<PAGE>   1
                                                                    EXHIBIT 4.13


                                AMENDMENT NO. 11


        THIS AMENDMENT NO. 11, dated as of May 31, 2001 (the "Amendment")
relating to the Credit Agreement referenced below, by and among NATIONAL MEDICAL
CARE, INC., a Delaware corporation, certain subsidiaries and affiliates party to
the Credit Agreement and identified on the signature pages hereto, and BANK OF
AMERICA, N.A., (formerly known as NationsBank, N.A), as Paying Agent for and on
behalf of the Lenders. Terms used but not otherwise defined shall have the
meanings provided in the Credit Agreement.

                               W I T N E S S E T H

        WHEREAS, a $2.5 billion credit facility has been extended to National
Medical Care, Inc. and certain subsidiaries and affiliates pursuant to the terms
of that Credit Agreement dated as of September 27, 1996 (as amended and
modified, the "Credit Agreement") among National Medical Care, Inc., the other
Borrowers, Guarantors and the Lenders identified therein, and NationsBank, N.A.,
as Paying Agent.

        WHEREAS, the Company has requested the modification of certain covenants
and certain other changes to the Credit Agreement more fully set forth herein;

        WHEREAS, the requested consents and modifications described herein
require the consent of the Required Lenders; and

        WHEREAS, the Required Lenders have consented to the requested
modifications on the terms and conditions set forth herein and have authorized
the Paying Agent to enter into this Amendment on their behalf to give effect to
this Amendment.

        NOW, THEREFORE, IN CONSIDERATION of these premises and other good and
valuable consideration, the receipt and sufficiency of which is hereby
acknowledged, the parties hereto agree as follows:

        1.      The Credit Agreement is amended and modified in the following
respects:

                1.1     Section 8.1(m) is hereby amended by deleting the
        reference to "$950 million" and replacing it with a reference to "$1.20
        billion".

                1.2     It is hereby agreed that the provisions of Section 3.3
        shall not apply with respect to any Net Proceeds of Additional Subdebt
        issued on or after the date hereof and clause (D) of Section 3.3(b)(ii)
        is hereby deleted in it entiriety.

        2.      The effectiveness of this Amendment is subject to receipt by the
Paying Agent of the following:

                (i)     copies of this Amendment executed by the Company and the
        other members of the Consolidated Group identified on the signature
        pages hereto, and

                (ii)    the consent of the Required Lenders.


<PAGE>   2

        3.      Except as modified hereby, all of the terms and provisions of
the Credit Agreement (and Exhibits and Schedules) remain in full force and
effect.

        4.      The Credit Parties hereby affirm (i) the representations and
warranties set out in Section 6 of the Credit Agreement are true and correct as
of the date hereof (except those which expressly relate to an earlier period)
and (ii) no Default or Event of Default presently exists.

        5.      The Company agrees to pay all reasonable costs and expenses of
the Paying Agent in connection with the preparation, execution and delivery of
this Amendment, including without limitation the reasonable fees and expenses of
Moore & Van Allen, PLLC.

        6.      This Amendment may be executed in any number of counterparts,
each of which when so executed and delivered shall be deemed an original and its
shall not be necessary in making proof of this Amendment to produce or account
for more than one such counterpart.

        7.      This Amendment, and the Credit Agreement as amended hereby,
shall be governed by and construed and interpreted in accordance with the laws
of the State of New York.


                  [Remainder of Page Intentionally Left Blank]



                                       2
<PAGE>   3


        IN WITNESS WHEREOF, each of the parties hereto has caused a counterpart
of this Amendment to be duly executed and delivered as of the date first above
written.


BORROWERS:                          NATIONAL MEDICAL CARE, INC.,
                               a Delaware corporation

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               FRESENIUS MEDICAL CARE AG

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               NMC DO BRASIL LTDA.,
                               a Brazil corporation

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               NATIONAL MEDICAL CARE OF SPAIN, S.A.,
                               a Spanish corporation

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               NATIONAL MEDICAL CARE OF TAIWAN, INC.,
                               a Delaware corporation

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               NMC CENTRO MEDICO NACIONAL, LDA.,
                               a Portuguese corporation

                               By
                                 ---------------------------------
                               Name:
                               Title:



<PAGE>   4

                               FRESENIUS MEDICAL CARE ARGENTINA, S.A.,
                               as successor by merger to
                               NMC DE ARGENTINA, S.A.,
                               an Argentine corporation

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               FRESENIUS USA, INC.,
                               a Massachusetts corporation

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               FRESENIUS MEDICAL CARE DEUTSCHLAND GmbH,
                               a German corporation

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               FRESENIUS MEDICAL CARE GROUPE FRANCE
                               (formerly known as Fresenius Groupe France S.A.),
                               a French corporation

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               FRESENIUS MEDICAL CARE HOLDING, S.p.A.,
                               an Italian corporation

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               FRESENIUS MEDICAL CARE ESPANA S.A.,
                               a Spanish corporation

                               By
                                 ---------------------------------
                               Name:
                               Title:



<PAGE>   5

                               FRESENIUS MEDICAL CARE MAGYAROSZA KfG,
                               a Hungarian corporation

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               BIO-MEDICAL APPLICATIONS OF ALABAMA, INC.

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               BIO-MEDICAL APPLICATIONS OF FLORIDA, INC.

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               BIO-MEDICAL APPLICATIONS OF GEORGIA, INC.

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               BIO-MEDICAL APPLICATIONS OF INDIANA, INC.

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               BIO-MEDICAL APPLICATIONS OF KENTUCKY, INC.

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               BIO-MEDICAL APPLICATIONS OF LOUISIANA, INC.

                               By
                                 ---------------------------------
                               Name:
                               Title:



<PAGE>   6


                               BIO-MEDICAL APPLICATIONS OF MARYLAND, INC.

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               BIO-MEDICAL APPLICATIONS OF
                                 MASSACHUSETTS, INC.

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               BIO-MEDICAL APPLICATIONS OF
                                 NORTH CAROLINA, INC.

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               BIO-MEDICAL APPLICATIONS OF OHIO, INC.

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               BIO-MEDICAL APPLICATIONS OF PENNSYLVANIA, INC.

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               BIO-MEDICAL APPLICATIONS OF
                                 SOUTH CAROLINA, INC.

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               BIO-MEDICAL APPLICATIONS OF TEXAS, INC.

                               By
                                 ---------------------------------
                               Name:
                               Title:



<PAGE>   7


                               BIO-MEDICAL APPLICATIONS OF VIRGINIA, INC.

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               LIFECHEM, INC.,
                               a Delaware corporation

                               By
                                 ---------------------------------
                               Name:
                               Title:

GUARANTORS:                    FRESENIUS MEDICAL CARE HOLDINGS, INC.,
                               a New York corporation formerly known as WRG-NY

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               NATIONAL MEDICAL CARE, INC.,
                               a Delaware corporation

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               BIO-MEDICAL APPLICATIONS MANAGEMENT CO.,
                               INC., a Delaware corporation

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               FRESENIUS MEDICAL CARE AG,
                               a German corporation

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               By
                                 ---------------------------------
                               Name:
                               Title:



<PAGE>   8


                               FRESENIUS USA, INC.,
                               a Massachusetts corporation

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               FRESENIUS MEDICAL CARE DEUTSCHLAND
                               GmbH, a German corporation

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               FRESENIUS MEDICAL CARE GROUPE FRANCE, a
                               French corporation (formerly known as
                               Fresenius Groupe France S.A.)

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               FRESENIUS SECURITIES, INC.,
                               a California corporation

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               NEOMEDICA, INC.,
                               a Delaware corporation

                               By
                                 ---------------------------------
                               Name:
                               Title:

                               FMC FINANCE S.A.,
                               a Luxembourg corporation

                               By
                                 ---------------------------------
                               Name:
                               Title:



<PAGE>   9


                               FMC TRUST FINANCE S.a.r.l. LUXEMBOURG,
                               a Luxembourg corporation

                               By
                                 ---------------------------------
                               Name:
                               Title:

PAYING AGENT:                  BANK OF AMERICA, N.A. (formerly known as
                               NationsBank, N.A.), as Paying Agent for and on
                               behalf of the Lenders

                               By
                                 ---------------------------------
                               Name:
                               Title:




<PAGE>   10


                           CONSENT TO AMENDMENT NO. 11


Bank of America, N.A. (formerly known as NationsBank, N.A.),
  as Paying Agent
101 N. Tryon Street, 15th Floor
NC1-001-15-04
Charlotte, North Carolina 28255
Attn:  James D. Young, Agency Services

        Re:     Credit Agreement dated as of September 27, 1996 (as amended and
                modified, the "Credit Agreement") among National Medical Care,
                Inc., the other Borrowers, Guarantors and Lenders identified
                therein and NationsBank, N.A. (now known as Bank of America,
                N.A.), as Paying Agent. Terms used but not otherwise defined
                shall have the meanings provided in the Credit Agreement.

                Amendment No. 11 dated May 31, 2001 (the "Subject Amendment")
                relating to the Credit Agreement

Ladies and Gentlemen:

        This should serve to confirm our receipt of, and consent to, the Subject
Amendment. We hereby authorize and direct you, as Paying Agent for the Lenders,
to enter into the Subject Amendment on our behalf in accordance with the terms
of the Credit Agreement upon your receipt of such consent and direction from the
Required Lenders, and agree that Company and the other Credit Parties may rely
on such authorization.


                                            Sincerely,




                                            -----------------------------
                                                   [Name of Lender]


                                            By:
                                               --------------------------
                                            Name:
                                            Title: