Localizing Arithmetic Processes in the Brain: Evidence from a Transient Deficit During Cortical Stimulation

John Whalen, Michael McCloskey, Ronald P. Lesser, and Barry Gordon The Johns Hopkins University

Abstract

Although substantial progress has been made in charac- terizing the cognitive processes involved in simple arithmetic, the localization of these processes in the brain is not yet well understood. In this article we consider the localization of a specific arithmetic process, the retrieval of arithmetic table facts from memory. We report a single-patient study in which cortical stimulation was used to create transient disruption of

brain activity in localized regions of the cortex. We show that stimulation at a left parietal site impaired performance on simple multiplication problems and further that the impair- ment reflected stimulation-induced disruption of arithmetic fact retrieval. Our findings support the hypothesis (e.g., War- rington, 1982) that the left parietal lobe is implicated in the arithmetic fact retrieval process.

INTRODUCTION

Solving arithmetic problems (e.g., 47 x 83) requires a variety of cognitive processes, including comprehension and production of digits (e.g., 3,7), retrieval of arithmetic “table” facts (e.g., 3 x 7 = 21), and execution of proce- dures specrfying the sequence of steps to be carried out (e.g., multiply the digits in the rightmost column, write the 1s digit of the product, and so forth). Recent research with normal subjects and braindamaged patients has contributed substantially to our understanding of these processes at a functional level (e.g., Ashcraft, 1992; De- haene & Cohen, 1995; McCloskey, 1992; McCloskey, Har- ley, & Sokol, 1991). However, less progress has been made in discovering how (or whether) arithmetic proc- esses are localized in the brain (see Kahn & Whitaker, 1991, for a recent review).

A number of findings suggest that posterior cortical regions--and especially parietal regions-may play a role in arithmetic abilities (e.g., Benson & Weir, 1972; Grafman, Passafiume, Faglioni, & Boller, 1982; Hecaen, Angelergues & Houillier, 1961 ; Inouye, Shinosaki, Iyama, & Matsumoto, 1993; Jackson & Warrington, 1986; Rosselli & Ardila, 1989; Warrington, 1982). However, many other brain areas have also been implicated, including the frontal lobes (Lucchelli & De Renzi, 1993; Roland & Friberg, 1985), thalamus (Ojemann, 1974), and basal gan- glia (Corbett, McCusker, & Davidson, 1986; Hittmair- Delazer, Semenza, & Denes, 1994).

Interpreting the available evidence is not entirely straightforward, in part because most studies have

0 1997 Massachusetts Institute of Technology

sought to relate brain areas to arithmetic tusks and not to specific cognitive processes such as arithmetic fact retrieval. For example, studies exploring lesiondeficit correlations have typically focused on identrfying the lesion loci associated with impaired performance on some calculation task or tasks (e.g., Benson & Weir, 1972; Cohn, 1961; Corbett et al., 1986; Grafman, Kampen, Rosenberg, Salazar, & Boller, 1989; Luccelli & De Renzi, 1993; Takayama, Sugishita, Akiguchi, & Kimura, 1994). However, an association between a lesion site and im- pairment on a calculation task does not in itself consti- tute strong evidence that the damaged brain area is implicated in arithmetic processing, because the im- paired performance could have resulted from disruption to nonarithmetic processes required by the task (e.g., attention, working memory, numeral comprehension, nu- meral production). Although some researchers have at- tempted to control for this possibility, the controls have usually not been sufficient to rule out plausible nonarith- metic interpretations for the calculation task impair- ment.

These points also apply to research involving electro- physiological recording and cortical stimulation meth- ods. In several recent studies subjects performed a serial subtractions task (e.g., count backward by 7s from 100) while brain activity was recorded (Roland & Friberg, 1985; Inouye et al., 1993) or cortical stimulation was applied (Morris, Luders, Lesser, Dinner, & Hahn, 1984; Ojemann, 1974). A number of brain areas were found to be associated with performance on the task, including the left parietal lobe (Roland & Friberg, 1985; Inouye

et al., 1993; Morris et al., 1984), the frontal lobes (Roland & Friberg, 1985), and thalamic regions (Ojemann, 1974). Although intriguing, these findings do not necessarily imply that the identified brain areas are implicated in arithmetic processing; the reported data do not exclude the possibility that some or all of the brain areas are instead involved in nonarithmetic processes required by the serial subtractions task ( e g , comprehending the initial stimulus number, producing responses).

Arithmetic Fact Retrieval

In this article we consider the localization of a particular arithmetic process, the retrieval of arithmetic table facts (eg., 6 x 7 = 42). Evidence bearing specifically on this issue is sparse. Warrington (1982) described a patient (DRC) with a calculation deficit, demonstrating through careful cognitive testing that he was selectively impaired in retrieval of arithmetic facts. CT revealed a focal lesion in the left posterior parieto-occipital region, suggesting that this area may play a role in arithmetic fact retrieval. More recently, Hittmair-Delazer et al. (1994) documented an arithmetic fact retrieva! impairment in a patient (BE) with a lesion confined to the left basal ganglia and concluded that this region may also be implicated in the fact retrieval process. Although several other cases of selectively impaired arithmetic fact retrieval have been reported (e.g., Dagenbach & McCloskey, 1992; Dehaene & Cohen, 1991; McCloskey, Aliminosa, & Sokol, 1991; McCloskey, Caramazza, & Basili, 1985; Sokol, McCloskey, Cohen, & Aliminosa, 1991), the brain lesions in these cases were very extensive, or lesion localization data were not available.

In the present study we used cortical stimulation to explore the localization of arithmetic fact retrieval. Pa- tient AA, a young man suffering from a left-hemisphere brain tumor and associated seizures, underwent for clini- cal purposes a procedure in which arrays of electrodes were surgically placed on the surface of the left hemi- sphere. The arrays, which remained in place until resec- tion of the tumor 16 days later, were used for recording aimed at localizing the seizure foci and for stimulation carried out to map the functions of cortical areas that might be affected in the resection. In the functional mapping mild stimulation was applied briefly across ad- jacent electrodes, creating transient disruption of brain activity in localized regions. Sensory, motor, and cogni- tive tasks were presented during stimulation to deter- mine what functions (if any) were transiently impaired. The cortical stimulation results reported in this article come from the clinical stimulation testing, supplemented by additional testing carried out for research purposes.

CASE HISTORY

Patient AA is a left-handed male. In 1986, at age 9, he began to experience seizures involving shaking of the

right arm and periods of unresponsiveness. Rarely, these progressed to general tonic-clonic seizures. Neurological evaluation revealed a tumor in the left parasagittal parie- tal region, identified upon resection as a grade C oligo- dendroglioma. WADA testing prior to surgery revealed that the left hemisphere was dominant for language.

In 1992, at age 16, AA again began to experience seizures. When these proved refractory to medication, he was admitted to the Johns Hopkins Hospital for evalu- ation. MRI with and without gadolinium contrast sug- gested recurrence of the tumor at the same location (Figure l), and this diagnosis was subsequently confir- med at surgery.

Neuropsychological Evaluation

Neuropsychological assessment carried out prior to the cortical stimulation study revealed that despite the tu- mor and seizure disorder, AA’s performance was normal on tests of general intellectual and language abilities. On the WISC-R (Wechsler, 1974) he obtained a full-scale IQ of 97 (Verbal = 103, Performance = 91). He scored 89/90 (99%) for auditory comprehension on the Token Test (De Renzi & Vignolo, 1962), and 88/90 (98%) for reading comprehension. Performance was normal (54/60) on the Boston Naming Test (Goodglass & Kaplan, 1983), and oral word reading was performed without error (1 17/117). Spontaneous speech was fluent and meaning- ful, without obvious articulatory difficulties, word-finding problems, or paraphasias.

On the Wide Range Achievement Test (WRAT; Jastak & Wilkinson, 1984) AA scored at the eleventh grade level in reading, and the tenth grade level in spelling. Because of school missed as a result of his seizures and the ensuing surgery in 1986, AA was completing grade 9 at the time of testing, one grade behind that expected for his age. His reading and spelling scores are therefore above average for someone at his grade level and at or above the norm for students of his age.

Assessment of Numerical Processing

In the cortical stimulation study singledigit multiplica- tion and addition problems were presented visually (e.g., 8 x 7), and AA said the answer aloud (e.g., “fifty-six”). These tasks require comprehension of numerals in ara- bic form (eg., 8, 7), retrieval of arithmetic table facts (e.g., 8 x 7 = 56), and production of numerals in the form of spoken words. Accordingly, several tasks designed to probe these processes were administered in the absence of stimulation.

AA was 99% correct (1 19/120) across six tasks in which he translated numerals from one form to another (e.g., written stimulus 2041, spoken response ”two thou- sand forty-one”), suggesting intact numeral comprehen- sion and production abilities. For tasks requiring arabic

41 0 Journal of Cognitive Neuroscience Volume 9, Number 3

Figure 1. Horizontal and coronal MRI sections from scan conducted at the time of the cortical stimulation study, prior to AA's second resection surgery.

numeral comprehension or spoken numeral production he was 100% correct (80/80).

On speeded tests of singledigit multiplication and addition (e.g., 9 x 4 , 8 + 6) AA was 98% correct (246/250) for multiplication and 100% correct (45/45) for addition. Mean correct reaction time was 1644 msec for multipli- cation and 1562 msec for addition. These results demon- strate that AA was able to solve the problems by retrieving stored arithmetic table facts, since the re-

sponse times are considerably faster than would be ex- pected (see, eg., Ashcraft, 1982; Siegler, 1988) if he were using some nonretrieval strategy (e.g., adding seven 8s to solve 8 x 7).

On pencil-and-paper tests of addition, subtraction, and multiplication AA was 98% correct (59/60) for single- digit problems and 83% correct (25/30) for multidigit problems (eg., 413 x 59), within normal limits for adults (McCloskey, Aliminosa, & Macaruso, 1991). The errors on

Whalen et al. 41 I

Inferior Front a1

Posterior Anterior Medial Frontal Parietal Parietal

Figure 2. Diagram of location of specific neuropsychological deficits produced by electrical stimulation.

multidigit problems reflected occasional slips in execut- ing calculation procedures (e.g., forgetting a carry digit); retrieval of arithmetic table facts on these problems was uniformly accurate. Further evidence of intact fact re- trieval comes from the arithmetic subtest of the WRAT. Although AA scored at the seventh grade level, his errors stemmed from difficulty in dealing with algebra, expo- nents, and quadratics; performance on arithmetic facts was excellent.

The numerical processing results suggest that in spite of the tumor and associated seizures, AA’s numerical abilities are relatively normal. In particular, the numeral comprehension, numeral production, and arithmetic fact retrieval processes required for the cortical stimulation study appear to be intact.

RESULTS

Transient Impairment of Multiplication Performance

Singledigit multiplication was tested during cortical stimulation at each pair of adjacent electrodes in the inferior frontal, anterior parietal, and medial parietal elec- trode arrays (Figure 2), except for sites where stimula- tion was found to affect motor or sensory functions. Problems were presented in digit form (e.g., 9 x 4), and AA was allowed up to 7 sec to say the answer aloud. Stimulation appeared to affect multiplication perfor- mance for only one electrode pair: AP18-26, located in the anterior parietal region. The AP18-26 site is distant from both the tumor and the seizure foci (which were

412 Journal of Cognitive Neuroscience Volume 3, Number 3

located on the medial aspect of the hemisphere); AP18- 26 stimulation did not induce seizures.

Under AP18-26 stimulation AA responded correctly to only 27% (17/63) of the multiplication problems admin- istered over several days. In contrast, he was 98% correct (246/250) on intermixed control trials without stimula- tion, x2 ( 1 , N = 313) = 191.2,p c .0001. In 27 of the 46 errors on stimulated trials AA produced an incorrect answer (eg., 8 x 4 = “forty”; 6 x 5 = “twenty five”; 7 x 9 = “eighty two”); on the remaining 19 trials he produced no response within the 7-sec stimulation period. On many of the trials in which he failed to respond correctly during stimulation, AA gave the correct response imme- diately after stimulation was terminated.

A more carefully controlled comparison confirmed that performance on the multiplication task was im- paired by stimulation at the AP18-26 site. For each of the 57 problems tested with and without stimulation (e.g., 7 x S),’ a mean accuracy was computed for stimu- lated trials and for nonstimulated control trials. AA’s accuracy was significantly lower for the stimulated trials (28% correct) than for the matched control trials (99% correct), t(56) = 11.67,p c .0001.

On trials involving stimulation at sites other than AP18-26, AA was 94% correct (138/147). Even for elec- trode pairs adjacent to AP18-26, stimulation had no effect on multiplication performance: AA’s accuracy un- der stimulation at these sites was 98% (43/44). Results for stimulated and nonstimulated trials are summarized in Table 1 .

cognitive processes required by singledigit multiplication and addition tasks with arabic stimuli and spoken responses.

8 x 2 +

Identifying the Cognitive Process(es) Disrupted by Stimulation

Having established that stimulation at AP18-26 impaired performance on the multiplication task, we may next consider which of the cognitive processes required by the task were disrupted by stimulation. Several findings bear on this issue.

Arabic Multiplication Spoken Numeral Fact Numeral “sixteen“

Comprehension Retrieval Production

Table 1. AA’s Performance on Multiplication Problems with Spoken Responses

Number of Number Percent Stimulation Site Problems Correct Correct

AP 18-26 6 3 17 27

All Other Sites 147 138 94

Adjacent to AP 18-26 44 43 98

None 250 246 98

Under AP18-26 stimulation AA performed without er- ror on screening tests of spontaneous language produc- tion (6/6), object naming (8/8), reading aloud (8/8), and responding to commands (4/4). These results suggest that the stimulation-induced deficit on the multiplication task did not result from disruption of speech production or from impairment of some general cognitive function such as attention. Given that tasks such as object naming, reading aloud, and spontaneous speech (instruction: de- scribe your high school and home state) required AA to recall from memory several different types of informa- tion, it also seems unlikely that AP18-26 stimulation produced some sort of general memory impairment.

In addition to processes such as attention or speech production, the multiplication task implicates several forms of numerical processing: comprehension of arabic digits ( e g , 7 , €9, retrieval of stored arithmetic facts (e.g, 7 x 8 = 56), and spoken production of numerals (e.g., “fifty-six”). To assess which of these processes were af- fected by stimulation, we compared AA’s performance on multiplication and addition tasks. In the addition task, as in the multiplication task, singledigit problems were presented in arabic form ( e g , 6 + 9), and AA said the answers aloud (e.g., ‘liftfifteen’’). Thus, both tasks required arabic numeral comprehension and spoken numeral pro- duction (Figure 3). However, the two tasks differed in arithmetic fact retrieval processes: the multiplication

Figure 3. Comparison of the

Addition

Comprehensio Retrieval Production Numeral Numeral “sixteen”

Whalen et al. 413

task required retrieval of stored multiplication facts, whereas the addition task required retrieval of addition facts.

If the stimulation-induced impairment of multiplica- tion resulted solely from disruption of arabic numeral comprehension or spoken numeral production, we would expect performance to be equally impaired on the addition task. If, however, stimulation affected arith- metic fact retrieval, performance under stimulation might differ between the addition and multiplication tasks. Because addition facts may be better learned than, or stored separately from, multiplication facts (see, e.g., Dagenbach & McCloskey, 1992; Siegler & Engle, 1994), stimulation might well affect addition and multiplication fact retrieval to different extents.

Under stimulation at the AP18-26 site AA’s perfor- mance was much more impaired for multiplication (17/63; 27% correct) than for addition (26/30; 87% cor- rect), x2 (1, N = 313) = 29.12,p e .001. This finding suggests that the stimulation affected arithmetic fact retrieval and more specifically that the stimulation dis rupted retrieval of multiplication facts to a greater extent than retrieval of addition facts.

However, before firm conclusions can be drawn on this point, we must ensure that the addition and multi- plication tasks are adequately matched on their numeral comprehension and production requirements. Whereas saying the answer to a singledigit multiplication prob- lem often requires spoken production of two number words (e.g., “fifty” and “six” for 7 x €9, all singledigit addition problems have one-word answers (e.g., ‘‘fifleen” for 7 + 8). The multiplication task may therefore place greater demands than the addition task on spoken nu- meral production processes and so might be more seri- ously affected by disruption of this process. The finding of greater multiplication than addition impairment under AP18-26 stimulation might, then, reflect disruption not of arithmetic fact retrieval, but rather of spoken numeral production.

To evaluate this possibility we compared performance on singledigit multiplication and addition problems that have the same answer (e.g., 9 + 7 , 8 x 2) and therefore the same spoken numeral production requirements. For each of 13 answers shared between addition and multi- plication problems, a mean accuracy was computed for multiplication and for addition. ’Ikenty-five addition tri- als and twenty-three multiplication trials contributed to the analysis. Under stimulation, AA’s performance was reliably worse for the multiplication problems (50% cor- rect) than for the answer-matched addition problems (87% correct), t(12) = 2.7,p e .05. Therefore, even when the two tasks were equated on spoken numeral produc- tion requirements, stimulation at the AP18-26 site led to greater impairment for multiplication than for addition. This finding strongly suggests that the multiplication-ad- dition dissociation under stimulation reflects an effect of stimulation on arithmetic fact retrieval.

However, we must also consider whether the dissocia- tion could be due to differences between tasks in arabic numeral comprehension requirements. Here again, the answer-matched problems prove useful. For addition and multiplication problems with the same answer, the mul- tiplication problems usually have the smaller operands (e.g., 3 x 6 versus 9 + 9); in our answer-matched problem sets the mean operand magnitude was 3.4 for multipli- cation and 4.3 for addition. Therefore, the multiplication problems were if anything less demanding than the ad- dition problems in their arabic numeral comprehension requirements.

Thus, relative to the addition problems the answer- matched multiplication problems placed equal demands on spoken numeral production and equal or lesser de- mands on arabic numeral comprehension. The greater impairment of multiplication than addition under AP18- 26 stimulation therefore cannot be attributed to effects of stimulation on numeral comprehension or production processes. Hence, the result points strongly to the con- clusion that stimulation disrupted arithmetic fact re- trieval, with multiplication being affected to a greater degree than addition.

Whether AP18-26 stimulation had any effect on re- trieval of addition facts is uncertain. Addition perfor- mance was slightly worse on stimulated trials (87%) than on nonstimulated control trials (loo%), x2 (1, N = 75) = 3.97,p c .05. However, we cannot be certain that this result reflects stimulation-induced disruption of addition fact retrieval, because mild disruption of numeral com- prehension or production could have been responsible instead. (Note that the addition-multiplication compari- sons did not rule out the possibility that stimulation had some effect on numeral comprehension or production; rather, these comparisons established that the stimula- tion had effects on multiplication fact retrieval over and above any effects it might have had on numeral compre- hension and production.)

Why might AP18-26 stimulation have substantially dis rupted multiplication fact retrieval while affecting addi- tion fact retrieval to a lesser extent or not at all? One possibility is that multiplication facts are typically not as well learned as addition facts and therefore are more susceptible to disruption. Another possibility is that ad- dition and multiplication facts are localized to different brain areas, as some recent evidence from braindamaged patients suggests (e.g., Dagenbach & McCloskey, 1992; Siegler & Engle, 1994).

Stimulation-Induced Impairment on Other Multiplication Tasks

Given the conclusion that AP18-26 stimulation impaired retrieval of multiplication table facts, we should expect to observe stimulation-induced impairment on any task requiring multiplication fact retrieval. In a verification task problems were presented with candidate answers

41 4 Journal of Cognitive Neuroscience Volume 9, Number 3

(e.g., 3 x 2 = 8), and AA indicated whether the answer was correct or incorrect by touching the appropriate word (‘Yes’’ or ‘‘no’’) on a card in front of him. He was uniformly correct on nonstimulated control trials (6/6) but performed at chance under stimulation at the AP18- 26 site (3/6). Although too few trials were administered to permit firm conclusions, the results are consistent with the conclusion that AP18-26 stimulation impaired multiplication fact retrieval.

In another task singledigit multiplication problems were presented in arabic form, and AA typed the answers on a numerical keypad. He was 97% correct (68/70) on nonstimulated control trials but only 64% correct (14/22) on stimulated trials, x2 (1, N = 92) = 19.39,p c .001 . Thus, even when AA was not required to produce spoken responses, M18-26 stimulation significantly im- paired multiplication performance.

Performance under stimulation was somewhat better in the keypad response task (64% correct) than in the task with spoken responses (27% correct). This result suggests that stimulation, in addition to disrupting mul- tiplication fact retrieval, may have produced a mild im- pairment of spoken numeral production. This possibility, it should be emphasized, does not affect the arguments underpinning our conclusion that Stimulation disrupted multiplication fact retrieval. As discussed in the preced- ing section, the greater impairment for multiplication than for addition under stimulation cannot be attributed to effects of stimulation on numeral comprehension or production and points clearly to a stimulation-induced impairment of multiplication fact retrieval. Also, the re- sults reported in the present section show that stimula- tion disrupted multiplication performance even in tasks not requiring spoken numeral production.

DISCUSSION

Our principal findings may be summarized succinctly: Cortical stimulation at a single site in the left parietal region impaired patient AA’s performance on singledigit multiplication problems, and results from other tasks indicated that the stimulation specifically disrupted re- trieval of stored multiplication facts. Accordingly, our findings suggest that the left parietal area is implicated in arithmetic fact retrieval.

This conclusion must be drawn with some caution. In the first place, it is possible that AA’s functional brain organization is atypical in some respects, due to his brain tumor. Against this possibility it may be noted that the tumor was distant from the AP18-26 stimulation site and affected a brain area that has not been linked with arithmetic processing. Also, extensive testing of AA’s nu- merical processing prior to the cortical stimulation study revealed no abnormalities; arithmetic fact retrieval in particular appeared normal. Hence, it seems unlikely that arithmetic fact retrieval was localized atypically in AA; however, the possibility cannot be ruled out entirely.

A more general reason for caution is that the number of studies speaking to the localization of arithmetic fact retrieval remains very small. In addition to our results from AA, the available evidence consists primarily of Warrington’s (1982) study of patient DRC and Hittmair- Delazer et al.’s (1994) study of patient BE. Many more studies will have to be conducted before strong conclu- sions can be drawn.

A considerable amount of evidence is needed in part because relationships between cognitive processes and brain areas may be quite complex. Multiple brain regions may be involved in implementing a cognitive process, and multiple cognitive processes may draw upon a given area of the brain. Also, there may be significant individual variation in localization of cognitive functions. Given these potential complexities, we can hope to clarlfy localization issues only by assessing the brain regions associated with a cognitive process in many individual subjects and preferably through a variety of methods.

In light of these points it is interesting to compare our results from patient AA with the previous findings from patients DRC (Warrington, 1982) and BE (Hittmair- Delazer et al., 1994). At first glance the AA results appear to converge with those from DRC-who showed impair- ment in arithmetic fact retrieval following left parieto- occipital damage-to suggest involvement of some dominant-hemisphere parietal region in arithmetic fact retrieval. However, the AP18-26 stimulation site is some- what anterior to the locus of DRC’s structural lesion, and it is far from obvious that the brain area affected by stimulation in AA overlapped with the area damaged in DRC.2 The picture is complicated further by Hittmair- Delazer et al.’s (1994) patient BE; this patient’s lesion was apparently confined to the left basal ganglia, a re- gion unlikely to have been affected in either AA or DRC. The apparent lack of consistency across studies may reflect the involvement of multiple brain areas in arith- metic fact retrieval or individual differences in localiza- tion of this cognitive process, or some other factor(@ may be responsible. Additional evidence will be needed to clarrfy the situation.

Arithmetic fact retrieval is not at all atypical with respect to the complexities of localization issues, or the limited nature of the conclusions warranted by the avail- able evidence. Notwithstanding the insights gained from traditional methods such as lesiondeficit correlation, and the development of powerful new techniques like cor- tical stimulation and fMRI, we are still in the early stages of understanding the functional organization of the brain.

METHOD

Cortical Stimulation

Informed Consent

This study was reviewed and approved by the Johns Hopkins Joint Committee on Clinical Investigation. Fol-

Whalen et al. 415

lowing a full explanation of the procedures, AA and his parents gave for all research testing. The study

for the safe use of the cortical stimulation technique. The effects of cortical stimulation and issues of safety have been discussed elsewhere (Gordon et al., 1990; Lesser et al., 1987; Nathan et al., 1993).

Cognitive Neuroscience. The study would not have been POS- sible without AA's consistent willingness to work through eve- nings and weekends, and the help of Barbara Cysvk, Dr. John

guidelines by Lesser et al. (1987) Hart, Erica palmer, Sarah Reusing, and Pamela Schwerdt.

Reprint requests should be sent to Michael McCloskey, Depart- ment of Cognitive Science, The Johns Hopkins University, Bal- timore, MD 21218, or via e-mail to: michael.mccloskey@ jhu.edu.

Procedure Note Subdural arrays of electrodes were surgically placed on the surface of the cortex. The electrodes were 2.3-mm disc-, placed 10 mm from center to center, in arrays externaUy connected through a multiminicable system. As FiguR illustrates, arrays were placed in the posterior frontal, anterior Parietal, and medial Parietal regions, oriented approximately parallel to the sylvian fissure. A 2 x 8 amv was also Placed in the inferior

1 . Six problems were tested twice during stimulation; 57 (63 - 6) unique problems were presented under stimulation. 2. Although the effects of electrical stimulation on brain activ- ity are far from fully understood, the best available evidence suggests that at the intensity used in the present study the effects are localized to the area immediately surrounding the electrodes (Nathan, Sinha, Gordon, Lesser, & Thakor, 1993). Similarly, although the boundaries of vascular lesions may be difficult to establish with certainty, it does not appear likely

frontal region orient& approxim~tely perpendicular to the previous three arrays. Four other 2 x 5 arrays (not

that DRC's lesion extended as far forward as the anterior parietal region stimulated in AA.

shown in Figure 2) were placed in the anterior frontal, medial frontal, anterior intercerebral, and posterior inter- cerebral areas. Electrode positions were determined in- dependently by direct visual inspection at the time of operative placement and removal, as well as by CT-scan and plain skull x-rays.

Electrical stimulation was administered with a Grass Model 5 12 stimulator at an intensity of 15 mA. Stimula- tion was applied between adjacent electrodes, in 300- msec square wave pulses of alternating polarity at a frequency of 50 Hz. For each electrode pair, AA was first examined during stimulation for signs of motor or sen- sory impairment. He then received screening tests prob- ing object naming, word reading, responding to commands, auditory comprehension, spontaneous lan- guage production, and singledigit multiplication. Stimu- lation trials were intermixed with nonstimulated control trials. AA was not informed of which trials would involve stimulation and was typically unaware when stimulation was applied. On stimulated trials, the onset of stimulation preceded the presentation of the test item by approxi- mately 1 sec; stimulation continued until AA responded or the end of the response period was reached.

Stimulation at certain sites on the posterior and infe- rior frontal strips (Figure 2) elicited sensations and/or movement of the right leg, arm, hand, fingers, mouth, or tongue (see Urasaki, Uematsu, Gordon, & Lesser, 1994). At one inferior frontal site, stimulation produced audi- tory hallucinations and disrupted auditory comprehen- sion. Stimulation was not found to impair language comprehension or production at any other site.

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