<PAGE>

                                                                     EXHIBIT 4.5

            THIS WARRANT AND THE SHARES OF COMMON STOCK ISSUABLE UPON EXERCISE
            OF THIS WARRANT HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF
            1933, AS AMENDED, OR ANY STATE SECURITIES LAWS. THIS WARRANT AND THE
            COMMON STOCK ISSUABLE UPON EXERCISE OF THIS WARRANT MAY NOT BE SOLD,
            OFFERED FOR SALE, PLEDGED OR HYPOTHECATED IN THE ABSENCE OF AN
            EFFECTIVE REGISTRATION STATEMENT AS TO THIS WARRANT UNDER SAID ACT
            AND ANY APPLICABLE STATE SECURITIES LAWS OR AN OPINION OF COUNSEL
            REASONABLY SATISFACTORY TO CARDIOGENESIS CORPORATION THAT SUCH
            REGISTRATION IS NOT REQUIRED.

           Right to Purchase up to 2,640,000 Shares of Common Stock of
                            CardioGenesis Corporation
                            -------------------------
                   (subject to adjustment as provided herein)

                          COMMON STOCK PURCHASE WARRANT

No. _________________                             Issue Date:  October 26, 2004

      CARDIOGENESIS CORPORATION, a corporation organized under the laws of the
State of California (the "Company"), hereby certifies that, for value received,
LAURUS MASTER FUND, LTD., or assigns (the "Holder"), is entitled, subject to the
terms set forth below, to purchase from the Company (as defined herein) from and
after the Issue Date of this Warrant and at any time or from time to time before
5:00 p.m., New York time, through the close of business October 26, 2011 (the
"Expiration Date"), up to 2,640,000 fully paid and nonassessable shares of
Common Stock (as hereinafter defined), $0.01 par value per share, at the
applicable Exercise Price per share (as defined below). The number and character
of such shares of Common Stock and the applicable Exercise Price per share are
subject to adjustment as provided herein.

      As used herein the following terms, unless the context otherwise requires,
have the following respective meanings:

            (a) The term "Company" shall include CardioGenesis Corporation and
      any corporation which shall succeed, or assume the obligations of,
      CardioGenesis Corporation hereunder.

            (b) The term "Common Stock" includes (i) the Company's Common Stock,
      par value $0.01 per share; and (ii) any other securities into which or for
      which any of the securities described in (a) may be converted or exchanged
      pursuant to a plan of recapitalization, reorganization, merger, sale of
      assets or otherwise.

            (c) The term "Other Securities" refers to any stock (other than
      Common Stock) and other securities of the Company or any other person
      (corporate or otherwise) which the holder of the Warrant at any time shall
      be entitled to receive, or shall have received, on the exercise of the
      Warrant, in lieu of or in addition to Common Stock, or

<PAGE>

      which at any time shall be issuable or shall have been issued in exchange
      for or in replacement of Common Stock or Other Securities pursuant to
      Section 4 or otherwise.

            (d) The "Exercise Price" applicable under this Warrant shall be a
      price of $0.50 for all shares acquired hereunder.

      1. Exercise of Warrant.

            1.1 Number of Shares Issuable upon Exercise. From and after the date
hereof through and including the Expiration Date, the Holder shall be entitled
to receive, upon exercise of this Warrant in whole or in part, by delivery of an
original or fax copy of an exercise notice in the form attached hereto as
Exhibit A (the "Exercise Notice"), shares of Common Stock of the Company,
subject to adjustment pursuant to Section 4.

            1.2 Fair Market Value. For purposes hereof, the "Fair Market Value"
of a share of Common Stock as of a particular date (the "Determination Date")
shall mean:

            (a) If the Company's Common Stock is listed for trading on the
      American Stock Exchange or another national exchange or is quoted on the
      National or SmallCap Market of The Nasdaq Stock Market, Inc.("Nasdaq"),
      then the closing or last sale price, respectively, reported for the last
      business day immediately preceding the Determination Date.

            (b) If the Company's Common Stock is not traded on the American
      Stock Exchange or another national exchange or on the Nasdaq but is traded
      on the NASD OTC Bulletin Board, then the mean of the average of the
      closing bid and asked prices reported for the five (5) trading days
      immediately preceding the Determination Date.

            (c) Except as provided in clause (d) below, if the Company's Common
      Stock is not publicly traded, then as the Holder and the Company agree or
      in the absence of agreement by arbitration in accordance with the rules
      then in effect of the American Arbitration Association, before a single
      arbitrator to be chosen from a panel of persons qualified by education and
      training to pass on the matter to be decided.

            (d) If the Determination Date is the date of a liquidation,
      dissolution or winding up, or any event deemed to be a liquidation,
      dissolution or winding up pursuant to the Company's charter, then all
      amounts to be payable per share to holders of the Common Stock pursuant to
      the charter in the event of such liquidation, dissolution or winding up,
      plus all other amounts to be payable per share in respect of the Common
      Stock in liquidation under the charter, assuming for the purposes of this
      clause (d) that all of the shares of Common Stock then issuable upon
      exercise of the Warrant (and all other shares issuable upon the exercise
      of options and/or warrants that will have an exercise price that is lower
      than the Fair Market Value) are outstanding at the Determination Date.

            1.3 Company Acknowledgment. The Company will, at the time of the
partial exercise of the Warrant, upon the request of the holder hereof
acknowledge in writing its continuing obligation to afford to such holder any
rights to any unexercised portion of the Warrant which such holder shall
continue to be entitled after such exercise in accordance with

                                       2
<PAGE>

the provisions of this Warrant. If the holder shall fail to make any such
request, such failure shall not affect the continuing obligation of the Company
to afford to such holder any such rights. This Warrant does not entitle the
Holder to any voting rights or other rights as a shareholder prior to the
exercise hereof. Upon surrender of this Warrant and the payment of the aggregate
Exercise Price (or by means of a cashless exercise) the shares of Common Stock
so purchased shall be deemed to be issued to such Holder as the record owner of
such shares as of the close of business on the later of the date of such
surrender or payment.

            1.4 Trustee for Warrant Holders. In the event that a bank or trust
company shall have been appointed as trustee for the holders of the Warrant
pursuant to Subsection 3.2, such bank or trust company shall have all the powers
and duties of a warrant agent (as hereinafter described) and shall accept, in
its own name for the account of the Holder or such successor person as may be
entitled thereto, all amounts otherwise payable to the Holder or such successor,
as the case may be, on exercise of this Warrant pursuant to this Section 1.

      2. Procedure for Exercise.

            2.1 Delivery of Stock Certificates, Etc., on Exercise. The Company
agrees that the shares of Common Stock purchased upon exercise of this Warrant
shall be deemed to be issued to the Holder as the record owner of such shares as
of the close of business on the date on which this Warrant shall have been
surrendered and payment made for such shares in accordance herewith. As soon as
practicable after the exercise of this Warrant in full or in part, and in any
event within three (3) business days thereafter, the Company at its expense
(including the payment by it of any applicable issue taxes) will cause to be
issued in the name of and delivered to the Holder, or as such Holder (upon
payment by such Holder of any applicable transfer taxes) may direct in
compliance with applicable securities laws, a certificate or certificates for
the number of duly and validly issued, fully paid and nonassessable shares of
Common Stock (or Other Securities) to which such Holder shall be entitled on
such exercise, plus, in lieu of any fractional share to which such holder would
otherwise be entitled, cash equal to such fraction multiplied by the then Fair
Market Value of one full share, together with any other stock or other
securities and property (including cash, where applicable) to which such Holder
is entitled upon such exercise pursuant to Section 1 or otherwise.

            2.2 Exercise. Payment may be made either (i) in cash or by certified
or official bank check payable to the order of the Company equal to the
applicable aggregate Exercise Price, (ii) by delivery of the Warrant, or shares
of Common Stock and/or Common Stock receivable upon exercise of the Warrant in
accordance with the formula set forth below, or (iii) by a combination of any of
the foregoing methods, for the number of Common Shares specified in such
Exercise Notice (as such exercise number shall be adjusted to reflect any
adjustment in the total number of shares of Common Stock issuable to the Holder
per the terms of this Warrant) and the Holder shall thereupon be entitled to
receive the number of duly authorized, validly issued, fully-paid and
non-assessable shares of Common Stock (or Other Securities) determined as
provided herein. Notwithstanding any provisions herein to the contrary, if the
Fair Market Value of one share of Common Stock is greater than the Exercise
Price (at the date of calculation as set forth below), in lieu of exercising
this Warrant for cash, the Holder may elect to receive shares equal to the value
(as determined below) of this Warrant (or the portion thereof being exercised)
by surrender of this Warrant at the principal office of the

                                       3
<PAGE>

Company together with the properly endorsed Exercise Notice in which event the
Company shall issue to the Holder a number of shares of Common Stock computed
using the following formula:

      X= Y *           (A-B)
                       -----
                         A

      Where X = the number of shares of Common Stock to be issued to the Holder

      Y =       the number of shares of Common Stock
                purchasable under the Warrant or, if only a
                portion of the Warrant is being exercised, the
                portion of the Warrant being exercised (at the
                date of such calculation)

      A =       the Fair Market Value of one share of the Company's Common Stock
                (at the date of such calculation)

      B =       Exercise Price (as adjusted to the date of such calculation)

      3. Effect of Reorganization, Etc.; Adjustment of Exercise Price.

            3.1 Reorganization, Consolidation, Merger, Etc. In case at any time
or from time to time, the Company shall (a) effect a reorganization, (b)
consolidate with or merge into any other person, or (c) transfer all or
substantially all of its properties or assets to any other person under any plan
or arrangement contemplating the dissolution of the Company, then, in each such
case, as a condition to the consummation of such a transaction, proper and
adequate provision shall be made by the Company whereby the Holder of this
Warrant, on the exercise hereof as provided in Section 1 at any time after the
consummation of such reorganization, consolidation or merger or the effective
date of such dissolution, as the case may be, shall receive, in lieu of the
Common Stock (or Other Securities) issuable on such exercise prior to such
consummation or such effective date, the stock and other securities and property
(including cash) to which such Holder would have been entitled upon such
consummation or in connection with such dissolution, as the case may be, if such
Holder had so exercised this Warrant, immediately prior thereto, all subject to
further adjustment thereafter as provided in Section 4.

            3.2 Dissolution. In the event of any dissolution of the Company
following the transfer of all or substantially all of its properties or assets,
the Company, concurrently with any distributions made to holders of its Common
Stock, shall at its expense deliver or cause to be delivered to the Holder the
stock and other securities and property (including cash, where applicable)
receivable by the Holder of the Warrant pursuant to Section 3.1, or, if the
Holder shall so instruct the Company, to a bank or trust company specified by
the Holder and having its principal office in New York, NY as trustee for the
Holder of the Warrant (the "Trustee").

            3.3 Continuation of Terms. Upon any reorganization, consolidation,
merger or transfer (and any dissolution following any transfer) referred to in
this Section 3, this Warrant shall continue in full force and effect and the
terms hereof shall be applicable to the shares of stock and other securities and
property receivable on the exercise of this Warrant after the consummation of
such reorganization, consolidation or merger or the effective date of
dissolution following any such transfer, as the case may be, and shall be
binding upon the issuer

                                       4
<PAGE>

of any such stock or other securities, including, in the case of any such
transfer, the person acquiring all or substantially all of the properties or
assets of the Company, whether or not such person shall have expressly assumed
the terms of this Warrant as provided in Section 4. In the event this Warrant
does not continue in full force and effect after the consummation of the
transactions described in this Section 3, then the Company's securities and
property (including cash, where applicable) receivable by the Holders of the
Warrant will be delivered to Holder or the Trustee as contemplated by Section
3.2.

      4. Extraordinary Events Regarding Common Stock. In the event that the
Company shall (a) issue additional shares of the Common Stock as a dividend or
other distribution on outstanding Common Stock, (b) subdivide its outstanding
shares of Common Stock, or (c) combine its outstanding shares of the Common
Stock into a smaller number of shares of the Common Stock, then, in each such
event, the Exercise Price shall, simultaneously with the happening of such
event, be adjusted by multiplying the then Exercise Price by a fraction, the
numerator of which shall be the number of shares of Common Stock outstanding
immediately prior to such event and the denominator of which shall be the number
of shares of Common Stock outstanding immediately after such event, and the
product so obtained shall thereafter be the Exercise Price then in effect. The
Exercise Price, as so adjusted, shall be readjusted in the same manner upon the
happening of any successive event or events described herein in this Section 4.
The number of shares of Common Stock that the holder of this Warrant shall
thereafter, on the exercise hereof as provided in Section 1, be entitled to
receive shall be increased to a number determined by multiplying the number of
shares of Common Stock that would otherwise (but for the provisions of this
Section 4) be issuable on such exercise by a fraction of which (a) the numerator
is the Exercise Price that would otherwise (but for the provisions of this
Section 4) be in effect, and (b) the denominator is the Exercise Price in effect
on the date of such exercise.

      5. Certificate as to Adjustments. In each case of any adjustment or
readjustment in the shares of Common Stock (or Other Securities) issuable on the
exercise of the Warrant, the Company at its expense will promptly cause its
Chief Financial Officer or other appropriate designee to compute such adjustment
or readjustment in accordance with the terms of the Warrant and prepare a
certificate setting forth such adjustment or readjustment and showing in detail
the facts upon which such adjustment or readjustment is based, including a
statement of (a) the consideration received or receivable by the Company for any
additional shares of Common Stock (or Other Securities) issued or sold or deemed
to have been issued or sold, (b) the number of shares of Common Stock (or Other
Securities) outstanding or deemed to be outstanding, and (c) the Exercise Price
and the number of shares of Common Stock to be received upon exercise of this
Warrant, in effect immediately prior to such adjustment or readjustment and as
adjusted or readjusted as provided in this Warrant. The Company will forthwith
mail a copy of each such certificate to the holder of the Warrant and any
Warrant agent of the Company (appointed pursuant to Section 11 hereof).

      6. Reservation of Stock, Etc., Issuable on Exercise of Warrant. The
Company will at all times reserve and keep available, solely for issuance and
delivery on the exercise of the Warrant, shares of Common Stock (or Other
Securities) from time to time issuable on the exercise of the Warrant.

                                       5
<PAGE>

      7. Assignment; Exchange of Warrant. Subject to compliance with applicable
securities laws, this Warrant, and the rights evidenced hereby, may be
transferred by any registered holder hereof (a "Transferor") in whole or in
part. On the surrender for exchange of this Warrant, with the Transferor's
endorsement in the form of Exhibit B attached hereto (the "Transferor
Endorsement Form") and together with evidence reasonably satisfactory to the
Company demonstrating compliance with applicable securities laws, which shall
include, without limitation, the provision of a legal opinion of customary scope
and content from the counsel reasonably acceptable to the Company (at the
Transferor's expense) that such transfer is exempt from the registration
requirements of applicable securities laws, and with payment by the Transferor
of any applicable transfer taxes) will issue and deliver to or on the order of
the Transferor thereof a new Warrant of like tenor, in the name of the
Transferor and/or the transferee(s) specified in such Transferor Endorsement
Form (each a "Transferee"), calling in the aggregate on the face or faces
thereof for the number of shares of Common Stock called for on the face or faces
of the Warrant so surrendered by the Transferor.

      8. Replacement of Warrant. On receipt of evidence reasonably satisfactory
to the Company of the loss, theft, destruction or mutilation of this Warrant
and, in the case of any such loss, theft or destruction of this Warrant, on
delivery of an indemnity agreement or security reasonably satisfactory in form
and amount to the Company or, in the case of any such mutilation, on surrender
and cancellation of this Warrant, the Company at its expense will execute and
deliver, in lieu thereof, a new Warrant of like tenor.

      9. Registration Rights. The Holder of this Warrant has been granted
certain registration rights by the Company. These registration rights are set
forth in a Registration Rights Agreement entered into by the Company and Holder
dated as of even date of this Warrant.

      10. Maximum Exercise. The Holder shall not be entitled to exercise this
Warrant on an exercise date, in connection with that number of shares of Common
Stock which would be in excess of the sum of (i) the number of shares of Common
Stock beneficially owned by the Holder and its affiliates on an exercise date,
and (ii) the number of shares of Common Stock issuable upon the exercise of this
Warrant with respect to which the determination of this proviso is being made on
an exercise date, which would result in beneficial ownership by the Holder and
its affiliates of more than 4.99% of the outstanding shares of Common Stock of
the Company on such date. For the purposes of the proviso to the immediately
preceding sentence, beneficial ownership shall be determined in accordance with
Section 13(d) of the Securities Exchange Act of 1934, as amended, and Regulation
13d-3 thereunder. Notwithstanding the foregoing, the restriction described in
this paragraph may be revoked upon 75 days prior notice from the Holder to the
Company and is automatically null and void upon an Event of Default under the
Note made by the Company to the Holder dated the date hereof (as amended,
modified or supplemented from time to time, the "Note").

      11. Warrant Agent. The Company may, by written notice to the each Holder
of the Warrant, appoint an agent for the purpose of issuing Common Stock (or
Other Securities) on the exercise of this Warrant pursuant to Section 1,
exchanging this Warrant pursuant to Section 7, and replacing this Warrant
pursuant to Section 8, or any of the foregoing, and thereafter any such
issuance, exchange or replacement, as the case may be, shall be made at such
office by such agent.

                                       6
<PAGE>

      12. Transfer on the Company's Books. Until this Warrant is transferred on
the books of the Company, the Company may treat the registered holder hereof as
the absolute owner hereof for all purposes, notwithstanding any notice to the
contrary.

      13. Notices, Etc. All notices and other communications from the Company to
the Holder of this Warrant shall be mailed by first class registered or
certified mail, postage prepaid, at such address as may have been furnished to
the Company in writing by such Holder or, until any such Holder furnishes to the
Company an address, then to, and at the address of, the last Holder of this
Warrant who has so furnished an address to the Company.

      14. Miscellaneous. This Warrant and any term hereof may be changed,
waived, discharged or terminated only by an instrument in writing signed by the
party against which enforcement of such change, waiver, discharge or termination
is sought. This Warrant shall be governed by and construed in accordance with
the laws of State of New York without regard to principles of conflicts of laws.
Any action brought concerning the transactions contemplated by this Warrant
shall be brought only in the state courts of New York or in the federal courts
located in the state of New York; provided, however, that the Holder may choose
to waive this provision and bring an action outside the state of New York. The
individuals executing this Warrant on behalf of the Company agree to submit to
the jurisdiction of such courts and waive trial by jury. The prevailing party
shall be entitled to recover from the other party its reasonable attorney's fees
and costs. In the event that any provision of this Warrant is invalid or
unenforceable under any applicable statute or rule of law, then such provision
shall be deemed inoperative to the extent that it may conflict therewith and
shall be deemed modified to conform with such statute or rule of law. Any such
provision which may prove invalid or unenforceable under any law shall not
affect the validity or enforceability of any other provision of this Warrant.
The headings in this Warrant are for purposes of reference only, and shall not
limit or otherwise affect any of the terms hereof. The invalidity or
unenforceability of any provision hereof shall in no way affect the validity or
enforceability of any other provision hereof. The Company acknowledges that
legal counsel participated in the preparation of this Warrant and, therefore,
stipulates that the rule of construction that ambiguities are to be resolved
against the drafting party shall not be applied in the interpretation of this
Warrant to favor any party against the other party.

                   [BALANCE OF PAGE INTENTIONALLY LEFT BLANK;
                            SIGNATURE PAGE FOLLOWS.]

                                       7
<PAGE>

      IN WITNESS WHEREOF, the Company has executed this Warrant as of the date
first written above.

                                             CARDIOGENESIS, CORPORATION

WITNESS:

                                             By:______________________________
                                             Name:____________________________
___________________________                  Title:___________________________

                                       8
<PAGE>

                                    EXHIBIT A

                              FORM OF SUBSCRIPTION
                   (To Be Signed Only On Exercise Of Warrant)

TO:   CardioGenesis, Corporation

      Attention: Chief Financial Officer

      The undersigned, pursuant to the provisions set forth in the attached
Warrant (No.____), hereby irrevocably elects to purchase (check applicable box):

________    _________ shares of the Common Stock covered by such Warrant; or

________    the maximum number of shares of Common Stock covered by such Warrant
            pursuant to the cashless exercise procedure set forth in Section 2.

      The undersigned herewith makes payment of the full Exercise Price for such
shares at the price per share provided for in such Warrant, which is
$___________. Such payment takes the form of (check applicable box or boxes):

_______     $__________ in lawful money of the United States; and/or

_______     the cancellation of such portion of the attached Warrant as is
            exercisable for a total of _______ shares of Common Stock (using a
            Fair Market Value of $_______ per share for purposes of this
            calculation); and/or

_______     the cancellation of such number of shares of Common Stock as is
            necessary, in accordance with the formula set forth in Section 2.2,
            to exercise this Warrant with respect to the maximum number of
            shares of Common Stock purchasable pursuant to the cashless exercise
            procedure set forth in Section 2.

      The undersigned requests that the certificates for such shares be issued
in the name of, and delivered to ______________________________________________
whose address is
______________________________________________________________________________

      The undersigned represents and warrants that all offers and sales by the
undersigned of the securities issuable upon exercise of the within Warrant shall
be made pursuant to registration of the Common Stock under the Securities Act of
1933, as amended (the "Securities Act") or pursuant to an exemption from
registration under the Securities Act.

Dated:______________                          __________________________________
                                              (Signature must conform to name of
                                              holder as specified on the face of
                                              the Warrant)

                                              Address:__________________________
                                              __________________________________

                                      A-1
<PAGE>

                                    EXHIBIT B

                         FORM OF TRANSFEROR ENDORSEMENT
                   (To Be Signed Only On Transfer Of Warrant)

      For value received, the undersigned hereby sells, assigns, and transfers
unto the person(s) named below under the heading "Transferees" the right
represented by the within Warrant to purchase the percentage and number of
shares of Common Stock of CardioGenesis, Corporation into which the within
Warrant relates specified under the headings "Percentage Transferred" and
"Number Transferred," respectively, opposite the name(s) of such person(s) and
appoints each such person Attorney to transfer its respective right on the books
of CardioGenesis, Corporation with full power of substitution in the premises.

<TABLE>
<CAPTION>
                                              Percentage             Number
   Transferees             Address            Transferred          Transferred
   -----------             -------            -----------          -----------
<S>                   <C>                 <C>                  <C>
___________________   _________________   ___________________  _________________

___________________   _________________   ___________________  _________________

___________________   _________________   ___________________  _________________

___________________   _________________   ___________________  _________________
</TABLE>

Dated:_______________________          ________________________________________
                                       (Signature must conform to name of holder
                                       as specified on the face of the Warrant)

                                       Address:_________________________________
                                               _________________________________


                                       SIGNED IN THE PRESENCE OF:

                                       _________________________________________
                                                       (Name)
ACCEPTED AND AGREED:
[TRANSFEREE]

_______________________________
        (Name)

                                      B-1