Computational models of the heart have reached a maturity level that render them useful for in silico studies of arrhythmia and other cardiac diseases. However, the translation to the clinic of cardiac simulations critically depends on demonstrating the accuracy, robustness, and reliability of the underlying computational models under the presence of uncertainties. In this work, we study for the first time the effect of parameter uncertainty on 2 state-of-the-art coupled models of excitation-contraction of cardiac tissue. To this end, we perform forward uncertainty propagation and sensitivity analyses to understand how variability in key maximal conductances affect selected quantities of interest, such as the action potential duration (APD ), maximum intracellular calcium concentration, cardiac stretch, and stress. Our results suggest a strong linear relationship between selected maximal conductances and quantities of interest for a variability in parameters up to 25%, which justifies the construction of linear response surfaces that are used to compute the empirical probability density functions of all the quantities of interest under study. For both electromechanical models analyzed, uncertainty in the material parameters associated to the passive mechanical response of cardiac tissue does not affect the duration of action potentials, neither the amplitude of intracellular calcium concentrations. Our results confirm the poor mechanoelectric feedback that classical models of cardiac electromechanics have, even under the presence of parameter uncertainty.
It is quite common to consider GNSS satellites as highly accurate clocks orbiting the Earth and it is with the aid of these orbiting clocks that GNSS users are able to obtain precise positioning solutions. As for any other satellite navigation system, Galileo's satellite clocks are one of the critical technologies in the system. In the particular case of Galileo, each satellite is equipped with four redundant clocks: two primary Passive Hydrogen Masers (PHM) measuring time to within 0.45 ns over 12 hours, which is four times better than the performance of the two secondary Rubidium clocks, accurate to within 1.8 ns over 12 hours, see [Ref. 1.].Notwithstanding the reported and now identified Galileo satellite clock failures, see [Ref. 2.], the observed behaviour of the Galileo clocks, when operating nominally, seems to be very stable, especially in the short term. The clock stability feature is a key element: on the one hand for the accuracy of the navigation solutions and on the other hand for its non-negligible impact on the system complexity and associated costs.Clock stability, as well as the navigation solution accuracy, are directly related, together with other factors, to clock predictability. Higher stability implies more accurate predictability, and better predictions mean better ephemeris. Not only better standard ephemeris for navigation solutions, but also better long term ephemeris for assisted navigation. On top of that, better clock stability can also potentially contribute to reduce the complexity of the GNSS ground segment. Standard ODTS (Orbit Determination & Time Synchronisation) approaches implement snapshot strategies for the clock restitution, based on obtaining epoch by epoch estimates of all satellite's and station receiver's clock parameters. This approach implies the management of a large number of parameters in the estimation process, which could be drastically reduced if some information about the physical behaviour of the clocks in the system could be input to the processing filter, for example, if the snapshot estimation strategy could be replaced by a pure model or by a mixed model-snapshot strategy.This paper is aimed at observing the behaviour of the Galileo satellite apparent clocks, with the purpose of finding interesting features allowing potential improvements in at least the following aspects: accuracy of the navigation solutions, accuracy of long term ephemeris and ground segment complexity.The results included in this paper are based on the analysis of apparent clocks obtained through accurate restitution by means of ODTS processes, implementing state-of-the-art algorithms and models. Typical trends and anomalous events of the Galileo satellite clocks are going to be described and analysed. Comparisons with other GNSS satellite clocks are going to be shown, and conclusions, driven out of the performed research, are going to be extracted.
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