Analyze the Impact of Healthy Behavior on Weight Change with a Mathematical Model using the Harris-Benedict Equations

Abstract

Abstract Background: Lifestyle diseases are the leading cause of death worldwide. The gradual increase of negative behavior in humans because of physical inactivity, unhealthy habit, and improper nutrition expedites the growth of lifestyle diseases. Proper lifestyle management in the obesity context may help to reach personal weight goal or maintain a normal weight range with optimization of health behaviors (physical activity, diet, and habits). Objective: In this study, we develop a mathematical model to analyze the impact of regular physical activity, a proper diet, and healthy habits on weight change, targeting obesity as a study case. Followed by, we design an algorithm to verify our proposed model with simulated data and compare it with related proven models based on the defined constrains. Methods: We proposed a weight-change mathematical model as a function of activity, habit, and nutrition with the first law of thermodynamics, basal metabolic rate ( BMR ), total daily energy expenditure ( TDEE ), and body-mass-index ( BMI ) to establish a relationship between health behavior and weight change. Followed by, we verify the model with simulated data and compared it with related established models. In this study, we have used revised Harris-Benedict equations (HB) for BMR and TDEE calculation. Results: The proposed mathematical model showed a strong relationship between health behavior and weight change. We verified the mathematical model with a proposed algorithm using simulated data with defined constraints. The adoption of BMR and TDEE calculation following revised Harris-Benedict equations has beaten the classical Wishnofsky’s rule (3500 cal. ≈ 1 lb.) , and the models proposed by Toumasis et al., Azzeh et. Al., and Mickens et. al. with a standard deviation of ±1.829, ±2.006, ±1.85, and ±1.80, respectively. Conclusions: This study helped us to understand the impact of healthy behavior on weight change with mathematical implications and the importance of a healthy lifestyle. As a future research scope, we wish to use this model in a health eCoach system to generate personalized lifestyle recommendations to optimize health behaviors to accomplish personal weight goals.