SHORTREPORT - BMJ

34ournal of Neurology, Neurosurgery, and Psychiatry 1993;56:304-307

SHORT REPORT

Primary dyscalculia after a medial frontal lesion ofthe left hemisphereF Lucchelli, E De Renzi

AbstractA patient had an infarct in the territoryof the left anterior cerebral artery, whichdestroyed the medial cortex of the frontallobe, and presented with a picture of pri-mary dyscalculia. Lexical and syntacticprocessing of verbal and arabic numbersand comprehension of operation symbolswere intact, but retrieval of basic, over-

learned facts was mildly impaired andexecution of calculation procedures was

more severely impaired. As the same

type of procedure could be passed or

sometimes failed it suggests a deficit ofactivation of the appropriate procedures.The location of the lesion was unusualand suggested participation of medialfrontal areas in calculation processes.

(J Neurol Neurosurg Psychiatry 1993;56:304-307)

NeurologicalDepartment, ModenaUniversity, Modena,ItalyF LucchelliE De RenziCorrespondence to:Dr De Renzi, NeurologicalDepartment Via del Pozzo71, 41100 Modena, ItalyReceived 24 February 1992and in revised form1 May 1992.Accepted 14 May 1992

An impairment of number processing and cal-culation skills is not an uncommon manifesta-tion of brain damage, but in the majority ofcases it results from the derangement of moregeneral abilities, such as language, attention,memory, space perception, that take placewhen performing arithmetical tasks. Thedyscalculia observed in these patients hasbeen labeled secondary and contrasted withprimary dyscalculia,' in which the deficitstands out as particularly severe for other cog-nitive abilities and suggests the disruption ofspecific mechanisms.'3

Dyscalculia has been recently analysed withmodels that specify the component native ofthe cognitive mechanisms underlying calcula-tion.45 There are two distinct systems: one fornumber processing and the other for calcula-tion. The former would comprise indepen-dent subsystems for comprehension andproduction of arabic and verbal number form,the latter subsystems for comprehension ofarithmetical signs (for example, x, +, -),retrieval of arithmetical facts (for example, themultiplication table) and execution of calcula-tion procedures. The model assumes that theinput of number processing is converted to an

abstract representation, which is used both toactivate the calculation system and to triggerappropriate commands for speech and writingcentres.The modular nature of this functional

architecture predicts the selective breakdownof its components after brain damage and a

search of the literature enabled McCloskeyand Caramazza4 to collect evidence support-

ing several dissociations that agree with theexpectations from the model.The patient we report is unusual for two

reasons: 1) Because the case shows a deficitstrictly confined to the calculation system,with preservation not only of other cognitiveabilities, but also of the number processingsystem; 2) Because of the unusual site of thelesion, which involved the medial areas of theleft frontal lobe.

Case reportThe patient, a 22 year old male, was a thirdyear music student. Before entering the acad-emy of music to study the organ, he hadattended liceo classico, the most demandingtype of high school in Italy. He did not havedifficulty in learning mathematics. In June of1990 he complained of headache andunsteadiness. Admitted to a neurosurgicaldepartment, a cerebellar tumour was diag-nosed and on 10 July 1990 he had a grade 2cystic glioma of the vermis and the right infe-rior cerebellar peduncle which was completelyresected. The post-operative course wasuneventful until 23 July 1990, when he com-plained of a severe headache and a right lowerlimb weakness. He subsequently becamemute and presented with a complete paresisof the right lower limb. When we first saw thepatient on 9 August 1990, he showed the syn-drome of crural and proximal arm paresis typ-ical of anterior cerebral artery infarction.Grasping, but not groping, was present inboth hands. His behaviour was abnormal. Hespontaneously kept his eyes closed and didnot initiate talking. He gave correct answersto simple questions but with no more thantwo words. With more complex questions (forexample, "tell me how Jesus Christ died") heremained silent. Visual naming was in thenormal range (54/60) according to a test stan-dardised on 70 normal controls.1" He gaveonly five names of animals in one minute andfour names on three phonetic cues (P, F, L),with one minute for each.On 24 August 1990, an MRI confirmed the

presence of an infarct involving the wholeterritory of the left anterior cerebral artery(figure). The lesion encroached upon areas10, 11, 12, 24, 23 and the medial extension ofarea 6 and 4.6 The anterior half of the corpuscallosum was also damaged.No cause for the cerebrovascular accident

was identified by neurosurgeons.The patient progressively improved and by

September his language had recovered,

304 on D

ecember 24, 2021 by guest. P

rotected by copyright.http://jnnp.bm

j.com/

J Neurol N

eurosurg Psychiatry: first published as 10.1136/jnnp.56.3.304 on 1 M

arch 1993. Dow

nloaded from

Primary dyscalculia after a medialfrontal lesion of the left hemisphere

IExtent of the MRI lesion. A and B: axial slices.

though he remained somewhat limited inspontaneous speech. During this period a dif-ficulty with calculation was noted by thepatient which prompted the investigationsthat were carried out from September toNovember 1990.Most of the tests were carried out in

September 1990, and those that did not yieldscores in the normal range were repeated inOctober or November 1990.The WAIS FS IQ was 98 in September

and 111 in October, with an improvement ofmore than 20 points on the PIQ (from 82 to104) and a largely stable VIQ (from 110 to114). On the arithmetic subtest the patienthad a weighted score of 8 in both sessionswith failure on the last, more complex items.His intellectual proficiency was confirmed bythe scores achieved on the Raven ProgressiveMatrices, series A, B, C, D (43/48),Wisconsin Card Sorting Test (6 categories of6) and revised Wegl test (9 of 15).7The patient was given: a) Verbal learning

tests (story recall, paired associates, 10-wordlist); b) Visual memory tests (Rey figure,recurring face recognition); and c) Spatialmemory tests (visual stepping stone maze).On all tests he performed in the normalrange.No deficit of oral and written language was

apparent on a standardised aphasia battery.He scored 32/36 on the Token Test and72/85 on the Boston Naming Test. He wasalso able to read musical scores and theancient Greek tragedy Medea, which he knewfrom his classical studies, with correct met-rics.Up to the middle of October the patient

occasionally presented the alien hand symp-tom, with the right hand carrying out perfor-mances that interfered with his activity, forexample, when turning the pages of a book hewas reading. The symptom then subsided.On a limb movement imitation test he scored70/72 with the right hand and 68/72 with theleft hand (cut-off score 62/72), but on a testrequiring him to mime the use of singleobjects, his performance with either hand wasawkward and.inaccurate, though the generalconfiguration of the movement was correct.His copy of the Rey figure was flawless(36/36).

Arithmetic performance Processing of verbaland arabic numbers was rapid and correct,for both comprehension and production. Heread and wrote numbers up to 7 digits with-out error and hesitation, easily pointed to thelarger number in a pair and quickly gave acorrect estimation of a random array of 2-100black dots (2 seconds exposure) in 60 trials.8He had no difficulty in transcoding Arabicnumbers to written verbal numbers and viceversa.He named and understood without diffi-

culty the meaning of operation symbols ( +,-, x ), responded correctly to 10 generalknowledge questions concerning numericalfacts (such as, days of the week, pairs in adozen,) and gave reasonably correct answersto 10 numerical estimation questions (suchas, the height of an average Italian woman).8

Oral calculations His impairment in oral cal-culation became apparent when he wasrequested to retrieve basic arithmetic facts,that is, facts that are learnt from memory byvirtually every educated adult, such as thoseinvolved in multiplication tables and in addi-tion and subtraction of digits from 1 to 19.

Addition On thirty seven trials requiringhim to add combinations of numbers from 1to 9 (such as, 5 + 3), he produced two errorsand seven delayed correct responses (morethan 2 seconds).

His ability to add number combinations of1 to 9 to number combinations of 11 to 19was tested giving the larger of the two num-bers either first (such as, 15 + 3) or second(such as, 8 + 12). Only responses given under5 seconds and without self-corrections wereaccepted as correct. There was no differencebetween the two conditions (83% correctresponses in the former and 82% in the lat-ter) and they were combined for a total of144 trials, which produced a 6% error rate,with 3% self-corrected errors and 9% delayedcorrect responses (more than 5 seconds).When numbers from 11 to 19 were added tonumbers from 11 to 19 (such as 15 + 13) therate of correct responses decreased to 68%.In 110 trials there was an 18% error rate,

305 on D

ecember 24, 2021 by guest. P

rotected by copyright.http://jnnp.bm

j.com/

J Neurol N

eurosurg Psychiatry: first published as 10.1136/jnnp.56.3.304 on 1 M

arch 1993. Dow

nloaded from

Lucchelli, De Renzi

with 9% self-corrected errors and 5% delayedcorrect responses.Ten trials requiring the addition of two

digit numbers, both larger than 19, yielded 5errors and two correct responses given after30 seconds.

SubtractionThirty six subtractions of single digit num-bers were all correct, though in two casesdelayed ( > 2 seconds). Seventy two attemptsto subtract a single digit from a two digitnumber, (for example, 11 to 19), produced78% correct responses, 4% errors, 3% self-corrected errors and 15% delayed responses(more than 5 seconds).

Forty five trials in which a two digit num-ber is subtracted from a two digit number, allcomprised between 10 and 19, produced91% correct responses, 4% errors, 2% self-corrected errors and 3% delayed responses(more than 5 seconds). When, the largernumber was from 20 to 99, however, therewere only 40% correct responses, 30% errorsand 30% delayed responses (more than 5seconds) of 10 trials.

MultiplicationMultiplying all number combinationsbetween 2 and 9 yielded 84% correctresponses, 8% delayed responses (more than5 seconds), 5% self-corrected errors and 3%errors.

DivisionHe was given 30 division calculations, 10with a two digit dividend and 20 with a threedigit dividend. The divisor always had onedigit and all divisions were without remain-der. Only responses given in 15 seconds wereaccepted. He made 15 errors (50%).Two normal controls, matched for sex, age

and years of education, performed the aboveoral calculations accurately and rapidly.

Written cakulationsThe errors made in written calculations var-ied according to the type of operation. Onaddition, only errors of facts were observed(for example, 83 + 15 = 99). When subtract-ing, errors of borrowing were by far the mostfrequent. Errors of addition and of carryingwere the main cause of faulty multiplications,but in one instance a complete misconceptionof the overall operation schema was noticed:in performing 38 x 4, the patient wrotedown separately the products of 8 x 4 and 3x 4 and then added them up. Errors point-ing to a severe disruption of procedurebecame more frequent with divisions.Sometimes there was a complete block whenconfronted by elementary divisions, such as 6

* 4, where he commented: "It strikes methat I ought to write 0," but actually wrotenothing. Requested to divide 450 by 3, hetook the first two figures together (45) andwrote 9 as the quotient. Having to divide 36by 41, he correctly wrote 0 at the quotient,then subtracted 36 from 41, wrote 5, lowered0 and divided 50 by 41. A common error

occurred when, having underestimated thenumber of times the divisor was contained inthe dividend, he failed to realise that theremainder was larger than the divisor andthat the operation had to be checked. Whenthe dividend was smaller than the divisor, hefrequently became confused and did notknow how to proceed.

Errors increased on more complex opera-tions. He had forgotten the rule for carryingout multiplication and division of numbersfollowed by a decimal point.He was unable to mentally calculate simple

percentages (for example, 50% of 10, or 20%of 100). When the calculation was carried outwith written numbers, he was no longer ableto recall the correct procedure: such as, com-puting 20% of 50 when he divided 50 by 20.After a number of trials, he spontaneouslyremembered the method and was able to cal-culate 70% of 200 and 17% of 3400, but helater forgot the method again and relapsedinto the error of dividing the number by thepercentage. The conversion of a fraction intoa number (such as, 1/5 = 0 20) was almostalways incorrect when calculated mentallyand produced serious difficulty in written cal-culations.

However, the concept of the square rootand of power was preserved and using themfor simple calculations were carried out cor-rectly.The patient was seen again ih November

1991 and found to be unchanged.

DiscussionThe present case adds to the understandingof acalculia in two ways: 1) It provides anexample of a disorder strictly confined to thecognitive systems for calculation, and 2) Itslesion involves anatomical structures of theleft hemisphere that have not been previouslyimplicated in the mechanisms of calculationdeficits.

At the time of testing, the neurological andneuropsychological symptoms caused by theleft anterior cerebral artery infarct had clearedalmost completely, leaving the patient freefrom language, praxis, visuoperceptual andvisuo-spatial impairments. Intellectual abili-ties were well within normal limits and nodeficits were shown by tests considered sensi-tive to frontal lobe damage. Verbal, visualand spatial memory was intact. Thus dyscal-culia was an isolated area of cognitive deficit,independent of the impairment of other men-tal abilities and demonstrated the disruptionof a specific system subserving arithmeticalprocesses. Its impairment concerned the twomajor components of the calculation system,retrieval of basic arithmetical facts and execu-tion of calculation procedures.9 However, itleft the mechanisms intact for number pro-cessing and the ability to comprehend opera-tional symbols.The difficulty in remembering arithmetical

information was minor, mainly resulting inthe lengthening of the time taken to make acorrect response or in self-corrected errors. It

306 on D

ecember 24, 2021 by guest. P

rotected by copyright.http://jnnp.bm

j.com/

J Neurol N

eurosurg Psychiatry: first published as 10.1136/jnnp.56.3.304 on 1 M

arch 1993. Dow

nloaded from

PIimary dyscalculia after a medialfrontal lesion of the left hemisphere

must be stressed that arithmetical facts arehighly automatic in a person with the educa-tional background of our patient.What was more severe and independent of

number facts impairment were the errorsattributable to a faulty retrieval of calculationprocedures. They can be classified under twoheadings, those associated with the inabilityto remember "carry" and "borrow" proce-dures, and those reflecting a more profoundmisconception of the nature of the requestedoperation. The former, which are sometimesalso observed in normal subjects, is likely tobe dependent on the attentional loaddemanded by a dual task, in which an ele-ment of the previous step of the operationmust be kept in mind while focusing on thenext one. The latter, which occurred in morecomplex operations, caused a momentaryblock in retrieving the pertinent procedureand resulted either in a state of bewildermentand inability to proceed, or in the applicationof rules inappropriate for that operation. Fornone of the operations tested, including per-centages, fractions and powers, was there evi-dence of an irreparable loss of ability, or for aconsistent pattern of errors, and his erraticperformance can be best interpreted asdepending on the faltering activation of thecalculation functional system.The lesion responsible for the symptoms

was unusual, since no previous case of dyscal-culia has been reported following damage tothe medial regions of the left frontal lobe.There is consensus in the literature that thearea crucially involved in the production ofprimary acalculia (namely, in the absence ofspatial and language deficits) is centredaround the temporo-parietal-occipital cortexon the lateral surface of the left hemisphere.'0No evidence of damage to this region wasshown by MRI. The relation that the frontallocus of lesion bore to dyscalculia can only bea matter of speculation. It is known thatinjury to the medial frontal cortex and cingu-late gyrus can produce, especially if bilateral,a state of akinesia and mutism, of which ourpatient gave clear evidence in the early stageof his disease. This was no longer apparentwhen dyscalculia was investigated. There wasno evidence of an inability to initiate mentalprocesses, even when the patient was engaged

in difficult intellectual tasks, certainly equallyor more demanding in terms of attentionalresources than the retrieval of numericalfacts. An alternative hypothesis is that the leftmedial frontal lobe plays a direct role in theretrieval of calculation procedures, but thatits autonomous contribution has escaped theattention of neuroscientists as it has neverbeen formally tested. Oral calculation is listedamong the tasks given to 10 consecutivepatients with left anterior cerebral arteryinfarct" 12, but unfortunately monitoring wasnot made of their performance. The assess-ment of computation may be difficult inpatients who show an inhibition of their abili-ty to give verbal responses, as is frequentlythe case in the early stage of a left anteriorcerebral artery infarct.

This study implies that careful investiga-tion of calculation processes may be useful inpatients with medial frontal lesion.

This research was supported by grants from CNR and MPI toDr E. De Renzi. We are grateful to Dr H Buchtel for his com-ments on an earlier version of the paper.

1 Berger H Ueber Rechenstoerungen bei Herderkrankungendes Grosshims. Arch f Psychiat U Nervenkr 1926;78:238-67.

2 Boller F, Grafman J. Acalculia: historical developmentand current significance. Brain and Cogn 1983;2:205-23.

3 Hecaen H, Angelergues R, Houilier S. Les varietes clin-iques des acalculies au cours des lesions retro-rolandiques. Approche statistique du probleme. RevNeurol 1961;105:85-103

4 McCloskey M, Caramazza A. Cognitive mechanisms innumber processing and calculation: evidence fromdyscalculia. Brain and Cogn 1985;4:171-196.

5 McCloskey M, Sokol SM, Goodman RA. Cognitiveprocesses in verbal number production: inferences fromthe performance of brain-damaged subjects. J ExpPsychol: Gen 1986;115:307-30.

6 Damasio H, Damasio A. Lesion analysis in neuropsychology.New York. Oxford University Press, 1989.

7 De Renzi E, Faglioni P, Savoiardo M, Vignolo LA. Theinfluence of aphasia and of hemispheric side of the cere-bral lesion on abstract thinking. Cortex 1966;2:399-420.

8 Warrington EK. The fractionation of arithmetical skills: asingle case study. QuartJ Exp Psychol 1982;34A:31-5 1.

9 Sokol SM, McCloskey M, Cohen NJ, Aliminosa D.Cognitive representations and processes in arithmetic:inferences fromthe performance of brain-damaged sub-jects. J Exp Psychol: Learn Mem and Cogn 1991;17:355-76.

10 Benton AL. Mathematical disability and the Gerstmannsyndrome. In: Deloche G and Seron X, eds. Mathe-matical disabilities. A cognitive neuropsychological perspec-tive. Hillsdale: L Erlbaum, 1987:111-120

11 Bogousslavsky J, Assal G, Regli F. Infarctus du territoirede l'artere cerebrale anterieure gauche. II. Troubles dulangage. Rev Neurol 1987;143:121-7.

12 Bogousslavsky J, Regli F. Anterior cerebral artery territoryinfarction in the Lausanne Stroke Registry. Clinical andetiologic patterns. Arch Neurol 1990;47:144-150.

307 on D

ecember 24, 2021 by guest. P

rotected by copyright.http://jnnp.bm

j.com/

J Neurol N

eurosurg Psychiatry: first published as 10.1136/jnnp.56.3.304 on 1 M

arch 1993. Dow

nloaded from