Bit of heart from luvvie CBS paid to broadcast (8,5)

I believe the answer is:

bicuspid valve

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'bit of heart' is the definition.
The definition and answer can be both body parts as well as being singular nouns.
Perhaps they are linked in a way I don't understand?

'luvvie cbs paid to broadcast' is the wordplay.
'to broadcast' indicates an anagram (letters scattered or cast around).
'luvvie'+'cbs'+'paid'='luvviecbspaid'
'luvviecbspaid' is an anagram of 'BICUSPID VALVE'.

'from' is the link.

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I've seen this clue in The Independent.

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