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                                                                    EXHIBIT 10.3

                             STOCK PURCHASE WARRANT

                          To Subscribe for and Purchase
                                 Common Stock of

                                   Aksys, Ltd.

          THIS CERTIFIES THAT, for value received, U.S. Bancorp Piper Jaffray
Inc. (herein called "Purchaser"), or registered assigns, is entitled to
subscribe for and purchase from Aksys, Ltd. (herein called the "Company"), a
corporation organized and existing under the laws of the State of Delaware, at
the price specified below (subject to adjustment as noted below) at any time
after June 19, 2002 to and including December 19, 2006 (the "Expiration Date")
One Hundred Fifty-Nine Thousand Seven Hundred Sixty-Two (159,762) fully paid and
nonassessable shares of Common Stock (herein the "Common Stock") (subject to
adjustment as noted below). This Warrant has been issued pursuant to an
Engagement Agreement dated as of October 5, 2001 between Purchaser and the
Company.

          The warrant purchase price (subject to adjustment as noted below)
shall be $4.90 per share.

          This Warrant is subject to the following provisions, terms and
conditions:

          1.   The rights represented by this Warrant may be exercised by the
holder hereof, in whole or in part, by written notice of exercise delivered to
the Company and by the surrender of this Warrant (properly endorsed if required)
at the principal office of the Company and upon payment to it by wire transfer
of the purchase price for such shares. The Company agrees that the shares so
purchased shall be and are deemed to be issued to the holder hereof 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 as
aforesaid. Subject to the provisions of the next succeeding paragraph, the
Company shall use its best efforts to cause certificates for the shares of stock
so purchased to be delivered to the holder hereof within a reasonable time, not
exceeding 10 days, after the rights represented by this Warrant shall have been
so exercised, and, unless this Warrant has expired, a new Warrant representing
the number of shares, if any, with respect to which this Warrant shall not then
have been exercised shall also be delivered to the holder hereof within such
time.

          2.   Notwithstanding the foregoing, however, the Company shall not be
required to deliver any certificate for shares of stock upon exercise of this
Warrant except in accordance with the provisions, and subject to the
limitations, of paragraph 7 hereof.

          3.   The Company represents and warrants that this Warrant has been
duly authorized by all necessary corporate action, has been duly executed and
delivered and is a legal and binding obligation of the Company. The Company
covenants and agrees that all shares which are issued upon the exercise of the
rights represented by this Warrant according to the terms hereof will, upon
issuance, be duly authorized and issued, fully paid and nonassessable. The
Company further covenants and agrees that during the period within which the
rights represented by this

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Warrant may be exercised, the Company will at all times have authorized, and
reserved for the purpose of issue or transfer upon exercise of the subscription
rights evidenced by this Warrant, a sufficient number of shares of its Common
Stock to provide for the exercise of the rights represented by this Warrant.

          4.   The above provisions are, however, subject to the following:

          (a)  The warrant purchase price shall, from and after the date of
issuance of this Warrant, be subject to adjustment from time to time as
hereinafter provided. Upon each adjustment of the warrant purchase price, the
holder of this Warrant shall thereafter be entitled to purchase, at the warrant
purchase price resulting from such adjustment, the number of shares obtained by
multiplying the warrant purchase price in effect immediately prior to such
adjustment by the number of shares purchasable pursuant hereto immediately prior
to such adjustment and dividing the product thereof by the warrant purchase
price resulting from such adjustment.

          (b)  In case the Company shall (i) make a dividend upon the Common
Stock payable in Common Stock (other than a dividend declared to effect a
subdivision of the outstanding shares of Common Stock, as described in
subparagraph (b) below) or any obligations or any shares of stock of the Company
which are convertible into or exchangeable for Common Stock (such obligations or
shares of stock being hereinafter referred to as "Convertible Securities"), or
in any rights or options to purchase any Common Stock or Convertible Securities,
or (ii) make any other dividend or make any other distribution upon the Common
Stock payable otherwise than out of earnings or surplus, then thereafter the
holder of this Warrant upon the exercise hereof will be entitled to receive the
number of shares of Common Stock to which such holder shall be entitled upon
such exercise, and, in addition and without further payment therefor, such
number of shares of Common Stock, such that upon exercise hereof, such holder
would receive such number of shares of Common Stock as a result of each dividend
described in clause (i) above and each dividend or distribution described in
clause (ii) above which such holder would have received by way of any such
dividend or distribution if continuously since the record date for any such
dividend or distribution such holder (i) had been the record holder of the
number of shares of Common Stock then received, and (ii) had retained all
dividends or distributions in stock or securities (including Common Stock or
Convertible Securities, or in any rights or options to purchase any Common Stock
or Convertible Securities) payable in respect of such Common Stock or in respect
of any stock or securities paid as dividends or distributions and originating
directly or indirectly from such Common Stock. For the purposes of the
foregoing, a dividend or distribution other than in cash shall be considered
payable out of earnings or surplus only to the extent that such earnings or
surplus are charged an amount equal to the fair value of such dividend as
determined by the Board of Directors of the Company.

          (c)  In case the Company shall at any time subdivide its outstanding
shares of Common Stock into a greater number of shares, the warrant purchase
price in effect immediately prior to such subdivision shall be proportionately
reduced, and conversely, in case the outstanding shares of Common Stock of the
Company shall be combined into a smaller number of shares, the

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warrant purchase price in effect immediately prior to such combination shall
be proportionately increased.

          (d) If any capital reorganization or reclassification of the capital
stock of the Company, or consolidation or merger of the Company with another
corporation, or the sale of all or substantially all of its assets to another
corporation shall be effected in such a way that holders of Common Stock shall
be entitled to receive stock, securities or assets with respect to or in
exchange for Common Stock, then, as a condition of such reorganization,
reclassification, consolidation, merger or sale, lawful and adequate provision
shall be made whereby the holder hereof shall thereafter have the right to
purchase and receive, upon the basis and upon the terms and conditions specified
in this Warrant and in lieu of the shares of the Common Stock of the Company
immediately theretofore purchasable and receivable upon the exercise of the
rights represented hereby, such shares of stock, securities or assets as may be
issued or payable with respect to or in exchange for a number of outstanding
shares of such Common Stock equal to the number of shares of such stock
immediately theretofore purchasable and receivable upon the exercise of the
rights represented hereby had such reorganization, reclassification,
consolidation, merger or sale not taken place.

          (e)  Upon any adjustment of the warrant purchase price, then and in
each such case the Company shall give written notice thereof, by first-class
mail, postage prepaid, addressed to the registered holder of this Warrant at the
address of such holder as shown on the books of the Company, which notice shall
state the warrant purchase price resulting from such adjustment and the increase
or decrease, if any, in the number of shares purchasable at such price upon the
exercise of this Warrant, setting forth in reasonable detail the method of
calculation and the facts upon which such calculation is based.

          (f)  In case any time:

               (1)  the Company shall declare any cash dividend on its capital
     stock at a rate in excess of the rate of the last cash dividend theretofore
     paid;

               (2)  the Company shall pay any dividend payable in stock upon its
     capital stock or make any distribution (other than regular cash dividends)
     to the holders of its capital stock;

               (3)  the Company shall offer for subscription pro rata to the
     holders of its capital stock any additional shares of stock of any class or
     other rights;

               (4)  there shall be any capital reorganization, or
     reclassification of the capital stock of the Company, or consolidation or
     merger of the Company with, or sale of all or substantially all of its
     assets to, another corporation; or

               (5)  there shall be a voluntary or involuntary dissolution,
     liquidation or winding up of the Company;

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then, in any one or more of said cases, the Company shall give written notice,
by first-class mail, postage prepaid, addressed to the registered holder of this
Warrant at the address of such holder as shown on the books of the Company, of
the date on which (aa) the books of the Company shall close or a record shall be
taken for such dividend, distribution or subscription rights, or (bb) such
reorganization, reclassification, consolidation, merger, sale, dissolution,
liquidation or winding up, or conversion or redemption shall, or is expected to,
take place, as the case may be. Such notice shall also specify the date as of
which the holders of capital stock of record shall participate in such dividend,
distribution or subscription rights, or shall be entitled to exchange their
capital stock for securities or other property deliverable upon such
reorganization, reclassification, consolidation, merger, sale, dissolution,
liquidation or winding up, or conversion or redemption, as the case may be. Such
written notice shall be given at least 20 days prior to the action in question
and not less than 20 days prior to the record date or the date on which the
Company's transfer books are closed in respect thereto.

          (g)  No fractional shares of Common Stock shall be issued upon the
exercise of this Warrant, but, instead of any fraction of a share which would
otherwise be issuable, the Company shall pay a cash adjustment (which may be
effected as a reduction of the amount to be paid by the holder hereof upon such
exercise) in respect of such fraction in an amount equal to the same fraction of
the Market Price per share of Common Stock as of the close of business on the
date of the notice required by paragraph l above. "Market Price" shall mean, if
the Common Stock is traded on a securities exchange or on the NASDAQ National
Market System, the average of the closing prices of the Common Stock on such
exchange or the NASDAQ National Market System on the 20 trading days ending on
the trading day prior to the date of determination, or, if the Common Stock is
otherwise traded in the over-the-counter market, the average of the closing bid
prices on the 20 trading days ending on the trading day prior to the date of
determination. If at any time the Common Stock is not traded on an exchange or
the NASDAQ National Market System, or otherwise traded in the over-the-counter
market, the Market Price shall be deemed to be the higher of (i) the book value
thereof as determined by any firm of independent public accountants of
recognized standing selected by the Board of Directors of the Company as of the
last day of any month ending within 60 days preceding the date as of which the
determination is to be made, or (ii) the fair value thereof determined in good
faith by the Board of Directors of the Company as of a date which is within 15
days of the date as of which the determination is to be made.

          5.   This Warrant shall not entitle the holder hereof to any voting
rights or other rights as a stockholder of the Company.

          6.   The holder of this Warrant, by acceptance hereof, agrees that
this warrant may only be transferred to "accredited investors" (as defined in
Regulation D promulgated under the Securities Act of 1933, as amended) and to
give written notice to the Company before transferring this Warrant or
transferring any Common Stock issuable or issued upon the exercise hereof of
such holder's intention to do so, describing briefly the manner of any proposed
transfer of this Warrant or such holder's intention as to the disposition to be
made of shares of Common Stock issuable or issued upon the exercise hereof. Such
holder shall also provide the Company with an

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opinion of counsel satisfactory to the Company to the effect that the proposed
transfer of this Warrant or disposition of shares may be effected without
registration or qualification (under any Federal or State law) of this Warrant
or the shares of Common Stock issuable or issued upon the exercise hereof. Upon
receipt of such written notice and opinion by the Company, such holder shall be
entitled to transfer this Warrant, or to exercise this Warrant in accordance
with its terms and dispose of the shares received upon such exercise or to
dispose of shares of Common Stock received upon the previous exercise of this
Warrant, all in accordance with the terms of the notice delivered by such holder
to the Company, provided that an appropriate legend respecting the aforesaid
restrictions on transfer and disposition may be endorsed on this Warrant or the
certificates for such shares.

          7.   Subject to the provisions of paragraph 6 hereof, this Warrant and
all rights hereunder are transferable, in whole or in part, at the principal
office of the Company by the holder hereof in person or by duly authorized
attorney, upon surrender of this Warrant properly endorsed. Each taker and
holder of this Warrant, by taking or holding the same, consents and agrees that
the bearer of this Warrant, when endorsed, may be treated by the Company and all
other persons dealing with this Warrant as the absolute owner hereof for any
purpose and as the person entitled to exercise the rights represented by this
Warrant, or to the transfer hereof on the books of the Company, any notice to
the contrary notwithstanding; but until such transfer on such books, the Company
may treat the registered holder hereof as the owner for all purposes.

          8.   This Warrant is exchangeable, upon the surrender hereof by the
holder hereof at the principal office of the Company, for new Warrants of like
tenor representing in the aggregate the right to subscribe for and purchase the
number of shares which may be subscribed for and purchased hereunder, each of
such new Warrants to represent the right to subscribe for and purchase such
number of shares as shall be designated by said holder hereof at the time of
such surrender.

          9.   The Company covenants and agrees that the Purchaser shall have
the rights granted under the Registration Rights Agreement dated December 19,
2001 by and between the Company and the Purchaser.

          10.  All questions concerning this Warrant will be governed and
interpreted and enforced in accordance with the internal law, not the law of
conflicts, of the State of Delaware.

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          IN WITNESS WHEREOF, Aksys, Ltd. has caused this Warrant to be signed
by its duly authorized officer and this Warrant to be dated as of December 19,
2001.

                                                AKSYS, LTD.


                                                By:  /s/ William C. Dow
                                                Its:  President & CEO



                             RESTRICTION ON TRANSFER

          "The securities evidenced hereby may only be transferred only to an
"accredited investor" (as defined in Regulation D promulgated under the Federal
Securities Act of 1933) and may not be transferred without (i) the opinion of
counsel satisfactory to this corporation that such transfer may be lawfully made
without registration under the Federal Securities Act of 1933 and all applicable
state securities laws or (ii) such registration."

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                                SUBSCRIPTION FORM

           To be Executed by the Holder of this Warrant if such Holder
              Desires to Exercise this Warrant in Whole or in Part:

To: Aksys, Ltd. (the "Company")

        The undersigned ___________________________________

                     Please insert Social Security or other
                        identifying number of Subscriber:

                         _______________________________

hereby irrevocably elects to exercise the right of purchase represented by this
Warrant for, and to purchase thereunder, _______________ shares of the Common
Stock (the "Common Stock") provided for therein and tenders payment herewith to
the order of the Company in the amount of $___________, such payment being made
as provided on the face of this Warrant.

          The undersigned requests that certificates for such shares of Common
Stock be issued as follows:

Name: __________________________________________________________________________

Address: _______________________________________________________________________

Deliver to: ____________________________________________________________________

Address: _______________________________________________________________________

and, if such number of shares of Common Stock shall not be all the shares of
Common Stock purchasable hereunder, that a new Warrant for the balance remaining
of the shares of Common Stock purchasable under this Warrant be registered in
the name of, and delivered to, the undersigned at the address stated above.

Dated:  ________________________

                               Signature _______________________________________

                                     Note: The signature on this Subscription
                                     Form must correspond with the name as
                                     written upon the face of this Warrant in
                                     every particular, without alteration or
                                     enlargement or any change whatever.

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                               FORM OF ASSIGNMENT
                       (To Be Signed Only Upon Assignment)


          FOR VALUE RECEIVED, the undersigned hereby sells, assigns and
transfers unto

this Warrant, and appoints ______________________________________ to transfer
this Warrant on the books of the Company with the full power of substitution in
the premises.


Dated:_____________________________

In the presence of:________________




                                    ____________________________________________

                                    (Signature must conform in all respects to
                                    the name of the holder as specified on the
                                    face of this Warrant without alteration,
                                    enlargement or any change whatsoever, and
                                    the signature must be guaranteed in the
                                    usual manner)

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