Most of the literature I read use mu_rel = 1 for biological tissues, with the exception being for blood containing, of course, iron. Thus the perfusion of tissue has an effect on permeability. In addition, the oxygenated state of the blood matters according to http://scitation.aip.org/content/aip/journal/pof2/17/7/10.1063/1.1978807. What would you do with the data? What is your greater goal?
My far-field goal is to solve inverse problem of electromagnetic scattering on human skin. We have examined the diffraction on the capillary. The scattered field has a component that is proportional to the difference between the magnetic permeability of air and the capillary. We're going to take into account the curvature, torsion, and the change in thickness of the capillary. From my point of view, some of the objects in the skin (blood, sweat) must have the magnetic susceptibility not equal to 1. But I can not find accurate data,.
The relative permeability of human tissues is very close to that of free-space. Deviations from unity are very small so any scattering due to magnetic properties of tissues will be small too. However, it is customary to use the magnetic properties of water to represent most tissue types, water being slightly diagmagnetic. Probably the best source of information for magnetic susceptibility data of human tissues will be from papers on functional magnetic resonance imaging (fMRI) since this technique exploits the contrast in susceptibility between oxygenated and de-oxygenated blood. I've attached a link to a paper by Schenck which gives an overview of magnetic susceptibility in relation to MRI which contains some data on magnetic susceptibility of tissues including blood. Hope this helps :)
I am also in search of the data on magnetic permeability or magnetic diffusivity of blood. I want to estimate the magnetic Reynolds number that involves these parameters. Were you able to get any data?
For permeability of blood, per(blood) = Relative permeability(blood) * permeability of free space can be used. Further, Relative permeability of blood = 1 + susceptibility of blood can be used since the permeability of blood depending on whether it is oxygenated or de-oxygenated (paramagnetic / diamagnetic) is available in the literature. Similarly, such data are perhaps available for other organs.
There is device which change color under the influence of magnetic field ,i think blue and green color and it is reversible . Related to these device's data could help more