Exhibit 99.1

Endocardial Solutions

Intends to Vigorously Defend Patent Infringement Claims

ST. PAUL, MN, October 15, 2004 — Endocardial Solutions, Inc. (NASDAQ:ECSI) announced today that a lawsuit has been filed against it by Biosense Webster, Inc., a subsidiary of Johnson & Johnson, alleging that the Endocardial Solutions EnSite® mapping and navigation system, including its EnSite NavX ™ surface electrode product, infringe certain Biosense Webster patents. The suit, which was filed in the U.S. Federal District Court in Los Angeles, California, seeks monetary damages and injunctive relief.

On September 23, 2004, Endocardial Solutions and St. Jude Medical Inc. (NYSE: STJ) jointly announced the signing of a definitive agreement whereby St. Jude Medical will acquire Endocardial Solutions, Inc. for $11.75 per share in cash consideration, representing an aggregate purchase price of approximately $273 million.

James W. Bullock, President and Chief Executive Officer of Endocardial Solutions, stated “We will vigorously defend our EnSite products and technology. We find the timing of this lawsuit to be very curious. The Biosense Webster patents cited in this lawsuit were issued between 1995 and 1998. Our EnSite System has been in the U.S. market since 1999, but no lawsuit was filed until St. Jude Medical announced its intention to acquire Endocardial Solutions. St. Jude Medical has been made aware of this lawsuit, and both Endocardial Solutions and St. Jude Medical continue to press forward to close this transaction as soon as possible.”

Based in St. Paul, Minnesota, Endocardial Solutions (www.endocardial.com) develops, manufactures and markets the EnSite System used for the diagnostic mapping of arrhythmias (abnormally rapid heartbeats caused by irregular electrical activity in the heart) with a 3D graphical display of the heart’s electrical activity, and the navigation and localization of conventional catheters (diagnostic or therapeutic) used during electrophysiology procedures. The U.S. Food and Drug Administration cleared the EnSite System for use in diagnostic mapping of complex arrhythmias in the right atrium of the heart during the second quarter of 1999, and cleared the EnSite NavX Surface Electrode Kit to display the position of conventional electrophysiology catheters in any chamber of the heart in the second quarter of 2003.

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This press release contains forward-looking statements within the meaning of the Private Securities Litigation Reform Act of 1995. Such statements include, but are not limited to, statements about the pending transaction between St. Jude Medical, Inc. (“St. Jude Medical”) and Endocardial Solutions, Inc. (“ESI”). Such statements are based upon the current beliefs and expectations of St. Jude Medical’s and ESI’s management and are subject to significant risks and uncertainties. Actual results may differ from those set forth in the forward-looking statements.

The following factors, among others, could cause actual results to differ from those set forth in the forward-looking statements: the ability to obtain the approval of the transaction by ESI’s stockholders; the ability to satisfy other closing conditions; the risk that the businesses will not be integrated

successfully; the risk that the cost savings from the transaction may not be fully realized or may take longer to realize than expected; the ability to develop and execute comprehensive plans for asset rationalization; disruption from the transaction making it more difficult to maintain relationships with customers, employees or suppliers; increased competition and its effect on pricing, spending, third-party relationships and revenues; and the risk of new and changing regulation in the U.S. and internationally. Additional factors that could cause ESI’s results to differ materially from those described in the forward-looking statements can be found in the 2003 Annual Report on Form 10-K of ESI filed with the Securities and Exchange Commission and available at the Securities and Exchange Commission’s Internet site (http://www.sec.gov).

ESI will file a proxy statement in connection with its special meeting to approve the proposed transaction. Stockholders are urged to read the proxy statement regarding the proposed transaction when it becomes available, because it will contain important information. ESI, its executive officers and directors may be deemed to be participants in the solicitation of proxies in connection with the proposed transaction. Information regarding ESI’s directors and executive officers is available in its proxy statement filed with the SEC on April 22, 2004. Other information regarding the participants in the proxy solicitation and a description of their direct and indirect interests, by security holdings or otherwise, will be included in the proxy statement and other relevant materials to be filed with the SEC when they become available.

Stockholders will be able to obtain a free copy of the proxy statement, as well as other filings containing information about St. Jude Medical and ESI, without charge, at the Securities and Exchange Commission’s Internet site (http://www.sec.gov). Copies of the proxy statement and the filings with the SEC that will be incorporated by reference in the proxy statement can also be obtained, without charge, by directing a request to Endocardial Solutions, Inc., 1350 Energy Lane, Suite 110, St. Paul, Minnesota 55108, Attention: Secretary, or by telephone at (651) 523-6900.

Contacts:

Jim Bullock, President & CEO, Endocardial Solutions (651) 523-6928 jbullock@endocardial.com

J. Robert Paulson, CFO, Endocardial Solutions (651) 523-6916 bpaulson@endocardial.com

Brenda Gutzke, Investor Relations, Endocardial Solutions (651) 523-6959 bgutzke@endocardial.com

ENDOCARDIAL SOLUTIONS INC 8-K