QuickLinks -- Click here to rapidly navigate through this document

Exhibit (a)(1)(D)

OFFER TO PURCHASE FOR CASH
ALL OUTSTANDING SHARES OF COMMON STOCK
(together with any associated rights)
of
ADVANCED NEUROMODULATION SYSTEMS, INC.
at
$61.25 NET PER SHARE
by
APOLLO MERGER CORP.
a wholly-owned subsidiary of
ST. JUDE MEDICAL, INC.

THE OFFER (AS DEFINED HEREIN) AND WITHDRAWAL RIGHTS WILL EXPIRE AT
12:00 MIDNIGHT, NEW YORK CITY TIME, ON TUESDAY, NOVEMBER 15, 2005 UNLESS THE OFFER IS EXTENDED.

October 18, 2005

To Brokers, Dealers, Commercial Banks,
    Trust Companies and Other Nominees:

        We have been engaged to act as Dealer Manager in connection with the third party tender offer by Apollo Merger Corp., a Texas corporation ("Purchaser") and a wholly-owned subsidiary of St. Jude Medical, Inc., a Minnesota corporation ("Parent"), to purchase all of the outstanding shares of common stock of Advanced Neuromodulation Systems, Inc. (the "Company"), par value $0.05 per share (together with the associated rights issued pursuant to the Rights Agreement dated August 30, 1996 between Quest Medical, Inc. and KeyCorp Shareholder Services, Inc., as rights agent, as amended by the Amendment to Rights Agreement dated January 25, 2002 between the Company and Computershare Investor Services LLC and the Second Amendment to Rights Agreement dated October 14, 2005 between the Company and Computershare Investor Services LLC (as so amended, the "Rights Plan")) (the "Shares"), at a price of $61.25 per Share, net to the seller in cash, less any required withholding of taxes and without payment of any interest, upon the terms and subject to the conditions set forth in the Offer to Purchase, dated October 18, 2005 (the "Offer to Purchase"), and in the related letter of transmittal for the Shares (the "Letter of Transmittal," which, together with the applicable Offer to Purchase, as each may be amended or supplemented from time to time, collectively constitute the "Offer").

The Offer is conditioned upon, among other things, (i) there being validly tendered and not properly withdrawn a majority of the total outstanding Shares on a "fully-diluted basis" (as defined in the Offer to Purchase) as of the date Shares are accepted for payment pursuant to the Offer and (ii) the expiration or termination of any applicable waiting period under the Hart-Scott-Rodino Antitrust Improvements Act of 1976, as amended, or similar statutes or regulations of foreign jurisdictions. The Offer also is subject to certain other terms and conditions.

        For your information and for forwarding to your clients for whom you hold Shares registered in your name or in the name of your nominee or who hold Shares registered in their own names, we enclose the following documents:

        1.     Offer to Purchase, dated October 18, 2005.

        2.     Letter of Transmittal to tender Shares (including Guidelines for Certification of Taxpayer Identification Number on Substitute Form W-9) for your use and for the information of your clients who hold Shares. Facsimile copies of the Letter of Transmittal may be used to tender Shares.

        3.     A letter to clients, which may be sent to your clients for whose account you hold Shares, registered in your name or in the name of your nominee, with space provided for obtaining such clients' instructions with regard to the Offer.

        4.     Notice of Guaranteed Delivery to be used to accept the Offer if Share Certificates (as defined in the Offer to Purchase) are not immediately available or time will not permit the Share Certificates and all required documents to reach the Depositary on or prior to the Expiration Date (as defined in the Offer to Purchase) or if the procedures for delivery by book-entry transfer, as set forth in the Offer to Purchase, cannot be completed on a timely basis.

        5.     Letter to shareholders of the Company from the President and Chief Executive Officer, accompanied by the Company's Solicitation/Recommendation Statement on Schedule 14D-9.

        6.     Return envelope addressed to Computershare Shareholder Services, Inc., as Depositary.

        In accordance with the terms and subject to the satisfaction or waiver (where applicable) of the conditions to the Offer, Purchaser will accept for payment, purchase and pay for, all Shares validly tendered and not properly withdrawn pursuant to the Offer at the earliest time following expiration of the Offer when all such conditions shall have been satisfied or waived (where applicable). For purposes of the Offer, Purchaser will be deemed to have accepted for payment (and thereby purchased), Shares validly tendered and not properly withdrawn if, as and when Purchaser gives oral or written notice to the Depositary of Purchaser's acceptance for payment of such Shares pursuant to the Offer. Upon the terms and subject to the conditions of the Offer, payment for Shares accepted for payment pursuant to the Offer will be made only after timely receipt by the Depositary of (1) the Share Certificates, or Book-Entry Confirmation (as defined in the Offer to Purchase) of a book-entry transfer of such Shares into the Depositary's account at the Book-Entry Transfer Facility (as defined in the Offer to Purchase) pursuant to the procedures set forth in Section 3 of the Offer to Purchase; (2) the Letter of Transmittal to tender Shares (or a facsimile thereof) properly completed and duly executed, with any required signature guarantees, or, in the case of a book-entry transfer, an Agent's Message (as defined in the Offer to Purchase) in lieu of the Letter of Transmittal; and (3) any other documents required under the Letter of Transmittal.

        Purchaser will not pay any commissions or fees to any broker, dealer or other person (other than the Depositary, the Information Agent and the Dealer Manager, as described in the Offer to Purchase) in connection with the solicitation of tenders of Shares pursuant to the Offer. Purchaser will, however, upon request, reimburse you for customary clerical and mailing expenses incurred by you in forwarding any of the enclosed materials to your clients.

        Purchaser will pay any stock transfer taxes with respect to the transfer and sale of Shares to it or to its order pursuant to the Offer, except as otherwise provided in Instruction 6 of the enclosed Letter of Transmittal.

Your prompt action is requested. We urge you to contact your clients as promptly as possible. Please note that Offer and withdrawal rights expire at 12:00 Midnight, New York City time, on Tuesday, November 15, 2005, unless the Offer is extended.

        In order for a shareholder of the Company to take advantage of the Offer, the Letter of Transmittal to tender Shares (or a facsimile thereof), properly completed and duly executed, together with any required signature guarantees (or, in the case of a book-entry transfer, an Agent's Message in lieu of the Letter of Transmittal) and any other documents required by such Letter of Transmittal should be sent to the Depositary and Share Certificates should be delivered, or Shares should be tendered pursuant to the procedure for book-entry transfer, all in accordance with the instructions set forth in the Letter of Transmittal and the Offer to Purchase.

2

        Holders of Shares whose Share Certificates are not immediately available or who cannot deliver their Share Certificates and all other required documents to the Depositary on or prior to the Expiration Date of the Offer, or who cannot complete the procedure for delivery by book-entry transfer on a timely basis, must tender their Shares according to the guaranteed delivery procedures set forth in Section 3 of the Offer to Purchase.

        Inquiries you may have with respect to the Offer should be addressed to the Information Agent or the Dealer Manager as set forth on the back cover page of the Offer to Purchase. Requests for copies of the Offer to Purchase, the Letter of Transmittal and all other tender offer materials may be directed to the Information Agent.

Very truly yours,
BANC OF AMERICA SECURITIES LLC

Enclosures

Nothing contained herein or in the enclosed documents shall constitute you or any other person as an agent of Parent, Purchaser, the Depositary, the Information Agent, the Dealer Manager or any affiliate of any of them, or authorize you or any other person to make any statement or use any document on behalf of any of them in connection with the Offer other than the enclosed documents and the statements contained therein.

3

QuickLinks

Exhibit (a)(1)(D)