Alzheimer’s Disease: Modeling the Effect of Daily Steps

Abstract

There is now clear evidence that exercise measured by step count per day can reduce the risk of developing dementia. A mathematical model is presented in this paper that predicts the reduction in risk for both men and women as a function of age, gender, and steps/day. The model is based on the theory that exercise increases slow-wave sleep, which in turn increases the flushing of waste materials from the brain, resulting in a reduced risk of developing dementia. Based on observed measured data, exercise as measured by daily step count has both a positive and a negative effect. The negative effect starts to dominate at high step counts. These two effects were mathematically modeled based on the assumption that exercise has a positive effect on slow-wave sleep by increasing cardiorespiratory fitness. It was also assumed that exercise increases aches, muscle pain, blisters, etc., which interfere with slow-wave sleep. While these assumptions were not verified directly, the model based on these assumptions was successful in predicting risks for dementia in association with daily step count. Simulations with the model matched measured data reported in the literature with high R 2 values and statistical significance.