Personalizing physical exercise in a computational model of fuel homeostasis

Abstract

The beneficial effects of physical activity for the prevention and management of several chronic diseases are widely recognized. Mathematical modeling of the effects of physical exercise in body metabolism and in particular its influence on the control of glucose homeostasis is of primary importance in the development of eHealth monitoring devices for a personalized medicine. Nonetheless, to date only a few mathematical models have been aiming at this specific purpose. We have developed a whole-body computational model of the effects on metabolic homeostasis of a bout of physical exercise. Built upon an existing model, it allows to detail better both subjects' characteristics and physical exercise, thus determining to a greater extent the dynamics of the hormones and the metabolites considered.

Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Fig 1. Whole body system diagram.

Exercise stimulates epinephrine release which influences the pancreatic secretion of insulin and glucagon and acts as a neuroendocrine signal for the heart and skeletal muscle (gray lines). Consequently, modifications in the glucagon and insulin production modulate in a coordinated way the metabolic flux rates of the different organs. Each organ is connected via the arterial/venous circulation (red/blue lines). Arterial glucose concentration (dotted line) signals the pancreas to set the levels of insulin and glucagon, whose ratio is used by the liver, GI tract and the adipose tissue. Two more ODEs are added to the KSC to model the exercise-induced effect of epinephrine, for a total of 136 ODEs consisting in the multi-scale computational model.

Fig 2. Dynamics of insulin and glucagon in response to exercise.

Model fit (solid line) vs experimental data (circles), expressed as mean ± SEM from study 3 [28]. Parameter estimation is performed using data obtained during an exercise session of 60 min. The gray zone refers to the exercise period. The inset plots refer to the weighted residuals. A: Plasma insulin concentration. B: Plasma glucagon concentration.

Fig 3. Dynamics of suprabasal plasma insulin concentration in response to exercise.

Model fit (red areas) vs experimental data (circles) expressed as mean ± SEM from the study 1. The red areas show the range of the dynamic responses of the model to the variability of the subjects’ characteristics as reported in Table 2; individual response curves related to each simulation are available. The gray zone refers to the exercise period. The dark gray zone refers to the exercise performed above the LT until minute 32. A: Trained individuals. B: Untrained individuals.

Fig 4. Dynamics of suprabasal plasma glucagon concentration in response to exercise.

Model fit (red areas) vs experimental data (circles), expressed as mean ± SEM. The red areas show the range of the dynamic responses of the model to the variability of the subjects’ characteristics as reported in Table 2; individual response curves related to each simulation are available. The gray zone refers to the exercise period. The dark gray zone refers to the exercise performed above the LT until minute 32. A: Trained individuals from the study 1. B: Untrained individuals from the study 1. C: Individuals from the study 2.

Fig 5. Dynamics of suprabasal plasma epinephrine concentration in response to exercise.

Model fit (colored areas) vs experimental data (circles and squares) expressed as mean ± SE. The colored areas show the range of the dynamic responses of the model to the variability of the subjects’ characteristics as reported in Table 2 (black circles and red area: males; open squares and blue area: females); individual response curves related to each simulation are available. The gray zone refers to the exercise period. The dark gray zone refers to the exercise performed above the LT until minute 32. A: Trained individuals from the study 1. B: Untrained individuals from the study 1. C: Individuals from the study 3. D: Individuals from the study 5 (black circles and red area: males; open squares and blue area: females).

Fig 6. Dynamics of suprabasal plasma glucose concentration in response to exercise.

Model fit (red areas) vs experimental data (circles) expressed as mean ± SE. The red areas show the range of the dynamic responses of the model to the variability of the subjects’ characteristics as reported in Table 2; individual response curves related to each simulation are available. The gray zone refers to the exercise period. The dark gray zone refers to the exercise performed above the LT until minute 32. A: Trained individuals from the study 1. B: Untrained individuals from the study 1. C: Individuals from the study 2.

Fig 7. Dynamics of suprabasal plasma glycerol concentration in response to exercise.

Model fit (colored areas) vs experimental data (circles and squares) expressed as mean ± SE. The colored areas show the range of the dynamic responses of the model to the variability of the subjects’ characteristics as reported in Table 2 (black circles and red area: males; open squares and blue area: females); individual response curves related to each simulation are available. The gray zone refers to the exercise period. The dark gray zone refers to the exercise performed above the LT until minute 32. A: Trained individuals from the study 1. B: Untrained individuals from the study 1. C: Individuals from the study 2. D: Individuals from the study 5.

Fig 8. Dynamics of suprabasal plasma alanine concentration in response to exercise.

Model fit (red areas) vs experimental data (circles) expressed as mean ± SE from the study 1. The red areas show the range of the dynamic responses of the model to the variability of the subjects’ characteristics as reported in Table 2; individual response curves related to each simulation are available. The gray zone refers to the exercise period. The dark gray zone refers to the exercise performed above the LT until minute 32. A: Trained individuals. B: Untrained individuals.

Fig 9. Dynamics of suprabasal plasma lactate concentration in response to exercise.

Model fit (colored areas) vs experimental data (circles) expressed as mean ± SE. The colored areas show the range of the dynamic responses of the model to the variability of the subjects’ characteristics as reported in Table 2 (blue: females; red: males); individual response curves related to each simulation are available. The gray zone refers to the exercise period. The dark gray zone refers to the exercise performed above the LT until minute 32. The colored area shows the dynamic responses of the model to the variability of the subjects’ characteristics as reported in Table 2. A: Trained individuals from the study 1. B: Untrained individuals from the study 1. C: Trained individuals from the study 4. D: Untrained individuals from the study 4. E: Individuals from the study 5.

Fig 10. Dynamics of suprabasal plasma FFA concentration in response to exercise.

Model fit (colored areas) vs experimental data (circles) expressed as mean ± SE. The colored areas show the range of the dynamic responses of the model to the variability of the subjects’ characteristics as reported in Table 2 (black circles and red area: males; open squares and blue area: females); individual response curves related to each simulation are available. The gray zone refers to the exercise period. The dark gray zone refers to the exercise performed above the LT until minute 32. A: Trained individuals from the study 1. B: Untrained individuals from the study 1. C: Individuals from the study 2. D: Individuals from the study 3. E: Individuals from the study 5.

Fig 11. Reactions in liver.

Simulations of net hepatic glycogen breakdown (solid line) and net hepatic gluconeogenesis (dotted line) in response to the exercise performed in the study 3. The gray zone refers to the exercise period.

Fig 12. Dynamics of suprabasal concentration of glycogen in muscle in response to exercise.

Model fit (red areas) vs experimental data (circles) expressed as mean ± SE in the study 6. The gray zone refers to the exercise period. The red areas show the range of the dynamic responses of the model to the variability of the subjects’ characteristics as reported in Table 2; individual response curves related to each simulation are available.

Fig 13. Dynamics of suprabasal plasma glycerol concentration in response to exercise.

Model fit (colored lines) vs experimental data (circles) expressed as mean ± SE. The colored lines show the different simulated dynamic responses of the eight subjects from the study 2 [32]. The gray zone refers to the exercise period.