Exhibit 10.77

AMENDMENT NO. 3 TO

DEVELOPMENT AND SUPPLY AGREEMENT

This Amendment No. 3 to Development and Supply Agreement (this “Amendment”) is entered into as of May 18, 2011, by and between Luna Innovations Incorporated, a Delaware corporation, together with Luna Technologies, Inc., a Delaware corporation (acting jointly and severally, individually and collectively, “Luna”), and Hansen Medical, Inc., a Delaware corporation (“Hansen”).

RECITALS

WHEREAS, Luna and Hansen are parties to that certain Development and Supply Agreement having an effective date of January 12, 2010 and amended by Amendment Nos. 1 and 2 to Development and Supply Agreement dated as of February 17, 2010 and April 2, 2010, respectively (collectively, the “Agreement”);

WHEREAS, Luna and Hansen desire to amend and restate Exhibits A and B of the Agreement to amend certain existing Specifications and estimated budget amounts (for Development Milestones [***]) and add new Development Milestones ([***]) and Specifications therefor;

WHEREAS, Luna and Hansen desire to deem Development Milestone [***] (“[***]”) to have been successfully achieved;

WHEREAS, Luna and Hansen desire to amend the Agreement to provide for a payment structure whereby Luna shares [***]% of the Development Fees up to a certain amount and to change the mechanism for calculating the Holdback Amount as a result;

WHEREAS, Luna and Hansen desire to amend the Agreement to lower the discount on the Commercial Transfer Price from [***]% to [***]% and to increase the limit on the Commercial Transfer Price per unit with respect to the Interrogators part of the Luna Product from $[***] to $[***] (until [***] units have been purchased);

WHEREAS, as Luna expects to refinance its existing credit facility with Silicon Valley Bank on or prior to May 18, 2011, Luna and Hansen also desire to agree, pursuant to the separate Amendment to Secured Promissory Note and Payoff Letter (“Amendment and Payoff Letter”) entered into by the Parties contemporaneously with this Amendment, to a discount on the Promissory Note of $190,000 in connection with Luna paying it off within five (5) business days of the date hereof, and this Amendment is contingent upon Luna and Hansen entering into the Amendment and Payoff Letter and Luna making the payments to Hansen set forth therein.

NOW, THEREFORE, for good and valuable consideration, receipt of which is hereby acknowledged, Luna and Hansen hereby agree to the following terms and conditions and to amend the Agreement as follows:

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AMENDMENT AND AGREEMENT

1. Definitions. Except as otherwise provided herein, capitalized terms used in this Amendment shall have the definitions set forth in the Agreement.

2. Amendment and Restatements of Exhibits A and B. Exhibits A and B of the Agreement are hereby amended and restated and replaced in their entirety by the exhibits attached hereto as Exhibits A and B, respectively.

3. [***] Achievement. The Parties hereby deem [***] to have been successfully achieved as of March 31, 2011, with any otherwise applicable penalties in respect of [***] deemed waived, and the related [***] Amount of [***] shall be due and payable within thirty (30) days after the effective date of this Amendment.

4. Amendment to Section 4.1 of the Agreement regarding Payment and the Holdback Amount. Section 4.1 of the Agreement shall be amended as follows:

(a) Section 4.1.1 ([***] Fees) of the Agreement shall be replaced in its entirety with the following:

[***] Fees. [***]

(b) The second sentence of Section 4.1.2 (Invoicing and Payment) of the Agreement shall be replaced in its entirety with the following:

[***]

(c) The second-to-last sentence of Section 4.1.3 ([***]) of the Agreement shall be replaced in its entirety with the following:

[***]

5. Commercial Transfer Price. Section 3.3.2 (Commercial Transfer Price) of the Agreement shall be amended as follows:

(a) The second sentence of Section 3.3.2 (Commercial Transfer Price) of the Agreement shall be replaced in its entirety with the following:

[***]

(b) Clause (a) in the proviso at the end of the last sentence of Section 3.3.2 (Commercial Transfer Price) of the Agreement shall be replaced in its entirety with the following:

[***], and

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6. Manufacturing Technology Transfer. Section 3.7(c) of the Agreement shall be replaced in its entirety with the following:

(c)[***],

7. Discount to Promissory Note. Pursuant to the Amendment and Payoff Letter, Hansen intends to provide Luna with a $190,000 discount against the outstanding principal balance and accrued interest on the Promissory Note. This Amendment is contingent upon Luna paying in full such discounted balance and accrued interest in accordance with the terms of the Amendment and Payoff Letter. If Luna does not pay in full such amounts in accordance therewith, this Amendment shall, without further action by the Parties, automatically terminate and be deemed null and void and of no force and effect.

8. Terms and Conditions of Agreement. Except as expressly modified hereby, all terms, conditions and provisions of the Agreement shall continue in full force and effect.

9. Conflicting Terms. In the event of any inconsistency or conflict between the Agreement and this Amendment, the terms, conditions and provisions of this Amendment shall govern and control.

10. Term and Termination. This Amendment shall become effective upon its execution by each of Luna and Hansen and shall continue unless terminated as set forth in Section 6 of this Amendment.

11. Entire Agreement. This Amendment and the Agreement constitute the entire and exclusive agreement between the Parties with respect to this subject matter. All previous discussions and agreements with respect to this subject matter are superseded by the Agreement and this Amendment. This Amendment may be executed in one or more counterparts, each of which shall be an original and all of which taken together shall constitute one and the same instrument.

[Signature Page to Follow]

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IN WITNESS WHEREOF, the Parties have caused this Amendment to be executed by their duly authorized representatives as of the date first listed above.

SIGNATURE PAGE TO AMENDMENT NO. 3 TO DEVELOPMENT AND SUPPLY AGREEMENT

Exhibit A

Development Milestones

[***]

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Exhibit B

Development Plan

[***]

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