Global sensitivity analysis with multifidelity Monte Carlo and polynomial chaos expansion for vascular haemodynamics.

Computational models of the cardiovascular system are increasingly used for the diagnosis, treatment, and prevention of cardiovascular disease. Before being used for translational applications, the predictive abilities of these models need to be thoroughly demonstrated through verification, validation, and uncertainty quantification. When results depend on multiple uncertain inputs, sensitivity analysis is typically the first step required to separate relevant from unimportant inputs, and is key to determine an initial reduction on the problem dimensionality that will significantly affect the cost of all downstream analysis tasks. For computationally expensive models with numerous uncertain inputs, sample-based sensitivity analysis may become impractical due to the substantial number of model evaluations it typically necessitates. To overcome this limitation, we consider recently proposed Multifidelity Monte Carlo estimators for Sobol' sensitivity indices, and demonstrate their applicability to an idealized model of the common carotid artery. Variance reduction is achieved combining a small number of three-dimensional fluid-structure interaction simulations with affordable one- and zero-dimensional reduced-order models. These multifidelity Monte Carlo estimators are compared with traditional Monte Carlo and polynomial chaos expansion estimates. Specifically, we show consistent sensitivity ranks for both bi- (1D/0D) and tri-fidelity (3D/1D/0D) estimators, and superior variance reduction compared to traditional single-fidelity Monte Carlo estimators for the same computational budget. As the computational burden of Monte Carlo estimators for Sobol' indices is significantly affected by the problem dimensionality, polynomial chaos expansion is found to have lower computational cost for idealized models with smooth stochastic response.

Age and sex-dependent sensitivity analysis of a common carotid artery model.

The common carotid artery (CCA) is an accessible and informative site for assessing cardiovascular function which makes it a prime candidate for clinically relevant computational modelling. The interpretation of supplemental information possible through modelling is encumbered by measurement uncertainty and population variability in model parameters. The distribution of model parameters likely depends on the specific sub-population of interest and delineation based on sex, age or health status may correspond to distinct ranges of typical parameter values. To assess this impact in a 1D-CCA-model, we delineated specific sub-populations based on age, sex and health status and carried out uncertainty quantification and sensitivity analysis for each sub-population. We performed a structured literature review to characterize sub-population-specific variabilities for eight model parameters without consideration of health status; variations for a healthy sub-populations were based on previously established references values. The variabilities of diameter and distensibility found in the literature review differed from those previously established in a healthy population. Model diameter change and pulse pressure were most sensitive to variations in distensibility, while pressure was most sensitive to resistance in the Windkessel model for all groups. Uncertainties were lower when variabilities were based on a healthy sub-population; however, the qualitative distribution of sensitivity indices was largely similar between the healthy and general population. Average sensitivity of the pressure waveform showed a moderate dependence on age with decreasing sensitivity to distal resistance and increasing sensitivity to distensibility and diameter. The female population was less sensitive to variations in diameter but more sensitive to distensibility coefficient than the male population. Overall, as hypothesized input variabilities differed between sub-populations and resulted in distinct uncertainties and sensitivities of the 1D-CCA-model outputs, particularly over age for the pressure waveform and between males and females for pulse pressure.

Electrical Stimulation in the Human Cochlea: A Computational Study Based on High-Resolution Micro-CT Scans.

Background: Many detailed features of the cochlear anatomy have not been included in existing 3D cochlear models, including the microstructures inside the modiolar bone, which in turn determines the path of auditory nerve fibers (ANFs). Method: We captured the intricate modiolar microstructures in a 3D human cochlea model reconstructed from µCT scans. A new algorithm was developed to reconstruct ANFs running through the microstructures within the model. Using the finite element method, we calculated the electrical potential as well as its first and second spatial derivatives along each ANF elicited by the cochlear implant electrodes. Simulation results of electrical potential was validated against intracochlear potential measurements. Comparison was then made with a simplified model without the microstructures within the cochlea. Results: When the stimulus was delivered from an electrode located deeper in the apex, the extent of the auditory nerve influenced by a higher electric potential grew larger; at the same time, the maximal potential value at the auditory nerve also became larger. The electric potential decayed at a faster rate toward the base of the cochlea than toward the apex. Compared to the cochlear model incorporating the modiolar microstructures, the simplified version resulted in relatively small differences in electric potential. However, in terms of the first and second derivatives of electric potential along the fibers, which are relevant for the initiation of action potentials, the two models exhibited large differences: maxima in both derivatives with the detailed model were larger by a factor of 1.5 (first derivative) and 2 (second derivative) in the exemplary fibers. More importantly, these maxima occurred at different locations, and opposite signs were found for the values of second derivatives between the two models at parts along the fibers. Hence, while one model predicts depolarization and spike initiation at a given location, the other may instead predict a hyperpolarization. Conclusions: Although a cochlear model with fewer details seems sufficient for analysing the current spread in the cochlear ducts, a detailed-segmented cochlear model is required for the reconstruction of ANF trajectories through the modiolus, as well as the prediction of firing thresholds and spike initiation sites.

Influence of the Cochlear Implant Electrode Array Placement on the Current Spread in the Cochlea.

Three-dimensional (3D) computational models of the inner ear have been utilised to assist in investigating the factors that influence cochlear implant (CI) outcomes. A volume conductor cochlear model with an implanted electrode array was reconstructed from X-ray microtomography $(\mu$ CT) scans of a cadaveric human temporal bone. To mimic an in-vivo setting, the cochlea was embedded in a head model. The finite element (FE) method was used to analyse the electrical potential $\varphi$ in the cochlear nerve as a result of CI stimulation. In order to study the influence of electrode array placement on the current spread within the cochlea and the modiolus, computer simulations with six electrode array placements were conducted. $\varphi$ was evaluated at the tip of nerve fibres reconstructed within the cochlear nerve so as to predict the stimulation of a neuron population. It was found in most cases that a medial electrode array placement produced a narrower $\varphi$ peak at the fibre tip than a lateral one, although the differences were small.

A conserved tyrosine in the neck of a fungal kinesin regulates the catalytic motor core.

The neck domain of fungal conventional kinesins displays characteristic properties which are reflected in a specific sequence pattern. The exchange of the strictly conserved Tyr 362, not present in animals, into Lys, Cys or Phe leads to a failure to dimerize. The destabilizing effect is confirmed by a lower coiled-coil propensity of mutant peptides. Whereas the Phe substitution has only a structural effect, the Lys and Cys replacements lead to dramatic kinetic changes. The steady state ATPase is 4- to 7-fold accelerated, which may be due to a faster microtubule-stimulated ADP release rate. These data suggest that an inhibitory effect of the fungal neck domain on the motor core is mediated by direct interaction of the aromatic ring of Tyr 362 with the head, whereas the OH group is essential for dimerization. This is the first demonstration of a direct influence of the kinesin neck region in regulation of the catalytic activity.