## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Case** & \multicolumn{3}{c}{**First Cluster (C1)**} & \multicolumn{3}{c}{**Second Cluster (C2)**} & \multicolumn{3}{c}{**Third Cluster (C3)**} \\ \hline
**ID** & **BMI** & **Muscle** & **Div.** & **BMI** & **Muscle** & **Div.** & **BMI** & **Muscle** & **Div.** \\ \hline  
\hline Mean & & & & & & & & & \\ Mode & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Overview of BMI, muscle test values (1—low; 2—high), and Kullback–Leibler divergence results, including average values calculated across three clusters. Figure 4: The visual representation of the experimental research results for three clusters. within the same cluster consistently exhibited higher BMI values and superior muscle test scores. These findings suggest a negative correlation between the BMI and the degree of brain changes. The final methodology involved extending the cluster analysis to create four distinct clusters. It is worth noticing that the subgroups of patients with the lowest BMI and low muscle scores and those with a higher BMI and superior muscle scores remained consistent with previous cluster schemas. One of the new clusters comprised patients with an average BMI of 28.59 and a muscle index of 2, while individuals with a relatively higher BMI, originally part of the second cluster, were separated to form the fourth cluster. According to the Kullback-Leibler divergence measure, this newly formed fourth cluster exhibited the most favorable outcomes, with participants showing the lowest degree of brain tissue changes. In contrast, participants assigned to the second cluster demonstrated the most unfavorable outcomes. The classification of patients into separate subgroups showed that those with a moderate BMI and less physical activity exhibited the most significant differences in the brain structure. These observations endorse the fact that the combined state of a lower BMI and reduced muscle mass is the least beneficial condition for brain changes that occur in dementia or Alzheimer's disease. This observation corroborates earlier findings on having excess weight, which could reduce the mortality risk in old age through protective influences against osteoporotic fractures and cognitive decline. Furthermore, a higher body weight may serve as an energy reserve, protecting against protein-energy malnutrition [30]. The concept of \"fraility\" pertains to the overall health status of older adults. Fraility is theoretically characterized as a clinically identifiable condition marked by heightened vulnerability due to age-related declines in physiological reserves and function across multiple systems, which impair the ability to manage routine or acute stressors [31]. Studies have proposed that excess body weight may protect against mortality in individuals experiencing moderate or severe frailty [32]. The comparison of results across clusters indicated a positive association between higher body mass index (BMI) scores and a slower progression of structural brain changes. It should be noted that increased physical activity may lead to weight gain during specific lifestyle transitions, particularly following an athletic career, potentially resulting in elevated BMI values [33]. Considering this alongside the longitudinal trajectory of brain changes, individuals with a higher BMI in older age may have engaged in more excellent physical activity during their youth compared to those with lower BMI values. The findings suggest that older adults with higher BMI values may have been more active in physical activity during their youth. This hypothesis is reinforced by evidence that resistance training significantly influences the body composition and muscle strength in older adults [34]. Since muscle tissue is denser than fat, a higher muscle mass can result in an elevated BMI [35]. Within this framework, a higher BMI in older adults is more advantageous than a particularly low BMI.