Newly explored electrical properties of normal skin and special skin sites.

Skin impedance measurements at various skin sites yield different impedance loci for normal skin and special skin sites. The results of skin impedance measurements taken at such sites with a two-electrode measurement system are presented herein. Some of these sites can be identified as acupuncture points. Data from 4 volunteers were acquired by means of a data acquisition board and a measuring system consisting of the measurement circuit, including several electrode types, and a power supply. The Cole model is a model for an equivalent electrical circuit of the skin-electrode system. The system was used to derive skin-typical parameters from the Bode plot of the whole system. These parameters are the fractional power a, the pseudo-capacity K, the parallel resistance Rp, and the serial resistance Rs of the equivalent electrical circuit. The results show that the measured parameters differ between normal skin and special skin sites. These effects have not previously been discovered by other authors, since there has been no systematic investigation of many acupuncture points to date, and there has been no apparent need for such an investigation. A number of necessary criteria for acupuncture point detection can be derived from the results obtained.     

Quantifying the impact of ecological memory on the dynamics of interacting communities

Ecological memory refers to the influence of past events on the response of an ecosystem to exogenous or endogenous changes. Memory has been widely recognized as a key contributor to the dynamics of ecosystems and other complex systems, yet quantitative community models often ignore memory and its implications.Recent modeling studies have shown how interactions between community members can lead to the emergence of resilience and multistability under environmental perturbations. We demonstrate how memory can be introduced in such models using the framework of fractional calculus. We study how the dynamics of a well-characterized interaction model is affected by gradual increases in ecological memory under varying initial conditions, perturbations, and stochasticity.Our results highlight the implications of memory on several key aspects of community dynamics. In general, memory introduces inertia into the dynamics. This favors species coexistence under perturbation, enhances system resistance to state shifts, mitigates hysteresis, and can affect system resilience both ways depending on the time scale considered. Memory also promotes long transient dynamics, such as long-standing oscillations and delayed regime shifts, and contributes to the emergence and persistence of alternative stable states. Our study highlights the fundamental role of memory in communities, and provides quantitative tools to introduce it in ecological models and analyse its impact under varying conditions.     

Human skin permittivity determined by millimeter wave reflection measurements

Millimeter wave reflection from the human skin was studied in the frequency range of 37-74 GHz in steps of 1 GHz. The forearm and palm data were used to model the skin with thin and thick stratum corneum (SC), respectively. To fit the reflection data, a homogeneous unilayer and three multilayer skin models were tested. Skin permittivity in the mm-wave frequency range resulted from the permittivity of cutaneous free water which was described by the Debye equation. The permittivity increment found from fitting to the experimental data was used for determination of the complex permittivity and water content of skin layers. Our approach, first tested in pure water and gelatin gels with different water contents, gave good agreement with literature data. The homogeneous skin model fitted the forearm data well. Permittivity of the forearm skin obtained with this model was close to the skin permittivity reported by others. To fit reflection from the palmar skin with a thick SC, a skin model containing at least two layers was required. Multilayer models provided better fitting to both the forearm and palmar skin reflection data. The fitting parameters obtained with different models were consistent with each other.     

A second generation global analysis program for the recovery of complex inhomogeneous fluorescence decay kinetics

A flourescence spectroscopy global data analysis environment is described. Within this analysis environment multidimensional fluoroscence decay data (time and frequency domains) can be analyzed in terms of a wide variety of photophysical models. A generalized compartmental analysis structure is utilized, where one can specify the functions used to link the various compartments together. All fitting parameters may be characterized by either discrete or distributed values. Applications of these new analysis programs to the examination of phase transitions in lipid/membrane systems are described.     

Quasi-Linear Vacancy Dynamics Modeling and Circuit Analysis of the Bipolar Memristor

The quasi-linear transport equation is investigated for modeling the bipolar memory resistor. The solution accommodates vacancy and circuit level perspectives on memristance. For the first time in literature the component resistors that constitute the contemporary dual variable resistor circuit model are quantified using vacancy parameters and derived from a governing partial differential equation. The model describes known memristor dynamics even as it generates new insight about vacancy migration, bottlenecks to switching speed and elucidates subtle relationships between switching resistance range and device parameters. The model is shown to comply with Chua''s generalized equations for the memristor. Independent experimental results are used throughout, to validate the insights obtained from the model. The paper concludes by implementing a memristor-capacitor filter and compares its performance to a reference resistor-capacitor filter to demonstrate that the model is usable for practical circuit analysis.     

A second-generation computational modeling of cardiac electrophysiology: response of action potential to ionic concentration changes and metabolic inhibition

Background

Cardiac arrhythmias are becoming one of the major health care problem in the world, causing numerous serious disease conditions including stroke and sudden cardiac death. Furthermore, cardiac arrhythmias are intimately related to the signaling ability of cardiac cells, and are caused by signaling defects. Consequently, modeling the electrical activity of the heart, and the complex signaling models that subtend dangerous arrhythmias such as tachycardia and fibrillation, necessitates a quantitative model of action potential (AP) propagation. Yet, many electrophysiological models, which accurately reproduce dynamical characteristic of the action potential in cells, have been introduced. However, these models are very complex and are very time consuming computationally. Consequently, a large amount of research is consecrated to design models with less computational complexity.

Results

This paper is presenting a new model for analyzing the propagation of ionic concentrations and electrical potential in space and time. In this model, the transport of ions is governed by Nernst-Planck flux equation (NP), and the electrical interaction of the species is described by a new cable equation. These set of equations form a system of coupled partial nonlinear differential equations that is solved numerically. In the first we describe the mathematical model. To realize the numerical simulation of our model, we proceed by a finite element discretization and then we choose an appropriate resolution algorithm.

Conclusions

We give numerical simulations obtained for different input scenarios in the case of suicide substrate reaction which were compared to those obtained in literature. These input scenarios have been chosen so as to provide an intuitive understanding of dynamics of the model. By accessing time and space domains, it is shown that interpreting the electrical potential of cell membrane at steady state is incorrect. This model is general and applies to ions of any charge in space and time domains. The results obtained show a complete agreement with literature findings and also with the physical interpretation of the phenomenon. Furthermore, various numerical experiments are presented to confirm the accuracy, efficiency and stability of the proposed method. In particular, we show that the scheme is second-order accurate in space.

     

落叶松人工林树干形状模型和可变参数

对以往树木干形的一系列可变参数削度方程进行比较,根据模型拟合统计量(残差平方和及相关指数),选出其中对落叶松干形拟合效果较好(残差平方和较小、相关指数较高)的模型,并根据模型中可变参数的意义提出了5种描述干形的指数.结果表明:Lee等提出的削度方程的拟合效果较好,可以用来描述落叶松人工林的树干形状;5种描述干形的指数分别为根部梢头削度率、影响点、圆柱体和抛物线体范围值、最小可变参数、最小可变参数所在的相对高度,这些指数可以作为比较干形的方法和工具.较大密度(870株.hm-2)和较小密度林分(275株.hm-2)的林木干形质量都较差,只有适中密度林分(487株.hm-2)的落叶松干形质量较好.     

Estimation of growth regulation in natural populations by extended family of growth curve models with fractional order derivative: Case studies from the global population dynamics database

Estimating the trend in population time series data using growth curve models is a central idea in population ecology. Several models, mainly governed by differential or difference equations, have been applied to real data sets to identify general growth pattern and make predictions. In this article, we analyze ecological time series data by fitting mathematical models governed by fractional differential equations (FDE). The order of the FDE (α) is used to quantify the evidence of memory in the population processes. The application of FDE is exemplified by analyzing time series data on two bird species Phalacrocorax carbo (Great cormorant) and Parus bicolor (Tufted titmouse) and two mammal species Castor canadensis (Beaver) and Ursus americanus (American black bear) extracted from the global population dynamics database. Five different population growth models were fitted to these data; density-independent exponential, negative density-dependent logistic and θ-logistic model, positive density-dependent exponential Allee and strong Allee model. Both ordinary and fractional derivative representations of these models were fitted to the time series data. Markov chain Monte Carlo (MCMC) method was used to estimate the model parameters and Akaike information criterion was used to select the best model. By estimating the return rate for each of the time series, we have shown that populations governed by FDE with a small value of α (high level of memory) return to the stable equilibrium faster. This demonstrates a synergistic interplay between memory and stability in natural populations.     

Population persistence in river networks

Organisms inhabiting river systems contend with downstream biased flow in a complex tree-like network. Differential equation models are often used to study population persistence, thus suggesting resolutions of the ‘drift paradox’, by considering the dependence of persistence on such variables as advection rate, dispersal characteristics, and domain size. Most previous models that explicitly considered network geometry artificially discretized river habitat into distinct patches. With the recent exception of Ramirez (J Math Biol 65:919–942, 2012), partial differential equation models have largely ignored the global geometry of river systems and the effects of tributary junctions by using intervals to describe the spatial domain. Taking advantage of recent developments in the analysis of eigenvalue problems on quantum graphs, we use a reaction–diffusion–advection equation on a metric tree graph to analyze persistence of a single population in terms of dispersal parameters and network geometry. The metric graph represents a continuous network where edges represent actual domain rather than connections among patches. Here, network geometry usually has a significant impact on persistence, and occasionally leads to dramatically altered predictions. This work ranges over such themes as model definition, reduction to a diffusion equation with the associated model features, numerical and analytical studies in radially symmetric geometries, and theoretical results for general domains. Notable in the model assumptions is that the zero-flux interior junction conditions are not restricted to conservation of hydrological discharge.     

Quantitative comparison of dipole models for steady-state currents in excitable membranes

The dipole models for steady-state currents in excitable membranes of Arndt, Bond and Roper and of Hamel and Zimmerman are compared by fitting the equations to the data of Gilbert and Ehrenstein. The more complex Hammel and Zimmerman model does not fit the data as well as does the simpler Arndt, Bond and Reper model. When fitting the data, the Hammel and Zimmerman current equation reduces to the Arndt, Bond and Roper current equation because of the values assumed by the parameters. An interpretation is given for the parameter values obtained with the Arndt, Bond and Roper model.     

Electrical bioimpedance measurement during hypothermic rat kidney preservation for assessing ischemic injury

Non-heart-beating donors sustain an ischemic insult of unknown severity and duration, which can compromise the viability of the graft. This preliminary study aimed to assess whether electrical bioimpedance monitoring of cold preserved organs could be useful to identify kidneys that have suffered previous warm ischemia (WI). Two rat groups were studied during 24 h of preservation in University of Wisconsin solution (UW): a control cold ischemia group and another group subjected previously to 45 min of WI. Multi-frequency bioimpedance was monitored during preservation by means of a miniaturized silicon probe and the results were modeled according to the Cole equation. Tissular ATP content, lactate dehydrogenase in UW solution and histological injury were assessed. Renal function and cell injury, evaluated during 3 h of ex vivo reperfusion using the isolated perfused rat kidney model, demonstrated differences between groups. Bioimpedance results showed that the time constant and the high frequency resistivity parameters derived from the Cole equation were able to discriminate between groups at the beginning of the preservation (Deltatau approximately 78%, DeltaRinfinity approximately 36%), but these differences tended to converge as preservation time advanced. Nevertheless, another of the Cole parameters, alpha, showed increasing significant differences until 24 h of preservation (Deltaalpha approximately 15%).     

Propagators and time-dependent diffusion coefficients for anomalous diffusion

Complex diffusive dynamics are often observed when one is investigating the mobility of macromolecules in living cells and other complex environments, yet the underlying physical or chemical causes of anomalous diffusion are often not fully understood and are thus a topic of ongoing research interest. Theoretical models capturing anomalous dynamics are widely used to analyze mobility data from fluorescence correlation spectroscopy and other experimental measurements, yet there is significant confusion regarding these models because published versions are not entirely consistent and in some cases do not appear to satisfy the diffusion equation. Further confusion is introduced through variations in how fitting parameters are reported. A clear definition of fitting parameters and their physical significance is essential for accurate interpretation of experimental data and comparison of results from different studies acquired under varied experimental conditions. This article aims to clarify the physical meaning of the time-dependent diffusion coefficients associated with commonly used fitting models to facilitate their use for investigating the underlying causes of anomalous diffusion. We discuss a propagator for anomalous diffusion that captures the power law dependence of the mean-square displacement and can be shown to rigorously satisfy the extended diffusion equation provided one correctly defines the time-dependent diffusion coefficient. We also clarify explicitly the relation between the time-dependent diffusion coefficient and fitting parameters in fluorescence correlation spectroscopy.     

Moment arms and musculotendon lengths estimation for a three-dimensional lower-limb model

This paper presents a set of polynomial expressions that can be used as regression equations to estimate length and three-dimensional moment arms of 43 lower-limb musculotendon actuators. These equations allow one to find, at a low computational cost, the musculotendon geometric parameters required for numerical simulation of large musculoskeletal models. Nominal values for these biomechanical parameters were established using a public-domain musculoskeletal model of the lower limb (IEEE Trans. Biomed. Eng. 37 (1990) 757). To fit these nominal values, regression equations with different levels of complexity were generated, based on the number of generalized coordinates of the joints spanned by each musculotendon actuator. Least squares fitting was used to identify regression equation coefficients. The goodness of the fit and confidence intervals were assessed, and the best fitting equations selected.     

Quantitative modeling of viable cell density,cell size,intracellular conductivity,and membrane capacitance in batch and fed‐batch CHO processes using dielectric spectroscopy

Dielectric spectroscopy was used to analyze typical batch and fed‐batch CHO cell culture processes. Three methods of analysis (linear modeling, Cole–Cole modeling, and partial least squares regression), were used to correlate the spectroscopic data with routine biomass measurements [viable packed cell volume, viable cell concentration (VCC), cell size, and oxygen uptake rate (OUR)]. All three models predicted offline biomass measurements accurately during the growth phase of the cultures. However, during the stationary and decline phases of the cultures, the models decreased in accuracy to varying degrees. Offline cell radius measurements were unsuccessfully used to correct for the deviations from the linear model, indicating that physiological changes affecting permittivity were occurring. The β‐dispersion was analyzed using the Cole–Cole distribution parameters Δε (magnitude of the permittivity drop), f_c (critical frequency), and α (Cole–Cole parameter). Furthermore, the dielectric parameters static internal conductivity (σ_i) and membrane capacitance per area (C_m) were calculated for the cultures. Finally, the relationship between permittivity, OUR, and VCC was examined, demonstrating how the definition of viability is critical when analyzing biomass online. The results indicate that the common assumptions of constant size and dielectric properties used in dielectric analysis are not always valid during later phases of cell culture processes. The findings also demonstrate that dielectric spectroscopy, while not a substitute for VCC, is a complementary measurement of viable biomass, providing useful auxiliary information about the physiological state of a culture. © 2010 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

Fractal modeling of human isochronous serial interval production

The Hurst exponent (H) was estimated for series of 256 time intervals produced by human participants, collected in 5 sessions performed on different days. Each series was obtained during the continuation phase following synchronization with 25 isochronous intervals generated by a computer and presented through headphones. Dispersional analysis yielded estimates of H > 0.5. These were sufficiently stable to yield statistically significant differences between participants and between each target interval duration (0.5, 0.8, 1.1, and 1.5s). The results indicate that variability in isochronous serial interval production (ISIP) can be modeled as fractional Gaussian noise, which corroborates and qualifies previous research indicating positive serial dependency or long memory in ISIP data in terms of drift and 1/f noise characteristics. It is concluded that ISIP is a more complex process than is assumed by influential timing models and theories, and that realistic modeling of human timing must account for nonlinear variability patterns.Abbreviations Bm Brownian motion - f frequency - fGn fractional Gaussian noise - H Hurst exponent - ISIP isochronous serial interval production - IOI inter onset interval     

Influence of blood flow and millimeter wave exposure on skin temperature in different thermal models

Recently we showed that the Pennes bioheat transfer equation was not adequate to quantify mm wave heating of the skin at high blood flow rates. To do so, it is necessary to incorporate an "effective" thermal conductivity to obtain a hybrid bioheat equation (HBHE). The main aim of this study was to determine the relationship between non-specific tissue blood flow in a homogeneous unilayer model and dermal blood flow in multilayer models providing that the skin surface temperatures before and following mm wave exposure were the same. This knowledge could be used to develop multilayer models based on the fitting parameters obtained with the homogeneous tissue models. We tested four tissue models consisting of 1-4 layers and applied the one-dimensional steady-state HBHE. To understand the role of the epidermis in skin models we added to the one- and three-layer models an external thin epidermal layer with no blood flow. Only the combination of models containing the epidermal layer was appropriate for determination of the relationship between non-specific tissue and dermal blood flows giving the same skin surface temperatures. In this case we obtained a linear relationship between non-specific tissue and dermal blood flows. The presence of the fat layer resulted in the appearance of a significant temperature gradient between the dermis and muscle layer which increased with the fat layer thickness.     

Differential dynamic properties of scleroderma fibroblasts in response to perturbation of environmental stimuli

Diseases are believed to arise from dysregulation of biological systems (pathways) perturbed by environmental triggers. Biological systems as a whole are not just the sum of their components, rather ever-changing, complex and dynamic systems over time in response to internal and external perturbation. In the past, biologists have mainly focused on studying either functions of isolated genes or steady-states of small biological pathways. However, it is systems dynamics that play an essential role in giving rise to cellular function/dysfunction which cause diseases, such as growth, differentiation, division and apoptosis. Biological phenomena of the entire organism are not only determined by steady-state characteristics of the biological systems, but also by intrinsic dynamic properties of biological systems, including stability, transient-response, and controllability, which determine how the systems maintain their functions and performance under a broad range of random internal and external perturbations. As a proof of principle, we examine signal transduction pathways and genetic regulatory pathways as biological systems. We employ widely used state-space equations in systems science to model biological systems, and use expectation-maximization (EM) algorithms and Kalman filter to estimate the parameters in the models. We apply the developed state-space models to human fibroblasts obtained from the autoimmune fibrosing disease, scleroderma, and then perform dynamic analysis of partial TGF-beta pathway in both normal and scleroderma fibroblasts stimulated by silica. We find that TGF-beta pathway under perturbation of silica shows significant differences in dynamic properties between normal and scleroderma fibroblasts. Our findings may open a new avenue in exploring the functions of cells and mechanism operative in disease development.     

Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers''-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers''-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.     

Study design and parameter estimability for spatial and temporal ecological models

The statistical tools available to ecologists are becoming increasingly sophisticated, allowing more complex, mechanistic models to be fit to ecological data. Such models have the potential to provide new insights into the processes underlying ecological patterns, but the inferences made are limited by the information in the data. Statistical nonestimability of model parameters due to insufficient information in the data is a problem too‐often ignored by ecologists employing complex models. Here, we show how a new statistical computing method called data cloning can be used to inform study design by assessing the estimability of parameters under different spatial and temporal scales of sampling. A case study of parasite transmission from farmed to wild salmon highlights that assessing the estimability of ecologically relevant parameters should be a key step when designing studies in which fitting complex mechanistic models is the end goal.