International Journal of Psychoph_vsiologv 4 (1986) 167-173

Elsevier

167

PSP 00119

Research Reports

THE EFFECTS OF LEVEL OF DIFFICULTY OF MENTAL ARITHMETIC CHALLENGE ON HEART RATE AND OXYGEN CONSUMPTION

DOUGLAS CARROLL. J. RICK TURNER and REKHA PRASAD

Department of Psychology, University of Birminghum, Birmingham B15 2TT (U.K.)

(Accepted March 20th, 1986)

Kqv words: heart rate - oxygen consumption - respiration - mental arithmetic - difficulty level

Heart rate plus various metabolic and ventilatory indices were monitored while 18 young males engaged in a mental arithmetic

task, structured to include 3 levels of difficulty; easy, difficult and impossible. Measurements were also taken while subjects

undertook graded isotonic exercise on a bicycle ergometer; for each subject heart rate was plotted against oxygen consumption over

the various exercise loads. Knowing oxygen consumption during the psychological tasks, these regression equations permitted the

calculation of expected heart rates during each task condition and thus the computation of ‘additional heart rate’ as the difference

between actual and predicted heart rate values. Additional heart rate was sensitive to variations in difficulty level; the difficult

condition elicited reliably more additional heart rate than the easy and impossible conditions. Subjects’ performance as well as their

perceptions closely reflected the a priori classification of difficulty. Although subjects rated the easy condition as particularly

unengaging, the impossible condition attracted relatively high rates of task involvement, It was argued that self-reports of this sort are

probably more susceptible than cardiac activity to social demand characteristics.

INTRODUCTION

Recent research has revealed that certain be- havioural challenges elicit, in certain individuals, cardiac reactions that appear metabolically inap- propriate (Carroll et al., in press; Langer et al., 1985; Sherwood et al., 1986 Stoney et al., sub- mitted; Turner and Carroll, 1985). The’tasks de- ployed in these various studies range from shock- avoidance procedures through video games to mental arithmetic. As a consequence it is difficult to discern the precise situational determinant of such supra-metabolic cardiac adjustments. How- ever, one plausible uniting attribute is task diffi- culty; in general, the challenge posed by these

Correspondence: D. Carroll, Department of Psychology, Uni- versity of Birmingham, Birmingham B15 2TT, U.K.

various tasks would seem to be that success is neither assured nor unrealizable. Such conditions, it might be argued, are likely to prove optimal for sustained vigilance.

Few studies, though, have directly addressed the issue of difficulty in this context. In an early study, Obrist et al. (1978) reported findings very much in line with the idea of optimal difficulty. Relatively sustained increases in heart rate and carotid dP/dt were apparent during a shock-avoi- dance reaction time procedure only when the criterion for avoidance was hard; when it was easy to the extent that avoidance was guaranteed or difficult to the extent that avoidance was impossi- ble, cardiac reactions showed decidedly more at- tenuation over time. However, in a subsequent study employing an appetitive reaction time task, Light and Obrist (1983) reported that while cardiac activity, as indexed by pre-ejection period and pulse transit time, decreased with an impossible

0167-8760/86/$03.50 0 1986 Elsevier Science Publishers B.V.

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criterion relative to a difficult one, relatively high levels of activity were displayed when the task was easy. It is possible, though, that monetary incen- tive effects (Fowles et al., 1982; Perkins, 1984) could account for these inconsistencies. Finally, Van Schijndel et al. (1984) found that while heart rate was relatively insensitive to variations in diffi- culty, systolic blood pressure varied systematically with the percentage of anagram puzzles which

were soluble. Again, the relationship was curvi- linear, with their moderately difficult condition eliciting the largest increases.

In a recent study carried out in our laboratory using mental arithmetic and Raven’s matrices (Carroll et al., in press), in which problems were selected as easy, difficult and impossible, heart rate proved highly sensitive to difficulty level. In both tasks, the easy condition elicited significantly smaller heart rate reactions than the difficult con- dition. However, difficult and impossible prob- lems induced largely similar increases in heart rate. Further, unlike early research, this study monitored metabolic activity to ensure that any changes in heart rate with varying difficulty were not simply a product of variations in energy ex- penditure. Changes in oxygen consumption and carbon dioxide production did not vary signifi- cantly with difficulty.

The absence of an attenuation of heart rate reaction during the impossible condition in that study was clearly contrary to expectations derived from previous research. One possibility is that insufficient time was allowed in the impossible condition to facilitate disengagement and reduce vigilance. Subjects’ self-report data certainly indi- cated that they appeared to be both relatively aroused and engaged by the impossible condition. It is possible that with more protracted experience of impossibility subjects eventually would stop trying and that some attenuation of heart rate reaction would occur.

The present study, then, was undertaken firstly to attempt to replicate the result that heart rate is sensitive to differences in difficulty and that such effects are not attributable to variations in energy expenditure, and secondly to examine whether with more lengthy exposure to impossible prob- lems less marked heart rate reactions would occur.

METHODS

Subjects

Subjects were 18 male undergraduate students at the University of Birmingham, aged between 18 and 25 years. As far as could be determined by preliminary questioning, none suffered from any cardiovascular disorder. Each subject was able to earn up to &2.88 depending on his performance during mental arithmetic (MA). In addition, there was a further &5.00 to be won by the subject who answered the most problems correctly.

Apparatus Heart rate (HR) was recorded on a Beckmann

type R511A dynograph. Beckman electrodes were attached in a V5 configuration using adhesive collars and Beckman electrode paste. Output from the electrodes was fed into a type 9806A AC coupler, using a time constant of 0.03 and an amplification setting of 0.02 mV/cm. Oxygen con- sumption (VO,), carbon dioxide production (VCO,), respiratory volume (V), tital volume (TV) and respiratory rate (RR) were measured and automatically printed out every two minutes using a Beckman Metabolic Measurement Cart (MMC) (see Turner et al., 1983).

The MA task employed was structured to en- compass 3 blocks of trials corresponding to 3 levels of difficulty, each block lasting 8 min. It comprised problems and answers prerecorded on

a Sony C-90 HF cassette and presented to subjects on a Sony cassette recorder. In all, the task com- prised 144 discrete, 10-s problem trials. Each problem trial consisted of a problem, delivery of which took 6 s, followed 2 s later by an answer, delivery of which took one second. An interval of one second, during which the subject had to re- spond as to the correctness of the given answer, preceded the next problem. Problems, then, fell into 3 difficulty levels, each comprising 48 prob- lems. The easy problems consisted of the addition or subtraction of two single-digit numbers, the ratio of addition to subtraction problems being 2 : 1. The difficult problems were those used by Turner and Carroll (1985). Here, addition and subtraction involved 2-digit and 3-digit numbers, the ratio of addition to subtraction problems being

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3 : 7. Finally, problems in the impossible category consisted of multiplication and division involving 2-digit and 3-digit numbers. While these problems were not actually impossible to solve, they were adjudged to be so in the time available on the basis of pilot testing using a comparable subject

sample. Graded isotonic exercise was performed on a

mechanically braked bicycle ergometer (Monark model 668). Subjects were required to maintain a steady pedalling rate of 50 revolutions per minute (rpm) throughout this task, using the attached tachometer to synchronise their pedalling. Ex- ercise load was varied by adjusting wheel friction. Four increasingly demanding loads each lasting 4 min, were employed; these were 0.5, 1.0, 1.5 and 2.0 kiloponds generating, when coupled with the required pedalling rate, power outputs of 150, 300, 450 and 600 kilopond metres per minute (kpm/ min) respectively.

Two 21-point rating scales, assessing subjects’ perceptions of ‘difficulty’ and ‘active engagement’, were employed in the study; the limits of these were designated as ‘extremely easy’ and ‘impossi- ble’, and ‘completely uninvolved, not trying at all hard’ and ‘extremely involved, trying as hard as possible’, respectively.

Procedure On their arrival at the laboratory, subjects were

informed as to the general nature of the MA task and additional examples, in the hard range, were presented by way of illustration. MA was always undertaken first and excercise last.

Within the MA task, the order of presentation of the different blocks of trials (easy, hard and impossible) was counterbalanced across subjects; consequenty, each possible order was undertaken by 3 subjects. Each block of trials was preceded by a formal 4-min relaxation period. Subjects were not informed explicitly about changes in task dif- ficulty; while the instructions given to subjects explained that the MA task comprised 3 8-min blocks of trials, each preceded by a 4-min relaxa- tion period, no mention was made of variation in difficulty level. Subjects were informed that after each block of trials they would be asked to indi- cate quickly how difficult and how engaging they

found the problems in the preceding block. The response requirements of the MA task

were then explained. It was emphasized that in the one-second interval following presentation of each tape-recorded answer, subjects should indicate whether the given answer was correct or not; if correct, they should signify this by raising the index finger of their right hand, while a judgement that the given answer was incorrect should be signalled by raising the index finger of the left hand. Failure to raise either finger in the time allowed, they were informed, would be regarded as an erroneous response. Subjects were then told of the monetary incentives; each appropriate re- sponse on their part would earn them 2 pence, while each erroneous response would lead to a deduction of 2 pence. Earnings could therefore vary between nothing and E2.88. They were also told that the subject who performed best overall would receive an additional E5.00.

Upon completion of MA, subjects were allowed ca. 5 min respite, and were reminded of the re- quirements of the graded exercise task. The bi- cycle saddle was adjusted to each subject’s pre- ferred height. Exercise proper was preceded by a 4-min baseline period during which subjects re- laxed as much as possible while sitting on the bicycle. Subjects were instructed to keep their rate of pedalling at a constant 50 rpm throughout all 4 exercise loads, using the attached tachometer.

When subjects had completed the exercise task they were paid, debriefed and thanked for their participation in the study. They were also asked not to divulge any of the details of the experiment to potential subjects. Upon completion of the whole study, &5.00 was duly paid to the best performer.

Data reduction In all, then, the experiment comprised 3 4-min

baseline periods, each followed by an 8-min block of MA; there was then another 4-min baseline followed by 4 4-min periods of exercise. Through- out, VO, in millilitres per minute (mlpm), VCO, (mlpm), V in litres per minute (lpm), TV in milli- litres (ml) and RR in cycles per minute (cpm) were automatically given every two minutes by the MMC. To obtain HR, R-waves on the dynograph

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records were simply counted over the same two- minute epochs and converted to beats per minute (bpm) statements.

RESULTS

Physiological changes during exercise Attention focussed on the last two minutes of

the pre-exercise baseline rest period and the last two minutes of activity during each of the exercise load periods, in order to ensure that a steady state had been achieved. The overall averages for each of the physiological variables are presented in Table I. Analysis by means of one-factor re- peated-measures ANOVAs indicated highly sig- nificant period effects for all variables: HR (F4,68 = 227.3); VO, ( F4,68 = 346.5); VCO, ( F4,68 = 295.3), V (F4,68= 171.3), TV (F4,6s=56.9), and

RR (4.68 = 27.8) (all P’s < 0.001). Thus as workload increased, so too did physiological activ- ity: the magnitudes of the F-ratios indicate just how orderly the effect was.

Physiological activity during MA A one-factor repeated measures ANOVA was

undertaken to compare HR level during the last two minutes of each of the 3 pre-task baseline periods; F was less than unity.

Change scores were then computed by subtract- ing activity during the last two minutes of the pre-task baseline period from activity during each of the two-minute task periods. A series of two- factor (difficulty level and periods) repeated-mea- sures ANOVAs was then computed. The Greenhouse-Geisser correction of degrees of free- dom was applied in testing all levels of difficulty main effects and interactions (Winer, 1970). The only variable to show anything approaching a significant main effect of difficulty was HR ( Fl,,, = 3.34, P < 0.10).

The average HR increases for the 3 levels were 2.7, 5.8 and 3.0 bpm for the easy, difficult and impossible conditions respectively. Subsequent two-factor ANOVAs contrasting pairs of condi- tions, however, revealed only marginal differences between the difficult and easy conditions ( Fl,17 = 3.92, P < 0.10) and difficult and impossible condi-

TABLE I

Physiological activity during rest and at each of the friction loads

The slight discrepancy between V and RR XTV is due to

setting the MMC in a time mode rather than a breath mode.

The former monitors over a strict time base (in our case 2

min), whereas the latter waits for the completion of the ongo-

ing respiratory cycle. With the time mode, then, RR statements

almost invariaby include an uncompleted respiratory cycle, as

the RR counter on the MMC is triggered by breath onset.

Since TV and V are measured continuously and independently

of RR, as flow via a volume counter, some slight mismatch

between V and RRXTV is inevitable using a time-based as

opposed to a respiratory cycle-based mode of measurement.

Physiological Work Loads (kpm / min) variables

Rest 150 300 450 600

HR @pm) 78.5 97.1 109.5 124.9 139.7

VO, (mlpm) 311.7 817.2 1050.0 1295.4 1546.1 VCO, (mlpm) 279.4 717.9 976.2 1270.0 1540.6

V (Ipm) 11.9 24.4 32.3 41.5 50.5 TV (ml) 876.1 1403.3 1540.5 1743.0 2033.1

RR (cpm) 15.2 18.8 21.9 24.7 26.3

tions ( Fl,17 = 4.12, P < 0.10). The F ratio for the easy versus impossible comparison was less than unity.

Significant periods effects, on the other hand, were observed for all variables with the exception of V: for HR (F,,,, = 11.83, P < 0.001); for VO, ( F3,51 = 7.05, P < 0.001); for VCO, ( F3,51 = 8.05, P < 0.001); for TV (F& = 14.84, P < 0.001); and

for RR (&i = 3.92, P < 0.05). With the excep- tion of RR, the most positive changes occurred during the first two minutes at each difficulty level; the reverse was true for RR. With regard to

V (F3,51 = 1.51, n.s.), the lack of a reliable periods effect undoubtedly stemmed from the almost mir- ror image effects evident for TV and RR. Whereas TV decreased least during the first two minutes and showed fairly uniform changes during the last 6 min in each condition, RR, as indicated, showed a much lower increase in the first two minutes than in the subsequent 6 min.

Finally, there were no significant difficulty levels x periods interaction effects.

Additional HR during MA HR changes during MA were also analysed in

terms of additional HR (see Turner and Carroll,

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1985). Briefly, for each subject the HR and VO, values recorded during the last two minutes of rest and the last two minutes of each of the 4 exercise loads were used to obtain individual regression equations. The characteristics of these regressions were similar to those reported in earlier studies (Carroll et al., in press; Turner and Carroll, 1985): correlation coefficients ranged from 0.90 to 1.00 (the mean was 0.98); slopes ranged from 0.028 to 0.097 (mean 0.050); and the intercepts varied be- tween 38.1 and 75.6 (mean 60.5).

TABLE II

Number of subjects who showed HRs during MA lying above, below or within 2 S.E.s of the HR- VO, exercise regression

Easv Difficult Impossible

Above 3 ’ 10 3 Within 13 8 14 Below 2 0 1

x2(4) = 9.92, P < 0.05.

Table II reports the number of subjects whose responses in the different difficulty conditions, actual average HR during the MA task lay more were subjected to a one-factor repeated measures than 2 standard errors (S.E.s) above their exercise ANOVA, using the Greenhouse-Geisser correc- regression line (2 S.E.s is equivalent to the 95% tion. Level of difficulty exerted a highly signifi- confidence limit). Inspection of Table II indicates cant effect (Fl,17 = 147.83, P < 0.001). The aver- that while the vast majority of subjects displayed age numbers of correct responses were 47.2, 39.1 HRs during the easy and impossible conditions and 26.7 for the easy, difficult and impossible that lay within the 2 S.E.s boundary, the difficult conditions respectively. Thus, while virtually all condition occasioned HRs in a large number of subjects solved all the easy problems, performance subjects that were more than 2 S.E.s above the in the impossible condition did not depart from exercise regression line. chance level.

The regression equations calculated for each subject were then used in conjunction with the VO, values during MA to predict task HR values and to compute additional HR as the difference between actual and predicted HR levels. A two- factor (difficulty level and period) repeated-mea- sures ANOVA applied to these additional HR values yielded a significant main effect of diffi-

culty (Fi 17 = 6.82, P < 0.02). Again the Green- house-Geisser correction was applied. The average additional HRs (actual HR minus predicted HR) were 4.2, 8.0 and 5.3 bpm for the easy, difficult and impossible conditions respectively. There was no reliable periods effect nor a difficulty level x

periods interaction. Subsequent two-factor ANOVAS contrasting pairs of conditions, how- ever, revealed significant differences between the easy and difficult conditions (F& = 8.91, P < 0.01) and difficult and impossible conditions ( F,,17 = 6.35, P < 0.05), but no reliable difference be- tween the easy and impossible conditions. None of these analyses yielded either periods effects or difficulty levels x periods interactions.

Self-report data The average ratings of perceived difficulty were

1.7, 11.3 and 18.4 for the easy, difficult and im- possible conditions respectively. A one-factor re- peated-measures ANOVA revealed that the dif- ference among conditions was highly significant

(4.17 = 211.70, P -C 0.001). Subsequent analysis using the Newman-Keuls methods indicated that every difficulty level was perceived as different from every other one (P < 0.01).

For reported active engagement, the average ratings were 8.7, 15.1 and 13.9 for the easy, dif- ficult and impossible conditions respectively. Again, the effect was significant ( Fl,17 = 12.7, P < 0.01). Subsequent paired comparisons indicated that while both the difficult and impossible condi- tions were judged to be more engaging than the easy condition, there was no reliable difference between the difficult and impossible conditions in this regard.

DISCUSSION

Performance during MA Performance data, i.e. the number of correct

The present results confirm those previously reported that HR during challenging MA is, for a

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large number of subjects, substantially greater than would be expected on the basis of HR-VO, regres- sions during isotonic exercise (Turner and Carroll, 1985). Further, in line with the findings of Carroll

et al. (in press), the present data suggest that task difficulty would appear to be an important factor. HRs significantly above the exercise regression lines were a particular feature of the difficult MA condition; for the vast majority of subjects, easy and impossible problems occasioned HR levels within 2 S.E.s confidence limits.

With physiological activity represented as change from baseline, only HR from all the varia- bles monitored displayed anything approaching a reliable effect of level of difficulty. Subsequent analysis indicated that it was the difficult condi- tion which tended to elicit larger magnitude HR reactions than either the easy or impossible condi- tions. Neither VO, nor VCO, showed any varia- tion with task difficulty. When HR activity was represented as the difference between actual HR and HR predicted from the HR-VO, regression equation and task VO,, i.e. as additional HR, difficulty level exerted an unambiguous effect. The easy and impossible conditions elicited signifi- cantly less additional HR than did the difficult condition, a finding consistent with the imbalance among task conditions in the frequency of individ- uals displaying HRs substantially above the ex- ercise regression lines. In previous publications (e.g. Carroll et al., in press; Turner and Carroll, 1985) we have argued that additional HR con- stitutes a more appropriate representation of HR change in this context. The present data would appear to support our advocacy; additional HR would certainly appear to be a more sensitive index of difficulty than the more conventional representation, i.e. HR change from resting base- line. While Carroll et al. (in press) found that HR was responsive to difficulty, both difficult and impossible problems elicted substantially greater HR activity than the easy condition. As indicated, self-report of active engagement at the different difficulty levels paralleled the cardiac effects. The absence of a decline in HR activity during the impossible condition ran counter to expectations based on previous research (Light and Obrist, 1983; Obrist et al., 1978; Van Schijndel et al.,

1984). The possibility examined in this study was that we allowed insufficient exposure to the im- possible problems, and that with more protracted experience of impossibility, some reduction in HR activity would be observed. Our current data are largely consistent with this view, particularly when HR activity is portrayed in terms of additional HR.

As in our previous study, both performance data and reports of perceived difficulty closely reflected the a priori designations of difficulty. Accordingly, it would appear to be actual dif- ferences in difficulty level that underlay the cardiac effects observed, and not some other variant such as monetary incentive. However, while subjects reported being relatively unengaged in the easy condition, the impossible condition continued to attract ratings betokening substantial task involve- ment. It is quite likely, though, that such ratings are susceptible to demand characteristics in a way that HR is not, and, given the backgrounds of our subjects, some reticence in admitting defeat and disenchantment in the face of impossibility would be expected.

While the effects of difficulty on HR provide further evidence of cardiac-metabolic indepen- dence, the effect of periods within conditions indi- cate that such independence occurs only in re- sponse to some variables. While HR changes from baseline declined across periods, so too did VO, and VCO,. The net effect of this is evident from the additional HR data; there was no reliable periods effect on additional HR. These results also attest to the wisdom of representing HR change in terms of additional HR, rather than relying solely on baseline-task differences.

ACKNOWLEDGEMENT

This research was conducted while J.R.T. was a Medical Research Council Fellow.

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