The most striking problem with this paper is how easy all of the tests of viability they used are to game. There are a bunch of simple tests you can do to check for viability, and it's fairly common for non-viable tissue to produce decent-looking results on at least a couple, if you do enough. (A couple of weeks ago, I was reading a paper by Fahy which described the presence of this effect in tissue slices.)
It may be worth pointing out that they only cooled the hearts to -3 C, as well.
Yeah, -3 C was exactly as intended by the authors, since they were (supposedly) suppressing the freezing of water in the experimental group - much colder and the water in their experimental organs would have stopped being liquid :)
This is great, by using small interlocking magnetic fields, you can keep the water in a higher vibrational state, allowing a "super-cooling" without getting crystallization and cell rupture
Subzero 12-hour Nonfreezing Cryopreservation of Porcine Heart in a Variable Magnetic Field
"invented a special refrigerator, termed as the Cells Alive System (CAS; ABI Co. Ltd., Chiba, Japan). Through the application of a combination of multiple weak energy sources, this refrigerator generates a special variable magnetic field that causes water molecules to oscillate, thus inhibiting crystallization during ice formation18 (Figure 1). Because the entire material is frozen without the movement of water molecules, cells can be maintained intact and free of membranous damage. This refrigerator has the ability to achieve a nonfreezing state even below the solidifying point."
http://mobile.journals.lww.com/transplantationdirect/_layouts/15/oaks.journals.mobile/articleviewer.aspx?year=2015&issue=10000&article=00005#ath