For the estimation of the variation of the glucose level in the blood of a person the present invention uses the variation of the volume of the interstitial fluid compartments in muscular tissue due to a shift of fluid between the extracellular and intracellular compartments caused by variations of the osmotic pressure of the extracellular fluids which is in turn correlated with the glucose level. The variation of the volume of the interstitial fluid compartments is detected by means of a non-invasive conductometry measurement using electrodes placed in contact with the skin of the person overlying a portion of soft tissue including muscular fibers. To eliminate the adverse effect of the conductivity of the capillary vessels the invention measures the conductivity of the tissue independently in two directions, namely parallel and transverse to the muscular fibers. Because of the chaotic orientation of the capillary vessels, a variation of the conductivity caused by a variation of the volume of the vessels should be almost equal in both measuring directions. On the other hand, the conductivity parallel to the muscular fibers is in a larger scale determined by the volume of the interstitial fluid than transverse to the muscular fibers. A variation of the volume of the interstitial compartment thereby has a greater effect on the conductivity parallel than transverse to the muscular fibers.