<PAGE>
 
                                                                   Exhibit 10.11


                                 PATENT LICENSE


                                    Parties

     This Agreement with its appendices, exhibits and schedules, (the
"Agreement") is made as of March 11, 1996 (the "Execution Date") between
ALLERGAN, 8301 Mars Drive, Waco, Texas 76712 and ALLERGAN, INC., having a
principal place of business at 2525 Dupont Drive, Irvine, California 92715
(hereinafter collective "LICENSOR"), and AKSYS, LTD., a Delaware corporation,
having a principal place of business at 1113 S. Milwaukee Avenue, Suite 300,
Libertyville, Illinois 60048 (hereinafter "LICENSEE").


                                    Recitals

     A.  LICENSOR is the sole owner and Assignee of U.S. Patent No. 5,392,653,
Zanger et al., entitled "Pressure Transducer Magnetically-Coupled Interface
Complementing Minimal Diaphragm Movement During Operation," issued February 28,
1995 and its foreign counterparts (hereinafter "Licensed Patents") as currently
set forth in Exhibit A hereto.

     B.  The LICENSEE is developing machines and systems for performing kidney
dialysis of humans and intends to manufacture, or have manufactured for it, its
kidney dialysis machines in the United States and overseas, and to sell said
machines in the United States and worldwide. The kidney dialysis machines of
LICENSEE comprise many different systems and subcomponents, one of which are
pressure sensors.

     C.  The LICENSEE represents that it independently conceived and reduced to
practice a non-invasive pressure sensor for use with its kidney dialysis
machines, without having any prior knowledge of the Licensed Patents or the work
of Allergan relating to pressure sensors.

     D.  LICENSEE is interested in obtaining an exclusive license, in the field
of use of kidney dialysis machines and methods, under the Licensed Patents and
LICENSOR is


<PAGE>
 
willing to grant an exclusive license to LICENSEE and its Affiliates under the
Licensed Patents limited to the field of use of kidney dialysis machines and
methods.

                            ARTICLE 1:  DEFINITIONS

     1.0  "Defined Terms". Terms defined in this Article 1 and elsewhere,
parenthetically, in this Agreement, shall have the same meaning throughout the
Agreement. Defined Terms may be used in the singular or plural.

     1.1  "Party".  Party means the LICENSEE and/or the LICENSOR.

     1.2  "PRESSURE SENSOR" means a non-invasive pressure sensor as generally
described in the Licensed Patents, used to measure the positive or negative
pressure of the medium (either fluid or air) that is contained within the
pressure sensor chamber, including the diaphragm, metal disc, magnetic member,
strain gauge and electrical outputs that supply signals from the pressure sensor
to signal processing equipment.

     1.3  "Licensed Products" means any Pressure Sensors and Constituent
components of dialysis machines including extracorporeal circuits manufactured
by LICENSEE under the license acquired under this Agreement and covered by one
or more claims of any unexpired patent in Licensed Patents.

     1.4  "Field of Use" means the field of kidney dialysis.

     1.5  "Affiliate(s)" means a company which, directly or indirectly,
controls, is controlled by, or are under common control of a party.

                           ARTICLE 2:  LICENSE GRANT

     2.1  "Patent Grant". Subject to the terms and conditions of this Agreement,
LICENSOR hereby grants to LICENSEE and its Affiliates an exclusive, worldwide
license under the Licensed Patents, in the Field of Use, to make, have made, use
and sell Licensed Products, with the right to sublicense the right to use and
sell, but without the right to sublicense manufacturing rights without prior
written approval by LICENSOR, which approval shall not be unreasonably withheld.
The license shall not otherwise be transerable except as
<PAGE>
 
provided in Article 8.15 hereof. LICENSEE agrees not to use or sell Licensed
Products outside the Field of Use and agrees not to sell Licensed Products to
third parties for use outside the Field of Use.

     2.2  "Patent Marking". All Licensed Products made, used or sold by Licensee
in the U.S. during the life of the Licensed Patents shall bear a marking in
compliance with 35 U.S.C. (S) 287(a).

                          ARTICLE 3:  LICENSE PAYMENTS

     3.1  "Lump Sum Payment". In consideration for the license granted to the
LICENSEE under Article 2, the LICENSEE shall pay to the LICENSOR a License Fee
in the amount of Fifteen Thousand Dollars ($15,000) within ten (10) business
days after this Agreement shall become effective, and another Fifteen Thousand
Dollars ($15,000) upon the LICENSEE's first commercial sale after FDA regulatory
approval (510K) of a Licensed Product. However, the entire License Fee will
become immediately due and payable upon the LICENSOR's termination of this
Agreement for default under Article 7.

     3.2  "Running Royalty". In addition to the sums in Section 3.1, LICENSEE
shall pay to LICENSOR on behalf of itself and its Affiliates Thirty Cents
($0.30) for every Pressure Sensor Set (tubing assembly containing two (2)
Pressure Sensors) manufactured and released as finished goods available for sale
by LICENSEE or its Affiliates that is covered by any Licensed Patent during the
term of the Licensed Patent. LICENSEE and its Affiliates shall maintain records
adequate to account for the manufacture of Pressure Sensor Sets during the term
of the Licensed Patent. Payments under this running royalty shall be made
quarterly within sixty (60) days of the end of each calendar quarter and shall
be accompanied with a report of such manufacture of Pressure Sensor Sets.

     3.3  "Minimum Annual Royalty". LICENSEE shall pay to LICENSOR during the
term of this Agreement the following minimum annual royalty payments:
<PAGE>
 
<TABLE>
<CAPTION>
                        Amount        Calendar Year
                        ------        -------------
                        <S>           <C>
                        $20,000       1998
                        $30,000       1999
                        $40,000       2000
                        $50,000       2001 and annually thereafter
</TABLE>                              during the term of the
                                      Agreement


     Minimum annual royalties shall be due and payable annually at the time the
Fourth Quarter running royalty payment is due.  Running royalties paid according
to Section 3.2 shall be credited against minimum annual royalties and minimum
annual royalties shall be payable to the extent the running royalties for the
applicable calendar year are less than the minimum royalty obligation for such
calendar year.  Failure to pay applicable minimum royalties when due shall
result, upon written notice thereof by LICENSOR to LICENSEE, in LICENSEE's
exclusive license being converted to a non-exclusive license.  Failure to pay at
least one-half (1/2) of the applicable minimum royalties when due shall result,
upon written notice thereof by LICENSOR to LICENSEE, in termination of the
license.  For the avoidance of doubt, in the event LICENSEE pays at least one-
half (1/2) of the applicable minimum royalties, but less than the full amount,
LICENSEE's exclusive license, upon written notice thereof by LICENSOR, shall be
converted to a non-exclusive license.

     3.4  "Late Payments".  If the LICENSEE shall fail or refuse to make any
payment due hereunder on or before the date on which such payment is due, the
LICENSEE shall pay to the LICENSOR, at the time such payment is actually made,
an administrative fee equal to One Percent (1%) of the amount of such payment
for each month, or fraction of a month, that such payment is overdue.

                  ARTICLE 4:  REPRESENTATIONS AND LIMITATIONS

     4.1  The LICENSOR makes no warranty or representation that the LICENSEE's
or its Affiliate's utilization of the license received from the LICENSOR will
not infringe patents owned by any third party, nor any warranty or
representation as to the validity or scope of
<PAGE>
 
any patent under which a license is granted. The LICENSEE and its Affiliates
assume all risks of liability to any third person by reason of infringement of
patents owned by such third persons.

     4.2  "Disclaimer of Warranties". Nothing in this Agreement shall be
construed as:

               (a)  a warranty or representation that anything made, used, sold
                    or otherwise disposed of under any license granted in this
                    Agreement is or will be free from infringement of patents of
                    third persons; or

               (b)  a requirement that either party shall file any patent
                    application, secure any patent, or maintain any patent in
                    force except that LICENSOR agrees to use reasonable efforts
                    to prosecute and maintain the Licensed Patents; or

               (c)  an obligation to bring or defend or prosecute actions or
                    suits against or by third parties for infringement of any
                    patent; or

               (d)  granting by implication, estoppel, or otherwise, any
                    licenses or rights under patents other than the Licensed
                    Patents.

     The LICENSOR does not make any representations, extend any warranties of
any kind, either express or implied, including but not limited to warranties of
fitness for a particular purpose or of merchantability or otherwise, or assume
any responsibilities whatever with respect to use, sale, or other disposition by
the LICENSEE or its Affiliates or its vendees or transferees of products
incorporating or made by use of any information obtained or patents licensed
under this Agreement.

                      ARTICLE 5:  INDEMNITY AND INSURANCE

     5.1  "Indemnity".  LICENSEE shall defend, indemnify and

hold LICENSOR and its employees, officers and directors harmless from and
against any and all damages, injuries, causes of action, costs, losses and
expenses, including without limitation, Court costs and reasonable attorney
fees, if any, resulting from claims made against LICENSOR by virtue of the
license granted herein to LICENSEE and its Affiliates.
<PAGE>
 
     5.2  "INSURANCE".  LICENSEE and its Affiliates shall obtain and maintain a
policy or policies of liability insurance covering Licensed Products in the
amount of not less than Five Million Dollars ($5,000,000) and shall have
LICENSOR named as an additional insures. LICENSEE agrees to have the policy in
force prior to first commercial sale.

                    ARTICLE 6: GOVERNMENTAL AUTHORIZATION

     6.1  "EXPORT AUTHORIZATION".  This Agreement may be subject to restrictions
concerning the export of products from the United States which may be imposed by
the U.S. Government or any other competent authority. Accordingly, LICENSEE and
its Affiliates agrees not to export or re-export, directly or indirectly,
Licensed Products for which the U.S. Government or other competent authority at
the time of export requires an export license or other approval, without first
obtaining the written consent to do so from the Department of Commerce or other
agency of the U.S. Government or from other competent authority when required by
an applicable statute or regulation. The LICENSOR shall provide to the LICENSEE
reasonable assistance for determining the need for, and the procuring of, such
consent.

                        ARTICLE 7: TERM AND TERMINATION

     7.1  "EFFECTIVENESS".  This Agreement shall become effective on the
Execution Date, and , unless terminated earlier in accordance with Section 7.2,
shall remain in effect until the expiration or lapse or declaration of
invalidity or unenforceability by a Court or agency of competent jurisdiction,
of the last to expire of the Licensed Patents. In the event the U.S. patent is
held invalid or unenforceable by a Court or Agency of competent jurisdiction,
the minimum royalty obligations of Article 3.3 shall be reduced to one-half
(1/2) of the amounts set forth for payments due following the date of such a
holding.

     7.2  "TERMINATION".  This Agreement may be terminated (1) for cause by
either party serving notice of such termination if a Party shall default in the
performance or observance of any of its obligations under this Agreement, and
such default shall continue for ninety (90) days after notice specifying such
default has been served upon the defaulting Party, or (2) without cause by
LICENSEE on ninety (90) days written notice, subject to the payment of all
royalty obligations through the date of termination, including pro-rata payment
of any minimum royalties.
<PAGE>
 
     Such right to termination shall not be exclusive, and exercise by either
Party shall not preclude the exercise by such Party of any other right or remedy
that it may have by law against the defaulting Party on account of any default
by the defaulting Party.


     7.3  "SURVIVAL".  Except as expressly otherwise proviced in this Agreement,
its termination shall not relieve any party of any obligation or liability
accrued hereunder prior to such termination.

                    ARTICLE 8: GENERAL TERMS AND CONDITIONS

     8.1  "MARK AND PUBLICITY".  Nothing contained in this Agreement shall be
construed as conferring any right to use in advertising, publicity or other
promotional activities any name, trade name, trademark, or other designation
(including any contraction, abbreviation, or simulation of any of the
foregoing), without the express written approval of the other Party, no party
shall use any designation of the other Party in any promotional activity
associated with this Agreement or the Licensed Product. Neither Party shall
issue any press release or make any public statement in regard to this Agreement
without the prior written approval of the other Party.

     8.2  "FORCE MAJEURE".  Neither the LICENSOR nor the LICENSEE shall be held
responsible for any delay or failure in the performance of this Agreement to the
extent such delay or failure is caused by fire, flood, explosion, war, embargo,
the act of any civil or military authority, acts of God, inability to secure
transportation facilities, acts or omissions of carriers, power outages, or by
any other causes beyond its control whether or not similar to the foregoing,
provided that the hindered Party (a) notifies the other Party of such cause, (b)
exercises reasonable effort to cure such delay or failure and resume
performance, and (c) excuses performance by the other Party during the period of
such delay or failure.

     8.3  "NOTICES".  Notices and payment under this Agreement shall be in
writing and sent by first class mail as follows:

          As to AKSYS, LTD.                     Lawrence H.N. Kinet
                                                Chairman and CEO
                                                AKSYS, LTD.
                                                1113 S. Milwaukee Avenue
                                                Suite 300
                                                Libertyville, IL 60048
<PAGE>
 
          As to ALLERGAN, INC.                  General Counsel
                                                ALLERGAN, INC.
                                                2525 Dupont Drive
                                                Irvine, CA  92715


     8.4  "RIGHT TO CONTINUE WORK WITH THIRD PARTIES".  Subject to the terms of
this Agreement, each Party shall be free to engage in other work, alone or with
others, and to furnish information to and receive information from others.

     8.5  "LIMITATION OF RIGHTS".  Except as expressly provided in this
Agreement, nothing contained herein shall be construed as conferring any license
or other rights by implication, estoppel or otherwise, under any patent or
patent applications, or any copyrights, trademarks, trade names or trade dress.

     8.6  "LIMITATION OF LIABILITY".  Neither Party will be liable to the other
for any indirect, special or consequential damages whatsoever, whether grounded
in tort (including negligence), strict liability or contract, and neither
Party's liability under any circumstances shall exceed the contract price
hereunder.

     8.7  "INDEPENDENT CONTRACTOR".  In the performance of this Agreement, the
status of the parties, including its employees and agents, shall be that of
independent contractors and not as employees or agents, or fiduciaries of the
other Party, and as such, neither Party shall have the right to make commitments
for or on behalf of the other Party.

     8.8  "GENERAL INDEMNIFICATION".  Each Party shall be responsible for (a)
the safety of its own employees and agents while engaged in work under the
Agreement, and (b) any liability for damages or personal injuries, including
death, resulting from work under the Agreement, without any warranty, liability,
or indemnification on the part of the other Party.

     8.9  "NO WAIVER".  Failure at any time to require performance of any of the
provisions herein shall not waive or diminish a Party's right thereafter to
demand compliance therewith or with any other provision. Waiver of any default
shall not waive any other default. A Party shall not be deemed to have waived
any rights hereunder unless such waiver is in writing and signed by a duly
authorized officer of the Party making such waiver.
<PAGE>
 
     8.10  "SEVERABILITY".  If one or more of the provisions of this Agreement
shall be held invalid, illegal or unenforceable, the remaining provisions shall
not in any way be affected for impaired thereby. In the event any provision is
held invalid, illegal or unenforceable, the parties shall use reasonable efforts
to substitute a valid, legal and enforceable provision which, insofar as is
practical, implements purposes of the section held invalid, illegal and
unenforceable.

     8.11  "APPLICABLE LAW".  This Agreement shall be governed by and construed
and enforced in accordance with the laws of the State of California and/or the
United States of America as may be applicable.

     8.12  "SETTLEMENT OF DISPUTES".  In the event of occurrence of any dispute
or disagreement other than payment of minimum royalties, the Parties shall first
exert their best efforts in good faith to resolve the matter amicably between
themselves as provided for in this Section 8.12. Within thirty (30) days after
written demand by either Party, each Party shall designate two (2)
representatives from among those personnel acquainted with the work involved who
shall discuss and attempt to resolve the dispute or disagreement at the offices
of the Party on which demand was served, or such other place agreeable to the
Parties. If a resolution has not been achieved within thirty (30) days from the
date on which the written demand for such working-level discussions was
originally made, then either Party may demand in writing that an officer (vice
president, president or director) from each Party discuss and attempt to resolve
the dispute or disagreement at a place mutually agreed upon by the Parties. If a
resolution has not been achieved within thirty (30) days after the written
demand for discussions between officers of the Parties, then either Party shall
be free to resort to a court of justice having jurisdiction over the Parties and
the subject matter of the dispute provided, however, that both Parties hereby
waive irrevocably any right to have such dispute or disagreement tried before a
jury.

     8.13  "AMENDMENTS".  No addition to, deletion from or modification of any
of the provisions of this Agreement shall be binding upon the Parties unless
made in writing and signed by a duly authorized representative of each Party.

     8.14  "ENTIRE AGREEMENT".  This Agreement and the attached Exhibit
constitute the entire agreement between the Parties with respect to its subject
matter, and supersede all previous discussions, representations and
understandings.
<PAGE>
 
     8.15  "ASSIGNMENT".  This Agreement may not be assigned or transferred in
any manner by either Party without the prior written consent of the other Party,
except that either Party may assign or transfer this Agreement to a third party
in connection with the transfer or sale of all or substantially all of its
business to which this Agreement pertains or the merger or consolidation of a
Party with or into a third party if said third party agrees in writing to accept
all of the terms and conditions of this Agreement.



                                   EXECUTION

     In consideration of the foregoing terms and conditions, the LICENSOR and
LICENSEE have executed this Agreement as of the date first written above.



AKSYS, LTD.                            ALLERGAN, INC.

By: /s/ Lawrence H.N. Kinet            By: /s/ Richard M. Haugen
    -----------------------                ---------------------
Name: L.H.N. Kinet                     Name: Richard M. Haugen
      ------------                           -----------------
Title: Chairman & CEO                  Title: COO
       --------------                         ---
Date: 3/4/96                           Date: 3/11/96
      ------                                 -------



ALLERGAN

By: /s/ Martin A. Voet
    ------------------
Name: Martin A. Voet
      --------------
Title: Ass't Secretary
       ---------------
Date: 3/7/96
      ------
<PAGE>
 
                                   EXHIBIT A

                              "LICENSED PATENTS"


               Country              Patent (Appln) Number
               -------              ---------------------

               U.S.                      5,392,653
               Australia                 (43959/93)
               Canada                    (2,136,640)
               EPO                       (0 643 823)
               Japan                     (500788/94)