Uncertainty quantification of a thrombosis model considering the clotting assay PFA-100

Mathematical models of thrombosis are currently used to study clinical scenarios of pathological thrombus formation. Most of these models involve inherent uncertainties that must be assessed to increase the confidence in model predictions and identify avenues of improvement for both thrombosis modeling and anti-platelet therapies. In this work, an uncertainty quantification analysis of a multi-constituent thrombosis model is performed considering a common assay for platelet function (PFA-100). The analysis is performed using a polynomial chaos expansion as a parametric surrogate for the thrombosis model. The polynomial approximation is validated and used to perform a global sensitivity analysis via computation of Sobol coefficients. Six out of fifteen parameters were found to be influential in the simulation variability considering only individual effects. Nonetheless, parameter interactions are highlighted when considering the total Sobol indices. In addition to the sensitivity analysis, the surrogate model was used to compute the PFA-100 closure times of 300,000 virtual cases that align well with clinical data. The current methodology could be used including common anti-platelet therapies to identify scenarios that preserve the hematological balance.

Limitations of ROC on Imbalanced Data: Evaluation of LVAD Mortality Risk Scores

Objective: This study illustrates the ambiguity of ROC in evaluating two classifiers of 90-day LVAD mortality. This paper also introduces the precision recall curve (PRC) as a supplemental metric that is more representative of LVAD classifiers performance in predicting the minority class. Background: In the LVAD domain, the receiver operating characteristic (ROC) is a commonly applied metric of performance of classifiers. However, ROC can provide a distorted view of classifiers ability to predict short-term mortality due to the overwhelmingly greater proportion of patients who survive, i.e. imbalanced data. Methods: This study compared the ROC and PRC for the outcome of two classifiers for 90-day LVAD mortality for 800 patients (test group) recorded in INTERMACS who received a continuous-flow LVAD between 2006 and 2016 (mean age of 59 years; 146 females vs. 654 males) in which mortality rate is only %8 at 90-day (imbalanced data). The two classifiers were HeartMate Risk Score (HMRS) and a Random Forest (RF). Results: The ROC indicates fairly good performance of RF and HRMS classifiers with Area Under Curves (AUC) of 0.77 vs. 0.63, respectively. This is in contrast with their PRC with AUC of 0.43 vs. 0.16 for RF and HRMS, respectively. The PRC for HRMS showed the precision rapidly dropped to only 10% with slightly increasing sensitivity. Conclusion: The ROC can portray an overly-optimistic performance of a classifier or risk score when applied to imbalanced data. The PRC provides better insight about the performance of a classifier by focusing on the minority class.

A non-linear fluid suspension model for blood flow

Motivated by the complex rheological behaviors observed in small/micro scale blood vessels, such as the Fahraeus effect, plasma-skimming, shear-thinning, etc., we develop a non-linear suspension model for blood. The viscosity is assumed to depend on the volume fraction (hematocrit) and the shear rate. The migration of the red blood cells (RBCs) is studied using a concentration flux equation. A parametric study with two representative problems, namely simple shear flow and a pressure driven flow demonstrate the ability of this reduced-order model to reproduce several key features of the two-fluid model (mixture theory approach), with much lower computational cost.

Transport of platelets induced by red blood cells based on mixture theory

Thrombosis is a common complication following the surgical implantation of blood contacting devices, and is strongly influenced by the phenomenon of near-wall enrichment of platelets. This paper describes a multi-constituent continuum approach to study this phenomenon. A mixture-theory model is used to describe the motion of the plasma and the red blood cells (RBCs) and the interactions between the two components. A transport model is developed to study the influence of the RBC field on the platelets. The model is used to study blood flow in a rectangular micro-channel, a sudden expansion micro-channel, and a channel containing micro crevices (representing a practical problem encountered in most blood-wetted devices). The simulations show that in the rectangular channel the concentration of platelets near the walls is about five times higher than the concentration near the centerline of the channel. It is also noticed that in the channel with crevices, extremely a large number of platelets accumulate in the deep part of the crevices and this may serve as the nidus for thrombosis occurring in medical devices. Keywords: Platelets; Blood flow; RBCs; Micro-channel; Mixture theory; Two-fluids; Thrombosis

Normal stress effects in the gravity driven flow of granular materials

In this paper, we study the fully developed gravity-driven flow of granular materials between two inclined planes. We assume that the granular materials can be represented by a modified form of the second-grade fluid where the viscosity depends on the shear rate and volume fraction and the normal stress coefficients depend on the volume fraction. We also propose a new isotropic (spherical) part of the stress tensor which can be related to the compactness of the (rigid) particles. This new term ensures that the rigid solid particles cannot be compacted beyond a point, namely when the volume fraction has reached the critical/maximum packing value. The numerical results indicate that the newly proposed stress tensor has an obvious and physically meaningful effects on both the velocity and the volume fraction fields.