## 1 Introduction  
Propofol is a widely utilized agent for anesthetic induction owing to its rapid onset and smooth recovery profile, making it a cornerstone of modern anesthesia practice (Figure 1) [1]. Propofol causes central nervous system depression by enhancing inhibition via GABAA receptors, resulting in sedation, hyponsis, and anesthesia [2]. However, its dose-dependent adverse effect of hypotension remains a significant concern, especially in vulnerable populations, such as older individuals and those with heart disease [3, 4]. Intraoperative hypotension has been linked to severe complications, such as postoperative stroke, acute kidney injury, myocardial injury after non-cardiac surgery, and increased 30-day mortality [5, 6, 7]. Therefore, it is crucial to determine the correct propofol dose for anesthetic induction, and to mitigate this issue, dose adjustments must be made by thoroughly considering the individual patient's risks.  
Older patients require lower propofol doses for anesthesia induction [8]. They are also more prone to dose-dependent hypotension, because propofol administration can cause a decrease in systemic vascular resistance due to arterial dilation, making age-adjusted dose adjustments crucial [9; 10]. For example, a study comparing young adults aged 25-39 years with older adults aged 66-80 years found that the induction dose, the dose needed to initiate anesthesia, was approximately 2.2 mg/kg for young adults and 1.7 mg/kg for older individuals [11].  
A formula employing structural equation modeling has been proposed for predicting the propofol induction dose, where the prediction equation for model P was defined as follows: propofol dose (mg) = [2.374 \(-\) 0.0113 \(\times\) age (years) \(-\) 0.0788 (if ASA-PS 3 or 4) + 0.057 (if female) + 0.1087 \(\times\) fentanyl dose (\(\mu\)g/kg)] \(\times\) body weight (kg) [12]. However, there are no studies utilizing neural networks. Considering the possibility that the relationship between the propofol dose and age may be nonlinear, a neural network model, as one type of machine learning model, was developed to predict propofol induction doses and its performance was evaluated.  
Utilizing this novel model, we simulated the predicted propofol dose for all the analyzed cases, setting the patient age to a hypothetical value of 20 years and repeating the simulation at 10-year increments up to 90 years. The simulation of the age-related changes in the propofol induction doses provided valuable insights into appropriate age-adjusted dosing strategies. Traditionally, the dose of anesthetic drugs was determined empirically based on patient factors such as age, weight, and medical history, including ischemic heart disease [12]. However, through this quantification via simulation, anesthesiologists can adjust the propofol dose swiftly and objectively based on the patient's age. The insights gained from this study may help reduce the risk of adverse effects due to over- or under-dosing, such as hypertension or pain caused by insufficient dosing, and hypotension or bradycardia caused by excessive dosing, thereby contributing to improved patient safety.  
This article is a revised and expanded version of a paper titled \"Quantification of the Relationship between Aging and Propofol Induction Dose Using Neural Network Model Simulation: A Single-Center Retrospective Observational Study\", which was presented in Japanese at the 71 st Annual Meeting of the Japanese Society of Anesthesiologists, Kobe Portopia Hotel, Kobe, Japan, 6-8 June 2024 [13]. More than 50% of the content in this manuscript is newly added, including detailed discussions and expanded analyses that were not part of the original presentation.  
Figure 1: Chemical structure of propofol (IUPAC name: 2,6-diisopropylphenol). Source: ChEBI, EMBL-EBI (ChEBI ID: 44915), accessed 20 May 2025.