Neuropsyrhologia . Vol.30,No.12 .pp .1101-I loft 1992 Paned m Genet Britons. 0328-2932, 52 55 .00+0,00 1992 Pcrgamon Pros Ltd NOTE A STIMULUS-RESPONSE RELATIONSHIP IN UNILATERAL NEGLECT : THE POWER FUNCTION ANJAN CHATTERIES,* MARK MENNEMEIER and KENNETH M . HEILMANt Center for Neuropsychological Studies and the Department of Neurology, University of Florida College of Medicine and the Neurology Service, Department of Veterans Affairs Medical Center . Gainesville, Florida, U .S .A . (Received 6 January 1992 : accepted 5 August 1992) Abstract We have previously suggested that patients with unilateral neglect may be limited in their ability to sequentially attend or act upon stimuli . To assess the nature of this capacity limitation, we examined the relationship between number of stimuli presented on cancellation arrays and howmany targets a patient with neglect cancelled . This relationship was systematic and described by a power function : targets cancelled= K (targets prcscntcd)°, in which the constant and exponent were derived empirically . Density of targets and time taken to cancel targets did not account for the relationship . Improvement on subsequent testing was reflected in an increase in the constant . However. the exponent of the power function did not change . suggesting that same critical aspect of her dysfunction remained the same . These data also imply that she had implicit knowledge of quantity of stimuli presented, and that this knowledge systematically influenced her explicit behavior . INTRODUCTION PATIENTS WITH UN 11 AmRAI . NECI F.c1 fail to orient towards, attend to, or act on stimuli in space contra lateral to their lesion [6] . On cancellation tasks these patients cancel ipsilesional targets and tend to ignore contralateral ones [1] . However, if explicitly instructed to act in contralateral space, some patients are capable of doing so . We recently reported the performance of a patient with left-sided neglect on a number of cancellation tasks [5] . On traditional cancellations, her performance was typical of most patients with neglect . She cancelled targets on the right side of the array and ignored those on the left . She was then instructed to cancel targets such that after cancelling a target on the right she had to cancel a target on the left . She continued in a right- and-left alternating manner until she indicated she had cancelled all the targets . Under these conditions, rather than exhibiting a change in the extent of her neglect (as measured by number of cancelled targets), she demonstrated a change in the spatial distribution of neglect . In some trials she cancelled targets on the extreme right and left sides of the array, while neglecting targets in the middle . despite passing over these target between every cancellation . These results were interpreted as demonstrating that she had a limited capacity to attend to or act upon targets sequentially, and this capacity limitation was not confined to a specific spatial location . In this report, we further investigate the nature of this capacity limitation in the same patient . A limited capacity to sequentially attend to or act upon stimuli might be expressed in a number of ways . If this patient neglected some fixed percentage of space, such as 50% . then she would always fail to cancel targets encompassed within this space regardless of how many targets were present . This failure could he related to a defective internal representation of space [3] . When presented with 16 evenly distributed targets she would cancel eight, and when presented with 32 she would cancel 16 . Alternatively, her defect could be related to the means by which stimuli recruit processing resources . If she has a reduced attentional capacity that is fixed such that there is a limited number of targets of which she can be aware, then only that many targets would he cancelled, irrespective of how many were presented in the array . For example, if she cancelled eight targets on an array of 16, she would also *Now at The University of Alabama at Birmingham, 454 Sparks Center, 1720 Seventh Avenue South, Birmingham, AL 35294, U .S .A . tAddress for correspondence : Kenneth M, Heilman, M .D ., Box J-100236, JIIMHC. University of Florida, Gainesville, FL 32610-0236, U .S .A . Hot 1102 N oar. canal eight on an array of 32 targets . There could he other more complex, albeit lawful, relationships between number of targets presented and targets cancelled . The elucidation of such relationships may provide Curt her insight into the mechanisms underlying neglect. The following experiments attempt to sort out these possible relationships between stimuli and her response . PA IIENT HISTORY M .F. was a 73-year-old . right-handed woman who was tested between 8 and 14 weeks after a right-hemisphere stroke. She was alert, oriented and aware of her stroke . I Icr memory, language comprehension and repetition were normal . I ler language production was fluent . grammatie, well articulated, but aprosodic . She did not suffer from an agnosia or apraxia . She demonstrated extinction of left-sided visual, auditory and tactile stint ti She did not haven persistent deviation other eyes or head and did not have a visual field defect . She had a dense left hemiplegia . A computer tomography ICI )scan of her head done I weak after her stroke showed a Large infarct in the right middle cerebral artery distribution, involving the right parietal and frontal lobes (Fig . I ) . METHODS Proc . ,dure The patient was tested in her room . which was quiet and secluded, in an assisted living home. Stimulus arrays were placed in front of M .F, centered al tier mid-saggital plane . There. were no distractors, and the targets were arrayed with an equal number of targets randomly distributed In each quadrant. Each cancellation task was considered completed when M .F . indicated she was done . If she stopped cancelling the targets, but made no indication, after 15 see she was asked if the task was completed . The next task was initiated only when she said she was done . Conditions were given randomly for each trial . Short breaks were taken every 20 min . and testing sessions were about 2 hr long- Testing sessions were stopped at the patient's request or if she appeared tired . txperinent I M-F . was asked to cancel "0 's distributed war 466 .1 sq . can on a white sheet of paper, 21 .6 x 279 cm . There were three conditions, which consisted of either 16, 31 or 64 identical targets . She performed 20 trials . . with 32 targets she cancelled 21 .2 Re .,ults . On arrays with 16 targets M F cancelled 14 .6 (+2 .1I or 91 _570 I ±3 .8) or 66 .25 ., and wilt 64 targets she cancelled 27 .611 5 .21 or 43 .13".. of [he targets . In seeking a relationship between the nunther of targets presented and how many she cancelled, we realized that the variance in her performance increased on stitmdus arrays with more targets . A logarithmictranslormation could he u,sel Lo stabilise this increasing variance [8] . The number of targets on the stimulus arrays also increased exponentially 12' . ^_`, 1") . Thus, both the dependent variable Inumber of targets cancelled) and the independent variable Inumber of tar gets on the array) were logarithmically transformed . Regression resulted in the linear equation : log(targets cancelled)-0 46 logltargets presented)+0 .61 . This relationship is mathcmaIteally equivalent Lo [lie power function targets cancelled-4 .07 (targets pi esentedI" .-1, 5R : F=120 .14, P<0.000I ) . The 95% confidence interval lot . The regression line had a correlation o1'0 .82 (dl the exponent was 0 .30 0 .62 . 17te power function accounted for 67of the variance in perfor nancc . A simple linear correlation between turrets cancelled and targets presented accounted for 614x . . and an exponeraial relationship Bust the targets cancelled Iogarithnuclly transformed) accounted for 6-i. . of the variance . The distribution of her neglect was assessed by dividing stimulus arrays into four columns : far felt_ middle left . middle right, and far right . She demonstrated a gradient of neglect front loft to right, and this gradient also varied such that it was steeper on arrays with more targets . The percent targets That she cancelled within these columns Ibr each condition are shown in Fig . 2(a) . No targets were repeatedly cancelled . . does not just interact with a specificarea of span :, or she Discussion . Front these results it is apparent that M .F would have cancelled the same percentage of Targets on each array . Also, she did not have a fixed allcntiunal capacity, such that she would cancel only a spenif ie number of target.. With more targets on the slim alas array, she cancelled more targets (in absolute numbers I . while neglecting a grealci percentage of the array . Her response appears it) be inlh2need in a systematic fashion by the quantity ofslimuli presented . However, on those arrays, density of l argets . i n addition to nunther oft argots, was sysaeniatically changed . Arrays with more targets were also more dense, and the critical variable affecting her performance tray have been density rather than number of Largels . Furthermore, arrays with more Largess also have a greater number of targets in ipsifaleral space . 11 could have been that just the shcer presence of more stimuli in attended space compelled a sx :stematie asienlional bias Ihal was captured mathematically To ass ,s these pussihliilies, Fxperimenl 2 was conducted- Nom Fig . I . CT scan done I week following a stroke showing a large infarct in the right middle cerebral artery distribution and involving the right parietal and frontal lobes . 1103 N(Yrb: 1105 (a) (b) (e) Columns Fig . 2 . Distribution of targets cancelled for 1al Experiment I. 1b) Experiment 2 and (c) Experiment 3 : 16 targets, 32 targets . WOM 64 targets, I1 128 targets . wed F\perintent 2 In this experiment there were eight conditions . The three conditions of the first experiment were repeated . In addition . the same mini her of targets were distrrhtited in half the area, such that there were 16 . 32 and 64 targets distributed over 233 .1 s q . c m . If density was the critical variable, performance on 16 targets in ihesinallerarea would be similar to that in 32 targets in the larger area, and performance on arrays with 32 targets in the smaller area would be similar to performance on arrays with 64 targets . The hypothesis that number of targets was the important independent variable could be tested against the hypothesis that density of targets was the critical variable . There were two additional conditions with and 32 targets in the smaller area hound by a square clearly drawn around the targets . This square was surrounded by an equal number of `O''s as were in the box, to till up the tot at 466 .1 sq, em . If there were 32 targets in the box of 233 .1 sq . cm, there acre 64 targets in 466 .1 sq . cm. M .F . was asked to only cancel targets in the box . These conditions would assess the influence of the sheer presence of more stimuli in attended space . Ten trials of all the conditions were administered . M 1106 Norn Results . As is shown in Table l, on the tasks with 16 targets, M .F . performed at a ceiling Ieve], cancelling over 95°,'0 of targets . The data from these conditions were excluded from further analysis . M .F : s cancellations did not vary with density of targets, and the regression lines described by each did not differ (d .f.=2, 36 ; h'=0 .32, P=11 .73) . The data, analyzed as a single group using logarithmic transformations for both variables (as was done in Experiment I ) resulted in the regression line : log(responsc)-0 .47logltargets presented)+0 .75 or the power function response =6.03 (targets presented 1 11 4 -' The regression line had a correlation of 0,72 (d .f- 1 .38 ; F=39 .77, P<0 .000l) . Both a power function and an exponential function accounted fur 52% of the variance in performance . whereas a simple correlation accounted for 50% of the variance . Table I . Performance on cancellation task : Experiment 2 A B C 16 Targets presented 32 15 .5(±0 .7) 152 (±f01 15 .7 (±0 .5) 228 .9(±2 .1) 27 .9 ( 1_2 .31 26 .2 (±2 .5) 64 392(+8 .2) 40 .7 (+7 .2) A Targets were identical "O"s distributed over 466 .1 sq . em. B-Targets were identical "O's distributed over 233 .1 sq . cut . C-Targets were identical 'O"s boxed in 233 .1 sq, cm, surrounded by an equal number of targets in an overall area of 466.1 sq, cm . The response on the targets with and without surround distracors were compared using the Wilcoxon Signed Ranks Test . For 32 targets . the response of 27 .9 (±2 .5) . or 87]9%, on arrays without distracters was different than the response of 26 .2 (±2 .6), or 81 .88%, on arrays with distractors (P=11 .0125) . As in Experiment I, the arrays were divided into four columns from left to right . The data for arrays distributed over 466.1 sq . c m and 233 .1 sq . c m were combined . As in Experiment t, there was a left-to-right gradient in her neglect that also varied depending on the number of targets presented . The percent that she cancelled within each column for arrays of 16, 32 or 64 targets are displayed in Fig .2(b) . In all the cancellations there were two targets in the middle left column from arrays with 64 targets that were cancelled twice . Discussion . M,F .'s performance clearly demonstrated that number of targets and not density was the critical variable influencing performance . The condition with targets enclosed within the box demonstrated that, although the presence of more stimuli in ipsilmeral space had an influence on performance, the nag titude of this effect was trivial compared to the decrease in percent of arrays cancelled with increasing number of targets . During the interim between Experiments I and 2, M .F .'s performance improved such that she cancelled more targets overall . She had a ceiling performance on arrays with 16 targets . However, despite improvement, the exponent in her power function did not change . Her improvement was reflected in an increase in the constant of the power function . It was possible that, given a set ofstimuli . M .F . allotted a certain amount of time for the task and stopped at the end of that time . The number of targets she cancelled may have been a consequence of how much lime was allotted for the task . Experiment 3 would assess whether targets cancelled or time allotted for the task was the critical dependent variable . A task requiring both discrimination and detection would he expected to take longer than simple detection . I( this expectation were true, the two alternative hypotheses could be pitted against each other . If she was allocating a specific amount of time to do the task and this allocation was being determined by the number of stimuli, then she would use the same amount of time in the task requiring discrimination and detection but cancel less targets. Alternatively . she might cancel the same number of targets on the task requiring both discrimination and detection as the task requiringjust detection but take longer . Again, it was possible that there was some complex interaction between time taken per task and number of targets presented . Finally, since she had a ceiling performance on the array with 16 targets in Experiment ',a new condition with 128 targets was added to test the stability of our findings . Experirneni 3 This experiment consisted of six conditions . Three of the conditions had either 32, 64 or 128 targets in 466 .1 sq . cm . The other three conditions had letters and numbers in a ratio of 3 :1 . There were either 32, 64 or 128 letter,number target sin 466 .1 s q . c m . Fifteen trials were given . Each cancellation task was tuned from start to finish . 1107 Notn Results . As is shown in Table 2 . there was no difference in number of targets cancelled depending on whether she had to just detect where the "O's were, or whether she had to also discriminate between letters and numbers . The regression lines described by the data were not different between the two tasks (d .f.=2, 86 ; F=0 .19, P=0 .83) . The data were considered as a single group and best fit the regression line log(response)0 .42log(targets presented)-0 .84 or the power function response =6.92(targets presented)" 4 ` . The line had a correlation oft) 70 Id .f.= 1 . 88 ; F=84 .79 . P<0 .0001 I . The power function accounted for 49' ;. of the variance in performance, whereas, an exponential function and a simple correlation would account for 47 and 42% of the variance, respectively . Table 2 . Performance on cancellation task : Experiment 3 Targets presented 64 128 Targets cancelled A 29 .0(±2 .3 ) B 29 .1 (±2 .4) 37 .5 (18 .4) 42 .41±11.1) 55 .81±19 .9) 52 .81±21 .9) Time (sec) A 31 .01±3 .11 B 34 .4 (±5 .4) 36 .2 (±8 .8) 49 .1 113 .7) 54 .1( ±21 .0) 58 .0 (±21 .9) 32 A-Target were identical `O"s distributed over 466 .1 sq . cm . B Targets were letters and numbers distributed over 466 .1 s q . c m . Correlations using time as the dependent variable rather than number of targets cancelled was also significant, but weaker (r=0 .56, d .f.=1, 88': F=40 .04, P<0 .0001 ) . The regression lines described by the "O" cancellation and the letterinumber cancellation were significantly different (d .f .-2. 86 ; F-3 .27 . P<0 .05) . As in the previous experiments the stimulus arrays were divided into four columns . Data from the cancellations and the letter,/number cancellations were combined The percent targets that she cancelled within each column are shown in Fig . 2(c). again demonstrating a variable gradient of neglect from left to right . A total of one target in the middle left column on an array with 64 targets and three targets in the middle right column on arrays with 128 targets were cancelled twice . Discussion . The results demonstrate that M .FF cancelled the same number of targets on the arrays with letters%numbers and arrays with just "O"s . The added demand of identifying targets in addition to detecting their location did not affect how many targets she cancelled . Instead she took longer to cancel the same number of targets on the lettcruumber arrays . Again, the exponent of the power function did not change significantly from the previous two experiments. GENERAL DISCUSSION We have previously demonstrated that M . F . has a limited capacity to attend or act upon target in a cancellation task, and that this limited capacity was not confined to a specific spatial location [5] . Cancellation tasks put several demands on altentional and intentional systems . There is a phasic demand in every act of cancelling a specific target . There are Ionic demands in sequentially cancelling targets within a trial, and there are tonic demands of sustaining performance across multiple trials . We have focused on capacity limitations to attend or act upon targets within a trial, and the experiments described in this report are attempts to further uncover the nature of this limited capacity . From Experiments I and 2 . it is clear that N41 I, is not confined to a fixed proportion of external space within which she is capable of acting . If this were the ease . she would always cancel the same proportion of targets regardless of the absolute number encompassed within this space . The distribution of her neglect demonstrated the expected gradient from left to right, however, the gradient itself varied depending on how many targets were presented . Neither a simple-minded notion of neglect to the left of a midline, nor a simple-minded fixed gradient of performance front right to left adequately accounts [or these data . It is also clear that M .F . is not confined to cancelling a specific number of targets . Instead, when presented with more targets . she cancels more fin absolute terms) while neglecting 1108 Nor g a greater proportion of the array . There appears to be a systematic relationship between the number of stimuli and her response, which is described by a power function R=KS' : where R Iher reponseI is the number of largets cancelled, S is the number of stimuli on the array . and B and K are exponents and constants derived from the data . Fxperintent 2 demonstrates that this lawful relationship is determined by number and not density of targets . Between the first and second testing session there was some improvement in M .F's perform anec-With arrays of 16 targets she performed almost flawlessly . Fit her art increase in the constant or an increase in the exponent of the power function or a combination of both would result in improved performance . There was no way to predict. a priori, how recovery would alter the power function . In M .F .'s case it was the constant that increased and not the exponent. For her, the threshold beyond which neglect would be evident had increased . There was no change in the exponent. suggesting that despite improvement, some important aspect of her dysfunction had not changed . Simply counting the number of targets cancelled as a measure of improvement would have obscured this observation 'I lie power function may provide a method by which It) chart and examine the nature of recovery in neglect . Rmt101 0 and HLxivHRt yS [tO] have argued that preattentive processing is teladvety preserved in contradateral space of patients with neglect. but this information is not adequately utilized by conscious attention . which is required to make discrimination judgements . They suggest that leftward stimuli lend not to "capture" attcntion . but when they do, discrimination nay occur . Our data suggests that additional attentional demands Of disc] initiating letters from numbers does not ittfuence the capacity limitation being described by the power function . The power function . indeseribinoastimulus response relationship . may he speei flea I ly describing pathologic limit at ions oft he "where' visual system . In keeping with this idea is the fact that her lesion involves the parietal lobe . preferentially affecting the dorsal stieant and not the inferotemporal ventral stream of visual processing . At this point. the functional significance of the power function with respect to psychological or brain mechanisms cannot he specified . However . the existence of a systematic stimulus response relationship hits theoretical implications for mechanisms underlying the neglect syndrome . Since the number (if targets presented influences performance on cancellation tasks . the subject must he acting on some knowledge of targets that she appears to be neglecting . Several studies with neglect patients have suggested that patients with neglect may act as though they have some knowledge of neglected stimuli [2, 4, 7, 9, 11], '[he extent to which neglected stimuli are processed and how they influence behavior is far from well understood . Whether the influence of "neglected" targets is mediated by early preattentive visual processing that may he relatively preserved in neglected space Or by more clahorate processing that has not penetrated consciottsnes .s is lint known . 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