Journal of Vestibular Research, Vol . 8, No. I, pp. 95-105, 1998 Copyright

0957-4271198 $19.00 + .00

ELSEVIER PII S0957 -4271 (97)00058-X

Original Contribution

HUMAN HEART RATE VARIABILITY RELATION IS UNCHANGED DURING MOTION SICKNESS

Thomas J. Mullen, Ronald D. Berger, Charles M. Oman, and Richard J. Cohen

Harvard-MIT Division of Health Sciences and Technology and Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts

Reprint address: Thomas J . Mullen, Harvard-MIT, Division of Health Sciences and Technology, Massachusetts

o Abstract - In a study of 18 human subjects, we applied a new technique, estimation of the trans-fer function between instantaneous lung volume (IL V) and instantaneous heart rate (HR), to assess autonomic activity during motion sickness. Two control recordings of IL V and electrocardiogram (ECG) were made prior to the development of mo-tion sickness. During the first, subjects were seated motionless, and during the second they were seated rotating sinusoidally about an earth vertical axis. Subjects then wore prism goggles that reverse the left-right visual field and per-formed manual tasks until they developed moder-ate motion sickness. Finally, ILV and ECG were recorded while subjects maintained a relatively constant level of sickness by intermittent eye clo-sure during rotation with the goggles. Based on analyses of IL V to HR transfer functions from the three conditions, we were unable to demonstrate a changt· in autonomic colltrol of hear! rate due tn rotatin l1 alolle or dut' to motinJl sicknes!o. Thesl finding!. d(o !lot suppo,; tht· lIotion tha . moden lte moti nH sici,;n ·.·s~ is manifested a~ a g~'ne:-alize(' :Jl1. Wnomit' respnnse. (f'! ! ol)~: S!s!:'vie r- Science In~·.

:=i Keyworu - -Ilause~: and vomiting syndromes: parasympatlletic: sympathetic; autonomic nervous system: transfer function estimation.

Introduction

Motion sickness is a nausea and vomiting syn-drome that is induced by certain types of real or

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perceived body motions. It is characterized by signs and symptoms. such as pallor, cold sweat-ing. headache, fatigue. nausea and vomiting, that are qualitatively similar to those of other nausea and vomiting syndromes (1). It is well established that only certain types of motion en-vironments will induce motion sickness, and the sensory conflict theory provides a reliable means of predicting which environments may be pro-vocative (2,3). However, despite significant re-search (well reviewed in [4-6]), the physiology of motion sickness remains poorly understood.

It seems clear that some degree of vestibular function is required, since labyrinthine defec-tives are immune to motion sickness (6) . It is also known that impulses from the vestibular nerve impinge on the lateral medulla. but the roles of other afferent pathway!> and of central processing in till generatior. of si(;knes~ remain uJ1ciea;'

Ear]\ srudie~ indicai'c:u lila the cerebellar Jl o ou ill :-- and UVUI

The cOller-pt of discretely local' ' . I , ')mitil : centers relllillJ ' ,· ler question, bUL rhe central importance of the lateral medulla is generally accepted (1). A similar situation exists in regard to the efferent pathways implicated in motion sickness. It is generally accepted that somatic efferents controlling respiration and abdominal musculature, and visceral efferents affecting gastric tone and motility are involved (1). How-ever. tl,!c role of the autonomic nervous system fANS, "1 the development of mmion sickness continues to be controversial.

.-\ wide' varier\' of inJirect evidence "ug:;l~q-; mal l1e ANS llay play a role in the Jeve!op-ment of motion sickness. First, some signs and symptoms of sickness. such as pallor and sweat-ing, are considered autonomic manifestations. Second, many of the most effective drug thera-pies are sympathomimetics or parasympatholyt-ics, and it is speculated that the autonomic actions of these drugs serve to alleviate symp-toms. Third, successes have been reported in the experimental use of biofeedback and autogenic training in alleviating sickness (12,13). More quantitative studies have been conducted in which "autonomic manifestations" such as changes in heart rate, blood pressure, gastrointes-tinal motility, and skin resistance have been monitored during motion sickness (14-18). Trends in these parameters have been inter-preted to indicate that motion sickness involves a widespread increase in sympathetic activity similar to a generalized "stress" response (14. 19). However, the trends in these parameters have been inconsistent between studies. and a

nnr'" rn'''' pro autonorruc activity. The two ANS subdivisions, the parasympathetic and the sympathetic systems, provide the pri-mary pathways for regulation of HR over the short term, and therefore variability in HR re-flects variability in autonomic outflow to the heart. It is important to recognize that while mean HR is determined by mean autonomic fir-ing rates, variability in HR is due to the variabil-ity in autonomic firing rates. Ishii, Igarashi, and their colleagues (20,21) studied HR variability in motion sick squirrel monkeys and quantified

T. J. Mullen et al

variability j ! .... :·ilb of the coefficient of varia-tion (CV) of R-R intervals (defined as the stan-dard deviation of R-R intervals expressed as a percentage of their mean). They found a marked increase in CV prior to emesis, and, based in part on a companion pharmacological study, they concluded that this change was parasympa-thetically mediated. More recently, powerful new approaches for quantifying autonomic ac-tivity through the use of HR variability have been developed,

:-rc4uency domain ~\I1alyses of HR variabil-it~' 'la"e :'cve~l!ed that the parasympathetic sys-tem may mediate HR variability across a wide range of frequencies below 0.5 Hz while the sympathetic system may mediate variability only below approximately 0.15 Hz (22). There-fore, shifts in parasympathetic and sympathetic modulation of HR may be ret1ected in distinct characteristics of the HR power spectrum (23). However, a change in the HR power spectrum may be due to a change in the responsiveness of the ANS or to a change in the input perturbations to the ANS, and therefore interpretation of the HR power spectrum is complicated. By control-ling an input perturbation and monitoring the resultant fluctuations in HR, one may more di-rectly quantify the responsiveness or "gain" of the underlying autonomic coupling mechanism. This approach is referred to as transfer function estimation, and its advantages have been previ-ously discussed (24,25).

Respiration continually perturbs HR, result-ing in the respiratory sinus arrhythmia, and non-invasive measurements of instantaneous lung volume tIL V) are

tonomically mediated coupling between respi-ration and HR provides a useful tool for evaluat-ing autonomic activity. Since accurate estimation of transfer function relations requires the use of a broad band input perturbation (26), we have developed a technique termed random interval breathing (RIB) to induce broad band respira-tory fluctuations (27). Using this approach, we have successfully measured the ILV to HR transfer relation and demonstrated its sensitivity to alterations in autonomic function (25). The sympathetic system influences the transfer func-

Heart Rate Variability during Motion Sickness

tion only in the frequency range below approxi-mately 0.15 Hz, while the parasympathetic sys-tem influences the transfer function at all frequencies below 0.5 Hz (24,25,27-29). There-fore, the IL V to HR transfer function magnitude may be used as a metric for quantifying the rela-tive "gain" of the two branches of the auto-nomic nervous system (24,25).

The objective of the present study was to measure the transfer relation between instanta-neous lung volume and HR, both before and

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when prompted by the experimenter. In this fashion, symptom estimates were acquired at a rate of approximately one per minute.

Subjects were also trained in and allowed to practice the technique of random interval breathing (RIB). RIB segments were completed in the same manner as developed by Berger (31). A IS-min sequence of computer-generated tones was replayed from cassette tape for each segment. Subjects were asked to initiate an in-spiratory-expiratory cycle each time they were

1.1 1 .... - ~ - .. 1.1. ,I~ •• ,.. -t ... 1'- I •• , ,- .. I - 1'-~ .. ~\ . • '..J~ .,-." ~.:.-.......,.. ~ .. ~ •• ,.. -w' ..... , ~_ _ _... .... ?"_, ~ ...... __ .. ~ __ oJ,.. .... · . _ ..... 1" ._.-....: .. • •••••• .......,..,

••• 'II. II!. • I • ':'. ,~ ._.ii -• I .1. " •• !If"""" ••• " .• " •• 1 lung volume and HR.

Method

All subjects provided written informed con-sent under a protocol approved by the MIT Committee on the Use of Humans as Experi-mental Subjects.

Subjects

Eighteen healthy volunteers with no history of gastrointestinal, cardiovascular. or vestibular disorders participated in the study (7 female. 11 male. average age 22.3 y. range 18 to 30 y). Each subject participated in one 4-hour session which began between 153('1 and 1630. Prior to the cxperimcm. subject" wen: asked I \ f{I gel [1 norma! nig h; '!-- sieep. ~ I i( consumt' nc, medica-lJ o n ~ or aicoho l for 24 hour". ::;, to e,l' a lIormal meal between ! 200 and I :::; {) and tt , fast there-after. 4 ) to a\ 'o id caffeine and smol.lng for 12 hours. and 5) to avoid heav) exercise 1"or 6 hours .

Subjects were trained in the use of a standard magnitude estimation technique for reporting symptoms of nausea (15,30). This technique re-quires subjects to choose a level of nausea from their past experience that they consider "half-way to vomiting" and assign it a numerical value of 5. Subsequent reports of nausea given during experiments are expressed in numerical terms relative to this standard level. Subjects re-ported sympt\llllS whenever they changed or

volume. During the remaining time. tones were separated by random intervals derived from a modified Poisson distribution with a mean of 5 seconds. The modified distribution excludes in-tervals outside the range of 1 to 15 seconds.

Experiment Protocol

Electrocardiogram (EeG) was recorded from a standard limb lead selected to maximize QRS complex magnitude (Hewlett-Packard, Model 7803A). Instantaneous lung volume was re-corded by single belt, inductance plethysmogra-phy (Ambulatory Monitoring Systems, Model 10-9020) calibrated by an 800 cc known vol-ume change. Electrogastrogram (EGG), an ab-dominal surface potential, was recorded for a companion study (32). After instrumentation. subjects were seated in a computer-controlled rOlatinf chair where the:- remuinec! throug:hoLP the e,· nerimem.

Pi'\ ~lolo!2ica! re::()~\lin~" i\ ere maGI: OUrilJ~ three 15-min RIB segmems. 1\\ 0 01 the seg-I1lenr ~ were control recording~. Tht fir~t \\'a~ made while the subject was stationary. and the second was made while the subject was pas-sively, sinusoidally rotated with peak velocity of 1200/s at a frequency of 0.1 Hz. With these parameters, a full 360° of rotation was com-pleted in each half cycle. Although the parame-ter choice is not critical, pilot experiments indi-cated that slow rotation rates encompassing a wide angle best allowed subjects to maintain and control sickness during the experimental re-cording.

After the two control recordings, the subject was fitted with a pair of reversing prism goggles that use specialized optics to "mirror reverse" the visual field. Objects to the subject's left ap-pear to the right and vice versa. This reversal of a sensory input serves to produce the sensory contlict necessary to induce sickness. In combi-nation with manual tasking protocols. pri~m goggles are a pl)tcnt. yet controllable stimulus for inducing :notion sickness i 15.'>0.33). While we:.lrin~ :he -;i)ggies. "ubiects followed 'I man-~l:.lj Laskin!! ant ~1e:.ld 'T' I)" .;:ment ))'(1[()c;)i ie-:,igneJ In induce mOlic!1 ';Icknes~ in 1110,,;[ ,ub-jects within apljro'(immely ..J.5 min. The ',l~king: protocol is described in A.ppendix A. When subjects reported a magnitude estimate of nau-sea between 3 and 4 (where 5 is "halfway to vomiting"), they were asked to moderate their activity in order to maintain but not exceed these symptoms. They were instructed in the therapeutic value of closing their eyes and hold-ing their heads still, and they applied these tech-niques to control their symptom level. While their nausea levels remained between 3 and 4, they continued tasking, but when their symp-toms began to increase above this level they stopped tasking, relaxed, and closed their eyes until symptoms began to subside. The tasking period was ended under one of four conditions: 1) the subject maintained for 15 minutes a sick-ness level between 3 and 4 on the magnitude es-timate scale, 2) 1.5 h of tasking was completed. 3) the experimenter opted to terminate the ses-sion in the best interest of the subject, and -I.) the

T. J, Mullen et al

RIB segment was completed as subjects rotated while maintaining the desired symptom level.

This protocol allows for the passive induc-tion and maintenance of motion sickness and therefore avoids confounding influences of pos-ture change or exercise on the ANS. Further, the inclusion of both :.l stationary and rorating con-trol condition allows for an accounting of :.lny changes in ~llltonomic :.lL' tivity that may be due to rotation ,ilone.

Anal,',';is

After antialiasing filtering, the ECG clnd IL V were sampled at 360 Hz to computer (Mass-comp MC-500). The ILV signals were digitally filtered and decimated to an effective sampling rate of 3 Hz. From the ECG, R waves were de-tected, and a smoothed instantaneous HR time series was derived at a sampling rate of 3 Hz timed synchronously with the corresponding IL V signals (for details of this technique, see reference 34). Each subject's mean HR during each RIB segment was calculated and changes in mean HR associated with rotation or with motion sickness were statistically evaluated us-ing paired t tests.

From each IS-min RIB segment, two non-overlapping, 6-min segments of IL V and HR were then extracted. Thus, for each subject, 6 IL V and HR time series were derived (2 from each of 3 conditions). Power spectra of HR and ILV were estimated using the Blackman-Tukey

. -

Su ~ ~ I- -\'!' .• ' , • ~~"""",_""" ...... ~~ __ A~~ __ __

Heart Rate Variability during Motion Sickness

associated with individual transfer function esti-mates, and population variance, due to individ-ual differences across the population. This first approach allows quantitative comparison be-tween conditions across the population. A sec-ond method was developed to allow quantita-tive comparison between conditions for a single individual (33). For each subject we calculated the statistics Cs[f] and Cr[f] over a range of in-dependent frequencies. The statistic Cs[f] is used to compare the transfer functions from the rotat-

the rotating condition. The statistics are derived from an analysis of the variance of the transfer function as a function of frequency (see Appen-dix B). Essentially, CsLf] and Clf] may be con-sidered as ratios of transfer function variance between two experimental conditions to the variance within the conditions. Under the null hypothesis that there is no change in the transfer function magnitudes due to rotation, CrLf1 will be distributed according to an F2,2 distribution. Similarly, if there is no change due to motion sickness CsLf1 will be distributed as F2,2'

Results

Of the 18 subjects, 2 did not develop signifi-cant symptoms in 1.5 h of tasking, 2 subjects experienced emesis. and 2 experiments were aborted by the experimenter. Thu~. a total of 6· subjects were excluded from the data analysis. Analyses were conducted on the remaining suh-popuiation of 12 subjects who reached the de-sired experimental endpoint (6 male. 6 female: age 18 to 25 y. average 21.5 yl. One of the 12 subjects completed only 8 min of the final RIB segment. Data from this experiment was in-cluded in the group average, but CsLf1 could not be calculated for this subject.

The 12 subjects all experienced significant nausea, which they controlled near a mean level between 3 and 4 on their magnitude estimate scale during the final RIB segment. The group mean magnitude esti!ll1te If'vel during the fi · d RIB segment was 3.4 l~l"ndard error DS).

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Each of the 12 subjects showed significant signs of sickness (evident to two experienced observ-ers) such as pallor and sweating. During the tasking period, when verbal reports of symp-toms were possible, or retrospectively. after the final RIB segment, each subject reported other symptoms of sickness accompanying their nau-sea. Of the 12 subjects, 7 reported sweating, 7 reported subjective feelings of warmth or cold, 4 reported increased salivation, 4 reported fa-tigue, and all reported feelings of "fullness in

ject are given in Figure power spectrum is broadened relative to that of spontaneous breathing illustrated in Figure 2. Group mean heart rate plus or minus standard error was 74.8 :!:::: 0.7 bpm during the stationary control, 74.3 ± 0.6 bpm during rotating control, and 76.8 ± 0.8 bpm during the rotating and mo-tion sick period. Paired t tests did not reveal sta-tistically significant changes in mean HR due to either rotation or motion sickness. Furthermore, in comparing the stationary to rotating but non-sick condition, heart rate was decreased in 5 subjects but increased in the other 7. In compar-ing the rotating but nonsick and the rotating and motion-sick conditions, a different group of 5 patients demonstrated an increased HR, whereas the remaining 7 experienced a decreased rate. Thus, there was no trend toward an increased HR associated with motion sickness.

The group average transfer functions witr. 95g( confidence imervals for the three condi-tions are given in Figure 3. The transfer function 11lagnillld~s are not significantly different from one another over any frequency band belo\~ 0.5 Hz. The transfer function phases appear to differ only in a frequency band below 0.03 Hz. How-ever. at these very low frequencies, the transfer function estimates are generally not reliable as they are associated with low coherence.

The statistics Cs[f1 and elf1 were calcu-lated at independent frequencies for each sub-ject. They were plotted as a function of fre-quency and as histograms. Representative plots for a single subject are given in Figure 4. The plots r)f C. Lf1 versus frequency were inspected for peaks occurring at similar frequencies [or different

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Heart Rate Variability during Motion Sickness

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Figure 2. Representative instantaneous lung volume (ILV) time series and power spectrum from a single subject during spontaneous breathing. Note that the power in the ILV spectrum is contained in a small re-gion about the mean respiratory frequency.

Our finding that motion sickness is not ac-companied by shifts in autonomic control of HR may surprise many. In particular, this result is in apparent disagreement with those of Ishii and colleagues (21). They reported a consistent and marked increase in the CV of HR immediately prior to emesis, followed by a consistent decrease

------I------i-mTnp'rliately-thereafter. However, it is not-pos-

sible to determine whether this increase in CV was a:-.socimed with Lt. change III parasvlllpa-thetic outflc1\\ . "ymputhetic outJ"lO\\. or ,~ C:OJ1l-bination oj tile two. Ishii and colleagues (21)

postulated that rcaCliom. .ill~l prior {(1 "omiting are parasympathetically mediated or. 1l10I"t spe-cifically. that there is an increase in parasympa-thetic outflow immediately plior to vomiting. In arriving at this conclusion, Ishii and colleagues assume that motion sickness involves an in-crease in mean parasympathetic outflow, which, in turn, is associated with an increase in the variability of parasympathetic outflow, which, in turn, causes increased heart rate variability. I\!lhough Tshii and colleague, ' '2 1) made these

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assumptions based in part on prior pharmaco-logical studies, their validity is subject to question.

Three distinctions must be drawn between our experimental paradigm and that of Ishii and colleagues. First, Ishii and colleagues explored the entire range of motion sickness symptoms, up to and including emesi5. and they report that the most significant changes in CV occurred just prior to emesis. Although our 12 subjects experienced significant nausea. they did not reach the point of vomiting. Thus, our experi-ment provides no evidence concerning the act

and the autonomic activation

crease in parasympathetic modulation of HR did occur as emesis became imminent, the IL V to HR transfer function would be expected to show a relative increase in gains in the high fre-quency range (above 0.15 Hz). A second dis-tinction between the two paradigms is that Ishii and colleagues did not control or record respira-tion. If the monkeys in their study tended to be-gin panting as vomiting became imminent, the change in CV could be due to the changing ef-fect of respiration on HR. In effect, Ishii and colleagues may have characterized changes in an input to the regulatory system and not a change in the responsiveness of the autonomic system itself. Third, the possibility of species-dependent differences must be considered.

One hypothesis that would explain our re-sults is that the autonomic nervous system does not playa role in motion sickness. However, de-spite the apparent constancy of autonomic influ-ence on HR throughout tht study. a number of sign:-- cOl1s isien : with au roflomi c change;; ,\'cre 11()' '(1 CILI": 11" 11' ()' I'( )I-' :' ; ("' 1 1~ '"'' ; ". ·' .,. .. ·'· ll ;·l'· . '1'1.0 U:: 1 ! t :: I . t , ..... h. I;. ..... . l. . " '.' ".I L1... I" , . l .... presence of panor ami sweaung II, mall) Oi Oll!' ~ub.iects suggest~ that the mean ~ YI11Pat lie li c outflow to the blood vessels and sweat glands in the skin may have increased. It i~ difficult to reconcile these observations and the experimen-tal data with models of autonomic activity dur-ing motion sickness that incorporate a general-

ized autonomic response. Such models have generally assumed that

the autonomic nervous system and, in particu-lar, the sympathetic system exert undifferenti-ated, b0cl; -'.,,:rj(' 'ontrol. That is, the mean level

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A

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T. J . Mullen et al

Transfer Phase (radians)

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Frequency (Hz) Frequency (Hz)

Figure 3. Mean transfer function estimates from the (A) nonsick and stationary, (8) nonsick and rotating, and (C) motion sick and rotating conditions. Average magnitudes and phases are plotted with associated 95% con-fidence intervals. There are no significant differences between the group average transfer functions from differ-ent conditions, which suggests that ANS control of HR is not altered during rotation or motion sickness across the group.

the system that is uniform across organ systems. If an increase in "sympathetic tone" accompa-nied motion sickness in the subjects in this study, then it must be true that a compensatory change in "parasympathetic tone" prevented any change in mean HR. Furthermore, such changes in mean levels of autonomic outt1ow must have occurred in the absence of changes in their variances or the "gains" of the central au-tonomic responses. This combination of events would reconcile the current fmdings to such models, but seems rather unlikely. An alterna-tive hypothesis is that the autonomic nervous

involving neural control of HR. Microneurographic studies have demonstrated

that the sympathetic nervous system can exert very narrow, isolated control (35). In particular, sympathetic nerves in the skin and in muscle demonstrate dissociated activity. As a result of these and other studies, it is now well recog-nized that both the sympathetic and the para-sympathetic nervous system may function in an organ-specific or differentiated fashion (36-38). One possibility, therefore, is that changes in au-tonomic control may be present during motion sickness if the changes are not global but rather

Heart Rate Variability during Motion Sickness

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ceptor feedback while skin sympathetic activity is not, it seems reasonable to hypothesize such dissociation.

The absence' of changes in autonomic control of HR during motion sickness is not consistent with models that incorporate a generalized auto-nomic response during motion sickness. If the autonomic nervous system is involved in the de-velopment of motion sickness, it seems likely that its effects are localized, with different ef-fector subsystems receiving independent auto-nomic activity. In particular, the neural control

_~.......,_-\!:~~~el;;Ip.s..nOL,!~U..J~e involved.

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Figure 4. Comparison of individual transfer functions by variance ratio. (A) The statistic C. plotted as a function of frequency for a representative subject. Dashed and dot-dashed lines represent the 95% and 90% confidence levels, respectively, of the F2•2 distri-bution. Note that only two outliers exceed these lim-its. There was no consistent frequency at which these outliers occurred. (8) The histogram of Cs for the same single subject approximates the F2•2 distribution (superimposed). Therefore, the null hypothesis that there is no difference between the transfer functions from nonsick and sick conditions cannot be reiected for this subject. Simiiar results were seer. in each sub-ject. TheSE results suggest that ANS control of HI=; i~ not altereo durin9 motion sickness ir. an)' subject.

are localized [(l particular organ systems. In par-ticular. increased sympathetic outflow to the skin may occur through a pathway that is inde-pendent of sympathetic activity in muscle and cardiac nerves. The increase in skin sympathetic activity would elicit the sweating and pallor ac-companying sickness. Cardiac sympathetic ac-tivity, on the other hand, may not be affected. Since the two organ systems are involved in dif-ferent primary control tasks and since cardiac y!"nllthetic outflow j" i nnJlf'nred by barore-

Appendix A

Tasking Protocol

The tasking protocol was designed to require head movements and eye-hand coordination. Subjects remained seated on the rotating chair and were provided with a retractable work sur-face on which to complete the tasks. The proto-col is similar to that used by Eagon (15).

The first task was completion of a one-page questionnaire that was printed mirror reversed so that it appeared normal to the subject. It re-quired that the subject write simple words, copy simple pictures, and solve simple math prob-lems. This task was performed for a maximum of 15 min. Subjects were not required to com-plete the entire questionnaire in this time.

The second Lasl: was can structure buildinf: A schematic drawing repre~enting ! 5 aluminul1i can~

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allowed 5 min to complete the structure. A complete can structure protocol required repeti-tion of this process until a total of 10 structures were attempted.

The third tasking protocol involved copying drawings and solving simple mathematical prob-lems on a blackboard. A 2- by 3-foot blackboard marked with 2 drawings and 4 mathematical problems was positioned in front of the subject. The subject 'vas asked to replicate the Jrawings and solve ~hl! problems.

:_"~:Ul~ _.~1.1 1 :~·..: .. ~0n .. i' ,"i~c ·',fLlL.\.ouar ....... t:"l:\.. th~ ,ui'ject unde!'lOGK ..L )l::qUC[jL'~ ul :\\() ;norl! -:an ;trucfures and then repeated the oiad::board ta~h. with new Jrawill~s antl problem~ . The proces:, of blackboard \Vork followed by two can struc-tures was repeated, as necessary, for the remain-der of the tasking period.

Appendix B

Calculation ofCs and Cr

The statistics of Cs and Cr were developed to allow quantitative comparison of the transfer functions from the different experimental con-ditions for a single individual (33). Given two transfer functions from each of two experimen-tal conditions to be compared, the statistic is de-rived as follows:

Let Hll[J] and Hdf] be two complex trans-fer function estimates from the first experimen-tal condition. and let H'll [f] and Hdf] be com-

change in experimental conditions. Under this null hypothesis each of the four transfer func-tion estimates may be considered a realization of the same random process with unknown vari-ance 0'2. Then, an analysis of variance gives the

T. J. Mullen et al

general form for the statistic C, as a function of independent frequencies, I. as

(1)

it ,i1I)uld :)e nOLed [hat due [0 fiireril1!! effects in . - . the ~ransr'er fUllction e~[imatjon ;rocedure, esti-mmes at adjacent discrete frequencies are in general not inuependent. Independent estimates were obtained by calculating local averages over predetermined frequency bands. Each of the squared differences in Equation [1] is dis-tributed as chi-square with one degree of free-dom (X~). The numerator and denominator are sums of two X~ statistics and therefore are dis-tributed as X~. Finally, C[J] is the ratio of two X~ statistics, which is by definition an F distri-bution with two numerator degrees of freedom and two denominator degrees of freedom (F2,2).

The statistic Cs is used for comparison of the rotating control condition with the rotating and motion sick condition to assess the effect of mo-tion sickness. It therefore relies on the four transfer function estimates from these condi-tions. Similarly, Cr is used to compare the two nonsick control conditions to assess the effect of rotation.

analyses presented in this work. This study was sup-ported in part by NASA Grant NAGW-3927, NASA-JSC Grant NAG9-244, and NIH Grant lROlHL39291. Fellowship support was provided to T. 1. Mullen by an Air Force Laboratory Graduate Fellowship.

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2. Oman CM. A heuristic mathematical model for the

Heart Rate Variability during Motion Sickness 105

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