Prediction of Cortical Bone Thickness Variations in the Tibial Diaphysis of Running Rats
Abstract
:1. Introduction
2. Experiments
- Sedentary control group: the rats were 26.7 (±1.1) cm long and weighed 492.1 (±34.6) g. They were left to their everyday activity (eating and walking), without any specific running activity, for 8 weeks. At the end of this program, the mean cortical bone thickness of the tibial diaphysis was 957 (±110) µm. This value was normalized to 1 to facilitate comparisons between groups. The mechanical load (body weight) for the bone remodeling was assumed to be constant over time.
- Continuous running group: the rats were 26.4 (±0.7) cm long and weighed 486.4 (±31.8) g. This group was subjected to 8 weeks of running for 45 min per day at an intensity of 70% of the maximal aerobic speed (MAS) (Figure 1a). At the end of the exercise program, the mean cortical bone thickness of the tibial diaphysis was 708 µm (±65 µm).
- Intermittent running group: the rats were 26.5 (±0.6) cm long and weighed 475.1 (±30.3) g. This group was subjected to an interval-training running activity for 42 min per day for 8 weeks. This protocol consisted in 7 repetitions of blocks of 3 min at 50% of the MAS, followed by 2 min at 100% of the MAS and 1 min of passive rest (Figure 1b). At the end of the exercise program, the mean cortical bone thickness of the tibial diaphysis was 1024 (±112) µm.
2.1. Post-Mortem Micro-Computed Tomography (µCT) and Computation
2.2. Bone Histology
2.3. Occupation Rate of Osteocyte Lacunae
2.4. TRAP Histochemistry
2.5. Statistical Analysis
3. Theoretical Model
3.1. Theory
- -
- In the trabecular bone (center part), cells are located in the bone marrow and are ready to be biologically activated. However, they are not very active, as they are far away from the cortical-trabecular interface and the mechanical support of the bone.
- -
- Around the cortical-trabecular interface (on each side) is where the cell activity is at its maximum for the bone remodeling to occur.
- -
- In the cortical bone, mainly osteocytes are present to sense the mechanical load, without osteoblasts and with a minority of osteoclasts; hence almost no bone remodeling occurs.
3.2. Application
3.3. Parameter Identification
- -
- W0: Homeostasis, where no bone density variation occurs within the sedentary control group. It was evaluated directly from the rat body weight and bone geometry at the beginning of the experiments using the standard mechanics of elasticity.
- -
- W1: Energy for the maximum mineral bone density increase, assumed to correspond to the bone density increase after 8 weeks of exercise in the intermittent running group. It was evaluated from the experimental data. This energy was extrapolated from the maximum cortical bone thickness observed experimentally in the intermittent running scenario.
- -
- W3: The energy level corresponding to the maximum resorption rate (depending on cell availability), whatever the extra-increase in the mechanical energy. It was assumed to be the maximum degradation rate observed in the continuous running group after 8 weeks of running with the minimum cortical bone thickness.
- -
- W2: The threshold energy level at which bone density will start to decrease if the energy level increases. It corresponds to the linear interpolation between W1 and W3, where osteoblast and osteoclast activity are considered to be equal.
4. Results and Discussion
4.1. Numerical Model Parameter Identification
4.2. Theoretical Model Results
4.3. Bone Density Prediction
4.3.1. Intermittent Running Scenario
4.3.2. Continuous Running Scenario
4.4. Correlation between Cell Scale Experimental Results and Bone Scale Numerical Results
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Sedentary Control | Continuous Running | Intermittent Running | |
---|---|---|---|
Cortical tibial thickness (µm) | 957 (±110) Normalized = 1 | 708 (±65) Normalized = 0.74 | 1024 (±112) Normalized = 1.07 |
Loading type | Constant load (body weight) | 1 week for 25 min/day, 8 weeks for 45 min/day, Oxygen = 70% MAS | 1 week for 25 min/day continuous, 8 weeks intermittent for 42 min/day, Oxygen = 50%, 100% MASand rest |
Sedentary Control | Continuous Running | Intermittent Running | |
---|---|---|---|
BMD (g HA/cm3) | 113.11 (± 4.12) | 109.16 (± 4.31) * | 106.13 (± 4.22) * |
Parameters Determined from Experimental Data (×10−4 mJ) | Parameters Calculated (ki = mg·mJ−1·mm−3·56d−1; Ai = mg·mm−3·56d−1) | ||||||
---|---|---|---|---|---|---|---|
W0 | W1 | W2 | W3 | k1 | k2 | A1 | A2 |
3.1847 | 3.7 | 3.72 | 3.78 | 386.64 × 105 | −375 × 105 | 1992.36 | −2232.38 |
Osteoblast Activity Coefficient at W1 | Osteoclast Activity Coefficient at W1 | Osteoblast Activity Coefficient at W3 | Osteoclast Activity Coefficient at W3 | Cellular Activity Power at W1 | Cellular Activity Power at W3 |
---|---|---|---|---|---|
α = 1.0009 | α = 1.0 | α = 1.0007 | α = 1.0 | n = 13.6 | n = 5 |
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George, D.; Pallu, S.; Bourzac, C.; Wazzani, R.; Allena, R.; Rémond, Y.; Portier, H. Prediction of Cortical Bone Thickness Variations in the Tibial Diaphysis of Running Rats. Life 2022, 12, 233. https://doi.org/10.3390/life12020233
George D, Pallu S, Bourzac C, Wazzani R, Allena R, Rémond Y, Portier H. Prediction of Cortical Bone Thickness Variations in the Tibial Diaphysis of Running Rats. Life. 2022; 12(2):233. https://doi.org/10.3390/life12020233
Chicago/Turabian StyleGeorge, Daniel, Stéphane Pallu, Céline Bourzac, Rkia Wazzani, Rachele Allena, Yves Rémond, and Hugues Portier. 2022. "Prediction of Cortical Bone Thickness Variations in the Tibial Diaphysis of Running Rats" Life 12, no. 2: 233. https://doi.org/10.3390/life12020233