Modeling Anaerobic Muscle Metabolism

Is it possible for a minimal model of anaerobic muscle contraction to describe measured data? There have been many models trying to describe separate parts of the human body with various results. In this thesis a model has been created to describe all the essential biochemical reactions of anaerobic muscle metabolism during contraction but with as few states and parameters as possible. A toolbox in Matlab was used for simulation and also for parameter estimation. The best model eventually got validated to see statistically how well it can describe the measured data…


1 Introduction
1.1 Introduction
1.2 Thesis objectives
1.3 Problem definition
1.4 Thesis disposition
2 Background
2.1 Biochemical terms
2.1.1 Glycolysis
2.1.2 NAD+ and NADH
2.1.3 3 important nucleotides
2.2 Creating a minimal model
2.2.1 ODEs for the model
2.3 Nuclear Magnetic Resonance
2.4 Measurement data
2.4.1 Measured signal – PME
2.4.2 Measured signal – P
2.4.3 Measured signal – PCr
2.4.4 Measured signal – ATP
2.4.5 Measured signal – pH
2.5 Optimization
2.5.1 Nelder-Mead simplex method
2.5.2 Simulated annealing method
2.6 Testing and validating the model
2.6.1 Identification cycle
2.6.2 Statistical test and validation
2.6.3 Residual analysis
2.6.4 χ2 test
3 Modeling
3.1 Implementing the contraction
3.2 Modifying the original model
3.2.1 Simplifying the Ca-terms
3.2.2 Expanding the differential equation for H
ix3.2.3 Measuring G6P
3.2.4 Expanding the vGP-reaction
3.2.5 Re-writing some parameters as constants
3.3 Assumptions about vCK
3.4 Optimizing the optimization
3.4.1 Scaling the measured signals
3.4.2 Weighting the parameters
3.4.3 Weighting and adjusting the cost function
4 Results
4.1 Standard deviation and mean value of measurement data
4.2 Filtering standard deviation
4.3 Wrong assumption revealed
4.4 Simulating the first model
4.5 Simulating a scaled and modified model
4.5.1 Resting phase
4.5.2 Contraction phase
4.5.3 Recovery phase
4.5.4 The whole model
4.6 The final model
4.6.1 Weighting the final model
4.6.2 Resting phase
4.6.3 Contraction
4.6.4 Recovery phase
4.6.5 The whole model
5 Discussion and Conclusion
5.1 Error in the model
5.2 Discussion
5.3 Further objectives
5.4 Conclusions

Author: Maksai, Tibor

Source: Linköping University

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