We obtain analytical lower bounds on the concurrence of bipartite quantum systems in arbitrary dimensions related to the violation of separability conditions based on local uncertainty relations and on the Bloch representation of density matrices. We also illustrate how these results complement and improve those recently derived [K. Chen, S. Albeverio, and S.-M. Fei, Phys. Rev. Lett. 95, 040504 (2005)] by considering the Peres-Horodecki and the computable cross norm or realignment criteria.