<PAGE>
 
                                                                     EXHIBIT 3.1

                          CERTIFICATE OF INCORPORATION
                                       OF
                              ASCEND MEDICAL CORP.


     THE UNDERSIGNED, for the purpose of forming a corporation pursuant to the
provisions of the General Corporation Law of Delaware, does hereby certify as
follows:

     FIRST:  The name of the Corporation is Ascend Medical Corp.

     SECOND:  The address of the Corporation's registered office in the State of
Delaware is 1209 Orange Street, Wilmington, New Castle County.  The name of the
Corporation's registered agent at such address is The Corporation Trust Company.

     THIRD:  The purpose or the Corporation is to engage in any lawful act or
activity for which corporations may be organized under the General Corporation
Law of Delaware.

     FOURTH:  The total number of shares of stock which the Corporation shall
have authority to issue is two million (2,000,000) shares, divided into two
classes consisting of one million (1,000,000) Preferred Shares, and the other
class consisting of one million (1,000,000) Common Shares, each or which shall
have the par value of $.01 per share.

     The Board of Directors or the Corporation shall have the power by
resolution to (a) provide for the issuance of shares of preferred stock in
series, (b) determine the number of shares of such stock in such series, and (c)
fix the designations, preferences, qualifications, limitations, restrictions and
special or relative rights of shares of preferred stock or any series thereof.

     FIFTH:  The name and mailing address of the incorporator is as follow:

          Name                           Mailing Address
          ----                           ---------------

          Kyle M. Fink, M.D.             c/o HOA
                                         2005 Franklin Street
                                         Suite 150
                                         Denver, Colorado  80205

                                       1
<PAGE>
 
     SIXTH:  In furtherance and not in limitation of the general powers
conferred by the laws of the State of Delaware, the Board of Directors is
expressly authorized to make, alter or repeal the Bylaws of the Corporation,
except as specifically otherwise provided therein.

     SEVENTH:  A director of the Corporation shall have no personal liability to
the Corporation or its stockholders for monetary damages for breach of fiduciary
duty as a director except to the extent that Section 102(b)(7) (or any successor
provision) of the Delaware General Corporation Law, as amended from time to
time, expressly provides that the liability of a director not be eliminated or
limited.

     EIGHTH:  Whenever a compromise or arrangement is proposed between this
Corporation and its creditors or any class of them and/or between this
Corporation and its stockholders or any class of them, any court of equitable
jurisdiction within the State of Delaware may, on the application in a summary
way of this Corporation or of any creditor or stockholder thereof or on the
application of any receiver or receivers appointed for this Corporation under
the provisions of Section 291 of Title 8 of the Delaware Code or on the
application of trustees in dissolution or of any receiver or receivers appointed
for this Corporation under the provisions of Section 279 of Title 8 of the
Delaware Code, order a meeting of the creditors or class of creditors, and/or of
the stockholders or class of stockholders of this Corporation, as the case may
be, to be summoned in such manner as the said court directs.  If a majority in
number representing three-fourths in value of the creditors or class of
creditors, and/or of the stockholders or class of stockholders or this
Corporation, as the case may be, agree to any compromise or arrangement and to
any reorganization of this Corporation as consequence of such compromise or
arrangement, the said compromise or arrangement and the said reorganization
shall, if sanctioned by the court to which the said application has been made,
be

                                       2
<PAGE>
 
binding on all the creditors or class of creditors, and/or on all the
stockholders or class of stockholders of this Corporation as the case may be,
and also on this Corporation.

     NINTH:  The term of existence of the Corporation shall be perpetual.

     TENTH:  Any director or the entire Board of Directors may be removed, with
or without cause, by the holders of a majority of the shares entitled to vote at
an election of directors.

     IN WITNESS WHEREOF, the undersigned, being the incorporator hereinabove
named, does hereby execute this Certificate of Incorporation this 30th day of
October, 1992.


                         /s/ Kyle M. Fink, M.D.
                         --------------------------------
                         Kyle M. Fink, M.D., Incorporator

                                       3
<PAGE>
 
                            CERTIFICATE OF AMENDMENT
                                       OF
                          CERTIFICATE OF INCORPORATION
                                       OF
                              ASCEND MEDICAL CORP.


     Ascend Medical Corp., a corporation organized and existing under and by
virtue of the General Corporation Law of the State of Delaware, does hereby
certify:

     FIRST:  That the Sole Director of the corporation, by written consent,
filed with the minutes of the Board, adopted a resolution proposing and
declaring advisable the following amendment to the Certificate of Incorporation
of the corporation:

          RESOLVED, that the amendment of Article FIRST of the Corporation's
     Certificate of Incorporation to read in its entirety as follows (the
     "Amendment") is hereby proposed and declared to be advisable and in the
     best interests of the Corporation:

          "FIRST, the name of the corporation is AMERICAN ONCOLOGY RESOURCES,
     INC."

     SECOND:  That the sole stockholder has given a written consent to said
amendment in accordance with the provisions of Section 228 of the General
Corporation Law of the State of Delaware.

     THIRD:  That the amendment has been duly adopted in accordance with the
provisions of Section 242 and 228 of the General Corporation Law of the State of
Delaware.

     IN WITNESS WHEREOF, the corporation has caused its corporate seal to be
hereunto affixed and this certificate to be signed by its President and attested
by its Secretary, this 10th day of November, 1992.

                                    ASCEND MEDICAL CORP.



                                    By:/s/ Kyle M. Fink, M.D.
                                       -------------------------------
                                         Kyle M. Fink, M.D., President

                                       4
<PAGE>
 
                            CERTIFICATE OF AMENDMENT
                                       OF
                          CERTIFICATE OF INCORPORATION
                                       OF
                       AMERICAN ONCOLOGY RESOURCES, INC.


     It is hereby certified that:

     1.   The name of the corporation (hereinafter called the "Corporation") is
AMERICAN ONCOLOGY RESOURCES, INC.

     2.   The certificate of incorporation of the Corporation is hereby amended
by striking out the first paragraph of the fourth article thereof and by
substituting in lieu of said paragraph the following new paragraph:

          "The total number of shares of capital stock which the Corporation
          shall have authority to issue is twenty-six million (26,000,000)
          shares, consisting of one million (1,000,000) shares of preferred
          stock, par value $.01 per share, and twenty-five million (25,000,000)
          shares of common stock, par value $.01 per share."

     3.   The amendment of the certificate of incorporation herein certified has
been duly adopted in accordance with the provisions of Section 228 and 242 of
the General Corporation Law of the State of Delaware.  The holders of a majority
of outstanding stock entitled to vote thereon, by written consent in accordance
with the provisions of Section 228 of the General Corporation Law of the State
of Delaware, voted in favor of the amendment.  Prompt written notice of the
adoption of the amendment herein certified has been given to those stockholders
who have not consented in writing thereto, as provided in Section 228 of the
General Corporation Law of the State of Delaware.

     IN WITNESS WHEREOF, the Corporation has caused this certificate to be
signed by its Chairman of the Board and Chief Executive Officer and attested to
by its Secretary, this 9th day of March, 1994.

                              AMERICAN ONCOLOGY RESOURCES, INC.


                              By:/s/ R. Dale Ross
                                 --------------------------------------------
                                     R. Dale Ross, Chairman of the Board and
                                     Chief Executive Officer

ATTEST:


/s/ Leo E. Sands
-----------------------
Leo E. Sands, Secretary

                                       5
<PAGE>
 
                            CERTIFICATE OF AMENDMENT
                                       OF
                          CERTIFICATE OF INCORPORATION
                                       OF
                       AMERICAN ONCOLOGY RESOURCES, INC.


     It is hereby certified that:

     1.   The name of the corporation (hereinafter called the "Corporation") is
AMERICAN ONCOLOGY RESOURCES, INC.

     2.   The certificate of incorporation of the Corporation is hereby amended
by striking out the first paragraph of the fourth article thereof and by
substituting in lieu of said paragraph the following new paragraph:

          "The total number of shares of capital stock which the Corporation
          shall have authority to issue is forty-one million (41,000,000)
          shares, consisting of one million (1,000,000) shares of preferred
          stock, par value $.01 per share, and forty million (40,000,000) shares
          of common stock, par value $.01 per share."

     3.   The amendment of the certificate of incorporation herein certified has
been duly adopted in accordance with the provisions of Section 228 and 242 of
the General Corporation Law of the State of Delaware.  The holders of a majority
of outstanding stock entitled to vote thereon, by written consent in accordance
with the provisions of Section 228 of the General Corporation Law of the State
of Delaware, voted in favor of the amendment.  Prompt written notice of the
adoption of the amendment herein certified has been given to those stockholders
who have not consented in writing thereto, as provided in Section 228 of the
General Corporation Law of the State of Delaware.

     IN WITNESS WHEREOF, the Corporation has caused this certificate to be
signed by its Chairman of the Board and Chief Executive Officer and attested to
by its Secretary, this 2nd day of May, 1995.

                              AMERICAN ONCOLOGY RESOURCES, INC.


                              By:/s/ R. Dale Ross
                                 -------------------------------------------
                                     R. Dale Ross, Chairman of the Board and
                                     Chief Executive Officer

ATTEST:


/s/ Leo E. Sands
-----------------------
Leo E. Sands, Secretary

                                       6
<PAGE>
 
                            CERTIFICATE OF AMENDMENT
                                       OF
                          CERTIFICATE OF INCORPORATION
                                       OF
                       AMERICAN ONCOLOGY RESOURCES, INC.


     It is hereby certified that:

     1.   The name of the corporation (hereinafter called the "Corporation") is
AMERICAN ONCOLOGY RESOURCES, INC.

     2.   The certificate of incorporation of the Corporation is hereby amended
by striking out the first paragraph of the fourth article thereof and by
substituting in lieu of said paragraph the following new paragraph:

          "The total number of shares of capital stock which the Corporation
          shall have authority to issue is sixty-one million (61,000,000)
          shares, consisting of one million (1,000,000) shares of preferred
          stock, par value $.01 per share, and sixty million (60,000,000) shares
          of common stock, par value $.01 per share."

     3.   The amendment of the certificate of incorporation herein certified has
been duly adopted in accordance with the provisions of Section 242 of the
General Corporation Law of the State of Delaware; the amendment was duly adopted
by resolution of the Board of Directors on February 8, 1996, and the necessary
shares as required by statute were voted in favor of the amendment of the Annual
Meeting of Stockholders held on May 9, 1996.

     IN WITNESS WHEREOF, the Corporation has caused this certificate to be
signed by its Chairman of the Board and Chief Executive Officer and attested to
by its Secretary, this 9th day of May, 1996.

                              AMERICAN ONCOLOGY RESOURCES, INC.


                              By:/s/ R. Dale Ross
                                 -------------------------------------------
                                     R. Dale Ross, Chairman of the Board and
                                     Chief Executive Officer

ATTEST:


/s/ Leo E. Sands
-----------------------
Leo E. Sands, Secretary

                                       7
<PAGE>
 
                            CERTIFICATE OF AMENDMENT
                                       OF
                          CERTIFICATE OF INCORPORATION
                                       OF
                       AMERICAN ONCOLOGY RESOURCES, INC.


     It is hereby certified that:

     1.   The name of the corporation (hereinafter called the "Corporation") is
AMERICAN ONCOLOGY RESOURCES, INC.

     2.   The certificate of incorporation of the Corporation is hereby amended
by striking out the first paragraph of the fourth article thereof and by
substituting in lieu of said paragraph the following new paragraph:

          "The total number of shares of capital stock which the Corporation
          shall have authority to issue is eighty-one million (81,000,000)
          shares, consisting of one million (1,000,000) shares of preferred
          stock, par value $.01 per share, and eighty million (80,000,000)
          shares of common stock, par value $.01 per share."

     3.   The amendment of the certificate of incorporation herein certified has
been duly adopted in accordance with the provisions of Section 242 of the
General Corporation Law of the State of Delaware; the amendment was duly adopted
by resolution of the Board of Directors on February 8, 1997, and the necessary
shares as required by statute were voted in favor of the amendment of the Annual
Meeting of Stockholders held on May 8, 1997.

     IN WITNESS WHEREOF, the Corporation has caused this certificate to be
signed by its Chairman of the Board and Chief Executive Officer and attested to
by its Secretary, this 8th day of May, 1997.

                              AMERICAN ONCOLOGY RESOURCES, INC.


                              By:   /s/ R. Dale Ross
                                    -------------------------------------------
                                        R. Dale Ross, Chairman of the Board and
                                        Chief Executive Officer

ATTEST:

/s/ Leo E. Sands
----------------------- 
Leo E. Sands, Secretary

                                       8