Is the Brain the “Person”?

FOREWARNING: This posting is likely to seriously anger people with strong convictions about abortion. While I accept that as a normal consequence of this type of posting, please note that it is not my intent to anger. This issue concerns what I see as a valid question of the Catholic church’s opposition to abortion. Please read the referenced article and my complete post before posting a knee-jerk response.

I’m against abortion (yes, even for rape and incest), but the referenced article gives me pause. Anencephalic babies, according to the NIH (according to the article) are born with little to no brain (see quote below) and have no chance of “consciousness”.

Although some individuals with anencephaly may be born with a rudimentary brain stem, the lack of a functioning cerebrum permanently rules out the possibility of ever gaining consciousness ... [R]esponses to sound or touch may occur ...

It is my understanding that the Catholic church says a person is buried where their head is buried (someone please correct me if I am wrong). That could be taken to mean that the brain of a person is that person. Going further, if a body doesn’t have a brain, it could be said that it is not a “person” in the normal sense of the word.

Is, then, an anencephalic baby a “person”? If I understood the article correctly, this isn’t merely an underdeveloped brain. This is a brain with none of the parts that generally contain the “person” part of a body. This is a body with no brain that can ever sustain consciousness.

The Vatican has this to say in section 65 of the encyclical “Evangelium Vitae” about euthanasia:

In such situations, when death is clearly imminent and inevitable, one can in conscience "refuse forms of treatment that would only secure a precarious and burdensome prolongation of life, so long as the normal care due to the sick person in similar cases is not interrupted".

Effectively, you can choose to not artificially prolong the life of someone who is clearly about to die, but you cannot take steps to artificially hasten their demise. However, the quoted section of Evangelium Vitae concerns euthanasia, which is generally considered to be killing someone who was once alive, someone who is/was a “person”, with the ostensible goal of ending their suffering. And this could be the answer, but there still seems to be some gray area.

My question boils down to this: Is the abortion of an anencephalic baby the killing of a “person” if it never had a brain capable of sustaining consciousness?