The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interests exist. 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 [ 1 ]. BMD loss is an established fracture risk factor due to bone weakening as measured in large epidemiological studies correlating BMD with the incidence of fragility fractures [ 2 — 4 ].
It is well known that long-duration spaceflights induce BMD loss in weight-bearing bones although there is considerable individual variability [ 6 — 12 ]. BMD loss as a function of spaceflight duration remains poorly understood, with an average rate of loss typically between 1—1. These calculations are based in DXA measurements before and after missions usually of 4—6 months in length.
Thus, defining potential health implications of such exposure is necessary before proceeding with interplanetary explorations [ 15 ]. According to the latest edition of the ISECG Global Exploration Roadmap [ 16 ], released in January , a mutual driving objective between agencies is to enable human presence on Mars. 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 [ 13 ], which is not valid for long duration spaceflights. Specifically, BMD loss in the femoral neck has been modeled as a linear decrease: 1. However, a linear decrease is not realistic for very long duration, interplanetary missions, as it predicts nonphysical negative BMD values for longer time spans. In contrast, BMD recovery on Earth in the bones of various astronauts after spaceflights is well described by an exponential function [ 19 ].
Furthermore, there is terrestrial evidence that the loss of bone matrix and bone mineral due to conditions that result prolonged bed rest e. Thus, a non-linear, exponential decline of BMD in weight-bearing bones is a reasonable approach to model progressive bone loss in long-duration space missions. 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 [ 18 , 20 , 21 ]. Further, there are no supporting data from astronauts available for time-frames relevant to interplanetary travel all the candidate missions are in the order of years given current rocket capabilities.
However, spinal cord injury provides an example where a plateau in BMD decrements occurs 1. Furthermore, previous studies demonstrated that the alterations that occur following spinal cord injury and exposure to microgravity are remarkably similar [ 22 ].
Therefore, we formulate that the change of areal BMD in weight-bearing bones at time t, BMD t , during spaceflights as a one-phase exponential decay:.
P corresponds to the plateau. The maximum total BMD loss has been previously estimated to be Therefore, assuming that the BMD loss will eventually plateau at this maximum value:. We performed a nonlinear regression of the available data for BMD loss in the femoral neck. Femoral neck was chosen between other weight-bearing bones because it is the recommended by the World Health Organization WHO [ 25 ] to determine the fragility fracture risk associated T-score, as well as to diagnose osteoporosis in clinical practice [ 18 ].
All the obtained data can be found in S1 — S5 Tables. The values obtained from the non-linear regression are summarized in Table 2. Previous studies have calculated the duration of different strong candidate human missions to Mars [ 26 , 27 ]. By using our model, we predicted the BMD loss for these potential missions to Mars. In Fig 1 , we plotted the previous function versus time in order to show its predictions for the BMD loss in long-duration spaceflights.
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 — days area with red dots and ii conjunction-class, with a duration of — days area with red lines. A comparison with the unphysical linear model can be found in S1 — S3 Figs.
Differences are measured in units named standard deviations SDs. The more standard deviations below 0, the lower the BMD of the patient, and therefore, the higher the risk of fracture. The Symposia will feature exciting new research concerning the effects of bed-rest on bone loss, in addition to studies showing that externally applied vibrations stimulate bone regeneration for both astronauts and patients alike.
Numerous other topics will also be addressed, including the role of nutrition in space flight, and the effects of exercise countermeasures. Osteoporosis, in which the bones become porous and break easily, is one of the world's most common and debilitating diseases.
The result: pain, loss of movement, inability to perform daily chores, and in many cases, death. One out of three women over 50 will experience osteoporotic fractures, as will one out of five men 1, 2, 3. Unfortunately, screening for people at risk is far from being a standard practice.
Osteoporosis can, to a certain extent, be prevented, it can be easily diagnosed and effective treatments are available. The International Osteoporosis Foundation IOF is the only worldwide organization dedicated to the fight against osteoporosis. It brings together scientists, physicians, patient societies and corporate partners. Working with its member societies in 85 locations, and other healthcare-related organizations around the world, IOF encourages awareness and prevention, early detection and improved treatment of osteoporosis.
How many women have osteoporosis? 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 — days , and ii Conjunction class trajectory — days. 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 [ 1 ].
BMD loss is an established fracture risk factor due to bone weakening as measured in large epidemiological studies correlating BMD with the incidence of fragility fractures [ 2 — 4 ]. It is well known that long-duration spaceflights induce BMD loss in weight-bearing bones although there is considerable individual variability [ 6 — 12 ]. BMD loss as a function of spaceflight duration remains poorly understood, with an average rate of loss typically between 1—1.
These calculations are based in DXA measurements before and after missions usually of 4—6 months in length. Thus, defining potential health implications of such exposure is necessary before proceeding with interplanetary explorations [ 15 ]. According to the latest edition of the ISECG Global Exploration Roadmap [ 16 ], released in January , a mutual driving objective between agencies is to enable human presence on Mars.
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 [ 13 ], which is not valid for long duration spaceflights.
Specifically, BMD loss in the femoral neck has been modeled as a linear decrease: 1. However, a linear decrease is not realistic for very long duration, interplanetary missions, as it predicts nonphysical negative BMD values for longer time spans. In contrast, BMD recovery on Earth in the bones of various astronauts after spaceflights is well described by an exponential function [ 19 ]. Furthermore, there is terrestrial evidence that the loss of bone matrix and bone mineral due to conditions that result prolonged bed rest e.
Thus, a non-linear, exponential decline of BMD in weight-bearing bones is a reasonable approach to model progressive bone loss in long-duration space missions. 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 [ 18 , 20 , 21 ].
Further, there are no supporting data from astronauts available for time-frames relevant to interplanetary travel all the candidate missions are in the order of years given current rocket capabilities.
However, spinal cord injury provides an example where a plateau in BMD decrements occurs 1. Furthermore, previous studies demonstrated that the alterations that occur following spinal cord injury and exposure to microgravity are remarkably similar [ 22 ].
Therefore, we formulate that the change of areal BMD in weight-bearing bones at time t, BMD t , during spaceflights as a one-phase exponential decay:. P corresponds to the plateau. The maximum total BMD loss has been previously estimated to be Therefore, assuming that the BMD loss will eventually plateau at this maximum value:.
We performed a nonlinear regression of the available data for BMD loss in the femoral neck. Femoral neck was chosen between other weight-bearing bones because it is the recommended by the World Health Organization WHO [ 25 ] to determine the fragility fracture risk associated T-score, as well as to diagnose osteoporosis in clinical practice [ 18 ]. All the obtained data can be found in S1 — S5 Tables. The values obtained from the non-linear regression are summarized in Table 2.
Previous studies have calculated the duration of different strong candidate human missions to Mars [ 26 , 27 ]. By using our model, we predicted the BMD loss for these potential missions to Mars. In Fig 1 , we plotted the previous function versus time in order to show its predictions for the BMD loss in long-duration spaceflights.
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 — days area with red dots and ii conjunction-class, with a duration of — days area with red lines.
A comparison with the unphysical linear model can be found in S1 — S3 Figs. Differences are measured in units named standard deviations SDs. The more standard deviations below 0, the lower the BMD of the patient, and therefore, the higher the risk of fracture. We estimated fracture risk in astronauts in a potential mission to Mars as the output of the predictive model. We predict astronauts will lose Food and Farm Innovation. Sustainable Fuels. Biobased Manufacturing.
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