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.     

A resolved two-way coupled CFD/6-DOF approach for predicting embolus transport and the embolus-trapping efficiency of IVC filters

Inferior vena cava (IVC) filters are medical devices designed to provide a mechanical barrier to the passage of emboli from the deep veins of the legs to the heart and lungs. Despite decades of development and clinical use, IVC filters still fail to prevent the passage of all hazardous emboli. The objective of this study is to (1) develop a resolved two-way computational model of embolus transport, (2) provide verification and validation evidence for the model, and (3) demonstrate the ability of the model to predict the embolus-trapping efficiency of an IVC filter. Our model couples computational fluid dynamics simulations of blood flow to six-degree-of-freedom simulations of embolus transport and resolves the interactions between rigid, spherical emboli and the blood flow using an immersed boundary method. Following model development and numerical verification and validation of the computational approach against benchmark data from the literature, embolus transport simulations are performed in an idealized IVC geometry. Centered and tilted filter orientations are considered using a nonlinear finite element-based virtual filter placement procedure. A total of 2048 coupled CFD/6-DOF simulations are performed to predict the embolus-trapping statistics of the filter. The simulations predict that the embolus-trapping efficiency of the IVC filter increases with increasing embolus diameter and increasing embolus-to-blood density ratio. Tilted filter placement is found to decrease the embolus-trapping efficiency compared with centered filter placement. Multiple embolus-trapping locations are predicted for the IVC filter, and the trapping locations are predicted to shift upstream and toward the vessel wall with increasing embolus diameter. Simulations of the injection of successive emboli into the IVC are also performed and reveal that the embolus-trapping efficiency decreases with increasing thrombus load in the IVC filter. In future work, the computational tool could be used to investigate IVC filter design improvements, the effect of patient anatomy on embolus transport and IVC filter embolus-trapping efficiency, and, with further development and validation, optimal filter selection and placement on a patient-specific basis.     

彩超系统中壁滤波器设计和性能比较

本文首先介绍了多普勒原理和血流多普勒信号模型,推出了壁滤波器设计在彩色超声成像系统中具有极其重要的地位;其次分析了如何通过无限脉冲冲激响应（IIR）滤波器和回归型滤波器设计壁滤波器的原理,其中无限脉冲冲激响应（IIR）滤波器根据初始状态的不同又可以分为零初始化、阶跃初始化和投影初始化三种滤波器;然后根据上述原理分别对各种形式的壁滤波器进行设计,得到它们的频谱图;最后根据频谱图,对这几种壁滤波器进行性能比较,得到它们的优缺点,对从事壁滤波器设计相关的工作者有一定得借鉴意义。     

Effect of particle size distribution on filtration performance of cell culture medium

Cell culture media used in CHO-based biologic processes are typically sterile filtered to prevent microbial contamination prior to inoculation. In this study, the impact of common sterile filter throughput on a different, commercially available cell culture media was evaluated from the intermediate-adsorption fouling model of the filtration model. The key particle size range for optimum filter performance was discussed and identified by measuring the submicron order particle size distribution. It may be possible to predict the performance of filter capacity with size-exclusive separation by understanding the media particle counts and size distribution.     

Modeling of ion permeation in calcium and sodium channel selectivity filters

Structure-function studies have shown that it is possible to convert a sodium channel to a calcium-selective channel by a single amino acid substitution in the selectivity filter locus. Ion permeation through the "model selectivity filter" was modeled with a reduced set of functional groups representative of the constituent amino acid side chains. Force-field minimizations were conducted to obtain the energy profile of the cations as they get desolvated and bind to the "model selectivity filter." The calculations suggest that the ion selectivity in the calcium channel is due to preferential binding, whereas in the sodium channel it is due to exclusion. Energetics of displacement of a bound cation from the calcium "model selectivity filter" by another cation suggest that "multi-ion mechanism" reduces the activation barrier for ion permeation. Thus, the simple model captures qualitatively most of the conduction characteristics of sodium and calcium channels. However, the computed barriers for permeation are fairly large, suggesting that ion interaction with additional residues along the transport path may be essential to effect desolvation.     

Hydraulic performance of horizontal subsurface flow constructed wetlands for different strategies of filling the filter medium into the filter basin

A quasi-two-dimensional flow cell model of a horizontal subsurface flow constructed wetland was used to investigate how partitioning the wetland into smaller vertical sections prior to filling a heterogeneous filter medium into the filter basin altered the filter material packing and thereby the flow distribution. The flow through the filter medium was visualized using Nigrosine dye. Breakthrough curves for the flow cell were obtained using chloride tracer. Three inlet–outlet configurations were examined to assess the effects of the inlet and outlet positions on the flow since the inlet–outlet locations in addition to the filter medium heterogeneity may promote the development of preferential paths and dead zones. The filter medium packing patterns were dependent on the number of sections. If the wetland model was not partitioned prior to filling (one section), the filter material formed roughly horizontal layers with alternate layers of coarse and fine material. However, increasing the number of sections reduced the layer continuity and increased the flow distribution. This yielded longer retention times and higher hydraulic efficiency factors. The effect of the inlet–outlet configuration on the hydraulic parameters was greater when the number of sections was small. These results suggest that dividing the constructed wetland into several sections prior to filling the filter medium into the basin will improve the treatment efficiency.     

Modeling the system dynamics for nutrient removal in an innovative septic tank media filter

A next generation septic tank media filter to replace or enhance the current on-site wastewater treatment drainfields was proposed in this study. Unit operation with known treatment efficiencies, flow pattern identification, and system dynamics modeling was cohesively concatenated in order to prove the concept of a newly developed media filter. A multicompartmental model addressing system dynamics and feedbacks based on our assumed microbiological processes accounting for aerobic, anoxic, and anaerobic conditions in the media filter was constructed and calibrated with the aid of in situ measurements and the understanding of the flow patterns. Such a calibrated system dynamics model was then applied for a sensitivity analysis under changing inflow conditions based on the rates of nitrification and denitrification characterized through the field-scale testing. This advancement may contribute to design such a drainfield media filter in household septic tank systems in the future.     

Some laboratory investigations of anaerobic waste-water treatment process control in two different types of filter fermenters

Anaerobic degradation of a model waste water was investigated in two different types of fermenters (filter and hybride filter) under batch and continuous conditions. Gas production, COD removal, formation of fatty acids and the CoF₄₂₀–content of the biomass were monitored. At both modes of action the filter showed more process stability.     

A model-free method for mass spectrometer response correction

A new method for correction of mass spectrometer output signals is described. Response-time distortion is reduced independently of any model of mass spectrometer behavior. The delay of the system is found first from the cross-correlation function of a step change and its response. A two-sided time-domain digital correction filter (deconvolution filter) is generated next from the same step response data using a regression procedure. Other data are corrected using the filter and delay. The mean squared error between a step response and a step is reduced considerably more after the use of a deconvolution filter than after the application of a second-order model correction. O2 consumption and CO2 production values calculated from data corrupted by a simulated dynamic process return to near the uncorrupted values after correction. Although a clean step response or the ensemble average of several responses contaminated with noise is needed for the generation of the filter, random noise of magnitude less than or equal to 0.5% added to the response to be corrected does not impair the correction severely.     

Modeling permeation energetics in the KcsA potassium channel

The thermodynamics of cation permeation through the KcsA K(+) channel selectivity filter is studied from the perspective of a physically transparent semimicroscopic model using Monte Carlo free energy integration. The computational approach chosen permits dissection of the separate contributions to ionic stabilization arising from different parts of the channel (selectivity filter carbonyls, single-file water, cavity water, reaction field of bulk water, inner helices, ionizable residues). All features play important roles; their relative significance varies with the ion's position in the filter. The cavity appears to act as an electrostatic buffer, shielding filter ions from structural changes in the inner pore. The model exhibits K(+) vs. Na(+) selectivity, and roughly isoenergetic profiles for K(+) and Rb(+), and discriminates against Cs(+), all in agreement with experimental data. It also indicates that Ba(2+) and Na(+) compete effectively with permeant ions at a site near the boundary between the filter and the cavity, in the vicinity of the barium blocker site.     

Design and Optimization of the Multifunctional Rectangular Cavity Band-Pass Filter Based on the Surface Plasmon Polariton

Plasmonics - A novel multifunction filter based on the model of Fabry-Perot (F-P) resonant cavity is proposed in this paper. This filter is comprised of a rectangular cavity (400nm×200nm) and...     

A novel theoretical approach to correct for pathlength amplification and variable sampling loading in measurements of particulate spectral absorption by the quantitative filter technique

A simple theoretical model is described that takes into accountthe combined effects of pathlength amplification and variablesample loading in measurements of particulate spectral absorptionby the quantitative filter pad technique. The model differsfrom previous methods to correct for pathlength amplificationby explicitly considering variability in absorptance of samplematerial on the filter pad, A_fp, as a result of different degreesof particle loading on the filter. Functional expressions wereevaluated that describe the relationship between A_fp and theproduct of a dimensionless path factor,     

Comparison of the trickling filter models for the treatment of synthetic dairy wastewater

This paper describes the design implications of four existing trickling filter models. Experimental data from the treatment of synthetic dairy wastewater was used to evaluate the kinetic parameters. The four trickling filter models were examined for their ability to model the present data. Among the four models studied, Kincannon and Stover model based on the independent variable of surface organic loading rate gave superior results compared to other models.     

Flow characteristics of red cell containing fluids through pores. The effect of filter plugging, a mathematical model

A mathematical model was developed that describes the effects of filter plugging on flow through 3 micron pore polycarbonate filters as a function of time, pressure, and cell concentration, both under stirring and nonstirring conditions. The mathematical constants for the model were derived from experimental data generated with a filtration apparatus, and were tested by using various concentrations of cells that are able to plug filter pores. A computer simulation program was written to test the model over a wide range of nonfilterable cell concentrations.     

Possible roles of exceptionally conserved residues around the selectivity filters of sodium and calcium channels

In the absence of x-ray structures of sodium and calcium channels their homology models are used to rationalize experimental data and design new experiments. A challenge is to model the outer-pore region that folds differently from potassium channels. Here we report a new model of the outer-pore region of the NaV1.4 channel, which suggests roles of highly conserved residues around the selectivity filter. The model takes from our previous study (Tikhonov, D. B., and Zhorov, B. S. (2005) Biophys. J. 88, 184-197) the general disposition of the P-helices, selectivity filter residues, and the outer carboxylates, but proposes new intra- and inter-domain contacts that support structural stability of the outer pore. Glycine residues downstream from the selectivity filter are proposed to participate in knob-into-hole contacts with the P-helices and S6s. These contacts explain the adapted tetrodotoxin resistance of snakes that feed on toxic prey through valine substitution of isoleucine in the P-helix of repeat IV. Polar residues five positions upstream from the selectivity filter residues form H-bonds with the ascending-limb backbones. Exceptionally conserved tryptophans are engaged in inter-repeat H-bonds to form a ring whose π-electrons would facilitate passage of ions from the outer carboxylates to the selectivity filter. The outer-pore model of CaV1.2 derived from the NaV1.4 model is also stabilized by the ring of exceptionally conservative tryptophans and H-bonds between the P-helices and ascending limbs. In this model, the exceptionally conserved aspartate downstream from the selectivity-filter glutamate in repeat II facilitates passage of calcium ions to the selectivity-filter ring through the tryptophan ring. Available experimental data are discussed in view of the models.     

Comparison of Filtering Methods for the Modeling and Retrospective Forecasting of Influenza Epidemics

A variety of filtering methods enable the recursive estimation of system state variables and inference of model parameters. These methods have found application in a range of disciplines and settings, including engineering design and forecasting, and, over the last two decades, have been applied to infectious disease epidemiology. For any system of interest, the ideal filter depends on the nonlinearity and complexity of the model to which it is applied, the quality and abundance of observations being entrained, and the ultimate application (e.g. forecast, parameter estimation, etc.). Here, we compare the performance of six state-of-the-art filter methods when used to model and forecast influenza activity. Three particle filters—a basic particle filter (PF) with resampling and regularization, maximum likelihood estimation via iterated filtering (MIF), and particle Markov chain Monte Carlo (pMCMC)—and three ensemble filters—the ensemble Kalman filter (EnKF), the ensemble adjustment Kalman filter (EAKF), and the rank histogram filter (RHF)—were used in conjunction with a humidity-forced susceptible-infectious-recovered-susceptible (SIRS) model and weekly estimates of influenza incidence. The modeling frameworks, first validated with synthetic influenza epidemic data, were then applied to fit and retrospectively forecast the historical incidence time series of seven influenza epidemics during 2003–2012, for 115 cities in the United States. Results suggest that when using the SIRS model the ensemble filters and the basic PF are more capable of faithfully recreating historical influenza incidence time series, while the MIF and pMCMC do not perform as well for multimodal outbreaks. For forecast of the week with the highest influenza activity, the accuracies of the six model-filter frameworks are comparable; the three particle filters perform slightly better predicting peaks 1–5 weeks in the future; the ensemble filters are more accurate predicting peaks in the past.     

Current and selectivity in a model sodium channel under physiological conditions: Dynamic Monte Carlo simulations

A reduced model of a sodium channel is analyzed using Dynamic Monte Carlo simulations. These include the first simulations of ionic current under approximately physiological ionic conditions through a model sodium channel and an analysis of how mutations of the sodium channel's DEKA selectivity filter motif transform the channel from being Na(+) selective to being Ca(2+) selective. Even though the model of the pore, amino acids, and permeant ions is simplified, the model reproduces the fundamental properties of a sodium channel (e.g., 10 to 1 Na(+) over K(+) selectivity, Ca(2+) exclusion, and Ca(2+) selectivity after several point mutations). In this model pore, ions move through the pore one at a time by simple diffusion and Na(+) versus K(+) selectivity is due to both the larger K(+) not fitting well into the selectivity filter that contains amino acid terminal groups and K(+) moving more slowly (compared to Na(+)) when it is in the selectivity filter.     

Homology modeling and molecular dynamics simulation studies of an inward rectifier potassium channel

A homology model has been generated for the pore-forming domain of Kir6.2, a component of an ATP-sensitive K channel, based on the x-ray structure of the bacterial channel KcsA. Analysis of the lipid-exposed and pore-lining surfaces of the model reveals them to be compatible with the known features of membrane proteins and Kir channels, respectively. The Kir6.2 homology model was used as the starting point for nanosecond-duration molecular dynamics simulations in a solvated phospholipid bilayer. The overall drift from the model structure was comparable to that seen for KcsA in previous similar simulations. Preliminary analysis of the interactions of the Kir6.2 channel model with K(+) ions and water molecules during these simulations suggests that concerted single-file motion of K(+) ions and water through the selectivity filter occurs. This is similar to such motion observed in simulations of KcsA. This suggests that a single-filing mechanism is conserved between different K channel structures and may be robust to changes in simulation details. Comparison of Kir6.2 and KcsA suggests some degree of flexibility in the filter, thus complicating models of ion selectivity based upon a rigid filter.     

Firing-rate models capture essential response dynamics of LGN relay cells

Firing-rate models provide a practical tool for studying signal processing in the early visual system, permitting more thorough mathematical analysis than spike-based models. We show here that essential response properties of relay cells in the lateral geniculate nucleus (LGN) can be captured by surprisingly simple firing-rate models consisting of a low-pass filter and a nonlinear activation function. The starting point for our analysis are two spiking neuron models based on experimental data: a spike-response model fitted to data from macaque (Carandini et al. J. Vis., 20(14), 1–2011, 2007), and a model with conductance-based synapses and afterhyperpolarizing currents fitted to data from cat (Casti et al. J. Comput. Neurosci., 24(2), 235–252, 2008). We obtained the nonlinear activation function by stimulating the model neurons with stationary stochastic spike trains, while we characterized the linear filter by fitting a low-pass filter to responses to sinusoidally modulated stochastic spike trains. To account for the non-Poisson nature of retinal spike trains, we performed all analyses with spike trains with higher-order gamma statistics in addition to Poissonian spike trains. Interestingly, the properties of the low-pass filter depend only on the average input rate, but not on the modulation depth of sinusoidally modulated input. Thus, the response properties of our model are fully specified by just three parameters (low-frequency gain, cutoff frequency, and delay) for a given mean input rate and input regularity. This simple firing-rate model reproduces the response of spiking neurons to a step in input rate very well for Poissonian as well as for non-Poissonian input. We also found that the cutoff frequencies, and thus the filter time constants, of the rate-based model are unrelated to the membrane time constants of the underlying spiking models, in agreement with similar observations for simpler models.     

A three plus three parameters mechanistic model for viral filtration

Viral filtration is an expensive regulatory requirement in downstream processing of monoclonal antibodies (mAbs). This process step is typically operated with an overdesigned filter in order to account for any batch to batch variability in the filter, as well as the feed characteristics. Here, we propose a simple, six‐parameter mechanistic model for viral filtration where three parameters are membrane‐specific while the other three depend on feed characteristics and membrane‐feed interactions. Viruses are considered as passive particles which are retained by the membrane on the basis of size exclusion. The model envisages that the viral filter contains two kind of pores: virus‐retentive, small‐sized pores and non‐retentive, large‐sized pores. The small‐sized pores get blocked during filtration resulting in decrease in active membrane area, while the large‐sized pores get constricted during filtration. The length of constricted part increases during filtration and contributes to increase in hydraulic resistance of the filter. Rate of these processes (blocking and constriction) are assumed to be proportional to the instantaneous rate of retention of the viral particles. The general nature of the model is validated with the experimental data on viral filtration for four different commercial membranes used in biotech industries as well as different model viruses. The proposed model has been demonstrated to describe the behavior of filters with very good accuracy. The best‐fit model parameter values indicate about the various phenomena that are responsible for differences in the behavior of the membranes as well as change in retention and flux with feed concentration. The proposed model can be used for improving design of virus filters as well as in appropriate sizing of the filters during processing. © 2017 American Institute of Chemical Engineers Biotechnol. Prog., 33:1538–1547, 2017