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The comparison of the results of direct detection of Dark Matter, obtainedwith various target nuclei, requires model-dependent, or even arbitrary,assumptions. Indeed, to draw conclusions either the spin-dependent (SD) or thespin-independent (SI) interaction has to be neglected. In the light of the nullresults from supersymmetry searches at the LHC, the squark sector is pushed tohigh masses. We show that for a squark sector at the TeV scale, the frameworkused to extract contraints from direct detection searches can be redefined asthe number of free parameters is reduced. Moreover, the correlation observedbetween SI and SD proton cross sections constitutes a key issue for thedevelopment of the next generation of Dark Matter detectors.

Extracting constraints from direct detection searches of supersymmetric dark matter in the light of null results from the LHC in the squark sector