Effects of Uncertainty of Outlet Boundary Conditions in a Patient-Specific Case of Aortic Coarctation

Computational Fluid Dynamics (CFD) simulations of blood flow are widely used to compute a variety of hemodynamic indicators such as velocity, time-varying wall shear stress, pressure drop, and energy losses. One of the major advances of this approach is that it is non-invasive. The accuracy of the cardiovascular simulations depends directly on the level of certainty on input parameters due to the modelling assumptions or computational settings. Physiologically suitable boundary conditions at the inlet and outlet of the computational domain are needed to perform a patient-specific CFD analysis. These conditions are often affected by uncertainties, whose impact can be quantified through a stochastic approach. A methodology based on a full propagation of the uncertainty from clinical data to model results is proposed here. It was possible to estimate the confidence associated with model predictions, differently than by deterministic simulations. We evaluated the effect of using three-element Windkessel models as the outflow boundary conditions of a patient-specific aortic coarctation model. A parameter was introduced to calibrate the resistances of the Windkessel model at the outlets. The generalized Polynomial Chaos method was adopted to perform the stochastic analysis, starting from a few deterministic simulations. Our results show that the uncertainty of the input parameter gave a remarkable variability on the volume flow rate waveform at the systolic peak simulating the conditions before the treatment. The same uncertain parameter had a slighter effect on other quantities of interest, such as the pressure gradient. Furthermore, the results highlight that the fine-tuning of Windkessel resistances is not necessary to simulate the post-stenting scenario.

SteadyCellPhenotype: A web-based tool for the modeling of biological networks with ternary logic

We introduce SteadyCellPhenotype, a browser based interface for the analysis of ternary biological networks. It includes tools for deterministically finding all steady states of a network, as well as the simulation and visualization of trajectories with publication quality graphics. Stochastic simulations allow us to approximate the size of the basin for attractors and deterministic simulations of trajectories nearby specified points allow us to explore the behavior of the system in that neighborhood.

Interpretability and variability of metamodel validation statistics in engineering system design optimization: a practical study

Prediction accuracy of a metamodel of an engineering system in comparison to the simulation model it approximates is one fundamental criterion that is used in metamodel validation. Many statistics are used to quantify prediction accuracy of metamodels in deterministic simulations. The most frequently used ones include the root-mean-square error (RMSE) and the R-square metric derived from it, and to a lesser degree the average absolute error (AAE) and its derivates such as the relative average absolute error (RAAE). In this paper, we compare two aspects of these statistics: interpretability of results returned by these statistics and their sample-to-sample variations, putting more emphasis on the latter. We use the difference-mode to common-mode ratio (DMCMR) as a measure of sample-to-sample variations for these statistics. Preliminary results are obtained and discussed via a number of analytic and electronic engineering examples.

Efficacy of calf:cow ratios for estimating calf production of arctic caribou

Caribou (Rangifer tarandus granti) calf:cow ratios (CCR) computed from composition counts obtained on arctic calving grounds are biased estimators of net calf production (NCP, the product of parturition rate and early calf survival) for sexually-mature females. Sexually-immature 2-year-old females, which are indistinguishable from sexually-mature females without calves, are included in the denominator, thereby biasing the calculated ratio low. This underestimate increases with the proportion of 2-year-old females in the population. We estimated the magnitude of this error with deterministic simulations under three scenarios of calf and yearling annual survival (respectively: low, 60 and 70%; medium, 70 and 80%; high, 80 and 90%) for five levels of unbiased NCP: 20, 40, 60, 80, and 100%. We assumed a survival rate of 90% for both 2-year-old and mature females. For each NCP, we computed numbers of 2-year-old females surviving annually and increased the denominator of CCR accordingly. We then calculated a series of hypothetical “observed” CCRs, which stabilized during the last 6 years of the simulations, and documented the degree to which each 6-year mean CCR differed from the corresponding NCP. For the three calf and yearling survival scenarios, proportional underestimates of NCP by CCR ranged 0.046–0.156, 0.058–0.187, and 0.071–0.216, respectively. Unfortunately, because parturition and survival rates are typically variable (i.e., age distribution is unstable), the magnitude of the error is not predictable without substantial supporting information. We recommend maintaining a sufficient sample of known-age radiocollared females in each herd and implementing a regular relocation schedule during the calving period to obtain unbiased estimates of both parturition rate and NCP.

System Reliability Estimation With Input Data From Deterministic Simulations

The possibility of estimating reliability of hardware, both for components and systems, is important in engineering design, since many failures result in substantial impact on safety or functional requirements. Existing reliability estimation methods require measured or estimated input data which can be difficult to retrieve. The objective of this paper is therefore to derive a simulation-driven method, including variation management, for combining deterministic simulations with Fault Tree Analysis, to estimate system reliability when measured data is not available. The research work started with a literature survey followed by description of a typical as-is situation and definition of a to-be scenario. Then, a simulation-driven method was derived and verified by a case study. In particular, the system used for the case study was modeled and simulated as a transient dynamical system to derive information about loads on components. It was found that deterministic simulations can be used to produce relevant input data for fault tree analysis. The derived simulation-driven system reliability estimation method includes variation management and can be used for evaluation of concepts in the early stages of product development when limited measurement data is available.