Nirvanashatkam says:
"[Real] I am not mind,intellect, heart or ego. I am Atman".
That which is thinking and roaming always is the mind. The sense of ego-centric 'I' and 'My'is caused by the functioning of mind.
Atmaa is All-pervading and ever changeless.
Gita says:
न जायते म्रियते वा कदाचि
न्नायं भूत्वा भविता वा न भूयः।
अजो नित्यः शाश्वतोऽयं पुराणो
न हन्यते हन्यमाने शरीरे।।2.20।।
2.20 Never is this One born, and never does It die; nor is it that having come to exist, It will again cease to be. This One is birthless, eternal, undecaying, ancient; It is not killed when the body is killed.
But mind is born and it dies when Atman is realised in Nirvikalpa-samadhi.
Also,
इन्द्रियाणि पराण्याहुरिन्द्रियेभ्यः परं मनः।
मनसस्तु परा बुद्धिर्यो बुद्धेः परतस्तु सः।।3.42।।
3.42 They say that the organs are superior (to the gross body); the mind is superior to the organs; but the intellect is superior to the mind. However, the one who is superior to the intellect is He.
Our brain controls our mind and intellect. Atmaa is beyond these. In fact Atmaa is the Knower and mind is its instument. Atmaa is realised at the Nirvikalpa-Samadhi samadhi state where there is no functioning of body, mind, intellect and so of brain.