Computational predictions of the embolus-trapping performance of an IVC filter in patient-specific and idealized IVC geometries

Embolus transport simulations are performed to investigate the dependence of inferior vena cava (IVC) filter embolus-trapping performance on IVC anatomy. Simulations are performed using a resolved two-way coupled computational fluid dynamics/six-degree-of-freedom approach. Three IVC geometries are studied: a straight-tube IVC, a patient-averaged IVC, and a patient-specific IVC reconstructed from medical imaging data. Additionally, two sizes of spherical emboli (3 and 5 mm in diameter) and two IVC orientations (supine and upright) are considered. The embolus-trapping efficiency of the IVC filter is quantified for each combination of IVC geometry, embolus size, and IVC orientation by performing 2560 individual simulations. The predicted embolus-trapping efficiencies of the IVC filter range from 10 to 100%, and IVC anatomy is found to have a significant influence on the efficiency results (\(P < 0.0001\)). In the upright IVC orientation, greater secondary flow in the patient-specific IVC geometry decreases the filter embolus-trapping efficiency by 22–30 percentage points compared with the efficiencies predicted in the idealized straight-tube or patient-averaged IVCs. In a supine orientation, the embolus-trapping efficiency of the filter in the idealized IVCs decreases by 21–90 percentage points compared with the upright orientation. In contrast, the embolus-trapping efficiency is insensitive to IVC orientation in the patient-specific IVC. In summary, simulations predict that anatomical features of the IVC that are often neglected in the idealized models used for benchtop testing, such as iliac vein compression and anteroposterior curvature, generate secondary flow and mixing in the IVC and influence the embolus-trapping efficiency of IVC filters. Accordingly, inter-subject variability studies and additional embolus transport investigations that consider patient-specific IVC anatomy are recommended for future work.     

Recurrent fracture of a recovery inferior vena cava filter with pulmonary migration

Inferior vena cava (IVC) filters are indicated in patients with venous thromboembolic disease in whom standard anticoagulation therapy is contraindicated or ineffective. A 32-year-old female presented to our hospital with chest pain 5 years after IVC filter placement. Imaging revealed sequential fracturing and embolization of two of the IVC filter arms to the pulmonary arteries. IVC filter fracture and subsequent migration to the lung is a rare complication. Systematic long-term follow-up in patients with IVC filters and, if possible, filter removal should be considered to prevent possible complications.     

Numerical analysis of the hemodynamics and embolus capture of a greenfield vena cava filter

BACKGROUND: Vena Cava filters are used to prevent pulmonary embolism in patients with deep vein thrombosis who are unresponsive to anticoagulation therapy. Various filter designs exist in the market with different characteristics distinguishing them. An understanding of the characteristics of these filters is desirable in order to develop better designs. METHODS: A computational fluid dynamical study of the flow over an unoccluded stainless steel Greenfield Vena Cava filter (Boston Scientific, Watertown, MA) to determine its properties has been performed. Simulation of flow over a filter placed axisymmetrically in a rounded inferior vena cava has been performed at a Reynolds numbers of 1000 and the consequences of the flow (by studying parameters like shear stress and stagnation zones) have been discussed. Furthermore, a new finite element based numerical method has been developed that allows the study of capturing properties of Inferior Vena Cava filters. The key idea is the introduction of a thin-wire-model (TWM) that enables a drastic reduction in the computational cost while still maintaining control on the physics of the problem. This numerical technique has been applied to evaluate the embolus capture characteristic of a Greenfield filter. RESULTS: The flow around the unoccluded filter is found to be steady and laminar at the conditions studied. A recirculation/stagnation zone develops immediately downstream of the filter head. This zone is significantly larger when the central hole is occluded. The shear stress and stagnation zone properties for such a flow over a Greenfield filter are compared with existing literature (in vitro studies). A graph showing the regions wherein clots escape or get captured has been determined by a means of numerical simulations. The data has further been analyzed to determine the probability of clot capture as function of the clot size. CONCLUSIONS: The stagnation zone formed behind the head of the Greenfield filter is found to be smaller in size when compared to that of the same filter with the central hole occluded. A map of the shear stress distribution shows a small region having the potential for thrombogenesis. The non-Newtonian properties of blood are not seen to cause much variation in the flow field when compared to the Newtonian model. However variation in the cava size leads to a significant change in the shear stresses. This study also establishes a novel method wherein computational means are used to determine the efficacy of clot capturing of filters. These techniques can further be used to compare the different characteristics among filters.     

Analysis of mechanical parameters on the thromboembolism using a patient-specific computational model

Ischemic stroke is a major cause of death and long-term disabilities worldwide. In this paper, we aim to represent a comprehensive simulation of the motion of emboli through cerebrovascular network within patient-specific computational model. The model consists of major arteries of the circle of Willis reconstructed from magnetic resonance angiography images, pulsatile flow and emboli with different sizes and material properties. Here, the fluid–structure interactions method was used to simulate the motion of deformable and rigid emboli through cerebral arteries. Hemodynamic changes in the circle of Willis due to the entrance of embolus are observed. The effect of material properties on the distribution ratio and dynamics of motion of the emboli in the cerebral arterial network is also analyzed. Our results reveal that as the rigidity of emboli increases, higher proportion of them tend to enter to the larger arteries (e.g., middle cerebral artery). Scrutinizing the amount of stress acting on the emboli represented in this paper can broaden our understanding of the rheological phenomenon (e.g., lysis or growth of emboli during embolism). The approach of considering different material properties of the thrombus in a patient-specific computational model not only enable us to better understand the roll of biomechanical parameters causing the embolism, but also lead to a better clinical decision making to manage patients with stroke.     

A mathematical model for the leukocyte filtration process

Leukocyte filters are applied clinically to remove leukocytes from blood. In order to optimize leukocyte filters, a mathematical model to describe the leukocyte filtration process was developed by modification of a general theoretical model for depth filtration. The model presented here can be used to predict the time-dependent leukocyte filtration as a function of cell-cell interaction in the filter, filter efficiency, filter capacity, filter dimensions, and leukocyte concentration in the suspension applied to the filter. The results of different leukocyte filtration experiments previously reported in the literature could be well described by the present model. (c) 1995 John Wiley & Sons, Inc.     

Verification, validation and sensitivity studies in computational biomechanics

Computational techniques and software for the analysis of problems in mechanics have naturally moved from their origins in the traditional engineering disciplines to the study of cell, tissue and organ biomechanics. Increasingly complex models have been developed to describe and predict the mechanical behavior of such biological systems. While the availability of advanced computational tools has led to exciting research advances in the field, the utility of these models is often the subject of criticism due to inadequate model verification and validation (V&V). The objective of this review is to present the concepts of verification, validation and sensitivity studies with regard to the construction, analysis and interpretation of models in computational biomechanics. Specific examples from the field are discussed. It is hoped that this review will serve as a guide to the use of V&V principles in the field of computational biomechanics, thereby improving the peer acceptance of studies that use computational modeling techniques.     

Utility of Epinephrine Levels in Determining Adrenal Vein Cannulation During Adrenal Venous Sampling for Primary Aldosteronism

ObjectiveIn patients with primary aldosteronism, adrenal venous sampling (AVS) is performed to determine the presence of unilateral or bilateral adrenal disease. During AVS, verification of catheter positioning within the left adrenal vein (AV) and the right AV by comparison of AV and inferior vena cava (IVC) cortisol levels can be variable. The objective of this study was to determine the utility of AV epinephrine levels in assessing successful AV cannulation.MethodsThis was a single institution, retrospective review of patients who underwent AVS with cosyntropin stimulation for primary aldosteronism between 2009 and 2018. Successful cannulation of the AV was defined by an AV/IVC cortisol ratio selectivity index (SI) ≥3:1. Epinephrine thresholds to predict catheter placement in the AV were determined using logistic regression. The calculated epinephrine thresholds were compared with previously published thresholds.ResultsAVS was performed on 101 consecutive patients and, based on the SI, successful cannulation of the left AV and right AV occurred in 98 (97%) and 91(90%) patients, respectively. The calculated optimal epinephrine threshold to predict AV cannulation was 364 pg/mL (sensitivity, 92.1%; specificity, 94.6%) and the calculated optimal AV/IVC epinephrine ratio threshold was 27.4, (sensitivity, 92.1%; specificity, 91.3%). Among the 14 patients with failed AV cannulation, 3 patients would have been considered to have successful AVS using AV epinephrine levels >364 pg/mL and AV/IVC epinephrine ratio >27.4 thresholds.ConclusionObtaining 2 right AV samples routinely as well as AV and IVC epinephrine levels during AVS could prevent unnecessary repeat AVS in patients with failed AV cannulation based on cortisol-based SI <3:1.     

Experimental verification of a computational technique for determining ground reactions in human bipedal stance

We have developed a three-dimensional (3D) biomechanical model of human standing that enables us to study the mechanisms of posture and balance simultaneously in various directions in space. Since the two feet are on the ground, the system defines a kinematically closed-chain which has redundancy problems that cannot be resolved using the laws of mechanics alone. We have developed a computational (optimization) technique that avoids the problems with the closed-chain formulation thus giving users of such models the ability to make predictions of joint moments, and potentially, muscle activations using more sophisticated musculoskeletal models. This paper describes the experimental verification of the computational technique that is used to estimate the ground reaction vector acting on an unconstrained foot while the other foot is attached to the ground, thus allowing human bipedal standing to be analyzed as an open-chain system. The computational approach was verified in terms of its ability to predict lower extremity joint moments derived from inverse dynamic simulations performed on data acquired from four able-bodied volunteers standing in various postures on force platforms. Sensitivity analyses performed with model simulations indicated which ground reaction force (GRF) and center of pressure (COP) components were most critical for providing better estimates of the joint moments. Overall, the joint moments predicted by the optimization approach are strongly correlated with the joint moments computed using the experimentally measured GRF and COP (0.78 < or = r(2) < or = 0.99,median,0.96) with a best-fit that was not statistically different from a straight line with unity slope (experimental=computational results) for postures of the four subjects examined. These results indicate that this model-based technique can be relied upon to predict reasonable and consistent estimates of the joint moments using the predicted GRF and COP for most standing postures.     

MMPI Drug-Eluting IVC Filter Decreases Adhesion Between Caval Wall and Filter

The implantation of inferior vena cava (IVC) filter was a safe and effective therapy for preventing fatal pulmonary embolism. However, there are risks associated with long-term implantation of filters. Retrievable filters are designed to be removed, but may also remain permanently. Retrieval can reduce risk of long-term complications. The difficulty or impossibility of retrieval is still an issue of retrieval filter. The major causes of filters retrieval failure were intimal overgrowth and severely tilted filter with apex embedded into the caval wall. Matrix metalloproteinases (MMPs) play a key role in neointimal hyperplasia. It is documented that neointimal hyperplasia can be reduced by inhibiting MMP activity and hence smooth muscle cell migration. MMP inhibitors (MMPI) can potently inhibit the activity of MMPs. We hypothesize that a drug-eluting filter which contains MMPI may inhibit IVC neointimal hyperplasia and decrease the adhesion between vascular wall and filter struts. After implantation of drug-eluting retrieval filter, MMPI is released slowly at the sites where the filter struts are in contact with the caval wall; the activity of MMPs of caval wall will be inhibited, injury in basement membrane is decreased, migration of SMC maybe reduced, and the release of extracellular matrix maybe lessened. Finally, neointimal hyperplasia maybe inhibited, the adhesion between vascular wall and filter maybe weakened, the success rate maybe increased, and the vascular injury during retrieval maybe reduced. The hypothesis might improve the long-term prognosis of venous thromboembolism patients.     

The effect of filtration method on the efficiency of environmental DNA capture and quantification via metabarcoding

Environmental DNA (eDNA) is a promising tool for rapid and noninvasive biodiversity monitoring. eDNA density is low in environmental samples, and a capture method, such as filtration, is often required to concentrate eDNA for downstream analyses. In this study, six treatments, with differing filter types and pore sizes for eDNA capture, were compared for their efficiency and accuracy to assess fish community structure with known fish abundance and biomass via eDNA metabarcoding. Our results showed that different filters (with the exception of 20‐μm large‐pore filters) were broadly consistent in their DNA capture ability. The 0.45‐μm filters performed the best in terms of total DNA yield, probability of species detection, repeatability within pond and consistency between ponds. However performance of 0.45‐μm filters was only marginally better than for 0.8‐μm filters, while filtration time was significantly longer. Given this trade‐off, the 0.8‐μm filter is the optimal pore size of membrane filter for turbid, eutrophic and high fish density ponds analysed here. The 0.45‐μm Sterivex enclosed filters performed reasonably well and are suitable in situations where on‐site filtration is required. Finally, prefilters are applied only if absolutely essential for reducing the filtration time or increasing the throughput volume of the capture filters. In summary, we found encouraging similarity in the results obtained from different filtration methods, but the optimal pore size of filter or filter type might strongly depend on the water type under study.     

Iterative species distribution modelling and ground validation in endemism research: an Alpine jumping bristletail example

Endemic species play an important role in conservation ecology. However, knowledge of the real distribution and ecology is still scarce for many endemics. The aims of this study were to predict the distribution of the short-range endemic Alpine jumping bristletail Machilis pallida; to evaluate the actual level of endemism via ground validation using an iterative approach for testing the models in field trips and increasing the quality of the prediction step by step; and to test the potential of species distribution modelling for increasing the knowledge about the ecological niche. Based on seven known locations of M. pallida, we used species distribution modelling via Maxent. After a set of seven field trips a new model was built if new locations were found. Three such iterations were performed to increase model quality. We discovered four new locations of M. pallida, increasing the area of known distribution from 470 to 4,890?km². The distribution of M. pallida is thus wider than formerly known, but our results support Eastern Alpine endemism of the species. The knowledge about the ecological niche could be increased due to the newly found locations. Our study showcases the potential of the iterative approach of modelling and ground validation to evaluate the actual level of endemism and the ecological niche in Alpine species and beyond.     

Survival of microorganisms on antimicrobial filters and the removal efficiency of bioaerosols in an environmental chamber

Exposure to bioaerosols causes various adverse health effects including infectious and respiratory diseases, and hypersensitivity. Controlling exposure to bioaerosols is important for disease control and prevention. In this study, we evaluated the efficacies of various functional filters coated with antimicrobial chemicals in deactivating representative microorganisms on filters or as bioaerosols. Tested functional filters were coated with different chemicals that included (i) Ginkgo and sumac, (ii) Ag-apatite and guanidine phosphate, (iii) SiO2, ZnO, and Al2O3, and (iv) zeolite. To evaluate the filters, we used a model ventilation system (1) to evaluate the removal efficiency of bacteria (Escherichia coli and Legionella pneumophila), bacterial spores (Bacillus subtilis spore), and viruses (MS2 bacteriophage) on various functional filters, and (2) to characterize the removal efficiency of these bioaerosols. All experiments were performed at a constant temperature of 25 degrees C and humidity of 50%. Most bacteria (excluding B. subtilis) rapidly decreased on the functional filter. Therefore, we confirmed that functional filters have antimicrobial effects. Additionally, we evaluated the removal efficiency of various bioaerosols by these filters. We used a six-jet collision nebulizer to generate microbial aerosols and introduced it into the environmental chamber. We then measured the removal efficiency of functional filters with and without a medium-efficiency filter. Most bioaerosol concentrations did not significantly decrease by the functional filter only but decreased by a combination of functional and medium-efficiency filter. In conclusion, functional filters could facilitate biological removal of various bioaerosols, but physical removal of these by functional was minimal. Proper use of chemical-coated filter materials could reduce exposure to these agents.     

Improving the iterative Linear Interaction Energy approach using automated recognition of configurational transitions

Recently an iterative method was proposed to enhance the accuracy and efficiency of ligand-protein binding affinity prediction through linear interaction energy (LIE) theory. For ligand binding to flexible Cytochrome P450s (CYPs), this method was shown to decrease the root-mean-square error and standard deviation of error prediction by combining interaction energies of simulations starting from different conformations. Thereby, different parts of protein-ligand conformational space are sampled in parallel simulations. The iterative LIE framework relies on the assumption that separate simulations explore different local parts of phase space, and do not show transitions to other parts of configurational space that are already covered in parallel simulations. In this work, a method is proposed to (automatically) detect such transitions during the simulations that are performed to construct LIE models and to predict binding affinities. Using noise-canceling techniques and splines to fit time series of the raw data for the interaction energies, transitions during simulation between different parts of phase space are identified. Boolean selection criteria are then applied to determine which parts of the interaction energy trajectories are to be used as input for the LIE calculations. Here we show that this filtering approach benefits the predictive quality of our previous CYP 2D6-aryloxypropanolamine LIE model. In addition, an analysis is performed of the gain in computational efficiency that can be obtained from monitoring simulations using the proposed filtering method and by prematurely terminating simulations accordingly.     

Validation of CFD predictions of flow in a 3D alveolated bend with experimental data

Verifying numerical predictions with experimental data is an important aspect of any modeling studies. In the case of the lung, the absence of direct in vivo flow measurements makes such verification almost impossible. We performed computational fluid dynamics (CFD) simulations in a 3D scaled-up model of an alveolated bend with rigid walls that incorporated essential geometrical characteristics of human alveolar structures and compared numerical predictions with experimental flow measurements made in the same model by particle image velocimetry (PIV). Flow in both models was representative of acinar flow during normal breathing (0.82ml/s). The experimental model was built in silicone and silicone oil was used as the carrier fluid. Flow measurements were obtained by an ensemble averaging procedure. CFD simulation was performed with STAR-CCM+ (CD-Adapco) using a polyhedral unstructured mesh. Velocity profiles in the central duct were parabolic and no bulk convection existed between the central duct and the alveoli. Velocities inside the alveoli were approximately 2 orders of magnitude smaller than the mean velocity in the central duct. CFD data agreed well with those obtained by PIV. In the central duct, data agreed within 1%. The maximum simulated velocity along the centerline of the model was 0.5% larger than measured experimentally. In the alveolar cavities, data agreed within 15% on average. This suggests that CFD techniques can satisfactorily predict acinar-type flow. Such a validation ensure a great degree of confidence in the accuracy of predictions made in more complex models of the alveolar region of the lung using similar CFD techniques.     

A Machine Learning Method for the Prediction of Receptor Activation in the Simulation of Synapses

Chemical synaptic transmission involves the release of a neurotransmitter that diffuses in the extracellular space and interacts with specific receptors located on the postsynaptic membrane. Computer simulation approaches provide fundamental tools for exploring various aspects of the synaptic transmission under different conditions. In particular, Monte Carlo methods can track the stochastic movements of neurotransmitter molecules and their interactions with other discrete molecules, the receptors. However, these methods are computationally expensive, even when used with simplified models, preventing their use in large-scale and multi-scale simulations of complex neuronal systems that may involve large numbers of synaptic connections. We have developed a machine-learning based method that can accurately predict relevant aspects of the behavior of synapses, such as the percentage of open synaptic receptors as a function of time since the release of the neurotransmitter, with considerably lower computational cost compared with the conventional Monte Carlo alternative. The method is designed to learn patterns and general principles from a corpus of previously generated Monte Carlo simulations of synapses covering a wide range of structural and functional characteristics. These patterns are later used as a predictive model of the behavior of synapses under different conditions without the need for additional computationally expensive Monte Carlo simulations. This is performed in five stages: data sampling, fold creation, machine learning, validation and curve fitting. The resulting procedure is accurate, automatic, and it is general enough to predict synapse behavior under experimental conditions that are different to the ones it has been trained on. Since our method efficiently reproduces the results that can be obtained with Monte Carlo simulations at a considerably lower computational cost, it is suitable for the simulation of high numbers of synapses and it is therefore an excellent tool for multi-scale simulations.     

Evaluation of individually ventilated cage systems for laboratory rodents: occupational health aspects

New ventilated caging systems for laboratory animals were compared with conventional caging regarding allergen distribution, ergonomic suitability, cage environment and animal welfare. This paper presents occupational health evaluations. Mice were placed in individually ventilated cage (IVC) systems, a ventilated cabinet, and in cages on open shelves (conventional husbandry). The IVC systems were studied at negative and positive airflow. Aeroallergens were sampled on filters (n = 204, including controls) in undisturbed rooms and during cage changing. Concentrations of mouse urinary allergen (Mus m 1) in filter eluates were measured using sandwich ELISA. An ergonomic evaluation was performed with measurement of traction forces. Staff exposure during cage changing was high in all systems, range 116-4430 ng Mus m 1/m3. In undisturbed animal rooms, allergen levels were orders of magnitude higher when using conventional caging compared with ventilated systems; P < 0.001. At positive pressure both IVCs leaked allergen (median Mus m 1 concentration was < 0.08 ng/m3 at negative, but 6.5 ng/m3 (IVC1) and 0.8 ng/m3 (IVC2S) at positive pressure). The IVC systems had ergonomic disadvantages compared with the conventional husbandry and the ventilated cabinet, for instance with cages in unsuitable working heights. Ventilated husbandry solutions reduce levels of airborne allergen substantially at negative pressure, but are ergonomically less suitable. To prevent allergen exposure during cage changing, we propose that this procedure should be performed under ventilated conditions. Producers and users must cooperate in optimizing animal caging systems for both animals and staff.     

The effect of extracellular conductivity on electroporation-mediated molecular delivery

In this work, the effect of extra-cellular conductivity on electroporation-mediated molecular delivery efficiency is investigated. A numerical model combining the Smoluchowski equation for membrane permeabilization and the Nernst–Planck equations for ion transport is used to simulate the evolution of ion concentration spatially and temporally. The results are compared with and used to interpret trends observed from previous experimental measurements. Agreements are found which suggest the critical importance of electrophoretic transport. This mechanism controls delivery efficiency on the quantitative level. Meanwhile, a simple formula is developed to predict the molecular content delivered via electrophoresis. The formula can be used as a compact model which provides good approximation to the full numerical model while avoiding the computational cost.     

Development and application of new positively charged filters for recovery of bacteriophages from water

Electronegative and electropositive filters were compared for the recovery of indigenous bacteriophages from water samples, using the VIRADEL technique. Fiber glass and diatomaceous earth filters displayed low adsorption and recovery, but an important increase of the adsorption percentage was observed when the filters were treated with cationic polymers (about 99% adsorption). A new methodology of virus elution was developed in this study, consisting of the slow passage of the eluent through the filter, thus increasing the contact time between eluent and virus adsorbed on the filters. The use of this technique allows a maximum recovery of 71.2% compared with 46.7% phage recovery obtained by the standard elution procedure. High percentages (over 83%) of phage adsorption were obtained with different filters from 1-liter aliquots of the samples, except for Virosorb 1-MDS filters (between 1.6 and 32% phage adsorption). Phage recovery by using the slow passing of the eluent depended on the filter type, with recovery ranging between 1.6% for Virosorb 1-MDS filters treated with polyethyleneimine and 103.2% for diatomaceous earth filters treated with 0.1% Nalco.     

Spatial configuration of charge and hydrophobicity tune particle transport through mucus

Mucus is a selectively permeable hydrogel that protects wet epithelia from pathogen invasion and poses a barrier to drug delivery. Determining the parameters of a particle that promote or prevent passage through mucus is critical, as it will enable predictions about the mucosal passage of pathogens and inform the design of therapeutics. The effect of particle net charge and size on mucosal transport has been characterized using simple model particles; however, predictions of mucosal passage remain challenging. Here, we utilize rationally designed peptides to examine the integrated contributions of charge, hydrophobicity, and spatial configuration on mucosal transport. We find that net charge does not entirely predict transport. Specifically, for cationic peptides, the inclusion of hydrophobic residues and the position of charged and hydrophobic residues within the peptide impact mucosal transport. We have developed a simple model of mucosal transport that predicts how previously unexplored amino acid sequences achieve slow versus fast passage through mucus. This model may be used as a basis to predict transport behavior of natural peptide-based particles, such as antimicrobial peptides or viruses, and assist in the engineering of synthetic sequences with desired transport properties.     

Inertial particle dynamics in large artery flows – Implications for modeling arterial embolisms

The complexity of inertial particle dynamics through swirling chaotic flow structures characteristic of pulsatile large-artery hemodynamics renders significant challenges in predictive understanding of transport of such particles. This is specifically crucial for arterial embolisms, where knowledge of embolus transport to major vascular beds helps in disease diagnosis and surgical planning. Using a computational framework built upon image-based CFD and discrete particle dynamics modeling, a multi-parameter sampling-based study was conducted on embolic particle dynamics and transport. The results highlighted the strong influence of material properties, embolus size, release instance, and embolus source on embolus distribution to the cerebral, renal and mesenteric, and ilio-femoral vasculature beds. The study also isolated the importance of shear-gradient lift, and elastohydrodynamic contact, in affecting embolic particle transport. Near-wall particle re-suspension due to lift alters aortogenic embolic particle dynamics significantly as compared to cardiogenic. The observations collectively indicated the complex interplay of particle inertia, fluid–particle density ratio, and wall collisions, with chaotic flow structures, which render the overall motion of the particles to be non-trivially dispersive in nature.