Lawyers for the schoolgirl, named only as W for legal reasons, say she needs at least two carers looking after her around the clock.
Judge Parker heard the girl is in phase two of her disease, which results in 'restless' and 'active' behaviour punctuated by 'violent outbursts'.
The report said that to expect the mother to continue to provide care was 'unrealistic, unfair and unjust', and instead she should focus on spending 'quality time' with the girl.
So far the council have offered one 'support worker', who will be employed for one and a half hours in the morning and one and a half hours in the evening - but that means the girl's mother still has to care for her as well.
In launching a judicial review, Ms Gerry said that wasn't good enough and argued the local authority had acted 'irrationally' in not offering two-to-one round-the-clock care.
The barrister also said that the council's stance was a breach of the Human Rights Act and violated the girl's right to a family and private life.
Her mother is said to be 'exhausted' and 'worn down' from looking after her, and Ms Gerry insisted the girl's behaviour is so 'challenging' and 'violent' there is effectively a 'cycle of abuse' with the daughter as the perpetrator.
Jonathan Swift, for the council, agreed that the local authority had a duty to care for the girl - who is still able to attend a special school - under the Children Act 1989, but said it was up to their officers to decide just how much looking after she required.
Mr Swift also pointed out that the council faces the difficult task of balancing the need to offer care services and the 'scarce resources' at its disposal.
Recognising the importance of the case, Judge Parker indicated he will reserve his decision and did not indicate when he would give his judgement.
STRAND NEWS SERVICE