Studies of many meson systems may be important for understanding certain 
nuclear systems, such as the interiors of neutron stars, and give us 
insight into the issues and possibilities of lattice QCD calculations of 
many hadron systems. In this talk, I will present a calculation of the 
ground state mass shifts of various baryons due to the presence of a 
medium of pions or kaons using lattice QCD with a canonical approach. 
 From the ground state energies we are able to calculate two- and 
three-body scattering parameters. We also extract low energy constants 
by comparing our results to tree level Chiral Perturbation Theory at 
non-zero isospin/kaon chemical potential.