NEUROSIGMA, INC. COMMON STOCK PURCHASE AGREEMENT

Exhibit 10.21

NEUROSIGMA, INC.

COMMON STOCK PURCHASE AGREEMENT

This Common Stock Purchase Agreement, dated as of October 23, 2012, (this “Agreement”) is entered into by and between NeuroSigma, Inc., a Delaware corporation (the “Company”), and PENSCO Trust Company Custodian FBO Norman E. Witt, Jr. (the “Investor”).

RECITALS

WHEREAS, on the terms and subject to the conditions set forth herein, Investor is willing to purchase from the Company, and the Company is willing to sell to Investor, 190,800 shares of the Company’s Common Stock (the “Shares”) for $522,792.

AGREEMENT

NOW THEREFORE, in consideration of the foregoing, and the representations, warranties, and conditions set forth below, the parties hereto, intending to be legally bound, hereby agree as follows:

1. Sale and Issuance of Shares.

(a) Sale of Shares. At the Closing (as defined below), the Company agrees to issue and sell to Investor, and Investor agrees to purchase, the Shares for $522,792 (the “Purchase Price”).

(b) Delivery. The sale and purchase of the Shares shall take place at a closing (the “Closing”) to be held at such place and time as the Company and Investor may determine (the “Closing Date”). At the Closing, the Company will deliver to Investor a stock certificate representing the Shares against receipt by the Company of the Purchase Price.

2. Representations and Warranties of the Company. The Company represents and warrants to Investor that:

(a) Due Incorporation, Qualification, etc. The Company (i) is a corporation duly incorporated, validly existing and in good standing under the laws of the State of Delaware; (ii) has the power and authority to own, lease and operate its properties and carry on its business as now conducted; and (iii) is qualified to do business and is in good standing as a foreign corporation in the State of California.

(b) Authority. The execution, delivery and performance by the Company of this Agreement and the consummation of the transactions contemplated hereby (i) are within the power of the Company and (ii) have been duly authorized by all necessary corporate action on the part of the Company.

(c) Enforceability. This Agreement has been duly executed and delivered by the Company and constitutes a legal, valid and binding obligation of the Company, enforceable against the Company in accordance with its terms, except as limited by bankruptcy, insolvency or other laws

of general application relating to or affecting the enforcement of creditors’ rights generally and general principles of equity.

3. Representations and Warranties of Investor. Investor represents and warrants to the Company on the date hereof and on the Closing Date:

(a) Binding Obligation. Such Investor has full legal capacity, power and authority to execute and deliver this Agreement and to perform its obligations hereunder. This Agreement is a valid and binding obligation of such Investor, enforceable in accordance with its terms, except as limited by bankruptcy, insolvency or other laws of general application relating to or affecting the enforcement of creditors’ rights generally and general principles of equity.

(b) Securities Law Compliance. Such Investor has been advised that the Shares are characterized as “restricted securities” under the federal securities laws and have not been registered under the Securities Act, or any state securities laws and, therefore, cannot be resold unless they are registered under the Securities Act and applicable state securities laws or unless an exemption from such registration requirements is available. Such Investor is aware that the Company is under no obligation to effect any such registration with respect to the Shares, or to file for or comply with any exemption from registration. Such Investor has not been formed solely for the purpose of making this investment and is purchasing the Shares for its own account for investment, not as a nominee or agent, and not with a view to, or for resale in connection with, any immediate distribution thereof, and that such Investor has no present intention of selling, granting any participation in, or otherwise distributing the same. Such Investor does not have any contract, undertaking, agreement or arrangement with any person to sell, transfer or grant participation to such person or to any third person, with respect to any of the Shares. Such Investor is an investor in securities of companies in the development stage and acknowledges that it has such knowledge and experience in financial and business matters that such Investor is capable of evaluating the merits and risks of such investment, is able to incur a complete loss of such investment and is able to bear the economic risk of such investment for an indefinite period of time. Such Investor is an “accredited investor” as such term is defined in Rule 501 of Regulation D under the Securities Act. The offer to sell the Shares was directly communicated to such Investor by the Company. At no time was such Investor presented with or solicited by any leaflet, advertisement, article, notice or other communication published in any newspaper, magazine, or similar media or broadcast over television or radio, or any other form of general advertising, or solicited or invited to attend a promotional meeting or any seminar or meeting by any general solicitation or general advertising.

(c) Access to Information. Such Investor acknowledges that the Company has given such Investor access to the corporate records and accounts of the Company and to all information in its possession relating to the Company, has made its officers and representatives available for interview by such Investor, and has furnished such Investor with all documents and other information required for such Investor to make an informed decision with respect to the purchase of the Shares.

(d) Brokers or Finders. Such Investor has not engaged any brokers, finders or agents, and the Company has not and will not incur, directly or indirectly, as a result of any action taken by Investor, any liability for brokerage or finders’ fees or agents’ commissions or any similar charges in connection with this Agreement or the Shares.

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4. Conditions to Obligations of Investor. Investor’s obligations at the Closing are subject to the fulfillment, on or prior to the Closing Date, of all of the following conditions, any of which may be waived in whole or in part by such Investor:

(a) Representations and Warranties. The representations and warranties made by the Company in Section 2 hereof shall have been true and correct when made, and shall be true and correct on the Closing Date.

(b) Governmental Approvals and Filings. Except for any notices required or permitted to be filed after the Closing Date with certain federal and state securities commissions, the Company shall have obtained all governmental approvals required in connection with the lawful sale and issuance of the Shares.

(c) Legal Requirements. At the Closing, the sale and issuance by the Company, and the purchase by such Investor, of the Shares shall be legally permitted by all laws and regulations to which such Investor or the Company are subject.

(d) Transaction Documents. The Company shall have duly executed and delivered this Agreement to Investor.

5. Conditions to Obligations of the Company. The Company’s obligation to issue and sell the Shares at the Closing is subject to the fulfillment, on or prior to the Closing Date, of the following conditions, any of which may be waived in whole or in part by the Company:

(a) Representations and Warranties. The representations and warranties made by Investor in Section 3 hereof shall be true and correct in all material respects when made, and shall be true and correct in all material respects on the Closing Date.

(b) Governmental Approvals and Filings. Except for any notices required or permitted to be filed after the Closing Date with certain federal and state securities commissions, the Company shall have obtained all governmental approvals required in connection with the lawful sale and issuance of the Shares.

(c) Legal Requirements. At the Closing, the sale and issuance by the Company, and the purchase by Investor, of the Shares shall be legally permitted by all laws and regulations to which Investor or the Company are subject.

(d) Transaction Documents. Investor shall have duly executed and delivered this Agreement to the Company.

(e) Purchase Price. Investor shall have delivered to the Company the Purchase Price in respect of the Shares.

6. Miscellaneous.

(a) Waivers and Amendments. Any provision of this Agreement may be amended, waived or modified only upon a writing signed by the Company and Investor.

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(b) Lock-Up Agreement. Investor agrees, in connection with the Company’s initial public offering of the Company’s securities, upon request of the Company or the underwriters managing any underwritten offering of the Company’s securities, not to sell, make any short sale of, loan, grant any option for the purchase of, or otherwise dispose of any of the Company’s securities (other than those included in the registration) without the prior written consent of the Company or such underwriters, as the case may be, for such period of time (not to exceed one hundred eighty (180) days) from the effective date of such registration as may be requested by the underwriters; provided however that such 180 day period may be extended to the extent necessary to permit any managing underwriter to comply with NASD Rule 2711(f)(4) or any successor rule thereto. Investor acknowledges that the Company will be caused to be placed on the Shares the following legend:

“THE SECURITIES REPRESENTED HEREBY ARE SUBJECT TO A LOCKUP PERIOD FOLLOWING THE EFFECTIVE DATE OF A REGISTRATION STATEMENT OF THE COMPANY FILED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, AS SET FORTH IN AN AGREEMENT BETWEEN THE ISSUER AND THE ORIGINAL HOLDER OF THESE SECURITIES, A COPY OF WHICH MAY BE OBTAINED AT THE PRINCIPAL OFFICE OF THE ISSUER. SUCH LOCKUP PERIOD IS BINDING ON TRANSFEREES OF THESE SHARES.”

(c) Governing Law. This Agreement and all actions arising out of or in connection with this Agreement shall be governed by and construed in accordance with the laws of the State of California, without regard to the conflicts of law provisions of the State of California or of any other state.

(d) Survival. The representations, warranties, covenants and agreements made herein shall survive the execution and delivery of this Agreement.

(e) Successors and Assigns. Subject to the restrictions on transfer described in Section 6(f) below, the rights and obligations of the Company and Investor shall be binding upon and benefit the successors, assigns, heirs, administrators and transferees of the parties.

(f) Restrictions on Transfer; Legend. Investor will not sell, transfer, pledge or otherwise dispose of or encumber any of the Shares that Investor receives unless and until (i) such shares are subsequently registered under the Securities Act and each applicable state securities law; or (ii) (1) an exemption from such registration is available thereunder, and (2) Investor has notified the Company of the proposed transfer and has furnished the Company with an opinion of counsel, reasonably satisfactory to the Company, that such transfer will not require registration of such shares under the Securities Act. Investor understands that the Company is not obligated, and does not intend, to register any such shares under the Securities Act or any state securities laws. Investor authorizes the Company and its agents to place on the certificates for the Shares a legend stating that such stock has not been registered under the Securities Act or any state securities law and setting forth the aforementioned restrictions on transfer, including the following legend:

“THESE SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933 OR ANY STATE SECURITIES LAWS. THEY MAY NOT BE SOLD, OFFERED FOR SALE, PLEDGED OR HYPOTHECATED IN THE ABSENCE OF A REGISTRATION STATEMENT IN EFFECT WITH

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RESPECT TO SUCH SHARES UNDER THE ACT AND APPLICABLE STATE SECURITIES LAWS OR AN OPINION OF COUNSEL REASONABLY SATISFACTORY IN FORM AND CONTENT TO THE COMPANY THAT SUCH REGISTRATION IS NOT REQUIRED.”

(g) Entire Agreement. This Agreement constitutes and contains the entire agreement between the Company and Investor and supersedes any and all prior agreements, negotiations, correspondence, understandings and communications among the parties, whether written or oral, respecting the subject matter hereof.

(h) Notices. All notices, requests, demands, consents, instructions or other communications required or permitted hereunder shall in writing and faxed, mailed or delivered to each party as follows: (i) if to Investor, at Investor’s address or facsimile number set forth on the signature page hereto, or at such other address as Investor shall have furnished the Company in writing, or (ii) if to the Company, at NeuroSigma, Inc., Attn: Leon Ekchian, 10960 Wilshire Boulevard, Suite 1230, Los Angeles, California 90024, or at such other address or facsimile number as the Company shall have furnished to Investor in writing, with a copy to Dorsey & Whitney LLP, Attn: David Hayes, Esq., 600 Anton Boulevard, Suite 2000, Costa Mesa, California 92626 (Fax: 714 ###-###-####). All such notices and communications will be deemed effectively given the earlier of when received, (ii) when delivered personally, (iii) one business day after being delivered by facsimile (with receipt of appropriate confirmation), (iv) one business day after being deposited with an overnight courier service of recognized standing or (v) four days after being deposited in the U.S. mail, first class with postage prepaid.

(i) Severability of this Agreement. If any provision of this Agreement shall be judicially determined to be invalid, illegal or unenforceable, the validity, legality and enforceability of the remaining provisions shall not in any way be affected or impaired thereby.

(j) Counterparts. This Agreement may be executed in one or more counterparts, each of which will be deemed an original, but all of which together will constitute one and the same agreement. Facsimile copies of signed signature pages will be deemed binding originals.

[Signature Page Follows]

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IN WITNESS WEREOF, the parties have caused this Agreement to be duly executed and delivered by their proper and duly authorized officers as of the date and year first written above.

[Signature page for Common Stock Purchase Agreement]

[Signature page for Common Stock Purchase Agreement]