Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We hereby consent to the incorporation by reference in this Registration Statement on Form S-8 of our report dated May 7, 2004 relating to the financial statements of ABIOMED, Inc., which appears in ABIOMED, Inc.’s Annual Report on Form 10-K for the year ended March 31, 2004.

PricewaterhouseCoopers LLP

Boston, Massachusetts

March 29, 2005