Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We hereby consent to the incorporation by reference in the Registration Statements on Form S-8 (Nos. 33-23053, 33-38030, 33-65192, 333-38865, 333-66029, 333-103245, and 333-114066) of ABIOMED, Inc. of our report dated May 7, 2004 relating to the financial statements of ABIOMED, Inc, which appears in the ABIOMED, Inc. Form 10-K for the fiscal year ended March 31, 2004.

/s/ PricewaterhouseCoopers LLP

Boston, Massachusetts

May 26, 2004