Bone turnover and mineralisation kinetics control trabecular BMDD and apparent bone density: insights from a discrete statistical bone remodelling model
Bibliographic record
Abstract
Abstract The mechanical quality of trabecular bone is influenced by its mineral content and spatial distribution, which is controlled by bone remodelling and mineralisation. Mineralisation kinetics occur in two phases: a fast primary mineralisation and a secondary mineralisation that can last from several months to years. Variations in bone turnover and mineralisation kinetics can be observed in the bone mineral density distribution (BMDD). Here, we propose a statistical spatio-temporal bone remodelling model to study the effects of bone turnover (associated with the activation frequency $$\mathrm {Ac.f}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Ac</mml:mi> <mml:mo>.</mml:mo> <mml:mi>f</mml:mi> </mml:mrow> </mml:math> ) and mineralisation kinetics (associated with secondary mineralisation $$T_\textrm{sec}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mtext>sec</mml:mtext> </mml:msub> </mml:math> ) on BMDD. In this model, individual basic multicellular units (BMUs) are activated discretely on trabecular surfaces that undergo typical bone remodelling periods. Our results highlight that trabecular BMDD is strongly regulated by $$\mathrm {Ac.f}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Ac</mml:mi> <mml:mo>.</mml:mo> <mml:mi>f</mml:mi> </mml:mrow> </mml:math> and $$T_\textrm{sec}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mtext>sec</mml:mtext> </mml:msub> </mml:math> in a coupled way. Ca wt% increases with lower $$\mathrm {Ac.f}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Ac</mml:mi> <mml:mo>.</mml:mo> <mml:mi>f</mml:mi> </mml:mrow> </mml:math> and short $$T_\textrm{sec}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mtext>sec</mml:mtext> </mml:msub> </mml:math> . For example, a $$\mathrm {Ac.f}=$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mi>Ac</mml:mi> <mml:mo>.</mml:mo> <mml:mi>f</mml:mi> </mml:mrow> <mml:mo>=</mml:mo> </mml:mrow> </mml:math> 4 BMU/year/mm $$^3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mn>3</mml:mn> </mml:msup> </mml:math> and $$T_\textrm{sec}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mtext>sec</mml:mtext> </mml:msub> </mml:math> = 8 years result in a mean Ca wt% of 25, which is in accordance with Ca wt% values reported in quantitative backscattered electron imaging (qBEI) experiments. However, for lower $$\mathrm {Ac.f}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Ac</mml:mi> <mml:mo>.</mml:mo> <mml:mi>f</mml:mi> </mml:mrow> </mml:math> and shorter $$T_\textrm{sec}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mtext>sec</mml:mtext> </mml:msub> </mml:math> (from 0.5 to 4 years) one obtains a high Ca wt% and a very narrow skew BMDD to the right. This close link between $$\mathrm {Ac.f}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Ac</mml:mi> <mml:mo>.</mml:mo> <mml:mi>f</mml:mi> </mml:mrow> </mml:math> and $$T_\textrm{sec}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mtext>sec</mml:mtext> </mml:msub> </mml:math> highlights the importance of considering both characteristics to draw meaningful conclusion about bone quality. Overall, this model represents a new approach to modelling healthy and diseased bone and can aid in developing deeper insights into disease states like osteoporosis.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".