ARTICLE OPENMental imagery of object motion in weightlessnessSilvio Gravano1,2, Francesco Lacquaniti 1,2✉ and Myrka Zago 1,3✉Mental imagery represents a potential countermeasure for sensorimotor and cognitive dysfunctions due to spaceflight. It mighthelp train people to deal with conditions unique to spaceflight. Thus, dynamic interactions with the inertial motion of weightlessobjects are only experienced in weightlessness but can be simulated on Earth using mental imagery. Such training might overcomethe problem of calibrating fine-grained hand forces and estimating the spatiotemporal parameters of the resulting object motion.Here, a group of astronauts grasped an imaginary ball, threw it against the ceiling or the front wall, and caught it after the bounce,during pre-flight, in-flight, and post-flight experiments. They varied the throwing speed across trials and imagined that the ballmoved under Earth’s gravity or weightlessness. We found that the astronauts were able to reproduce qualitative differencesbetween inertial and gravitational motion already on ground, and further adapted their behavior during spaceflight. Thus, theyadjusted the throwing speed and the catching time, equivalent to the duration of virtual ball motion, as a function of the imaginary0 g condition versus the imaginary 1 g condition. Arm kinematics of the frontal throws further revealed a differential processing ofimagined gravity level in terms of the spatial features of the arm and virtual ball trajectories. We suggest that protocols of this kindmay facilitate sensorimotor adaptation and help tuning vestibular plasticity in-flight, since mental imagery of gravitational motion isknown to engage the vestibular cortex.npj Microgravity (2021) 7:50 ; https://doi.org/10.1038/s41526-021-00179-zINTRODUCTIONSpace missions expose humans to the risk of multiple physiolo-gical alterations, due to weightlessness, ionizing radiations,confinement, and other stressors1–4. In particular, a decline insensorimotor and cognitive performance can result from the lackof gravity effects5–7 and can persist over several weeks after theend of the mission8. These alterations are potentially incapacitat-ing during flight and upon landing9–13.Many approaches are followed to develop countermeasures forphysiological deconditioning in space (e.g., refs. 10–13), includingphysical exercise14, lower-body negative pressure15, haptic andproprioceptive stimuli16, and artificial gravity17. Recently, the useof mental imagery has been also advocated to prepare forthe rapid changes in gravitational forces after launch, to reducethe adverse effects of weightlessness exposition, and to preparefor landing18–20. Imagery is a voluntary mental experience ofobjects, scenes, or actions that are not present to our senses. It hasproven very useful for sports training and rehabilitation ofneurological disorders21–23. Motor imagery can enhance physicalpractice in both terrestrial23 and astronaut populations18,24.Mental imagery might be especially useful for training peopleto deal with conditions that are experienced only in weightless-ness. For instance, motor imagery has been used to test theability of naïve subjects to imagine rotating their body whilefloating above the floor25. The dynamic interaction of differentbody parts with weightless, free-floating objects is anothercondition that is not normally experienced under Earth gravity(e.g., neutral buoyancy simulations involve a significant viscousresistance that does not apply to spaceflight), but can besimulated using mental imagery. Astronauts and cosmonautsface the problem of interaction with free-floating objectsroutinely, as when they shift various tools and equipment on-board. To do so effectively, they must produce lower forces toimpart lower momenta to the handled object than thoserequired on Earth, else they risk damaging equipment and/orinjuring themselves26,27. In general, they must produce finelygraded arm movements as part of their duties28. However, it isknown that people may initially encounter difficulties incalibrating the forces required to shift objects or move aroundthe space vehicle, and they may need some considerable time toadapt their control strategies to weightlessness, as well as to re-adapt upon return to Earth26,29,30. Interestingly, some of thesedifficulties were documented in the hilarious yet accurateanimation of Man in Space (1955), a television episode resultingfrom the collaboration between Walt Disney and Wernher vonBraun, produced well before any human flew to space. A trainingprogram for astronauts has been recommended30 to encouragefine-graded motions in order to increase controllability andreduce the risk of injury.In particular, the control of hand forces poses special problemsin weightlessness. During object manipulation in weightlessness,the load force at the fingertips decreases by an amount equal tothe weight of the object. Therefore, the minimum grip forcerequired to avoid object slippage from the fingers is lower than onground. Paradoxically, instead, when first exposed to 0 g duringparabolic flight, subjects (especially, but not exclusively, theinexperienced ones) adopt the opposite strategy: they increasethe grip force relative to 1 g, although the temporal couplingbetween grip and load force is preserved31–35. With practice, theyadapt by progressively decreasing the grip forces31,32. Grip-forceadaptation to weightlessness is especially compromised whenobject manipulation must be coordinated with arm movementsinvolving significant inertial torque loads33,36,37. Moreover, persis-tent alterations are observed when subjects must respond to atarget force displayed on a screen by pushing an isometricjoystick. In this case, subjects produce significantly higher hand1Laboratory of Neuromotor Physiology, IRCCS Santa Lucia Foundation, 00179 Rome, Italy. 2Department of Systems Medicine and Center of Space BioMedicine, University of RomeTor Vergata, 00133 Rome, Italy. 3Department of Civil Engineering and Computer Science Engineering & Center of Space BioMedicine, University of Rome Tor Vergata, 00133Rome, Italy. ✉email: lacquaniti@med.uniroma2.it; myrka.zago@uniroma2.itwww.nature.com/npjmgravPublished in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA1234567890():,;forces at 0 g than 1 g, and they do not adapt even after severaltrials28,38, possibly because of altered vestibular input39,40.The correct estimate of the time duration of object motionrepresents another critical issue in weightlessness. People areaccustomed through a life-long experience that unsupportedobjects accelerate downward due to Earth’s gravity. When gravityeffects are absent, however, “up” and “down” no longer exist, andobjects move at constant speed in the direction of the initial force.According to anecdotal reports, some novice astronauts andcosmonauts expect unconsciously that an object slipping fromtheir hand should fall “down” instead of moving forwardinertially41. Objective measurement of the behavioral effects of aprior bias of persistent Earth gravity effects was obtained duringthe Neurolab mission42. Astronauts were asked to catch a ballprojected from the ceiling towards them at random, constantspeeds. They systematically underestimated the motion durationof the incoming ball and activated their arm muscles too early aspredicted by an internal model of gravity effects. Prematureresponses were observed for all tests during the 15 days of themission, but there was evidence of adaptation towards the end ofthe mission42. In addition, some astronauts and cosmonauts havereported a “time compression syndrome” in orbit, elapsed timebeing perceived as compressed relative to the correspondingperceptions during training on ground3. In parabolic flight,Clément43 found that the durations of different stimuli in aduration-reproduction task were significantly underestimated in 0g compared with 1 g.In sum, the combination of inappropriately high forces whenmanipulating objects with the possible underestimate of theduration of the resulting object motion may be detrimental for in-flight mission operations. However, since mental imagery engagesbrain regions partially distinct from those involved in motorinteraction with real objects44–46, we hypothesize that visualimagery might overcome the limitations of perceptual-motorinteractions with weightless objects. If so, mental imagery mightbe useful to train people to deal with weightless objects inpreparation for a space mission, as well as during the mission tofacilitate space adaptation.With this in mind, we put forth a protocol of mental imageryand pantomime, actual arm actions being performed on virtualobjects to mimic the interaction with a ball47,48. In the mainprotocol, the participants are asked to grasp an imaginary ball inthe hand, to throw it “up” so as to bounce on the ceiling, and tocatch it on the fly when they think it has come back to be grasped(Fig. 1A). They must vary the throwing force and speed acrosstrials and, in different blocks of trials, to imagine that the ballmoves under Earth gravity (1 g) or weightlessness (0 g). Animpulsive force exerted by the hand on a ball results in a changeof its momentum. The start and end of ball motion are implicitlysignaled by the throwing and catching actions, respectively.Accordingly, the relationship between the overall duration (T) ofball motion (from throwing to catching) and the throwing speed(V) reflects the kinematics of the ball47.At 0 g (assuming no air resistance and a constant elastic bounceagainst the ceiling), T is related to V by the hyperbolic equationT= K/V, where K corresponds to the distance between the ceilingand the hand at the time of release plus the distance at the timeof catch, yielding the total path length of travel of the ball. Thus,the ball can reach the ceiling and bounce back when thrown “up”at any speed, even at very low speeds. At 1 g, T is related to V by adifferent equation, T ¼ 2g V ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV2 gKp . This implies that thereis a minimum throwing speed (Vmin ¼ffiffiffiffiffiffigKp) below which the ballwould fall back without contacting the ceiling. For V > Vmin andrelatively low values of K (as in the case of the presentexperiments), T values expected at 1 g are very similar to thoseexpected at 0 g. This can be appreciated in Fig. 1B plottingexemplary results of throws of a real ball against the ceiling onground (red dots) and in-flight (blue dots). Despite inter-trialvariability of both ball path length and elastic bounce on theceiling, the data-points for both 1 g and 0 g conditions are roughlydistributed along the hyperbolic function (black curve) with Kequal to the mean path length. However, as expected, the dataobtained at 0 g encompass V values considerably lower and Tvalues considerably longer than the data obtained at 1 g.Of course, in contrast with the results of throwing a real ball,throwing speed V and duration of motion T of a task involving animaginary ball are not constrained by physics to covary uniquely:instead, T can vary with V arbitrarily as a function of the mentalmodel used by each individual. Here, we report the resultsobtained with the protocol of mental imagery described above inseven astronauts before, during, and after their mission on-boardthe International Space Station (ISS). Four more astronauts werebackups and carried out only the pre-flight experiments. For the0 1 2 3 4 5 6V [m/s]00.511.522.533.54T [s]in-flightgroundT=K/VT=2V/gA BFig. 1 Setup. A Picture of astronaut Garrett Reisman on the ISS, performing the protocol of throwing the imaginary ball to the ceiling andcatching it on the rebound. Written informed consent for the publication of the picture was obtained from Garrett Reisman. Image courtesy ofNASA. B Throws of a real ball on ground (red) and in-flight (blue). Black continuous and red dashed curves correspond to T= K/V and T= 2 V/g,respectively. K= 2.4 m (mean path length of ball trajectory, see text).S. Gravano et al.2npj Microgravity (2021) 50 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA1234567890():,;sake of comparison, we also report the results of eight controlsubjects who performed the experiment in our laboratory47. Oneadditional astronaut performed a variant of the protocol, throwingthe imaginary ball against the front wall instead of the ceiling. Thisvariant differed from the main protocol also in the arm kinematics,the throws being underarm in the main protocol and overarm inthe variant.We hypothesized that, with both protocols, the astronauts wereable to simulate qualitatively the characteristics of inertial motionof weightless objects already on ground, and that they furtheradapted their behavior to the real weightless conditions ofspaceflight. We also hypothesized that they could reproduce someof the key differences between target motion under weightless-ness and under gravity. In particular, on average they shouldthrow the virtual ball at a lower speed (due to lower impulsiveforces of the hand) and should wait for a longer time beforecatching the ball after the rebound for the imaginary 0 g conditionthan the imaginary 1 g condition, as in the case of the throws of areal ball in Fig. 1B. Another prediction concerns the protocol ofthrowing the imaginary ball against the front wall. Here, thepresence or absence of gravity effects constrains the spatialcharacteristics of the virtual trajectory of the ball. Under Earthgravity, the possible trajectories back and forth from the targetwould be parabolas. In weightlessness, however, all trajectoriesshould be straight lines. Therefore, adjustments of the throwingand catching gestures to 0 g versus 1 g conditions should beapparent in arm kinematics, in addition to the T versus V functions.METHODSParticipantsThe study was approved by the Institutional Review Boards of theItalian Space Agency (ASI), NASA Johnson Space Center, EuropeanSpace Agency (ESA), Human Research Multilateral, and Santa LuciaFoundation. The research was in accord with the Code of Ethics ofthe World Medical Association (Declaration of Helsinki). Twelveastronauts (11 males, 1 female, 46 ± 4 years old, mean ± SD) wereenrolled, provided written informed consent, and completedstandard pre-flight medical screening with clearance from theirflight surgeon before participating in the study. The individual timepoints for the experiments of the astronauts are given in Table 1.The time schedule of the experiments differed across participantsdue to operational and mission constraints. Seven astronautsperformed pre-flight, in-flight, and post-flight sessions. Oneastronaut performed pre-flight and in-flight sessions. Four astro-nauts performed only pre-flight sessions, as backup participants forthe main protocol. Eleven astronauts were right-handed and one(S8) left-handed, as assessed by a 13-item questionnaire derivedfrom the Dutch Handedness Questionnaire49. S3, S5, S6, S10, S11,and S12 were rookies at the time of experiment performance, whilethe other astronauts had previous spaceflight experience. Theauthors affirm that the astronaut Dr. Garrett Reisman providedwritten informed consent for publication of his image taken whilecarrying out the experiment on the ISS (Fig. 1A).For the sake of comparison, we re-analyzed the data of eightcontrol participants from47. These included six females, two males(21 ± 2 years), six right-handed, one left-handed, and oneambidextrous. They performed the main protocol in ourlaboratory under conditions very similar to those of the astronautson ground.SetupIn four astronauts (S1–S4), hand movements were recorded at127.75 Hz by means of the HPA (Hand Posture Analyzer) system50.This system consists of a lycra glove, instrumented with 15 sensorsmeasuring the flexion-extension angles of the fingers plus theadduction-abduction angle of the thumb (0.4° resolution, 1°accuracy), and an inertial system wrapped at the wrist with threelinear accelerometers and three orthogonal gyroscopes. In eightastronauts (S5–S12), hand and arm movements were recorded at200 Hz by means of the ELITE-S2 system, with a 1-mm accuracyafter calibration51,52. This system consists of four TV camerasmonitoring the 3D position of eight retroreflective markers(15 mm in diameter) attached to the skin overlying the shoulder,elbow (humerus lateral epicondyle), wrist (radial styloid process),metacarpophalangeal joint of the thumb, and index finger, thenail of thumb and index fingers (distal phalanges), and handdorsum on the third metacarpal bone of the dominant arm. Inparticipant S12 (who performed the variant protocol), additionalmarkers were placed on the metacarpophalangeal joint of thelittle finger, the nail of middle and ring fingers, ear (tragion),forehead (glabella), chin (menton), neck (C7 vertebra), lower trunk(L4 vertebra), superior iliac crest, anterior and posterior superioriliac spines, hip (greater trochanter), knee (femur lateral epicon-dyle), and ankle (lateral malleolus). In participants S8, S9, S11, wetracked head movements from on-board video recordings (H264-MPEG-4 AVC) by means of Kinovea software (ver. 0.8.15, JoanCharmant). Pre-flight and post-flight tests were performed atNASA JSC or KSC, in a mockup of the ISS Destiny module or in alaboratory with a fake ceiling placed at the same height (2.16 m)as the ceiling of the ISS module. Control participants performedthe experiment in our laboratory with a fake ceiling placed at2.16 m. Their hand and arm movements were recorded at 100 Hzby means of the Optotrak-3020 system (Northern Digital, Water-loo, Ontario, 100-Hz, spatial accuracy better than 0.1 mm) usingthe same marker placement as for ELITE-S2.Experimental proceduresParticipants stood in normal erect (on ground) or quasi-erect (in-flight) posture (Fig. 1A). They faced the experimental PC with theinstructions placed at about eye-level, at a distance of about 1.5 m.For in-flight tests, the astronauts performed the task with the feetinserted in restraints fixed to the floor of the station. They couldhold a fixed pole or a handle with their nondominant hand tostabilize their posture.In the starting position, the dominant limb was adducted, quasi-“vertical” along the body side, with the hand supinated. Theparticipants were asked to imagine grasping a tennis ball with thedominant hand as if the ball were physically present. In the mainexperiments, participants (S1–S11) had to throw the imaginary ballTable 1. Session schedule.Astronaut BDC In-flight Post-flightS1 −68, −31 20, 89, 181 +8, +14S2 −155, −86 146, 174 +8, +16S3 −102 9 +1, +6, +12, +44S4 −30 7, 9 -S5 1 - -S6 1 - -S7 1, 21, 40 - -S8 −113, −92, −73, −22 16, 30 +2, +7, +42S9 −153, −84, −76 6, 15, 85 +2, +6, +67S10 1, 91, 134 - -S11 −147, −56, −13 17, 31, 52 +3, +6, +61S12 −137, −59 4, 29 +6, +11Days before launch are indicated for pre-flight experiments (BDC), flightdays for in-flight experiments, and days after landing for post-flightexperiments. For backup participants, days are relative to the firstexperiment.S. Gravano et al.3Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2021) 50 against the ceiling with an underarm movement47. The “upward”thrust involved flexing the upper arm, forearm, and wrist, andfinally opening the grip so as to virtually release the ball from thehand. They waited with the limb in roughly the same posture aswhen they threw the ball until they thought that the ball hadbounced back from the ceiling, and then they closed the grip so asto virtually grasp the incoming ball on the fly. In the experimentsof the variant protocol, the participant (S12) was asked to throwthe imaginary ball against a bullseye target attached to the frontwall at chin height, about 1 m distance, and to catch it back on therebound. The required throw involved an overarm movement53.In each trial of all experiments, one of three different levels ofthrowing force (low, medium, and high) was indicated by a bar ofcorresponding height displayed on the monitor. In different blocksof trials, the participants were asked to imagine that the motion ofthe ball was either affected by Earth gravity (1 g trials) orunaffected by gravity as in the spacelab (0 g trials). Experimentswith HPA involved two blocks of 12 trials each, one block for theimaginary 1g-condition and one block for the imaginary 0g-condition. Experiments with ELITE-S2 involved four blocks of 12trials each, two blocks for the imaginary 1g-condition and twoblocks for the imaginary 0g-condition. 1 g and 0 g blocks alwaysalternated between each other. The trial duration was 20 s afterthe presentation of the instruction on the monitor, the instructionspecifying imaginary 1 g or 0 g, plus the level of throwing force(low, medium, or high). During the first 10 s, the participant wasasked to look at the instruction and concentrate on theforthcoming action by mentally simulating it. After a GO signaland over the following 10 s, the participant had to execute thethrowing and catching sequence that he/she imagined in theprevious phase.Participants did not practice with a real ball in the context ofthese experiments, except for one participant (S9) who, outsidethe protocol schedule, decided to execute a few throws of a realrubber ball (size similar to a tennis ball) against the ISS ceiling aftertwo in-flight experiments (flight-day 6 and 85). This participantperformed 7 and 12 throws of the real ball the first and the secondtime, respectively. These results are plotted in Fig. 1B (blue dots).Control experiments with participants throwing a real ball againsteither the ceiling or front wall in our laboratory have beenreported in previous publications47,53. Representative results fromone control subject are plotted in Fig. 1B (red dots).Data analysisNo data were excluded from the analyses. In the sporadic caseswhen the participant did not respond to the GO signal, reactedtoo late due to lack of attention or arm kinematics could not bereconstructed due to missing markers, the trial was marked asmissing. All analyses (including the statistical ones) were carriedout in MATLAB (MathWorks, Natick, MA, USA). Kinematic data werenumerically low-pass filtered (bi-directional, zero-phase second-order Butterworth filter, 10-Hz-cutoff) and time-differentiated. Westudied the relationships between the throwing speed (V) of eachtrial and the duration of motion of the imaginary ball to and fro(T), since these relationships are revealing of the strategy used as afunction of the context. For each trial of throws to the ceiling, wecomputed V as the maximum value of the “vertical” component ofthe velocity of the index tip. T1 was the time of occurrence of Vand corresponded to the time of the virtual release of the ballfrom the hand. T2 was the time of virtual ball catch and wascomputed as the time of occurrence of hand closure around theball, estimated from the minimum value of the rate of change ofthe distance between the index tip and the metacarpophalangealjoint of the thumb. T was the time interval between these twoevents, T= T2 – T1. For frontal throws, V corresponded to themaximum value of the modulus of the velocity of the ringfingertip, and T2 corresponded to the time of minimum angularvelocity of the upper arm segment in the sagittal plane. Theseestimates have been previously validated in laboratory experi-ments involving throws of a real ball against the ceiling or a wall,where we monitored the kinematics of both the hand and a realball47,53,54.Next, we best-fitted (minimum root-mean-square-error RMSE)the relationship between the T and V values of all trials of eachcondition and experiment with the following equation:T ¼ KV(1)Equation 1 describes motion at a constant speed, such as in theabsence of gravity effects and air resistance, and assuming anelastic bounce of the ball against the ceiling or the wall with aconstant restitution coefficient. For a physically realistic throw, Kwould correspond to the total path length of the ball motion. Inour experiments, this corresponds to the distance betweenthe ceiling (or the wall in the variant protocol) and the hand atthe time of release plus the same distance at the time of catch. Weestimated these distances in the experiments with ELITE-S2 usingthe measured spatial coordinates of the hand at release and catchtimes and assuming a nominal contact point of the ball at bouncetime located on the vertical line of the throwing position for themain protocol and on the horizontal line for the variant protocol.Notice, however, that these estimates are approximate since thetrajectory of the imaginary ball was unknown. Moreover, we couldnot estimate these distances in the experiments with HPA,because this system does not provide the spatial coordinates ofthe hand but only its velocity.Ball motion in the presence of gravity effects theoretically obeysthe following equation (again assuming no air resistance and anelastic bounce of the ball on the ceiling):T ¼ 2gV ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV2 gKp (2)However, one can notice in Fig. 1B that experimental throws ofa real ball on ground can be adequately fit by Eq. 1, alsoconsidering the variability of both ball path length and elasticrestitution at contact with the ceiling. Moreover, we previouslyfound that Eq. 1 fit the throws of an imaginary ball at 1 gadequately for control participants47, and here we found that itfit the present results as well. Indeed, the main differencebetween 1 g and 0 g is that gravity dictates a minimum throwingspeed below which the ball would fall without contacting theceiling (or wall):Vmin ¼ffiffiffiffiffiffigKp(3)We quantified the adequacy of Eq. 1 to fit the observed data ofeach experiment by computing the normalized RMSE of thepredicted T* values versus the observed T values in all n trials ofeach condition and experiment:NRMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiΣ T Tð Þ2=nqT(4)T is the mean T value over n trials. To characterize the rate atwhich participants adapted to spaceflight, the individual K-valuesof in-flight experiments were normalized (Kn) to the mean K valuesof the corresponding pre-flight experiments. Changes of Kn of allexperiments and participants with flight-day were best-fitted with:K 0n ¼ a eðbFDÞ=τ þ c (5)where K 0n is the best-fitting value of Kn, FD is the flight-day, τ is thetime-constant, a, b, c are constants.In the ELITE-S2 experiments, we also computed the elevationangles relative to the “vertical” in the movement plane (sagittal)for the upper arm, forearm, metacarpus, and fingers. Head pitch inthe sagittal plane was estimated as the angle with the “vertical” ofS. Gravano et al.4npj Microgravity (2021) 50 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASAthe projected segment connecting the markers on ear tragus andglabella in participant S12, and as the corresponding angle of thesegment tragus-lateral eye canthus in participants S8, S9, and S11.In participant S12, we also estimated the prono-supination of theforearm from the coordinates of the markers on this segment. Forstatistical purposes, we considered the difference between themean value of prono-supination angle over the last 100ms beforeand including the throwing time and the 100 ms following andincluding the catch time. In this participant, we also consideredthe difference between the mean values of head pitch over thesame time intervals.Questionnaires of imageryIn the astronauts who performed pre-flight, in-flight, and post-flight sessions, we administered a paper-and-pencil questionnaireto assess the vividness of mental imagery about one week afterthe return from the mission, at the time of a post-flightexperiment. We used the “Vividness of Mental Imagery Ques-tionnaire” (VMIQ55), including 24 movement imageries fromsimple (e.g., standing) to complex (e.g., jumping off a high wall).The questionnaire requires imagining one item at a time from twodifferent perspectives: (i) “watching somebody else” (third-personperspective) and (ii) “doing it yourself” (first-person perspective).Vividness had to be rated by the participants on a five-pointLikert-type scale: extreme scores of 1 and 5 reflect extremely vividimages and the inability to produce a mental image, respectively.StatisticsDescriptive statistics include mean, SD, and uncertainty given bythe 95% confidence interval (CI). Statistical differences betweenconditions were assessed using either three-way ANOVA withimaginary gravity level, session type, and subject as factors on thedata separately averaged over each astronaut, or two-way ANOVAwith imaginary gravity level and session type on the pooledresults of all corresponding trials of all experiments. Bonferronimultiple comparison correction was used for all post hoc tests.Before hypothesis testing, we carried out a rigorous examinationof the distribution of model residuals. Statistical significance of alltests was set at α= 0.05.Reporting SummaryFurther information on research design is available in the NatureResearch Reporting Summary linked to this article.RESULTSWe first report the results of the main protocol involving throws tothe ceiling. Overall, there were five missing trials out of 2208 trials(about 0.2%).Relationship between target motion duration and throwingspeedAlthough the instructions specified three discrete levels ofthrowing force (low, medium, high), all participants varied thethrowing speed V widely across repetitions of the same referenceforce. Importantly, however, throwing speed and catching timecould differ appreciably as a function of the imagined gravity leveland experimental session.Figure 2 shows the scatter plots of T versus V, for all trials of thepre-flight, in-flight, and post-flight experiments performed byone participant (S2), as well as the trials of sample sessions fromthree other participants (S1, S8, and S9). These plots arequalitatively reminiscent of the T versus V plots of the throws ofa real ball in Fig. 1B, although they can deviate from physics insome relevant respects. We first consider the points of resem-blance with the throws of a real ball. The data-points of Fig. 2 areroughly distributed along hyperbolic functions of the form T= K/Vfor both the imaginary 0 g condition and the imaginary 1 gcondition. Adherence to the hyperbolic model was better in somesessions than others in the same participant (e.g., IF2 vs. IF1 of S2),or in some participants compared to another one (e.g., S1 vs. S9).Importantly, on average, the participants threw the virtual ball at alower speed and waited for a longer time before catching backthe ball for the imaginary 0 g than the imaginary 1 g condition, aswas the case for the throws of a real ball in Fig. 1B. In several cases,however, the performance was far from being quantitativelyconsistent with physics. Thus, the minimum throwing speed forthe imagined 1 g was considerably lower than the theoreticalvalue expected under Earth gravity effects (dashed lines in Fig. 2)in several cases, for instance in S2 IF1 and S8 PF1. Moreover, theparameters K of the fitting hyperbolas were congruent with theestimated path length of the imaginary ball only in-flight, as wewill see later.The performance of all participants was qualitatively compar-able but differed in the range of individual V and T values.Therefore, to obtain a global picture (Fig. 3), we pooled the resultsof all participants with in-flight experiments (n= 7, total numberof trials= 1824) after normalization of the individual T values (seeMethods). Despite inter-trial variability, the normalized data-pointsof the imaginary task are reasonably well-fitted by hyperbolicfunctions.We carried out three-way ANOVA with imaginary gravity level,session type, and subject as factors, on the original data separatelyaveraged over each astronaut. We found that V differedsignificantly with imagined gravity level (0 g, 1 g, F(1,11)= 96.22,P < 0.001), session (pre-flight, in-flight, post-flight, F(2,11)= 164.26,P < 0.001), and subject (F(6,11)= 55.75, P < 0.001). T dependedsignificantly on the imagined gravity (F(1,11)= 41.92, P < 0.001),and subject (F(6,11)= 76.09, P < 0.001), but did not dependsignificantly on the session (F(2,11)= 0.36, P= 0.563).Since the schedule of the experiments differed acrossastronauts, we also carried out two-way ANOVA with imaginarygravity level and session type on the pooled results of V and T (notnormalized values) of all corresponding trials of the experimentsof participants with in-flight sessions. The results were veryconsistent with those reported above. V differed significantly withboth imagined gravity level (F(1,1812)= 235.68, P < 0.001) andsession (F(2,1812)= 166.93, P < 0.001), with no significant interac-tion (F(2,1812)= 1.51, P= 0.222). All post hoc comparisonsbetween imagined gravity levels and between sessions weresignificant (P < 0.001, Bonferroni-corrected). T depended signifi-cantly on the imagined gravity (F(1,1812)= 228.75, P < 0.001), butdid not depend significantly on the session (F(2,1812)= 1.15, P=0.317) or the interaction (F(2,1812)= 0.70, P= 0.499). All post hoccomparisons between imagined gravity levels were significant(P < 0.001, Bonferroni-corrected), but no post hoc comparisonbetween sessions was significant (all P > 0.99).Figure 4A plots the mean values and 95% confidence limits of Vand T for the different conditions for all trials of the astronautswith in-flight experiments. The results show that, on average,these participants threw the virtual ball at considerably lowerspeeds and waited for a longer time before catching back the ballwhen they imagined a 0 g condition than a 1 g condition.Moreover, during in-flight experiments, they threw the virtualball at lower speeds than on ground. In the backup astronauts(n= 4) who performed the experiment only for baseline datacollection on ground, T depended significantly on the imaginedgravity (F(1,382)= 12.51, P < 0.001), whereas V did not (F(1,382)=1.35, P= 0.246).For the sake of comparison, Fig. 4A also reports the results ofcontrol subjects (n= 8) who performed the experiment in thelaboratory (see Methods). The statistical trend of their responses asa function of imagined gravity level was similar to that exhibitedby the astronauts of Fig. 4A. Thus, both V and T of controls differedS. Gravano et al.5Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2021) 50 significantly with imagined gravity level (F(1,380)= 10.63 and32.09 respectively, P < 0.001). However, the mean values of V and Tfor the 0 g condition in the controls were much higher than thecorresponding values of the BDC sessions in the astronauts.To quantify the extent to which hyperbolic functions T= K/V fitthe scatter plots of T versus V, we computed the normalized root-mean-square-error NRMSE of the fitting functions. On average,NRMSE was 0.227 (CI[0.206,0.248]), and it did not dependsignificantly on imagined gravity level (F(1,108)= 1.63, P=0.204), session (F(2,108)= 2.15, P= 0.121), or interaction(F(2,108)= 0.51, P= 0.599). Post hoc tests did not detect anysignificant difference of NRMSE between any session comparison(pre-flight, in-flight, and post-flight). However, for the imaginary 0g conditions of all participants, we observed a significant decreaseof both the NRMSE and the confidence intervals of the regressioncoefficient between the first and the last BDC, as well as betweenthe first and the last in-flight experiment (by >28% and by >34%for NRMSE and confidence intervals respectively, all P < 0.05,paired t-test), indicating improved adherence to the hyperbolicfunctions with practice both pre-flight and in-flight (see forexample the results of S2 in Fig. 2). For this analysis, we comparedthe first and the last experiment of the astronauts who performedat least two experiments in the corresponding session (BDC or in-flight). No such trend was observed for post-flight 0 g, nor for anyof the imaginary 1 g sessions.The constant K of the best-fitting functions differed significantly(two-way ANOVA on the pooled results) with imagined gravity level(F(1,1812)= 28.1, P < 0.001), session (F(2,1812)= 187.11, P < 0.001),and interaction (F(2,1812)= 15.41, P < 0.001, Fig. 4A). The interac-tion depended on the fact that the imagined gravity levelsignificantly affected only the pre-flight results (P < 0.001, posthoc Bonferroni-corrected), but not in-flight and post-flight results(P > 0.9). The main changes of K-values were related to the session.Thus, K was significantly lower in-flight than either pre- or post-flight for both imaginary 0 g and 1 g (P < 0.001, post hoc Bonferroni-corrected). K-values post-flight were significantly higher than thosein-flight, but lower than at pre-flight (all P < 0.001, Fig. 4A). A similartrend was revealed by three-way ANOVA on the data separatelyaveraged over each astronaut. In this case, K differed significantlywith session (F(2,11)= 31.47, P < 0.001), and subject (F(6,11)=53.56, P < 0.001), but did not differ significantly with imaginedgravity level (F(1,11)= 0.4, P= 0.54) nor was there a significantinteraction between session and gravity level (F(2,11)= 0.54,P= 0.60). In Fig. 4A, it can be noticed that the mean value of0 1 2 3 4 50.00.51.01.52.0T [s]S2, BDC10 1 2 3 4 50.00.51.01.52.0S2, BDC20g1g0 1 2 3 4 50.00.51.01.52.0T [s]S2, IF10 1 2 3 4 50.00.51.01.52.0S2, IF20 1 2 3 4 5V [m/s]0.00.51.01.52.0T [s]S2, PF10 1 2 3 4 5V [m/s]0.00.51.01.52.0S2, PF20 1 2 3 4 50.00.51.01.52.02.5S9, BDC10 1 2 3 4 50.00.51.01.52.02.5S1, IF30 1 2 3 4 5V [m/s]0.01.02.03.04.0S8, PF1Fig. 2 Imaginary motion duration vs. throwing speed. Scatter plots of T, V values for all trials performed by participants S2, S9, S1, and S8,pre-flight, in-flight, and post-flight, with best-fitting hyperbolic functions of imaginary 0 g (blue) and 1 g (red) data-points. Dashed curvescorrespond to T= 2 V/g.S. Gravano et al.6npj Microgravity (2021) 50 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASAK for the 0 g condition in the controls was considerably higher thanthe corresponding values in the astronauts.As remarked in the Introduction, in the case of a ball motioncomplying with ideal Newtonian mechanics (assuming no airresistance and a constant elastic bounce against the ceiling), Kcorresponds to the total path length of ball motion, back and forthbetween the hand and the ceiling. We could only estimate pathlength approximately in the present experiments since the contactpoint of the imaginary ball with the ceiling was indeterminate.Nevertheless, we computed the 95% confidence interval of anestimated path length in a subset of cases (see Methods), and weplotted it as a theoretical reference in Fig. 4A (gray area). It can benoticed that the mean K-values of in-flight experiments for bothimaginary 0 g and 1 g are much closer to the estimated pathlength than the mean K-values of all ground experiments (controlsubjects, BDC, and post-flight sessions in astronauts). Thus,participants exhibited better compliance of mental imagery ofball motion with the hand-to-ceiling distance during in-flight thanground experiments.The changes of K-values in-flight relative to ground have anadditional, important implication. The constant K of the best-fitting function T= K/V also defines the position of the data in theFig. 4 Global performance parameters. Mean values and 95% confidence limits of V, T, and K over all trials, imaginary 0 g (blue) and 1 g (red),pre-flight, in-flight, and post-flight. A Main experiment: seven astronauts and eight controls (labeled C). The gray area denotes the 95%confidence interval for the mean estimated hand-to-ceiling distance. B Frontal throws (participant S12).0 2 4 60.00.51.01.52.02.5Tn [s/m]BDC0g0 2 4 60.00.51.01.52.02.5IF0g0 2 4 60.00.51.01.52.02.5PF0g0 2 4 6V [m/s]0.00.51.01.52.02.5Tn [s/m]1g0 2 4 6V [m/s]0.00.51.01.52.02.51g0 2 4 6V [m/s]0.00.51.01.52.02.51gFig. 3 Pooled normalized T vs. V. Pooled results of all trials of all participants of the main protocol with in-flight experiments, afternormalization of the individual T values to the best-fitting K value of each experiment. Black curves are best-fitting hyperbolic functions overall trials of each condition.S. Gravano et al.7Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2021) 50 T versus V diagram: the smaller is K, the closer is the function tothe origin and the lower is the throwing speed necessary to obtaina given duration of ball motion. Therefore, lower K values in-flightindicate that adjustment to spaceflight involved a shift toward theorigin of T versus V functions interpolating the trials. This shift canbe appreciated in Fig. 5 comparing the results for the experimentsperformed pre-flight, in-flight, and post-flight by one participant.In-flight data-points (red) are closer to the origin than pre-flightdata (blue), while post-flight data (green) have an intermediateposition, denoting a partial return to the baseline. Thus, K valuesfor imagined 0 g (1 g) data of Fig. 5 were 4.42 (2.87), 2.50 (1.94),and 2.94 (2.4) pre-flight, in-flight, and post-flight, respectively. InFig. 5, the experimental results are compared with the predictionsbased on the hand-to-ceiling distance estimated for this subjectin-flight (dashed curves). As in the case of the populationensemble of Fig. 4A, in-flight results come closer to the predictionsthan ground results.We also searched for trends of changes of K-values with days offlight (which are independent of the trends reported above forNRMSE and confidence intervals of the regression coefficient).Across participants, adaptation with spaceflight duration wasevident for the condition of imaginary 0 g ball motion, but not forimaginary 1 g. Since the time schedules of the experimentsdiffered across astronauts (see Table 1), we considered the resultsof all astronauts together under the assumption that theyadapted to the flight similarly. Since the individual K-values ofpre-flight experiments did not show any significant trend withtime (r2= 0.039, n= 16), we normalized the individual K-values ofin-flight experiments by the mean K-values of the correspondingpre-flight experiments. Figure 6 plots the normalized values of Kfor all experiments involving the imaginary 0 g condition as afunction of the flight-day of the experiment. Participants aredenoted by color-coding. It can be noticed that S4, S8, S9 (andS12, see below) showed a substantial decrement of normalized Kwith flight-day, whereas S1, S2, and S11 did not. However, thelatter subjects performed all in-flight sessions after the globaltrend (estimated over all astronauts) has reached a plateau.Indeed, when considered together, the data-points of allparticipants roughly follow an exponential trend with flight-day(r2= 0.622), indicating a decrease of normalized K-values byabout 40% over the first 17 days, and relatively stable values inthe following days (<0.5% change between consecutive days).K-values for imaginary 0 g at the return from the mission did notexhibit any significant trend with the day after landing (r2= 0.020,n= 17). No significant trend was found for imaginary 1 g ballmotion, pre-, in- or post-flight (r2 < 0.095).Arm and head kinematicsIn all sessions, throwing the virtual ball in the air was accomplishedby relatively stereotyped movements, involving ballistic flexion ofthe shoulder, elbow, wrist, and metacarpophalangeal joints (Fig. 7A).The time changes of the elevation angles of the limb segments(upper arm, forearm, metacarpus, and fingers) were quasi-synchro-nous, as were the corresponding changes in the opposite directionat catching time (Fig. 7B). Arm and hand kinematics wasqualitatively comparable for the two imaginary gravity levels (0 g,1 g), as well as for the experiments performed on ground (pre- andpost-flight) and in-flight. In particular, the limb elevation anglescovaried tightly in all conditions. However, on average, armmovements tended to be slower for imaginary 0 g than 1 g, andslower in-flight than on ground, as detailed in the previous section.Arm movements were preceded by head movements. Partici-pants pitched the head up and down by about 60°, as if theytracked part of the imaginary trajectory of the ball. Figure 8 showsexemplary traces (orange) of the time changes of the intersectionof the ear-eye line with the virtual ball path (see Methods),compared with the corresponding changes of the “vertical”position of the index finger (blue) for trials performed pre-flight,in-flight and post-flight. In general, the peak velocity of the headmovement led to peak velocity of the index. Lead-time dependedsignificantly on the imagined gravity level (F(1,240)= 7.72, P=0.0059, two-way ANOVA), but did not depend significantly onsession (F(2,240)= 0.98, P= 0.376) or interaction (F(2,240)= 0.89,P= 0.412). On average, lead-time was 214ms (CI[146 ms,282 ms])and 360 ms (CI[292 ms,428 ms]) for imaginary 0 g and 1 g,respectively.Experiments with frontal throwsThe results of the main experiments showed that the participantssimulated the qualitative characteristics of inertial motion ofweightless objects in the specific case of imaginary motion alongthe apparent vertical as defined by the ceiling and floor. To extendthe findings, we asked one astronaut (S12) to throw the imaginaryball against a target placed on the front wall at shoulder level andto catch it on the rebound. In these experiments, there were fivemissing trials out of 288 trials (about 1.7%).Figure 9A shows the stick diagrams of two representative trialsperformed pre-flight, and Fig. 9B shows the correspondingchanges of head pitch, upper arm, forearm, and prono-supination angles, upper arm angular velocity, and ring fingervelocity. The overarm throw involved the forward projection ofthe hand to impart momentum to the virtual ball. In imaginary 0 gtrials, the forearm was mid-pronated throughout, from throwingtime to catching time. Moreover, the hand caught the virtual ballon the rebound at about the same height from the floor as that atV [m/s]012345T [s]0g0 1 2 3 4 5 0 1 2 3 4 5V [m/s]012345T [s]1gBDCIFPFFig. 5 T vs. V curves pre-flight, in-flight, and post-flight. Results forthree different experiments (left to right, imaginary 0 g and 1 g)performed pre-flight (blue), in-flight (red), and post-flight (green) byparticipant S11. Notice the shift of T-V curves in-flight closer to thedashed curves, which depict the predictions based on the hand-to-ceiling distance estimated for this subject in-flight.0 20 40 60 80 100 120 140 160 180 200Flight Day00.10.20.30.40.50.60.70.80.91KNS1S2S3S4S8S9S11S12Fig. 6 In-flight adaptation. KN, normalized K-values of all in-flightexperiments plotted as a function of the experimental flight-day.Inset: color-coding of different astronauts. Parameters of exponen-tial fitting (Eq. 5): τ = 3.666, a= 1.317, b= 0.896, c= 0.606.S. Gravano et al.8npj Microgravity (2021) 50 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASAthrowing time. On average over all 0 g trials (n= 140), thedifference in “vertical” position of the index finger at throw andcatch times was 2.75 cm (CI[2.61 cm,2.89 cm]). In these trials, thehead rotated to a very limited extent. Overall, head, arm, and handgestures were compatible with throwing and catching a ball thatmoved along a straight path back and forth from the wall,consistent with inertial motion in the absence of gravity effects.In contrast, in imaginary 1 g trials (n= 143 trials), the forearmwas mid-pronated at throwing time but became mid-supinated atcatching time, as in an underarm catch. Moreover, to catch thevirtual ball on the rebound, on average the hand was lowered by17.38 cm (CI[16.64 cm,18.13 cm]). In 1 g trials, the head pitchedslightly downward after the throw, as if it tracked the imaginarydownward trajectory of the ball. Overall, head and arm gesturesFig. 7 Arm kinematics. A Six representative trials of participant S9. Left to right, stick diagrams (every 50ms) of trials performed pre-flight, in-flight, and post-flight, for imaginary 0 g (top) and 1 g (bottom). B Two representative trials of participant S8 (left-handed). Left: stick diagrams(every 50ms) prior to throw, and after catch. Red and green sticks correspond to throw and catch times; the other sticks were sampledbackward or forward relative to throw and catch, respectively. Right: time course of the elevation angles of the upper arm, forearm, firstmetacarpus, thumb, index, and “vertical” component of index velocity. Red and green vertical lines correspond to throw and catch times.-2 -1 0 1 2 -1 -0.50 0.5 1 y [m]BDC-2 -1 0 1 2 -1 -0.50 0.5 1 IF-2 -1 0 1 2 -1 -0.50 0.5 1 PFheadindex-2 -1 0 1 2 time [s]-1 -0.50 0.5 1 y [m]BDC-2 -1 0 1 2 time [s]-1 -0.50 0.5 1 IF-2 -1 0 1 2 time [s]-1 -0.50 0.5 1 PF0g1gFig. 8 Head and index finger motion. Head and index motion for throwing to the ceiling. Red: time course of the intersection of the ear-eyeline with the virtual ball path along the “vertical”. Blue: time course of the “vertical” position of the index finger. Data were averaged over alltrials performed pre-flight, in-flight, and post-flight by participant S11.S. Gravano et al.9Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2021) 50 were qualitatively compatible with throwing and catching a ballthat fell downward, consistent with gravity effects.To assess the statistical differences of the throwing-catchingsequence between conditions, we considered the changes of bothprono-supination and head pitch between throw and catch (seeMethods). We found that prono-supination depended significantlyon imagined gravity level (F1,278)= 280.79, P < 0.001), session(F(2,278)= 25.76, P < 0.001), and interaction (F(2,278)= 29.08, P <0.001). On average, the forearm rotated toward supination by91.9° (CI[84.7°,99.2°]) in imaginary 1 g trials, while it rotated by20.4° (CI[9.3°,27.4°] in imaginary 0 g trials. Notice that prono-supination per se does not fully capture hand orientation in 3Dspace. Indeed, small amounts of adduction/abduction and axialrotation at the glenohumeral joint, plus flexion-extension, andabduction-adduction at the wrist also contribute to handorientation56.Head pitch also depended significantly on imagined gravitylevel (F(1,278)= 57.07, P < 0.001) and interaction (F(2,278)= 4.75,P < 0.01), but did not depend significantly on session (F(2,278)=1.17, P= 0.31). The head was pitched downward by 5.57° (CI[4.90°,6.25°]) in imaginary 1 g trials, while the pitch rotation was2.59° (CI[2.18°,3.00°]) in imaginary 0 g trials. Since the imaginaryball in 1 g trials shifted along the vertical by a small extentbetween the throw and the catch, the corresponding headmovements were also of small amplitude compared with those ofthe main experiment, when the imaginary ball shifted along aconsiderable vertical path.The trends of T, V, and K-values were similar to those describedfor the main experiments, consistent with a differential processingof imaginary gravity level and with adaptation to flight (Fig. 4B). Allthree parameters differed significantly with imagined gravity level(F(1,278)= 116.27, 38.63, and 74.14 for V, T, and K respectively, P <0.001), session (F(2,278)= 41.69, 18.08, and 18.66, P < 0.001), andinteraction (F(2,278)= 4.66, 4.42, and 4.0, P < 0.02). For in-flightimaginary 0 g trials, V was significantly lower and T significantlyhigher than the corresponding values at pre- and post-flight (bothP < 0.001, post hoc Bonferroni-corrected). V and T of imaginary 1 gtrials depended less on the session than the corresponding valuesof 0 g trials. V in-flight was not significantly different from pre-flight (P= 1) but was significantly lower than post-flight (P < 0.001,post hoc Bonferroni-corrected). T in-flight was not significantlydifferent from either pre-flight (P= 1) or post-flight (P= 0.152).Also, this participant showed adaptation of K-values of 0 g trials in-flight, with a decrement over the two successive in-flightexperiments. The corresponding data-points (blue in Fig. 6) areroughly aligned with the exponential function fitting the results ofthe main experiment.Rating of imagery vividnessAll tested participants reported good levels of the vividness ofmental imagery in the questionnaire provided after the experi-ments. Thus, the mean scores of VMIQ were 1.57 (CI[1.40,1.74]) and1.87 (CI[1.73,2.02]) for the imagery items in the first-person andthird-person perspective, respectively, corresponding to scoresintermediate between “Perfectly clear and as vivid as normalvision” (score= 1) and “Clear and reasonably vivid” (score= 2) ofthe scale.DISCUSSIONThe results are consistent with the hypothesis that the participantswere able to simulate mentally the qualitative characteristics of0.5 m0 2 4 60 40 80 120Elevation angles [deg]70 90 110Head Pitch [°]0gHead pitchUpper armForearmSupin0 2 4 6Time [s]02468Speed [m/s]-8-40 4 8 Angular velocity [°/s]RingUpper arm0 2 4 60 40 80 120Elevation angles [deg]70 90 110Head Pitch [°]1g0 2 4 6Time [s]02468Speed [m/s]-8-40 4 8 Angular velocity [°/s]AB0g1gFig. 9 Throws of the imaginary ball to a frontal target. A From left to right, stick diagrams at 100ms before throw, throw, 100ms after throw,catch, and 100ms after catch. The short vertical bar on the right of each panel depicts the bullseye target. B Upper row: time course of headpitch, upper arm, forearm, and prono-supination angles. Lower row: upper arm angular velocity and ring finger velocity. Red and greenvertical lines correspond to throw and catch times. Two representative trials of participant S12, imaginary 0 g and 1 g condition, pre-flight.S. Gravano et al.10npj Microgravity (2021) 50 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASAinertial motion of weightless objects already on ground, and thatthey further adapted their behavior to the real weightlessconditions of spaceflight. On average, the participants threw thevirtual ball at lower speeds V and waited for a longer time T beforecatching back the ball for the imaginary 0 g condition than the 1 gcondition. Moreover, the T versus V function interpolating theimaginary 0 g trials performed during spaceflight shifted closer tothe origin compared to the corresponding function of the baselinetrials performed on ground. We quantified the shift in terms of theconstant K of the hyperbolic function fitting T versus V data-points.Mean K-values were significantly lower in-flight than either pre- orpost-flight, indicating that the astronauts used a lower throwingspeed to obtain a given duration of ball motion. Moreover, thenormalized K-values of 0 g trials pooled across participantsdecreased exponentially with flight-day, suggesting adaptationwith increasing exposure to spaceflight. Practice with theimaginary 0 g condition led to improved adherence to the idealmodel of inertial motion both on ground and in-flight, as shownby the reduced fitting errors. Finally, the analysis of armkinematics of the frontal throws revealed a differential processingof imagined gravity level (0 g versus 1 g) also in terms of thespatial features of the virtual ball trajectory and arm movements.Agreement of mental imagery with physics was generallyqualitative rather than quantitative, and there were cases ofsignificant departure from Newtonian mechanics. Thus, throwingspeeds for imagined 1 g were often lower than the minimumspeed theoretically compatible with throws hitting the ceiling.Also, participants exhibited reasonably accurate compliance ofmental imagery with the hand-to-ceiling distance only during in-flight experiments. In the following, we consider the implicationsof the results, including alternative explanations.Although the astronauts were instructed to imagine the motionof the virtual ball, they could have followed a simpler strategy ofmental calculation57 that would result in an inverse relationshipbetween throwing speed and duration of flight of the virtual ball:for a higher throwing speed, wait a longer time before catching.However, there are important clues that the participants didsimulate the motion of a virtual ball. First, the data-points of eachcondition were reasonably well-fitted by a hyperbolic functionwith a single K constant, indicating adherence to a specific mentalmodel of target motion. To replicate these findings, the mentalcalculation would need to be rather accurate. Furthermore, weobserved that the participants of the main experiment pitchedthe head “up” and “down” by about 60° as if they tracked part ofthe imaginary trajectory of the ball. Head movements system-atically led to arm movements, lead-time being much longer forimaginary 1 g than 0 gmotions, indicating a differential processingof the imaginary gravity level. Similarly, in the experiments withfrontal throws, head movements, arm prono-supination and handposition at catch time were all indicative of a differentialprocessing of the imaginary gravity level, rather than of a simplemental calculation of elapsed time.Since the instructions about the throwing force to apply in eachgiven trial were identical for the 0 g and 1 g trials, it was theparticipants’ decision to tune their forces to the imaginary gravitylevel, resulting in lower throwing speeds for 0 g trials, on average.In addition, the mean V values for both 0 g and 1 g trialsperformed in-flight were lower than the corresponding values forthe trials on ground. In line of principle, the latter finding might berelated to a general slowing of movements in weightlessness.Previous reports in the literature on this subject are conflicting.Some studies reported a tendency for movement slowing for bothvertical and horizontal pointing movements performed inspace58–60 or parabolic flight36,61,62. In particular, Mechtcheriakovet al.59 reported significant slowing of aiming arm movementsover the initial in-flight sessions and a tendency to havemovement durations comparable to pre-flight sessions in latersessions (about 50 days after launch). In other studies, instead, thepeak velocity of arm movements was not significantly affected byweightlessness63–67. In the Neurolab experiments, Bock et al.68found slowing of pointing movements but not of trackingmovements. Overall, it appears that the effects of weightlessnesson arm kinematics are task-dependent.Importantly, a generic slowing of movements cannot accountfor the shift of the T-V scatter plots closer to the origin (Fig. 5),resulting in lower values of the K parameter for in-flight data(Fig. 4). Had the participants used lower throwing speeds whilekeeping the same mental image of the virtual ball kinematicsin-flight as on ground, the T-V data-points should have shiftedalong the same or a similar hyperbolic function in-flight as thatfound on ground, yielding similar K-values.In theory, mental imagery of ball kinematics might change inrelation to a misperception of velocity, time or distance. Thus, simplearithmetic shows that lower values of K-values in-flight mightdepend on either an overestimate of the motion duration of thevirtual ball for a given throwing speed or an overestimate ofthrowing speed for a given ball motion duration. For a given V, ahypothetical duration overestimate would result in lower values of Tthan anticipated by the subject. However, if this were the case, wewould expect shorter T values in-flight than on ground, which wasnot the case. Moreover, previous studies reported underestimatesrather than overestimates of time durations in weightlessness,suggesting a time-compression effect for spaceflight42,43,69.As for hypothetical speed overestimates, these would result inlower values of V for a given T than anticipated by the subject.Overestimates of movement speed are theoretically possible dueto gain changes of sensory inflow from muscle spindles inducedby weightlessness. Spindles gain attenuation -due to bothreduced otolith influences and mechanical unloading of thebody- has been advocated to explain possible alterations of armand leg motor control, position sense, perceptual judgments ofobject length, heaviness, and mass5. However, the observationthat V- and K-values remained significantly lower than the pre-flight baseline values even several weeks after return to theground indicates that the adaptation of mental imagery wasmaintained independently of weightless conditions, indicating aminor role of spindles gain attenuation.Still another hypothetical explanation for the decrease ofK-values in-flight is that the participants underestimated thehand-to-ceiling distance when they threw and caught theimaginary ball. Indeed, for a physically realistic throw, the constantK corresponds to this distance. However, misperceptions ofdistances have been reported in the opposite direction duringparabolic flight, with overestimates of upward distances at alltested gravity levels, including 0 g70. Here, the average K-values ofin-flight experiments did not differ significantly from theestimated summed hand-to-ceiling distances at the throw andcatch time, implying that participants implicitly used a correctestimate of these distances in-flight. If anything, the observationthat the average K-values of ground experiments were higher thanthe hand-to-ceiling distance would be consistent with distanceoverestimates on ground70.We remark that, if throwing speed, time duration, or ceilingdistance were misrepresented, the parameter K, which dependson these perceptual variables, should covary tightly in imaginary0g and 1 g trials. In particular, one would expect a similarexponential decay of normalized K values with flight-day for bothimaginary conditions, which was not the case (see next section).Thus, although misperceptions of the above variables aretheoretically possible, a more plausible interpretation is that of agenuine adaptation of mental imagery to spaceflight. Specifically,the astronauts appeared to achieve a better representation of 0 ginertial motion in weightlessness and better discrimination relativeto 1 g gravitational motion.The results indicate that the participants managed to adjust tospaceflight by shifting the T versus V function interpolating theS. Gravano et al.11Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2021) 50 imaginary throws closer to the origin for both 0 g and 1 g trials(Fig. 5). Moreover, considering the overall trend over allastronauts, we found evidence for a further adaptation ofnormalized K-values of 0 g trials (but not 1 g trials) with prolongedexposure to weightlessness (Fig. 6). This adaptation implied thatastronauts employed lower throwing speeds to obtain a givenduration of imaginary ball motion, precisely the kind of adaptationadvocated in the Introduction as necessary to impart lowermomenta to handled objects during spaceflight than on Earth26,71.On the other hand, the results also indicated that mentalimagery of target motion under gravity often deviated substan-tially from physical predictions. Thus, the minimum throwingspeed for an imagined 1 g was often considerably lower than thetheoretical value predicted by Newtonian mechanics. In thisrespect, the current results are consistent with previous findings incontrol participants on ground47,57 showing that mental imageryof gravity-accelerated motion does not conform to the quantita-tive parameters of Newtonian mechanics. Notice, however, thatwe cannot expect that the results of mental imagery of 1 greplicate all features of Newtonian mechanics. Indeed, the T versusV function of a real ball motion under any gravity value (not just 1g) is non-monotonic, so that T increases linearly with V withoutcontacting the ceiling up to a threshold speed (see dashed lines inFig. 1B and Fig. 2), while T decreases non-linearly with increasing Vabove that threshold. However, we instructed our participants tothrow the imaginary ball in such a manner as to contact theceiling, so that we would expect that T should decrease withincreasing V for imagined 1 g just as for imagined 0 g, which iswhat we found.On Earth, the vertical direction is estimated by a combination ofgravity, body, and vision cues, each weighted based on itsreliability72. In weightlessness, the motor and perceptual “vertical”are often dominated by body-centered cues73–75. In the presentexperiments, there were no gravity-related cues nor visual cuesabout the imaginary ball trajectory. However, the ISS modules areendowed with abundant visual cues about “up” and “down”,providing a visual reference for the “vertical”. Body-centered andvisual cues about the “up” direction were aligned in ourexperiments so that we cannot distinguish between the relativeroles of different references frames for mental imagery.The T-V characteristics of the protocol involving frontal throwswere qualitatively similar to those of the main protocol, showingthat mental imagery of gravitational or inertial motion can occuralso for motion directions roughly orthogonal to the visual andbody-centered “vertical”. Moreover, the analysis of arm kinematicsrevealed that the participant threw and caught the imaginary ballas if they anticipated a linear trajectory of the virtual ball forimaginary 0 g trials but a downward parabolic trajectory forimaginary 1 g trials. Therefore, the presence or absence of gravityeffects appears to constrain not only the temporal but also thespatial characteristics of the imaginary trajectory.The study had some limitations. We reconstructed headmovements in the sagittal plane, but we could not monitor eyemovements. The time course of adaptation with flight-day shouldbe interpreted cautiously since its analysis relied on between-subjects comparisons, time-schedules being different acrossparticipants. We were able to enroll only one astronaut for thefrontal throws. We could not discriminate possible differences inperformance between rookies (first-time fliers) and experiencedastronauts, given the limited number of participants. Three out offour of the backup astronauts were rookies at the time ofexperiments, but so were three out of seven of the astronauts whoperformed in-flight experiments (see Methods). Therefore, we donot know whether the different performance of backups relativeto the baseline performance (BDC) of astronauts who laterperformed the main protocol in-flight depended on the lack ofprevious flight exposure.An important comparison is that of the astronauts’ perfor-mance with the performance of our control subjects (obviouslywithout any spaceflight experience) who carried out the sameprotocol of throwing an imaginary ball to the ceiling. The controlparticipants showed a statistical trend of the responses as afunction of imagined gravity similar to that of the astronauts.However, on average, they employed throwing speeds (and K-values) for the 0 g condition much higher than those of theastronauts. This difference further highlights the specific fitnessof the astronauts to weightlessness, possibly derived from theirprior training in parabolic flight or previous experience withspaceflight.In conclusion, the protocol of mental imagery of inertial motionof weightless objects lends itself to training people in preparationfor a space mission, as well as during the mission to facilitatespace adaptation. Similarly, mental imagery of gravitationalmotion might be used during long-term missions to facilitatere-adaptation to gravity effects in preparation for landing. Sincethe motor cortex shows plastic changes during motor learning bymental training76, it is possible that training astronauts with ourmental imagery protocols may enhance motor plasticity, pro-gressively inducing adaptation of the hand forces employed toshift objects as a function of the gravity level. Moreover, this orsimilar protocols of mental imagery may help tuning vestibularplasticity in-flight. The reasoning is as follows. Vestibular sensorydeprivation and altered central interpretation of vestibular inputsare key factors underlying several sensorimotor and cognitiveimpairments during and after spaceflight5,6. Recent neuroimagingstudies found evidence for vestibular cortex reorganizationfollowing spaceflight, suggesting that space-related factorsdeeply influence the neural correlates of vestibular processingin several brain regions including the insulae71,77,78. Moreover,functional magnetic resonance studies showed that the visualeffects of gravitational motion are processed in the vestibularcortex, whose hub regions are the insula, retro-insula, and parietaloperculum79,80. Finally, the imaginary performance of actionsnormally affected by gravity activates insular regions close tothose encoding the visual effects of real gravity45. Therefore, theability to engage the vestibular cortex with mental imagery raisesthe interesting possibility of modulating central vestibularnetworks and reducing maladaptive responses to spaceflight.The imagery might modulate vestibular networks using top-downpredictive mechanisms of target motion under normal or reducedgravity effects81.DATA AVAILABILITYData of Fig. 3 including the results of all trials of all deidentified participants of themain protocol with in-flight experiments are deposited at https://figshare.com/s/7e9060139c5a93cdf585.CODE AVAILABILITYCustom codes for analyses will be made available upon reasonable request to thecorresponding author.Received: 10 June 2021; Accepted: 27 October 2021;REFERENCES1. Barratt, M. R. & Pool, S. L. (eds) in Principles of Clinical Medicine for Space Flight(Springer, 2008).2. Blaber, E., Marcal, H. & Burns, B. P. Bioastronautics: the influence of microgravityon astronaut health. Astrobiology 10, 463–473 (2010).3. Bloomberg, J. 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Funct. 221, 2873–2876 (2016).78. Pechenkova, E. et al. Alterations of functional brain connectivity after long-duration spaceflight as revealed by fMRI. Front. Physiol. 10, 761 (2019).79. Indovina, I. et al. Structural connectome and connectivity lateralization of themultimodal vestibular cortical network. Neuroimage 222, 117247 (2020).80. Indovina, I. et al. Representation of visual gravitational motion in the humanvestibular cortex. Science 308, 416–419 (2005).81. Maffei, V. et al. Visual gravity cues in the interpretation of biological movements:neural correlates in humans. Neuroimage 104, 221–230 (2015).ACKNOWLEDGEMENTSWe thank Dr. Vittorio Cotronei (ASI) for support of the HPA missions, Dr. GabrieleMascetti (ASI) for support of the ELITE-S2 missions, Dr. William L. Miller for help withtraining some astronauts and for experimental insights, and all astronauts for theirenthusiastic participation to the experiments. Kayser Italia S.r.l. provided the motioncapture equipment funded by the Italian Space Agency (ASI), while ALTEC and ASIprovided ground support. The work was supported by ASI grants I/006/06/0 and2019-11-U.0. The funder had no role in study design, data collection and analysis,decision to publish, or preparation of the manuscript.AUTHOR CONTRIBUTIONSF.L. and M.Z. designed research; S.G., F.L. and M.Z. performed research; S.G., F.L. andM.Z. analyzed and interpreted the data; S.G., F.L. and M.Z. wrote the paper.COMPETING INTERESTSThe authors declare no competing interests.ADDITIONAL INFORMATIONSupplementary information The online version contains supplementary materialavailable at https://doi.org/10.1038/s41526-021-00179-z.Correspondence and requests for materials should be addressed to FrancescoLacquaniti or Myrka Zago.Reprints and permission information is available at http://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard to jurisdictional claimsin published maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in anymedium or format, as long as you giveappropriate credit to the original author(s) and the source, provide a link to the CreativeCommons license, and indicate if changes were made. The images or other third partymaterial in this article are included in the article’s Creative Commons license, unlessindicated otherwise in a credit line to the material. If material is not included in thearticle’s Creative Commons license and your intended use is not permitted by statutoryregulation or exceeds the permitted use, you will need to obtain permission directlyfrom the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2021S. Gravano et al.14npj Microgravity (2021) 50 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA

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