An integral dynamic model for the UASB reactor

In this article a dynamic model of a continuous working UASB reactor is described. It results from the integration of the fluid flow pattern in the reactor, the kinetic behavior of the bacteria (where inhibition and limitation were taken into account), and the mass transport phenomena between different compartments and different phases. The mathematical equations underlying the model and describing the important mechanisms were programmed and prepared for computations and simulations by computer. The settler efficiency has to be over 99% to prevent the reactor from wash-out. When the settler efficiency is over 99%, the total sludge content of the reactor increases steadily, so the reactor is hardly ever in a steady state. This implies dynamic modeling. The model is able to predict the various observable and nonobservable or difficult to observe state variables, e.g., the sludge bed height, the sludge blanket concentration, the short-circuiting flows over bed and blanket, and the effluent COD concentration as a function of the hydrodynamic load, COD load, pH, and settler efficiency. The optimal pH value is between 6.0 and 8.0; fatty acid shock loadings are difficult to handle outside this optimal pH range.     

An equivalence result for integral equations with application to branching processes

A theorem is proved, concerning expected values of a multitype branching process in a varying environment. The consequence of the theorem is that the branching process can be treated (in the sense of expected values) as a dynamical system with control terms. This is of importance in situations where the process serves as an abstract model of the dynamics of malignant cells for use in chemotherapy. A simple example of this kind is given. Work supported by the Polish Academy of Sciences Research Problem No. 10.4.3.01.4.     

An axisymmetric single-path model for gas transport in the conducting airways

In conventional one-dimensional single-path models, radially averaged concentration is calculated as a function of time and longitudinal position in the lungs, and coupled convection and diffusion are accounted for with a dispersion coefficient. The axisymmetric single-path model developed in this paper is a two-dimensional model that incorporates convective-diffusion processes in a more fundamental manner by simultaneously solving the Navier-Stokes and continuity equations with the convection-diffusion equation. A single airway path was represented by a series of straight tube segments interconnected by leaky transition regions that provide for flow loss at the airway bifurcations. As a sample application, the model equations were solved by a finite element method to predict the unsteady state dispersion of an inhaled pulse of inert gas along an airway path having dimensions consistent with Weibel's symmetric airway geometry. Assuming steady, incompressible, and laminar flow, a finite element analysis was used to solve for the axisymmetric pressure, velocity and concentration fields. The dispersion calculated from these numerical solutions exhibited good qualitative agreement with the experimental values, but quantitatively was in error by 20%-30% due to the assumption of axial symmetry and the inability of the model to capture the complex recirculatory flows near bifurcations.     

An application of the micropipette technique to the measurement of the mechanical properties of cultured bovine aortic endothelial cells

The mechanical properties of endothelial cells were measured using the micropipette technique. The cells employed were collected from bovine aortic endothelium and cultured in our laboratory. Endothelial cells from confluent monolayers under no-flow conditions were detached from their substrate by trypsin or by a mechanical method and suspended in modified Dulbecco medium (MDM). In the micropipette technique, a part of the cell is aspirated into the tip of the micropipette under a microscope, and the deformation measured from a photograph. In this study, the data obtained were analyzed using a model where the cytoskeletal elements, which are considered to be the primary stress bearing components, are assumed to reside in a submembranous, cortical layer. Detached cells were found to have almost homogeneous mechanical properties based on measurements from different regions of the surface of a single cell. However, a hysteresis loop was observed in the relation between pressure and cell deformation during the loading and unloading processes. The calculated elastic shear moduli obtained for the trypsin-detached cells were as much as 10-20 times larger than those of a red blood cell. Mechanically-detached cells had moduli approximately twice that of the trypsin detached cells. Passage time, i.e., cell culture age, had no influence on the mechanical properties of the trypsin-detached cells, but did have an effect on the mechanically-detached cells, with both the younger and older cells being somewhat stiffer.     

An integral equation model for the control of a smallpox outbreak

An integral equation model of a smallpox epidemic is proposed. The model structures the incidence of infection among the household, the workplace, the wider community and a health-care facility; and incorporates a finite incubation period and plausible infectivity functions. Linearisation of the model is appropriate for small epidemics, and enables analytic expressions to be derived for the basic reproduction number and the size of the epidemic. The effects of control interventions (vaccination, isolation, quarantine and public education) are explored for a smallpox epidemic following an imported case. It is found that the rapid identification and isolation of cases, the quarantine of affected households and a public education campaign to reduce contact would be capable of bringing an epidemic under control. This could be used in conjunction with the vaccination of healthcare workers and contacts. Our results suggest that prior mass vaccination would be an inefficient method of containing an outbreak.     

Solving a combinatorial problem via self-organizing process: An application of the Kohonen algorithm to the traveling salesman problem

We present an application of the Kohonen algorithm to the traveling salesman problem: Using only this algorithm, without energy function nor any parameter choosen ad hoc, we found good suboptimal tours. We give a neural model version of this algorithm, closer to classical neural networks. This is illustrated with various numerical examples.     

Using empirical social contact data to model person to person infectious disease transmission: An illustration for varicella

With the aim to improve dynamic models for infections transmitted predominantly through non-sexual social contacts, we compared three popular model estimation methods in how well they fitted seroprevalence data and produced estimates for the basic reproduction number R₀ and the effective vaccination level required for elimination of varicella. For two of these methods, interactions between age groups were parameterized using empirical social contact data whereas for the third method we used the current standard approach of imposing a simplifying structure on the ‘Who Acquires Infection From Whom’ (WAIFW) matrix. The first method was based on solving a set of differential equations to obtain an equilibrium value of the proportion of susceptibles. The second method was based on finding a solution for the age-specific force of infection using the formula of the mass action principle by means of iteration. Both solutions were contrasted with observed age-specific seroprevalence data. The best fit of the WAIFW matrix was obtained with contacts involving touching, and lasting longer than 15 min per day. Plausible values for R₀ for varicella in Belgium ranged from 7.66 to 13.44. Both approaches based on empirical social contact data provided a better fit to seroprevalence data than the current standard approach.     

EpiFire: An open source C++ library and application for contact network epidemiology

ABSTRACT: BACKGROUND: Contact network models have become increasingly common in epidemiology, but we lack a flexible programming framework for the generation and analysis of epidemiological contact networks and for the simulation of disease transmission through such networks. RESULTS: Here we present EpiFire, an applications programming interface and graphical user interface implemented in C++, which includes a fast and efficient library for generating, analyzing and manipulating networks. Network-based percolation and chain-binomial simulations of susceptible-infected-recovered disease transmission, as well as traditional non-network mass-action simulations, can be performed using EpiFire. CONCLUSIONS: EpiFire provides an open-source programming interface for the rapid development of network models with a focus in contact network epidemiology. EpiFire also provides a point-and-click interface for generating networks, conducting epidemic simulations, and creating figures. This interface is particularly useful as a pedagogical tool.     

A systems biology approach to the blood-aluminium problem: the application and testing of a computational model

Transport and distribution of systemic aluminium are influenced by its interaction with blood. Current understanding is centred upon the role played by the iron transport protein transferrin which has been shown to bind up to 90% of serum total aluminium. We have coined what we have called the blood-aluminium problem which states that the proportion of serum aluminium which, at any one moment in time, is bound by transferrin is more heavily influenced by kinetic constraints than thermodynamic equilibria with the result that the role played by transferrin in the transport and distribution of aluminium is likely to have been over estimated. To begin to solve the blood-aluminium problem and therewith provide a numerical solution to the aforementioned kinetic constraints we have applied and tested a simple computational model of the time-dependency of a putative transferrin ligand (L) binding aluminium to form an Al-L complex with a probability of existence, K(E), between 0% (no complex) and 100% (complex will not dissociate). The model is based upon the principles of a lattice-gas automaton which when ran for K(E) in the range 0.1-98.0% demonstrated the emergence of complex behaviour which could be defined in the terms of a set of parameters (equilibrium value, E(V), equilibrium time, E(T), peak value, P(V), peak time, P(T), area under curve, AUC) the values of which varied in a predictable way with K(E). When K(E) was set to 98% the model predicted that ca. 90% of the total aluminium would be bound by transferrin within ca. 350 simulation timesteps. We have used a systems biology approach to develop a simple model of the time-dependency of the binding of aluminium by transferrin. To use this approach to begin to solve the blood-aluminium problem we shall need to increase the complexity of the model to better reflect the heterogeneity of a biological system such as the blood.     

A new approach to the solution of the linear mixing model for a single isotope: application to the case of an opportunistic predator

Mixing models are used to determine diets where the number of prey items are greater than one, however, the limitation of the linear mixing method is the lack of a unique solution when the number of potential sources is greater than the number (n) of isotopic signatures +1. Using the IsoSource program all possible combinations of each source contribution (0–100%) in preselected small increments can be examined and a range of values produced for each sample analysed. We propose the use of a Moore Penrose (M-P) pseudoinverse, which involves the inverse of a 2×2 matrix. This is easily generalized to the case of a single isotope with (p) prey sources and produces a specific solution. The Antarctic leopard seal (Hydrurga leptonyx) was used as a model species to test this method. This seal is an opportunistic predator, which preys on a wide range of species including seals, penguins, fish and krill. The M-P method was used to determine the contribution to diet from each of the four prey types based on blood and fur samples collected over three consecutive austral summers. The advantage of the M-P method was the production of a vector of fractions f for each predator isotopic value, allowing us to identify the relative variation in dietary proportions. Comparison of the calculated fractions from this method with means from IsoSource allowed confidence in the new approach for the case of a single isotope, N.     

A torsion pendulum for measurement of the viscoelasticity of biopolymers and its application to actin networks

This report describes the design, construction, and method of operation of a torsion pendulum which is specifically designed for the measurement of soft and fragile biopolymer gels. The pendulum can be assembled and employed in a standard biological laboratory and provides data that currently require access to specialized equipment usually limited to physics or material science laboratories. This instrument measures the shear moduli of viscoelastic materials by applying either steady or oscillating shear forces to a disc-shaped sample and measuring the resulting angular displacement of a pendulum attached to one face of the sample. The device is easily constructed using commercially available materials and no specialized machinery. Shear stresses as low as 0.03 Pa and shear rates as low as 0.00003 s-1 can be measured in steady shear experiments, and dynamic shear moduli from 1 to 2500 Pa measured by oscillatory measurements with sample volumes as low as 0.5 ml. The use of the torsion pendulum is illustrated by measuring the effects of two different actin binding proteins on the viscoelasticity of actin filament networks.     

An extended biphasic model for charged hydrated tissues with application to the intervertebral disc

Finite element models for hydrated soft biological tissue are numerous but often exhibit certain essential deficiencies concerning the reproduction of relevant mechanical and electro-chemical responses. As a matter of fact, singlephasic models can never predict the interstitial fluid flow or related effects like osmosis. Quite a few models have more than one constituent, but are often restricted to the small-strain domain, are not capable of capturing the intrinsic viscoelasticity of the solid skeleton, or do not account for a collagen fibre reinforcement. It is the goal of this contribution to overcome these drawbacks and to present a thermodynamically consistent model, which is formulated in a very general way in order to reproduce the behaviour of almost any charged hydrated tissue. Herein, the Theory of Porous Media (TPM) is applied in combination with polyconvex Ogden-type material laws describing the anisotropic and intrinsically viscoelastic behaviour of the solid matrix on the basis of a generalised Maxwell model. Moreover, other features like the deformation-dependent permeability, the possibility to include inhomogeneities like varying fibre alignment and behaviour, or osmotic effects based on the simplifying assumption of Lanir are also included. Finally, the human intervertebral disc is chosen as a representative for complex soft biological tissue behaviour. In this regard, two numerical examples will be presented with focus on the viscoelastic and osmotic capacity of the model.     

An application of Lacker's mathematical model for the prediction of ovarian response to superstimulation

Introduction. A mathematical model of ovarian follicular growth is applied to the problem of predicting ovarian response in a superstimulation protocol. Methods. Fifty-four women enrolled in an ovarian superstimulation program of therapy for the amelioration of idiopathic infertility had their ovarian cycles synchronized by taking Demulen 30 for two weeks prior to the study. Daily ultrasonographic imaging, measurements of serum estradiol and doses of hMG began on day 5 after the patients stopped taking Demulen. The diameters of individual follicles were measured and followed daily. When the largest follicle attained a diameter of 19 mm, hCG was given to induce ovulation. Individual follicle growth data were fit to a mathematical model of ovarian follicle maturation and the resulting parameters were used to classify patients into low and high ovarian response groups. Results. The parameters computed from the mathematical model fit were found to be predictive of ovarian response with a sensitivity of 71% and a specificity of 70%. The parameters were also meaningful within the context of the original mathematical model and have value for determining how doses of hMG may be adjusted during the course therapy to increase the ovarian response in individuals. Conclusion. Mathematical modeling of ultrasonographically derived follicular growth data has significant potential for clinical application in ovarian superstimulation protocols. The method of fitting follicular growth data to a mathematical follicle maturation surface furthermore provides a straightforward approach for the characterization of ovarian follicular dynamics in general.     

An immunocytochemical method for histamine: application to the planarians

Histamine-immunoreactivity was investigated in the planarians Dugesia tigrina and Polycelis nigra. Specific antisera against a histamine-protein conjugate were used, and 1-ethyl—3 (3-dimethyl-aminopropyl) carbodiimide was used both as coupling agent to prepare the antigen and as a tissue fixative. In D. tigrina, histamine-immunoreactivity was restricted to photoreceptor cells in the cerebral eye. In P. nigra, nerve fibers were found in the ventral nerve cord and nerves running laterally from these. The epidermal eyes did not display histamine-immunoreactivity. The results suggest that histamine may be a transmitter in some of the most primitive animals. They also suggest that the distribution of histamine may differ in planarians.