Dominik Obrist

Red blood cell distribution in simplified capillary networks

A detailed model of red blood cell (RBC) transport in a capillary network is an indispensable element of a comprehensive model for the supply of the human organism with oxygen and nutrients. In this paper, we introduce a two-phase model for the perfusion of a capillary network. This model accounts for the special role of RBCs, which have a strong influence on network dynamics. Analytical results and numerical simulations with a discrete model and a generic network topology indicate that there exists a local self-regulation mechanism for the flow rates and a global de-mixing process that leads to an inhomogeneous haematocrit distribution. Based on the results from the discrete model, we formulate an efficient algorithm suitable for computing the pressure and flow field as well as a continuous haematocrit distribution in large capillary networks at steady state.

Predicting sizes of droplets made by microfluidic flow-induced dripping

We present a model to predict the size of droplets dripping into an immiscible flowing fluid in glass capillary microfluidic devices. Despite the complex flow behavior in the confined geometry of microfluidic devices, we find that the size of dripping droplets can be accurately predicted by a simple analytic expression based on the ratio of shear and interfacial forces acting on the droplet surface, also known as the Capillary number. We show that data obtained for a wide range of fluid properties and flow conditions including single and multiple dripping events and other experimental data previously reported in the literature can be quantitatively described using one single universal value for the critical Capillary number leading to droplet rupture.

Directivity of acoustic emissions from wave packets to the far field

We investigate the acoustic emission from wave packets to the far field. To this end, we develop a theory for one- and two-dimensional source fields in the shape of wave packets with Gaussian envelopes. This theory is based on an approximation to Lighthills acoustic analogy for distant observers. It is formulated in the spectral domain in which a Gaussian wave packet is represented again by a Gaussian. This allows us to determine the directivity of the acoustic emission (e.g. superdirectivity and Mach waves) by simple geometric constructions in the spectral domain. It is shown that the character of the acoustic emission is mainly governed by the aspect ratio and the Mach number of the wave packet source. To illustrate the relevance of this theory we use it to study two prominent problems in subsonic jet aeroacoustics.

In vitro model of a semicircular canal: Design and validation of the model and its use for the study of canalithiasis

We present an experimental model for a semicircular canal with canalithiasis. Canalithiasis is a pathological condition where free-floating particles disturb the flow field in the semicircular canals. It may lead to a specific form of vertigo known as BPPV or top-shelf vertigo. A careful scaling of the physical and geometrical parameters allows us to study the mechanics of this disease on an enlarged model of a single semicircular canal with laser vibrometry and video particle tracking. Early results confirm the proper operation of the model canal and support the current theories on the mechanisms of BPPV.

Fluid-particle dynamics in canalithiasis

The semicircular canals (SCCs; located in the inner ear) are the primary sensors for angular motion. Angular head movements induce a fluid flow in the SCCs. This flow is detected by afferent hair cells inside the SCCs. Canalithiasis is a condition where small particles disturb this flow, which leads to benign paroxysmal positional vertigo (top-shelf vertigo). The present work investigates the interaction between the fluid flow and the particles on the basis of an idealized analytical model. Numerical solutions of the full model and a thorough analytical study of the linearized model reveal the principal mechanisms of canalithiasis. We propose a set of dimensionless numbers to characterize canalithiasis and derive explicit expressions connecting these dimensionless numbers directly to the typical clinical symptoms.

Vortical flow in the utricle and the ampulla: a computational study on the fluid dynamics of the vestibular system

We present a computational study of the fluid dynamics in healthy semicircular canals (SCCs) and the utricle. The SCCs are the primary sensors for angular velocity and are located in the vestibular part of the inner ear. The SCCs are connected to the utricle that hosts the utricular macula, a sensor for linear acceleration. The transduction of angular motion is triggered by the motion of a fluid called endolymph and by the interaction of this fluid with the sensory structures of the SCC. In our computations, we observe a vortical flow in the utricle and in the ampulla (the enlarged terminal part of the SCCs) which can lead to flow velocities in the utricle that are even higher than those in the SCCs. This is a fundamentally new result which is in contrast to the common belief that the fluid velocities in the utricle are negligible from a physiological point of view. Moreover, we show that the wall shear stresses in the utricle and the ampulla are maximized at the positions of the sensory epithelia. Possible physiological and clinical implications are discussed.

Algebraically decaying modes and wave packet pseudo-modes in swept Hiemenz flow

The modal structure of the swept Hiemenz flow, a model for the flow near the attachment line of a swept wing, consists of eigenfunctions which exhibit (super-)exponential or algebraic decay as the wall-normal coordinate tends to infinity. The subset of algebraically decaying modes corresponds to parts of the spectrum which are characterized by a significant sensitivity to numerical discretization. Numerical evidence further suggests that a continuous spectrum covering a two-dimensional range of the complex plane exists. We investigate the family of uniform swept Hiemenz modes using eigenvalue computations, numerical simulations and the concept of wave packet pseudo-modes. Three distinct branches of the family of algebraically decaying eigenmodes are identified. They can be superimposed to produce wavefronts propagating towards or away from the boundary layer and standing or travelling wave packets in the free stream. Their role in the exchange of information between the free stream and the attachment-line boundary layer for the swept Hiemenz flow is discussed. The concept of wave packet pseudo-modes has been critical in the analysis of this problem and is expected to lead to further insights into other shear flows in semi- or bi-infinite domains.

Flow disturbances in stent-related coronary evaginations: A computational fluid-dynamic simulation study

AIMS Angiographic ectasias and aneurysms in stented segments have been associated with late stent thrombosis. Using optical coherence tomography (OCT), some stented segments show coronary evaginations reminiscent of ectasias. The purpose of this study was to explore, using computational fluid-dynamic (CFD) simulations, whether OCT-detected coronary evaginations can induce local changes in blood flow. METHODS AND RESULTS OCT-detected evaginations are defined as outward bulges in the luminal vessel contour between struts, with the depth of the bulge exceeding the actual strut thickness. Evaginations can be characterised cross-sectionally by depth and along the stented segment by total length. Assuming an ellipsoid shape, we modelled 3-D evaginations with different sizes by varying the depth from 0.2-1.0 mm, and the length from 1-9 mm. For the flow simulation we used average flow velocity data from non-diseased coronary arteries. The change in flow with varying evagination sizes was assessed using a particle tracing test where the particle transit time within the segment with evagination was compared with that of a control vessel. The presence of the evagination caused a delayed particle transit time which increased with the evagination size. The change in flow consisted locally of recirculation within the evagination, as well as flow deceleration due to a larger lumen - seen as a deflection of flow towards the evagination. CONCLUSIONS CFD simulation of 3-D evaginations and blood flow suggests that evaginations affect flow locally, with a flow disturbance that increases with increasing evagination size.

Acoustic emissions from convected wave packets

Localized acoustic sources can often be modeled by wave packets. It has been recognized for a long time that the particular structure of these wave packet sources has a strong influence on the character of the acoustic emission to the far field. In the present work, we study the acoustic emission patterns with respect to the phase velocity, group velocity, size, and aspect ratio of the wave packet sources. To this end, the acoustic problem is formulated on the basis of Lighthill’s acoustic analogy and then recast to the geometrical problem of conic sections. This leads to the notion of elliptic (subsonic), parabolic (sonic), and hyperbolic (supersonic) acoustic emission patterns. The resulting geometric theory for acoustic emissions from wave packets includes phenomena such as Mach waves, bi- and superdirectivity, Doppler shift, and silent directions.Localized acoustic sources can often be modeled by wave packets. It has been recognized for a long time that the particular structure of these wave packet sources has a strong influence on the character of the acoustic emission to the far field. In the present work, we study the acoustic emission patterns with respect to the phase velocity, group velocity, size, and aspect ratio of the wave packet sources. To this end, the acoustic problem is formulated on the basis of Lighthill’s acoustic analogy and then recast to the geometrical problem of conic sections. This leads to the notion of elliptic (subsonic), parabolic (sonic), and hyperbolic (supersonic) acoustic emission patterns. The resulting geometric theory for acoustic emissions from wave packets includes phenomena such as Mach waves, bi- and superdirectivity, Doppler shift, and silent directions.

Quantitative analysis of benign paroxysmal positional vertigo fatigue under canalithiasis conditions

In our daily life, small flows in the semicircular canals (SCCs) of the inner ear displace a sensory structure called the cupula which mediates the transduction of head angular velocities to afferent signals. We consider a dysfunction of the SCCs known as canalithiasis. Under this condition, small debris particles disturb the flow in the SCCs and can cause benign paroxysmal positional vertigo (BPPV), arguably the most common form of vertigo in humans. The diagnosis of BPPV is mainly based on the analysis of typical eye movements (positional nystagmus) following provocative head maneuvers that are known to lead to vertigo in BPPV patients. These eye movements are triggered by the vestibulo-ocular reflex, and their velocity provides an indirect measurement of the cupula displacement. An attenuation of the vertigo and the nystagmus is often observed when the provocative maneuver is repeated. This attenuation is known as BPPV fatigue. It was not quantitatively described so far, and the mechanisms causing it remain unknown. We quantify fatigue by eye velocity measurements and propose a fluid dynamic interpretation of our results based on a computational model for the fluid-particle dynamics of a SCC with canalithiasis. Our model suggests that the particles may not go back to their initial position after a first head maneuver such that a second head maneuver leads to different particle trajectories causing smaller cupula displacements.