Characteristics of inspiratory inhibition by phasic volume feedback in cats

The dependence of phrenic efferent discharge on vagal-volume feedback was examined in barbiturate-anesthetized, paralyzed cats ventilated by a phrenic-driven servo respirator. The characteristics of the respiratory were altered for a single breath, and the resulting change in phrenic activity was quantitated by comparison with phrenic activity without phasic volume feedback. The relation between volume feedback and phrenic inhibition was determined both when inspiratory termination occurred during the rising phase of phrenic discharge and during the plateau observed with barbiturate-induced apneusis. Inhibition of inspiratory activity occurred only when lung volume exceeded a time-dependent threshold. Above this threshold, andextending over a substantial volume range, volume feedback caused graded and reversible inhibition of phrenic discharge. The threshold for graded inhibition declined progressively during the inspiratory phase, showing no obvious relation to the level of inspiratory activity. At any particular time, the relation between volume and phrenic inhibition was convex to the volume axis, and the slope of the relationship increased with inspiratory time. The results indicate that a) volume feedback inhibits inspiration in a graded manner, b) partial inhibition of phrenic activity renders it more susceptible to additional inhibition, and c) inhibitory effectiveness of volume feedback increases with time.     

A kinetic model for lipoxygenases based on experimental data with the lipoxygenase of reticulocytes

A comprehensive kinetic model for lipoxygenase catalysis is proposed which includes the simultaneous occurrence of dioxygenase and hydroperoxidase activities and is based on the assumption of a single binding site for substrate fatty acid and product. The aerobic reaction of purified lipoxygenase from rabbit reticulocytes with 9,12(Z,Z)-octadecadienoic acid (linoleic acid) as substrate was studied. The rate constants and the dissociation constants of this enzyme were calculated for the model from progress curves; the model describes correctly the experimental data. The following kinetic features of the reticulocyte enzyme are assumed to apply generally to lipoxygenases. (a) The enzyme shows autoactivation by its product. (b) The rate-limiting step is the hydrogen abstraction. (c) Both substrate fatty acid and its product are competitive inhibitors of the lipoxygenase. (d) Lowering the oxygen concentration enhances the degree of substrate inhibition, whereas product inhibition is not influenced. (e) If substrate is in excess the oxygen concentration determines the share of dioxygenase and hydroperoxidase activities of the enzyme. As predicted from the model it was found that at low concentrations of oxygen the regio- and stereo-specificities of the dioxygenation are diminished. During the autoactivation phase the steady-state approximation does not hold.     

A network model for the control of the differentiation process in Th cells

T helper cells differentiate from a precursor type, Th0, to either the Th1 or Th2 phenotypes. While a number of molecules are known to participate in this process, it is not completely understood how they regulate each other to ensure differentiation. This article presents the core regulatory network controlling the differentiation of Th cells, reconstructed from published molecular data. This network encompasses 17 nodes, namely IFN-gamma, IL-4, IL-12, IL-18, IFN-beta, IFN-gammaR, IL-4R, IL-12R, IL-18R, IFN-betaR, STAT-1, STAT-6, STAT-4, IRAK, SOCS-1, GATA-3, and T-bet, as well as their cross-regulatory interactions. The reconstructed network was modeled as a discrete dynamical system, and analyzed in terms of its constituent feedback loops. The stable steady states of the Th network model are consistent with the stable molecular patterns of activation observed in wild type and mutant Th0, Th1 and Th2 cells.     

A mathematical model of hind-limb control in cats when walking backward

The “walking backward” mode was achieved within a single model of cat hind-limb locomotion with the balance maintenance only due to a change in the controlling actions (in addition to the “forward walking” mode). The skeletal part of the model contains the spine, pelvis, and two limbs consisting of the thigh, shin, and foot. The hip joint and spine mount in the thoracic region have three degrees of freedom; the knee and ankle joints have one degree of freedom. The pelvis is rigidly connected to the spine. Control is performed by model muscles (flexors and extensors of the thigh, shin, and foot). The muscle activation is performed by the effects that are typical for motoneurons that control the muscles. The feet in the support phase touch the treadmill, which moves at a constant speed. The model qualitatively reproduces multiple characteristics of feline movements during forward and backward walking (supporting its validity).     

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 spring model and equivalent neural network for arm posture control

A model is introduced for the motor program which controls final position. The first part of the model relates the biomechanical properties of the muscles to the EMG activities of the extensor and flexor muscles and thereby generates quatitative predictions for the relationships between the EMGs, final position, external forces, muscle stiffness, and muscle tension. To the extent that comparable data exist, the model is shown to give correct quantitative predictions. When only qualitative comparisons can be made, the model is consistent with the data in the literature. The model is complete and can be tested quantitatively in detail in the future. An equivalent circuit for the neural network that innervates the muscles is given. It is shown to have the advantages of making the programming of final position simple to either compute or lookup in a table. In addition, new situations, such as adapting to a force, or an unusual viewing angle, lead to very simple changes in the basic program in terms of the equivalent circuit.     

A stochastic model of cellular senescence. II. Concordance with experimental data

This report presents the results of computer simulations of a mathematical model for cell proliferation and senescence. The mathematical model is based on the idea that the in vitro proliferative potential of normal cells is determined by the number of a certain class of self-replicating particles it possesses. In the simulation model these particles are lost by both stochastic and deterministic processes. When all self-replicating particles are lost a cell can divide up to seven times before it irreversibly ceases to replicate. The simulated in vitro lifespans of clones and subclones are shown to be in close agreement with experimental data. We also show that other properties of finitely proliferating cultures can be simulated by this model.     

A general method of deriving the best binding site model consistent with experimental binding data

An analysis of binding data is presented which yields the best binding site model consistent with the experimental data. The analysis is applicable to homotropic binding and yields the number of independent sites, number of interacting sites (dimers and tetramers of sites), intrinsic association constants, and degree of interaction. The information is derived from the roots of a binding polynomial constructed by the fitted Adair constants.     

Numerical investigation of inspiratory airflow in a realistic model of the human tracheobronchial airways and a comparison with experimental results

In this article, the results of numerical simulations using computational fluid dynamics (CFD) and a comparison with experiments performed with phase Doppler anemometry are presented. The simulations and experiments were conducted in a realistic model of the human airways, which comprised the throat, trachea and tracheobronchial tree up to the fourth generation. A full inspiration/expiration breathing cycle was used with tidal volumes 0.5 and 1 L, which correspond to a sedentary regime and deep breath, respectively. The length of the entire breathing cycle was 4 s, with inspiration and expiration each lasting 2 s. As a boundary condition for the CFD simulations, experimentally obtained flow rate distribution in 10 terminal airways was used with zero pressure resistance at the throat inlet. CCM+ CFD code (Adapco) was used with an SST k-\(\upomega \) low-Reynolds Number RANS model. The total number of polyhedral control volumes was 2.6 million with a time step of 0.001 s. Comparisons were made at several points in eight cross sections selected according to experiments in the trachea and the left and right bronchi. The results agree well with experiments involving the oscillation (temporal relocation) of flow structures in the majority of the cross sections and individual local positions. Velocity field simulation in several cross sections shows a very unstable flow field, which originates in the tracheal laryngeal jet and propagates far downstream with the formation of separation zones in both left and right airways. The RANS simulation agrees with the experiments in almost all the cross sections and shows unstable local flow structures and a quantitatively acceptable solution for the time-averaged flow field.     

A semi-Markov model for survival data with covariates

Clinical trials are often concerned with the evaluation of two or more time-dependent stochastic events and their relationship. The information on covariates for individuals in the studies is valuable in assessing the survival function. This paper develops a multistate stochastic survival model which incorporates covariates. It is assumed that the underlying process follows a semi-Markov model. The proportional hazards techniques are applied to estimate the force of transition in the process. The maximum likelihood estimators are derived along with the survival function for competing risks problems. An application is given to analyzing the survival of patients in the Stanford Heart Transplant Program.     

A constitutive model for two-dimensional soft tissues and its application to experimental data

A constitutive relation proposed by Shoemaker (Ph.D. dissertation, 1984) to model the mechanical behavior of membraneous or two-dimensional soft tissues is described. Experiments by Schneider (Ph.D. dissertation, 1982) on human skin and Lee et al. (Am. J. Physiol., 249, H222-H230, 1985) on canine pericardium, and the application of the constitutive model to biaxial stress-strain data from these experiments, are discussed. Some experimental data and predictions of the model obtained by curvefitting are presented for comparison. Values of material parameters are also presented. It is concluded that the constitutive model is well able to fit results of individual tests, and that its generality (judged by consistency of parameters from test to test of the same specimen), though not complete, does compare favorably with some other results presented in the literature.     

A model for hormonal control of the menstrual cycle: Structural consistency but sensitivity with regard to data

This study presents a 13-dimensional system of delayed differential equations which predicts serum concentrations of five hormones important for regulation of the menstrual cycle. Parameters for the system are fit to two different data sets for normally cycling women. For these best fit parameter sets, model simulations agree well with the two different data sets but one model also has an abnormal stable periodic solution, which may represent polycystic ovarian syndrome. This abnormal cycle occurs for the model in which the normal cycle has estradiol levels at the high end of the normal range. Differences in model behavior are explained by studying hysteresis curves in bifurcation diagrams with respect to sensitive model parameters. For instance, one sensitive parameter is indicative of the estradiol concentration that promotes pituitary synthesis of a large amount of luteinizing hormone, which is required for ovulation. Also, it is observed that models with greater early follicular growth rates may have a greater risk of cycling abnormally.     

A unified framework for unraveling the functional interaction structure of a biomolecular network based on stimulus-response experimental data

We propose a unified framework for the identification of functional interaction structures of biomolecular networks in a way that leads to a new experimental design procedure. In developing our approach, we have built upon previous work. Thus we begin by pointing out some of the restrictions associated with existing structure identification methods and point out how these restrictions may be eased. In particular, existing methods use specific forms of experimental algebraic equations with which to identify the functional interaction structure of a biomolecular network. In our work, we employ an extended form of these experimental algebraic equations which, while retaining their merits, also overcome some of their disadvantages. Experimental data are required in order to estimate the coefficients of the experimental algebraic equation set associated with the structure identification task. However, experimentalists are rarely provided with guidance on which parameters to perturb, and to what extent, to perturb them. When a model of network dynamics is required then there is also the vexed question of sample rate and sample time selection to be resolved. Supplying some answers to these questions is the main motivation of this paper. The approach is based on stationary and/or temporal data obtained from parameter perturbations, and unifies the previous approaches of Kholodenko et al. (PNAS 99 (2002) 12841-12846) and Sontag et al. (Bioinformatics 20 (2004) 1877-1886). By way of demonstration, we apply our unified approach to a network model which cannot be properly identified by existing methods. Finally, we propose an experiment design methodology, which is not limited by the amount of parameter perturbations, and illustrate its use with an in numero example.     

A model for experimental bacterial cystitis in the dog

To induce an experimental model of bacterial cystitis, ten preconditioned dogs underwent bladder irritation with a 0.1% alcoholic solution of salicylic acid followed in 24 hours by an intravesicular infusion of Proteus mirabilis. The dogs were observed for the following 14 days (five dogs) and 17 days (five dogs) and then euthanatized and necropsied. Tenesmus, dysuria, hematuria, and pollakiuria occurred in all dogs, but the severity of these signs diminished with time. The total white cell, neutrophil, and monocyte counts in the peripheral blood increased and urinalysis results were consistent with infection and severe inflammation. The infection persisted for the duration of the study, although the average quantitative bacterial count in urine progressively declined. No changes occurred in the measured clinical chemistry values. Severe inflammation was present on gross examination of the bladder and microscopic examination of the bladder, prostate, and renal pelvis. Less severe inflammation was present on microscopic examination of the urethra and ureter.     

A Bayesian model for time-to-event data with informative censoring

Randomized trials with dropouts or censored data and discrete time-to-event type outcomes are frequently analyzed using the Kaplan-Meier or product limit (PL) estimation method. However, the PL method assumes that the censoring mechanism is noninformative and when this assumption is violated, the inferences may not be valid. We propose an expanded PL method using a Bayesian framework to incorporate informative censoring mechanism and perform sensitivity analysis on estimates of the cumulative incidence curves. The expanded method uses a model, which can be viewed as a pattern mixture model, where odds for having an event during the follow-up interval $$({t}_{k-1},{t}_{k}]$$, conditional on being at risk at $${t}_{k-1}$$, differ across the patterns of missing data. The sensitivity parameters relate the odds of an event, between subjects from a missing-data pattern with the observed subjects for each interval. The large number of the sensitivity parameters is reduced by considering them as random and assumed to follow a log-normal distribution with prespecified mean and variance. Then we vary the mean and variance to explore sensitivity of inferences. The missing at random (MAR) mechanism is a special case of the expanded model, thus allowing exploration of the sensitivity to inferences as departures from the inferences under the MAR assumption. The proposed approach is applied to data from the TRial Of Preventing HYpertension.