. We also thank Antoine Picot and Denis Greuet who provided expertise in animal experiments. Finally, we acknowledge and express gratitude to EDMOS platform.

**Supplementary materials**

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.jmps.2024.105715.
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