Alzheimer´s disease (AD) is the most common cause of dementia. The most important risk factor for AD is old age; modifiable risk factors for AD include metabolic risk factors, i.e. diabetes, and obesity. Insulin resistance seems to be associated with AD pathology and cognitive decline. Previous studies suggest that AD and mild cognitive impairment (MCI) due to AD, a stage between normal cognition and AD dementia, would be associated with central nervous system (CNS) insulin resistance. Insulin resistance can be measured using a sophisticated hyperinsulinemic-euglycemic clamp technique. Insulin-stimulated glucose uptake of muscles and adipose tissue is known to be reduced in an insulin resistant subject compared to healthy insulin sensitive subjects. Central nervous system insulin resistance, however, is more difficult to assess, while a clear-cut definition is thus far lacking. Previous studies have demonstrated that whole-body insulin resistance in obese subjects is accompanied with higher brain glucose-uptake (BGU) during the insulin clamp, compared to lean controls, and that BGU increases from the fasting to the insulin clamp state. On the contrary, there is no difference in BGU under fasting conditions between obese subjects and healthy lean controls. No previous studies have evaluated brain glucose uptake in clamp conditions in subjects with MCI or early AD. The aim of this study is to evaluate if brain glucose uptake is increased in MCI/ early AD subjects in a similar manner as in morbidly obese subjects in an insulin-stimulated state (during a hyperinsulinemic clamp) when compared to the fasting state, and when compared to controls. The investigators hypothesize that MCI subjects would have CNS insulin resistance that could, in time, contribute to the pathological process of AD. The investigators will recruit altogether 20 MCI subjects from the local memory clinic, and healthy controls through advertisements. All participants will undergo two \[18F\]-fluorodeoxyglucose (FDG) positron emission tomography (PET) scans (one in the fasting state and one during the hyperinsulinemic clamp), a magnetic resonance image scan for structural changes, blood sampling, and comprehensive cognitive testing. The participants will also undergo a \[11C\]PIB-PET scan to measure brain amyloid accumulation. Understanding the metabolic changes in the brain preceding AD could help in developing disease-modifying treatments in the future.