Supplement No. 2 dated as of October 27, 2011, to the Amended and Restated Security Agreement dated as of March 2, 2009, as supplemented, by and among the subsidiary grantor named therein and Bank of America, N.A., as collateral agent

Exhibit 4.5(b)

SUPPLEMENT NO. 2 dated as of October 27, 2011, to the Amended and Restated Security Agreement dated as of March 2, 2009, as Supplemented by Supplement No. 1, dated as of March 4, 2010 (as supplemented, the “Security Agreement”) among HCA INC., a Delaware corporation (the “Company”), each Subsidiary of the Company listed on Schedule A thereto (each such subsidiary individually a “Subsidiary Grantor” and, collectively, the “Subsidiary Grantors”; the Subsidiary Grantors and the Company are referred to collectively herein as the “Grantors”), BANK OF AMERICA, N.A., as Collateral Agent (in such capacity, the “Collateral Agent”) for the benefit of the First Lien Secured Parties.

A. Reference is made to the Credit Agreement, dated as of November 17, 2006 and as amended and restated as of May 4, 2011, among the Company, HCA UK Capital Limited, a limited liability company (company no. 04779021) formed under the laws of England and Wales (the “European Subsidiary Borrower” and together with the Company, the “Borrowers”), the lending institutions from time to time parties thereto (the “Lenders”) and Bank of America N.A., as Administrative Agent, Swingline Lender and Letter of Credit Issuer (as the same may be further amended, restated, supplemented or otherwise modified, refinanced or replaced from time to time, the “Credit Agreement”).

B. Capitalized terms used herein and not otherwise defined herein shall have the meanings assigned to such terms in the Credit Agreement and Security Agreement, as applicable.

C. The Grantors have entered into the Security Agreement in order to induce the Administrative Agent, the Collateral Agent, the Lenders and the Letter of Credit Issuer to enter into the Credit Agreement and to induce the respective Lenders and the Letter of Credit Issuer to make their respective Extensions of Credit to the Borrowers under the Credit Agreement and to induce one or more Cash Management Banks or Hedge Banks to enter into Secured Cash Management Agreements and Secured Hedge Agreements with the Company and/or its Subsidiaries and to induce the holders of any Additional First Lien Obligations to make their respective Extensions of Credit thereunder.

D. Section 9.11 of the Credit Agreement and/or the equivalent provision of any other Additional First Lien Agreement and Section 8.13 of the Security Agreement provide that each Subsidiary of the Company that is required to become a party to the Security Agreement pursuant to Section 9.11 of the Credit Agreement and/or any equivalent provision of any other Additional First Lien Agreement shall become a Grantor, with the same force and effect as if originally named as a Grantor therein, for all purposes of the Security Agreement upon execution and delivery by such Subsidiary of an instrument in the form of this Supplement. The undersigned Subsidiary (the “New Grantor”) is executing this Supplement in accordance with the requirements of the Security Agreement to become a Subsidiary Grantor under the Security Agreement in order to induce the Lenders and the Letter of Credit Issuer to make additional Extensions of Credit and as consideration for Extensions of Credit previously made and to induce the holders of any Additional First Lien Obligations to extend credit thereunder and as consideration for Extensions of Credit previously made.

Accordingly, the Collateral Agent and the New Grantor agree as follows:

SECTION 1. In accordance with subsection 8.13 of the Security Agreement, the New Grantor by its signature below becomes a Grantor under the Security Agreement with the same force and effect as if originally named therein as a Grantor and the New Grantor hereby (a) agrees to all the terms and provisions of the Security Agreement applicable to it as a Grantor thereunder and (b) represents and warrants that the representations and warranties made by it as a Grantor thereunder are true and correct on and as of the date hereof. In furtherance of the foregoing, the New Grantor, as security for the payment

and performance in full of the First Lien Obligations, does hereby bargain, sell, convey, assign, set over, mortgage, pledge, hypothecate and transfer to the Collateral Agent for the benefit of the First Lien Secured Parties, and hereby grants to the Collateral Agent for the benefit of the First Lien Secured Parties, a Security Interest in all of the Collateral of the New Grantor, in each case whether now or hereafter existing or in which it now has or hereafter acquires an interest. Each reference to a “Grantor” in the Security Agreement shall be deemed to include the New Grantor. The Security Agreement is hereby incorporated herein by reference.

SECTION 2. The New Grantor represents and warrants to the Collateral Agent and the other First Lien Secured Parties that this Supplement has been duly authorized, executed and delivered by it and constitutes its legal, valid and binding obligation, enforceable against it in accordance with its terms.

SECTION 3. This Supplement may be executed by one or more of the parties to this Supplement on any number of separate counterparts (including by facsimile or other electronic transmission), and all of said counterparts taken together shall be deemed to constitute one and the same instrument. A set of the copies of this Supplement signed by all the parties shall be lodged with the Collateral Agent and the Company. This Supplement shall become effective as to the New Grantor when the Collateral Agent shall have received counterparts of this Supplement that, when taken together, bear the signatures of the New Grantor and the Collateral Agent.

SECTION 4. The New Grantor hereby represents and warrants that (a) set forth on Schedule I hereto is (i) the legal name of the New Grantor, (ii) the jurisdiction of incorporation or organization of the New Grantor, (iii) the mailing address for the New Grantor, (iv) the identity or type of organization or corporate structure of the New Grantor and (v) the Federal Taxpayer Identification Number and organizational number of the New Grantor and (b) as of the date hereof (i) Schedule II hereto sets forth, in all material respects, all of the New Grantor’s Copyright Licenses, (ii) Schedule III hereto sets forth in all material respects, in proper form for filing with the United States Copyright Office, all of the New Grantor’s Copyrights (and all applications therefor), (iii) Schedule IV hereto sets forth in all material respects all of the New Grantor’s Patent Licenses, (iv) Schedule V hereto sets forth in all material respects, in proper form for filing with the United States Patent and Trademark Office, all of the New Grantor’s Patents (and all applications therefor), (v) Schedule VI hereto sets forth in all material respects all of the New Grantor’s Trademark Licenses and (vi) Schedule VII hereto sets forth in all material respects, in proper form for filing with the United States Patent and Trademark Office, all of the New Grantor’s Trademarks (and all applications therefor).

SECTION 5. Except as expressly supplemented hereby, the Security Agreement shall remain in full force and effect.

SECTION 6. THIS SUPPLEMENT AND THE RIGHTS AND OBLIGATIONS OF THE PARTIES HEREUNDER SHALL BE GOVERNED BY, AND CONSTRUED AND INTERPRETED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.

SECTION 7. Any provision of this Supplement that is prohibited or unenforceable in any jurisdiction shall, as to such jurisdiction, be ineffective to the extent of such prohibition or unenforceability without invalidating the remaining provisions hereof and in the Security Agreement, and any such prohibition or unenforceability in any jurisdiction shall not invalidate or render unenforceable such provision in any other jurisdiction. The parties hereto shall endeavor in good faith negotiations to replace the invalid, illegal or unenforceable provisions with valid provisions the economic effect of which comes as close as possible to that of the invalid, illegal or unenforceable provisions.

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SECTION 8. All notices, requests and demands pursuant hereto shall be made in accordance with Section 14.2 of the Credit Agreement (whether or not then in effect). All communications and notices hereunder to any Subsidiary Grantor shall he given to it in care of the Company at the Company’s address set forth in Section 14.2 of the Credit Agreement (whether or not then in effect) and all notices to any holder of obligations under any Additional First Lien Agreements, at its address set forth in the Additional First Lien Secured Party Consent, as such address may be changed by written notice to the Collateral Agent and the Company.

IN WITNESS WHEREOF, the New Grantor and the Collateral Agent have duly executed this Supplement to the Security Agreement as of the day and year first above written.

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SCHEDULE I

TO SUPPLEMENT NO. 2 TO THE

SECURITY AGREEMENT

COLLATERAL

S-I

SCHEDULE II

TO SUPPLEMENT NO. 2 TO THE

SECURITY AGREEMENT

COPYRIGHT LICENSES

None.

S-II

SCHEDULE III

TO SUPPLEMENT NO. 2 TO THE

SECURITY AGREEMENT

COPYRIGHTS

S-III

SCHEDULE IV

TO SUPPLEMENT NO. 2 TO THE

SECURITY AGREEMENT

PATENT LICENSES

None.

S-IV

SCHEDULE V

TO SUPPLEMENT NO. 2 TO THE

SECURITY AGREEMENT

PATENTS

None.

S-V

SCHEDULE VI

TO SUPPLEMENT NO. 2 TO THE

SECURITY AGREEMENT

TRADEMARK LICENSES

None.

S-VI

SCHEDULE VII

TO SUPPLEMENT NO. 2 TO THE

SECURITY AGREEMENT

TRADEMARK LICENSES

U.S. Trademark Registrations and Applications

S-VII