The authors have declared that no competing interests exist.
A round-trip human mission to Mars is anticipated to last roughly three years. Spaceflight conditions are known to cause loss of bone mineral density (BMD) in astronauts, increasing bone fracture risk. There is an urgent need to understand BMD progression as a function of spaceflight time to minimize associated health implications and ensure mission success. Here we introduce a nonlinear mathematical model of BMD loss for candidate human missions to Mars: (i) Opposition class trajectory (400–600 days), and (ii) Conjunction class trajectory (1000–1200 days). Using femoral neck BMD data (N = 69) from astronauts after 132-day and 228-day spaceflight and the World Health Organization’s fracture risk recommendation, we predicted post-mission risk and associated osteopathology. Our model predicts 62% opposition class astronauts and 100% conjunction class astronauts will develop osteopenia, with 33% being at risk for osteoporosis. This model can help in implementing countermeasure strategies and inform space agencies’ choice of crew candidates.
A fracture occurs when a certain applied load exceeds the ultimate strength of the bone. A measurable, critical component for the bone strength is the areal bone mineral density (BMD) [
During the >54 million kilometers traversed during a mission to Mars, astronauts will be exposed to the longest microgravity and cosmic radiation conditions in the history of spaceflight. Thus, defining potential health implications of such exposure is necessary before proceeding with interplanetary explorations [
A predictive mathematical model for BMD loss during long-duration spaceflights could help space agencies make decisions about mission duration and crew selection to minimize fracture risk. To our knowledge, each and every prior work assume a linear decrease of the BMD in astronauts to make predictions [
In this paper, we introduce for the first time a predictive mathematical model for the BMD loss defined by an exponential decrease in load bearing bones of the astronauts. By using this model, we predict BMD loss in the femoral neck for two potential missions to Mars.
There is terrestrial evidence that bone density is likely to plateau after a long period of loss in weight-bearing bones [
BMD change is here expressed as percentage [%],
P corresponds to the plateau. The maximum total BMD loss has been previously estimated to be 69.0% relative to the astronauts’ pre-flight BMD [
We performed a nonlinear regression of the available data for BMD loss in the femoral neck. In order to obtain the decay rate (
11 | 0 | 69 | [ |
132 | -1.3 | 1 | [ |
132 | -6.0 | 1 | [ |
145 | -4.5 | 1 | [ |
150 ± 30 | -9.4 ± 6.4 | 16 | [ |
169 | -3.5 | 1 | [ |
169 | -3.1 | 1 | [ |
176 | -11.4 | 1 | [ |
176 | -5.3 | 1 | [ |
181 ± 47 | -6.8 ± 1.1 | 46 | [ |
Once we calculated BMD loss by using the previous equation, we calculated the T-score for different ethnicities and sexes by using normative data from the
In the previous formula, <
Here, <
After the <
The values obtained from the non-linear regression are summarized in
Previous studies have calculated the duration of different strong candidate human missions to Mars [
Grey dots represent experimental data obtained in previous missions as measured by dual-energy x-ray absorptiometry (DXA). Two different potential human missions to Mars are highlighted: (i) opposition-class, with a duration of 400–600 days (area with red dots) and (ii) conjunction-class, with a duration of 1000–1200 days (area with red lines). The predictive model is represented by the solid, black line, with the 95% confidence interval limits plotted in dashed, black lines, and the plateau by the dot-dashed, black line. A comparison with the (unphysical) linear model can be found in
Decay rate, |
6.371∙10−4 (a.u.) |
Half life, |
1088 days |
Time constant, |
1570 days |
Based on these results, we obtained T-scores or each gender/ethnicity/age group and summarized them in
The color code is defined as by the international reference standard, osteoporosis is colored in red (T-score < -2.5), and osteopenia in orange (-2.5 < T-score < -1). Normal T-score is colored in green (T-score > -1). NASA´s non-permissible outcome is T-score < -2, highlighted by bold numbers in the table.
Mission time (days) | Mars |
Astronaut age (yr) | Male | Female | ||||
---|---|---|---|---|---|---|---|---|
Non-Hispanic white | Non-Hispanic black | Mexican American | Non-Hispanic white | Non-Hispanic black | Mexican American | |||
400 | Opposition-class (min) | 30–39 | -0.91 | -0.08 | -0.67 | -1.35 | -0.73 | -1.05 |
40–49 | -1.25 | -0.58 | -1.03 | -1.58 | -0.72 | -1.18 | ||
600 | Opposition-class (max) | 30–39 | -1.38 | -0.62 | -1.16 | -1.79 | -1.22 | -1.52 |
40–49 | -1.70 | -1.08 | -1.49 | -1.20 | -1.64 | |||
1000 | Conjunction-class (min) | 30–39 | -1.49 | -1.96 | ||||
40–49 | -1.88 | -1.99 | ||||||
1200 | Conjunction-class (max) | 30–39 | -1.86 | |||||
40–49 |
We estimated fracture risk in astronauts in a potential mission to Mars as the output of the predictive model. We predict astronauts will lose 32.4–36.8% of their BMD in their femoral neck during the longer conjunction-class mission, which is the most likely duration of a human mission to Mars. By using mean values of BMD in the femoral neck, we predicted astronauts will return from such a mission with T-scores ranging from -1.49 to -2.93, depending on their pre-flight BMD. Thus, a subset of the astronauts is predicted to meet the diagnostic criteria for osteoporosis or osteopenia in a human mission to Mars. NASA´s medical standards for crewmember’s health establish a non-permissible T-score limit of -2. This means that to keep the skeletal health of crewmembers after a spaceflight, the T-score should be maintained above the non-permissible outcome limit. Yet, for the majority of the cases included in this analysis, bone loss exceeds the non-permissible limit (T-score < -2). Previous studies using linear models to estimate the risk of fragility fractures in crewmembers showed low risk on missions <1 year in duration [
Even if it is more challenging from a technological point of view, an opposition class mission to Mars seems to be much safer with respect to risk for bone fracture (15.6–22.0% BMD loss in the femoral neck). Predicted T-scores range from -0.08 to -2.01, depending on sex, ethnicity, age and total duration of the mission. This means that an opposition class mission to Mars will present an acceptable risk of fracture (T-score > -2) for the majority of the astronauts. While some crew are likely to develop osteopenia, none are predicted to develop osteoporosis.
Consistent with terrestrial values from the NHANES reference database, non-Hispanic, 30–39 year old black males would have the lowest risk of bone fracture in any of the missions, while non-Hispanic, 40–49 years old, white females would have the highest risk for bone fracture amongst the different groups analyzed.
The mathematical model presented is the first to our knowledge that does not assume a linear decrease in the BMD of astronauts [
Our model presents a simple and powerful mathematical tool enabling a quick estimation of the BMD loss and T-score for any astronaut in a long-duration spaceflight. Yet, some limitations arise. For example, our model does not take into account possible use of exercise, pharmaceutical (
Our model offers the possibility of giving individual predictions for the T-score at any time point of the mission. In this study, the “pre-flight” BMDs input to obtain the T-scores were obtained from the NHANES reference database, while for an actual mission to Mars, individual pre-launch BMD of each astronaut would be need to supply data for input into the model. It is important to note that during missions, the risk of fracture is minimal as sudden mechanical overloads are very unlikely to happen in a microgravity environment. However, for astronauts landing on the surface of Mars, the risk of fracture increases, as falls or crushes would be more likely to happen in Mars’ fractional gravity (3.71 m/s2
Bone density is an important parameter that contributes to bone strength, but it would be both interesting and important to include other parameters that contribute to so-called “bone quality” in future studies (such as microarchitecture and material properties) to gain a more accurate estimate of fracture probability [
In conclusion, we have presented a mathematical model for BMD loss in crewmembers that can be used to predict T-scores during long-duration spaceflights. This model helps us understand the potential fracture risk for a potential mission to Mars, which is of paramount importance for NASA and other space agencies. T-scores < -2, NASA’s non-permissible outcome, were predicted for the 79% of the cases analyzed regarding a conjunction-class trajectory (the strongest candidate today for a human mission to the red planet). A bone fracture in an astronaut during a mission to Mars would endanger the mission goals and also could provoke medical complications (microgravity’s effect on bone cell performance could impair bone healing or induce sepsis or thromboembolic blood clots) that may result in morbidity or mortality. This model will help in designing mitigation strategies (use of ARED and adequate nutrition) for future human missions to Mars.
Percent loss in bone mineral density at fermoral neck in astronauts (N = 69) after 400, 600, 1000 and 1200 day-spaceflights were statistically analyzed via unpaired t tests between all groups, whereby a two-tailed p value of p < 0.0001 was observed in all cases.
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Authors are very grateful to Dr. Joy Wu for critical discussions.