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.     

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.     

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.     

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 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.     

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.     

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.     

Investigation into the foundations of the track-event theory of cell survival and the radiation action model based on nanodosimetry

This work aims at elaborating the basic assumptions behind the “track-event theory” (TET) and its derivate “radiation action model based on nanodosimetry” (RAMN) by clearly distinguishing between effects of tracks at the cellular level and the induction of lesions in subcellular targets. It is demonstrated that the model assumptions of Poisson distribution and statistical independence of the frequency of single and clustered DNA lesions are dispensable for multi-event distributions because they follow from the Poisson distribution of the number of tracks affecting the considered target volume. It is also shown that making these assumptions for the single-event distributions of the number of lethal and sublethal lesions within a cell would lead to an essentially exponential dose dependence of survival for practically relevant values of the absorbed dose. Furthermore, it is elucidated that the model equation used for consideration of repair within the TET is based on the assumption that DNA lesions induced by different tracks are repaired independently. Consequently, the model equation is presumably inconsistent with the model assumptions and requires an additional model parameter. Furthermore, the methodology for deriving model parameters from nanodosimetric properties of particle track structure is critically assessed. Based on data from proton track simulations it is shown that the assumption of statistically independent targets leads to the prediction of negligible frequency of clustered DNA damage. An approach is outlined how track structure could be considered in determining the model parameters, and the implications for TET and RAMN are discussed.

     

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.     

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.     

On the role of reinfection in the transmission of infectious diseases

We introduce a spatial stochastic model for the spread of tuberculosis. After a primary infection, an individual may become sick (and infectious) through an endogenous reinfection or through an exogenous reinfection. We show that even in the absence of endogenous reinfection an epidemic is possible if the exogenous reinfection parameter is high enough. This is in sharp contrast with what happens for a mean field model corresponding to our spatial stochastic model.     

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.     

Towards a molecular theory of the nerve membrane: the significance of the quasithreshold behaviour

The threshold properties of a model of the nerve membrane are examined. A graded quasithreshold is found, and it can be characterized by an amplification factor μ. Upon introducing an activation enthalpy for one relaxation process, the temperature dependence of μ can be matched over nine decades to that previously found from the Hodgkin-Huxley equations. The reason for the unusual form of the temperature dependence is clearly indicated in the model. The central mechanism postulated in the model is shown to provide an integrative rationalization of the basic phenomena of nerve excitation.     

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.     

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.     

A model of the breakdown and removal of the chromatin components during Feulgen acid hydrolysis

Synopsis A stochastic model of Feulgen hydrolysis is proposed. The model, constructed so as to embody the main features of chromatin structure, is simple enough to allow the calculation of extraction rates. Extraction rate curves generated by the model are compared with experimental curves obtained under various conditions (different fixatives and hydrolysis solutions). A good correspondence is found between the experiments and the predictions of the model.     

Control systems model of the spontaneous and light-evoked patterns of the compound action potentials in the eye of Aplysia

The spontaneous and light-evoked firing patterns of the compound action potentials (CAPs) in the isolated eye of Aplysia are experimentally observed from a control systems viewpoint. The eye, exhibiting an endogenous bursting activity and a marked circadian rhythm in darkness, is a self-excited system and responds to illumination with a controlled electrical activity. It is represented by the nonlinear systems model predicting the firing-rate variation of the CAPs. Construction of the model is based on the eye's biological model reported in the literature, and involves an experimental analysis of the system characteristics using linear approximation and conventional control systems techniques. The model is simulated and found to adequately conform to the observed behavior of the eye under various experimental conditions.     

Theoretical calculations on hydrogenase kinetics: explanation of the lag phase and the enzyme concentration dependence of the activity of hydrogenase uptake

Two models of the hydrogenase reaction cycle were investigated by means of theoretical calculations and model simulations. The first model is the widely accepted triangular hydrogenase reaction cycle with minor modifications; the second is a modified triangular model, where we have introduced an autocatalytic step into the reaction cycle. Both models include a one-step activation reaction. The theoretical calculations and model simulations corroborate the assumed autocatalytic reaction step concluded from the experimental characteristics of the hydrogenase reaction.     

Critical evaluation of the one- versus the two-channel model for the operation of the ATP synthase's F(o) motor

The mechanism of converting an electrochemical gradient of protons or Na(+) ions across the membrane into rotational torque by the F(o) motor of the ATP synthase has been described by a two-channel model or by a one-channel model. Experimental evidence obtained with the F(o) motor from the Propionigenium modestum ATP synthase is described which is in accordance with the one-channel model, but not with the two-channel model. This evidence includes the ATP-dependent occlusion of one (22)Na(+) per ATP synthase with a mutated Na(+)-impermeable a subunit or the Na(+)(in)/(22)Na(+)(out) exchange which is not affected by modifying part of the c subunit sites with dicyclohexylcarbodiimide.