A modified mathematical model of the anatomy of the cardiac left ventricle

A modification of the mathematical model of the shape and fiber direction field of the left cardiac ventricle is presented. The model was developed based on the idea of nested spiral surfaces. The ventricle is composed of surfaces that model myocardial layers. Each layer is filled with curves corresponding to myocardial fibers. The tangents to these curves form the myofiber direction field. A modified spherical coordinate system is linked with the model left ventricle, where the ventricular boundaries are coordinate surfaces. The model is based on echocardiographic, computed-tomography, or magnetic-resonance-imaging data. For this purpose, four-chamber and two-chamber echocardiography views or sections along the long axis of the left ventricle from these tomographic data in several positions are approximated with a model profile. To construct a 3D model, we then interpolate model parameters by periodic cubic splines and the vector field of the tangents to the model fibers is calculated. For verification of the model, we used diffusion-tensor magneticresonance-imaging data of the human heart.     

Modeling the impact of immigration on the epidemiology of tuberculosis

This paper presents two new theoretical frameworks to investigate the impact of immigration on the transmission dynamics of tuberculosis. For the basic model, we present new analysis on the existence and stability of equilibria. Then, we use numerical simulations of the model to illustrate the behavior of the system. We apply the model to Canadian reported data on tuberculosis and observe a good agreement between the model prediction and the data. For the extended model, which incorporated the recruitment of the latent and infectious in immigrants to the basic model, we find that the usual threshold condition does not apply and a unique equilibrium exists for all parameter values. This indicates that the disease does not disappear and becomes endemic in host areas. This finding is also supported by numerical simulations with the extended model. Our study suggests that immigrants have a considerable influence on the overall transmission dynamics behavior of tuberculosis.     

Modelling the spread of European buckthorn in the Region of Waterloo

Established invasive species, such as European buckthorn (Rhamnus cathartica), pose a challenging problem for land managers who must decide when and how to control them. In order to make an informed decision land managers need to be able to predict the spread of these invasive species at local scales and without the need for excessive sampling. Our approach uses a hybrid model, combining habitat suitability and the presence of the invasive in neighbouring cells to predict the probability of a cell being invaded over time. A generalized linear mixed-effects model was used to create a habitat suitability model and a spread model. The habitat suitability model predicts the presence of buckthorn based on environmental characteristics and the results are used in the spread model. The spread model indicates that the invasion of buckthorn is influenced by the suitability of habitat and the presence of buckthorn in neighbouring cells. The success of the spread model suggests that this approach can be used to create a spatiotemporally explicit model with limited sampling effort.     

Pondering the procephalon: the segmental origin of the labrum

With accumulating evidence for the appendicular nature of the labrum, the question of its actual segmental origin remains. Two existing insect head segmentation models, the linear and S-models, are reviewed, and a new model introduced. The L-/Bent-Y model proposes that the labrum is a fusion of the appendage endites of the intercalary segment and that the stomodeum is tightly integrated into this segment. This model appears to explain a wider variety of insect head segmentation phenomena. Embryological, histological, neurological and molecular evidence supporting the new model is reviewed.     

A model of heart ventricles for electrocardiographic evaluation of the state of the myocardium

A mathematical model of heart excitation processes has been developed for describing an electrocardiogram. A verified archive of model electrocardiograms has been created with the use of the model. The model has been used to study how electrocardiograms are affected by individual variability in ventricle shape and heart position in the norm, in myocardial infarction of different localizations, and in ventricular hypertrophy. Correspondence of the specific features of real and model electrocardiograms is discussed.     

Assessing the Performance of Neural Encoding Models in the Presence of Noise

An analytical method is introduced for evaluating the performance of neural encoding models. The method addresses a critical question that arises during the course of the development and validation of encoding models: is a given model near optimal in terms of its accuracy in predicting the stimulus-elicited responses of a neural system, or can the predictive accuracy be improved significantly by further model development? The evaluation method is based on a derivation of the minimum mean-square error between actual responses and modeled responses. It is formulated as a comparison between the mean-square error of the candidate model and the theoretical minimum mean-square error attainable through an optimal model for the system. However, no a priori information about the nature of the optimal model is required. The theoretically minimum error is determined solely from the coherence function between pairs of system responses to repeated presentations of the same dynamic stimulus. Thus, the performance of the candidate model is judged against the performance of an optimal model rather than against that of an arbitrarily assumed model. Using this method, we evaluated a linear model for neural encoding by mechanosensory cells in the cricket cercal system. At low stimulus intensities, the best-fit linear model of encoding by single cells was found to be nearly optimal, even though the coherence between stimulus-response pairs (a commonly used measure of system linearity) was low. In this low-stimulus-intensity regime, the mean square error of the linear model was on the order of the power of the cell responses. In contrast, at higher stimulus intensities the linear model was not an accurate representation of neural encoding, even though the stimulus-response coherence was substantially higher than in the low-intensity regime.     

上颌第一前磨牙三维模型的建立与研究

目的：建立上颌第一前磨牙三维模型,以辅助牙体解剖学数字化教学和指导临床根管治疗术。方法：对人离体上颌第一前磨牙通过ConebeamCT扫描,获得DICOM格式影像,将获得的影像定位后利用Mimicsl0．0三维重建软件采集牙釉质、牙本质及髓腔的点数据,然后将采集到的点数据导入到MagicslO．0软件进行面网格化,将网格化后的图像标本进行光滑处理后保存,再次利用MimicslO．0三维重建软件进行数据处理,最终获得清晰的牙体及根管系统三维立体图像。结果：准确的建立了包含牙釉质、牙本质、牙髓腔的三维立体模型。结论：本实验方法建立的上颌第一前磨牙的三维模型,具有极高的真实性和精确性,对辅助教学、指导临床根管治疗都具有重要意义。为牙体解剖教学和口腔临床应用提供了一种简捷而精确的建模方法。     

Micromechanical modeling of the epimysium of the skeletal muscles

A micromechanical model has been developed to investigate the mechanical properties of the epimysium. In the present model, the collagen fibers in the epimysium are embedded randomly in the ground substance. Two parallel wavy collagen fibers and the surrounding ground substance are used as the repeat unit (unit cell), and the epimysium is considered as an aggregate of unit cells. Each unit cell is distributed in the epimysium with some different angle to the muscle fiber direction. The model allows the progressive straightening of the collagen fiber as well as the effects of fiber reorientation. The predictions of the model compare favorably against experiment. The effects of the collagen fiber volume fraction, collagen fiber waviness at the rest length and the mechanical properties of the collagen fibers and the ground substance are analyzed. This model allows the analysis of mechanical behavior of most soft tissues if appropriate experimental data are available.     

A model for the functioning of the striatum

A model is presented for the operation of the striatum. The model posits that the basal ganglia are responsible for driving smooth transitions of state for an organism. We propose that this is accomplished through the computation of a potential function within the striatum on which a gradient descent is performed toward the goal state. The model suggests that various somatotopic regions of the striatum correspond to state spaces, each of which pertains to a different aspect of the organism. This paper discusses this model only in the context of motor control, i.e., egomotion and limb movement. The model appears to account for a variety of experimental results, and for some unusual properties of the striatum.     

Reliability Analysis of the Groundwater Conceptual Model

The hydrologic model is the foundation of water resource management and planning. Conceptual model is the essential component of groundwater model. Due to limited understanding of natural hydrogeological conditions, the conceptual model is always constructed incompletely. Therefore, the uncertainty in the model's output is evitable when natural groundwater field is simulated by a single groundwater model. A synthetic groundwater model is built and regarded as the true model, and three alternative conceptual models are constructed by considering incomplete hydrogeological conditions. The outputs (groundwater budget terms from boundary conditions) of these groundwater models are analyzed statistically. The results show that when the conceptual model is closer to the true hydrogeological conditions, the distributions of outputs of the groundwater model are more concentrated on the true outputs. Therefore, the more reliable the structure of the conceptual model is, the more reliable the output of the groundwater model is. Moreover, the uncertainty caused by the conceptual model cannot be compensated by parameter uncertainty.     

A functional model of the wiring of the simple cells of visual cortex

A computer model of the simple cells in the mammalian visual cortex was constructed. The model cells received inputs from a great number of isopolar centre/surround cells assumed to be located in the lateral geniculate nucleus (LGN). The distribution of input to the model simple cells was either inhibitory/excitatory or inhibitory/excitatory/inhibitory. Such arrangements produced receptive fields containing four or five consecutively antagonistic subfields. Responses produced by the model cells to different types of stimuli (periodical as well as nonperiodical) were obtained and compared to responses of living cells reported from various laboratories under comparable stimulus conditions. In all the situations tested, the responses of the model cells corresponded qualitatively very well to those of living cells. It was seen that the same wiring mechanism was able to account for orientation selectivity, spatial frequency filtering, various phase relationships between stimulus and response, subfield orientational selectivity, and slight end-inhibition. Furthermore, the receptive fields of the model simple cells closely resemble Gabor functions.     

A model of heart ventricles for describing electrocardiograms in the estimation of the state of the myocardium

A mathematical model of heart excitation processes for describing the electrocardiograms was developed. By using the model, it is possible to create a verified archive of model electrocardiograms and study the effect of individual variability of ventricle shape and the position of the heart in norm, in infarctions of different localization, and in ventricle hypertrophy. The consistency of real electrocardiograms with those obtained by computer-assisted modeling is discussed.     

A test of the metapopulation model of the species–area relationship

Abstract Aim The species–area relationship is a ubiquitous pattern. Previous methods describing the relationship have done little to elucidate mechanisms producing the pattern. Hanski & Gyllenberg (Science, 1997, 275 , 397) have shown that a model of metapopulation dynamics yields predictable species–area relationships. We elaborate on the biological interpretation of this mechanistic model and test the prediction that communities of species with a higher risk of extinction caused by environmental stochasticity should have lower species–area slopes than communities experiencing less impact of environmental stochasticity. Methods We develop the mainland–island version of the metapopulation model and show that the slope of the species–area relationship resulting from this model is related to the ratio of population growth rate to variability in population growth of individual species. We fit the metapopulation model to five data sets, and compared the fit with the power function model and Williams's (Ecology, 1995, 76 , 2607) extreme value function model. To test that communities consisting of species with a high risk of extinction should have lower slopes, we used the observation that small‐bodied species of vertebrates are more susceptible to environmental stochasticity than large‐bodied species. The data sets were divided into small and large bodied species and the model fit to both. Results and main conclusions The metapopulation model showed a good fit for all five data sets, and was comparable with the fits of the extreme value function and power function models. The slope of the metapopulation model of the species–area relationship was greater for larger than for smaller‐bodied species for each of five data sets. The slope of the metapopulation model of the species–area relationship has a clear biological interpretation, and allows for interpretation that is rooted in ecology, rather than ad hoc explanation.     

Modelling the effect of urbanization on the transmission of an infectious disease

This paper models the impact of urbanization on infectious disease transmission by integrating a CA land use development model, population projection matrix model and CA epidemic model in S-Plus. The innovative feature of this model lies in both its explicit treatment of spatial land use development, demographic changes, infectious disease transmission and their combination in a dynamic, stochastic model. Heuristically-defined transition rules in cellular automata (CA) were used to capture the processes of both land use development with urban sprawl and infectious disease transmission. A population surface model and dwelling distribution surface were used to bridge the gap between urbanization and infectious disease transmission. A case study is presented involving modelling influenza transmission in Southampton, a dynamically evolving city in the UK. The simulation results for Southampton over a 30-year period show that the pattern of the average number of infection cases per day can depend on land use and demographic changes. The modelling framework presents a useful tool that may be of use in planning applications.     

Use of Satellite Data for the Estimation of the Specific Growth Rate of Phytoplankton in the Surface Layer of the Black Sea

Russian Journal of Marine Biology - A regional model is proposed for the estimation of the specific growth rate of phytoplankton in the sea surface layer using satellite data. The model is based on...     

Correlation between the osmotic second virial coefficient and the solubility of proteins

A correlation between the osmotic second virial coefficient and the solubility of proteins is derived from classical thermodynamics to support an empirical relation previously found by Wilson and co-workers (1). The model is based on the equality of fugacities of the protein in the equilibrium phases, with the details of the model depending on the standard state used. The parameters in this model have been fitted to data for several systems, mainly with lysozyme as the protein. The model is found to describe experimental data, with variations in protein concentration, salt type and concentration, temperature, and pH, both qualitatively and quantitatively. Agreement between the model and the experimental data is very good for protein solubilities up to 30 mg/mL. Above this value the model underpredicts the experimental data, probably as a result of multibody interactions that are not included in the model here. Variations of the model parameters with protein type, temperature, pH, and salt type are discussed.     

A network model for the control of the movement of a redundant manipulator

In an earlier investigation (Cruse and Brüwer 1987) an algorithmic model was proposed which describes targeting movements of a human arm when restricted to a horizontal plane. As three joints at shoulder, elbow and wrist are allowed to move, the system is redundant. Two models are discussed here which replace this algorithmic model by a network model. Both networks solve the static problem, i.e. they provide the joint angles which the arm has to adopt in order to reach a given point in the workspace. In the first model the position of this point is given in the form ofx —y coordinates, the second model obtains this information by means of a retina-like input layer. The second model is expanded by a simple procedure to describe movements from a start to an end point. The results qualitatively correspond to those obtained from human subjects. The advantages of the network models in comparison to the algorithmic model are discussed.     

A comprehensive model of the crypts of the small intestine of the mouse provides insight into the mechanisms of cell migration and the proliferation hierarchy

A comprehensive model has been formulated for the proliferative behaviour of the crypts of the small intestine based on individual cell to cell relationships rather than on the average effects of all cells. The model accommodates a wide range of cell kinetic data and provides an insight into the mechanisms involved in cell movement within the columnar sheet of cells and into the relationship between the stem cells and their progeny. The model permits the number of stem cells and transit generations to be estimated. The number of stem cells is predicted to be not less than 4 and not more than 16 per crypt with cell cycle times of between 12 and 32 h respectively. Certain conclusions can be drawn concerning the mechanisms involved in the initial cell displacements after cell division. The model also allows an estimation of parameters which cannot be measured directly such as the degree of cell generation disorder and the amount of dispersion of cells within a cell lineage.     

Simulation of the competition for light in forest stands of the same age

A model simulating the growth and interaction of trees during their competition for light has been proposed and verified. Qualitative analysis of the model behavior at various values of parameters determining the tree growth rate has been performed. The model verification shows a sufficiently high accuracy of the model approximation of empirical tree growth data. To study interspecific interactions in forest communities, some computing experiments on the development of mixed forest stands, represented by the main forest-forming wood species of the Far East, have been carried out.     

On the relation between extended forms of the sinusoidal perfusion and of the convection-dispersion models of hepatic elimination

Two models of hepatic elimination, the distributed sinusoidal perfusion model, and the convection-dispersion model, are extended and then compared for first order kinetics in the steady-state. The sinusoidal perfusion model is extended by the inclusion of intrahepatic sites of mixing between sinusoids. The degree of such mixing is estimated for taurocholate elimination by isolated perfused rat livers by a comparison of anatomical and kinetic estimates of uptake heterogeneity, using previously published data. The dispersion model is generalized by the inclusion of distributions of enzyme activity along the flow. Direct comparison of the two models in the limit in which the degree of dispersion is small, allows the flow-dependence of the dispersion coefficient to be determined, thereby greatly extending the explanatory power of the convection-dispersion model. Finally, the effect of intrahepatic mixing sites on uptake by Michaelis-Menten kinetics is quantified in terms of the distributed sinusoidal perfusion model, with results which may be applicable to capillary beds in general.