Mathematical Modeling

Antibodies have proven to be effective agents in cancer imaging and therapy. One of the major challenges still facing the field is the heterogeneous distribution of these agents in tumors when administered systemically. Large regions of untargeted cells can therefore escape therapy and potentially select for more resistant cells. We present here a summary of theoretical and experimental approaches to analyze and improve antibody penetration in tumor tissue.

Mathematical models of tumor-immune interactions provide an analytic framework in which to address specific questions about tumor-immune dynamics. We present a new mathematical model that describes tumor-immune interactions, focusing on the role of natural killer (NK) and CD8+ T cells in tumor surveillance, with the goal of understanding the dynamics of immune-mediated tumor rejection. The model describes tumor-immune cell interactions using a system of differential equations. The functions describing tumor-immune growth, response, and interaction rates, as well as associated variables, are developed using a least-squares method combined with a numerical differential equations solver. Parameter estimates and model validations use data from published mouse and human studies. Specifically, CD8+ T-tumor and NK-tumor lysis data from chromium release assays as well as in vivo tumor growth data are used. A variable sensitivity analysis is done on the model. The new functional forms develo...

In the past few years, Broadband ISDN (B-ISDN) has received increased attention as a communication architecture capable of supporting multimedia applications. Among the techniques proposed to implement B-ISDN, Asynchronous Transfer Mode (ATM) is considered to be the most promising transfer technique because of its ejiciency andjle.ribiliiy. In ATM networks. the performunce bottleneck of the network, which was once the channel transmission speed, is shifred to the processing speed at the network switching nodes and the propagation dela! of the channel. This ship is because the high-speed channel increuses the ratio ofpropagation delay to cell transmission time and the ratio of processing time to cell transmission time. Due to the increased ratio of propagation delay to cell transmission time. a large number of cells can be in trunsit between two ATM switching nodes. In addition, the increased ratio qf processing time to cell transmission time makes it difjirult to implement hop-by-hop control schemes. Therefore, trufjic control in ATM networks is a challenge, and new network urchitectures (j l o w control schemes, error control schemes, etc.) are required in ATM networks. This paper sun>eys a number of importunt research topics in ATM networks. The topics covered include marhemutical modeling of various types of trafic sources, congestion control and error control schemes for ATM networks, and priori5 schemes to support multiple classes of traflc.. Standard activitv for ATM networks and future re5earch problems in ATM are also presented.

This article is the second of a two-part paper on ELCIRC, an Eulerian-Lagrangian finite difference/finite volume model designed to simulate 3D baroclinic circulation across river-to-ocean scales. In part one , we described the formulation of ELCIRC and assessed its baseline numerical skill. Here, we describe the application of ELCIRC within CORIE, a coastal margin observatory for the Columbia River estuary and plume. We first introduce the CORIE modeling system and its multiple modes of simulation, external forcings, observational controls, and automated products. We then focus on the evaluation of highly resolved, year-long ELCIRC simulations, using two variables (water level and salinity) to illustrate simulation quality and sensitivity to modeling choices. We show that, process-wise, simulations capture well important aspects of the response of estuarine and plume circulation to ocean, river, and atmospheric forcings. Quantitatively, water levels are robustly represented, while salinity intrusion and plume dynamics remain challenging. Our analysis highlights the benefits of conducting model evaluations over large time windows (months to years), to avoid significant localized biases. The robustness and computational efficiency of ELCIRC has proved invaluable in identifying and reducing non-algorithmic sources of errors, including parameterization (e.g., turbulence closure and stresses at the airwater interface) and external forcings (e.g., ocean conditions and atmospheric forcings).

We review the state-of-the-art in the modelling of the aggregation and collective behavior of interacting agents of similar size and body type, typically called swarming. Starting with individual-based models based on "particle"-like assumptions, we connect to hydrodynamic/macroscopic descriptions of collective motion via kinetic theory. We emphasize the role of the kinetic viewpoint in the modelling, in the derivation of continuum models and in the understanding of the complex behavior of the system.

Deregulation of ErbB signaling plays a key role in the progression of multiple human cancers. To help understand ErbB signaling quantitatively, in this work we combine traditional experiments with computational modeling, building a model that describes how stimulation of all four ErbB receptors with epidermal growth factor (EGF) and heregulin (HRG) leads to activation of two critical downstream proteins, extracellular-signal-regulated kinase (ERK) and Akt. Model analysis and experimental validation show that (i) ErbB2 overexpression, which occurs in approximately 25% of all breast cancers, transforms transient EGF-induced signaling into sustained signaling, (ii) HRG-induced ERK activity is much more robust to the ERK cascade inhibitor U0126 than EGF-induced ERK activity, and (iii) phosphoinositol-3 kinase is a major regulator of post-peak but not pre-peak EGF-induced ERK activity. Sensitivity analysis leads to the hypothesis that ERK activation is robust to parameter perturbation at high ligand doses, while Akt activation is not.

Although the ERK pathway has a central role in the response of cells to growth factors, its regulatory structure and dynamics are incompletely understood. To investigate ERK activation in real time, we expressed an ERK-GFP fusion protein in human mammary epithelial cells. On EGF stimulation, we observed sustained oscillations of the ERK-GFP fusion protein between the nucleus and cytoplasm with a periodicity of B15 min. The oscillations were persistent (445 cycles), independent of cell cycle phase, and were highly dependent on cell density, essentially disappearing at confluency. Oscillations occurred even at ligand doses that elicited very low levels of ERK phosphorylation, and could be detected biochemically in both transfected and nontransfected cells. Mathematical modeling revealed that negative feedback from phosphorylated ERK to the cascade input was necessary to match the robustness of the oscillation characteristics observed over a broad range of ligand concentrations. Our characterization of single-cell ERK dynamics provides a quantitative foundation for understanding the regulatory structure of this signaling cascade.

A comprehensive three-dimensional simulation model was developed for entrained #ow coal gasi"ers. In the model, the numerical methods and the submodels conventionally used for the pulverized coal combustion modeling were used. An extended coal gas mixture fraction model with the Multi Solids Progress Variables (MSPV) method was applied to simulate the gasi"cation reaction and reactant mixing process. Four mixture fractions were employed to separately track the variable coal o!-gas from the coal devolatilization, char}O , char}CO , and char}H O reactions. The in#uence of turbulence on the gas properties was taken into account by the pdf model with a clipped Gaussian distribution function. A series of numerical simulations were performed for a 200 td\ two-stage air blown entrained #ow gasi"er recently developed for the IGCC process. The predicted gas temperature pro"le and the exit gas composition were in general agreement with the measurements. Model simulations illustrating the importance of accounting for varying coal o!-gas and the e!ects of turbulence/reaction a!ecting the prediction capability were also presented.

Lymphatic filariasis (LF) is a major cause of acute and chronic morbidity in the tropical and subtropical parts of the world. The availability of safe, single-dose, drug treatment regimens capable of suppressing microfilaremia to very low levels, along with improvements in techniques for diagnosing infection, has resulted in the targeting of this major mosquito-borne disease for global elimination. The Global Program to Eliminate Lymphatic Filariasis (GPELF) was launched in 2000 with the principal objective of breaking the cycles of transmission of Wuchereria bancrofti and Brugia spp. through the application of annual mass drug administrations (MDAs) to entire at-risk populations. Although significant progress in initiating MDA programs in endemic countries has been made, emerging challenges to this approach have raised questions regarding the effectiveness of using MDA alone to eliminate LF without the inclusion of supplementary vector control. Here, we review advances in knowledge of vector ecology, vector-parasite relationships, and both empirical and theoretical evidence regarding vector management to assess the feasibility and strategic value of including vector control in the GPELF initiative to achieve the global elimination of LF.

In this work a methodology is presented for the rigorous optimization of nonlinear programming problems in which the objective function and (or) some constraints are represented by noisy implicit black box functions. The special application considered is the optimization of modular process simulators in which the derivatives are not available and some units operations introduce noise preventing the calculation of accurate derivatives. The black box modules are substituted by metamodels based on a kriging interpolation that assumes that the errors are not independent but a function of the independent variables. A Kriging metamodel uses a non Euclidean measure of distance that avoid sensitivity to the units of measure. It includes adjustable parameters that weight the importance of each variable getting a good model representation, and it allows to calculate errors that can be used to establish stopping criteria and provide a solid base to deal with 'possible infeasibility' due to inaccuracies in the metamodel representation of objective function and constraints. The algorithm continues with a refining stage and successive bound contraction in the domain of independent variables with or without kriging recalibration until an acceptable accuracy in the kriging metamodel is obtained.

The kinetics of the reaction between human chorionic gonadotropin (hCG) and specific gonadotropin receptors in the rat testis were determined at 24 and 37O, over a wide range of hormone concentrations. Hormone concentrations were corrected for the binding activity of the [1251] hCG tracer preparations. Analysis of the experimental data was performed with an interactive nonlinear curve fitting program, based upon the second-order chemical kinetic differential equation. The mean values for the association rate constant ( k l ) were 4.7 X lo7 M-' min-' at 24O, and 11.0 X lo7 M-' min-l at 37O. At both temperatures, the values of kl were independent of hormone concentration. Initial dissociation rates were consistent with firstorder kinetics, with dissociation rate constant (k2) of 1.7 X and 4.6 X lob3 min-l at 24 and 37O, respectively.

Mathematical modeling and dynamic simulation of signal transduction pathways is a central theme in systems biology and is increasingly attracting attention in the postgenomic era. The estimation of model parameters from experimental data remains a bottleneck for a major breakthrough in this area. This study’s aim is to introduce a new strategy for experimental design based on parameter sensitivity analysis. The approach identifies key parameters/variables in a signal transduction pathway model and can thereby provide experimental biologists with guidance on which proteins to consider for measurement. The article focuses on applying this approach to the TNFα-mediated NF-κB pathway, which plays an important role in immunity and inflammation and in the control of cell proliferation, differentiation, and apoptosis. A mathematical model of this pathway is proposed, and the sensitivity analysis of model parameters is illustrated for this model by employing the Monte Carlo method over a br...

We review a large volume of literature concerning mathematical models of cancer therapy, oriented towards optimization of treatment protocols. The review, although partly idiosyncratic, covers such major areas of therapy optimization as phase-specific chemotherapy, antiangiogenic therapy and therapy under drug resistance. We start from early cell cycle progression models, very simple but admitting explicit mathematical solutions, based on methods of control theory. We continue with more complex models involving evolution of drug resistance and pharmacokinetic and pharmacodynamic effects. Then, we consider two more recent areas: angiogenesis of tumors and molecular signaling within and among cells. We discuss biological background and mathematical techniques of this field, which has a large although only partly realized potential for contributing to cancer treatment.

Circadian clocks are 24-h timing devices that phase cellular responses; coordinate growth, physiology, and metabolism; and anticipate the day-night cycle. Here we report sensitivity of the Arabidopsis thaliana circadian oscillator to sucrose, providing evidence that plant metabolism can regulate circadian function. We found that the Arabidopsis circadian system is particularly sensitive to sucrose in the dark. These data suggest that there is a feedback between the molecular components that comprise the circadian oscillator and plant metabolism, with the circadian clock both regulating and being regulated by metabolism. We used also simulations within a three-loop mathematical model of the Arabidopsis circadian oscillator to identify components of the circadian clock sensitive to sucrose. The mathematical studies identified GIGANTEA (GI) as being associated with sucrose sensing. Experimental validation of this prediction demonstrated that GI is required for the full response of the circadian clock to sucrose. We demonstrate that GI acts as part of the sucrose-signaling network and propose this role permits metabolic input into circadian timing in Arabidopsis. mathematical modeling | optimization | photosynthesis | oscillations | carbohydrates T he Arabidopsis thaliana circadian clock confers growth and competitive advantage (1). The phase of circadian rhythms in plants is adjusted by light signals to entrain the clock to dawn and dusk (2). Additionally, it has been proposed that the Arabidopsis circadian clock is sensitive to nitrogen acting as a nutritional cue (3) and phytohormones, possibly as an input from stress signaling and growth pathways (4). In Arabidopsis, circadian oscillations are generated and maintained by interlocking transcriptionaltranslational feedback loops and posttranslational regulation (1, 5-8). In the morning, light activates the expression of two Myblike transcription factors, CIRCADIAN CLOCK ASSOCIATED 1 (CCA1) and LATE ELONGATED HYPOCOTYL (LHY), leading to expression of PSEUDO RESPONSE REGULATORS (PRR) 7 and 9, which in turn repress CCA1 and LHY expression. This "morning" loop of the oscillator is connected to "evening" expressed genes through direct repression of the expression of TIMING OF CAB EXPRESSION 1 (TOC1/PRR1) by binding of LHY/CCA1 to the TOC1 promoter. TOC1 is expressed in the evening and feeds back to activate LHY/CCA1 through an unknown pathway. TOC1 physically interacts with and antagonizes CCA1 HIKING EXPEDITION (CHE), a transcriptional repressor of CCA1 (9). CCA1 and LHY are also coupled with TOC1 through GIGANTEA (GI). LHY/CCA1 repress GI and GI forms a loop with TOC1, GI activating TOC1 and TOC1 repressing GI. GI encodes a protein of unknown biochemical function but in blue light, GI physically interacts with and stabilizes ZEITLUPE (10), an F-box protein that targets TOC1 for degradation (11). To entrain the circadian oscillator, signals are incorporated from light, second messengers, and metabolites to alter circadian clock gene expression and modulate circadian function (7, 12-15).

This experiment aimed to expand previous findings on the development of mental number representation. We tested the hypothesis that children's familiarity with numbers is directly reflected by the shape of their mental number line. This mental number line was expected to be linear as long as numbers lay within the range of numbers children were familiar with. Five-to 9-year-olds (N = 78) estimated the positions of numbers on an external number line and additionally completed a counting assessment mirroring their familiarity with numbers. A segmented regression model consisting of two linear segments described number line estimations significantly better than a logarithmic or a simple linear model. Moreover, the change point between the two linear segments, indicating a change of discriminability between numbers, was significantly correlated with children's familiar number range. Findings are discussed in terms of the accumulator model, assuming a linear mental representation with scalar variability.

We performed an analysis of a family of models relevant for the integrated modeling in metals biogeochemistry by two approaches: a hierarchical one and a disciplinary one. The hierarchical approach was performed in a theoretical framework accepting the existence of a hierarchy of ecological systems, and split the population of analyzed models into classes based on their relevance for various biological and ecological hierarchical levels. We identified two types of integrated models: between abiotic and biotic components at the same levels, and between biotic components across hierarchical levels. The complementary, disciplinary approach, focused on bioremediation models. The delineation of the class of bioremediation models proved that practically all biogeochemical models are relevant for this class, while only some of the analyzed models have been explicitly declared as 'bioremediation models'. Based on these analyses we identified a set of research directions, and proposed an alternative, complementary theoretical framework for basic research problems. With regard to bioremediation models, we could identify three levels of potential for development. The strategic potential: if correctly evaluated, models in bioremediation are the most useful tools for rational decision making. The tactical potential, of reactive type: internalizing the future knowledge arising from systems biology, and many other fields such as cognitive sciences biogeochemistry, ecotoxicology, soil science or plant science. The tactical potential of proactive type: (a) combining physico-chemical mechanistic ''in principle'' approach with uncovering the mathematical laws directly at the bio-geo level by empirical research and use of the existing new mathematical tools and (b) empirical research for delineating in situ the elementary units of models application and the use of programming in geographic information systems (GIS) and new generation GIS software for up-scaling the models' results from the elementary units of application to the site. And, finally, the operational potential: long-term research network for the study of contaminated sites as basic science experimental areas for implementing the proactive operational potential.

There have been many techniques developed in recent years to in silico model a variety of cancer behaviors. Agent-based modeling is a specific discrete-based hybrid modeling approach that allows simulating the role of diversity in cell populations as well as within each individual cell; it has therefore become a powerful modeling method widely used by computational cancer researchers. Many aspects of tumor morphology including phenotype-changing mutations, the adaptation to microenvironment, the process of angiogenesis, the influence of extracellular matrix, reactions to chemotherapy or surgical intervention, the effects of oxygen and nutrient availability, and metastasis and invasion of healthy tissues have been incorporated and investigated in agent-based models. In this review, we introduce some of the most recent agent-based models that have provided insight into the understanding of cancer growth and invasion, spanning multiple biological scales in time and space, and we furthe...

This paper is concerned with the simultaneous flow of liquid water and gaseous reactants in mini-channels of a proton exchange membrane (PEM) fuel cell. Envisaging the mini-channels as structured and ordered porous media, we develop a continuum model of two-phase channel flow based on two-phase Darcy's law and the M 2 formalism, which allow estimate of the parameters key to fuel cell operation such as overall pressure drop and liquid saturation profiles along the axial flow direction. Analytical solutions of liquid water saturation and species concentrations along the channel are derived to explore the dependences of these physical variables vital to cell performance on operating parameters such as flow stoichiometric ratio and relative humility. The two-phase channel model is further implemented for three-dimensional numerical simulations of two-phase, multi-component transport in a single fuel-cell channel. Three issues critical to optimizing channel design and mitigating channel flooding in PEM fuel cells are fully discussed: liquid water buildup towards the fuel cell outlet, saturation spike in the vicinity of flow cross-sectional heterogeneity, and two-phase pressure drop. Both the two-phase model and analytical solutions presented in this paper may be applicable to more general two-phase flow phenomena through mini-and micro-channels.

The PI3K/Akt/mTOR pathway plays an essential role in a wide range of biological functions, including metabolism, macromolecular synthesis, cell growth, proliferation and survival. Its versatility, however, makes it a conspicuous target of many pathogens; and the consequential deregulations of this pathway often lead to complications, such as tumorigenesis, type 2 diabetes and cardiovascular diseases. Molecular targeted therapy, aimed at modulating the deregulated pathway, holds great promise for controlling these diseases, though side effects may be inevitable, given the ubiquity of the pathway in cell functions. Here, we review a variety of factors found to modulate the PI3K/Akt/mTOR pathway, including gene mutations, certain metabolites, inflammatory factors, chemical toxicants, drugs found to rectify the pathway, as well as viruses that hijack the pathway for their own synthetic purposes. Furthermore, this evidence of PI3K/Akt/mTOR pathway alteration and related pathogenesis has inspired the exploration of computer-aided targeting of this pathway to optimize therapeutic strategies. Herein, we discuss several possible options, using computer-aided targeting, to reduce the toxicity of molecularly-targeted therapy, including mathematical modeling, to reveal system-level control mechanisms and to confer a low-dosage combination therapy, the potential of PP2A as a therapeutic target, the formulation of parameters to identify patients who would most benefit from specific targeted therapies and molecular dynamics simulations and docking studies to discover drugs that are isoform specific or mutation selective so as to avoid undesired broad inhibitions. We hope this review will stimulate novel ideas for pharmaceutical

Many models have been developed to calculate supercritical solubility behavior and most can be either a semi-empirical relationship or based on an equation of state. In this work, density-based, semi-empirical models were evaluated in terms of their ability to accurately correlate solid solubility in supercritical carbon dioxide. The models considered were the methods of Chrastil, del Valle and Aguilera, Adachi and Lu, Méndez-Santiago and Teja, and Bartle. Six binary systems (solid + supercritical carbon dioxide), each with three isotherms, were selected for this evaluation. The average error was calculated for all 18 isotherms with each of the models evaluated. The solid compounds used in this study were naphthalene, anthracene, fluorene, hydroquinone, 1,5-naphthalenediamine, and cholesterol. The solubility data were obtained from literature. Of the previously mentioned models, the Adachi-Lu and del Valle-Aguilera equations provided, in general, lower average error than the other models. Since the Adachi-Lu equation and the del Valle-Aguilera equation correct for different effects, a new model is proposed in this work as a combination of the previous two methods. The proposed equation provided the least overall average error compared to all other models considered in this study. The new model is particularly useful when the reduced density of the solvent is below 1 where previous models tend to fail. This work also emphasizes on the advantages of expressing density-based models in dimensionless form to avoid dimensional inconsistencies in Chrastil-type models. One of the benefits, for example, is that parameters obtained by different authors can be readily compared, regardless of the units used.

The main goal of this work is to introduce a theoretical model, based on cellular automata, to simulate epidemic spreading. Specifically, it divides the population into three classes: susceptible, infected and recovered, and the state of each cell stands for the portion of these classes of individuals in the cell at every step of time. The effect of population vaccination is also considered. The proposed model can serve as a basis for the development of other algorithms to simulate real epidemics based on real data.

1] Shear localization is a process of primary importance for the onset of subduction and the evolution of plate tectonics on Earth. In this paper we focus on a model in which shear localization is initiated through shear heating. The rheology employed is linear Maxwell viscoelastic with von Mises plasticity and an exponential dependence of viscosity on temperature. Dimensional analysis reveals that four nondimensional (0-D) parameters control the initiation of shear zones. The onset of shear localization is systematically studied with 0-D, 1-D, and 2-D numerical models, both under constant stress and under constant velocity boundary conditions. Mechanical phase diagrams demonstrate that six deformation modes exist under constant velocity boundary conditions. A constant stress boundary condition, on the other hand, exhibits only two deformation modes (localization or no localization). Scaling laws for the growth rate of temperature are computed for all deformation modes. Numerical and analytical solutions demonstrate that diffusion of heat may inhibit localization. Initial heterogeneities are required to initiate localization. The derived scaling laws are applied to Earth-like parameters. For a given heterogeneity size, stable (nonseismic) localization only occurs for a certain range of effective viscosities. Localization is inhibited if viscosity is smaller then a minimum threshold, which is a function of the heterogeneity size. The simplified rheological model is compared with a more realistic and more complex model of olivine that takes diffusion, power law, and Peierls creep into account. Good agreement exists between the models. The simplified model proposed in this study thus reproduces the main physics of ductile faulting. Two-dimensional late stage simulations of lithospheric-scale shear localization are presented that confirm the findings of the initial stage analysis.

Affinity-based drug delivery systems utilize interactions between the therapeutic drug and the delivery system to manipulate drug loading and to control drug release. In this paper, affinity-based drug delivery system syntheses, types of therapeutic factors delivered, and delivery system loading and release are discussed in detail. The paper is divided into three subsections, based on the type of delivery system: molecular imprinting systems, growth-factor delivery, and cyclodextrin-based delivery. The objective of this paper is to examine the current state of research, highlight the breakthroughs and challenges, point out potential impacts of this relatively new technology, and explore future developmental areas.

A design and planning approach is proposed for addressing general multi-period, multi-product closedloop supply chains (CLSCs), structured as a 10-layer network (5 forward plus 5 reverse flows), with uncertain levels in the amount of raw material supplies and customer demands. The consideration of a multi-period setting leads to a multi-stage stochastic programming problem, which is handled by a mixed-integer linear programming (MILP) formulation. The effects of uncertain demand and supply on the network are considered by means of multiple scenarios, whose occurrence probabilities are assumed to be known. Several realistic supply chain requirements are taken into account, such as those related to the operational and environmental costs of different transportation modes, as well as capacity limits on production, distribution and storage. Moreover, multiple products are considered, which are grouped according to their recovery grade. The objective function minimizes the expected cost (that includes facilities, purchasing, storage, transport and emissions costs) minus the expected revenue due to the amount of products returned, from repairing and decomposition centers to the forward network. Finally, computational results are discussed and analyzed in order to demonstrate the effectiveness of the proposed approach. Due to the large size of the addressed optimization problem containing all possible scenarios for the two uncertain parameters, scenario reduction algorithms are applied to generate a representative, albeit smaller, subset of scenarios.

Limitations on comprehensive tropospheric chemistry/transport models are discussed within the context of a ~et of issues currently facing the environmental scientific and policy-making communities. A number of central improvements are discussed in a prioritized manner, with consideration of the key progress nece ~sary to include feedback processes between meteorology and chemistry, aerosol formatiot~ in cloud development with subsequent effects on wet removal, dry deposition and surface exchangeprocesses, and impacts of chemical perturbations on radiation, climate, and weather. These improvements would result in a "third-generation model". The computational framework for this code is outlined, and estimates of required computer resources presented.

Calibrated blood oxygenation level dependent (BOLD) imaging, a technique used to measure changes in cerebral O 2 metabolism, depends on an accurate model of how the BOLD signal is affected by the mismatch between cerebral blood flow (CBF) and cerebral metabolic rate of O 2 (CMRO 2 ). However, other factors such as the cerebral blood volume (CBV) distribution at rest and with activation also affect the BOLD signal. The Davis model originally proposed for calibrated BOLD studies is widely used because of its simplicity, but it assumes CBV changes are uniformly distributed across vascular compartments, neglects intravascular signal changes, and ignores blood-tissue signal exchange effects as CBV increases and supplants tissue volume. More recent studies suggest that venous CBV changes are smaller than arterial changes, and that intravascular signal changes and CBV exchange effects can bias estimated CMRO 2 . In this paper, recent experimental results for the relationship between deoxyhemoglobin and BOLD signal changes are integrated in order to simulate the BOLD signal in detail by expanding a previous model to include a tissue compartment and three blood compartments rather than only the venous blood compartment. The simulated data were then used to test the accuracy of the Davis model of calibrated BOLD, demonstrating that the errors in estimated CMRO 2 responses across the typical CBF-CMRO 2 coupling range are modest despite the simplicity of the assumptions underlying the original derivation of the model. Nevertheless, the accuracy of the model can be improved by abandoning the original physical meaning of the two parameters α and β and treating them as adjustable parameters that capture several physical effects. For a 3 Tesla field and a dominant arterial volume change with activation, the accuracy of the Davis model is improved with new values of α=0.14 and β=0.91.

A mathematical model is developed in algorithmic form for the steady-state simulation of gasketed plate heat exchangers with generalized configurations. The configuration is defined by the number of channels, number of passes at each side, fluid locations, feed connection locations and type of channel-flow. The main purposes of this model are to study the configuration influence on the exchanger performance and to further develop a method for configuration optimization. The main simulation results are: temperature profiles in all channels, thermal effectiveness, distribution of the overall heat transfer coefficient and pressure drops. Moreover, the assumption of constant overall heat transfer coefficient is analyzed.

Mathematical models for hepatitis C viral (HCV) RNA kinetics have provided a means of evaluating the antiviral effectiveness of therapy, of estimating parameters such as the rate of HCV RNA clearance, and they have suggested mechanism of action against HCV for both interferon and ribavirin. Nevertheless, the model that was originally formulated by Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-alpha therapy. Science 282 (5386), 103-107] is unable to explain all of the observed HCV RNA profiles under treatment e.g., a triphasic viral decay and a viral rebound to baseline values after the cessation of therapy. Further, the half-life of productively HCV-infected cells, estimated from the second phase HCV RNA decline slope, is very variable and sometimes zero with no clear understanding of why. We show that extending the original model by including hepatocyte proliferation yields a more realistic model without any of these deficiencies. Further, we define and characterize a critical drug efficacy, such that for efficacies above the critical value HCV is ultimately cleared, while for efficacies below it, a new chronically infected viral steady-state level is reached. Published by Elsevier Ltd.

The effect of rhythmic cueing on spatiotemporal control of sequential reaching movements of the paretic arm was studied in 21 hemispheric stroke patients. Reaching movements were studied with and without rhythmic metronome cuing in a counterbalanced design. Metronome frequencies were entrained to the naturally selected frequency of the patient. Results indicate statistically significant (P < 0.05) improvements of spatiotemporal arm control during rhythmic entrainment. Variability of timing and reaching trajectories were reduced significantly. Time series analysis of sequential movement repetitions showed an immediate reduction in variability of arm kinematics during rhythmic entrainment within the first two to three repetitions of each trial. Rhythm also produced significant increases in angle ranges of elbow motion (P < 0.05). Analysis of acceleration and velocity profiles of the wrist joint showed significant kinematic smoothing during rhythmic cuing. The link between rhythmic sensory timing and spatiotemporal motor control was investigated using a mathematical optimization model with minimization of peak acceleration as criterion. Rhythmically cued acceleration profiles fit the predicted model data significantly closer (P < 0.01) than the self-paced profiles. Since velocity and acceleration are mathematical derivatives of position-time trajectories, the model data suggest that enhanced timing precision via temporal phase and period coupling of the motor pattern to the rhythmic time timekeeper enhances the brain's computational ability to optimally scale movement parameters across time.

Shelf life of minimally processed vegetables is often calculated by using the kinetic parameters of Gompertz equation as modified by Zwietering et al. [Zwietering, M.H., Jongenburger, F.M., Roumbouts, M., van&#39;t Riet, K., 1990. Modelling of the bacterial growth curve. Applied and Environmental Microbiology 56, 1875-1881.] taking 5x10(7) CFU/g as the maximum acceptable contamination value consistent with acceptable quality of these products. As this method does not allow estimation of the standard errors of the shelf life, in this paper the modified Gompertz equation was re-parameterized to directly include the shelf life as a fitting parameter among the Gompertz parameters. Being the shelf life a fitting parameter is possible to determine its confidence interval by fitting the proposed equation to the experimental data. The goodness-of-fit of this new equation was tested by using mesophilic bacteria cell loads from different minimally processed vegetables (packaged fresh-cut lett...

Global cellular responses induced by epidermal growth factor (EGF) receptor (EGFR) occur immediately with a less than 1% occupancy among tens of thousands of EGFR molecules on single cell surface. Activation of EGFR requires the formation of a signaling dimer of EGFR bound with a single ligand to each molecule. How sufficient numbers of signaling dimers are formed at such low occupancy rate is still not known. Here, we have analyzed the kinetics of EGF binding and the formation of the signaling dimer using single-molecule imaging and mathematical modeling. A small number of EGFR on the cell surface formed dimeric binding sites, which bound EGF two orders of magnitude faster than the monomeric binding sites. There was a positive cooperative binding of EGF to the dimeric binding sites through a newly discovered kinetic intermediate. These two mechanisms facilitate the formation of signaling dimers of EGF/EGFR complexes.