Gerstmann syndrome is a rare neurological disorder caused by damage to areas of the brain involved in understanding language and context-dependent recall. It is characterised by four symptoms (tetrad of symptoms):

• Acalculia: inability to perform calculations and arithmetic
• Finger agnosia: inability to recognise, distinguish or name fingers
• Agraphia: inability or loss of previous writing abilities
• Left-right disorientation: inability to distinguish left and right in one's own body or others¹

Overview of acalculia and Gerstmann syndrome

Most of us know the frustration of wracking our brains to make heads or tails of simple arithmetic, but getting nowhere. However, in Gerstmann syndrome, individuals who have acalculia routinely struggle with arithmetic and number-based activities ranging from timetable management to managing medication.

Acalculia is the result of alterations in one's ability to understand and perform mathematical tasks due to brain damage. It can be an acquired disorder or a defect in normal numerical skill development (a.k.a dyscalculia). Though many brain regions are involved in cognitive thinking, damage to the left parietal lobe (a brain area involved in language and mathematical processing) has been associated with the development of acalculia.²

Historical Context 

Joseph Gerstmann was an Austrian neuropsychiatrist who first described the symptoms of a 52-year-old woman who had recently experienced a stroke on the left side of her brain. Following this, the four cardinal symptoms were noted by Dr. Gerstmann: acalculia, finger agnosia, agraphia, and left-right disorientation in several other individuals following damage to the same brain area. Despite the notable recognition of this disease state and the symptoms it is expected to present with, there have been reports of other symptoms including alexia (reading disorder) and aphasia (disturbances in comprehending and using verbal communication).³

Neuroanatomy of Acalculia in Gerstmann syndrome

Brain Regions Implicated

The brain has labyrinth-like connections between different areas, which enables us to seamlessly perform even the simplest tasks throughout our daily lives. For mathematical processing, the left parietal lobe is often recruited.⁴

The parietal lobe is not a specific section, but more a region in the cerebral cortex. This area lies between the frontal (front of brain) and the occipital (back of brain) lobes. Within this region lies several other areas that correspond with more nuanced activities.⁵

For acalculia (and agraphia: language difficulty), damage to the brain area known as the supramarginal gyrus has been seen.⁶ However, the specificity of the brain regions involved remains contested and damage to other brain areas has also been shown to cause similar symptoms.^7,8

What causes acalculia and Gerstmann syndrome?

As mentioned earlier, the aetiology (the cause or the set of causes) for Gerstmann syndrome is damage to brain areas, but the cause of this damage can be wide-ranging:

• Ischemic stroke: blood supply to the brain is cut off causing brain cell death 
• Brain tumours: cancer cells can change the layout and function of specific brain cells and areas
• Middle cerebral artery aneurysm: brain bleed due to a burst artery in the region of the brain involved in language and mathematical processing
• Multiple sclerosis: the loss of brain cells due to immune cells attacking the outer protective layer (myelin sheath) of the neurons 
• Cortical atrophy: the death and loss of brain cells over time (e.g., Alzheimer’s disease)

Damage to brain regions can also occur due to exposure to certain environments or lifestyle choices: 

• Alcoholism: through chronic alcohol abuse, or increased susceptibility to alcohol poisoning, brain damage can occur as an increased likelihood of strokes and aneurysms
• Carbon monoxide poisoning: carbon dioxide can displace oxygen resulting in reduced oxygen to the brain causing ischemia
•  Anaphylactic shock/anaphylaxis: during an intense immune response, the body releases multiple chemicals that interfere with bodily functions, which can induce brain damage

Due to the variations in the cause of Gerstmann syndrome, it can occur in children, young, and elderly people. 

Diagnostic criteria and evaluation

Clinical Assessment of Gerstmann syndrome

To first identify damage to the brain and distinguish structural lesions in the brain, imaging techniques are used : 

• Magnetic Resonance Imaging (MRI): this non-invasive imaging technique uses large magnets in combination with radio waves to produce a detailed image of the brain. When imaged, damaged brain areas either appear as dark or light spots that do not match with surrounding normal tissues (groups of functionally and structurally similar cells)
• Computed tomography (CT) scan: though less detailed than an MRI, this imaging technique uses X-rays and computers to produce an image of the brain. It can be used during emergencies to show any ischemic damage
• Positron emission tomography (PET) scan: using radioactive materials that can create a 3D tracing of the brain, reduced blood flow can be detected in specific brain areas to characterise the disease

Acalculia-Specific Testing

The testing for acalculia can be done in several ways, but the easiest and most common are: 

• Written maths equations: asking the person to calculate and write down the answer to a mathematical equation (e.g., 25-13)
• Verbal testing: verbally present the person with a mathematical question and subsequently have them mentally find the answer and report it verbally

These simple diagnostic tools can indicate the severity of the brain damage and/or progression of the disease. However, there can be caveats including interference due to other disorders that can sometimes underlie acalculia.

Distinguishing Acalculia in Gerstman syndrome from other Conditions

Diseases must be correctly diagnosed, not only to ensure correct treatment but also to ensure patients' quality of life with fewer burdens. As such, the presence of acalculia is not synonymous with Gerstmann syndrome alone. 

• Alzheimer's disease: due to the progressive death of brain cells (neuronal degeneration), brain connections and networks become disrupted. Gerstmann syndrome may have some overlap and association with Alzheimer’s disease. Specifically, the progressive dysfunction of the posterior cortical areas(back of the brain) can cause overlapping symptoms associated with both diseases
• Learning disabilities: including developmental dyscalculia and dyslexia can be differentiated from acalculia in Gerstmann syndrome

Additional diagnostic tools such as cerebrospinal fluid sampling for Alzheimer’s disease, and psychiatric analyses for neuro-developmental disorders for dyscalculia and dyslexia further narrow potential diagnoses. 

Treatment and management of acalculia in Gerstmann syndrome

Since the cause of Gerstmann syndrome is caused by different aetiologies, the disease can be reversible.

• Tumour removal: reduced impact on the brain area affected and may restore functioning (fully or partially) 
• Rehabilitation following strokes or aneurysms may help re-learn mathematical skills that can be improved through regular practice

Due to the brain's limited capacity for tissue regeneration, damage to brain tissue often leads to permanent functional loss, resulting in lifelong symptoms.

Impact on daily life with acalculia

A study published in 2022 evaluated the quality of life experiences of twenty-three people living with acalculia after stroke and other forms of acquired brain injury. The study used a variety of participants ranging in age, gender, and resident countries.

The study found that individuals often had difficulties using timetables, organising social activities, employment and managing medication. The study states that empowering individuals through providing official recognition of their condition can impact positively on their self-confidence and self-esteem. 

Additionally, interventions designed to support acalculia symptoms to help improve numerical skills, but also help with emotional impact would show greater benefit. The presence of support groups that provide assistance greatly improves the quality of life for people who have acalculia (or related) conditions. 

Potential help sources

• NELFT: coordinated service to help children, young adults and adults having learning difficulties
• Stroke association

Summary

Acalculia is caused by damage to brain areas such as the supramarginal gyrus in the parietal lobe. It is one of four symptoms associated with Gerstmann syndrome. Though brain damage is irreversible, through rehabilitation and numerical practice, symptoms can be alleviated. Active education of acalculia to the wider public can help reduce stigma and assist those affected.

FAQs 

Is Gerstmann syndrome curable?

Due to the wide-ranging nature of Gerstmann syndrome, it can have mixed outcomes. Brain damage is permanent because neurons (brain cells) lack the ability to regenerate. Alleviation of symptoms can be achieved through numerical and language rehabilitation. 

How can I avoid Gerstmann syndrome?

Certain lifestyle choices increase the likelihood of Gerstmann syndrome or symptoms associated with it: chronic alcohol use, smoking, and lack of exercise can all increase the chances of strokes and brain damage.

Do maths classes help with acalculia?

Yes, it can help develop new brain connections making numeracy tasks easier over time.