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Acalculia following a dominant-hemisphere subcortical infarct.

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 putamen, 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.

Aphasia↗

A specific deficit for numbers in a case of dense acalculia.

In this study we investigated the acalculic condition of a patient, C.G., with the classical signs of Gerstmann's Syndrome: finger agnosia; right-left disorientation; a profound agraphia (but with an equally profound alexia) and a remarkably dense acalculia. Using a series of number processing and number knowledge tasks, a selective impairment for numbers was demonstrated. Within the category of numbers C.G. showed a largely preserved ability to deal with numbers below 4, in all tasks and in all modalities, while she was totally unable to deal with numbers above 4. The consistency of responses and the ineffectiveness of cueing indicated that numbers above 4 were lost, rather than hard to access. Further testing showed that this impairment did not result from a more general semantic memory problem, a difficulty in understanding quantities or a deficit in reasoning abilities thought to underlie the concept of numbers. Difficulty with some other ordinal structures was also present, but appeared unrelated to those affecting numbers.

Female↗

Progressive agraphia, acalculia, and anomia: a single case report.

A case of a 50-year-old, right-handed female, mono-lingual native Spanish-speaker with a university-level education and cognitive changes is reported. Over approximately 2 years, she presented with a progressive deterioration of writing abilities associated with acalculia and anomia. An MRI disclosed a left parietal temporal atrophy. Two years later, further significant cognitive decline consistent with a dementia of the Alzheimer's type was observed. Amnesia, executive dysfunction, and ideomotor apraxia were found. Writing was severely impaired, and some difficulties in reading were observed. Copying abilities, however, were relatively well preserved, and the patient could drive and go to different city locations without significant spatial orientation difficulties. A second MRI approximately 2 years later showed that brain atrophy had progressed significantly. Spontaneous writing and writing to dictation were impossible. The ability to read words was preserved, but the ability to read pseudowords was lost. Changes in calligraphy were noted. This case clearly illustrates the progression of focal cognitive defects over time and the spread of abnormalities to other domains.

Agraphia↗

Cortical areas differentially involved in multiplication and subtraction: a functional magnetic resonance imaging study and correlation with a case of selective acalculia.

A patient with an intracranial hemorrhage showed differential impairment among arithmetic types (impaired in multiplication but not in subtraction). A functional magnetic resonance imaging (fMRI) experiment using normal volunteers also revealed a differential activation between the two arithmetic types. The fMRI result could account for the selective acalculia of the patient in that the lesion shown by structural MRI included the region with multiplication-higher activation and spared subtraction-higher regions. These findings suggest that the cognitive mechanism and neural substrates differ among the simple arithmetic operations.

Adult↗

["Progressive acalculia": a variety of focal degenerative atrophy affecting number processing].

A 72-year-old man experienced increasing difficulties in calculating and processing numbers. He made many syntactic errors when he read and wrote numbers, both in arabic and number-word forms. Transcoding between arabic numerals and number-words was severely impaired. His calculation abilities were grossly impaired. He could not perform even simple multiplications, but additions and subtractions were preserved. He was unable to recite multiplication tables or the alphabet. In contrast, numerosity judgment, magnitude comparisons,and semantic evaluation of numbers were intact. The patient's deficit could be summarized as an Impairment in all tasks involving numbers in a verbal format, corresponding to the so-called "verbal anarithmetia'." It was noteworthy that verification of operations, including multiplications, was accurately performed. For example, the patient could not solve a multiplication like 8 x 9, but could estimate that 9 x 2=1 1 was closer to the exact result than 9 X 2=17, or could state that 8 x 2=16 was exact even though, at the same time, he expressed verbally the terms of the corresponding addition "eight plus two is ten." Other cognitive deficits were detected by neuropsychological tests which demonstrated mainly anomic aphasia, dysorthographic agraphia without alexia, impairment of short term and episodic memory, digital agnosia. However, the patient could not be considered to have demon-eti due to preserved self-sufficiency, except for tasks requiring calculation abilities. During the two years of follow-up, the impairment in processing numbers and calculation remained predominant over other deficits. Cerebral MRI showed an atrophy of the left temporal and parietal lobes, and SPECT study showed a reduction of regional cerebral blood flow of the left hemisphere. This original clinical presentation of a cerebral degenerative disease could be described as "primary progressive acalculia" whatever the underlying primary pathological process.

Aged↗

[Acalculia].

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Cognition Disorders↗

Two mental calculation systems: a case study of severe acalculia with preserved approximation.

We report the case of an aphasic and acalculic patient with selective preservation of approximation abilities. The patient's deficit was so severe that he judged 2 + 2 = 5 to be correct, illustrating a radical impairment in exact calculation. However, he easily rejected grossly false additions such as 2 + 2 = 9, therefore demonstrating a preserved knowledge of the approximate result. The dissociation between impaired exact processing and preserved approximation was identified in several numerical tasks: solving and verifying arithmetical operations, number reading, short-term memory, number comparison, parity judgement, and number knowledge. We suggest the existence of two distinct number-processing routes in the normal subject. One route permits exact number representation, memory and calculation using symbolic notation. The other route allows for approximate computations using an analog representation of quantities.

Adult↗

Acalculia from a right hemisphere lesion dealing with "where" in multiplication procedures.

The present study describes in detail, for the first time, a case of failure with multiplication procedures in a right hemisphere damaged patient (PN). A careful, step-by-step, error analysis made possible to show that an important portion of PN's errors could be better explained as spatial in nature and specifically related to the demands of a multi-digit multiplication. These errors can be distinguished from other types of errors, including those, expected after a right hemisphere lesion, determined by a generic inability to deal with spatial material, or from other deficits, like neglect, affecting cognitive capacities across the board. The best explanation for PN's problems is that he might have difficulties in relying on a visuo-spatial store containing a layout representation specific to multiplication. As a consequence, while knowing what, when and how to carry out the various steps, PN does not know where. What he may thus lack is a spatial schema of multiplication. Such schema is thought to help normal calculators in overcoming working memory demands of complex calculation by representing the information of where exactly each sub-step should be placed.

Adult↗

Acalculia, aphasia and spatial disorders in left and right brain-damaged patients.

The paper reports the performance of 50 left- and 26 vascular right-brain-damaged (LBD, RBD) patients in the EC301 Calculation Battery, which explores different aspects of number and calculation processing. All patients underwent a comprehensive neuropsychological testing that also included evaluation for the presence and type of aphasia in LBD patients, and of spatial disorders in RBD patients. LBD were subdivided in three groups: non-aphasic (NA), Broca and Wernicke aphasics. Results indicate that language and calculation disorders can dissociate. The relationship between spatial and calculation disorders in RBD patients is less clear. No significant difference was found between Broca and Wernicke aphasics, nor between NA and RBD patients. In the transcoding tasks (reading or writing to dictation numbers and number words, for instance) syntactic errors were the most frequent type of errors in all groups. They were also present when neither the input nor the required response was in the Arabic code, and a word-by-word strategy could have been used to read the number word or write a spoken number in the orthographic code.

Adult↗

[Acalculia].

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Dyscalculia↗

Thalamic acalculia.

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Cerebral Infarction↗

Spatial acalculia.

Twenty-one patients with right hemisphere damage were studied (11 men, 10 women; average age = 41.33; range 19-65). Patients were divided into two groups: pre-Rolandic (six patients) and retro-Rolandic (15 patients) right hemisphere damage. A special calculation test was given. Different types of calculation errors were analyzed. Spatial alexia and agraphia for numbers, loss of calculation automatisms, reasoning errors, and general spatial defects interfering with normal number writing and reading, were observed. Number processing was impaired, whereas the calculation system was partially preserved. Fact retrieval and procedural difficulties were observed, but arithmetical rules were properly used. It is concluded that calculation abilities in right hemisphere damaged patients are disrupted as a result of: (1) visuospatial defects that interfere with the spatial arrangement of numbers and the mechanical aspects of mathematical operations: (2) inability to recall mathematical facts and appropriately to use them; and (3) inability to normally conceptualize quantities and process numbers.

Adult↗

Acalculia: deficits of operational and quantity number knowledge.

We describe the standardization of three new tests of knowledge of quantity facts, number operations and multiplication facts. We also report a validation study in which a group of 50 patients with cortical degenerative disorders were tested on these three new tests of number processing. Our results show that the quantity facts and number operations tests are sensitive measures of number processing abilities. Performance on the three new tests and the Graded Difficulty Arithmetic (GDA) test were found to be significantly impaired in the Alzheimer's Disease (AD) group. The frontotemporal dementia (FTD) group was subdivided into those with a semantic dementia (SD) and those with prominent frontal features (Non-SD). The semantic dementia subgroup was more impaired than both the AD patient group and the nonsemantic FTD subgroup on the quantity facts test. A more fine grained analysis reveals several interesting patterns of performance, including a dissociation between impaired performance on the quantity facts and number operations tests and preserved performance on the GDA. The findings attest the value of comparing performance on the GDA and our new tests in delineating the nature of an individual's number processing deficits. Implications for the relation between simple arithmetic fact knowledge and higher level number processing are discussed.

Adult↗