Gravity-induced Motion Research Articles

Nano X Image Guidance in radiation therapy: feasibility study protocol for cone beam computed tomography imaging with gravity-induced motion

BackgroundThis paper describes the protocol for the Nano X Image Guidance (Nano X IG) trial, a single-institution, clinical imaging study. The Nano X is a prototype fixed-beam radiotherapy system developed to investigate the feasibility of a low-cost, compact radiotherapy system to increase global access to radiation therapy. This study aims to assess the feasibility of volumetric image guidance with cone beam computed tomography (CBCT) acquired during horizontal patient rotation on the Nano X radiotherapy system.MethodsIn the Nano X IG study, we will determine whether radiotherapy image guidance can be performed with the Nano X radiotherapy system where the patient is horizontally rotated while scan projections are acquired. We will acquire both conventional CBCT scans and Nano X CBCT scans for 30 patients aged 18 and above and receiving radiotherapy for head/neck or upper abdomen cancers. For each patient, a panel of experts will assess the image quality of Nano X CBCT scans against conventional CBCT scans. Each patient will receive two Nano X CBCT scans to determine the image quality reproducibility, the extent and reproducibility of patient motion and assess patient tolerance.DiscussionFixed-beam radiotherapy systems have the potential to help ease the current shortfall and increase global access to radiotherapy treatment. Advances in image guidance could facilitate fixed-beam radiotherapy using horizontal patient rotation. The efficacy of this radiotherapy approach is dependent on our ability to image and adapt to motion due to rotation and for patients to tolerate rotation during treatment.Trial registrationClinicalTrials.gov, NCT04488224. Registered on 27 July 2020.

Motion of long bubbles in gravity- and pressure-driven flow through cylindrical capillaries up to moderate capillary numbers

The motion of bubbles and drops through tubes in gravity- and pressure-driven flows is intensively studied numerically and experimentally. The Bretherton asymptotic expressions predict axisymmetric bubbles movement at low velocities. They describe the dependence of capillary (Ca) and Bond (Bo) numbers on the system parameters but are valid only in the ranges 0 < Ca < 0.005 and 0.84 < Bo < 1.04. This paper investigates the gravity-induced motion of bubbles with free or tangentially immobile interfaces in pressure-driven flows. We derive the exact solution of the hydrodynamic problem using the lubrication approximation in the zero- and first-order approximations for pressure and fluid velocity. The respective boundary value problem for the bubble shape is solved numerically to obtain the wetting film thickness, h, between the bubble and the capillary and the dependence of the capillary numbers on the flow parameters and magnitude of gravity. The proposed model expands the applicable solution ranges by 400 and 38 times, respectively (0 < Ca < 2 and 0 < Bo < 7.5), validated with available experimental data. The model's simplicity and transparency open the possibility to generalize this approach including determining new physicochemical properties of liquids and interfaces.

Cone-beam CT reconstruction with gravity-induced motion

Fixed-gantry cone-beam computed tomography (CBCT), where the imaging hardware is fixed while the subject is continuously rotated 360° in the horizontal position, has implications for building compact and affordable fixed-gantry linear accelerators (linacs). Fixed-gantry imaging with a rotating subject presents a challenging image reconstruction problem where the gravity-induced motion is coupled to the subject’s rotation angle. This study is the first to investigate the feasibility of fixed-gantry CBCT using imaging data of three live rabbits in an ethics-approved study. A novel data-driven motion correction method that combines partial-view reconstruction and motion compensation was developed to overcome this challenge. Fixed-gantry CBCT scans of three live rabbits were acquired on a standard radiotherapy system with the imaging beam fixed and the rabbits continuously rotated using an in-house programmable rotation cradle. The reconstructed images of the thoracic region were validated against conventional CBCT scans acquired at different cradle rotation angles. Results showed that gravity-induced motion caused severe motion blur in all of the cases if unaccounted for. The proposed motion correction method yielded clinically usable image quality with <1 mm gravity-induced motion blur for rabbits that were securely immobilized on the rotation cradle. Shapes of the anatomic structures were correctly reconstructed with <0.5 mm accuracy. Translational motion accounted for the majority of gravity-induced motion. The motion-corrected reconstruction represented the time-averaged location of the thoracic region over a 360° rotation. The feasibility of fixed-gantry CBCT has been demonstrated. Future work involves the validation of imaging accuracy for human subjects, which will be useful for emerging compact fixed-gantry radiotherapy systems.

A CBCT study of the gravity-induced movement in rotating rabbits

Fixed-beam radiotherapy systems with subjects rotating about a longitudinal (horizontal) axis are subject to gravity-induced motion. Limited reports on the degree of this motion, and any deformation, has been reported previously. The purpose of this study is to quantify the degree of anatomical motion caused by rotating a subject around a longitudinal axis, using cone-beam CT (CBCT).In the current study, a purpose-made longitudinal rotating was aligned to a Varian TrueBeam kV imaging system. CBCT images of three live rabbits were acquired at fixed rotational offsets of the cradle. Rigid and deformable image registrations back to the original position were used to quantify the motion experienced by the subjects under rotation.In the rotation offset CBCTs, the mean magnitude of rigid translations was 5.7 ± 2.7 mm across all rabbits and all rotations. The translation motion was reproducible between multiple rotations within 2.1 mm, 1.1 mm, and 2.8 mm difference for rabbit 1, 2, and 3, respectively. The magnitude of the mean and absolute maximum deformation vectors were 0.2 ± 0.1 mm and 5.4 ± 2.0 mm respectively, indicating small residual deformations after rigid registration. In the non-rotated rabbit 4DCBCT, respiratory diaphragm motion up to 5 mm was observed, and the variation in respiratory motion as measured from a series of 4DCBCT scans acquired at each rotation position was small.The principle motion of the rotated subjects was rigid translational motion. The deformation of the anatomy under rotation was found to be similar in scale to normal respiratory motion. This indicates imaging and treatment of rotated subjects with fixed-beam systems can use rigid registration as the primary mode of motion estimation. While the scaling of deformation from rabbits to humans is uncertain, these proof-of-principle results indicate promise for fixed-beam treatment systems.

Observations and modeling of the elastogravity signals preceding direct seismic waves.

After an earthquake, the earliest deformation signals are not expected to be carried by the fastest (P) elastic waves but by the speed-of-light changes of the gravitational field. However, these perturbations are weak and, so far, their detection has not been accurate enough to fully understand their origins and to use them for a highly valuable rapid estimate of the earthquake magnitude. We show that gravity perturbations are particularly well observed with broadband seismometers at distances between 1000 and 2000 kilometers from the source of the 2011, moment magnitude 9.1, Tohoku earthquake. We can accurately model them by a new formalism, taking into account both the gravity changes and the gravity-induced motion. These prompt elastogravity signals open the window for minute time-scale magnitude determination for great earthquakes.

Close-contact melting in a horizontal cylindrical enclosure with longitudinal plate fins: Demonstration, modeling and application to thermal storage

The present study deals with melting in a horizontal double-pipe concentric storage unit with a longitudinally finned inner tube. This geometry, applicable for thermal energy storage, has been extensively studied in the past. However, close-contact melting (CCM), which may significantly increase the melting rate, has not been explored for this sort of systems.In the present experiments, a laboratory-scale three-fin unit is transparent and thus the processes inside it are observed and recorded. Close-contact melting is achieved by supplying heat to the outer shell of the unit: the solid phase is detached from the shell and moves in the liquid phase. In the upper part of the unit, the solid phase translates vertically and melts on the inclined fin surfaces. In the lower parts of the unit, the solid phase approaches the vertical fin by rotation, while its outward surface slides on the shell. It is shown that close-contact melting shortens the melting time by a factor of 2.5 in that specific laboratory-scale device.A novel theoretical model includes gravity-induced rotational motion of the solid, primary melting on a vertical fin with non-uniform temperature distribution, secondary melting at the shell, and frictional resistance at the latter. The model is validated using the experimental results, and then used for a parametric investigation and dimensional analysis. It is revealed that the melt fraction depends on the Fourier and Stefan numbers combined as FoSte3/4, whereas the Nusselt number depends also on an additional group, Ste1/4. Further generalization is achieved when different angles between the fins are considered.The present paper presents a further proof of the special role that close-contact melting (CCM) can play in thermal energy storage units and finned systems in general. It is demonstrated that the fins, when properly designed and oriented, induce CCM in their vicinity, leading to a very significant increase in the melting rate.

Turbulent pair dispersion in the presence of gravity

Turbulent pair dispersion of heavy particles is strongly altered when particles of two different Stokes numbers (bidisperse) are considered, and this is further compounded when a uniform gravitational acceleration is present. Lagrangian trajectories of fluid tracers, and bidisperse heavy particles with and without gravity were calculated from a direct numerical simulation of homogeneous, isotropic turbulence. Particle pair dispersion shows a short-time, ballistic (Batchelor) regime and a transition to super-ballistic dispersion that is suggestive of the emergence of Richardson scaling. A simple equation of motion for inertial, sedimenting particles captures the essential features of the pair dispersion at very short time and length scales. Kolmogorov scaling arguments are able to qualitatively describe the competition between gravity-induced and fluid-induced relative motion in modifying the amount of time the heavy particles spend in the ballistic regime. The transition from ballistic to super-ballistic dispersion for fluid tracers and monodisperse inertial particles exhibits a pronounced sub-ballistic behavior that can be attributed to the mixed velocity–acceleration structure function. The sub-ballistic behavior is strongly suppressed for bidisperse particles, both in the presence or absence of gravity, primarily because of a reduction in the correlation between velocity and acceleration increments.

Assessment of hybrid rotation-translation scan schemes for in vivo animal SPECT imaging

To perform in vivo animal single photon emission computed tomography imaging on a stationary detector gantry, we introduced a hybrid rotation-translation (HRT) tomographic scan, a combination of translational and limited angle rotational movements of the image object, to minimize gravity-induced animal motion. To quantitatively assess the performance of ten HRT scan schemes and the conventional rotation-only scan scheme, two simulated phantoms were first scanned with each scheme to derive the corresponding image resolution (IR) in the image field of view. The IR results of all the scan schemes were visually assessed and compared with corresponding outputs of four scan scheme evaluation indices, i.e. sampling completeness (SC), sensitivity (S), conventional system resolution (SR), and a newly devised directional spatial resolution (DR) that measures the resolution in any specified orientation. A representative HRT scheme was tested with an experimental phantom study. Eight of the ten HRT scan schemes evaluated achieved a superior performance compared to two other HRT schemes and the rotation-only scheme in terms of phantom image resolution. The same eight HRT scan schemes also achieved equivalent or better performance in terms of the four quantitative indices than the conventional rotation-only scheme. As compared to the conventional index SR, the new index DR appears to be a more relevant indicator of system resolution performance. The experimental phantom image obtained from the selected HRT scheme was satisfactory. We conclude that it is feasible to perform in vivo animal imaging with a HRT scan scheme and SC and DR are useful predictors for quantitatively assessing the performance of a scan scheme.

Characterization of the heat transfer accompanying electrowetting or gravity-induced droplet motion

Electrowetting (EW) involves the actuation of liquid droplets using electric fields and has been demonstrated as a powerful tool for initiating and controlling droplet-based microfluidic operations such as droplet transport, generation, splitting, merging and mixing. The heat transfer resulting from EW-induced droplet actuation has, however, remained largely unexplored owing to several challenges underlying even simple thermal analyses and experiments. In the present work, the heat dissipation capacity of actuated droplets is quantified through detailed modeling and experimental efforts. The modeling involves three-dimensional transient numerical simulations of a droplet moving under the action of gravity or EW on a single heated plate and between two parallel plates. Temperature profiles and heat transfer coefficients associated with the droplet motion are determined. The influence of droplet velocity and geometry on the heat transfer coefficients is parametrically analyzed. Convection patterns in the fluid are found to strongly influence thermal transport and the heat dissipation capacity of droplet-based systems. The numerical model is validated against experimental measurements of the heat dissipation capacity of a droplet sliding on an inclined hot surface. Infrared thermography is employed to measure the transient temperature distribution on the surface during droplet motion. The results provide the first in-depth analysis of the heat dissipation capacity of electrowetting-based cooling systems and form the basis for the design of novel microelectronics cooling and other heat transfer applications.

Motion of a sphere down an inclined plane in a viscous flow

The motion of a rigid particle near a wall in a fluid flow is an important element of particle transport by fluids. The aim of this study was to carry out an experimental and theoretical investigation of the gravity-induced motion of a rigid sphere in a viscous fluid in the presence of a transverse flow. The experimental study of this configuration is a way of understanding the specific features of the hydrodynamically constrained particle motion. It is established that the transverse motion of the fluid substantially increases the particle settling velocity, which grows with increase in the transverse flow velocity. This effect is most pronounced for small angles of inclination of the plane. The difference in the particle settling velocities in the presence and absence of the transverse flow could reach a factor of two.

Gravity-induced motion of a uniformly heated solid particle in a gaseous medium

The steady motion of a uniformly heated spherical aerosol particle in a viscous gaseous medium is analyzed in the Stokes approximation under the condition that the mean temperature of the particle surface can be substantially different from the ambient temperature. An analytical expression for the drag force and the velocity of gravity-induced motion of the uniformly heated spherical solid particle is derived with allowance for temperature dependences of the gaseous medium density, viscosity, and thermal conductivity. It is numerically demonstrated that heating of the particle surface has a significant effect on the drag and velocity of gravity-induced motion.

Disturbed State constitutive modeling of two Pleistocene tills

The Disturbed State Concept (DSC) provides a general approach for constitutive modeling of deforming materials. Here, we briefly explain the DSC and present the results of laboratory tests on two regionally significant North American tills, along with the results of a numerical simulation to predict the behavior of one of the tills in an idealized physical system. Laboratory shear tests showed that plastic strain starts almost from the beginning of loading, and that failure and resulting motion begin at a critical disturbance, when about 85% of the mass has reached the fully adjusted or critical state. Specimens of both tills exhibited distributed strain, deforming into barrel shapes without visible shear planes. DSC parameters obtained from shear and creep tests were validated by comparing model predictions against test data used to find the parameters, as well as against data from independent tests. The DSC parameters from one of the tills were applied in a finite-element simulation to predict gravity-induced motion for a 5000-m long, 100-m thick slab of ice coupled to an underlying 1.5-m thick layer of till set on a 4° incline, with pore-water pressure in the till at 90% of the load. The simulation predicted that in the middle segment of the till layer (i.e., from x=2000 to 3000 m) the induced (computed) shear stress, strain, and disturbance increase gradually with the applied shear stress. Induced shear stress peaks at ∼60 kPa. The critical disturbance, at which failure occurs, is observed after the peak shear stress, at an induced shear stress of ∼23 kPa and shear strain of ∼0.75 in the till. Calculated horizontal displacement over the height of the entire till section at the applied shear stress of 65 kPa is ∼4.5 m. We note that the numerical prediction of critical disturbance, when the displacement shows a sharp change in rate, compares very well with the occurrence of critical disturbance observed in the laboratory triaxial tests, when a sharp change in the rate of strain occurs. This implies that the failure and concomitant initiation of motion occur near the residual state, at large strains. In contrast to the Mohr–Coulomb model, which predicts failure and motion at very small (elastic) strain, the DSC thus predicts failure and initiation of motion after the till has undergone considerable (plastic) strain. These results suggest that subglacial till may be able to sustain stress in the vicinity of 20 kPa even after the motion begins. They also demonstrate the potential of the DSC to model not only local behavior, including potential “sticky spot” mechanisms, but also global behavior for soft-bedded ice.

A multipole-accelerated algorithm for close interaction of slightly deformable drops

An efficient multipole-accelerated boundary-integral algorithm is developed to study close-contact, three-dimensional interaction of two drops at zero Reynolds numbers and very small, but non-zero, capillary numbers Ca, when the drops are nearly spherical. The numerical difficulties (compared to the case of larger deformations) include severe stability limitations on the time step and a singular perturbation for Ca ≪ 1, requiring very high surface resolution both in the small gap and in the “outer” region. The mesh triangle vertices are grouped into a large number of non-overlapping “patches,” with economical, rotation-based multipole reexpansions to handle patch-to-patch interactions and limit the use of expensive direct summations. A novel concept of a “dynamical projective mesh” is developed, to maintain fixed-topology, gap-adaptive surface triangulations. For O(10 5) boundary elements per drop in close contact, the algorithm has, at least, an order-of-magnitude advantage over the standard boundary-integral method, making such dynamical calculations feasible. In gravity-induced and shear-induced motion, exact results are obtained for the dynamics of the surface clearance h min (which attains values less than 0.001 of the drop radii) and for the “separation angle” β sep (determining the configuration when two drops in apparent contact start to separate). The shear flow problem is studied in the wide range of drop-to-medium viscosity ratios 0.25 ⩽ λ ⩽ 10. Comparisons are made with prior and extended asymptotic theories of coalescence (based on matching the thin-film solution with the outer solution for spherical drops) to determine their range of validity and assess the “pumping flow” effect neglected in the theories. Pumping flow is most important for small λ and/or nearly head-on collisions; otherwise, the drops move past each other with too little time for the pumping flow to have a strong effect. The asymptotic techniques are extended to λ ≫ 1, and shown to be very accurate for λ = 4 and 10 in the wide range of Ca ≪ 1. Scaling laws for h min and β sep are found, both numerically and analytically; in particular, for λ = O(1), β sep approaches its limiting value π/2 (corresponding to zero “driving force” in the asymptotic theory) extremely slowly, with a difference of O( Ca 1/3), as Ca → 0.

Direct numerical simulations of emulsion flows

In this paper, three-dimensional boundary integral computer simulations of emulsions in shear flows are described. Results for ordered BCC emulsions with dispersed-phase volume fractions below the critical concentration are presented. Complex rheological features including: shear-thinning viscosities, normal stress differences, and a nonlinear frequency response are also explored. For deformable drops, pairwise collision produces net cross-flow displacements that govern self-diffusion of drops. We compute trajectories of two interacting drops in shearing and present interesting numerical simulations of three dimensional gravity-induced motion of two drops. The results also demonstrate the feasibility of simulating high-volume-fraction emulsions and foam.

Sagittal gait of a biped robot during the single support phase. Part 1: passive motion

It has been shown that compass-like bipeds can walk passively by gravity-induced motion. Similarly, it has been stated that the unipodal phase of human gait may be regarded as a passive motion. This paper is aimed at determining precisely to what extent the swing phase of human-like walking can be considered as a non-actuated motion. More specifically, a method is developed that makes it possible to adjust initial conditions, step length and walk speed, as well as mass and inertia distribution of a bipedal robot, in order to generate a passive swing motion. The approach is demonstrated by using a 7-link planar biped. Numerical simulations show that purely passive unipodal transferring cannot be fully satisfactory. This approach is further considered in Part 2 of the paper which consists in computing optimal actuating joint torques to create perfectly feasible motions.

A novel boundary-integral algorithm for viscous interaction of deformable drops

A new three-dimensional boundary-integral algorithm for deformable drops moving in a viscous medium at low Reynolds numbers is developed, which overcomes some familiar difficulties with boundary-integral calculations. The algorithm is used to simulate different modes of interaction between drops or bubbles, primarily for buoyancy-driven motion. The present iterative method for mean curvature calculation is found to be more robust and accurate than contour integration schemes. A novel iterative strategy based on combining biconjugate gradient and simple iterations overcomes the poor convergence of “successive substitutions” for drops in very close approach with extreme viscosity ratio. A substantially new variational method of global mesh stabilization solves the problem of mesh degradation with advantageous, soft stability constraints. A curvatureless boundary-integral formulation is also derived and shown to provide, in principle, a more accurate description of the drop breakup than the conventional formulation. The efficiency of these techniques is demonstrated by numerical examples for two drops in gravity-induced motion with high surface resolutions. The present code successfully simulates mutual approach of slightly deformable drops to extremely small separations, as well as their rotation when in “apparent contact,” thus bridging the gap between finite deformation calculations and a recent asymptotic theory for small capillary numbers. Also provided is a 3D simulation of the experimental phenomenon of enhanced bubble coalescence, discovered by Manga and Stone [J. Fluid Mech. 256, 647 (1993); 300, 231 (1995)]. For drops of viscosity comparable to that of the surrounding fluid, it is shown in contrast that breakup is a typical result of hydrodynamic interaction in gravity-induced motion for large and even moderate capillary numbers. The code is readily applicable to any type of an ambient flow and may be adapted to more than two drops.

Motion of a spherical heat source in a melting medium

The gravity-induced steady motion of a heat source boring through a solid medium is investigated. It is shown that the temperature of its surface is substantially nonuniform. Expressions are obtained for the maximum values of the radius and velocity of the source at which this temperature attains the assigned maximum allowable value.

Experimental study of two interacting drops in an immiscible fluid

Experiments were performed in order to elucidate the effects of hydrodynamic interactions between two drops on their gravity-induced relative motion. The relative trajectories of two drops, their relative velocities, and the travel time for them to flow around each other were measured for different initial horizontal separations. Two size ratios and two viscosity ratios were investigated. Hydrodynamic interactions significantly reduce the relative velocity of two nearby drops and cause them to flow around each other with curved trajectories, resulting in a longer duration of the close encounter, compared with that for two non-interacting drops. These effects increase with decreasing drop separation, decreasing size ratio, and increasing viscosity ratio. Experimental results are in good agreement with theoretical predictions, except when the drops become sufficiently close that interface deformation occurs.

A reappraisal of ignimbrite emplacement: progressive aggradation and changes from particulate to non-particulate flow during emplacement of high-grade ignimbrite

We propose a mechanism by which massive ignimbrite and layered ignimbrite sequences — the latter liable to have been previously interpreted as multiple flow units-form by progressive aggradation during sustained passage of a single particulate flow. In the case of high-temperature eruptive products the mechanism simplifies interpretation of problematic deposits that exhibit pronounced vertical and lateral variations in texture, including between non-welded, eutaxitic, rheomorphic (lineated) and lava-like. Agglutination can occur within the basal part of a hot density-stratified flow. During initial incursion of the flow, agglutinate chills and freezes against the ground. During sustained passage of the flow, agglutination continues so that the non-particulate (agglutinate) layer thickens (aggrades) and becomes mobile, susceptible to both gravity-induced motion and traction-shear imparted by the overriding particulate part of the flow. The particulate to non-particulate (P-NP) transition occurs in and just beneath a depositional boundary layer, where disruptive collisions of hot viscous droplets give way, via sticky grain interactions, to fluidal behavior following adhesion. Because they have different rheologies, the particulate and non-particulate flow components travel at different velocities and respond to topography in different ways. This may cause detachment and formation of two independent flows. The P-NP transition is controlled by factors that influence the rheological properties of individual erupted particles (strain rate, temperature, and composition including volatiles), by cooling and volatile exsolution during transport, and by the particle-size population and concentration characteristics of the depositional boundary layer. At any one location along the flow path one or more of these can change through time (unsteady flow). Thus the P-NP transition can develop momentarily or repeatedly during the passage of an unsteady flow, or it can occur continuously during the passage of a quasi-steady flow supplied by a sustained explosive eruption. Vertical facies successions developed in the deposit (high-grade ignimbrite) reflect temporal changes in flow steadiness and in material supplied at source. The P-NP transition is also influenced by factors that affect flow behaviour, such as topography. It may occur at any location laterally between a proximal site of deflation (e.g. a fountain-fed lava) and a flow's distal limit, but it most commonly occurs throughout a considerable length of the flow path. Up-sequence variations in welding-deformation fabric (between oblate uniaxial to triaxial and prolate) reflect evolving characteristics of the depositional boundary layer (e.g. fluctuations from direct suspension-sedimentation to deposition via traction carpets or traction plugs), as well as possible modifications resulting from subsequent, post-depositional hot loading and slumping. Similar processes can also account for lateral lithofacies gradations in conduits and vents filled with welded tuff. Our consideration of high-grade ignimbrites has implications for ignimbrite emplacement in general, and draws attention to the limitations of the widely accepted models of emplacement involving mainly high-concentration non-turbulent transport and en masse ‘freezing’ of high-yield-strength plug flows.

The rate of coagulation of particles in a sedimenting dispersion at large Péclet number

The coagulation rate of a dilute polydisperse suspension of small particles is considered for large Péclet number, P ij , which provides a measure of the ratio of the relative gravity-induced motion to Brownian motion between two rigid spheres. In particular, a two-term expansion for the dimensionless coagulation rate (capture efficiency) as function of inverse Péclet number has been developed by using a regular perturbation method. It is found that Brownian diffusion can act to decrease the coagulation rate. Therefore, the additivity assumption is not valid in this regime.