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.     

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.     

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.     

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.     

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。     

Oscillator model reduction preserving the phase response: application to the circadian clock

Mathematical model reduction is a long-standing technique used both to gain insight into model subprocesses and to reduce the computational costs of simulation and analysis. A reduced model must retain essential features of the full model, which, traditionally, have been the trajectories of certain state variables. For biological clocks, timing, or phase, characteristics must be preserved. A key performance criterion for a clock is the ability to adjust its phase correctly in response to external signals. We present a novel model reduction technique that removes components from a single-oscillator clock model and discover that four feedback loops are redundant with respect to its phase response behavior. Using a coupled multioscillator model of a circadian clock, we demonstrate that by preserving the phase response behavior of a single oscillator, we preserve timing behavior at the multioscillator level.     

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.     

Can the sheep model fully represent the human model for the functional evaluation of cervical interbody fusion cages?

Sheep model is the most favourable choice for animal study for functional evaluation of the cervical fusion prostheses before clinical application; however, significantly large differences between sheep and human existed in terms of morphological characteristics and daily-activity motions. Questions should be raised as whether the differences between the two species have influence on the reliability of sheep model. Finite element models (FEM) of the cervical spinal system were built to characterize the differences between the two species with respect to the range of motion (ROM) and biomechanical behaviour, and experimental cadaver tests on both species were employed for validation purposes. Results indicate that sheep model represents the worst-case scenario of the human model with exaggerated stresses (up to 3 times more) and ROM (up to 10 times more). Moreover, sheep model is very sensitive to the variation of prostheses design, whilst human model does not, which denotes that the sheep model provides a rather amplified effect of a certain design for its biomechanical performance. Therefore, caution needs to be taken when sheep models were used as the animal model for functional evaluation over various design, and the FEM built in this study can be employed as an effective methodology for performance evaluation of cage prostheses of cervical spine.

     

Spectrin properties and the elasticity of the red blood cell membrane skeleton

Two models of spectrin elasticity are developed and compared to experimental measurements of the red blood cell (RBC) membrane shear modulus through the use of an elastic finite element model of the RBC membrane skeleton. The two molecular models of spectrin are: (i) An entropic spring model of spectrin as a flexible chain. This is a model proposed by several previous authors. (ii) An elastic model of a helical coiled-coil which expands by increasing helical pitch. In previous papers, we have computed the relationship between the stiffness of a single spectrin molecule (K) and the shear modulus of a network (μ), and have shown that this behavior is strongly dependent upon network topology. For realistic network models of the RBC membrane skeleton, we equate μ to micropipette measurements of RBCs and predict K for spectrin that is consistent with the coiled-coil molecular model. The value of spectrin stiffness derived from the entropic molecular model would need to be at least 30 times greater to match the experimental results. Thus, the conclusion of this study is that a helical coiled-coil model for spectrin is more realistic than a purely entropic model.     

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.     

Modeling differences in the vibration response characteristics of the human body

Mathematical models may provide a useful tool for the development and evaluation of seating systems for vibration mitigation. A five-degree-of-freedom (DOF) model was formulated based on the measured driving-point impedance and transmissibilities of major anatomical structures contributing to the observed resonance behaviors. The model was limited in its ability to simulate differences observed in the resonance behaviors of a broader population and was unable to simulate the multiple resonances observed in the thigh. This paper describes the effectiveness of a modified five DOF model in simulating the major resonance behaviors observed in the population using representative data from a 56 kg female and 75 kg male. In addition, the model was also evaluated for its ability to predict the effects of selected seat cushions. The modified lumped-parameter model improved the peak chest and spine transmissibility simulations. The model was effective in simulating both the lower impedance peak observed in the primary resonance region (4-8 Hz) and the prevalent impedance peak observed in the second resonance region (7-10 Hz) in the smaller subjects. However, the model was not effective in predicting the dampening observed in the second resonance peak with the use of cushions. Redistribution of the model coefficients for the legs and the consideration of coupling between the legs and other anatomical structures may further improve the ability of the lumped-parameter model to predict the effects of seating systems on vibration transmission in the human body.     

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.     

Modelling the spatial tuning of the Hermann grid illusion

PURPOSE: Does a physiologically plausible model of the retinal ganglion cell (RGC) receptive field (RF) predict the spatial tuning properties of the Hermann Grid Illusion (HGI)? METHODS: The spatial tuning of a single intersection HGI was measured psychophysically in normal observers using a nulling technique at different vertical grid line luminances. We used a model based upon a standard RGC RF, balanced to produce zero response under uniform illumination, to predict the response of the model cell to the equivalent range of stimulus conditions when placed in either the 'street' or the 'intersection' of a single element of a Hermann grid. We determined the equivalent of the nulling luminance required to balance these responses and minimise the HGI. RESULTS: The model and the psychophysical data demonstrated broad spatial tuning with similarly shaped tuning profiles and similar strengths of illusion. The line width at the peak of the model tuning function was around twice the model RGC RF centre size. Modelling the psychophysical functions gave RF centre sizes smaller than expected from human anatomical evidence but similar to that suggested by primate physiological evidence. In the model and psychophysically the strength of the illusion varied with the luminance of the vertical grid line when HGI strength was expressed as a Michelson nulling contrast, but this effect was smaller when HGI strength was expressed as a nulling luminance. CONCLUSIONS: The shape, width, height and position of the spatial tuning function of the HGI can be well modelled by a RGC RF based model. The broad tuning of these functions does not appear to require a broad range of different cell sizes either in the retina or later in the visual pathway.     

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.     

Spatial modeling of vesicle transport and the cytoskeleton: the challenge of hitting the right road

The membrane trafficking machinery provides a transport and sorting system for many cellular proteins. We propose a mechanistic agent-based computer simulation to integrate and test the hypothesis of vesicle transport embedded into a detailed model cell. The method tracks both the number and location of the vesicles. Thus both the stochastic properties due to the low numbers and the spatial aspects are preserved. The underlying molecular interactions that control the vesicle actions are included in a multi-scale manner based on the model of Heinrich and Rapoport (2005). By adding motor proteins we can improve the recycling process of SNAREs and model cell polarization. Our model also predicts that coat molecules should have a high turnover at the compartment membranes, while the turnover of motor proteins has to be slow. The modular structure of the underlying model keeps it tractable despite the overall complexity of the vesicle system. We apply our model to receptor-mediated endocytosis and show how a polarized cytoskeleton structure leads to polarized distributions in the plasma membrane both of SNAREs and the Ste2p receptor in yeast. In addition, we can couple signal transduction and membrane trafficking steps in one simulation, which enables analyzing the effect of receptor-mediated endocytosis on signaling.     

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.