Traditional Particle Tracking Research Articles

Comparison of automated and manual intracellular particle tracking using quantitative phase imaging

Transport within cells is commonly studied using particle tracking methods. However, these typically require either labeling or identification of specific organelles that can be identified and tracked from label-free imaging modalities, limiting application of this approach. Quantitative phase imaging (QPI) provides dynamic data on the redistribution of mass within live cells, potentially enabling broader application of particle tracking methods. In previous work, we developed quantitative phase velocimetry (QPV) to automatically track the motion of subcellular control volumes from QPI data. However, the relationship of QPV to traditional particle tracking methods has not been established. Here, we directly compare QPV to manual particle tracking across multiple drug treatment conditions. We find that QPV effective diffusivity is correlated with diffusivity measured from manual particle tracking. The differences between QPV and manual tracking are explained by the difference in effective size of particles tracked by QPV. Overall, these data indicate that automated tracking of the motion of cellular mass from QPI data can effectively be used to characterize effective diffusivity within living cells.

Cell encapsulation in gelatin methacryloyl bioinks impairs microscale diffusion properties.

Light-assisted bioprinted gelatin methacryloyl (GelMA) constructs have been used for cell-laden microtissues and organoids. GelMA can be loaded by desired cells, which can regulate the biophysical properties of bioprinted constructs. We study how the degree of methacrylation (MA degree), GelMA mass concentration, and cell density change mass transport properties. We introduce a fluorescent-microscopy-based method of biotransport testing with improved sensitivity compared to the traditional particle tracking methods. The diffusion capacity of GelMA with a higher MA significantly decreased compared to a lower MA. Opposed to a steady range of linear elastic moduli, the diffusion coefficient in GelMA varied when cell densities ranged from 0 to 10 × 106 cells/ml. A comparative study of different cell sizes showed a higher diffusivity coefficient for the case of larger cells. The results of this study can help bioengineers and scientists to better control the biotransport characteristics in light-assisted bioprinted microtissues and organoids.

Plate reader microrheology

In this work, we report the development of a simplified method to perform microrheology to rapidly assess soft materials. This approach uses fluorescence polarization and a plate reader format to measure the rotational diffusion of nanoparticles within a sample of interest. We have established that this technique can be used to characterize a range of soft materials based on the rotational diffusion of nanoparticles in materials with viscosities exceeding 100 cP. Using these fluorescence polarization-based measurements, we describe formalism that enables the estimation of viscosity in polymer solutions and gels composed of polyethylene glycol, hyaluronic acid, and Matrigel after accounting for the length-scale dependent effects of the polymer environment on the nanoparticle rotational diffusion. Using this analysis, we show that the plate reader microrheology measurements of viscosity are in reasonable agreement with traditional particle tracking microrheology. The use of a plate reader format allows this approach to be higher throughput, less technically challenging, and more widely accessible than standard macro- and micro-rheological methods, making it available to non-experts. This approach has potential applications in clinical settings where conventional rheological equipment may not be available to rapidly characterize patient-derived samples.

Solving Time-Fractional Advection–Dispersion Equation by Variable Weights Particle Tracking Method

Particle tracking method is an efficient and reliable method to solve time-fractional advection-dispersion equation, which can describe anomalous transport in heterogeneous porous media. However, this method will lead to severe fluctuation or disappearance of solutions if the concentration value is small. A variable weights method is developed to conquer the shortcoming of particle tracking method. Then, one-dimensional and two-dimensional time-fractional advection-dispersion equations are solved by the variable weights particle tracking method. Compared to traditional particle tracking method, the variable weights version may eliminate the fluctuation and improve the accuracy by orders of magnitude without more computational cost.

Principal-component analysis of particle motion.

We demonstrate the application of principal-component analysis (PCA) to the analysis of particle motion data in the form of a time series of images. PCA has the ability to resolve and isolate spatiotemporal patterns in the data. Using simulated data, we show that this translates into the ability to separate individual frequency components of the particle motion. We also show that PCA can be used to extract the fluid viscosity from images of particles undergoing Brownian motion. PCA thus provides an efficient alternative to more traditional particle-tracking methods for the analysis of microrheological data.

Frame rate free image velocimetry for microfluidic devices

Here, we introduce Streamline Image Velocimetry, a method to derive fluid velocity fields in fully developed laminar flow from long-exposure images of streamlines. Streamlines confine streamtubes, in which the volumetric flow is constant for incompressible fluid. Using an explicit analytical solution as a boundary condition, velocity fields and emerging properties such as shear force and pressure can be quantified throughout. Numerical and experimental validations show a high correlation between anticipated and measured results, with R2 > 0.91. We report spatial resolution of 2 μm in a flow rate of 0.15 m/s, resolution that can only be achieved with 75 kHz frame rate in traditional particle tracking velocimetry.

Quasi-equilibrium electron density along a magnetic field line

A methodology is developed to determine the density of high-energy electrons along a magnetic field line for a low-β plasma. This method avoids the expense and statistical noise of traditional particle tracking techniques commonly used for high-energy electrons in bombardment plasma generators. By preserving the magnetic mirror and assuming a mixing timescale, typically the elastic collision frequency with neutrals, a quasi-equilibrium electron distribution can be calculated. Following the transient decay, the analysis shows that both the normalized density and the reduction fraction due to collision converge to a single quasi-equilibrium solution.

A coupled finite element–global random walk approach to advection-dominated transport in porous media with random hydraulic conductivity

Solute transport through heterogeneous porous media considered in environmental and industrial problems is often characterized by high Péclet numbers. In this paper we develop a new numerical approach to advection-dominated transport consisting of coupling an accurate mass-conservative mixed finite element method (MFEM), used to solve Darcy flows, with a particle method, stable and free of numerical diffusion, for non-reactive transport simulations. The latter is the efficient global random walk (GRW) algorithm, which performs the simultaneous tracking of arbitrarily large collections of particles on regular lattices at computational costs comparable to those of single-trajectory simulations using traditional particle tracking (PT). MFEM saturated flow solutions are computed for spatially heterogeneous hydraulic conductivities parameterized as samples of random fields. The coupling is achieved by projecting the velocity field from the MFEM basis onto the regular GRW lattice. Preliminary results show that MFEM–GRW is tens of times faster than the full MFEM flow and transport simulation.

Development of FBMINC model for particle diffusion in fluids

Abstract An accurate particle tracking method using FBMINC (new fractional Brownian motion) is outlined. It generates non-Fickian diffusion rather than Fickian diffusion as traditional particle tracking model does. The FBMINC model is based on fractional Brownian motion (fBm) which is generalization of regular Brownian motion. The two models of fBms (FBM model and FBMINC model) were explored and the differences of the two models are compared from the three aspects: the standard deviation of each step, the small memory and the effect of the number of particles in the cloud. The results show the FBMINC model is a better model as it produces more accurate statistics. The effect of simple shear dispersion for both Brownian and fBm was investigated. The power law scaling of fBm shear dispersion was correctly identified. In addition, a scaling coefficient was found numerically. The FBMINC model is then used for producing both superdiffusive and subdiffusive particle paths, therefore, the non-Fickian diffusion of soil particle clouds can be modelled. The particle clouds represent soil contaminant are released in an idealised coastal bay and the fBm particle tracking method is used for simulation the particle cloud spreading in the bay. There is a noticeable increase in the spreading rate of the cloud. In addition, owning to the spreading rate of the cloud, a noticeable part of it has escaped the bay area and transported downstream. The variation of the Hurst exponent can lead to an area of the flow being affected by a contaminant cloud which is not picked up by the regular Brownian motion models. The purpose of this paper is to bring soil transport engineers a new angle on soil particle transport research in fluids. Using FBMINC particle tracking model allows more flexibility in simulation of diffusion in soil contaminant spread in coastal bay or ocean surface.

Transport of Finite-Sized Particles in Chaotic Flow

By extending traditional particle tracking techniques, we study the dynamics of neutrally buoyant finite-sized particles in a spatiotemporally chaotic flow. We simultaneously measure the flow field and the trajectories of millimeter-scale particles so that the two can be directly compared. While the single-point statistics of the particles are indistinguishable from the flow statistics, the particles often move in directions that are systematically different from the underlying flow. These differences are especially evident when Lagrangian statistics are considered.

Three-dimensional particle tracking using micro-particle image velocimetry hardware

A method for tracking the three-dimensional position and computing the three velocity components of a micro-particle using information encoded in the ring structure of the particle image is introduced. The proposed technique can be employed in most existing micro-particle image velocimetry systems without any additional hardware and details of the optical train are not required. The technique utilizes a set of calibration images of a particle at various known distances from the focal plane (in the out-of-plane direction) in order to create a calibration curve. The calibration curve, which relates the radius of the outermost ring to the distance of the particle from focus is used to deduce the out-of-plane location of particles in experimental images. From successive images the particle's velocity is computed. The in-plane particle velocity is deduced from traditional particle tracking methods.

A Numerical Study of the Influence of Particle Density on Lift Force-Induced Separation in a Micro-Separator/Classifier by a Macroscopic Particle Model

A Macroscopic Particle Model (MPM), which can be regarded as a quasi direct numerical simulation and hence does not need any drag and lift force models, is applied to examine the effect of particle density on lift force-induced separation in a micro-separator/classifier. The computational domain is a 30-degrees arc channel with a radius of 20 mm connecting to 5-mm straight channels at the both ends. In this study the modeled is an upper-half of the channel with a width of 200 μm and a depth of 75 μm. The particle diameter was chosen to be 20 μm, which is well separable in experiments and is suitable for MPM in which a particle should contain several fluid cells. The density was examined in the range of slightly lighter to denser, compared with water. The particle trajectories from representative points are predicted by MPM and also by a traditional particle tracking method (DPM) for comparison. The DPM without a lift force model predicted that the trajectories expanded over the cross-sectional plane with an increase of particle density since a secondary flow pattern called Dean vortices caused strong centrifugal force acting outwards from its center. On the other hand, the trajectories predicted by MPM were almost confined in the outer-half of the plane due to the lift force acting inwards to the vortex center. It seems that encountering lift force due to a steep shear and centrifugal force due to the Dean vortices are balanced regardless of the particle density since both forces likely increase with particle inertia. It is notable that particles can be hydraulically separable regardless of the density ranging slightly lighter to denser compared to the medium.

Coastal Dispersion Modelling Using an Accelerated fBm Particle Tracking Method

The most popular coastal diffusion modelling technique is the traditional particle tracking method which can only model Fickian diffusion. However, in reality, non-Fickian diffusion dispersion in coastal surface waters has been observed by some researchers. A new Particle Tracking technique is introduced in this article that generates non-Fickian diffusion by employing fractional Brownian motion (fBm). The authors found that for coastal surface waters, the Hurst exponent H is not restricted to the range 0 ∼ 1. A newly developed Particle Tracking method that generates non-Fickian diffusion by employing accelerated fractional Brownian motion (AfBm) has been first studied and introduced. Numerical techniques to model the non-Fickian spreading observed in the real coastal data have been successfully developed and the simulation results are encouraging when compared with the observed data and the results of conventional dispersion modelling.

A forward particle tracking Eulerian–Lagrangian Localized Adjoint Method for solution of the contaminant transport equation in three dimensions

The contaminant transport equation is solved in three dimensions using the Eulerian–Lagrangian Localized Adjoint Method (ELLAM). Trilinear and finite volume test functions defined by the characteristics of the governing equation are employed and compared. Integrations are simplified by forward tracking of integration points along the characteristics. The resulting equations are solved using a preconditioned conjugate gradient method. The algorithm is coupled to a block-centered finite difference approximation of the groundwater flow equation similar to that used in the popular MODFLOW code. The ELLAM is tested by comparison with 1D and 3D analytic solutions. The method is then applied with random, spatially correlated hydraulic conductivities in a simulation of a tracer experiment performed on Cape Cod, Massachusetts. The linear test function ELLAM was found to perform better than the finite volume ELLAM. Both ELLAM formulations were found to be robust, computationally efficient and relatively straightforward to implement. When compared to traditional particle tracking and characteristics codes commonly used with MODFLOW, the ELLAM retains the computational advantages of traditional characteristic methods with the added advantage of good mass conservation.

An efficient particle tracking equation with specified spatial step for the solution of the diffusion equation

The traditional diffusive particle tracking equation provides an updated particle location as a function of its previous location and molecular diffusion coefficient while maintaining a constant time step. A smaller time step yields an increasingly accurate, yet more computationally demanding solution. Selection of this time step becomes an important consideration and, depending on the complexity of the problem, a single optimum value may not exist. The characteristics of the system under consideration may be such that a constant time step may yield solutions with insufficient accuracy in some portions of the domain and excess computation time for others. In this work, new particle tracking equations specifically designed for the solution of problems associated with diffusion processes in one, two, and three dimensions are presented. Instead of a constant time step, the proposed equations employ a constant spatial step. Using a traditional particle tracking algorithm, the travel time necessary for a particle with a diffusion coefficient inversely proportional to its diameter to achieve a pre-specified distance was determined. Because the size of a particle affects how it diffuses in a quiescent fluid, it is expected that two differently sized particles would require different travel times to move a given distance. The probability densities of travel times for plumes of monodisperse particles were consistently found to be log-normal in shape. The parameters describing this log-normal distribution, i.e., mean and standard deviation, are functions of the distance specified for travel and the diffusion coefficient of the particles. Thus, a random number selected from this distribution approximates the time required for a given particle to travel a specified distance. The new equations are straightforward and may be easily incorporated into appropriate particle tracking algorithms. In addition, the new particle tracking equations are as accurate and often more computationally efficient than the traditional particle tracking equation.

Continuous groundwater velocity fields and path lines in linear, bilinear, and trilinear finite elements

Darcy velocity fields obtained from finite element solutions of heads in groundwater flow exhibit discontinuities at element boundaries, thus giving rise to inaccuracies in path line construction. Several methods have been developed to resolve those inaccuracies including global postprocessing of velocity fields, mixed hybrid finite element formulations, and stream function formulations. All of these techniques either lead to a considerable increase in the computational effort or are not general enough for all purposes. The point of view taken here is that standard finite element flow models yield exact water balances, which in the usual approach to path line computation are not fully used. By starting out from patches with flux‐conserving boundaries, a new postprocessing procedure is derived that allows construction of a continuous flux distribution over the whole model domain. In this procedure only the head gradients of adjacent elements are used, thus avoiding the solution of another global system of equations. Furthermore, application of a stream function interpolation inside each patch allows the fast computation of path lines without any time stepping. The path lines computed with the proposed procedure are compared to path lines computed by usual particle tracking and examples are presented showing that the new method is vastly superior to traditional particle tracking.