<PAGE>
 
                                                                     EXHIBIT 99d

                         REGISTRATION RIGHTS AGREEMENT

          REGISTRATION RIGHTS AGREEMENT (this "Agreement"), dated as of April
30, 1999, by and among Organogenesis Inc., a Delaware corporation, with
headquarters located at 150 Dan Road, Canton, MA  02021 (the "Company"), and
Baxter Healthcare Corporation, a Delaware corporation with headquarters located
at One Baxter Parkway, Deerfield, IL 60015 (the "Purchaser").

     WHEREAS:

     A.  In connection with the Asset Purchase Agreement by and among the
parties dated April 30, 1999 (the "Asset Purchase Agreement"), the Company has
agreed, upon the terms and subject to the conditions of the Asset Purchase
Agreement, to issue and sell to the Purchaser shares of the Company's common
stock, $.01 par value per share (the "Common Stock"); and

     B.  To induce the Purchaser to execute and deliver the Asset Purchase
Agreement, the Company has agreed to provide certain registration rights under
the Securities Act of 1933, as amended, and the rules and regulations
thereunder, or any similar successor statute (collectively, the "1933 Act"), and
applicable state securities laws.

     NOW, THEREFORE, in consideration of the premises and the mutual covenants
contained herein and other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the Company and the Purchaser
hereby agree as follows:

     1.   DEFINITIONS.
          ----------- 

          As used in this Agreement, the following terms shall have the
following meanings:

          a.  "Person" means a corporation, a limited liability company, an
association, a partnership, an organization, a business, an individual, a
governmental or political subdivision thereof or a governmental agency.

          b.  "Register," "registered," and "registration" refer to a
registration effected by preparing and filing one or more Registration
Statements in compliance with the 1933 Act and pursuant to Rule 415 under the
1933 Act or any successor rule providing for the offering securities on a
continuous basis ("Rule 415"), and the declaration or ordering of effectiveness
of such Registration Statement(s) by the United States Securities and Exchange
Commission (the "SEC").
<PAGE>
 
          c.  "Registrable Securities" means the 50,000 shares of Common Stock
issued by the Company to the Purchaser on the date hereof in connection with and
subject to the terms and conditions of the Asset Purchase Agreement.

          d.  "Registration Statement" means a registration statement of the
Company filed under the 1933 Act.

     Capitalized terms used herein and not otherwise defined herein shall have
the respective meanings set forth in the Asset Purchase Agreement.

     2.   REGISTRATION.
          ------------ 

          a.  Subject to Sections 2(b) and (c), on or before May 14, 1999, the
Company shall prepare and file with the SEC a Registration Statement or
Registration Statements (as is necessary) on Form S-3 (or, if such form is
unavailable for such a registration, on such other form as is available for such
a registration, subject to the consent of the Purchaser and the provisions of
Section 2(b), which consent will not be unreasonably withheld), covering the
resale of all of the Registrable Securities.  The Company shall use its best
efforts to have the Registration Statement declared effective by the SEC within
ninety (90) days after the filing of the Registration Statement with the SEC.
In the event that the SEC shall be closed for business for any period greater
than ten consecutive days, the time periods set forth in this Section 2(a) shall
be extended by the same number of days.

          b.  The Company covenants that it will use its best efforts to meet
the requirements for the use of Form S-3 for registration of the sale by the
Purchaser of the Registrable Securities on and after May 14, 1999 and the
Company has filed and shall file all reports required to be filed by the Company
with the SEC in a timely manner so as to obtain and maintain such eligibility
for the use of Form S-3.  In the event that Form S-3 is not available for sale
by the Purchaser of the Registrable Securities, then the Company (i) with the
consent of the Purchaser pursuant to Section 2(a), shall register the sale of
the Registrable Securities on another appropriate form and (ii) the Company
shall undertake to register the Registrable Securities on Form S-3 as soon as
such form is available, provided that the Company shall maintain the
effectiveness of the Registration Statement then in effect until such time as a
Registration Statement on Form S-3 covering the Registrable Securities has been
declared effective by the SEC.

          c.  Notwithstanding the foregoing, the parties agree that if (i) in
the good faith judgment of the Board of Directors of the Company such
registration would be seriously detrimental to the Company, and the Board of
Directors of the Company concludes, as a result, that it is essential to defer
the filing of such Registration Statement or Registration Statement(s), and 
(ii) the Company shall furnish to the Purchaser a certificate signed by the
Chief Executive Officer of the Company stating that in the good faith judgment
of the Board of Directors of the Company, it would be seriously detrimental to
the Company for such Registration Statement or Registration Statement(s) to be
filed in the near future, then the Company shall have the right to defer such
filing for a period of ninety (90) days.

                                      -2-
<PAGE>
 
     d.  Notwithstanding any provision of this Agreement to the contrary, upon
the sale of any of the Registrable Securities to the Company pursuant to Section
6.03 of the Asset Purchase Agreement, the Company shall have no further
obligations hereunder with respect to any such Registrable Securities.

     3.   RELATED OBLIGATIONS.
          ------------------- 

     At such time as the Company is obligated to file a Registration Statement
with the SEC pursuant to Section 2(a), the Company will use its best efforts to
effect the registration of the Registrable Securities in accordance with the
intended method of disposition thereof and, pursuant thereto, the Company shall
have the following obligations:

          a.  Subject to Section 2(c), the Company shall promptly prepare and
file with the SEC a Registration Statement with respect to the Registrable
Securities on or before May 14, 1999 and use its best efforts to cause such
Registration Statement(s) relating to Registrable Securities to become effective
as soon as practicable (but no later than ninety (90) days) after the filing of
the Registration Statement with the SEC, and keep the Registration Statement(s)
effective pursuant to Rule 415 at all times until the earlier of (i) the date as
of which the Purchaser may sell all of the Registrable Securities without
restriction pursuant to Rule 144(k) promulgated under the 1933 Act (or successor
thereto) or (ii) the date on which the Purchaser shall have sold all the
Registrable Securities (the "Registration Period"), which Registration
Statement(s) (including any amendments or supplements thereto and prospectuses
contained therein) shall not contain any untrue statement of a material fact or
omit to state a material fact required to be stated therein, or necessary to
make the statements therein, in light of the circumstances in which they were
made, not misleading.

          b.  The Company shall prepare and file with the SEC such amendments
(including post-effective amendments) and supplements to the Registration
Statement(s) and the prospectus(es) used in connection with the Registration
Statement(s), which prospectus(es) are to be filed pursuant to Rule 424
promulgated under the 1933 Act, as may be necessary to keep the Registration
Statement(s) effective at all times during the Registration Period, and, during
such period, comply with the provisions of the 1933 Act with respect to the
disposition of all Registrable Securities of the Company covered by the
Registration Statement(s) until such time as all of such Registrable Securities
shall have been disposed of in accordance with the intended methods of
disposition by the seller or sellers thereof as set forth in the Registration
Statement(s).

          c.  The Company shall furnish to the Purchaser and the Purchaser's
legal counsel without charge (i) promptly after the same is prepared and filed
with the SEC at least one copy of the Registration Statement and any amendment
thereto, including financial statements and schedules, all documents
incorporated therein by reference and all exhibits, the prospectus(es) included
in such Registration Statement(s) (including each preliminary prospectus) and,
with regards to the Registration Statement, any correspondence by or on behalf
of the Company to the SEC or the staff of the SEC and any correspondence from
the SEC or the staff of the SEC to the Company or its representatives, (ii) upon
the effectiveness of any 

                                      -3-
<PAGE>
 
Registration Statement, five (5) copies of the prospectus included in such
Registration Statement and all amendments and supplements thereto and (iii) such
other documents, including any preliminary prospectus, as the Purchaser may
reasonably request in order to facilitate the disposition of the Registrable
Securities.

          d.  The Company shall use reasonable efforts to (i) register and
qualify the Registrable Securities covered by the Registration Statement under
such other securities or "blue sky" laws of such jurisdictions in the United
States as the Purchaser reasonably requests, (ii) prepare and file in those
jurisdictions, such amendments (including post-effective amendments) and
supplements to such registrations and qualifications as may be necessary to
maintain the effectiveness thereof during the Registration Period, (iii) take
such other actions as may be necessary to maintain such registrations and
qualifications in effect at all times during the Registration Period, and 
(iv) take all other actions reasonably necessary or advisable to qualify the
Registrable Securities for sale in such jurisdictions; provided, however, that
the Company shall not be required in connection therewith or as a condition
thereto to (x) qualify to do business in any jurisdiction where it would not
otherwise be required to qualify but for this Section 3(d), (y) subject itself
to general taxation in any such jurisdiction, or (z) file a general consent to
service of process in any such jurisdiction. The Company shall promptly notify
the Purchaser of the receipt by the Company of any notification with respect to
the suspension of the registration or qualification of any of the Registrable
Securities for sale under the securities or "blue sky" laws of any jurisdiction
in the United States or its receipt of actual notice of the initiation or
threatening of any proceeding for such purpose.

          e.  As promptly as practicable after becoming aware of such event, the
Company shall notify the Purchaser in writing of the happening of any event as a
result of which the prospectus included in a Registration Statement, as then in
effect, includes an untrue statement of a material fact or omission to state a
material fact required to be stated therein or necessary to make the statements
therein, in light of the circumstances under which they were made, not
misleading, and promptly prepare a supplement or amendment to the Registration
Statement to correct such untrue statement or omission, and deliver five (5)
copies of such supplement or amendment to the Purchaser.  The Company shall also
promptly notify the Purchaser in writing (i) when a prospectus or any prospectus
supplement or post-effective amendment has been filed, and when a Registration
Statement or any post-effective amendment has become effective, (ii) of any
request by the SEC for amendments or supplements to a Registration Statement or
related prospectus or related information, and (iii) of the Company's reasonable
determination that a post-effective amendment to a Registration Statement would
be appropriate.

          f.  The Company shall use its best efforts to prevent the issuance of
any stop order or other suspension of effectiveness of a Registration Statement,
or the suspension of the qualification of any of the Registrable Securities for
sale in any jurisdiction and, if such an order or suspension is issued, to
obtain the withdrawal of such order or suspension at the earliest possible
moment and to notify the Purchaser of the issuance of such order and the
resolution thereof or its receipt of actual notice of the initiation or threat
of any proceeding for such purpose.

                                      -4-
<PAGE>
 
          g.  The Company shall permit the Purchaser and a single firm of
counsel, initially Sidley & Austin, or such other counsel as thereafter
designated as the Purchaser's counsel to review and comment upon the
Registration Statement(s) and all amendments and supplements thereto at least
seven (7) days prior to their filing with the SEC, and not file any document in
a form to which such counsel reasonably objects.  The Company shall not submit a
request for acceleration of the effectiveness of a Registration Statement(s) or
any amendment or supplement thereto without the prior approval of such counsel,
which consent shall not be unreasonably withheld.

          h.  The Company shall hold in confidence and not make any disclosure
of information concerning the Purchaser provided to the Company unless 
(i) disclosure of such information is necessary to comply with federal or state
securities laws, (ii) the disclosure of such information is necessary to avoid
or correct a misstatement or omission in any Registration Statement, (iii) the
release of such information is ordered pursuant to a subpoena or other final,
non-appealable order from a court or governmental body of competent
jurisdiction, or (iv) such information has been made generally available to the
public other than by disclosure in violation of this or any other agreement. The
Company agrees that it shall, upon learning that disclosure of such information
concerning the Purchaser is sought in or by a court or governmental body of
competent jurisdiction or through other means, give prompt written notice to the
Purchaser and allow the Purchaser, at the Purchaser's expense, to undertake
appropriate action to prevent disclosure of, or to obtain a protective order
for, such information.

          i.  The Company shall use its best efforts either to (i) cause all the
Registrable Securities covered by a Registration Statement to be listed on each
securities exchange on which securities of the same class or series issued by
the Company are then listed, if any, if the listing of such Registrable
Securities is then permitted under the rules of such exchange, or (ii) if the
securities of the same class or series issued by the Company as the Registrable
Securities are not then listed on any securities exchange, secure designation
and quotation of all the Registrable Securities covered by the Registration
Statement on the Nasdaq National Market System or, if, despite the Company's
best efforts to satisfy the preceding clause (i) or (ii), the Company is
unsuccessful in satisfying the preceding clause (i) or (ii), to secure the
inclusion for quotation on the Nasdaq SmallCap Market for such Registrable
Securities and, without limiting the generality of the foregoing, to arrange for
at least two market makers to register with the National Association of
Securities Dealers, Inc. ("NASD") as such with respect to such Registrable
Securities.  The Company shall pay all fees and expenses in connection with
satisfying its obligation under this Section 3(i).

          j.  The Company shall cooperate with the Purchaser to facilitate the
timely preparation and delivery of certificates representing the Registrable
Securities to be offered pursuant to a Registration Statement, which certificate
shall not bear any restrictive legend other than the lock-up legend referenced
in the Asset Purchase Agreement, if applicable, and enable such certificates to
be in such denominations or amounts, as the case may be, as the Purchaser may
reasonably request and registered in such names as the Purchaser may request.
As soon as practicable after the date on which any Registration Statement
registering the resale of Registrable Securities is declared effective, the
Company shall deliver to its transfer agent 

                                      -5-
<PAGE>
 
instructions, accompanied by any reasonably required opinion of counsel, that
permit sales of unlegended securities in a timely fashion that complies with
then mandated securities settlement procedures for regular way market
transactions.

          k.  The Company shall take all other reasonable actions necessary to
expedite and facilitate disposition by the Purchaser of Registrable Securities
pursuant to a Registration Statement.

          l.  The Company shall use its best efforts to cause the Registrable
Securities covered by the applicable Registration Statement to be registered
with or approved by such other governmental agencies or authorities as may be
necessary to consummate the disposition of such Registrable Securities.

          m.  The Company shall otherwise use its best efforts to comply with
all applicable rules and regulations of the SEC in connection with any
registration hereunder.

     4.   OBLIGATIONS OF THE PURCHASER.
          ---------------------------- 

          a.  At least seven (7) business days prior to the anticipated filing
date of the Registration Statement, the Company shall notify the Purchaser in
writing of the information the Company requires from the Purchaser if the
Purchaser elects to have any of the Purchaser's Registrable Securities included
in the Registration Statement.  It shall be a condition precedent to the
obligations of the Company to complete the registration pursuant to this
Agreement with respect to the Registrable Securities that the Purchaser shall
furnish to the Company such information regarding itself, the Registrable
Securities held by it and the intended method of disposition of the Registrable
Securities held by it as shall be reasonably required to effect the registration
of such Registrable Securities and shall execute such documents in connection
with such registration as the Company may reasonably request.

          b.  The Purchaser agrees to cooperate with the Company as reasonably
requested by the Company in connection with the preparation and filing of the
Registration Statement hereunder.

          c.  The Purchaser agrees that, upon receipt of any notice from the
Company of the happening of any event of the kind described in Section 3(f) or
the first sentence of 3(e), the Purchaser will immediately discontinue
disposition of Registrable Securities pursuant to the Registration Statement
covering such Registrable Securities until the Purchaser's receipt of the copies
of the supplemented or amended prospectus contemplated by Section 3(f) or the
first sentence of 3(e) and, if so directed by the Company, the Purchaser shall
deliver to the Company (at the expense of the Company) or destroy all copies in
the Purchaser's possession, of the prospectus covering such Registrable
Securities current at the time of receipt of such notice.

     5.   EXPENSES OF REGISTRATION.
          ------------------------ 

          All reasonable expenses incurred in connection with the filing of the
Registration Statement contemplated hereby, including, without limitation, all
registration, listing and 

                                      -6-
<PAGE>
 
qualifications fees, printers and accounting fees, shall be paid by the Company.
Notwithstanding the foregoing, in the event that the Purchaser requests the use
of a form other than Form S-3 for registration, then the Company shall not be
obligated to pay for any expenses in excess of those set forth in the prior
sentence.

     6.   INDEMNIFICATION.
          --------------- 

          In the event any Registrable Securities are included in a Registration
Statement under this Agreement:

          a.  To the fullest extent permitted by law, the Company will, and
hereby does, indemnify, hold harmless and defend the Purchaser, the directors,
officers, partners, employees, agents and each Person, if any, who controls the
Purchaser  within the meaning of the 1933 Act or the Securities Exchange Act of
1934, as amended (the "1934 Act")(each an "Indemnified Person"), against any
losses, claims, damages, liabilities, judgments, fines, penalties, charges,
costs, reasonable attorneys' fees or  expenses (collectively, "Claims"),
incurred in investigating, preparing or defending any action, claim, suit,
inquiry, proceeding, investigation or appeal taken from the foregoing by or
before any court or governmental, administrative or other regulatory agency,
body or the SEC, whether pending or threatened, whether or not an indemnified
party is or may be a party thereto ("Indemnified Damages"), to which any of them
may become subject insofar as such Claims (or actions or proceedings, whether
commenced or threatened, in respect thereof) arise out of or are based upon: 
(i) any untrue statement or alleged untrue statement of a material fact in a
Registration Statement or any post-effective amendment thereto or in any filing
made in connection with the qualification of the offering under the securities
or other "blue sky" laws of any jurisdiction in which Registrable Securities are
offered ("Blue Sky Filing"), or the omission or alleged omission to state a
material fact required to be stated therein or necessary to make the statements
therein, in light of the circumstances under which the statements therein were
made, not misleading, (ii) any untrue statement or alleged untrue statement of a
material fact contained in any preliminary prospectus if used prior to the
effective date of such Registration Statement, or contained in the final
prospectus (as amended or supplemented, if the Company files any amendment
thereof or supplement thereto with the SEC) or the omission or alleged omission
to state therein any material fact necessary to make the statements made
therein, in light of the circumstances under which the statements therein were
made, not misleading, or (iii) any violation or alleged violation by the Company
of the 1933 Act, the 1934 Act, any other law, including, without limitation, 
any state securities law, or any rule or regulation thereunder relating to the
offer or sale of the Registrable Securities pursuant to a Registration Statement
(the matters in the foregoing clauses (i) through (iii) being, collectively,
"Violations"). Subject to the restrictions set forth in Section 6(d) with
respect to the number of legal counsel, the Company shall reimburse the
Purchaser, promptly as such expenses are incurred and are due and payable, for
any reasonable legal fees or expenses incurred by it in connection with
investigating or defending any such Claim. Notwithstanding anything to the
contrary contained herein, the indemnification agreement contained in this
Section 6(a): (i) shall not apply to a Claim arising out of or based upon a
Violation which occurs in reliance upon and in conformity with information
furnished in writing to the Company by any Indemnified Person expressly for use
in connection with the preparation of the Registration Statement or any such

                                      -7-
<PAGE>
 
amendment thereof or supplement thereto, if such prospectus was timely made
available by the Company pursuant to Section 3(c); (ii) with respect to any
preliminary prospectus, shall not inure to the benefit of any such person from
whom the person asserting any such Claim purchased the Registrable Securities
that are the subject thereof (or to the benefit of any person controlling such
person) if the untrue statement or omission of material fact contained in the
preliminary prospectus was corrected in the prospectus, as then amended or
supplemented, if such prospectus was timely made available by the Company
pursuant to Section 3(c), and the Indemnified Person was promptly advised in
writing not to use the incorrect prospectus prior to the use giving rise to a
Violation and such Indemnified Person, notwithstanding such advice, used it;
(iii) shall not be available to the extent such Claim is based on a failure of
the Purchaser to deliver or to cause to be delivered the prospectus made
available by the Company; and (iv) shall not apply to amounts paid in settlement
of any Claim if such settlement is effected without the prior written consent of
the Company, which consent shall not be unreasonably withheld. Such indemnity
shall remain in full force and effect regardless of any investigation made by or
on behalf of the Indemnified Person and shall survive the transfer of the
Registrable Securities by the Purchaser pursuant to Section 9.

          b.  In connection with the Registration Statement, the Purchaser
agrees to indemnify, hold harmless and defend, to the same extent and in the
same manner as is set forth in Section 6(a), the Company, each of its directors,
officers and each Person, if any, who controls the Company within the meaning of
the 1933 Act or the 1934 Act (collectively and together with an Indemnified
Person, an "Indemnified Party"), against any Claim or Indemnified Damages to
which any of them may become subject, under the 1933 Act, the 1934 Act or
otherwise, insofar as such Claim or Indemnified Damages arise out of or are
based upon any Violation, in each case to the extent, and only to the extent,
that such Violation occurs in reliance upon and in conformity with written
information furnished to the Company by the Purchaser expressly for use in
connection with such Registration Statement; and, subject to Section 6(d), the
Purchaser will reimburse any legal or other expenses reasonably incurred by them
in connection with investigating or defending any such Claim; provided, however,
that the indemnity agreement contained in this Section 6(b) and the agreement
with respect to contribution contained in Section 7 shall not apply to amounts
paid in settlement of any Claim if such settlement is effected without the prior
written consent of the Purchaser, which consent shall not be unreasonably
withheld; provided, further, however, that the Purchaser shall be liable under
this Section 6(b) for only that amount of a Claim or Indemnified Damages as does
not exceed the gross proceeds to the Purchaser as a result of the sale of
Registrable Securities pursuant to such Registration Statement.  Such indemnity
shall remain in full force and effect regardless of any investigation made by or
on behalf of such Indemnified Party and shall survive the transfer of the
Registrable Securities by the Purchaser pursuant to Section 9.  Notwithstanding
anything to the contrary contained herein, the indemnification agreement
contained in this Section 6(b) with respect to any preliminary prospectus shall
not inure to the benefit of any Indemnified Party if the untrue statement or
omission of material fact contained in the preliminary prospectus was corrected
on a timely basis in the prospectus, as then amended or supplemented.

          c.  The Company shall be entitled to receive indemnities from
underwriters, selling brokers, dealer managers and similar securities industry
professionals participating in any 

                                      -8-
<PAGE>
 
distribution, to the same extent as provided above, with respect to information
such persons so furnished in writing expressly for inclusion in the Registration
Statement.

          d.  Promptly after receipt by an Indemnified Person or Indemnified
Party under this Section 6 of notice of the commencement of any action or
proceeding (including any governmental action or proceeding) involving a Claim,
such Indemnified Person or Indemnified Party shall, if a Claim in respect
thereof is to be made against any indemnifying party under this Section 6,
deliver to the indemnifying party a written notice of the commencement thereof,
and the indemnifying party shall have the right to participate in, and, to the
extent the indemnifying party so desires, jointly with any other indemnifying
party similarly noticed, to assume control of the defense thereof with counsel
mutually satisfactory to the indemnifying party and the Indemnified Person or
the Indemnified Party, as the case may be; provided, however, that an
Indemnified Person or Indemnified Party shall have the right to retain its own
counsel with the fees and expenses to be paid by the indemnifying party, if, in
the reasonable opinion of counsel retained by the indemnifying party, the
representation by such counsel of the Indemnified Person or Indemnified Party
and the indemnifying party would be inappropriate due to actual or potential
differing interests between such Indemnified Person or Indemnified Party and any
other party represented by such counsel in such proceeding.  The Indemnified
Party or Indemnified Person shall cooperate fully with the indemnifying party in
connection with any negotiation or defense of any such action or claim by the
indemnifying party and shall furnish to the indemnifying party all information
reasonably available to the Indemnified Party or Indemnified Person which
relates to such action or claim.  The indemnifying party shall keep the
Indemnified Party or Indemnified Person fully apprised at all times as to the
status of the defense or any settlement negotiations with respect thereto.  
No indemnifying party shall be liable for any settlement of any action, claim or
proceeding effected without its written consent, provided, however, that the
indemnifying party shall not unreasonably withhold, delay or condition its
consent. No indemnifying party shall, without the consent of the Indemnified
Party or Indemnified Person, consent to entry of any judgment or enter into any
settlement or other compromise which does not include as an unconditional term
thereof the giving by the claimant or plaintiff to such Indemnified Party or
Indemnified Person of a release from all liability in respect to such claim or
litigation. Following indemnification as provided for hereunder, the
indemnifying party shall be subrogated to all rights of the Indemnified Party or
Indemnified Person with respect to all third parties, firms or corporations
relating to the matter for which indemnification has been made. The failure to
deliver written notice to the indemnifying party within a reasonable time of the
commencement of any such action shall not relieve such indemnifying party of any
liability to the Indemnified Person or Indemnified Party under this Section 6,
except to the extent that the indemnifying party is prejudiced in its ability to
defend such action.

          e.  The indemnification required by this Section 6 shall be made by
periodic payments of the amount thereof during the course of the investigation
or defense, as and when bills are received or Indemnified Damages are incurred.

          f.  The indemnity agreements contained herein shall be in addition to
(i) any cause of action or similar right of the Indemnified Party or Indemnified
Person against the 

                                      -9-
<PAGE>
 
indemnifying party or others, and (ii) any liabilities the indemnifying party
may be subject to pursuant to the law.

     7.   CONTRIBUTION.
          ------------ 

     If any Claim or Indemnified Damages under Section 6(a) or 6(b) is
unavailable to an Indemnified Party because of a failure or refusal of a
governmental authority to enforce such indemnification in accordance with its
terms (by reason of public policy or otherwise), then each indemnifying party,
in lieu of indemnifying such Indemnified Party, shall contribute to the amount
paid or payable by such Indemnified Party as a result of such Claims or
Indemnified Damages, in such proportion as is appropriate to reflect the
relative fault of the indemnifying party and Indemnified Party in connection
with the actions, statements or omissions that resulted in such Claims or
Indemnified Damages as well as any other relevant equitable considerations.  
The relative fault of such indemnifying party and Indemnified Party shall be
determined by reference to, among other things, whether any action in question,
including any untrue or alleged untrue statement of a material fact or omission
or alleged omission of a material fact, has been taken or made by, or relates to
information supplied by, such indemnifying party or Indemnified Party, and the
parties' relative intent, knowledge, access to information and opportunity to
correct or prevent such action, statement or omission. The amount paid or
payable by a party as a result of any Claims or Indemnified Damages shall be
deemed to include, subject to the limitations set forth in Section 6(d), any
reasonable attorneys' or other reasonable fees or expenses incurred by such
party in connection with any proceeding to the extent such party would have been
indemnified for such fees or expenses if the indemnification was available to
such party in accordance with its terms.

          The parties hereto agree that it would not be just and equitable if
contribution pursuant to this Section 7 were determined by pro rata allocation
                                                           --- ----           
or by any other method of allocation that does not take into account the
equitable considerations referred to in the immediately preceding paragraph.
Notwithstanding the provisions of this Section 7, the Purchaser shall not be
required to contribute, in the aggregate, any amount in excess of the amount by
which the proceeds actually received by the Purchaser from the sale of the
Registrable Securities subject to the proceeding exceeds the amount of any
damages that the Purchaser has otherwise been required to pay by reason of such
untrue or alleged untrue statement or omission or alleged omission.  No Person
guilty of fraudulent misrepresentation (within the meaning of Section 11(f) of
the Securities Act) shall be entitled to contribution from any Person who was
not guilty of such fraudulent misrepresentation.

          The indemnity and contribution agreements contained in Section 6 and
this Section 7 are in addition to any liability that the indemnifying parties
may have to the Indemnified Parties.

                                      -10-
<PAGE>
 
     8.   REPORTS UNDER THE 1934 ACT.
          -------------------------- 

          With a view to making available to the Purchaser the benefits of 
Rule 144 promulgated under the 1933 Act or any other similar rule or regulation
of the SEC that may at any time permit the Purchaser to sell securities of the
Company to the public without registration ("Rule 144"), the Company agrees to:

          a.  make and keep public information available, as those terms are
understood and defined in Rule 144;

          b.  file with the SEC in a timely manner all reports and other
documents required of the Company under the 1933 Act and the 1934 Act so long as
the Company remains subject to such requirements and the filing of such reports
and other documents is required for the applicable provisions of Rule 144; and

          c.  furnish to the Purchaser so long as the Purchaser owns Registrable
Securities, promptly upon request, (i) a written statement by the Company that
it has complied with the reporting requirements of Rule 144, the 1933 Act and
the 1934 Act, (ii) a copy of the most recent annual or quarterly report of the
Company and such other reports and documents so filed by the Company, and 
(iii) such other information as may be reasonably requested to permit the
Purchaser to sell such securities pursuant to Rule 144 without registration.

     9.   AMENDMENT OF REGISTRATION RIGHTS.
          -------------------------------- 

          Provisions of this Agreement may be amended and the observance thereof
may be waived (either generally or in a particular instance and either
retroactively or prospectively), only with the written consent of the Company
and the Purchaser.  Any amendment or waiver effected in accordance with this
Section 9 shall be binding upon the Purchaser and the Company.

     10.  MISCELLANEOUS.
          ------------- 

          a.  A person or entity is deemed to be a holder of Registrable
Securities whenever such person or entity owns of record such Registrable
Securities.  If the Company receives conflicting instructions, notices or
elections from two or more persons or entities with respect to the same
Registrable Securities, the Company shall act upon the basis of instructions,
notice or election received from the registered owner of such Registrable
Securities.

          b.  Any notices consents, waivers or other communications required or
permitted to be given under the terms of this Agreement must be in writing and
will be deemed to have been delivered (i) upon receipt, when delivered
personally; (ii) upon receipt, when sent by facsimile, provided a copy is mailed
by U.S. certified mail, return receipt requested; (iii) three (3) days after
being sent by U.S. certified mail, return receipt requested; or (iv) one (1) day
after deposit with a nationally recognized overnight delivery service, in each
case properly addressed to the party to receive the same.  The addresses and
facsimile numbers for such communications shall be:

                                      -11-
<PAGE>
 
          if to the Company:

               Organogenesis Inc.
               150 Dan Road
               Canton, MA  02021

               Telephone:  (781) 575-0775
               Facsimile:  (781) 575-1570

          with a copy to:

               Mintz, Levin, Cohn, Ferris, Glovsky and Popeo, P.C.
               One Financial Center
               Boston, MA 02111

               Telephone:  (617) 542-6000
               Facsimile:  (617) 542-2241
               Attention:  Jeffrey M. Wiesen, Esq.

          if to the Purchaser,


               Baxter Healthcare Corporation
               One Baxter Parkway
               Deerfield, IL 60015
               Attn:  Lee Blumenfeld, M.D.
               Fax:  (847) 270-5660

          with a copy to:

               Baxter Healthcare Corporation
               One Baxter Parkway
               Deerfield, IL 60015
               Attn:  Joseph B. Barrett, Esq.
               Fax:  (847) 270-5660

     Each party shall provide five (5) days prior notice to the other party of
any change in address, phone number or facsimile number.

          c.  Failure of any party to exercise any right or remedy under this
Agreement or otherwise, or delay by a party in exercising such right or remedy,
shall not operate as a waiver thereof.

          d.  This Agreement shall be governed by and interpreted in accordance
with the laws of the Commonwealth of Massachusetts without regard to the
principles of conflict of laws.  If any provision of this Agreement shall be
invalid or unenforceable in any jurisdiction, such invalidity or
unenforceability shall not affect the validity or enforceability of the
remainder 

                                      -12-
<PAGE>
 
of this Agreement in that jurisdiction or the validity or enforceability of any
provision of this Agreement in any other jurisdiction.

          e.  This Agreement and the Asset Purchase Agreement (including all
schedules and exhibits thereto) constitute the entire agreement among the
parties hereto with respect to the subject matter hereof and thereof.  There are
no restrictions, promises, warranties or undertakings, other than those set
forth or referred to herein and therein.  The aforementioned documents supersede
all prior agreements and understandings among the parties hereto with respect to
the subject matter hereof and thereof.

          f.  This Agreement shall inure to the benefit of and be binding upon
the permitted successors and assigns of each of the parties hereto.

          g.  The headings in this Agreement are for convenience of reference
only and shall not limit or otherwise affect the meaning hereof.

          h.  This Agreement may be executed in two or more identical
counterparts, each of which shall be deemed an original but all of which shall
constitute one and the same agreement.  This Agreement, once executed by a
party, may be delivered to the other party hereto by facsimile transmission of a
copy of this Agreement bearing the signature of the party so delivering this
Agreement.

          i.  Each party shall do and perform, or cause to be done and
performed, all such further acts and things, and shall execute and deliver all
such other agreements, certificates, instruments and documents, as the other
party may reasonably request in order to carry out the intent and accomplish the
purposes of this Agreement and the consummation of the transactions contemplated
hereby.

     IN WITNESS WHEREOF, the parties have caused this Registration Rights
Agreement to be duly executed as of day and year first above written.

COMPANY:                                 PURCHASER:

ORGANOGENESIS INC.                       BAXTER HEALTHCARE   CORPORATION    
                                                                            
                                                                            
By:                                      By:                                 
    ------------------------------           -------------------------------
                                                                            
Name:                                    Name:                              
      ----------------------------             -----------------------------
                                                                            
Its:                                     Its:                                
     -----------------------------            ------------------------------ 

                                      -13-