Mathematical Modeling and Simulation of Fatigue Muscle Fiber Mechanism

It is a common experience that we feel muscle pain after physical activities. A number of studies related to muscle fatigue had been conducted, but they mainly focused on biological and chemical mechanisms. In this study, we approached the fatigue muscle fiber mechanism by mathematical modeling and simulation on existing biological and chemical understanding. The aim of the research was to explain the process of generating muscle fatigue in a mathematical method. To generate an adequate mathematical muscle fatigue fiber model, we combined two mathematical models: muscle fiber and muscle fatigue models. The modified Huxley equation was mainly used in this study, which mathematically described the behavior of the muscle fiber mechanism. Then, we validated the generated mathematical model by data from previously performed by others in scientific researches. As a result, we found an integrated model that explained both muscle fiber mechanism and muscle fatigue action. The model was applied in computer simulation, and this model was in agreement with experimental data in scientific articles. The new muscle fatigue model was able to efficiently explain the muscle fatigue mechanism in muscle fiber

A Mathematical Modeling and Simulation of Bone Remodeling Control Mechanism

Bone remodeling occurs at spatially and temporally discrete sites of the skeleton and involves resorption by osteoclasts, followed by formation of new bone by osteoblasts. Specific region of bone are targeted for remodeling due to structural defects, thus maintaining the mechanical strength of the skeleton. Bone remodeling plays a major role in bone homeostasis in human body, so it should work in accordance with other factors. A number of studies related to bone remodeling process had been conducted, but they mainly focused on biological and chemical mechanisms. In this study, we approached the bone remodeling by mathematical modeling based on existing biological and chemical understandings. The aim of the research was to explain the process of bone remodeling and to simulate the control mechanism in a mathematical method. We constructed a mathematical model describing temporal changes in osteoblast and osteoclast populations and consequent changes in bone mass at a single site of bone remodeling. To summarize the net effect of factors on the rates of cell production, we also employed a power law approximation developed by Savageau which is now widely used in exploratory modeling and can be used with a wide range of analytical and computational techniques. Then, we validated the generated mathematical model by data from previously performed by others in scientific researches. As a result, we found an integrated model that explained bone remodeling process and control mechanism. The model was applied in computer simulation, and this model was in agreement with experimental data in scientific articles. The new mathematical modeling for bone remodeling was able to efficiently explain how other factors affect bone remodeling mechanism in the human skeleton. The new model can therefore become a highly useful tool in the medical field and exercise training program