Hi rajechP
Tough question, indeed. I picked E with only 50% confidence. Thanks God, it's correct.

The organs of pigs genetically modified by human stem-cells are now viewed as
forms of health insurance and as resources
a human is able to use to take care of
one’s later illnesses.
(A) a human is able to use to take care of one’s
Wrong. "one's" is not clearly. one refers to whom?
(B) that a human is able to use to take care of oneself in
Wrong. Shell game. Many people will pick B because of "that", but it's wrong. Because "organs" is object of the second clause "a human is able to use to take care....". Technically, there should be a
PREPOSITION before "that", for example,
by that a human is able to use........ If there is NO preposition, the relative clause does not make any sense.
(C) a human is able to use to take care of oneself in
Wrong. Same problem as in A. oneself is not clear.
(D) humans are able to use to take care of them in
Wrong. "them" is wrong.
Let try a quick test.I can use the organs to take care
MEI can use the organs to take care
myself ==> Clearly, "me" is not appropriate.
==>
I should use something to
take care myself. But,
he/she can use something to
take care me.
(E) humans are able to use to take care of themselves in
Correct. "themselves" is correct usage.
Hope it helps.