Acalculia

There are different aspect of mathematical thinking which in turn depend on different regions of the brain.There are those aspects which are language dependent, and those which are more "intuitive" and which involve the right and left parietal lobe. "exact arithmetic" (language dependent and involves linguistic processing in order to store tables of arithmetical information) "approximate arithmetic" (non-verbal, visual-spatial) - more dependent on the right as well as left parietal lobe. the IPL is directly implicated in mathematical and geometric thinking. Damage to the IPL, in turn can disrupt the ability to perform math or geometrical problems. Problems working with numbers or performing arithmetical operations can be secondary to a number of causes and may result from injuries involving different regions of the brain. In many instances a patient may appear to have difficulty performing math problems when in fact the basic ability to calculate per se is intact. That is, the apparent difficulty may in fact be due to spatial, linguistic, agnosic or alexic abnormalities.

However, in many instances, patients who are no longer able to perform calculations demonstrate a number of deficiencies. May erroneously substitute one operation for another: misreading the sign "+" as "x"; or they may reverse numbers i.e. "16" as "61",substitute counting for calculation, i.e. 21 + 6 = 22, or inappropriately group: 32 + 5 = 325.

On the otherhand, with left posterior lesions localized to the vicinity of the inferior parietal lobe, patients may have severe difficulty performing even simple calculations, e.g. carrying, stepwise computation, borrowing. When this occurs in the absence of alexia, aphasia, or visual-spatial abnormalities, and is accompanied by finger agnosia, agraphia, and right-left orientation, it is considered part of Gerstmann's syndrome. It has also been referred to as "anarithmetria", or pure acalculia when not accompanied by other abnormalities.

Acalculia is an isolated impairment of calculation in the absence of alexia or agrahic or spatial organization problems and involves a disturbance of basic math processes, e.g. carrying, stepwise computation, borrowing. It is manifested as an impairment in the ability to maintain order, to correctly plan in sequence, and to appropriately manipulate numbers, and/or it may be related to an amnesia for arithmetical facts. May be due to damage of the left inferior parietal lobe.
 * PURE ACALCULIA/ANARITHMETRIA**

Ex: a small circumscribed left parietal subdural hematoma in an auto accident - unable to add past 10 (e.g. 7+4), although able to read, write, speak appropriately, and recognize objects.

Alexia for numbers and digits is found in over 80% of individuals with left temporal-occipital lesions, and in less than 10% of those with right hemisphere lesions. As the name implies, the patient is unable to recognize numbers. Usually these individuals also suffer from generalized or literal alexia; i.e. an inability to recognize letters.
 * ALEXIA/AGNOSIA FOR NUMBERS**

In some cases acalculia may be associated with an alexia and/or an agraphia for numbers, as well as aphasic abnormalities (referred to as aphasic acalculia. Individuals with this disorder are unable to recognize or properly produce numbers in written form.
 * ALEXIA/AGRAPHIA FOR NUMBERS**

Ex: May be unable to write out or point to the number "4" vs the number "7" or the letter "B".

Lesion is usually in the left inferior parietal lobule and localized within the angular gyrus. Not all patients are aphasic however.

Right cerebral hemisphere is quite proficient in performing geometrical analysis. However, it's basic arithmetical abilities are limited to the performance of addition, subtraction and multiplication of simple sums and numbers below 10. However, it can also visually recognize correct answers, for small sums, when given a visual choice. Nevertheless, problems with arithmetical reasoning per se, are not usually due to right hemisphere lesions.
 * SPATIAL ACALCULIA**

However, when the right hemisphere is damaged, difficulties in calculation may result due to visual-spatial disturbances.

Ex: figures and digits may not be properly aligned, arranged or organized on the page when writing out a problem. Or, the patient may ignore the left half of numbers when adding, subtracting, etc. If given the opportunity to perform the same calculation verbally, frequently little difficulty is demonstrated indicating that the basic ability to calculate is intact.

//Regions Affected:// The majority of those with spatial acalculia have right inferior parietal lobe lesions. However, bilateral disturbances may be present.