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Gerstmann's syndrome (not to be confused with Gerstmann-Sträussler-Scheinker syndrome) is a rare neurological disorder, characterized by a constellation of cognitive impairments: inability to tell one finger from another (finger agnosia), disorientation for left and right, inability to perform basic calculations (acalculia), and the inability to write (agraphia). It is named after the Austrian neurologist, Josef Gerstmann (1887-1969), who first described its clinical features.

The syndrome occurs most often as the result of cerebrovascular disease, and is associated with lesions at the angular gyrus (Brodmann area 39), of the dominant parietal lobe. It is generally regarded as an acquired disorder, however, the same constellation of symptoms have been observed in children with no history of brain damage. This developmental disorder is referred to as developmental Gerstmann's syndrome, the etiology of which, is largely unknown.

The disorder is incompletely understood and as such is rarely diagnosed. Many theories exist which propose to explain the functional mechanisms underlying the symptoms, none of which are universally accepted. Gerstmann's syndrome is surrounded by controversy, with some researchers questioning whether or not it represents a distinct and clinically relevant syndrome.

Symptoms
The disorder comprises of a tetrad of neuropsychological deficits. It often occurs as an incomplete, or partial syndrome, with patients exhibiting two or three of the associated symptoms. Additionally, it may present in association with other deficits which are related to parietal lobe damage, including constructional apraxia and aphasia. A 'pure' Gerstmann's syndrome featuring all four symptoms, in the absence of additional cognitive deficits, is therefore, rare.

Finger agnosia
Finger agnosia is the loss of the ability to recognise and distinguish between the fingers. The inability often extends to the identification of the fingers on drawings, of fingers on a model and also to the fingers of the experimenter. Gerstmann considered finger agnosia alongside agraphia to be the salient features of the syndrome. Testing for finger agnosia involves asking patients to identify specific fingers by name, to point to named fingers on a drawing or to hold up the same finger as the experimenter.

Right-left disorientation
Patients with Gerstmann's syndrome are disorientated for left and right. Gerstmann proposed that the confusion between left and right, occurs with respect to their own body and with, "special reference to the hands and fingers". In patients with normal motor and sensory function, the deficit is tested by asking them to indicate their left and right limbs. Two step commands are also used, patients may for example, be asked to touch their right ear with their left hand. The deficit is often more pronounced when patients are required to carry out multi step commands.

Acalculia
Acalculia is an impaired ability to compute simple mathematical calculations, such as basic addition, subtraction, division and multiplication, whilst the ability to read and write numbers is often preserved. Gerstmann proposed a strong link between acalculia and finger agnosia, which he believed, stems from childhood were early calculations begin with the fingers. Patients may be able to answer previously memorised arithmetic knowledge, but lose the conceptual ability to perform calculations. Calculation difficulties are apparent whether the information is presented verbally or visually and whether individuals are required to give verbal or written responses. Acalculia is tested by asking individuals to perform basic mathematical calculations and to answer questions about number relations, such as which number is larger/smaller.

Agraphia
Agraphia is the loss of the ability to communicate through writing. In the case of Gerstmann's syndrome, the agraphia usually represents a pure apraxic agraphia, absent of alexia. Apraxic agraphia is thought to result from damage to the superior parietal area rather than to the angular gyrus, this may explain, why it is the symptom which is often missing in a partial Gerstmann's syndrome. The deficit is tested by asking patients to copy written text, to the write the name of a object presented to them, or to write to dictation.

Causes
Gerstmann's syndrome occurs most often, in adults, as the result of cerebrovascular disease, but can also occur as the result of traumatic brain injury or a central nervous system tumor. Gerstmann suggested that the tetrad of symptoms have a high localizing value, and are indicative of a lesion to the dominant parietal lobe, at the transition between the angular gyrus and the second occipital convolution. Recent studies have utilized advances in imaging techniques to provide support for the angular gyrus localisation. In a study which used elcro-stimulation of the cortex during brain surgery, researchers were able to elicit the symptoms of the syndrome, with stimulation of the cortex in the posterior parietal area. Gerstmann's syndrome has also been reported following a posterior thalamic lesion. Here, the authors concluded, that the lesion in the thalamus had damaged commuting tracts, therefore causing decreased activity in the inferior parietal lobe.

Disruption of body schema
Gerstmann speculated that the disorder results from damage to a single cognitive mechanism, which is responsible for each of the symptoms. He proposed, that the left-right confusion occurs “with special reference to the hands and fingers”, that the differentiation of fingers is necessary for writing and that the fingers are linked to the development of counting in childhood. He therefore speculated that the four symptoms have a common psycho-neurological basis and are related to a distortion of the body schema, which is restricted to the hands and fingers.

Spatial disorder
A further view, assumes a different common denominator (a deficit in mental rotations) is responsible for the tetrad of symptoms. Gold et al. (1995) investigated left-right confusion in a patient with Gerstmann's syndrome, and found that while they were able to point accurately to the left or right parts of the body they were unable to do this when mental rotation was required. The authors concluded that a deficit in horizontal transformation (mental-rotation) was the cause of the left-right confusion and speculated that it may account for the other symptoms which comprise the syndrome.

A recent review of the literature has proposed a new model for Gerstmann's syndrome which includes semantic aphasia and suggests a single underlying fact (a verbally mediated spatial deficit) may account for the syndrome. This model proposes agraphia as an additional symptoms only when damage includes the superior parietal area and suggests that the other symptoms are caused by a semantic aphasia and represent a deficit in the ability to verbally mediate spatial operations.

Disconnection
Several researchers have expressed the view that the four symptoms of the syndrome do not share an underlying cognitive mechanism that can account for all four of the symptoms and instead suggest that syndrome may be the result of interparietal disconnection of neighbouring, but separate regions. Kleinschmidt and Rusconi (2011) proposed that the syndrome results from damage to crossing fibre tracts in the subcortical white matter, which disconnect separate networks. An earlier study demonstrated, that the symptoms of Gerstmann's syndrome can be elicited, during open brain surgery, by stimulation of distinct areas of the parietal area, some researchers have argued is evidence for a disconnection via white matter tracts rather than for a focal lesion. A further study asked patients to perform tasks designed to test each of Gerstmann's tetrad in healthy population, and used fMRI to compare activations during to control conditions. This study revealed no overlap of cortical activation in the four Gerstmann conditions and led the authors to conclude that a single cognitive module could not account for all symptoms and that their co-occurrence results from their structural proximity rather than an from an underlying cognitive module.

Criticism
In 1961, Arthur Benton published a paper titled 'The Fiction of the Gerstmann Syndrome', which questioned the validity of Gerstmann's observations and the autonomy of the syndrome. Further criticisms followed, and centred largely on the seemingly dissociable symptoms of the syndrome. Cases often present an 'incomplete' tetrad of symptoms or more commonly present alongside additional deficits, causing some researchers to speculate that their co-occurrence in a 'pure' case is coincidental. Benton(1961) investigated a large cohort of brain damaged patients, he found that the symptoms of the syndrome, correlated as closely with each other as they correlated with other deficits, such as apraxia or reading impairment. He concluded that following parietal lobe damage, the four symptoms were no more likely than any other combination of parietal deficits and therefore, they do not represent a clinically distinct syndrome. The methodology and statistical analysis used in this study have been challenged.

Some authors have highlighted the syndromes strong association with aphasia and suggested that the symptoms of the syndrome can be explained as a manifestation of language deficits. Proponents of this theory argue that as the syndrome often presents alongside aphasia, and the deficits are often tested using verbal tasks, that any apparent deficits could be related to aphasia, rather than a distinct clinical syndrome. Cases of pure Gerstmann's syndrome in the absence of aphasia have been reported in the literature.