This work introduces a 4D flow magnetic resonance imaging (MRI) pressure reconstruction method which employs weighted least-squares (WLS) for pressure integration. Pressure gradients are calculated from the velocity fields, and velocity errors are estimated from the velocity divergence for incompressible flow. Pressure gradient errors are estimated by propagating the velocity errors through Navier-Stokes momentum equation. A weight matrix is generated based on the pressure gradient errors, then employed for pressure reconstruction. The pressure reconstruction method was demonstrated and analyzed using synthetic velocity fields as well as Poiseuille flow measured using in vitro 4D flow MRI. Performance of the proposed WLS method was compared to the method of solving the pressure Poisson equation which has been the primary method used in the previous studies. Error analysis indicated that the proposed method is more robust to velocity measurement errors. Improvement on pressure results was found to be more significant for the cases with spatially-varying velocity error level, with reductions in error ranging from 50% to over 200%. Finally, the method was applied to flow in patient-specific cerebral aneurysms. Validation was performed with in vitro flow data collected using Particle Tracking Velocimetry (PTV) and in vivo flow measurement obtained using 4D flow MRI. Pressure calculated by WLS, as opposed to the Poisson equation, was more consistent with the flow structures and showed better agreement between the in vivo and in vitro data. These results suggest the utility of WLS method to obtain reliable pressure field from clinical flow measurement data.

An insect's living systems-circulation, respiration, and a branching nervous system-extend from the body into the wing. Wing hemolymph circulation is critical for hydrating tissues and supplying nutrients to living systems such as sensory organs across the wing. Despite the critical role of hemolymph circulation in maintaining healthy wing function, wings are often considered "lifeless" cuticle, and flows remain largely unquantified. High-speed fluorescent microscopy and particle tracking of hemolymph in the wings and body of the grasshopper Schistocerca americana revealed dynamic flow in every vein of the fore- and hindwings. The global system forms a circuit, but local flow behavior is complex, exhibiting three distinct types: pulsatile, aperiodic, and "leaky" flow. Thoracic wing hearts pull hemolymph from the wing at slower frequencies than the dorsal vessel; however, the velocity of returning hemolymph (in the hindwing) is faster than in that of the dorsal vessel. To characterize the wing's internal flow mechanics, we mapped dimensionless flow parameters across the wings, revealing viscous flow regimes. Wings sustain ecologically important insect behaviors such as pollination and migration. Analysis of the wing circulatory system provides a template for future studies investigating the critical hemodynamics necessary to sustaining wing health and insect flight.

Typical approaches to patient-specific haemodynamic studies of cerebral aneurysms use image-based computational fluid dynamics (CFD) and seek to statistically correlate parameters such as wall shear stress (WSS) and oscillatory shear index (OSI) to risk of growth and rupture. However, such studies have reported contradictory results, emphasizing the need for in-depth multi-modality haemodynamic metric evaluation. In this work, we used in vivo 4D flow MRI data to inform in vitro particle velocimetry and CFD modalities in two patient-specific cerebral aneurysm models (basilar tip and internal carotid artery). Pulsatile volumetric particle velocimetry experiments were conducted, and the particle images were processed using Shake-the-Box, a particle tracking method. Distributions of normalized WSS and relative residence time were shown to be highly yet inconsistently affected by minor flow field and spatial resolution variations across modalities, and specific relationships among these should be explored in future work. Conversely, OSI, a non-dimensional parameter, was shown to be more robust to the varying assumptions, limitations and spatial resolutions of each subject and modality. These results suggest a need for further multi-modality analysis as well as development of non-dimensional haemodynamic parameters and correlation of such metrics to aneurysm risk of growth and rupture.