## 3 Results and Discussion
[PERSON] and [PERSON], in article [39], described the concept of the obesity paradox, which refers to the phenomenon in which a higher body mass index (BMI) in late life is associated with lower mortality and better health outcomes, even though obesity is considered a significant risk factor for cardiovascular disease, diabetes, and other metabolic conditions. The obesity paradox indicates that in the elderly, overweight and moderate obesity may have a protective effect on health and prolong survival compared to normal-weight individuals. This phenomenon has been documented in a number of chronic diseases, including coronary heart disease, heart failure, hypertension, stroke, and type 2 diabetes. Importantly, studies demonstrate that this protective effect is especially pronounced in older people, who may benefit from a higher BMI, particularly in terms of avoiding malnutrition and sarcopenia (the loss of muscle mass). These conditions are strongly associated with cognitive decline, underscoring the greater risk of malnutrition and weight loss in older people compared to moderate obesity. A lower BMI in the elderly may be an indication of underlying malnutrition, which is associated with accelerated cognitive decline and an elevated risk of dementia. However, it is essential to note that the BMI is a flawed indicator. It does not consider the fat to fat-free mass ratio, nutritional status, cardiorespiratory fitness level, and fat distribution. Research by [PERSON] and [PERSON] [39] suggests that the body composition, rather than the BMI alone, is the key protective factor. Specifically, high muscle mass and favorable fat distribution (i.e., less visceral fat and more subcutaneous fat) may reduce the risk of dementia. As demonstrated by the preceding studies, the relationship between the BMI and cognitive health can vary according to age. While being overweight in middle age is frequently linked to an elevated risk of chronic diseases, a moderately elevated BMI in late life may offer a protective benefit, aligning with the concept of the so-called \"obesity paradox\". This phenomenon posits that a higher body mass index may have a beneficial effect on older people, particularly in terms of reducing the risk of cognitive decline and dementia. However, it is crucial to acknowledge the limitations of the BMI as a metric. This index fails to differentiate between fat and muscle mass, potentially leading to erroneous conclusions regarding the health status. It is particularly salient given the findings of the [PERSON] et al. study [38], which identified low muscle mass, not body weight alone, as a pivotal risk factor for cognitive decline. These observations underscore the significance of preserving muscle mass during the aging process, which may serve as an effective protective mechanism against the development of cognitive impairment. When discussing the relationship between the BMI and cognitive health, it is crucial to consider the possibility of a so-called reverse causality effect. This is a scenario in which the onset of health problems leads to decreased body weight, even before the manifestation of disease symptoms. This issue is particularly salient in studies conducted on the elderly population. Consequently, further research is necessary to control for this effect and account for variability in the body composition, as well as the dynamics of BMI changes over time, especially within an aging population. Additionally, elucidating the mechanisms that might underpin the potential protective effect of a higher BMI in older age groups is imperative. In the current study, we analyzed data from the Alzheimer's Disease Neuroimaging Initiative (ADNI), focusing on a subset of 42 participants who underwent multiple MRI scans. We are aware that the relatively small sample size is a limitation, as larger cohorts are generally preferred to enhance statistical power and improve the generalizability of results.