Computational fluid dynamics models are increasingly used to simulate vascular flow. Patient-specific flow measurements are typically used to set flow boundary conditions that drive the simulations. When patient-specific flow measurements are unavailable, mean values of flow measurements across small cohorts are used as normative values. In reality, both the between-subjects and within-subject flow variability is large, and mean values across a cohort might not be indicative of flow in a particular individual. We highlight the importance of quantifying the uncertainty in CFD-based indicators, such as wall shear stress (WSS), due to the physiological variability of blood flow.
We develop data-driven statistical models for the between-subjects variability of internal carotid flow (Lassila et al. 2018). A log-linear mixed effects model describes the variability in the time-averaged flow rate, while a Gaussian process model describes the variability of the time-dependent flow fluctuations. The model parameters are identified from carotid ultrasound measurements in a cohort of 104 elderly volunteers. To model within-subject variability, we use a cerebral autoregulation model (Mader et al. 2015) to model the response of internal carotid flow to changes in heart rate and blood pressure. Our models provide: (i) cohort-specific boundary conditions to vascular CFD simulations in the case that patient-specific flow measurements are not available, and (ii) estimates of within-subject flow variability in cases where patient-specific flow measurements are available only as spot measurements.
The flow variability models are applied to study the effects of flow variability on WSS patterns in intracranial aneurysms. Different WSS-related indicators have been proposed for identifying aneurysms with high rupture risk. We have previously shown that two commonly used WSS-based indicators, oscillatory shear index (OSI) and transverse WSS (TransWSS), are sensitive to physiological flow variability (Sarrami-Foroushani et al. 2016), which may confound their interpretation. We further study the effects of exercise-induced variability of ICA flow on WSS-based indicators. While the cerebral autoregulation system holds the time-averaged flow rate relatively stable even under strenuous exercise, changes in the flow waveform are more dramatic and can lead to large uncertainty in WSS-based indicators.