3'ournal ofNeurology, Neurosurgery, and Psychiatry 1995;58:629-632

SHORT REPORT

Agraphia and acalculia after a left prefrontal(F1, F2) infarction

Hideo Tohgi, Kou Saitoh, Satoshi Takahashi, Hiroaki Takahashi, Kimiaki Utsugisawa,Hisashi Yonezawa, Kentaro Hatano, Toshiaki Sasaki

AbstractA patient presented with agraphia andacalculia associated with a left frontal(Fl, F2) infarction. He made mainlyphonological but also lexical errors inwriting (syllabograms), but his ability towrite kanji (morphograms) was relativelypreserved. Although he could add andsubtract numbers, he could neither mul-tiply nor divide them because of a diffi-culty in retrieving the multiplicationtables and calculation procedures.Positron emission tomography showeddecreased cerebral blood flow andmetabolism limited to the infarct site.These findings suggest that agraphia andacalculia may occur associated with a leftprefrontal lesion, and that the retrievalof arithmetic processes is modality spe-cific.

(7 Neurol Neurosurg Psychiatry 1995;58:629-632)

Keywords: agraphia; acalculia; prefrontal cortex

Department ofNeurology, IwateMedical University,Morioka, JapanH TohgiK SaitohS TakahashiH TakahashiK UtsugisawaH YonezawaNishina MemorWialCyclotron Center(Japan RadioisotopeAssociation) andCyclotron ResearchCenter, Iwate MedicalUniversity, Morioka,JapanK HatanoT SasakiCorrespondence to:Dr Hideo Tohgi,Department of Neurology,Iwate Medical University,19-1, Uchimaru, Morioka,020 Japan.Received 2 August 1994and in revised form17 October 1994.Accepted 27 October 1994

Pure agraphia was first ascribed to lesions inthe premotor cortex (Brodmann's area 6) byExner in 1881, and this view was supportedby early researchers.' 2 Many later studies,however, reported agraphia associated withparietal lesions,37 implicating the angulargyrus as a graphic centre,89 or to interruptionof the transfer of writing information betweenthe parietal and frontal cortices.10 Morerecently there have again been reports ofsome patients with pure agraphia due tofrontal lesions. 11-14 An isolated acalculia(anarithmia) has been also ascribed to a

parieto-occipital lesion in most cases,'5-"7 butto a frontal lesion in one patient. 18 Somepatients with agraphia or acalculia showeddissociations between different orthographic'419-21 or arithmetical operations,'6 22-24 suggest-ing domain specificity of individual processes

in the writing and calculation system. Wedescribe a patient with pure agraphia andacalculia associated with a left frontal lobe(Fl, F2) infarction.

Case reportThe patient, a 59 year old, right handed manhad had 11 years of formal education and had

been working in a construction company. Hisjob was mainly to procure building materials.For six years before admission he had dia-betes and hypertension, which were beingtreated but he had been in normal health.Two days before admission, when he wastalking with a carpenter, he suddenly becameunable to respond with even a single word.On admission, he was alert and well ori-

ented for both time and space. Neuro-logically, he had a mild right hemiparesis anda mild stocking type sensory disturbance dueto diabetic neuropathy. Computed tomogra-phy and MRI showed a haemorrhagic infarc-tion in the left frontal lobe; the high intensityarea on T2 weighted MRI involved mainlythe middle frontal gyrus, the upper part of theinferior frontal gyrus, and part of the precen-tral gyrus (figure, A, B). In other areas, only afew lacunes were found. Brain PET studiesshowed a severe (- 70%) reduction inregional cerebral blood flow (CBF) and meta-bolic rate of oxygen (CMRo2) in the left pre-frontal area (figure, C). CBF and CMRo2were some 20% less than controls in thesupramargical and angular gyri, and thereductions were symmetric (figure, C).

LANGUAGEThe Japanese writing system consists of kanaand kanji. Kana are syllabograms represent-ing vowels (a, i, u, e, o) or combinations ofconsonants (k, s, t, n, h, m, y, r, w) with vow-els (ka, ki, etc) and most kana are ortho-graphically regular. Kanji are morphograms,or ideographs, developed from Chinese char-acters, and are read using the originalChinese sound or the Japanese sound-forinstance, a kanji meaning "east" is read as[tou] (original sound) or as [higashi](Japanese sound) depending on the context.All Japanese sentences can be written withkana only, but are usually written with bothkanji (for nouns and roots of verbs, adjec-tives, and adverbs) and kana (for inflexions,conjunctions, and propositions).A week after onset, his auditory and read-

ing comprehension of words and sentenceswere normal (28/30, 93% for each), but hisability to carry out oral and written com-mands (such as to place a coin and a foun-tainpen on a handkerchief) was severelyimpaired (3/19, 30% for each). He could cor-rectly choose a kana that corresponded to a

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(A) T2 weighted MRI of horizontal planes (TR = 2500, TE = 110) at level of corpus callosum; (B) at level of centrum semiovale; the infarct areaincludes mainly Brodmann's areas 6 and 8, and a posterior part of area 9, but spares area 44; (C) PET images of cerebral blood flow (CBF), andcerebral metabolic rate of oxygen (CMRo,) in the horizontal planes 60 and 70 mm above and parallel to the orbitofrontal (om) line (8 weeks after onsetusing Headtome IV, Shimadzu, _Japan, with the full width at halfmaximum of 4-5 mm). The CBF and CMRo, were determined using C'502 inhalationmethods and 1502 respectively. The right side of the head is on the left in allfigures. The CBF and CMRo2 are profoundly decreased in the left prefrontalareas (arrowheads). Quantitative data are as follows (mlllOO mllmin): prefrontal area, CBF 33-8 and CMRo2 2-42 on the right, and CBF 12 2 andCMRo2 0-79 on the left; supramargznal gyrus, CBF 33-6 and CMRo2 2-51 on the right, and CBF 32-8 and 2-42 on the left; angular gyrus, CBF 29-8and CMRo2 2-45 on the right, and CBF 31 7 and CMRo2 2 58 on the left; and control values, CBFG 40 and CMRo2 - 3 0.

phoneme pronounced by the examiner(20/20, 100%), could name objects (18/20,90%), and could repeat words orally thatwere spoken by the examiner (10/10, 100%).He could describe what a person was doingon single action pictures (7/10, 70%), butcould not narrate a story for composite pic-tures. He could read aloud and comprehendperfectly single kana words written in kanjiand kana and sentences composed of bothkana and kanji (25/25, 100% for each). If hewas asked to say as many words as possible(word naming), he said only two words (con-trol > 12). His writing ability was severelyimpaired: the correct responses were far lessfrequent for spontaneous writing (1/25, 4%)than for dictation (7/25, 28%; x2 = 5-4,p < 0 025).

His linguistic abilities gradually recoveredafter admission. Seven weeks after onset, hemade almost no errors in speaking, listening,and reading, but made many errors in writ-ing. His writing errors for kana (24/62 words,39%) were significantly more frequent thanfor kanji (4/65 words, 6%) (P < 0 001). Hisoral responses to 60 pictures of the Bostonnaming test (40-55 for the average Japanese)were correct for 45 pictures (75%), but hisgraphic responses were correct for 31 pictures(52%)-that is, he made errors in writing in14 out of 45 words (31 %) that he couldexpress orally. His writing errors for kana

included (table) (a) omission of phoneticmarks (two dots on the right upper corner ofa kana) to convert voiceless consonants tovoiced ones (for example, h to b, k to g, s toz, and t to d), or of those to convert h to avoiceless bilabial sound p (a small circle onthe right upper corner of a kana) (60%); (b)difficulty in writing kana that are used todenote double vowels, or to prolong theprecedent kana's sound (kya, kyo, kyo, orhou, kou) (14%); (c) confusion with a graphi-cally similar kana (4%); (d) confusion withphonetically similar kana (2%); (e) confusionwith orthographically irregular kana (8%);and U) failure to complete a word (12%). Healso made similar errors in writing non-words. Although Japanese kana are in mostcases orthographically regular, there are a fewexceptions: the subject of a sentence is indi-cated by a kana postposition "ha" which ispronounced as [wa]; the object of a sentenceis indicated by a postposition written by akana used for "wo" in ancient times which inmodern Japanese is pronounced simply as"o". He almost always wrote kana "wa"instead of "ha" as the postposition for thesubject, and kana [o] instead of "wo" for theobject, which was inconsistent with his 11year educational history. He could correctlycopy words both in kanji and kana. The kanjicharacter is composed of a radical that isrelated to its meaning (semantic component)

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Agraphia and acalculia after a left prefrontal (Fl, F2) infarction

Examples of writing errors of the patient for kana (footnote 1 to 6) and kanji (footnote 7 and 8)

Types of er-r-ot-s Cor-rect Japaniese word Patient's writing English meaning

I Ak-t (mi/zuI) br (mi/su) Water1 + 6 A&s (eln/pi/tsu) i.Ax-_ (e/nb/tsu) Pencil2 Cf 1, (bo/u/shi) (f lU (bo/shi) Hat

[bo:shi]2 4 A < (sa/n/ki/ya/ku) AJbj < (sa/n/ka/ku) Tripod

[sankyaku]3 A, (me/n) ak (nu/n) Mask4 UjL 531 (bi/yo/u/bu) AJ -) . (_2I/yo/u/bu) Screen

[byo:bu]4+6 I (ya/ma) lft(yl/-) Hill5 VLW (watakushi wa) fLA2 (watakushi wa) I am5 fIA (watakushi o) VL4 (watakushi o) To me

2 + 3 + 6 C- tAAk7& j (ho/u/re/n/so/u) Uhak j (ho/ne/n/-/u) Spinach[ho:renso:]

I + 2 + 6 Ue1 L (ji/do/u/shilya) LC (ji/to/...) AutomobileUido:shya]

7 {ff (ko/do/mo) T Child8 41 (tsu/ku/e) j$ff Desk

Pronunciations for individual kana are shown in parentheses, and pronunciations for doublevowels in square brackets.1 = Omission of a mark (double dots at the right upper corner of a kana) to convert k to g, s toz, t to d, and h to b, or omission of a mark (a small circle at the right upper corner of a kana) toconvert h to p, or omission of kana denoting pa, pi, pu, pe or po; 2 = difficulty in writing kanathat are used to denote a double vowel, or to prolong a precedent kana's sound; 3 = confusionwith a graphically similar kana; 4 = confusion with a kana representing similar sound; 5 = errorsin orthographically irregular kana; 6 = failure to complete a word; 7 = errors in writing the radi-cal (left half) of kanji; 8 = errors in writing the non-radical portion (right half) of kanji.

and a non-radical portion that may provide aclue as to its Chinese way of reading (pho-netic component). The patient's errors inwriting kanji were in either the radical or non-radical portions (table).

CALCULATIONA week after onset, he could only performadditions of one digit numbers not includingcarrying (for example, 3 + 2 = 5), but couldnot add numbers requiring carrying processes(for example, 7 + 5 = 7 instead of 12), orsubtract one digit numbers. Multiplicationand division were totally impossible becausehe could not remember the multiplicationtables. He could, however, indicate which ofthe paired two numbers was greater, andwrite numbers corresponding to the numbersspoken, suggesting that he could read, under-stand, and write digits.

Seven weeks after onset, he became able toadd and subtract up to three digit numberswith carrying and borrowing. He sometimessucceeded in multiplying or dividing one digitnumbers, but still often made errors (forexample, 4 x 6 = 48 instead of 24, or 9 + 3= 9 instead of 3). He could not multiply ordivide two digit numbers, because of diffi-culty in completely remembering the multi-plication tables, and an inability to retrievecalculation procedures (for example, 18 x 8- 74 instead of 144).

Eight weeks after the onset, his Wechsleradult intelligence score (WAIS) was 71 forthe verbal tests and 89 for the performancetests.

DiscussionThe main findings are the rare associationsbetween pure agraphia and acalculia with aleft frontal lesion and the patterns of ortho-graphic and arithmetic errors.

The writing is generated by semantic orphonological inputs to orthography in the lin-guistic processes, and then is processedthrough an orthographic buffer, physical let-ter code, graphic motor pattern, and graphiccode in the peripheral aspects.2' Our patient'sability to select correct kana and kanji from avisual array indicates an intact physical lettercode. His ability to write well formed kanaand kanji, although with some confusions formorphologically or phonetically similar kana,suggests that his lexical and non-lexicalphonology, orthography, and stroke motorprogrammes (graphic motor pattern) wererelatively intact. The main feature of phono-logical agraphia as contrasted with lexicalagraphia in Indo-European languages is thedisproportionate failure in writing non-words,probably because each word (for example,water) is recognised as if it were an ideogram(whole word reading) rather than a simplecombination (w-a-t-e-r) of alphabetical let-ters. This is not usually the case in Japanesebecause kanji are ideograms and becausethere are no spaces between words in kanawriting (like writing "iamalondoner." insteadof "I am a Londoner." in English). Althoughour patient showed no dissociation betweenthe writings of real words and non-words, therelative preservation of writing kanji com-pared with kana and the most frequent errorsin using phonetic marks to convert pronunci-ations of consonants suggest that impair-ments of phoneme-grapheme conversion maybe the main cause of his agraphia. The failureto construct double vowels by combiningkana that are originally pronounced differ-ently (for example, kyou (today) from ki-yo-u) may apparently resemble those in surfacedysgraphia in Indo-European languages inwhich patients write phonetically correct butlexically incorrect words because of animpairment of the lexical route.'920 This view,however, cannot be applied to the findings inour patient's errors in Japanese. In French,for example, one cannot, like in kanji writing,write "eau" (/o/; water) without knowing itsmeaning, and the sound IoI is phoneticallyambiguous because it may be written in sev-eral different ways (o, au, aux, etc). By con-trast, the Japanese phoneme-graphemesystem is not ambiguous because one canwrite "kyou" using kana "ki-yo-u" withoutknowing its meaning, and there is no alterna-tive way of writing the same sound. By con-trast, our patient's errors in writingorthographically irregular kana that are usedas postpositions for subjects and objects ofsentences indicate that the patient could notcorrectly write different kana for the sound /oIand /wa/ depending on its syntactic signifi-cance. In addition, our patient's more severeimpairments of spontaneous writing than ofwriting to dictation, similar to the discrep-ancy between impaired spontaneous speechand preserved repetition and comprehensionin transcortical motor aphasia, suggest thathis lexical and semantic routes may also bedisturbed.

Agraphia associated with a left frontal

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lesion is rare: one patient described byGordnier' could not write or correctly form asingle letter, and those described by Aimardet all and Hodges"3 could write letters andwords correctly but extremely slowly andlaboriously. Agraphia in these patients mayprobably be due to kinaesthetic writing disor-ders. The patient reported by Rapcsaket al14could spell non-words and regular words bet-ter than irregular words, with most of hisspelling errors being phonologically correct,and was diagnosed as having lexical agraphia.In our patient phonological impairment wasgreater than lexical impairment. The neu-ropsychiatric characteristics of frontalagraphias seem, therefore, to be differentdepending on the cortical areas involved.The preserved ability to write numbers

despite the disorders in writing words in ourpatient is similar to the findings in the patient(with a left premotor lesion) reported byAnderson et al,12 indicating the domain speci-ficity for cognitive representations. Thepatient's failures in the processes of carryingand borrowing and in remembering the mul-tiplication tables in the early period despitehis well preserved aspects of numbers is con-sistent with isolated acalculia, not with asym-bolic (aphasic), or visuospatial acalculia.2 Inone of the current models of arithmetic pro-cessing,25 the calculation system consists of(a) comprehension of operation signs orwords, (b) retrieval of arithmetic facts, and (c)execution of calculation procedures, and theretrieval of arithmetic facts may involvemodality specific processes.24 The dissocia-tion between addition and subtraction andmultiplication and division and between rela-tively retained knowledge of the multiplica-tion tables and the inability to use them seenin the later stage are similar to the findings inthe patient reported by Benson and Weir.'5 Inthe patient with dyscalculia reported byLuchelli and Renzi after a left medial frontallesion simple calculations with square rootsand powers were preserved.'8

Although acalculia is most often associatedwith aphasia, a few studies have linked iso-lated acalculia with a left parieto-occipitallesion.'5 17 A regional cerebral blood flowstudy in normal volunteers, however, showedthat when the subject was attending to silentarithmetical mental activities there was a con-sistent activation of the anterior intermediateprefrontal cortex and the middle superior pre-frontal cortex, in addition to the supramar-ginal and angular gyri of both hemispheres.26The results from our patient suggest that thedomains of arithmetic knowledge and ofgraphemes may be located close together, butagraphia without acalculia may occur in rareinstances as in the patient reported byAnderson et al.'2

The present case illustrates that furthercareful studies on patients with frontal lesionsmay provide opportunities to reveal the func-tion of the frontal lobe in writing and calcula-tion.

We thank Ms Hiroko Ishikawa for her help in the neuropsy-chological testing, Miss Miharu Sawame for her secretarialassistance, and Dr Paul Langman for reviewing the manu-script.

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