The lumped constant of the deoxyglucose method was determined by the steady-state, model-independent method in the brain of normal conscious rats with arterial plasma glucose concentrations varying from normoglycemia (i.e., 8 mM) to hyperglycemia (i.e., 31 mM). The lumped constant for brain was found to decrease very gradually with increasing arterial plasma glucose concentration from a value of approximately 0.45 in the midnormoglycemic range (i.e., 7-8 mM) to approximately 0.38 at 28-31 mM. 3-O-[14C]Methylglucose was used to assess the distribution of glucose within the brain structures in hyperglycemia; the results indicated that the glucose concentration, and therefore also the values for the lumped constant, remain relatively uniform in hyperglycemia with arterial plasma glucose concentrations as high as 34 mM. The values for the lumped constant for rat brain determined in the present studies were combined with those previously determined in this laboratory for hypoglycemia and normoglycemia by the same method to provide a single source for the values for the lumped constant to be used over the full range of arterial plasma glucose concentrations. In several rats the lumped constant for cephalic extracerebral tissues was also evaluated in parallel with those for the brain. The lumped constant for the cephalic extracerebral tissues was found to be about twice that for brain and to be unaffected by changes in arterial plasma glucose levels.