PARTNERSHIP INTEREST PURCHASE AGREEMENT

Exhibit 10.4

PARTNERSHIP INTEREST PURCHASE AGREEMENT

THIS PARTNERSHIP INTEREST PURCHASE AGREEMENT (this “Agreement”), effective as of this 1st day of January, 2007 (the “Effective Date”, is entered into by and between U.S. Lithotripsy, a Texas limited partnership (“USL”) and Dr. Paul Thompson (“Seller”).

RECITALS

A. USL is a Texas limited partnership that develops lithotripsy equipment and related service ventures nationally.

B. Seller owns a 13.36 % interest in USL (the “Seller’s Interest”).

C. Seller desires to sell to USL, and USL desires to purchase from Seller, all of the Seller’s Interest, pursuant to the terms and conditions set forth herein and in the Limited Partnership Agreement of USL (the “Partnership Agreement”).

NOW THEREFORE, for and in consideration of the mutual representations and agreements hereinafter contained, the parties hereto do hereby contract and agree on the following terms:

1. Purchase of Limited Partnership Interest. Upon the satisfaction of the conditions stated herein, Seller hereby agrees to sell to USL, and USL hereby agrees to purchase from Seller, all of the Seller’s Interest.

2. Representations and Warranties of USL. Seller hereby represents and warrants to USL that:

(a) Seller is transferring to USL a 13.36 % partnership interest in USL as of the Closing Date;

(b) Subject to the restrictions set forth in the Partnership Agreement, Seller has the absolute and unrestricted right, power, authority and capacity to sell, assign, transfer and deliver the Seller’s Interest to USL hereunder;

(c) Subject to the restrictions set forth in the Partnership Agreement, Seller has the absolute and unrestricted right, power, authority and capacity to enter into this Agreement without the joinder of any other party;

(d) Subject to the restrictions set forth in the Partnership Agreement, this Agreement and all other agreements and instruments to be executed by Seller on or before the Closing Date (as defined below) pursuant hereto are valid and binding upon Seller and enforceable against the same in accordance with there respective terms;

(e) All necessary actions have been taken by Seller to ensure that the execution, delivery and performance by Seller of this Agreement and the consummation of the contemplated transactions have been duly authorized by Seller and Seller agrees to execute such further consents and approvals as may be reasonably requested to approve this transaction. This Agreement and all other agreements and instruments to be executed by Seller on or before the

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Closing Date (as defined below) pursuant hereto shall be duly executed and delivered by Seller and, assuming due execution by Seller, shall constitute the legal and binding obligation of Seller, enforceable against Seller in accordance with its terms; and

(f) To the best of Seller’s knowledge, neither this Agreement nor any of the exhibits, attachments, written statements, documents, certificates or other items prepared for or supplied to USL by or on behalf of Seller with respect to the transactions contemplated hereby contains any untrue statement of a material fact or omits a material fact necessary to make each statement contained herein or therein not misleading.

3. Representations and Warranties of USL. USL, by executing a copy of this Agreement, shall represent and warrant to Seller that, as of the Closing Date:

(a) USL has all requisite power and authority to execute, deliver and perform this Agreement and all agreements and instruments to be executed by it on or before the Closing Date pursuant hereto and to consummate the transactions contemplated hereby;

(b) USL is purchasing and receiving what is intended to be a 13.36% partnership interest in USL as of the Closing Date;

(c) USL has the absolute and unrestricted right, power, authority and capacity to enter into this Agreement;

(d) This Agreement and all other agreements and instruments to be executed by USL on or before the Closing Date (as defined below) pursuant hereto are valid and binding upon USL and enforceable against it in accordance with their respective terms;

(e) All necessary actions have been taken by USL to ensure that the execution, delivery and performance by it of this Agreement and the consummation of the contemplated transactions have been duly authorized by USL and USL agrees to execute such further consents and approvals as may be reasonably requested to approve this transaction. This Agreement and all other agreements and instruments to be executed by USL on or before the Closing Date (as defined below) pursuant hereto shall be duly executed and delivered by USL and, assuming due execution by Seller, shall constitute the legal and binding obligation of USL enforceable against it in accordance with its terms; and

(f) To the best of USL’s knowledge, neither this Agreement nor any of the exhibits, attachments, written statements, documents, certificates or other items prepared for or supplied to Seller by or on behalf of USL with respect to the transactions contemplated hereby contains any untrue statement of a material fact or omits a material fact necessary to make each statement contained herein or therein not misleading;

4. Purchase Price and Manner of Payment for Partnership Interest.

(a) The total aggregate purchase price to be paid by USL to Seller for the purchase of the Seller’s Interest (hereinafter referred to as the “Purchase Price”) shall be a fully executed and notarized note payable from USL to Seller in the amount of $2,474,074 in the form attached hereto as Exhibit A, to be delivered on or before the Closing (the “Note”), providing for payments to be made from USL to Seller as provided in the Note.

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(b) In order to evidence the transfer of the Seller’s Interest by Seller to USL, Seller hereby agrees, at the time of Closing, to execute an Assignment of Partnership Interest (hereinafter referred to as “Seller’s Assignment”) in the form of attached hereto as Exhibit B and incorporated herein by reference, assigning the Seller’s Interest to USL.

(c) In the event a payment required under the Note is not timely paid by USL, and remains unpaid more than thirty (30) days after Seller has provided USL of written notice of such non-payment, then USL shall be in “Payment Default” of this Agreement. In the event a USL is in Payment Default under this Agreement, then Seller’s Interest shall automatically revert back to Seller in its entirety, and, at the request of Seller, USL shall take such actions as shall be required under this Agreement and the Partnership Agreement to memorialize and agree to the transfer from USL to Seller the Partnership Interest transferred to Purchaser pursuant to this Agreement. This transfer is in addition to any other remedies provided in the Note or at law in connection with USL’s Payment Default. The transfer of Seller’s Interest pursuant to this Section 4(c) shall be deemed a default in the purchase of Seller’s Interest hereunder. The parties understand and agree that for so long as USL has any indebtedness payable to Bank of Texas, N.A. the contingent reversion of Seller’s Interest to Seller provided for under this section 4(c) shall occur only with the express written consent of Bank of Texas, N.A.

5. Conditions to Seller’s Obligation to Sell. The obligation of Seller hereunder to sell the Seller’s Interest to USL on the Closing Date is subject to the satisfaction, or waiver by USL, on or before the Closing Date, of each of the following conditions:

(a) USL shall have delivered to Seller an executed Note set forth in Section 4(a) above, which documents comprise the Purchase Price;

(b) All the representations and warranties of USL contained herein shall be true and correct on the Closing Date with the same force and effect as if made on and as of the Closing Date;

(c) USL shall have performed, satisfied and complied in all material respects with the covenants, agreements and conditions required by this Agreement to be performed, satisfied or complied with by USL on or prior to the Closing Date; and

(d) No statute, rule, regulation, executive order, decree, ruling or injunction shall have been enacted, entered, promulgated or endorsed by any court or governmental authority of competent jurisdiction or any self-regulatory organization having authority over the matters contemplated hereby which prohibits the consummation of any of the transactions contemplated by this Agreement.

6. Conditions to USL’s Obligation to Purchase. The obligation of USL to purchase Seller’s Interest on the Closing Date is subject to the satisfaction, or waiver by USL, on or before the Closing Date, of each of the following conditions:

(a) Seller shall have delivered to USL a duly executed Seller’s Assignment;

(b) All the representations and warranties of Seller contained herein shall be true and correct on the Closing Date with the same force and effect as if made on and as of the Closing Date;

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(c) Seller shall have performed, satisfied and complied in all material respects with the covenants, agreements and conditions required by this Agreement to be performed, satisfied or complied with by Seller on or prior to the Closing Date; and

(d) No statute, rule, regulation, executive order, decree, ruling or injunction shall have been enacted, entered, promulgated or endorsed by any account or governmental authority of competent jurisdiction or any self-regulatory organization having authority over the matters contemplated hereby which prohibits the consummation of any of the transactions contemplated by this Agreement.

7. USL Deliverables. At the time of the Closing of the transaction contemplated by this Agreement, USL shall deliver to Seller the following items:

(a) the Purchase Price;

(b) two (2) fully executed originals of this Agreement executed by USL; and

(c) such other instruments Seller has deemed necessary or advisable.

8. Seller’s Deliverables. At the time of the Closing of the transaction contemplated by this Agreement, Seller shall deliver to USL the following items:

(a) a fully executed original of Seller’s Assignment;

(b) two (2) fully executed originals of this Agreement;

(c) such other instruments of conveyance and transfer, in a form satisfactory to USL, as shall be reasonably required to vest-in USL good and enforceable title in and to Seller’s Interest.

9. Closing. The closing of the transactions described herein shall take place on or before January 1, 2007, at a time and place to be agreed upon by the parties (such date hereinafter referred to as the “Closing” or “Closing Date”); provided, however, that upon written consent of the parties, the Closing Date may be extended. Absent a written agreement extending this Agreement, in the event any party has not performed its conditions prerequisite to this Agreement or is unable to make the representations required of such party as of the Closing Date, this Agreement shall terminate on the Closing Date with respect to all parties hereto, with no further obligation required of any party hereto.

10. Non-Competition. As additional consideration for the Purchase Price paid by Buyer hereunder, and in order that USL may enjoy the benefits of this Agreement, for a period of two years from the Closing Date, Seller shall not, directly or indirectly, directly or indirectly, as an employee, employer, contractor, consultant, agent, principal, shareholder, corporate officer, director, or in any other individual or representative capacity, engage or participate in any business or practice within a fifteen (15) mile radius of any location in which any entity in which USL or an Affiliate of USL possesses an ownership interest provides any professional medical services, supplies, or equipment to health care service providers, that is in competition in any manner whatsoever with USL. Seller further agrees that for this same period of time, Seller shall not use or disclose to any person or entity (except as required by law) any information concerning the names and addresses of USL’s employees, customers, or patients, and shall not,

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on Seller’s behalf or on behalf of any other person or entity, solicit or attempt to induce any partner, employee, customer, or patient of USL to cease such person’s commercial relationship with USL, or otherwise interfere with the relationship between or among USL and its patients, customers, employees and/or partners. This covenant shall be construed as an agreement ancillary to the other provisions of this Agreement. Without limiting other possible remedies to USL for breach of this covenant, Seller agrees that injunctive or other equitable relief will be available to enforce the covenants of this provision, such relief to be without the necessity of posting a bond, cash, or otherwise. Seller further agrees that if any restriction contained in this section 10 is held by any court to be unenforceable or unreasonable, a lesser restriction will be enforced in its place and remaining restrictions contained herein will be enforced independently of each other. Seller agrees to pay USL’s and Seller’s own attorneys’ fees, court costs, and expenses in the event that USL chooses, in its sole discretion, to enforce any provision hereunder.

11. Notices. Any notice required or permitted to be given under this Agreement must be in writing and given either by personal delivery or by mailing the same by registered or certified mail, return receipt requested, to the party to whom the notice is directed at the address of such party provided under such party’s signature to this Agreement, or such other address as the parties may hereinafter designate in writing in accordance herewith:

12. Voidable Clause. In the event any clause or provision of this Agreement shall be invalid or void for any reason, such invalid or void clause or provision shall not affect the whole of this instrument, but the balance of the provisions hereof will remain in full force and effect.

13. Survival. This Agreement and all terms, warranties, representations, conditions and stipulations contained herein shall survive the Closing.

14. Governing Law and Venue. This Agreement shall be governed by the laws of the State of Texas without regard to the principles of conflicts or choice of law embodied therein, and all undertakings hereunder shall be performable in Tarrant County, Texas.

15. Further Assurances. Each party agrees that it will execute and deliver, or cause to be executed and delivered, on or after the date of Closing, all such instruments and will take all such actions as the other party may reasonably request from time to time in order to effectuate the provisions and purposes of this Agreement.

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IN WITNESS WHEREOF, USL and Seller have caused this Agreement to be duly executed to be effective as of the Effective Date.

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EXHIBIT A

PROMISSORY NOTE

FOR VALUE RECEIVED, U.S. Lithotripsy, L.P. (hereinafter “Debtor”) hereby promises to pay to the order of Dr. Paul Thompson (“Payee”) at such place as Payee or its assigns may designate, the principal sum of $2,474,074 or so much thereof as may be advanced in lawful money of the United States of America in immediately available funds, plus accrued interest thereon as described below.

This promissory note is and shall be payable at the times and in the amounts set forth in Exhibit A, attached hereto: provided that upon a Change in Control of U.S. Lithotripsy, L.P., this promissory note shall be immediately due and payable in its entirety on the date the Change in Control occurs. For purposes of this provision, a “Change in Control” shall be deemed to have occurred if (A) a person or group of affiliated persons collectively owning less than 50% of all of U.S. Lithotripsy, L.P.’s outstanding partnership interests as of the date of this promissory note is or becomes the beneficial owner(s), directly or indirectly, of more than 50% of the combined partnership interests of U.S. Lithotripsy, L.P. then outstanding; (B) U.S. Lithotripsy merges or consolidates with any entity other than USMD Inc. in a manner in which U.S. Lithotripsy is not the surviving entity; or (C) the partners of U.S. Lithotripsy, L.P. approve a plan of complete liquidation of U.S. Lithotripsy, L.P. or execute an agreement for the sale or disposition by the partnership of all or substantially all its assets in one transaction or a series of related transactions. Debtor and Payee understand and agree that for so long as USL has any indebtedness payable to Bank of Texas, N.A. this note shall be due and payable in its entirety only with the express written consent of Bank of Texas, N.A.

Interest on the outstanding balance due under this promissory note shall accrue at a rate of interest equal to the lesser of (i) nine percent per annum (9%), or (ii) the maximum rate permitted by applicable law (the “Interest Rate”). In the event any payment required under Exhibit A is not received by the Payee on or before the day on which such payment is due, interest (calculated on the basis of the actual number of days elapsed but computed as if each year consisted of 360 days) shall thereafter accrue on the unpaid principal balance from time to time owing hereon computed from such date until paid in full, at a per annum rate equal to the lesser of (y) the Interest Rate plus one percent (1%) or (z) the maximum rate permitted by applicable law. Thereafter, payments, whether full or partial, will be applied first to accrued interest and then to the reduction of principal. This promissory note may be prepaid at any time, in whole or in part, without penalty, and interest shall immediately cease on any amount so prepaid.

It is expressly provided and stipulated that notwithstanding any provision of this promissory note or any other instrument evidencing or securing the loan herein set forth, in no event shall the aggregate of all interest paid or contracted to be paid to Payee by the undersigned (or any guarantors or endorsers) ever exceed the maximum amount of interest that may lawfully

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be charged the undersigned by Payee on the principal balance of this promissory note from time to time advanced and remaining unpaid.

The undersigned and all endorsers, sureties, and guarantors hereof, as well as all persons to become liable on this promissory note, hereby jointly and severally waive all notice of nonpayment, demands for payment, presentations for payment, notices on intention to acceleration maturity, notices of actual acceleration of maturity, protests, notices of protest, and any other demands or notices of any kind as to this promissory note, diligence in collection hereof and in brining suit hereon, and any notice of, or defense on account of, the extension of time of payment or change in the method of payments, and without further notice hereby consent to any and all renewals and extensions in the time of payment hereof either before or after maturity and the release of any party primarily or secondarily liable hereon. The undersigned agrees that Payee’s acceptance of partial or delinquent payments or failure of Payee to exercise any right or remedy contained herein or in any instrument given as security for the payment of this promissory note shall not be a waiver of any obligation of the undersigned to Payee or constitute waiver of any similar default subsequently occurring.

The undersigned Debtor expressly agrees that in the event of default in the payment of this promissory note, Payee, or the holder hereof may, at is option, without notice of nonpayment, demand for payment, presentment of any kind, all of which are hereby expressly waived, declare the principal of this promissory note and all interest then accrued at once due and payable, and Payee or any other holder hereof may immediately exercise its rights hereunder and under any security documents executed in connection herewith. In the event there is a default under this promissory note, or the same is placed in the hands of an attorney for collection, or suit is brought on same, or the same is collected through any judicial proceeding whatsoever, or if any action of foreclosure be had hereon, then the undersigned agrees and promises to pay to the owner and holder, in addition to the other amounts due hereunder, all costs of court and other collection expenses including an additional sum as a reasonable attorney’s fee of not less than twenty percent (20%) of the unpaid principal and interest then due on the promissory note. Except to the extent that federal law may apply to this transaction, this promissory note shall be governed by Texas law. This promissory note is made and performable in Tarrant County, Texas and the undersigned agrees that venue for any dispute involving this promissory note shall be in a court of competent jurisdiction in Tarrant County, Texas.

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Debtor and Payee understand and acknowledge that all of Debtor’s obligations to make Note payments hereunder are subordinate to all obligations of Debtor to make loan payments under the following written agreements to which Debtor is a party:

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This instrument was acknowledged before me on this         day of                     , 200    , by                             , Authorized Manager of the general partner of U.S. Lithotripsy, on behalf of the aforesaid Debtor.

GIVEN under my hand and seal of office this          day of                     , 200    .

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EXHIBIT B

ASSIGNMENT OF SELLER’S INTEREST

Dr. Paul Thompson (hereafter, the “Assignor”), in consideration of the terms and provisions of the Partnership Interest Purchase Agreement entered into by and between Assignor and U.S. Lithotripsy, L.P. (hereafter, the “Assignee”) and the Purchase Price paid by Assignee to Assigner pursuant thereto, hereby assigns, transfers and conveys to Assignee a 13.36% partnership interest in Assignee.

IN WITNESS WHEREOF, Assignor and Assignee have executed this Assignment in multiple originals effective on January 1, 2007.

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