Exhibit (a) (1) (D)

Offer To Purchase For Cash

All Outstanding Shares of Common Stock,

All Outstanding Shares of Series A Convertible Preferred Stock and

All Outstanding Shares of Series B Convertible Preferred Stock

of

Derma Sciences, Inc.

at

$7.00 Net Per Share of Common Stock,

$32.00 Net Per Share of Series A Convertible Preferred Stock and

$48.00 Net Per Share of Series B Convertible Preferred Stock

Pursuant to the Offer to Purchase, dated as of January 25, 2017

by

Integra Derma, Inc.

an indirect wholly-owned subsidiary of

Integra LifeSciences Holdings Corporation

THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY TIME, ON FEBRUARY 22, 2017, UNLESS THE OFFER IS EXTENDED OR EARLIER TERMINATED (SUCH DATE AND TIME, AS IT MAY BE EXTENDED, THE “EXPIRATION DATE”).

January 25, 2017

To Our Clients:

Enclosed for your consideration are the Offer to Purchase, dated as of January 25, 2017 (as it may be amended or supplemented from time to time, the “Offer to Purchase”), and the related Letter of Transmittal (as it may be amended or supplemented from time to time, the “Letter of Transmittal,” which, together with the Offer to Purchase, collectively constitute the “Offer”) in connection with the offer by Integra Derma, Inc., a Delaware corporation (the “Purchaser”) and an indirect wholly-owned subsidiary of Integra LifeSciences Holdings Corporation, a Delaware corporation (“Parent”), to purchase all outstanding shares of common stock, par value $0.01 per share (the “Common Shares”), all outstanding shares of Series A Convertible Preferred Stock, par value $0.01 per share (the “Series A Preferred Shares”), and all outstanding shares of Series B Convertible Preferred Stock, par value $0.01 per share (the “Series B Preferred Shares” and, collectively with the Series A Preferred Shares and the Common Shares, the “Shares”) of Derma Sciences, Inc., a Delaware corporation (“Derma Sciences”), at a purchase price of $7.00 per Common Share (the “Common Offer Price”), $32.00 per Series A Preferred Share (the “Series A Offer Price”) and $48.00 per Series B Preferred Share (the “Series B Offer Price”), in each case, net to the seller in cash, without interest thereon and less any applicable withholding of taxes required by applicable law, upon the terms and subject to the conditions of the Offer.

Also enclosed is a letter to the shareholders of Derma Sciences from the Chief Executive Officer of Derma Sciences, accompanied by Derma Sciences’ Solicitation/Recommendation Statement on Schedule 14D-9.

We or our nominees are the holder of record of Shares held by us for your account. A tender of such Shares can be made only by us as the holder of record and pursuant to your instructions. The Letter of Transmittal accompanying this letter is furnished to you for your information only and cannot be used by you to tender Shares held by us for your account.

We request instructions as to whether you wish us to tender any or all of the Shares held by us for your account, upon the terms and subject to the conditions set forth in the Offer.

Please note carefully the following:

1. The offer price for the Offer is $7.00 per Common Share, $32.00 per Series A Preferred Share and $48.00 per Series B Preferred Share, in each case, net to you in cash, without interest thereon and less any applicable withholding taxes.

2. The Offer is being made for all outstanding Shares.

3. The Offer is being made in connection with the Agreement and Plan of Merger, dated as of January 10, 2017 (together with any amendments or supplements thereto, the “Merger Agreement”), by and among Derma Sciences, Parent and the Purchaser, pursuant to which, after the completion of the Offer and the satisfaction or waiver of the conditions set forth therein, the Purchaser will be merged with and into Derma Sciences as soon as practicable following the acceptance for payment of Shares in the Offer, without a vote of the shareholders of Derma Sciences, in accordance with Section 251(h) of the General Corporation Law of the State of Delaware, as amended (the “DGCL”), and Derma Sciences will be the surviving corporation (the “Merger”).

4. The board of directors of Derma Sciences: (i) approved and declared advisable the Merger Agreement and the transactions contemplated thereby, including the Offer and the Merger, upon the terms and subject to the conditions set forth therein, (ii) determined that the Merger Agreement and the Offer and the Merger are fair to, and in the best interests of, Derma Sciences and its shareholders, (iii) determined that the Merger should be effected as soon as practicable following the acceptance for payment of Shares validly tendered pursuant to the Offer, without a vote of the Company’s shareholders, pursuant to Section 251(h) of the DGCL, and (iv) recommended that Derma Sciences’ shareholders accept the Offer and tender their Shares pursuant to the Offer.

5. The Offer and withdrawal rights will expire at 12:00 midnight, New York City time, on February 22, 2017 (the “Expiration Date”), unless the Offer is extended by the Purchaser or earlier terminated.

6. There is no financing condition to the Offer. The Offer, and the obligation of the Purchaser to accept for payment and pay for Shares tendered pursuant to the Offer, is conditioned on there being validly tendered (and not properly withdrawn) prior to the Expiration Date, (i) that number of Shares that, together with the number of Shares (if any) then owned by Parent, equals at least a majority in voting power of the Shares then issued and outstanding, voting together as a single class, (ii) that number of Series A Preferred Shares that, together with the number of Series A Preferred Shares (if any) then owned by Parent, equals at least a majority of the Series A Preferred Shares then issued and outstanding and (iii) that number of Series B Preferred Shares that, together with the number of Series B Preferred Shares (if any) then owned by Parent, equals at least a majority of the Series B Preferred Shares then issued and outstanding. The Offer is also subject to other conditions as described in Section 14, entitled “Conditions of the Offer,” of the Offer to Purchase.

7. Tendering shareholders who are record owners of their Shares and who tender directly to Broadridge Corporate Issuer Solutions, Inc. (the “Depositary”) will not be obligated to pay brokerage fees, commissions or similar expenses or, except as otherwise provided in Instruction 6 of the Letter of Transmittal, stock transfer taxes with respect to the purchase of Shares by the Purchaser pursuant to the Offer. See Section 16, entitled “Fees and Expenses,” of the Offer to Purchase.

If you wish to have us tender any or all of your Shares, then please so instruct us by completing, executing, detaching and returning to us the Instruction Form on the detachable part hereof. An envelope to return your instructions to us is enclosed. If you authorize the tender of your Shares, then all such Shares will be tendered unless otherwise specified on the Instruction Form.

Your prompt action is requested. Your Instruction Form should be forwarded to us in ample time to permit us to submit the tender on your behalf before the Expiration Date.

In all cases, payment for Shares accepted for payment in the Offer will be made only after timely receipt by the Depositary of (i) Share certificates (or a timely Book-Entry Confirmation (as defined in the Offer to Purchase)), (ii) a properly completed and duly executed Letter of Transmittal (or manually signed facsimile thereof), with any required signature guarantees (or, in the case of a book-entry transfer effected pursuant to the procedures set forth in Section 3, entitled “Procedure for Tendering Shares,” of the Offer to Purchase, an Agent’s Message (as defined in the Offer to Purchase) in lieu of a Letter of Transmittal), and (iii) any other documents required by the Letter of Transmittal. Accordingly, tendering shareholders may be paid at different times depending upon when Share certificates or Book-Entry Confirmations with respect to Shares are actually received by the Depositary. UNDER NO CIRCUMSTANCES WILL INTEREST BE PAID ON THE PURCHASE PRICE OF THE SHARES, REGARDLESS OF ANY EXTENSION OF THE OFFER OR ANY DELAY IN MAKING PAYMENT.

The Offer is not being made to, nor will tenders be accepted from or on behalf of, holders of Shares in any state in which the making of the Offer or the acceptance thereof would not be in compliance with the securities, “blue sky” or other laws of such state. In those states where applicable laws require the Offer to be made by a licensed broker or dealer, the Offer shall be deemed to be made on behalf of the Purchaser by one or more registered brokers or dealers licensed under the laws of such state to be designated by the Purchaser.

INSTRUCTION FORM

With Respect to the Offer to Purchase for Cash

All Outstanding Shares of Common Stock,

All Outstanding Shares of Series A Convertible Preferred Stock and

All Outstanding Shares of Series B Convertible Preferred Stock

of

Derma Sciences, Inc.

at

$7.00 Net Per Share of Common Stock,

$32.00 Net Per Share of Series A Convertible Preferred Stock and

$48.00 Net Per Share of Series B Convertible Preferred Stock

Pursuant to the Offer to Purchase, dated as of January 25, 2017

by

Integra Derma, Inc.

an indirect wholly-owned subsidiary of

Integra LifeSciences Holdings Corporation

The undersigned acknowledge(s) receipt of your letter and the enclosed Offer to Purchase, dated as of January 25, 2017 (as it may be amended or supplemented from time to time, the “Offer to Purchase”), and the related Letter of Transmittal (as it may be amended or supplemented from time to time, the “Letter of Transmittal,” which, together with the Offer to Purchase, collectively constitute the “Offer”), in connection with the offer by Integra Derma, Inc., a Delaware corporation (the “Purchaser”) and an indirect wholly-owned subsidiary of Integra LifeSciences Holdings Corporation, a Delaware corporation, to purchase all outstanding shares of common stock, par value $0.01 per share (the “Common Shares”), all outstanding shares of Series A Convertible Preferred Stock, par value $0.01 per share (the “Series A Preferred Shares”), and all outstanding shares of Series B Convertible Preferred Stock, par value $0.01 per share (the “Series B Preferred Shares” and, collectively with the Series A Preferred Shares and the Common Shares, the “Shares”) of Derma Sciences, Inc., a Delaware corporation (“Derma Sciences”), at a purchase price of $7.00 per Common Share (the “Common Offer Price”), $32.00 per Series A Preferred Share (the “Series A Offer Price”) and $48.00 per Series B Preferred Share (the “Series B Offer Price”), in each case, net to the seller in cash, without interest thereon and less any applicable withholding of taxes required by applicable law, upon the terms and subject to the conditions of the Offer.

The undersigned hereby instruct(s) you to tender to the Purchaser the number of Shares indicated below or, if no number is indicated, all Shares held by you for the account of the undersigned, upon the terms and subject to the conditions set forth in the Offer. The undersigned understands and acknowledges that all questions as to validity, form and eligibility of the surrender of any certificate representing Shares submitted on my behalf will be determined by the Purchaser and such determination shall be final and binding.

Account Number:                                                                                                                                                                                      

Number and Class (Common Shares, Series A Preferred or Series B Preferred) of Shares Being Tendered Hereby*:

The method of delivery of this document is at the election and risk of the tendering shareholder. If delivery is by mail, then registered mail with return receipt requested, properly insured, is recommended. In all cases, sufficient time should be allowed to ensure timely delivery prior to the Expiration Date (as defined in the Offer to Purchase).

Dated:                                                                                                                                                                                                            

Signature(s):                                                                                                                                                                                                 

Name(s):                                                                                                                                                                                                       

(Please Print)

Address:                                                                                                                                                                                                        

(Include Zip Code)

Area Code and Telephone No.:                                                                                                                                                            

Tax Identification or Social Security No.:                                                                                                                                        

 * Unless otherwise indicated, it will be assumed that all Shares held by us for your account are to be tendered.