FORM OF WARRANT

Exhibit 10.12

FORM OF WARRANT

THESE SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED. THEY MAY NOT BE SOLD, OFFERED FOR SALE, PLEDGED, HYPOTHECATED OR OTHERWISE TRANSFERRED EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT AS TO THE SECURITIES UNDER SAID ACT OR, IF REQUESTED BY THE COMPANY, AN OPINION OF COUNSEL SATISFACTORY TO THE COMPANY THAT SUCH REGISTRATION IS NOT REQUIRED.

BIOCARDIA, INC.

WARRANT TO PURCHASE SHARES

This Warrant is issued to                                          by BioCardia, Inc., a Delaware corporation (the “Company”), pursuant to the terms of that certain Note and Warrant Subscription Agreement (the “Agreement”) of even date herewith, in connection with the Company’s issuance of a Convertible Promissory Note (the “Note”) to the original holder of this Warrant.

1. Purchase of Next Securities. Subject to the terms and conditions hereinafter set forth and set forth in the Agreement, the holder of this Warrant is entitled, upon surrender of this Warrant at the principal office of the Company (or at such other place as the Company shall notify the holder hereof in writing), to purchase from the Company up to the number of fully paid and nonassessable Next Securities (as defined below), that equals the quotient obtained by dividing (a) the Warrant Coverage Amount (as defined below) by (b) the Exercise Price (as defined below).

2. Definitions.

(a) Change of Control. The term “Change of Control” shall mean (i) any consolidation or merger involving the Company pursuant to which the Company’s stockholders own less than fifty percent (50%) of the voting securities of the surviving entity (other than pursuant to an equity financing transaction) or (ii) the sale of all or substantially all of the assets of the Company.

(b) Exercise Price. The exercise price for the Warrant Stock (as defined below) shall be the price per share of equity securities sold to investors in a Next Financing (such price, as adjusted from time to time, is herein referred to as the “Exercise Price”).

(c) Exercise Period. This Warrant shall be exercisable, in whole or in part, during the term commencing on the closing date of a Next Financing (as defined below) and ending on the expiration of this Warrant pursuant to Section 12 hereof.

(d) Next Financing. The term “Next Financing” shall mean the next equity financing transaction or series of related transactions involving aggregate gross proceeds to the Company of at least $4,000,000 (or any lesser amount if consented to in writing by the Company and the holders of a majority of the then outstanding principal amount of the Notes (as defined in the Agreement)) excluding amounts received pursuant to the conversion of any outstanding Notes.

(e) Next Securities. The term “Next Securities” shall mean the class and series of capital stock issued to investors in a Next Financing.

(f) Warrant Coverage Amount. The term “Warrant Coverage Amount” shall mean that amount which equals (a) 15% multiplied by (b) the principal amount of the Note.

(g) Warrant Stock. The term “Warrant Stock” shall mean the Next Securities for which this Warrant is exercisable or exercised.

3. Method of Exercise. While this Warrant remains outstanding and exercisable in accordance with Section 2 above, the holder may exercise, in whole or in part, the purchase rights evidenced hereby. Such exercise shall be effected by:

(i) the surrender of the Warrant, together with a notice of exercise to the Secretary of the Company at its principal offices; and

(ii) the payment to the Company of an amount equal to the aggregate Exercise Price for the number of Warrant Stock being purchased.

4. Net Exercise. In lieu of cash exercising this Warrant, the holder of this Warrant may elect to receive shares of Next Securities equal to the value of this Warrant (or the portion thereof being canceled) by surrender of this Warrant at the principal office of the Company together with notice of such election, in which event the Company shall issue to the holder hereof a number of Warrant Stock computed using the following formula:

Where

For purposes of this Section 4, the fair market value of a share of Next Securities shall mean the average of the closing bid and asked prices of the Next Securities quoted in the over-the-counter market in which the Next Securities are traded or the closing price quoted on any exchange on which

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the Next Securities are listed, whichever is applicable, as published in the Western Edition of The Wall Street Journal for the ten (10) trading days prior to the date of determination of fair market value (or such shorter period of time during which such stock was traded over-the-counter or on such exchange). If the Next Securities are not traded on the over-the-counter market or on an exchange, the fair market value shall be the price per share of the Next Securities that the Company could obtain from a willing buyer for Next Securities sold by the Company from authorized but unissued Next Securities, as such prices shall be determined in good faith by the Company’s Board of Directors.

5. Certificates for Warrant Stock. Upon the exercise of the purchase rights evidenced by this Warrant, one or more certificates for the number of Warrant Stock so purchased shall be issued as soon as practicable thereafter, and in any event within thirty (30) days of the delivery of the subscription notice.

6. Issuance of Warrant Stock. The Company covenants that the Warrant Stock, when issued pursuant to the exercise of this Warrant, will be duly and validly issued, fully paid and nonassessable and free from all taxes, liens, and charges with respect to the issuance thereof.

7. Adjustment of Exercise Price and Number of Warrant Stock. The number of and kind of securities purchasable upon exercise of this Warrant and the Exercise Price shall be subject to adjustment from time to time as follows:

(a) Subdivisions, Combinations and Other Issuances. If the Company shall at any time prior to the expiration of this Warrant subdivide the Next Securities, by split-up or otherwise, or combine the Next Securities, or issue additional shares of the Next Securities as a dividend, the number of Next Securities issuable on the exercise of this Warrant shall forthwith be proportionately increased in the case of a subdivision or stock dividend, or proportionately decreased in the case of a combination. Appropriate adjustments shall also be made to the purchase price payable per share, but the aggregate purchase price payable for the total number of Next Securities purchasable under this Warrant (as adjusted) shall remain the same. Any adjustment under this Section 7(a) shall become effective at the close of business on the date the subdivision or combination becomes effective, or as of the record date of such dividend, or in the event that no record date is fixed, upon the making of such dividend.

(b) Reclassification, Reorganization and Consolidation. In case of any reclassification, capital reorganization, or change in the capital stock of the Company (other than as a result of a subdivision, combination, or stock dividend provided for in Section 7(a) above), then the Company shall make appropriate provision so that the holder of this Warrant shall have the right at any time prior to the expiration of this Warrant to purchase, at a total price equal to that payable upon the exercise of this Warrant, the kind and amount of shares of stock and other securities and property receivable in connection with such reclassification, reorganization, or change by a holder of the same number of Next Securities as were purchasable by the holder of this Warrant immediately prior to such reclassification, reorganization, or change. In any such case appropriate provisions shall be made with respect to the rights and interest of the holder of this Warrant so that the provisions hereof shall thereafter be applicable with respect to any shares of stock or other securities and property deliverable upon exercise hereof, and appropriate adjustments shall be made to the purchase price per share payable hereunder, provided the aggregate purchase price shall remain the same.

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(c) Notice of Adjustment. When any adjustment is required to be made in the number or kind of shares purchasable upon exercise of the Warrant, or in the Exercise Price, the Company shall promptly notify the holder of such event and of the number of Next Securities or other securities or property thereafter purchasable upon exercise of this Warrant.

8. No Fractional Shares or Scrip. No fractional shares or scrip representing fractional shares shall be issued upon the exercise of this Warrant, but in lieu of such fractional shares the Company shall make a cash payment therefor on the basis of the Exercise Price then in effect.

9. Representations of the Company. The Company represents that all corporate actions on the part of the Company, its officers, directors and stockholders necessary for the sale and issuance of this Warrant have been taken.

10. Representations and Warranties by the Holder. The holder of this Warrant (“Holder”) represents and warrants to the Company as follows:

(a) This Warrant and the Warrant Stock issuable upon exercise thereof are being acquired for its own account, for investment and not with a view to, or for resale in connection with, any distribution or public offering thereof within the meaning of the Securities Act of 1933, as amended (the “Act”). Upon exercise of this Warrant, the Holder shall, if so requested by the Company, confirm in writing, in a form satisfactory to the Company, that the securities issuable upon exercise of this Warrant are being acquired for investment and not with a view toward distribution or resale.

(b) The Holder understands that the Warrant and the Warrant Stock have not been registered under the Act by reason of their issuance in a transaction exempt from the registration and prospectus delivery requirements of the Act pursuant to Section 4(2) thereof, and that they must be held by the Holder indefinitely, and that the Holder must therefore bear the economic risk of such investment indefinitely, unless a subsequent disposition thereof is registered under the Act or is exempted from such registration. The Holder further understands that the Warrant Stock have not been qualified under the California Securities Law of 1968 (the “California Law”) by reason of their issuance in a transaction exempt from the qualification requirements of the California Law pursuant to Section 25102(f) thereof, which exemption depends upon, among other things, the bona fide nature of the holder of this Warrant’s investment intent expressed above.

(c) The Holder has such knowledge and experience in financial and business matters that it is capable of evaluating the merits and risks of the purchase of this Warrant and the Warrant Stock purchasable pursuant to the terms of this Warrant and of protecting its interests in connection therewith.

(d) The Holder is able to bear the economic risk of the purchase of the Warrant Stock pursuant to the terms of this Warrant.

(e) The Holder is an “accredited investor” as such term is defined in Rule 501 of Regulation D promulgated under the Act.

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11. Rights of Stockholders. No holder of this Warrant shall be entitled, as a Warrant holder, to vote or receive dividends or be deemed the holder of the Next Securities or any other securities of the Company which may at any time be issuable on the exercise hereof for any purpose, nor shall anything contained herein be construed to confer upon the holder of this Warrant, as such, any of the rights of a stockholder of the Company or any right to vote for the election of directors or upon any matter submitted to stockholders at any meeting thereof, or to give or withhold consent to any corporate action (whether upon any recapitalization, issuance of stock, reclassification of stock, change of par value, consolidation, merger, conveyance, or otherwise) or to receive notice of meetings, or to receive dividends or subscription rights or otherwise until the Warrant shall have been exercised and the Warrant Stock purchasable upon the exercise hereof shall have become deliverable, as provided herein.

12. Expiration of Warrant; Notice of Certain Events Terminating This Warrant.

(a) This Warrant shall expire and shall no longer be exercisable upon the earlier to occur of:

(i) 5:00 p.m., California local time, on [            ], 2017;

(ii) Any Change of Control; or

(iii) The initial public offering of the Company’s Common Stock.

(b) The Company shall provide at least ten (10) days prior written notice of any event set forth in Section 12(a)(ii).

13. Notices. All notices and other communications required or permitted hereunder shall be in writing, shall be effective when given, and shall in any event be deemed to be given upon receipt or, if earlier, (a) five (5) days after deposit with the U.S. Postal Service or other applicable postal service, if delivered by first class mail, postage prepaid, (b) upon delivery, if delivered by hand, (c) one business day after the business day of deposit with Federal Express or similar overnight courier, freight prepaid or (d) one business day after the business day of facsimile transmission, if delivered by facsimile transmission with copy by first class mail, postage prepaid, and shall be addressed (i) if to the holder, at the holder’s address as set forth on the Agreement, and (ii) if to the Company, at the address of its principal corporate offices (Attention: President), with a copy to Wilson Sonsini Goodrich & Rosati, P.C., 650 Page Mill Road, Palo Alto, California 94304, or at such other address as a party may designate by ten (10) days advance written notice to the other party pursuant to the provisions above.

(a) “Market Stand-Off” Agreement. The holder hereby agrees that, if so requested by the Company or any representative of the underwriters in connection with any registration of the offering of any securities of the Company under the Act, the holder shall (i) not sell or otherwise transfer any securities held by the holder during the 180-day period (or such other period as may be requested in writing by the underwriter and agreed to in writing by the Company) (the “Market

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Standoff Period”) following the effective date of a registration statement of the Company filed under the Act, and (ii) execute any agreement reflecting (i) above as may be requested by the underwriters at the time of such offering; provided, however, that such one hundred eighty (180) day period may be extended to the extent necessary to permit any managing underwriter to comply with FINRA Rule 2711(f) or NYSE Rule 472(f)(4) or any successor provisions or amendments thereto. Such restriction shall apply only to the first registration statement of the Company to become effective under the Act that includes securities to be sold on behalf of the Company to the public in an underwritten public offering under the Act. The Company may impose stop-transfer instructions with respect to securities subject to the foregoing restrictions until the end of the Market Standoff Period.

14. Amendments. Except as otherwise set forth in the Agreement, any term of this Warrant may be amended and the observance of any term of this Warrant may be waived (either generally or in a particular instance and either retroactively or prospectively) with the written consent of the Company and the holders of a majority of the Warrant Stock exercisable pursuant to the then outstanding Warrants (as defined in the Agreement); provided, however, that any amendment or waiver that has the effect of increasing the obligations of any of the holders of the Warrants shall require the prior written consent of such affected holder; and, provided, further, that any amendment to a Warrant shall only be made if such amendment is made to all the Warrants.

15. Governing Law. This Warrant 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.

16. Rights and Obligations Survive Exercise of Warrant. Unless otherwise provided herein, the rights and obligations of the Company, of the holder of this Warrant and of the holder of the Warrant Stock issued upon exercise of this Warrant, shall survive the exercise of this Warrant.

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The Company issues this Warrant to Purchase Shares as of the date stated on the first page.

BioCardia, Inc. Signature Page to Warrant to Purchase Shares

EXHIBIT A TO WARRANT TO PURCHASE SHARES

NOTICE OF EXERCISE

1. The undersigned hereby elects to purchase                      shares of                      pursuant to the terms of the attached Warrant.

2. Method of Exercise (Please initial the applicable blank):

3. Please issue a certificate or certificates representing said shares in the name of the undersigned or in such other name as is specified below:

4. The undersigned hereby represents and warrants that the aforesaid shares are being acquired for the account of the undersigned for investment and not with a view to, or for resale, in connection with the distribution thereof, and that the undersigned has no present intention of distributing or reselling such shares and all representations and warranties of the undersigned set forth in Section 10 of the attached Warrant are true and correct as of the date hereof.