I’m pretty sure that they did find blood on one of the thorns, (maybe the thorn in Paris), and I’m pretty sure that it is the same blood type (AB) that matches the Shroud of Turin, the Sudarium, and the Eucharistic miracle of Lanciano.
Sudarium - http://www.shroudstory.com/faq-sudarium.htm
Lanciano - http://www.therealpresence.org/eucharst/mir/lanciano.html
Did you know that if you superimpose the Vilnius depiction of the Divine Mercy onto the shroud it is a perfect fit.