## 2 Materials and Methods
### Dataset Characteristics  
The Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset is a publicly accessible resource available through the ADNI website [17]. This dataset provides a comprehensive collection of data on individuals involved in Alzheimer's disease research, encompassing healthy controls, individuals with mild cognitive impairment (MCI), and patients diagnosed with Alzheimer's disease. The dataset includes high-resolution neuroimaging data (such as structural MRI scans), clinical assessments (including cognitive and diagnostic tests), and demographic information (e.g., age, gender, and education level). The present dataset has been painstakingly preprocessed for research purposes, handling missing values and converting categorical variables into numerical representations to enhance data analysis capabilities. Each subject is assigned a unique anonymous ID to ensure participant privacy and allow for the longitudinal evaluation of change over time and across visits and assessments. The ADNI dataset provides a tool for scientific research, leading to a better understanding of the progression of Alzheimer's disease and its relationship with demographic, clinical, and imaging markers. The dataset encompasses a variety of features that provide comprehensive information about the health status of participants. These include the following:  
* Magnetic Resonance Imaging (MRI) data that provide high-resolution scans of the brain, visualizing its structure and the detailed anatomical regions used to assess the brain volume, cortical thickness, and other neurodegenerative changes characteristic of Alzheimer's disease;
* The body mass index (BMI), calculated as the weight in kilograms divided by the height in square meters, which is a standard measure for assessing the body composition and classifying individuals into weight categories, including underweight, normal weight, overweight, and obese;
* Muscle mass estimates (1--low; 2--high) that refer to inferred values derived from physical examinations, imaging proxies, or other relevant clinical indicators, as direct muscle mass measurements are not explicitly provided;
* Demographic characteristics such as age, gender, education, and ethnicity enable analyses of how these factors influence the progression of Alzheimer's disease;Clinical assessments that include cognitive tests, medical histories, and diagnostic evaluations offer valuable insights into participants' mental health and the severity of neurodegenerative conditions. Our analysis utilized data from the Alzheimer's Disease Neuroimaging Initiative (ADNI), focusing on a cohort of 42 participants who underwent repeated MRI assessments. By comparing the initial and follow-up scans, we aimed to quantify structural brain alterations and explore their relationship with activity factors, including the BMI and muscle mass estimates. This cohort comprised 24 men and 18 women, ensuring a comparable distribution between sexes. As the ADNI dataset has been meticulously curated and maintained, the subset used in our analysis contained no missing values. Therefore, the need for multiple imputations or other techniques to handle missing data was eliminated. Moreover, the ADNI dataset has been developed and maintained through collaboration with neurologists and neuroscientists, ensuring the clinical relevance and accuracy of the data. Detailed documentation regarding the data collection procedures, including the completeness of the dataset, can be found in the ADNI documentation [18]. Consequently, the integrity of our analysis was preserved, as the results were based on fully available data, ensuring that no potential biases were introduced through imputation methods. Participants were selected based on the availability of longitudinal neuroimaging data and comprehensive clinical assessments pertinent to our research objectives.