In MRI why don't metals in the body get ripped out?

Question

Why doesn't the strong magnetic field cause iron in the blood to at least pool to the surface of the body.

Answer 1

Iron in the blood is present in haemoglobin, wherein the iron is bonded to other atoms to form the molecule. This results in the filling of all the electron shells in the iron, so that all electrons of opposite angular momentum are paired and thus cancel each other's magnetism (owing to both orbital angular momentum and their own spins) out.

In contrast, in iron metal, the iron ions sit in a lattice bound to an electron "sea". The ions themselves have unpaired electrons in unfilled shells, thus an unbalanced magnetic moment, and, moreover, tend to align themselves to one-another.

The unbalanced moment is what is acted on by a magnetic field; thus the haemoglobin molecule, with all its electrons in filled shells, is not acted on magnetically.

Answer 2

The answer is not as simple as it seems. The correct answer is it does, but the force is too small compared to other forces in the system. It is, in fact, not much different from the force acting on water in your body. Now, let me elaborate.

Almost all of the iron in our bodies (5 grams or so) is contained in two proteins - Haemoglobin and Ferritin (also see here). And as it turns out, both of these proteins are not ferromagnetic, despite having iron. Haemoglobin, in fact, depending if it has oxygen attached or not, will be either paramagnetic or diamagnetic (see this and this). As for Ferritin, it is paramagnetic (see this). Therefore, the forces acting on these proteins are not much larger than those acting for example on water or other organic tissues in our bodies. This is why we can say that the magnetic field does not really interact with iron in our blood. However, I want to highlight that the material does not have to be ferromagnetic to be influenced by the magnetic field.

First, why does magnetic field attract materials? In fact, it is not the field itself, it is the gradient (spatial change) of the field that does so. The force is given by

$\mathbf{F}=\nabla(\mathbf{m}\cdot\mathbf{B})$,

where m is the magnetic moment and B is the magnetic induction. Therefore, in order to have a force, one has to also have a magnetic moment. In addition to the force, there is also a torque given by

$\mathbf{\tau}=\mathbf{m}\times\mathbf{B}$,

This torque wants to rotate the magnetic moment and align it with the magnetic field. So, the field wants to align the moment and the gradient of the field exerts a force. Let's keep these two in mind as we proceed.

Regarding the gradient of the field, there is always one, especially in an MRI machine. Even if you try really hard it is challenging to create a completely uniform field (even in a small area in space). So the only thing to worry about in order to have a pull is the magnetic moment.

Materials are, in general, classified into 3 groups according to their magnetic properties:

1. Diamagnets (non-magnetic, sort of)
2. Paramagnets (magnetic, but not ordered)
3. Magnetically ordered (Ferromagnets, Ferrimagnets, Antiferromagnets, etc..)

In basic terms, atoms/molecules in a diamagnet do not possess a (considerable) magnetic moment. The ones in a paramagnet have magnetic moments, but they are aligned randomly, i.e. the structure is disordered. In magnetically ordered materials, however, the moments of all atoms are aligned in a particular order. The one we are interested in are Ferromagnets (Iron, Nickel, Cobalt..), where all the moments are aligned in the same direction, even in the absence of magnetic field.

The simplest way to classify the material is to look into the property called magnetic susceptibility, which tells you how much magnetic moment is induced in the bulk when a field is applied (e.g. due to the earlier mentioned torque). Basically

$\mathbf{m}=\chi\mathbf{H}$

where chi is the susceptibility and H is the field. For diamagnets, the susceptibility is small and negative, i.e. a small moment opposite the magnetic field is induced. Water is a typical diamagnet with a susceptibility of approximately -10-5. For paramagnets, the value is small positive. E.g. for Aluminium it is 2*10-5. For ferromagnets, however, the value is large and positive. E.g for Iron it is 200.000. This must ring a bell now, the moment is 100.000.000.000 times larger for the same magnetic field! And usually the gradient of the field is proportional to the magnitude of the field (given the same field distribution), therefore you will have a force that is hundreed billion times larger for the ferromagnet compared to a paramagnet or a diamagnet. However, this does not mean that the force is zero. Diamagnets are repelled from the field (move towards the areas with smaller field), whereas paramagnets and ferromagnets are attracted to the field (move towards areas of larger field). Have a look at the famous levitating frog experiment which won Andre Geim an Ig Nobel prize. Here, the water is the material that is pushed away by the magnetic field gradient.

In Physics, almost everything can be viewed in terms of energy scales and relatives sizes of forces. For example, I am right now pulling you due to the gravitational forces between me and you. However, this force is much smaller than all the other forces in the system, e.g. all the other gravitation forces acting on you, friction between you and the floor, etc.. So you are not really pulled towards me.

As for the example of X-men Magneto, in principle, something like that might be possible. He won't really be able to pull the iron out of your body, but consider the following. There is both paramagnetic and diamagnetic matter in our body. If the magnetic field gradient is large enough so that the dipole forces are larger than the forces keeping these together (e.g. electrostatic interactions), he could, in principle, rip us apart :) This is just a speculation though and open to discussion.