Locomotor function after long-duration space flight: effects and motor learning during recovery

Abstract

Astronauts returning from space flight and performing Earth-bound activities must rapidly transition from the microgravity-adapted sensorimotor state to that of Earth’s gravity. The goal of the current study was to assess locomotor dysfunction and recovery of function after long-duration space flight using a test of functional mobility. Eighteen International Space Station crewmembers experiencing an average flight duration of 185 days performed the functional mobility test (FMT) pre-flight and post-flight. To perform the FMT, subjects walked at a self selected pace through an obstacle course consisting of several pylons and obstacles set up on a base of 10-cm-thick, medium-density foam for a total of six trials per test session. The primary outcome measure was the time to complete the course (TCC, in seconds). To assess the long-term recovery trend of locomotor function after return from space flight, a multilevel exponential recovery model was fitted to the log-transformed TCC data. All crewmembers exhibited altered locomotor function after space flight, with a median 48% increase in the TCC. From the fitted model we calculated that a typical subject would recover to 95% of his/her pre-flight level at approximately 15 days post-flight. In addition, to assess the early motor learning responses after returning from space flight, we modeled performance over the six trials during the first post-flight session by a similar multilevel exponential relation. We found a significant positive correlation between measures of long-term recovery and early motor learning (P < 0.001) obtained from the respective models. We concluded that two types of recovery processes influence an astronaut’s ability to re-adapt to Earth’s gravity environment. Early motor learning helps astronauts make rapid modifications in their motor control strategies during the first hours after landing. Further, this early motor learning appears to reinforce the adaptive realignment, facilitating re-adaptation to Earth’s 1-g environment on return from space flight.

Appendix

Long-term recovery model

For the model in (1), μ _i (t _ij ) is the expected log TCC response for the ith astronaut on the first trial on the jth session occurring t _ij days after the ISS mission landing event. For pre-flight sessions, t _ij is defined as the negative of days prior to lift-off (t < 0.). We assume that for post-flight (t > 0) sessions, μ _i (t) is greater than μ _i (t < 0), and that for t > 0, μ _i (t) follows an exponential recovery trend back to μ _i (t < 0) as t increases. Earlier we defined μ _i (t _ij ) as

$$ u_{i} ({\text{t}}_{ij} ) = \left\{ {\begin{array}{*{20}c} {A_{i} } \hfill & {\text{pre-flight}} \hfill \\ {A_{i} + B_{i} {\text{e}}^{{ - C_{i} t_{ij} }} } \hfill & {{\text{post-flight}}} \hfill \\ \end{array} } \right. .$$

For statistical analysis we break down Ai, B _i , and C _i into fixed and random components as

$$ \begin{gathered} A_{i} = \beta_{0} + u_{0i} \hfill \\ B_{i} = \beta_{1} + u_{1i} \hfill \\ C_{i} = \theta + u_{2i} \hfill \\ \end{gathered} .$$

Thus,

$$ \mu _{i} \left( {t_{ij} } \right) = \left\{ {\begin{array}{*{20}c} {\beta_{0} + u_{0i} } \hfill & {\text{pre-flight}} \hfill \\ {\beta_{0} + u_{0i} + \left( {\beta_{1} + u_{1i} } \right)\exp \left( { - \left( {\theta + u_{2i} } \right)t_{ij} } \right)} \hfill & {\text{post-flight}} \hfill \\ \end{array} } \right. .$$

(4)

The parameter β₀ is the population expected pre-flight value of log TCC, and u _0i , u _1i , and u _2i are subject-specific random effects with the vector u = (u _0i , u _1i , u _2i )′ assumed to follow a multivariate normal distribution with mean 0 and covariance matrix V. The quantity β₁ + u _1i represents the expected change in log TCC for the ith subject on landing day, and θ + u _2i is the ith subject’s long-term recovery parameter (over days), the exponential constant that determines the speed of the recovery process (larger values of θ + u _2i are consistent with faster recovery).

Estimating model parameters

Let $\hat{\theta }$ be the maximum-likelihood estimate of θ, and let $\hat{\mu}_{i} (t_{ij} )$ be (Eq. 4) with θ = $\hat{\theta }$ fixed. With fixed $t_{ij} > 0$ (post-flight) and varying u _2i , we can consider μ _i (t _ij ) as a function of u _2i and expand exp(–u _2i t _ij ) around u _2i  = 0 to give

$$ \begin{gathered} \hat{\mu}_{i} (t_{ij} ) \, \dot{ = } \, \beta_{0} + u_{0i} + (\beta_{1} + u_{1i} )\exp ( - \hat{\theta }t_{ij} ) + u^{\prime}_{2i} t_{ij} \exp ( - \hat{\theta }t_{ij} ). \hfill \\ \, \dot{ = } \, \beta_{0} + u_{0i} + (\beta_{1} + u_{1i} )X_{1} + u^{\prime}_{2i} X_{2} \hfill \\ \end{gathered} $$

(5)

where

$$ \begin{gathered} u^{\prime}_{2i} = -\left( {\beta_{1} + u_{1i} } \right)u_{2i} , \hfill \\ X_{ 1} = \exp ( - \hat{\theta }t_{ij} ), \hfill \\ X_{ 2} = t_{ij} {\text{X}}_{ 1} . \hfill \\ \end{gathered} $$

(6)

By fitting a linear multilevel model to y _ij with X ₁ and X ₂ as explanatory variables in both the fixed and random parts of the model, one obtains regression coefficients b ₀, b ₁, and b ₂ corresponding to the constant, X ₁ and X ₂ in the fixed part of the model. From Eq. 5, it can be seen that b ₀ and b ₁ are estimates of β₀ and β₁, respectively, while b ₂ is an estimate of E($u^{\prime}_{2i}$) = –Cov$(u_{1i} ,u^{\prime}_{2i} )$ In addition, best linear unbiased predictors (BLUPs) of u _0i , u _1i , and $u^{\prime}_{2i}$ can be obtained. From the latter two of these, we can get a prediction of u _2i using Eq. 6:

$$ \hat{u}_{2i} = {\frac{{ - \hat{u}^{\prime}_{2i} }}{{b_{1} + \hat{u}_{1i} }}}, $$

(7)

where $\hat{u}_{1i}$ and $\hat{u}^{\prime}_{2i}$ are BLUPs of u _1i and $u^{\prime}_{2i}$, respectively, and from these estimates we calculate C _i  = θ + u _i .

We determined the maximum-likelihood estimate $\hat{\theta }$ using the profile-likelihood method. Under this method, trial values of $\hat{\theta }$ are substituted in the linearized model (Eq. 5). For each trial value, the model is then fit with respect to all other parameters, and the conditional likelihood is recorded. The value of θ which maximizes the conditional model likelihood is taken to be the maximum-likelihood estimate, $\hat{\theta }$, and the final estimates for the parameters are those obtained using this value of $\hat{\theta }$.

Short-term learning model

Let $z_{ij} = \log (y_{ij} )$. Then the equation (3)

$$ y_{ij} = D_{ij}\;{{e}}^{ - E(j - 1)} .$$

is equivalent to

$$ z_{ij} = D^{\prime}_{i} - E_{i} (j - 1) + e^{\prime}_{ij} $$

(8)

with $D_{ij} = \exp (D^{\prime}_{i} + e^{\prime}_{ij} )$. We again break these coefficients into fixed and random effects,

$$ \begin{gathered} D^{\prime}_{i} = \alpha_{0} + \upsilon_{0i} \hfill \\ E_{i} = \alpha_{1} + \upsilon_{1i} , \hfill \\ \end{gathered} $$

so the model for short-term learning is

$$ Z_{ij} = (\alpha_{0} + \upsilon_{0i} ) - (\alpha_{1} + \upsilon_{1i} )(j - 1) + e^{\prime}_{ij} . $$

(9)

Here, α ₀ and α ₁ are fixed parameters, $\upsilon_{0i}$ and $\upsilon_{1i}$ are random effects having a bivariate normal distribution, and $e^{\prime}_{ij}$ is an independent, normally distributed, within-subject error term. The coefficient $\alpha_{1} + \upsilon_{1i}$ (which should be positive) quantifies how quickly subjects can improve performance, trial-by-trial, during the day of testing. Larger values imply faster adaptation. Best linear unbiased predictors were used to calculate E _i .

Pre- versus post-flight learning comparison model

We used another mixed effects regression model similar to Eq. 9 for comparing the mean rate of improvement in performance during the last pre-flight session with rate of improvement during the first day after return:

$$ z_{ij} = \left\{ {\begin{array}{*{20}c} \begin{gathered} (\varphi_{0} + b_{0i} ) + (\varphi_{1} + b_{1i} )(j - 1) + e_{ij}^{\prime \prime } \hfill \\ (\varphi_{0} + b_{0i} ) + (\varphi_{1} + b_{1i} )(j - 1) \hfill \\ \end{gathered} & {\text{pre-flight}} \\ { + (\varphi_{2} + b_{2i} ) + (\varphi_{3} + b_{3i} )(j - 1) + e_{ij}^{\prime \prime } } & {\text{post-flight}} \\ \end{array} } \right. $$

(10)

The same 15 subjects were used for fitting this regression model as used for calculating BLUPs of v _1i ’s in Eq. 9.