circular canal could cause a spontane¬ ous downward drift of the eyes and compensatory upward saccades, re¬ sulting in primary position upbeat nystagmus. A tonic imbalance in ver¬ tical vestibulo-ocular signals in our patient could have resulted from the cerebellar lesion, which involved the brachium conjunctivum. As discussed previously, the lateral bias of the eyes seen in ocular lateropulsion may also result from an imbalance of central vestibular input. We believe that late¬ ropulsion and primary position up¬ beat nystagmus are clinical signs of an impaired central vestibular sys¬ tem. References 1. Ranalli PJ, Sharpe JA: Syndrome of the superior cerebellar artery: Contralateral saccadic lateropulsion and ipsilateral limb ataxia. Can J Neurol Sci 1985;12:209. 2. Fisher A, Gresty M, Chambers B, et al: Primary position upbeating nystagmus. Brain 1983;106:949-964. 3. Nakada T, Remler MP: Primary position upbeat nystagmus. J Clin Neuro Ophthalmol 1981;1:185-189. 4. Kommerell G, Hoyt WF: Lateropulsion of saccadic eye movements: EOG studies in a patient with Wallenberg's syndrome. Arch Neurol 1973;28:313-318. 5. Leigh RJ, Zee DS: The Neurology of Eye Movement. Philadelphia, FA Davis Co Publishers, 1983. 6. Frisen L: Lateropulsion of the eyes: A localizing brainstem sign. J Neurol 1978;218:171-177. 7. Meyer KT, Baloh RW, Krohel GB, et al: Ocular lateropulsion: A sign of lateral medullary disease. 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. Philadelphia, Harper & Row Publishers Inc, 1985, vol 2: Neuro-Ophthalmology. 9. Baloh RW, Spooner JW: Downbeat nystagmus: 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 excitation arising from semicircular canals of rabbits. Exp Brain Res 1976;24:257-271. 11. Yamamoto M, Shimoyama I, Highstein SM: Vestibular nucleus neurons relaying excita- tion from the anterior canal to the oculomotor nucleus. Brain Res 1978;148:31-42. 12. Highstein SM: The organization of the vestibulo-oculomotor and trochlear reflex pathways in the rabbit. Exp Brain Res 1973;17:285\x=req-\ 300. 13. Ghelarducci B, Highstein SM, Ito M: Origin of the preoculomotor projection through the brachium conjunctivum and their functional roles in the vestibulo-ocular reflex, in Baker RG, Berthoz A (eds): Developments in Neuroscience. Amsterdam, Elsevier Science Publishers, 1977, vol 6: Control of Gaze by Brain Stem Neurons, pp 167-175. 14. Daroff R, Troost BT: Upbeat nystagmus. JAMA 1973;225:312. 15. Gilman N, Baloh RW, Tomiyasu U: Primary position upbeat nystagmus. Neurology 1977;27:294-298. 16. Pawl RP: Upbeat nystagmus. JAMA 1973;226:565. 17. Sogg RL, Hoyt WF: Intermittent vertical nystagmus in a father and son. Arch Ophthalmol 1962;68:515-517. 18. Zee DS, Friendlich AR, Robinson DA: The mechanism of downbeat nystagmus. Arch Neurol 1974;30:227. 19. Kato I, Nakamura T, Watanabe J, et al: Primary position upbeat nystagmus: Localizing value. Arch Neurol 1985;42:819-821. 20. Daroff RB, Dell'Osso LF, Abel LA: Pursuit defect nystagmus. Ann Neurol 1979;6:458-459. Acalculia Following a Dominant-Hemisphere Subcortical Infarct Alastair 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 calculating ability following a subcortical infarct involving the head of the left caudate nucleus, the anterior superior puta- men, and the anterior limb of the internal capsule extending superiorly into the periventricular white matter. Acalculia resulted from defects of numerical syntax, the loss of ability to manipulate mathematical concepts, and impaired working memory. (Arch Neurol 1986;43:964-966) Acalculia, or impaired calculating ability, has been described as a of cerebral cortical lesions usually affecting the dominant hemisphere. Acalculia is generally associated with other neuropyschoconsequence logical deficits, most frequently apha¬ sia, spatial disorganization, and Accepted for publication March 20, 1986. From the Department of Medicine, University of Otago Medical School, Dunedin, New Zealand. Reprints not available. Downloaded From: http://archneur.jamanetwork.com/ by a New York University User on 05/29/2015 impaired short-term memory. We assessed a patient who had acalculia following a dominant-hemisphere subeortical infarct. REPORT OF A CASE Patient Description A 60-year-old, right-handed woman, a department store executive, experienced the sudden onset of speech arrest that improved over three hours. Her family physician noted her to be hypertensive (blood pressure, 240/140 mm Hg), con- fused, and aphasie, but with no limb weak¬ ness. Two months later the patient under¬ went neurologic assessment. She had returned to work but complained of per¬ sisting impairment of memory and word- finding with particular difficulty in calcu¬ lating, which was a major component of her work. On examination she had mini¬ mal right-sided facial weakness but no additional cranial nerve deficits. Examina¬ tion of the limbs demonstrated normal power, tone, coordination, and sensation. Muscle reflexes were brisk and symmetric. The right plantar response was extensor. The patient was alert and oriented, and there was no obvious speech disorder. She recalled three paired objects at three minutes. She made some mistakes on fin¬ ger naming, but there was no left-right disorientation, and color naming was intact. The patient was unable to calculate serial subtraction of sevens and calculated serial subtraction of fives with several mistakes. She could not perform simple multiplication and when asked to multi¬ ply, added numbers by counting on her fingers. She repeated five numbers for¬ ward and reversed these correctly after Computed tomographic scan shows area of decreased density involving left caudate nucleus, anterior superior putamen, and anterior limb of internal capsule extending superiorly into periventricular white matter. two attempts. A computed tomographic scan demon¬ strated an infarct involving the head of the left caudate nucleus, the superior anterior portion of the putamen, and the anterior extremity of the internal capsule extend¬ ing superiorly into the periventricular white matter (Figure). The patient underwent formal neuropsy¬ chological assessment six months follow¬ ing her stroke. She still complained of difficulty calculating, but she could other¬ wise perform her job satisfactorily, and an assistant had been assigned to carry out all of her calculations. Neuropsychological Assessment Numbers can be written in two notation systems: alphabetic and digital. Linguistic components of acalculia were investigated by studying the patient's ability to transcode from alphabetic to digital notation and the reverse.1 Our patient was pre¬ sented with a list of numbers in digital form and transcoded these verbally to alphabetic form. In transcoding larger numbers the patient tended to use a termby-term strategy, eg, 5, 201, 701 was trans- coded to "five million and two hundred and one and seven zero one." Errors made were errors in the syntactic structure of the serial organization of numerals. The patient was presented with numbers in alphabetic form verbally and then transcoded these to digital form. Again the patient used a term-by-term transcoding strategy for larger numbers, eg, forty thousand, one hundred ninety-nine was coded to 40 000 99. There was impairment in handling the syntactic structure of numerical strings. Syntactic errors of this type are often seen in association with Broca's aphasia.2 The patient's ability to comprehend the numerical difference between multidigit numbers was investigated by presenting a series of multidigit numbers and request- ing that she indicate the larger of the two numbers. An element of conflict was intro¬ duced when the smaller number of the pair contained higher digits in all categories below the highest.3 The patient performed this task without difficulty, indicating that her assessment of numerical value was based on the categorical structure of the number rather than evaluation of the com¬ ponent digits. The patient's ability to perform serial arithmetic operations was studied. She was able to count to 20 and then backward to zero without error. Three errors were made in counting backward from 20 by threes. She was unable to advance past 93 in 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 the number of items in a continuous or discon¬ tinuous series of dots. In some series the dots were divided into equal groups. The patient counted all of the series correctly. A multiplication strategy was employed in counting grouped items, indicating an abil¬ ity to use this operation spontaneously and appropriately. Oral arithmetic was tested by giving the patient a series of simple examples using each of the four basic operations. Errors were made in each of the operations, but were most frequent with division. Written arithmetic was tested. Addition performed with few errors. Sub¬ traction proved to be more difficult, with errors occurring predominantly in borrow¬ ing functions. Multiplication was per¬ formed accurately when it involved simple use of the multiplication tables. More com¬ plex multiplication caused greater difficul¬ ty with frequent errors. Importantly, there was no evidence for spatial disorganiza¬ tion, and a proper arrangement of columns was used. Division caused the greatest was well Downloaded From: http://archneur.jamanetwork.com/ by a New York University User on 05/29/2015 difficulty. The patient substituted other operations for division and could not cor¬ rect her errors when prompted. Complex arithmetical functions with less dependence on automatic processes were tested. Serial arithmetical operations involving three components, eg, 12 + 9 6 require memorized retention of part of the operation. The patient was unable to perform these serial operations without writing down the intermediate result. Arithmetical problems including the answer but excluding the sign rule out the possibility of automatic performance, 2 8. The patient was unable to eg, 10 complete these problems even when shown examples. The patient was also unable to perform calculations when the answer and sign were given but one component was 8. excluded, eg, 12 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 patient complained that difficulty concentrating — = ... = ... = - ... and poor memory accounted for impaired comprehension test results. The patient was tested with the Wech¬ sler Adult Intelligence Scale-Revised,5 and she performed within the average range expected for her age on all subsets but three. The exceptions were Arithmetic, Similarities, and Object Assembly. Her full-scale IQ was 82, and there was evi¬ dence to suggest this was below her pre¬ morbid intellectual ability. She performed within the normal range on the Williams Delayed Recall Test.6 She performed poor¬ ly on the Trail Making Test,7 with apparent impaired visual scanning skills and diffi¬ culty with sequential thinking. Perfor¬ mance on the Benton Visual Retention Test-Revised Form8 was significantly impaired. The patient's performance when tested with the Wisconsin Card Sorting Test' was markedly impaired, with many perseverative errors and an inability to achieve any categories. COMMENT The patient demonstrated a numer¬ ical linguistic defect with disturbance of syntax in transcoding large num¬ bers. Comprehension of the categori¬ cal structure of multidigit numbers was not disturbed. She retained her ability to perform simple, relatively automatic calculations, but there was impairment of more complex nonautomatized calculations, impaired working memory for calculations, and loss of ability to manipulate mathe¬ matical concepts. The patient showed impairment with a range of psycho¬ metric tasks with impaired immediate nonverbal memory, impaired visuo¬ spatial skills, and difficulty with sequential thinking. A computed tomographic scan obtained four months following her stroke demon¬ strated a subeortical lesion involving the head of the left caudate nucleus, the anterior superior putamen, and the anterior limb of the internal cap¬ sule extending superiorly into the per¬ iventricular white matter (Figure). It was presumed but not conclusively demonstrated that this lesion was an infarct in the territory of a lateral lenticulostriate vessel and that there was no additional cortical lesion. A classification of acquired disor¬ ders of calculation based on the mech¬ anisms presumed responsible has been proposed by Hécaen10: (1) alexia and agraphia for digits and numbers; (2) acalculia resulting from spatial defects; 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. This has been the result of either a lesion of the dominant hemisphere or bilat¬ eral cerebral disease. Acalculia of the spatial type is the result of impaired spatial organization of numbers. Associated neuropsychological distur¬ bances included spatial agnosia and visuoconstructive apraxias. The corre¬ sponding cerebral lesions involved the nondominant hemisphere or were bihemispheric. Anarithmetria is asso¬ ciated with additional neuropsycho¬ logical deficits but excludes alexia and agraphia for numbers and spatial dis¬ organization of numbers. In most cases the associated cerebral lesions involved the dominant hemisphere, but occasionally isolated, nondominant hemisphere pathologic features were seen. Our patient experienced difficulty calculating that was disproportionate to other areas of cognitive dysfunc¬ tion. Calculation is a complex psycho¬ logical procedure that may be dis¬ turbed at many levels. Our patient demonstrated intact ability to per¬ form elementary arithmetical opera¬ tions but difficulty with more complex calculations with defective numerical syntax, loss of ability to manipulate mathematical concepts, and impaired working memory best classified as anarithmetria. Impaired performance on the Trail Making Test and the Wisconsin Card Sorting Test indi¬ cated that defective conceptual think¬ ing and working memory were not confined to calculation. Other authors have reported defects of memory" or general cognitive impairment3 associ¬ ated with anarithmetria. Acalculia has previously been described as a consequence of cerebral cortical lesions. A single case of acal¬ culia following a deep, left hemispher¬ ic infarct involving the anterior and posterior lentiform nucleus, superior caudate nucleus, and the adjacent white matter has been reported by Whittaker et al.12 Both the described location of the lesion and the resulting acalculia are similar to those in our Animal studies have indicated the impairment of complex behavior fol¬ lowing bilateral lesion of the heads of the caudate nuclei." Caudate lesions impair performance on tasks involv¬ ing spatial choice and memory and disrupt responses to reinforcement and conditioning. Similar behavioral changes are produced by ablation of the corresponding frontal cortical areas that project to the caudate. Our patient had marked impairment of performance on the Wisconsin Card Sorting Test, a task generally ac¬ cepted to reflect frontal lobe function. Impairment of calculation with defects of complex calculations, par¬ ticularly those involving serial proce¬ dures, but intact elementary arith¬ metical operations has been described with frontal cortical lesions.3 Thus, our patient's lesion may have resulted in calculation disturbance by disrupt¬ ing frontal cortical projections. Other neuropsychological deficits have been described as the result of focal 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 striatum of the dominant hemisphere.1416 The resulting aphasia could not be classi¬ fied in terms of the classic cortical aphasie syndromes. The anatomy of this region and its relevance to apha¬ sie syndromes has been reviewed by Damasio et al.16 The locus of the lesion in our patient does not fully overlap that of the atypical aphasias. The lesion in our patient extended more superiorly to involve the periventricu¬ lar white matter. The aphasia lesions extended more inferiorly, involving more of the inferior part of the ante¬ rior limb of the internal capsule and of the putamen. The lack of this more inferior component may explain the absence of persistent aphasia in our patient. patient. References 1. Deloche G, Seron X: Some linguistic compo- nents of acalculia, in Rose CF (ed): Advances in Neurology. New York, Raven Press, 1984, vol 42: Progress in Aphasiology, pp 215-222. 2. Deloche G, Seron X: From three to 3: A differential analysis of skills in transcoding quantities between patients with Broca's and Wernicke's aphasia. Brain 1982;105:719-733. 3. Luria AR: Higher Cortical Functions in Man, ed 2. New York, Basic Books Inc, Publishers, 1980, pp 553-561. 4. Goodglass H, Kaplan E: The Assessment of Aphasia and Related Disorders. Philadelphia, Lea & Febiger, 1972. 5. Wechsler D: Wechsler Adult Intelligence Scale-Revised. New York, Harcourt Brace Jovanovich Publishers, 1981. 6. Williams M: The measurement of memory in clinical practice. Br J Soc Clin Psychol 1968;7:19-34. 7. Reitan RM: The relation of the Trail Making Test to organic brain damage. J Consult Clin Psychol 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 for measuring flexibility in thinking. J Gen Psychol 1948;39:15-22. 10. H\l=e'\caenH, Angelergues R, Houillier S: Les varietes cliniques des acalculies au cours des lesions retro-rolandiques: Approche statistique du probleme. Rev Neurol 1961;105:85-103. 11. Cohn R: Dyscalculia. Arch Neurol 1961; 4:301-307. 12. Whitaker H, Habiger T, Ivers R: Acalculia from a lenticular-caudate infarction. Neurology Downloaded From: http://archneur.jamanetwork.com/ by a New York University User on 05/29/2015 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, Pergamon Press Inc, 1979, pp 291-313. 14. Vignolo LA: Aphasias associated with computed tomography scan lesions outside Broca'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-Estabrooks N, et al: Aphasia with predominantly subcortical lesion sites. Arch Neurol 1982;39:2\x=req-\ 14. 16. Damasio AR, Damasio H, Rizzo M, et al: Aphasia with nonhemorrhagic lesions in the basal ganglia and internal capsule. Arch Neurol 1982;39:15-20.