# Predicting Bone Adaptation in Astronauts during and after Spaceflight

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## Abstract

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^{2}> 0.94) and statistically different (p < 0.0001) but with errors close to HR-pQCT precision limits. Dynamic morphometry, which captures rates of bone adaptation, was poorly estimated by our model (p < 0.0001). The Dice coefficient and symmetric distance indicated a reasonable local fit between observed and predicted bone volumes. This work applies a general and versatile computational framework to test bone adaptation models. Future work can explore and test increasingly sophisticated models (e.g., those including load or physiological factors) on a participant-specific basis.

## 1. Introduction

## 2. Methods

#### 2.1. Participants and HR-pQCT Image Acquisition

^{2}(2.1). One participant did not complete all measurements and was excluded, leaving 16 participants in the study. Participants gave written informed consent, and the study was approved by the University of Calgary Conjoint Health Research Ethics Board (REB14-0573), NASA Institutional Review Board (NASA7116301606HR), ESA Human Research Multilateral Review Board, and JAXA International Review Board for Human Research.

#### 2.2. Image Pre-Processing

#### 2.3. Computational Technique

^{−5}and $\gamma $ = 5 × 10

^{−4}from a sensitivity analysis for this specific astronaut population. Convergence for the inverse solver was defined as the L2 norm $|{\stackrel{\u20d1}{\theta}}^{k+1}-{\stackrel{\u20d1}{\theta}}^{k}|<$ 1 × 10

^{−8}where $k$ is the iteration number in gradient descent. We noted that simulations that exceeded 4000 iterations would likely never converge and were excluded.

#### 2.4. Morphometry and Surface Metrics

#### 2.5. Statistical Analysis

## 3. Results

#### 3.1. Short-Term Prediction

^{2}= 0.99, a linear regression slope close to 1.0, and close agreement in the line plots (Figure 3), as well as mean percentage errors of less than 2.5% at all time points (Table 1). This is confirmed by the linear mixed effects model, which shows no significant difference between observed and predicted Tb.BV/TV (Table 1). Despite being highly correlated (R

^{2}> 0.94), the observed Tb.Th, Tb.Sp, and Tb.N are not accurate. From the Bland–Altman plots in Figure 3, the prediction over-estimates Tb.Th and Tb.Sp, with large values of Tb.Th and Tb.Sp having larger errors. Tb.N is underestimated by the prediction. The resulting mean percentage errors (6.2 to 9.4%, Table 1) are significant for the linear mixed effects model. There is no significant effect of time indicating that static morphometrics do not change significantly between measurements. There is a significant group effect but no group-by-time interactions, meaning that observations and predictions are significantly different at all measurements.

#### 3.2. Long-Term Prediction

^{2}= 0.96, Figure 4) and not significantly different (p > 0.05, Figure 5), but the Bland–Altman plots show obvious proportional bias (Figure 4). Short- and long-term Tb.BV/TV are also similar (p > 0.05, Figure 5). Although observed and long-term Tb.Th, Tb.Sp, and Tb.N are highly correlated (R

^{2}> 0.94, Figure 4), they are significantly different (p < 0.0001, Figure 5), with mean percentage errors ranging from 18.1 to 20.6%, indicating that we did not accurately predict these parameters in the long-term. Tb.Th, Tb.Sp, and Tb.N determined at R+12 in the short- and long-term predictions are significantly different (p < 0.0001, Figure 5).

## 4. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Procedure for predicting short-term participant-specific bone adaptation. (

**A**) The observed data are fed into the inverse solver to estimate model parameters at each time interval. (

**B**) A single measurement and the corresponding model parameters are fed into the forward solver to predict bone adaptation.

**Figure 2.**Procedure for predicting long-term participant-specific bone adaptation (12 months). (

**A**) The observed data are fed into the inverse solver to estimate model parameters for the time interval R+0 to R+6. This is identical to the procedure in Figure 1A. (

**B**) The R+0 observed data and model parameters are fed into the forward solver to predict the bone structure at R+12.

**Figure 3.**Linear regression, Bland–Altman, and line plots for Tb.BV/TV, Tb.Th, Tb.Sp, and Tb.N comparing the observation and short-term prediction for the 70 converged short-term prediction datapoints. In the regression plots (

**top row**), the grey dashed line denotes the line of unity, and the black solid line denotes the regression line. In the Bland–Altman plots (

**middle row**), the grey dashed lines denote the limits of agreement, the black solid line denotes the mean, and the grey dotted line denotes zero error. The line plots (

**bottom row**) show the median and interquartile range of all participants and anatomical sites (i.e., right and left tibia).

**Figure 4.**Linear regression and Bland–Altman plots for Tb.BV/TV, Tb.Th, Tb.Sp, and Tb.N comparing observation and long-term prediction for all 26 converged long-term prediction datapoints at R+12. In the regression plots, the grey dashed line denotes the line of unity, and the black solid line denotes the regression line. In the Bland–Altman plots, the grey dashed lines denote the limits of agreement, the black solid line denotes the mean, and the grey dotted line denotes zero error.

**Figure 5.**Boxplots for Tb.BV/TV, Tb.Th, Tb.Sp, and Tb.N comparing observation, short-term, and long-term predictions for the 20 common datapoints at R+12. Significance is determined from F-tests: *** = p < 0.0001.

**Figure 6.**Spatial patterns of bone formation and resorption represented as an overlay between baseline and follow-up images of a representative dataset. (

**A**) Comparison of observation and short-term prediction and (

**B**) comparison of observation and long-term prediction. Voxels only present in the first image were considered resorbed bone (blue), voxels only present in the second image were considered formed bone (orange), and voxels present in both images were considered quiescent (grey).

**Table 1.**Percent error (%) in static morphometry between observation and short-term prediction at each measurement reported as mean ± standard deviation.

Parameter | Error R+0 [%] | Error R+6 [%] | Error R+12 [%] | p-Value |
---|---|---|---|---|

Tb.BV/TV | 1.6 ± 2.0 | 2.5 ± 3.2 | 1.0 ± 1.3 | 0.393 |

Tb.Th | 6.2 ± 2.6 | 6.2 ± 1.8 | 7.2 ± 2.3 | <0.0001 |

Tb.Sp | 7.4 ± 2.1 | 9.1 ± 5.2 | 8.2 ± 3.0 | <0.0001 |

Tb.N | 8.6 ± 2.3 | 9.4 ± 3.6 | 8.9 ± 2.1 | <0.0001 |

**Table 2.**Observed and predicted (short-term) dynamic morphometry at each measurement interval reported as median (Q1, Q3).

L - R+0 | R+0 - R+6 | R+6 - R+12 | |||||
---|---|---|---|---|---|---|---|

Parameter | Observation | Short-Term Prediction | Observation | Short-Term Prediction | Observation | Short-Term Prediction | p-Value |

BFR [$\mathrm{\%}/\mathrm{d}\mathrm{a}\mathrm{y}$] | 0.12 (0.11, 0.16) | 0.04 (0.02, 0.04) | 0.12 (0.12, 0.14) | 0.04 (0.03, 0.04) | 0.11 (0.10, 0.13) | 0.04 (0.03, 0.04) | <0.0001 |

BRR [$\mathrm{\%}/\mathrm{d}\mathrm{a}\mathrm{y}$] | 0.13 (0.12, 0.17) | 0.05 (0.04, 0.07) | 0.12 (0.11, 0.13) | 0.04 (0.03, 0.05) | 0.11 (0.10, 0.13) | 0.04 (0.03, 0.05) | <0.0001 |

MS [$\mathrm{\%}$] | 25.5 (24.29, 27.90) | 5.73 (4.42, 6.32) | 27.82 (25.83, 32.60) | 6.36 (5.77, 7.60) | 27.09 (25.12, 28.60) | 6.23 (5.60, 7.26) | <0.0001 |

ES [$\mathrm{\%}$] | 28.13 (26.41, 30.94) | 9.27 (8.33, 12.12) | 26.49 (25.26, 29.24) | 7.49 (6.58, 10.55) | 26.32 (25.59, 28.24) | 8.18 (6.87, 9.52) | <0.0001 |

MAR [$\mathsf{\mu}\mathrm{m}/\mathrm{d}\mathrm{a}\mathrm{y}$] | 0.73 (0.69, 0.92) | 0.72 (0.66, 0.88) | 0.75 (0.71, 0.77) | 0.73 (0.67, 0.75) | 0.71 (0.66, 0.74) | 0.67 (0.64, 0.73) | 0.477 |

MRR [$\mathsf{\mu}\mathrm{m}/\mathrm{d}\mathrm{a}\mathrm{y}$] | 0.73 (0.70, 0.93) | 0.73 (0.67, 0.89) | 0.74 (0.71. 0.77) | 0.74 (0.69, 0.76) | 0.69 (0.66, 0.74) | 0.68 (0.64, 0.73) | 0.162 |

**Table 3.**Embedding metrics reported as median (Q1, Q3) comparing observation and short-term prediction.

R+0 | R+6 | R+12 | |
---|---|---|---|

Dice coefficient | 0.86 (0.84, 0.88) | 0.87 (0.85, 0.88) | 0.87 (0.86, 0.88) |

$\mathrm{Symmetric}\mathrm{distance}\left[\mathsf{\mu}\mathrm{m}\right]$ | 41.6 (38.6, 46.2) | 40.6 (37.5, 48.4) | 40.0 (37.5, 43.2) |

**Table 4.**Observed and predicted (long-term) dynamic morphometry at the R+12 - R+0 measurement interval reported as median (Q1, Q3).

Parameter | Observation | Long-Term Prediction | p-Value |
---|---|---|---|

$\mathrm{BFR}[\mathrm{\%}/\mathrm{d}\mathrm{a}\mathrm{y}$] | 0.06 (0.06, 0.07) | 0.04 (0.04, 0.05) | <0.0001 |

$\mathrm{BRR}[\mathrm{\%}/\mathrm{d}\mathrm{a}\mathrm{y}$] | 0.06 (0.05, 0.06) | 0.04 (0.03, 0.05) | 0.0008 |

$\mathrm{MS}[\mathrm{\%}$] | 28.15 (27.06, 33.62) | 18.74 (17.11, 21.17) | <0.0001 |

$\mathrm{ES}[\mathrm{\%}$] | 26.32 (25.48, 28.56) | 20.35 (17.20, 25.11) | 0.0004 |

$\mathrm{MAR}[\mathsf{\mu}\mathrm{m}/\mathrm{d}\mathrm{a}\mathrm{y}$] | 0.35 (0.34, 0.38) | 0.35 (0.33, 0.35) | 0.0174 |

$\mathrm{MRR}[\mathsf{\mu}\mathrm{m}/\mathrm{d}\mathrm{a}\mathrm{y}$] | 0.35 (0.34, 0.37) | 0.35 (0.33, 0.35) | 0.0174 |

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**MDPI and ACS Style**

Kemp, T.D.; Besler, B.A.; Gabel, L.; Boyd, S.K.
Predicting Bone Adaptation in Astronauts during and after Spaceflight. *Life* **2023**, *13*, 2183.
https://doi.org/10.3390/life13112183

**AMA Style**

Kemp TD, Besler BA, Gabel L, Boyd SK.
Predicting Bone Adaptation in Astronauts during and after Spaceflight. *Life*. 2023; 13(11):2183.
https://doi.org/10.3390/life13112183

**Chicago/Turabian Style**

Kemp, Tannis D., Bryce A. Besler, Leigh Gabel, and Steven K. Boyd.
2023. "Predicting Bone Adaptation in Astronauts during and after Spaceflight" *Life* 13, no. 11: 2183.
https://doi.org/10.3390/life13112183