| The baroreceptor reflex is responsible for short term regulation of blood pressure. During orthostatic stress, such as posture changes, the baroreflex maintains constant blood pressure by regulating (among others) venous volume, systemic resistance and heart rate through the sympathetic and parasympathetic nervous system. This dissertation aims to develop a model for the baroreflex regulation of heart rate during head-up-tilt (HUT) considering blood pressure and respiration as input to the model. The model includes description of the strain of the arterial wall and the enclosed stretch-sensitivity baroreceptor neurons, the afferent neuron firing, sympathetic and parasympathetic activity, neurotransmitter concentrations at the synapse of the pacemaker cells of the heart, and a lumped description of intracellular pathways of the pacemaker cell and it's depolarization. The model is shown to exhibit positivity of solution under correct parametrization.;A correct mathematical description of the regulation of heart rate during orthostatic stress would make it possible to learn about system configuration not immediately measurable, through fitting of model output to experimental data. While this idea is simple, it posses several mathematical challenges, such as the question whether model parameters can be estimated, and what uncertainties follow such estimates and accompanying model predictions. The first question is answered through sensitivity and identifiability analysis, while the other is related to uncertainty quantification.;This dissertation provides a discussion of Sobol Indices and Morris elementary effects for global sensitivity analysis, and of structural correlation matrix method (SCM) and orthogonal sensitivities method (OSM) for identifiability analysis. The methods are applied to multiple examples of increasing complexity to present the underlying properties of each method, and possible forces and shortcomings of the methods.;Using the presented methods for identifiability analysis different subsets of parameters are constructed, and the model is fitted to experimental data for each subset, allowing only the chosen parameters to vary, while keeping the remaining fixed. Finally Delay-rejection adaptive Metropolis (DRAM) is used to determine parameter densities and model prediction intervals. Simulation results suggests that the model is able to produce an increase in heart rate following HUT, but that the implementation of respiration in it's current form do not increase the predictive power of the model, as it is unable to reproduce some of the faster dynamics. Furthermore, as an optimization where all parameters were allowed to vary produced the best fit, it is possible that the strategies used for building parameter subsets may be too restrictive in deeming parameters unidentifiable. |
