The "macroscopic formulation" of <PERSON>'s equations (linked by others in the comments) are often called "<PERSON>'s equations in matter" because they account for the fact that materials can be electrically polarized (when an electric dipole moment is induced in the matter) or magnetized (when a magnetic dipole moment is induced in the matter), which does indeed affect the behavior of the fields.
In this formulation, charges and currents are broken up into "free" charges/currents from the traditional <PERSON>'s vacuum equations, and "bound" charges/currents, which are a macroscopic approximation of the microscopic interaction between the charges that exist in materials which may interact with the fields, but cannot actually be conducted as bulk currents. The electrons within the atoms of an insulator are a good example of bound charges; despite the fact that the electron is thoroughly bound to the nucleus, the atoms may exhibit an induced dipole moment that has the effect of partially neutralizing the inducing field (here is an answer explaining how this happens).
The traditional $\mathbf{E}$ and $\mathbf{B}$ fields are related to their respective "auxiliary" equivalents $\mathbf{D}$ (the "displacement" field) and $\mathbf{H}$ (the "magnitizing" field) by the following formulas:
\begin{align} \mathbf{D}(\mathbf{r}, t) &= \varepsilon_0 \mathbf{E}(\mathbf{r}, t) + \mathbf{P}(\mathbf{r}, t) \ \mathbf{H}(\mathbf{r}, t) &= \frac{1}{\mu_0} \mathbf{B}(\mathbf{r}, t) - \mathbf{M}(\mathbf{r}, t) \end{align}
$\mathbf{P}$ and $\mathbf{M}$ describe the fields induced by the polarization and magnetization of the material, respectively, and $\mathbf{E}$, $\mathbf{B}$, $\varepsilon_0$, and $\mu_0$ describe the normal vacuum electric and magnetic fields, and permittivity/permeability of free space you're familiar with from the traditional vacuum <PERSON>'s equations. 469
You can see that each auxiliary field is simply equal to the sum of the vacuum field, and the additional field set up by the corresponding electromagnetic moment it induces in the medium.
In reality, you likely won't be able to measure $\mathbf{P}$ or $\mathbf{M}$ directly. You can approximate the auxiliary fields as $\mathbf{D} = \varepsilon \mathbf{E}$ and $\mathbf{H} = \frac{1}{\mu}\mathbf{B}$ based on known permittivity ($\varepsilon$) and permeability ($\mu$) values for your materials, although this can get complicated depending on the materials in question and your accuracy requirements. Fortunately I don't think the iron in your blood will be able to cause any of the nonlinearities associated with bulk quantities of ferromagnetic materials, but it's important to characterize and be aware of the limitations of your models. 28