This is the term Kovacs himself uses, and it's used in various places when referring to neuroreflexotherapy, a technique developed at the Kovacs Foundation in Palma de Mallorca. It's a curious word to use, since it normally refers to an engraving tool, but then it's a curious and distinctive object, neither a pin nor a needle.

F. M. Kovacs, "Neuroreflexotherapy Intervention for Exacerbations of Chronic Low Back Pain: Clinical Evidence and Biological Substrate".
[...]
"This procedure consists of temporary implantation of surgical staples in trigger points in the back and epidermal burins in referred tender points in the ear"
http://www.fasciaresearch.com/WCLBP/Vienna/Kovacs_Neurorelex...

Here's a picture of this "burin":

Francisco M. Kovacs et al., "Local and Remote Sustained Trigger Points Therapy for Exacerbations of Chronic Lower Back Pain: A Randomized "
Spine, 22 no. 7 (1997): 786-797
"Figure 1. Epidermal devices: epidermal burin (left) and surgical staple (right)" (p. 788)
On p. 790 is a picture of a patient with one (or more) of these things stuck in his ear.
http://www.cebp.nl/vault_public/filesystem/?ID=976
(This file is in an odd format, but it is a pdf and can be opened with Acrobat Reader.)

"In the procedure, small pieces of metal are placed in the skin of the back and ear: staples are placed through the outer layer of skin, and burins are implanted just beneath the skin surface"
http://en.wikipedia.org/wiki/Neuroreflexotherapy


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Note added at 1 hr (2013-08-01 23:41:08 GMT)
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Another reference, this one non-Spanish (multiple international authors, but a few British contributors):

"C11 (C) Neuro-Reflexotherapy
Definition of the procedure
Neuro-reflexotherapy intervention (NRT) is defined as the temporary implantation of epidermal devices (surgical staples (up to 90 days) and small metallic burins (which fall off after about 2 weeks)) in trigger points in the back at the site of clinically involved dermatomes in each case, and in referred trigger points located in the ear. "
http://es.scribd.com/doc/45607421/European-Guidelines-Chroni... (p. 177)

The term may or may not be ideally suitable, but it is at least established, which is presumably why they've used it here. I would use it, if only for this reason.

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Note added at 3 hrs (2013-08-02 01:40:47 GMT)
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I freely admit, and have said, that "burins" is an odd word for this. The main argument for using it, as I say, is that it's established in the medical literature, though I do think that if you use it, it would be a good idea to put it in inverted commas to show that it is Kovacs' term and a special use of the word:
epidermal "burins"

It's not easy to find what they normally call these things in Spanish (not "pins", as far as I can tell). I have found a reference here to "pequeños punzones dérmicos":
http://fibromialgia-noticias.blogspot.com.es/2006_04_01_arch...

That suggests to me that we might call them "spikes", which would be quite suitable since the term "spikes" is used for similar objects in body piercing. So as an alternative I would suggest:

epidermal spikes

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Note added at 3 hrs (2013-08-02 01:51:07 GMT)
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As a matter of fact there are a lot of references to "dermal spikes" in relation to body piercing, and the images of them are very like Kovacs' device in some cases. I think "small dermal spikes" could be a viable option.

I'm pretty sure the term "epidermal burin" didn't exist until Kovacs coined it.

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Note added at 4 hrs (2013-08-02 02:27:34 GMT)
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Sorry to keep adding notes, but it has just occurred to me where "burin" may comes from: one of the meanings of "punzón" is "buril", so maybe Kovacs looked up "punzón" in a Spanish-English dictionary, found "burin" as one of the translations, and used that. On the other hand, maybe he knew what "burin" means and used the word deliberately. But this possibility does make me more inclined to favour the word "spike" here.