SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549

                               ------------------

                                    FORM 6-K

                        REPORT OF FOREIGN PRIVATE ISSUER

                    Pursuant to Rule 13a-16 or 15d-16 of the
                         Securities Exchange Act of 1934


                           For the month of: May 2004

                        Commission File Number: 000-28882

                             World Heart Corporation
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               (Exact name of registrant as specified in charter)

                                       N/A
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                 (Translation of registrant's name into English)

                                     Ontario
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                         (Jurisdiction of organization)

                     1 Laser Street, Ottawa, Ontario K2E 7V1
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                    (Address of principal executive offices)

                  Registrant's telephone number: (613) 226-4278



Indicate by check mark whether the registrant files or will file annual reports
under cover of Form 20-F or Form 40-F.

                    Form 20-F   X            Form 40-F
                               ---                       ---


Indicate by check mark whether by furnishing the information contained in this
Form, the registrant is also thereby furnishing the information to the
Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934.

                     Yes                            No    X
                          ---                            ---

If "Yes" is marked, indicate below the file number assigned to the registrant in
connection with Rule 12g3-2(b): 82- ________

<PAGE>
This Form 6-K consists of the following:

1.   Press release of World Heart Corporation ("WorldHeart"), dated May 12,
2004, announcing that WorldHeart expects accelerated enrollment in it's RELIANT
Trial under the proposal announced May 11, 2004, by the Centers for Medicare and
Medicaid Services (CMS) in the United States.

The information contained in this Report is incorporated by reference into
Registration Statement No. 333-109876 on Form F-3 and Registration Statement No.
333-111512 on Form F-3.

<PAGE>
News & Events

Press Releases

WORLDHEART ANTICIPATES INCREASED RATE OF ENROLLMENT IN RELIANT TRIAL WITH CMS
PROPOSAL

OAKLAND, CALIFORNIA -May 12, 2004 (NASDAQ: WHRT, TSX: WHT)-World Heart
Corporation (WorldHeart) expects accelerated enrollment in it's RELIANT Trial
under the proposal announced yesterday by the Centers for Medicare and Medicaid
Services (CMS) in the United States. If approved the proposal would move
reimbursement for certain ventricular assist device implants from DRG 525 to DRG
103.

The effect of the proposal would be an increased reimbursement of approximately
30% over the current maximum to U.S. medical centers that are participating in
the RELIANT Trial for implants of either WorldHeart's Novacor(R) LVAS (left
ventricular assist system) or Thoratec Corporation's HeartMate(R) XVE LVAS. The
RELIANT Trial is expected to support a Premarket Approval Supplement to be filed
with the U.S. Food and Drug Administration (FDA) for the use of the Novacor LVAS
by non-transplant eligible patients (Destination Therapy). Yesterday, WorldHeart
announced that it had received conditional approval from the FDA to proceed with
the RELIANT Trial enrollment of up to 390 patients in 40 centers in the United
States.

"The current level of reimbursement is a significant concern to centers that
will participate in the RELIANT Trial, and this change would have a major
impact", said Roderick M. Bryden, WorldHeart's President and Chief
Executive Officer.

"We expect that enrollment of patients in the RELIANT Trial will begin this
month and continue through 2005." Mr. Bryden said.

About Novacor(R)LVAS
Novacor LVAS is an implanted electromagnetically driven pump that provides
circulatory support by taking over part or all of the workload of the left
ventricle. With implants in more than 1,500 patients, no deaths have been
attributed to device failure, and some recipients have lived with their original
pumps for as long as four years - statistics unmatched by any other implanted
electromechanical circulatory support device on the market. Novacor LVAS is
commercially approved as a bridge to transplantation in the U.S. and Canada.

In Europe, the Novacor LVAS has unrestricted approval for use as a bridge to
transplantation, an alternative to transplantation and to support patients who
may have an ability to recover the use of their natural heart. In Japan, the
device is commercially approved for use in cardiac patients at risk of imminent
death from non-reversible left ventricular failure for which there is no
alternative except heart transplantation.

About World Heart Corporation
World Heart Corporation is a global medical device company headquartered in
Ottawa, Ontario, Canada, with additional facilities in Oakland, California, USA
and Heesch, Netherlands.
<PAGE>
WorldHeart is currently focused on the development and commercialization of
pulsatile ventricular assist devices. Its Novacor LVAS is well established in
the marketplace and its next-generation technology is a fully implantable assist
device intended for long-term support of patients with end-stage heart failure.

Any forward-looking statements in this release are made pursuant to the safe
harbor provisions of the Private Securities Litigation Reform Act of 1995.
Investors are cautioned that all forward-looking statements involve risk and
uncertainties, including without limitation, risks in product development and
market acceptance of and demand for the Corporation's products, risks of
downturns in economic conditions generally, and in the medical devices markets,
risks associated with costs and delays posed by government regulation,
limitations on third-party reimbursement, inability to protect proprietary
technology, potential product liability and other risks detailed in the
Corporation's filings with the U.S. Securities and Exchange Commission.

For more information, please contact:
World Heart Corporation
Fay Dunbabin
(613) 226-4278 ext. 2215
www.worldheart.com

<PAGE>
                                   SIGNATURES


     Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned, thereunto duly authorized.


                                        World Heart Corporation


     Date:  May 12, 2004                By:      /s/ Mark Goudie
                                           -------------------------------------
                                           Name:   Mark Goudie
                                           Title:  Chief Financial Officer