Rusich:
More information is needed. Your intented purpose needs to be made clear.
A "broken heart" refers to the ache of a heart, but it is descriptive rather than a natural fact.
One can say anything they want in the context of descriptive language. Usually, people refer to a broken heart as a "broken heart". No further description is needed.
One does not seriously refer to "parts" or "pieces" because those do not physically exist.
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