circular canal could cause a spontane¬ous downward drift of the eyes andcompensatory upward saccades, re¬

sulting in primary position upbeatnystagmus. A tonic imbalance in ver¬tical vestibulo-ocular signals in our

patient could have resulted from thecerebellar lesion, which involved thebrachium conjunctivum. As discussedpreviously, the lateral bias of the eyesseen in ocular lateropulsion may alsoresult from an imbalance of central

vestibular input. We believe that late¬ropulsion and primary position up¬beat nystagmus are clinical signs ofan impaired central vestibular sys¬tem.

References

1. Ranalli PJ, Sharpe JA: Syndrome of thesuperior cerebellar artery: Contralateral saccad-ic lateropulsion and ipsilateral limb ataxia. CanJ Neurol Sci 1985;12:209.

2. Fisher A, Gresty M, Chambers B, et al:Primary position upbeating nystagmus. Brain1983;106:949-964.

3. Nakada T, Remler MP: Primary positionupbeat nystagmus. J Clin Neuro Ophthalmol1981;1:185-189.

4. Kommerell G, Hoyt WF: Lateropulsion ofsaccadic eye movements: EOG studies in a

patient with Wallenberg's syndrome. Arch Neu-rol 1973;28:313-318.

5. Leigh RJ, Zee DS: The Neurology of EyeMovement. Philadelphia, FA Davis Co Publish-ers, 1983.

6. Frisen L: Lateropulsion of the eyes: A local-izing brainstem sign. J Neurol 1978;218:171-177.

7. Meyer KT, Baloh RW, Krohel GB, et al:Ocular lateropulsion: A sign of lateral medullarydisease. Arch Ophthalmol 1980;98:1614-1616.

8. Dell'Osso LF, Daroff RB, Troost BT: Nys-

tagmus and saccadic intrusions and oscillations,in Duane TD (ed): Clinical Ophthalmology. Phila-delphia, Harper & Row Publishers Inc, 1985, vol2: Neuro-Ophthalmology.

9. Baloh RW, Spooner JW: Downbeat nystag-mus: A type of central vestibular nystagmus.Neurology 1981;31:304-310.

10. Ito M, Nisimaru N, Yamamoto M: Path-ways for the vestibulo-ocular reflex excitationarising from semicircular canals of rabbits. ExpBrain Res 1976;24:257-271.

11. Yamamoto M, Shimoyama I, HighsteinSM: Vestibular nucleus neurons relaying excita-tion from the anterior canal to the oculomotornucleus. Brain Res 1978;148:31-42.

12. Highstein SM: The organization of thevestibulo-oculomotor and trochlear reflex path-ways in the rabbit. Exp Brain Res 1973;17:285\x=req-\300.

13. Ghelarducci B, Highstein SM, Ito M: Originof the preoculomotor projection through the bra-chium conjunctivum and their functional roles inthe vestibulo-ocular reflex, in Baker RG, Berthoz

A (eds): Developments in Neuroscience. Amster-dam, Elsevier Science Publishers, 1977, vol 6:Control of Gaze by Brain Stem Neurons, pp167-175.

14. Daroff R, Troost BT: Upbeat nystagmus.JAMA 1973;225:312.

15. Gilman N, Baloh RW, Tomiyasu U: Prima-ry position upbeat nystagmus. Neurology1977;27:294-298.

16. Pawl RP: Upbeat nystagmus. JAMA1973;226:565.

17. Sogg RL, Hoyt WF: Intermittent verticalnystagmus in a father and son. Arch Ophthalmol1962;68:515-517.

18. Zee DS, Friendlich AR, Robinson DA: Themechanism of downbeat nystagmus. Arch Neurol1974;30:227.

19. Kato I, Nakamura T, Watanabe J, et al:Primary position upbeat nystagmus: Localizingvalue. Arch Neurol 1985;42:819-821.

20. Daroff RB, Dell'Osso LF, Abel LA: Pursuitdefect nystagmus. Ann Neurol 1979;6:458-459.

Acalculia Following a Dominant-HemisphereSubcortical InfarctAlastair J. Corbett, MBChB, FRACP; Elizabeth A. McCusker, MBBS, FRACP; Oliver R. Davidson, BSc

\s=b\A 60-year-old, right-handed woman

experienced persistent impairment of cal-culating ability following a subcorticalinfarct involving the head of the left cau-date nucleus, the anterior superior puta-men, and the anterior limb of the internalcapsule extending superiorly into the per-iventricular white matter. Acalculia re-sulted from defects of numerical syntax,the loss of ability to manipulate mathe-matical concepts, and impaired workingmemory.

(Arch Neurol 1986;43:964-966)

Acalculia, or impaired calculatingability, has been described as a

consequence of cerebral corticallesions usually affecting the dominanthemisphere. Acalculia is generallyassociated with other neuropyscho-logical deficits, most frequently apha¬sia, spatial disorganization, and

impaired short-term memory. Weassessed a patient who had acalculiafollowing a dominant-hemispheresubeortical infarct.

REPORT OF A CASEPatient Description

A 60-year-old, right-handed woman, adepartment store executive, experiencedthe sudden onset of speech arrest thatimproved over three hours. Her familyphysician noted her to be hypertensive(blood pressure, 240/140 mm Hg), con-

Accepted for publication March 20, 1986.From the Department of Medicine, University

of Otago Medical School, Dunedin, New Zea-land.Reprints not available.

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fused, and aphasie, but with no limb weak¬ness. Two months later the patient under¬went neurologic assessment. She hadreturned to work but complained of per¬sisting impairment of memory and word-finding with particular difficulty in calcu¬lating, which was a major component ofher work. On examination she had mini¬mal right-sided facial weakness but noadditional cranial nerve deficits. Examina¬tion of the limbs demonstrated normalpower, tone, coordination, and sensation.Muscle reflexes were brisk and symmetric.The right plantar response was extensor.The patient was alert and oriented, andthere was no obvious speech disorder. Sherecalled three paired objects at threeminutes. She made some mistakes on fin¬ger naming, but there was no left-rightdisorientation, and color naming wasintact. The patient was unable to calculateserial subtraction of sevens and calculatedserial subtraction of fives with severalmistakes. She could not perform simplemultiplication and when asked to multi¬ply, added numbers by counting on herfingers. She repeated five numbers for¬ward and reversed these correctly aftertwo attempts.

A computed tomographic scan demon¬strated an infarct involving the head of theleft caudate nucleus, the superior anteriorportion of the putamen, and the anteriorextremity of the internal capsule extend¬ing superiorly into the periventricularwhite matter (Figure).The patient underwent formal neuropsy¬

chological assessment six months follow¬ing her stroke. She still complained ofdifficulty calculating, but she could other¬wise perform her job satisfactorily, and anassistant had been assigned to carry out allof her calculations.

Neuropsychological Assessment

Numbers can be written in two notationsystems: alphabetic and digital. Linguisticcomponents of acalculia were investigatedby studying the patient's ability to trans-code from alphabetic to digital notationand the reverse.1 Our patient was pre¬sented with a list of numbers in digitalform and transcoded these verbally toalphabetic form. In transcoding largernumbers the patient tended to use a term-by-term strategy, eg, 5, 201, 701 was trans-coded to "five million and two hundred andone and seven zero one." Errors made wereerrors in the syntactic structure of theserial organization of numerals. Thepatient was presented with numbers inalphabetic form verbally and then trans-coded these to digital form. Again thepatient used a term-by-term transcodingstrategy for larger numbers, eg, fortythousand, one hundred ninety-nine wascoded to 40 000 99. There was impairmentin handling the syntactic structure ofnumerical strings. Syntactic errors of thistype are often seen in association withBroca's aphasia.2

The patient's ability to comprehend thenumerical difference between multidigitnumbers was investigated by presenting aseries of multidigit numbers and request-

Computed tomographic scan shows area of decreased density involving left caudate nucleus,anterior superior putamen, and anterior limb of internal capsule extending superiorly intoperiventricular white matter.

ing that she indicate the larger of the twonumbers. An element of conflict was intro¬duced when the smaller number of the paircontained higher digits in all categoriesbelow the highest.3 The patient performedthis task without difficulty, indicating thather assessment of numerical value wasbased on the categorical structure of thenumber rather than evaluation of the com¬

ponent digits.The patient's ability to perform serial

arithmetic operations was studied. Shewas able to count to 20 and then backwardto zero without error. Three errors weremade in counting backward from 20 bythrees. She was unable to advance past 93in serial subtraction of sevens from 100.Serial subtraction requires concentration,the ability to sequence arithmetical tasks,and stability of memory.

The patient was asked to calculate thenumber of items in a continuous or discon¬tinuous series of dots. In some series thedots were divided into equal groups. Thepatient counted all of the series correctly.A multiplication strategy was employed incounting grouped items, indicating an abil¬ity to use this operation spontaneously andappropriately.Oral arithmetic was tested by giving the

patient a series of simple examples usingeach of the four basic operations. Errorswere made in each of the operations, butwere most frequent with division.Written arithmetic was tested. Addition

was well performed with few errors. Sub¬traction proved to be more difficult, witherrors occurring predominantly in borrow¬ing functions. Multiplication was per¬formed accurately when it involved simpleuse of the multiplication tables. More com¬

plex multiplication caused greater difficul¬ty with frequent errors. Importantly, therewas no evidence for spatial disorganiza¬tion, and a proper arrangement of columnswas used. Division caused the greatest

difficulty. The patient substituted otheroperations for division and could not cor¬rect her errors when prompted.Complex arithmetical functions with

less dependence on automatic processeswere tested. Serial arithmetical operationsinvolving three components, eg, 12 + 9

—6 =

...

require memorized retention ofpart of the operation. The patient wasunable to perform these serial operationswithout writing down the intermediateresult. Arithmetical problems includingthe answer but excluding the sign rule outthe possibility of automatic performance,eg, 10

...

2 = 8. The patient was unable tocomplete these problems even when shownexamples. The patient was also unable toperform calculations when the answer andsign were given but one component was

excluded, eg, 12-...

= 8.Assessment by the Boston Diagnostic

Aphasia Evaluation4 demonstrated a nor¬mal profile with no aphasie deficit. Sepa¬rate tests of oral comprehension demon¬strated slight impairment. The patientcomplained that difficulty concentratingand poor memory accounted for impairedcomprehension test results.The patient was tested with the Wech¬

sler Adult Intelligence Scale-Revised,5 andshe performed within the average rangeexpected for her age on all subsets butthree. The exceptions were Arithmetic,Similarities, and Object Assembly. Herfull-scale IQ was 82, and there was evi¬dence to suggest this was below her pre¬morbid intellectual ability. She performedwithin the normal range on the WilliamsDelayed Recall Test.6 She performed poor¬ly on the Trail Making Test,7 with apparentimpaired visual scanning skills and diffi¬culty with sequential thinking. Perfor¬mance on the Benton Visual RetentionTest-Revised Form8 was significantlyimpaired. The patient's performance whentested with the Wisconsin Card Sorting

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Test' was markedly impaired, with manyperseverative errors and an inability toachieve any categories.

COMMENTThe patient demonstrated a numer¬

ical linguistic defect with disturbanceof syntax in transcoding large num¬bers. Comprehension of the categori¬cal structure of multidigit numberswas not disturbed. She retained herability to perform simple, relativelyautomatic calculations, but there was

impairment of more complex nonau-tomatized calculations, impairedworking memory for calculations, andloss of ability to manipulate mathe¬matical concepts. The patient showedimpairment with a range of psycho¬metric tasks with impaired immediatenonverbal memory, impaired visuo¬spatial skills, and difficulty withsequential thinking. A computedtomographic scan obtained fourmonths following her stroke demon¬strated a subeortical lesion involvingthe head of the left caudate nucleus,the anterior superior putamen, andthe anterior limb of the internal cap¬sule extending superiorly into the per¬iventricular white matter (Figure). Itwas presumed but not conclusivelydemonstrated that this lesion was aninfarct in the territory of a laterallenticulostriate vessel and that therewas no additional cortical lesion.A classification of acquired disor¬

ders of calculation based on the mech¬anisms presumed responsible hasbeen proposed by Hécaen10: (1) alexiaand agraphia for digits and numbers;(2) acalculia resulting from spatialdefects; and (3) anarithmetria—acal¬culia due to inability to perform arith¬metical operations. Alexia and agra¬phia for numbers is generally associ¬ated with other aphasie deficits. Thishas been the result of either a lesionof the dominant hemisphere or bilat¬eral cerebral disease. Acalculia of thespatial type is the result of impaired

spatial organization of numbers.Associated neuropsychological distur¬bances included spatial agnosia andvisuoconstructive apraxias. The corre¬

sponding cerebral lesions involved thenondominant hemisphere or were

bihemispheric. Anarithmetria is asso¬ciated with additional neuropsycho¬logical deficits but excludes alexia andagraphia for numbers and spatial dis¬organization of numbers. In mostcases the associated cerebral lesionsinvolved the dominant hemisphere,but occasionally isolated, nondomi-nant hemisphere pathologic featureswere seen.

Our patient experienced difficultycalculating that was disproportionateto other areas of cognitive dysfunc¬tion. Calculation is a complex psycho¬logical procedure that may be dis¬turbed at many levels. Our patientdemonstrated intact ability to per¬form elementary arithmetical opera¬tions but difficulty with more complexcalculations with defective numericalsyntax, loss of ability to manipulatemathematical concepts, and impairedworking memory best classified asanarithmetria. Impaired performanceon the Trail Making Test and theWisconsin Card Sorting Test indi¬cated that defective conceptual think¬ing and working memory were notconfined to calculation. Other authorshave reported defects of memory" or

general cognitive impairment3 associ¬ated with anarithmetria.Acalculia has previously been

described as a consequence of cerebralcortical lesions. A single case of acal¬culia following a deep, left hemispher¬ic infarct involving the anterior andposterior lentiform nucleus, superiorcaudate nucleus, and the adjacentwhite matter has been reported byWhittaker et al.12 Both the describedlocation of the lesion and the resultingacalculia are similar to those in our

patient.

Animal studies have indicated theimpairment of complex behavior fol¬lowing bilateral lesion of the heads ofthe caudate nuclei." Caudate lesionsimpair performance on tasks involv¬ing spatial choice and memory anddisrupt responses to reinforcementand conditioning. Similar behavioralchanges are produced by ablation ofthe corresponding frontal corticalareas that project to the caudate. Ourpatient had marked impairment ofperformance on the Wisconsin CardSorting Test, a task generally ac¬

cepted to reflect frontal lobe function.Impairment of calculation withdefects of complex calculations, par¬ticularly those involving serial proce¬dures, but intact elementary arith¬metical operations has been describedwith frontal cortical lesions.3 Thus,our patient's lesion may have resultedin calculation disturbance by disrupt¬ing frontal cortical projections.

Other neuropsychological deficitshave been described as the result offocal lesions involving the striatum.Aphasie syndromes have been de¬scribed with circumscribed infarc¬tions of the anterior limit of the inter¬nal capsule and the adjacent striatumof the dominant hemisphere.1416 Theresulting aphasia could not be classi¬fied in terms of the classic corticalaphasie syndromes. The anatomy ofthis region and its relevance to apha¬sie syndromes has been reviewed byDamasio et al.16 The locus of the lesionin our patient does not fully overlapthat of the atypical aphasias. Thelesion in our patient extended more

superiorly to involve the periventricu¬lar white matter. The aphasia lesionsextended more inferiorly, involvingmore of the inferior part of the ante¬rior limb of the internal capsule andof the putamen. The lack of this moreinferior component may explain theabsence of persistent aphasia in our

patient.

References

1. Deloche G, Seron X: Some linguistic compo-nents of acalculia, in Rose CF (ed): Advances inNeurology. New York, Raven Press, 1984, vol 42:Progress in Aphasiology, pp 215-222.

2. Deloche G, Seron X: From three to 3: Adifferential analysis of skills in transcodingquantities between patients with Broca's andWernicke's aphasia. Brain 1982;105:719-733.

3. Luria AR: Higher Cortical Functions inMan, ed 2. New York, Basic Books Inc, Publishers,1980, pp 553-561.

4. Goodglass H, Kaplan E: The Assessment ofAphasia and Related Disorders. Philadelphia,Lea & Febiger, 1972.

5. Wechsler D: Wechsler Adult IntelligenceScale-Revised. New York, Harcourt Brace Jova-novich Publishers, 1981.

6. Williams M: The measurement of memory

in clinical practice. Br J Soc Clin Psychol1968;7:19-34.

7. Reitan RM: The relation of the Trail MakingTest to organic brain damage. J Consult ClinPsychol 1955;19:393-394.

8. Benton AL: Revised Visual Retention Test,ed 4. New York, The Psychological Corp, 1974.

9. Berg EA: A simple objective technique formeasuring flexibility in thinking. J Gen Psychol1948;39:15-22.

10. H\l=e'\caenH, Angelergues R, Houillier S: Lesvarietes cliniques des acalculies au cours deslesions retro-rolandiques: Approche statistiquedu probleme. Rev Neurol 1961;105:85-103.

11. Cohn R: Dyscalculia. Arch Neurol 1961;4:301-307.

12. Whitaker H, Habiger T, Ivers R: Acalculiafrom a lenticular-caudate infarction. Neurology

1985;35(suppl 1):61.13. Oberg RGE, Divac I: 'Cognitive' functions

of the neostriatum, in Divac I, Oberg RGE (eds):The Neostriatum. Elmsford, NY, PergamonPress Inc, 1979, pp 291-313.

14. Vignolo LA: Aphasias associated withcomputed tomography scan lesions outside Bro-ca's and Wenicke's areas, in Rose CF (ed):Advances in Neurology. New York, Raven Press,1984: Progress in Aphasiology, pp 91-98.

15. Naeser MA, Alexander MP, Helm-Esta-brooks N, et al: Aphasia with predominantlysubcortical lesion sites. Arch Neurol 1982;39:2\x=req-\14.

16. Damasio AR, Damasio H, Rizzo M, et al:Aphasia with nonhemorrhagic lesions in thebasal ganglia and internal capsule. Arch Neurol1982;39:15-20.

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