Variation of Hilbert Coefficients

For a Noetherian local ring $(\text{RR},\text{m})$, the first two Hilbert coefficients, $e_0$ and $e_1$, of the $I$-adic filtration of an $\text{m}$-primary ideal $I$ are known to code for properties of $\text{RR}$, of the blowup of $\text{spec}(\text{RR})$ along $V(I)$, and even of their normalizations. We give estimations for these coefficients when $I$ is enlarged (in the case of $e_1$ in the same integral closure class) for general Noetherian local rings.