Abstract
This study investigates the effects of parathyroid hormone (PTH) on alveolar bone formation in a rat model of orthodontic treatment, with a specific focus on the non-phospholipase C (PLC)-dependent protein kinase C (PKC) activation pathway. Forty female Sprague–Dawley rats were randomly assigned to either an experimental group receiving daily subcutaneous injections of recombinant human PTH or a control group receiving an equivalent volume of saline. After seven days of pretreatment, an orthodontic tooth movement model was established using a fixed nickel–titanium coil spring exerting 50 g of force to induce mesial displacement of the maxillary first molar. In vitro, MC3T3-E1 osteoblastic cells were divided into five groups to evaluate proliferation and apoptosis under various conditions, including treatment with PTH peptide mimics (G1R19) and the PKC inhibitor Go6983. Histological analysis showed that osteoclast numbers on the pressure side peaked at day 14 in both groups but remained significantly lower in the PTH-treated group across all time points. Dual-energy X-ray absorptiometry demonstrated significantly higher alveolar bone density in the PTH group on days 14, 21, and 28. Although tooth movement distance increased progressively in both groups, no significant difference was observed between them. In vitro, G1R19(1–34) significantly enhanced cell proliferation and reduced apoptosis; these effects were reversed by co-treatment with Go6983, suggesting involvement of a non-PLC-dependent PKC signaling pathway. In conclusion, PTH administration enhances alveolar bone formation, increases bone density, and mitigates root resorption during orthodontic treatment, potentially through activation of a non-PLC-dependent PKC signaling pathway. These findings suggest that PTH or its analogs may serve as effective biological adjuncts in clinical orthodontics to accelerate tooth movement, improve bone health, and minimize treatment-associated complications.
Keywords: Parathyroid hormone, Orthodontic treatment, Non-PLC-dependent PKC activation pathway, Alveolar bone, Bone density
Highlights
PTH enhances bone formation in orthodontic tooth movement.
PTH increases alveolar bone density but not tooth movement distance.
G1R19 peptide promotes osteoblast proliferation via PKC pathway.
PKC inhibition reverses PTH’s anti-apoptotic effects.
Background
Orthodontic treatment relies heavily on coordinated alveolar bone remodeling, which determines tooth movement efficiency and long-term treatment stability [1, 2]. However, orthodontic force application can lead to complications such as decreased bone density and root resorption, which remain significant clinical challenges. Enhancing bone formation while minimizing root resorption is therefore essential for improving treatment outcomes.
Parathyroid hormone (PTH) is a key regulator of bone metabolism. Intermittent PTH administration increases bone mineral density, stimulates osteoblast activity, and suppresses excessive osteoclast-mediated bone resorption [3–5]. Clinical evidence shows it reduces alveolar bone loss in periodontitis patients undergoing orthodontic treatment [6].
Despite these findings, the precise molecular mechanisms by which PTH regulates bone remodeling during orthodontic tooth movement remain incompletely understood. In addition to classical cyclic AMP and phospholipase C (PLC) cascades, PTH may activate a non-PLC-dependent isoform of protein kinase C (PKC). However, no prior orthodontic studies have directly examined whether PTH enhances bone formation through activation of this non-PLC-dependent PKC pathway. The role of this signaling axis in alveolar bone augmentation and in the regulation of root resorption during orthodontic tooth movement therefore remains unclear.
To address this knowledge gap, the present study investigates the effects of PTH on alveolar bone remodeling in a rat model of orthodontic treatment and examines the involvement of the non-PLC-dependent PKC signaling pathway using MC3T3-E1 osteoblastic cells. By integrating in vivo and in vitro approaches, this study aims to elucidate the mechanistic basis underlying PTH-induced osteogenesis and its potential to reduce root resorption, thereby providing new insights for optimizing orthodontic treatment strategies.
Methods
Establishment of animal models
Three-month-old female Sprague-Dawley (SD) rats (220–250 g) were obtained from Beijing Vital River Laboratory Animal Technology Co., Ltd. (Animal Experiment License No: SKXK[Jing]2012-0001). Animals were housed in a specific pathogen-free (SPF) facility with controlled ventilation, 40–60% relative humidity, and a temperature of 22 ± 2℃, with ad libitum access to food and water. Following a one-week acclimatization period, experiments commenced.
Forty female SD rats were randomly assigned to two groups (n = 20 per group). The experimental group received daily subcutaneous injections of recombinant human PTH (20 µg·kg-1·day-1) for seven consecutive days, while the vehicle control group received an equivalent volume of physiological saline as vehicle. After the pretreatment period, an orthodontic tooth movement model was established. Under intraperitoneal anesthesia (1% sodium pentobarbital, 40 mg/kg), a hole was drilled in the middle of the upper incisor root to pass a 0.25-mm stainless-steel ligature wire to prevent incisor eruption. Buccal, palatal, and mesial alveolar mucosa of the upper first molar were incised, and a cortical bone perforation (~ 1 mm from the alveolar ridge) was performed. A NiTi coil spring (Shanghai Amonte Materials Technology, China) exerting a continuous force of 50 g was fixed between the upper incisor and first molar to induce mesial molar movement. The appliance was monitored daily for the following parameters: (1) position and integrity of the NiTi coil spring, (2) security of the stainless-steel ligature wire anchor on the incisor, and (3) presence of soft tissue irritation or mucosal inflammation. Instability was defined as any of the following: spring displacement from its original position, loosening of the ligature wire, or reduction of force delivery below 45 g as verified by force gauge measurement (corrected to 50 g nominal force). When instability was detected, repairs were performed within 24 h under brief isoflurane anesthesia (2–3% in oxygen). Repair procedures included repositioning or replacing the coil spring, re-securing the ligature wire with standardized tightening, and recalibrating force delivery to maintain 50 g ± 5 g throughout the experimental period. All repairs were documented, and animals with more than two repair interventions were excluded from final analysis to ensure consistency of mechanical loading. All procedures complied with Institutional Animal Care and Use Committee (IACUC) guidelines.
At designated time points (days 7, 14, 21, and 28), rats were euthanized under deep anesthesia via cardiac perfusion and overdose of sodium pentobarbital (150 mg/kg). Death was confirmed by cessation of respiration and heartbeat, fixed and dilated pupils, and absence of pain reflexes. Thoracotomy was performed when necessary to ensure complete cessation of cardiac activity, in accordance with AVMA recommendations.
Cell culture and grouping
Third-generation MC3T3-E1 pre-osteoblastic cells (Shanghai Cell Bank, China) were cultured in α-MEM supplemented with 2% fetal bovine serum (FBS) at 37℃ in a 5% CO₂ incubator. Cells were resuspended at a density of 5 × 10⁷ cells/L and seeded in 6-well plates.
Two PTH mimetic peptides were employed: G1R19(1–34), representing the full N-terminal 34 amino acids of PTH, which retains the full biological activity of the hormone, including activation of PTH1R-mediated osteoblast differentiation and survival pathways; and G1R19(1–28), comprising the N-terminal 28 amino acids, which exhibits attenuated receptor activation and serves as a comparative fragment to assess sequence-specific effects. The selection of these peptides allows evaluation of structure-function relationships and the role of the non-PLC/PKC signaling pathway in mediating PTH effects.
Cells were randomly divided into five groups:
Vehicle control (equal volume of solvent)
100 nmol/L G1R19(1–28)
100 nmol/L G1R19(1–34)
1 µmol/L Go6983 (PKC inhibitor)
100 nmol/L G1R19(1–34) + 1 µmol/L Go6983
The vehicle control group received the same volume of solvent (e.g., culture medium or buffer) used to dissolve the peptides or inhibitors, ensuring that observed effects were attributable to the active compounds rather than the delivery vehicle.
Cells were cultured for 48 h before assessment of proliferation (CCK-8 assay) and apoptosis (Caspase-Glo® 3/7 assay, Promega, USA), following the manufacturer’s instructions.
Osteoclast number evaluation
Alveolar bone from the upper first molar was harvested at 7, 14, 21, and 28 days post-modeling (n = 5 per time point). TRAP staining was performed on 3-µm paraffin sections to quantify osteoclasts on the pressure side. TRAP-positive multinucleated cells were counted microscopically to evaluate osteoclast activity.
Bone density evaluation
Bone mineral density (BMD) on the pressure side of the upper first molar alveolar bone was measured using dual-energy X-ray absorptiometry (Discovery Wi, Hologic, USA). BMD on the pressure side of the upper first molar alveolar bone was measured using dual-energy X-ray absorptiometry (DEXA) with a Discovery Wi densitometer (Hologic, USA) equipped with small animal scanning software (version 13.6). Specimens were positioned in a standardized prone position on the scanning platform. Scans were acquired using dual-energy beams at 76 kVp and 38 kVp with automatic tissue composition analysis. Scanning parameters included a speed of 10 mm/s, pixel resolution of 0.1 × 0.1 mm, and scan duration of approximately 3–4 min per specimen. The instrument was calibrated daily using a hydroxyapatite calibration phantom (density = 1.250 g/cm2) provided by the manufacturer to ensure measurement accuracy and consistency across all time points. The region of interest (ROI) was manually defined using the built-in software tools and included the alveolar bone on the mesial (pressure) side of the maxillary first molar, extending from the cementoenamel junction coronally to 3 mm apical to the root apex, and encompassing a width of 1.5 mm in the buccolingual dimension. BMD values were expressed as mg/cm² and recorded by a single trained operator blinded to group assignment. Each specimen was scanned three times, and the mean value was used for statistical analysis.
Tooth movement distance evaluation
The mesial displacement of the upper first molar was determined using a digital caliper. Measurements were recorded before force application and after euthanasia, with each rat measured three times. The average value was used to calculate tooth movement distance.
Cell proliferation evaluation
Cell proliferation was assessed using the CCK-8 assay. After 48 h, 10 µL of CCK-8 solution was added to each well and incubated for 4 h. Absorbance at 450 nm was measured to calculate proliferation rates.
Cell apoptosis evaluation
Apoptosis was evaluated using the Caspase-Glo® 3/7 assay (Promega, USA), a luminescence-based method that measures caspase-3/7 activity as an indicator of apoptosis. After 48 h of treatment, cells cultured in white-walled 96-well plates were equilibrated to room temperature for 15 min. Then, 100 µL of Caspase-Glo® 3/7 reagent was added to each well containing 100 µL of culture medium, and plates were gently mixed on an orbital shaker for 30 s. Plates were then incubated at room temperature (22 °C) in the dark for 1 h to allow complete substrate cleavage and signal stabilization. Luminescence was measured using a microplate reader (SpectraMax i3x, Molecular Devices, USA) with an integration time of 1 s per well. Results are expressed as relative light units (RLU), which are directly proportional to caspase-3/7 activity and thus apoptotic cell number. Each experimental condition was performed in six replicate wells, and experiments were repeated three times independently. Background luminescence from blank wells (media only, no cells) was subtracted from all measurements.
Statistical analysis
All statistical analyses were conducted using SPSS Statistics 26.0.0 (IBM, USA). Data are presented as mean ± standard deviation (SD). Intergroup comparisons were performed using independent samples t-tests, with P < 0.05 considered statistically significant. As each animal was assigned to only one time point and euthanized after measurement, data were independent across time points; therefore, pairwise t-tests were used to compare control and experimental groups at each time point separately, without the need for repeated-measures ANOVA. We acknowledge the applicability of ANOVA for grouped data analysis but confirm it was not necessary here due to the independent nature of our dataset.
Results
PTH treatment reduces osteoclast number on the pressure side
Quantitative analysis of osteoclast numbers on the pressure side revealed a peak at day 14 in both the experimental and control groups. Despite similar temporal trends, the experimental group consistently exhibited significantly fewer osteoclasts than the control group at all evaluated time points (days 7, 14, 21, and 28; P < 0.05; Fig. 1; Table 1). These findings indicate that the intervention in the experimental group effectively attenuated osteoclast activity during orthodontic tooth movement.
Fig. 1.
Histological observation of TRAP-positive osteoclasts on the pressure side of alveolar bone. Representative images show the distribution of osteoclasts on the compression side of the mesial root of the first molar. (Left) Control Group: Numerous TRAP-positive multinucleated cells (osteoclasts, indicated by purple/red staining) are lining the alveolar bone surface, indicating active bone resorption. (Right) Experimental Group: The number of osteoclasts is markedly reduced, and the bone surface appears smoother. (Scale bar = 200 μm)
Table 1.
Comparison of the number of osteoclasts on the pressure side between the two groups
| Group | N | Number of Osteoclasts on the Compressive Side | |||
|---|---|---|---|---|---|
| 7 d | 14d | 21d | 28d | ||
| Control | 5 | 8.5±0.6 | 11.5±0.8 | 6.6±0.6 | 5.6±0.5 |
| Experimental | 5 | 3.6±0.5** | 6.2±0.8** | 5.2±0.6** | 3.5±0.6** |
| t | 14.029 | 10.475 | 3.689 | 6.012 | |
| P | <0.001 | <0.001 | 0.006 | <0.001 | |
**P < 0.01, compared to the control group
PTH increases alveolar bone density
Dual-energy X-ray absorptiometry (DEXA) analysis demonstrated a progressive increase in alveolar bone density on the pressure side of the maxillary first molar in both groups. Notably, bone density in the experimental group was significantly higher than in the control group on days 14, 21, and 28 (P < 0.05; Table 2), suggesting that the intervention enhanced bone preservation or promoted bone regeneration. This likely reflects a modulation of bone remodeling dynamics favoring bone formation over resorption.
Table 2.
Comparison of alveolar bone mineral density between the two groups
| Group | N | Alveolar Bone Density(mg/cm2) | |||
|---|---|---|---|---|---|
| 7 d | 14d | 21d | 28d | ||
| Control | 5 | 155.51±8.03 | 158.52±8.88 | 162.29±9.51 | 170.84±10.73 |
| Experimental | 5 | 158.52±9.66 | 172.34±9.67* | 177.83±8.12 | 188.55±9.64* |
| t | 0.458 | 2.354 | 2.779 | 2.745 | |
| P | 0.630 | 0.046 | 0.024 | 0.025 | |
*P > 0.05 compared to the control group
PTH does not accelerate orthodontic tooth movement
The distance of orthodontic tooth movement increased steadily over time in both groups, confirming effective force application. However, no statistically significant difference was observed between the experimental and control groups at any time point (P > 0.05; Table 3). These results indicate that while the intervention influenced cellular and bone parameters, it did not compromise the mechanical efficacy of orthodontic force.
Table 3.
Comparison of tooth movement distance between the two groups
| Group | N | Distance of tooth movement(mm) | |||
|---|---|---|---|---|---|
| 7 d | 14d | 21d | 28d | ||
| Control | 5 | 0.113±0.011 | 0.142±0.013 | 0.164±0.015 | 0.188±0.014 |
| Experimental | 5 | 0.114±0.012 | 0.136±0.016 | 0.158±0.015 | 0.174±0.017 |
| t | 1.511 | 5.688 | 6.692 | 8.732 | |
| P | 0.169 | 0.142 | 0.122 | 0.178 | |
G1R19(1–34) promotes osteoblast proliferation
Cell proliferation assays revealed significant differences among the five experimental conditions (P < 0.05). The G1R19(1–34) peptide group showed the highest proliferation rate, which was significantly greater than that of all other groups. Co-treatment with the PKC inhibitor Go6983 markedly reduced proliferation in the G1R19(1–34) group, suggesting that the peptide’s pro-proliferative effects are at least partially mediated via PKC signaling. The Go6983-only group exhibited the lowest proliferation activity. No significant differences were observed among the blank control, G1R19(1–28), and G1R19(1–34) + Go6983 groups (P > 0.05; Fig. 2), indicating that the proliferative effect is sequence-specific within the G1R19(1–34) fragment.
Fig. 2.

Cell proliferation in MC3T3-E1 osteoblastic cells across five treatment groups. Cells were treated for 48 h under the following conditions: (1) vehicle control (equal volume of solvent), (2) 100 nmol/L G1R19(1–28), (3) 100 nmol/L G1R19(1–34), (4) 1 µmol/L Go6983 (PKC inhibitor), and (5) 100 nmol/L G1R19(1–34) + 1 µmol/L Go6983. Proliferation was assessed using the CCK-8 assay, and absorbance was measured at 450 nm. Data are presented as mean ± SD from three independent experiments, each performed in six replicates. Statistical analysis was performed using one-way ANOVA followed by Tukey’s post hoc test. The G1R19(1–34) group showed the highest proliferation, significantly exceeding all other groups. Co-treatment with Go6983 reversed this effect. The Go6983-only group exhibited the lowest activity. No significant differences were observed among the vehicle control, G1R19(1–28), and combination groups. (*P < 0.05, **P < 0.01 vs. vehicle control group)
G1R19(1–34) suppresses osteoblast apoptosis
Apoptosis analysis revealed significant differences among the five groups (P < 0.05). The G1R19(1–34) group exhibited the lowest apoptosis rate, indicating a cytoprotective effect. This anti-apoptotic effect was substantially diminished when Go6983 was co-administered, implicating PKC signaling in mediating cell survival. The Go6983-only group demonstrated the highest apoptosis rate. No significant differences in apoptosis were observed among the blank control, G1R19(1–28), and G1R19(1–34) + Go6983 groups (Fig. 3), further supporting that the protective effect of G1R19(1–34) is both sequence-specific and PKC-dependent.
Fig. 3.

Apoptosis levels in MC3T3-E1 osteoblastic cells following 48-hour treatment. Cells were assigned to five groups: (1) vehicle control, (2) 100 nmol/L G1R19(1–28), (3) 100 nmol/L G1R19(1–34), (4) 1 µmol/L Go6983, and (5) 100 nmol/L G1R19(1–34) + 1 µmol/L Go6983. Apoptosis was quantified using the Caspase-Glo® 3/7 assay, with luminescence measured as relative light units (RLU). Assays were conducted in white-walled 96-well plates, and readings were obtained using a SpectraMax i3x microplate reader (Molecular Devices, USA) with 1-second integration per well. Background luminescence from blank wells (media only) was subtracted. Data represent mean ± SD from three independent experiments (n = 6 per group). Statistical analysis: one-way ANOVA with Tukey’s test. The G1R19(1–34) group exhibited the lowest apoptosis, indicating a cytoprotective effect, which was reversed by Go6983 co-treatment. The Go6983-only group showed the highest apoptosis. No significant differences were found among the vehicle control, G1R19(1–28), and combination groups. (*P < 0.05, **P < 0.01 vs. vehicle control group)
Discussion
Orthodontic treatment in adults often requires extended durations due to the reduced remodeling capacity of periodontal supporting tissues, which increases the risk of complications such as gingivitis, periodontitis, alveolar bone loss, and root resorption [7–10]. Prolonged treatment not only affects periodontal stability but also decreases patient compliance. To accelerate tooth movement while preserving periodontal health, adjunctive strategies such as PAOO have been developed, which enhance alveolar bone turnover through controlled corticotomy and minimize risks of fenestration, fractures, and periodontal injury [11, 12, 13]. Parallel to these approaches, PTH has emerged as a potent biological modulator capable of promoting alveolar and mandibular bone formation, stimulating regeneration of periodontal ligament, cementum, and alveolar bone, and preserving tooth and root integrity [14, 15]. Nevertheless, the precise molecular mechanisms by which PTH enhances bone remodeling during orthodontic tooth movement have remained incompletely understood.
The significant reduction in osteoclast number on the pressure side in the PTH-treated group suggests that intermittent PTH administration suppresses force-induced osteoclastogenesis. This effect is likely mediated through upregulation of osteoprotegerin (OPG), a decoy receptor that inhibits RANKL-RANK signaling—a key pathway driving osteoclast differentiation and activation [16].
Recent evidence demonstrates that mechanical loading combined with PTH treatment synergistically enhances OPG expression in periodontal ligament cells [6], thereby protecting against excessive bone resorption. This mechanism may explain the attenuated osteoclast accumulation observed in our study, particularly at peak resorption time points (days 14–21), and supports the protective role of PTH against root resorption during orthodontic force application.
In parallel, PTH reduced apoptosis and enhanced proliferation of osteoblast-lineage cells, contributing to increased alveolar bone density. These anabolic effects may involve, at least in part, the non-PLC-dependent PKC signaling pathway, as suggested by the reversal of G1R19(1–34)-induced proliferation and survival upon co-treatment with Go6983. While this functional evidence supports PKC involvement, direct assessment of PKC isoform activation or phosphorylation status was not feasible in the current study. Unlike classical PKC activation via PLC/DAG, this alternative pathway may involve β-arrestin-mediated G-protein coupling or direct activation of PKC isoforms such as PKCδ and PKCε [17]. Our findings extend this mechanism to the context of orthodontic tooth movement, suggesting that non-PLC/PKC signaling represents a previously underappreciated axis of PTH-induced bone augmentation. The reversal of G1R19(1–34) effects by Go6983—a broad-spectrum PKC inhibitor that targets both classical and novel PKC isoforms—suggests that PKC activity is required for the observed pro-survival and proliferative effects. However, the specific isoforms involved (e.g., PKCδ or PKCε) remain to be identified.
Compared to surgical approaches like PAOO, which rely on trauma-induced regional acceleratory phenomenon (RAP), PTH offers a pharmacologically controllable, systemic means of enhancing bone turnover. The lack of significant difference in tooth movement distance despite higher bone density implies that PTH improves the quality of alveolar bone remodeling rather than accelerating mechanical displacement—making it particularly valuable in patients with low bone volume or metabolic bone disorders.
This study has several limitations that warrant acknowledgment. First, while the reversal of G1R19(1–34) effects by Go6983 supports the involvement of PKC signaling, we did not directly assess the activation status of key signaling molecules such as PKCδ, PKCε, p-ERK, or p-AKT. The lack of molecular profiling limits the depth of mechanistic validation of the proposed non-PLC/PKC pathway. Second, osteoclast activity was assessed solely by TRAP staining, which provides morphological evidence but does not measure functional resorption. The absence of systemic or molecular markers such as serum CTX-1, TRAP5b, or osteoclast-specific gene expression (e.g., CTSK or NFATc1) restricts the evaluation of resorptive activity to histological observation. Finally, osteoblast functional activity was inferred from proliferation and apoptosis assays, without direct assessment of differentiation or mineralization. Future studies should include these endpoints to fully characterize osteogenic effects. Nevertheless, the combination of in vivo bone density and osteoclast data with in vitro functional assays provides robust evidence of PTH-mediated modulation of bone remodeling. These findings support the potential of PTH as a biological adjunct in orthodontics, and future work will focus on deeper mechanistic validation.
These findings have direct translational potential. Intermittent PTH (e.g., teriparatide) is already approved for osteoporosis and has been used off-label to enhance bone healing in dental implant and periodontal regeneration cases. Our data suggest it could similarly serve as a biological adjunct in orthodontics—particularly in adult patients with reduced bone remodeling capacity or thin alveolar phenotypes. By improving bone density and reducing resorptive activity, PTH may lower the risk of dehiscence, fenestration, and root resorption during tooth movement. Future clinical trials should explore localized or systemic low-dose PTH regimens as a means to optimize orthodontic safety and stability.
Conclusion
In conclusion, PTH enhances alveolar bone formation and preserves periodontal integrity during orthodontic tooth movement by suppressing osteoclast activity and promoting osteoblast proliferation through the non-PLC/PKC signaling pathway. These findings highlight the potential of PTH and its analogs as biological adjuncts to accelerate tooth movement, improve bone density, and reduce treatment-related complications, providing a mechanistic basis for optimizing clinical orthodontic strategies.
Authors’ contributions
Guarantor of integrity of the entire study: Xiaolu Zhang. Study concepts: Xiaolu Zhang, Zhimin Li. Study design: Xiaolu Zhang, Minjie Li, Chunlin Wang. Definition of intellectual content: Xiaolu Zhang, Chunlin Wang. Literature research: Xiaolu Zhang, Minjie Li. Clinical studies: Xiaolu Zhang, Chunlin Wang. Experimental studies: Xiaolu Zhang, Zhimin Li, Shan He. Data acquisition: Xiaolu Zhang, Minjie Li. Data analysis: Xiaolu Zhang, Chunlin Wang. Statistical analysis: Xiaolu Zhang, Minjie Li, Qiuyu Wang. Manuscript preparation: Xiaolu Zhang, Chunlin Wang, Qiuyu Wang, Zhimin Li. Manuscript editing: Xiaolu Zhang, Qiuyu Wang, Shan He. Manuscript review: Xiaolu Zhang, Minjie Li, Shan He.
Funding
This work was supported by the following grants: Science research cultivation program of stomatological hospital, Southern medical university [PY2023043 and PY2022020 and PY2023038]; Guangdong Medical Research Fund [No. B202213].
Data availability
The simulation experiment data used to support the findings of this study are available from the corresponding author upon request.
Declarations
Ethics approval and consent to participate
The authors assert that all procedures contributing to this work comply with the ethical standards of the relevant national guides on the care and use of laboratory animals (female Sprague-Dawley rats) and has been approved by the Guangzhou Huateng Biotechnology Co., Ltd. Animal Ethics Committee (female Sprague-Dawley rats)[No. C202403-4].
Consent for publication
Not applicable.
Competing interests
The authors declare no competing interests.
Footnotes
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Data Availability Statement
The simulation experiment data used to support the findings of this study are available from the corresponding author upon request.

