Changes in nasal airflow and heat transfer correlate with symptom improvement after surgery for nasal obstruction

Surgeries to correct nasal airway obstruction (NAO) often have less than desirable outcomes, partly due to the absence of an objective tool to select the most appropriate surgical approach for each patient. Computational fluid dynamics (CFD) models can be used to investigate nasal airflow, but variables need to be identified that can detect surgical changes and correlate with patient symptoms. CFD models were constructed from pre- and post-surgery computed tomography scans for 10 NAO patients showing no evidence of nasal cycling. Steady-state inspiratory airflow, nasal resistance, wall shear stress, and heat flux were computed for the main nasal cavity from nostrils to posterior nasal septum both bilaterally and unilaterally. Paired t-tests indicated that all CFD variables were significantly changed by surgery when calculated on the most obstructed side, and that airflow, nasal resistance, and heat flux were significantly changed bilaterally as well. Moderate linear correlations with patient-reported symptoms were found for airflow, heat flux, unilateral allocation of airflow, and unilateral nasal resistance as a fraction of bilateral nasal resistance when calculated on the most obstructed nasal side, suggesting that these variables may be useful for evaluating the efficacy of nasal surgery objectively. Similarity in the strengths of these correlations suggests that patient-reported symptoms may represent a constellation of effects and that these variables should be tracked concurrently during future virtual surgery planning.     

Nonlinear modelling of renal vasoaction

The control of blood pressure is a complex mixture of neural, hormonal and intrinsic interactions at the level of the heart, kidney and blood vessels. While experimental approaches to understanding these interactions are useful, it remains difficult to conduct experiments to quantify these interactions as the number of parameters increases. Thus, modelling of such physiological systems can offer considerable assistance. Typical mathematical models which describe the ability of the blood vessels to change their diameter (vasoconstriction) assume linearity of operation. However, due to the interaction of multiple vasocontrictive and vasodilative effectors, there is a significant nonlinear response to the influence of neural factors, particularly at higher levels of nerve activity (often seen in subjects with high blood pressure) which leads to low blood flow rates. This paper proposes a number of nonlinear mathematical models for the relationship between neural influences (sympathetic nerve activity (SNA)) and renal blood flow, using a feedback path to model the predominantly nonlinear effect of local vasoactive modulators such as nitric oxide, which oppose the action of SNA. The model structures are motivated by basic physiological principles, while the model parameters are determined using numerical optimisation techniques using open-loop data collected from rabbits. The models were verified by demonstrating correlation between experimental results and model outputs.     

Mathematical modeling of the population dynamics of a distinct interactions type system with local dispersal

Distinct biotic interactions in multi-species communities are a ubiquitous force in the natural ecosystem, and this force is an essential determinant of community stability and species coexistence outcomes. We conduct numerical simulations and bifurcation analysis of partial differential equations to gain better understanding and ecological insights into how predation (a), predator handling time (h), and local dispersal affect multi-species community dynamics. This system consists of resource-mutualist-exploiter-competitor interactions and local dispersal. From the inspection of our numerical simulations and co-dimension one bifurcation analysis findings, we discover several critical values that correspond to transcritical bifurcation, subcritical and supercritical Hopf bifurcations. This occurs as we vary the bifurcation parameters a and h in this complex ecological system under symmetric and asymmetric dispersal scenarios. Furthermore, the interplay between these local bifurcation points results in an exciting co-dimension two bifurcations, i.e., Bogdanov-Takens and cusp bifurcation points, respectively, which act as the synchronization points in this complex ecological system. From an ecological viewpoint, we find that (i) the effect of the no-dispersal scenario supports the maintenance of species biodiversity when the predation strength is moderate; (ii) symmetric dispersal induces both subcritical and supercritical Hopf bifurcation and support species diversity for moderate predation strength; and (iii) asymmetric dispersal promotes species diversity as it simplifies the bifurcation changes in dynamics by eliminating the subcritical bifurcations that trigger uncertainty, and this dispersal mechanism mediates species coexistence outcomes. Fundamentally, stable limit cycles have been reported as predator handling time varies in some ecological models; however, we observed in our bifurcation analysis the emergence of the unstable limit cycle as predator handling time changes. We discover that intense predator handling time destabilizes this complex ecological community. In general, our results demonstrate the influential roles of predation, predator handling time, and local dispersal in determining this system’s coexistence dynamics. This knowledge provides a better understanding of species conservation and biological control management.     

Modeling heterogeneity in nest survival data

Current statistical methods for estimating nest survival rates assume that nests are identical in their propensity to succeed. However, there are several biological reasons to question this assumption. For example, experience of the nest builder, number of nest helpers, genetic fitness of individuals, and site effects may contribute to an inherent disparity between nests with respect to their daily mortality rates. Ignoring such heterogeneity can lead to incorrect survival estimates. Our results show that constant survival models can seriously underestimate overall survival in the presence of heterogeneity. This paper presents a flexible random-effects approach to model heterogeneous nest survival data. We illustrate our methods through data on redwing blackbirds.     

Numerical simulations of surface plasmon resonance system for monitoring DNA hybridization and detecting protein-lipid film interactions

This paper presents a simple method to extract information about thin organic films from surface plasmon resonance (SPR) spectra. From numerical simulations it was found that a shift (Δθ _SPR) of an absorption peak in the SPR spectrum was directly proportional to the product of the thin organic film thickness and the refractive index difference between the thin organic film and a buffer soaking the sample. It was also found that Δθ _SPR was not sensitive to the thin organic film support of a gold film and a glass cover slip. Relationships between Δθ _SPR and distributions of macromolecule structures, in the thin organic films were theoretically established. Formulae were derived for a homemade SPR system to calculate length, transverse area, density and surface concentration of macromolecules in the thin organic film. The validity of these treatments was checked by precisely measuring the size of a single distearoylphosphatidylcholine molecule on a gold-supported phospholipid film; by quantitatively monitoring hybridization of synthesized oligonucleotides strands based on a biotin/avidin system; and by quantitatively detecting the steric hindrance of rabbit C-reactive protein specifically bound to phospholipid monolayers composed of synthesized lipids. Received: 4 May 1998 / Revised version: 27 July 1998 / Accepted: 27 August 1998     

Optimal HIV treatment by maximising immune response

We present an optimal control model of drug treatment of the human immunodeficiency virus (HIV). Our model is based upon ordinary differential equations that describe the interaction between HIV and the specific immune response as measured by levels of natural killer cells. We establish stability results for the model. We approach the treatment problem by posing it as an optimal control problem in which we maximise the benefit based on levels of healthy CD4+ T cells and immune response cells, less the systemic cost of chemotherapy. We completely characterise the optimal control and compute a numerical solution of the optimality system via analytic continuation.Research supported by the Natural Science and Engineering Research Council (NSERC) and the Mathematics of Information Technology and Complex Systems (MITACS) of Canada     

Short-term changes in consumption and oviposition rates of Neoseiulus californicus strains (Acari: Phytoseiidae) after a diet shift

Short-term effects on consumption and oviposition rates of four strainsof Neoseiulus californicus (McGregor) after a diet shiftwere evaluated. The new feeding conditions experienced by the predators weresixfixed densities of eggs or protonymphs of Tetranychusurticae Koch placed on excised strawberry leaflet discs andmaintained under laboratory conditions (25±1°C,75–85% RH, 16L: 8D). The observations were made on the first and thefifthday of the experiment. The phytoseiids came from three long-term mass-rearedstrains fed on T. urticae, Dermatophagoides farinaeHughes,or Quercus spp. pollen, respectively. The fourth strainwascollected directly in a strawberry field. Time since diet transfer can be addedto the factors (i.e. feeding history and prey density) already known to affectthe functional and numerical responses of N. californicus,both when it feeds on prey eggs and protonymphs. If consumption rates wereaveraged over all strains and densities, 9.04 and 11.41 eggs, and 6.97 and 6.48protonymphs were consumed on the first and the fifth day, respectively. If thesame was done for oviposition rates, predators feeding on eggs produced 1.46and2.36 eggs/female/day, whereas predators feeding on protonymphs produced 1.35and2.29 eggs/female/day. Time had the greatest impact on the functional responseofthe strain that had previously fed on tetranychids, while an effect of time onthe numerical response was detectable in all strains.     

Magnesium gating of cardiac gap junction channels

We aimed to study kinetics of modulation by intracellular Mg²⁺ of cardiac gap junction (Mg²⁺ gate). Paired myocytes of guinea-pig ventricle were superfused with solutions containing various concentrations of Mg²⁺. In order to rapidly apply Mg²⁺ to one aspect of the gap junction, the non-junctional membrane of one of the pair was perforated at nearly the connecting site by pulses of nitrogen laser beam. The gap junction conductance (G_j) was measured by clamping the membrane potential of the other cell using two-electrode voltage clamp method. The laser perforation immediately increased G_j, followed by slow G_j change with time constant of 3.5 s at 10 mM Mg²⁺. Mg²⁺ more than 1.0 mM attenuated dose-dependently the gap junction conductance and lower Mg²⁺ (0.6 mM) increased G_j with a Hill coefficient of 3.4 and a half-maximum effective concentration of 0.6 mM. The time course of G_j changes was fitted by single exponential function, and the relationship between the reciprocal of time constant and Mg²⁺ concentration was almost linear. Based on the experimental data, a mathematical model of Mg²⁺ gate with one open state and three closed states well reproduced experimental results. One-dimensional cable model of thirty ventricular myocytes connected to the Mg²⁺ gate model suggested a pivotal role of the Mg²⁺ gate of gap junction under pathological conditions.     

A Mathematical Framework for Modeling Axon Guidance

In this paper, a simulation tool for modeling axon guidance is presented. A mathematical framework in which a wide range of models can been implemented has been developed together with efficient numerical algorithms. In our framework, models can be defined that consist of concentration fields of guidance molecules in combination with finite-dimensional state vectors. These vectors can characterize migrating growth cones, target neurons that release guidance molecules, or other cells that act as sources of membrane-bound or diffusible guidance molecules. The underlying mathematical framework is presented as well as the numerical methods to solve them. The potential applications of our simulation tool are illustrated with a number of examples, including a model of topographic mapping.