An engineering approach to modelling, decision support and control for sustainable systems

Engineering research and development contributes to the advance of sustainable agriculture both through innovative methods to manage and control processes, and through quantitative understanding of the operation of practical agricultural systems using decision models. This paper describes how an engineering approach, drawing on mathematical models of systems and processes, contributes new methods that support decision making at all levels from strategy and planning to tactics and real-time control. The ability to describe the system or process by a simple and robust mathematical model is critical, and the outputs range from guidance to policy makers on strategic decisions relating to land use, through intelligent decision support to farmers and on to real-time engineering control of specific processes. Precision in decision making leads to decreased use of inputs, less environmental emissions and enhanced profitability-all essential to sustainable systems.     

A rule-based approach to the modelling of bacterial ecosystems

This paper presents an approach to ecological/evolutionary modelling that is inspired by natural bacterial ecosystems and bacterial evolution. An individual-based artificial ecosystem model is proposed, which is designed to explore the evolvability of adaptive behavioural strategies in artificial bacteria represented by rule-based learning classifier systems. The proposed ecosystem model consists of a n-dimensional environmental grid, which can contain different types of artificial resources in arbitrary arrangements. The resources provide the energy that is necessary for the organisms to sustain life, and can trigger different types of behaviour in the organisms, such as movement towards nutrients and away from toxic substances, growth, and the controlled release of signalling resources. The balance between energy and material is modelled carefully to ensure that the ecosystem is dissipative. Those organisms that are able to efficiently exploit the available resources gradually accumulate enough energy to reproduce (by binary fission) and generate copies of themselves in the environment. Organisms are also able to produce their own resources, which can potentially be used as markers to send signals to other organisms (a behaviour known as quorum sensing). The complex relationships between stimuli and actions in the organisms are stochastically altered by means of mutations, thus enabling the organisms to adapt to their environment and maximise their lifespan and reproductive success. In this paper, the proposed bacterial ecosystem model is defined formally and its structure is discussed in detail. This is followed by results from simulation experiments that illustrate the model's operation and how it can be used in evolutionary modelling/computing scenarios.     

Stochastic modelling of apoptosis kinetics

Robust quantitative estimation of average whole cell mitochondrial dysfunction is a useful tool for assessing sensitivity to apoptotic stimuli induced either by novel agents, or following manipulation of apoptotic threshold by pharmacological or functional genomics approaches. We have mathematically modelled the kinetics of whole cell mitochondrial membrane potential depolarisation within a population of cells as a Bernouli transition. An exponential distribution enables the median latency preceding mitochondrial membrane potential disispation to be derived. The kinetic model can be fitted to in vitro single cell resolution data derived from kinetic flow cytometric studies by non-linear regression. We propose that kinetic determination of cumulative frequency distibutions provides a useful approach for estimating apoptosis sensitivity across cell populations over short time-frames.     

Mathematical modelling of intra-aortic balloon pump

Background: Ischemic heart diseases now afflict thousands of Iranians and are the major cause of death in many industrialised countries. Mathematical modelling of an intra-aortic balloon pump (IABP) could provide a better understanding of its performance and help to represent blood flow and pressure in systemic arteries before and after inserting the pump.

Methods: A mathematical modelling of the whole cardiovascular system was formulated using MATLAB software. The block diagram of the model consists of 43 compartments. All the anatomical data was extracted from the physiological references. In the next stage, myocardial infarction (MI) was induced in the model by decreasing the contractility of the left ventricle. The IABP was mathematically modelled and inserted in the model in the thoracic aorta I artery just before the descending aorta. The effects of IABP on MI were studied using the mathematical model.

Results: The normal operation of the cardiovascular system was studied firstly. The pressure–time graphs of the ventricles, atriums, aorta, pulmonary system, capillaries and arterioles were obtained. The volume–time curve of the left ventricle was also presented. The pressure–time curves of the left ventricle and thoracic aorta I were obtained for normal, MI, and inserted IABP conditions. Model verification was performed by comparing the simulation results with the clinical observations reported in the literature.

Conclusions: IABP can be described by a theoretical model. Our model representing the cardiovascular system is capable of showing the effects of different pathologies such as MI and we have shown that MI effects can be reduced using IABP in accordance with the modelling results. The mathematical model should serve as a useful tool to simulate and better understand cardiovascular operation in normal and pathological conditions.     

An integrated modelling approach to forecast the impact of human pressure in the Seine estuary

Within the framework of the European Water Framework Directive, the Seine-Normandie Water Agency has defined prospective scenarios describing possible trends of evolution of the pressures on water resources. In order to evaluate the resulting water quality improvement or degradation of water bodies in the Seine river basin, an integrated modelling was proposed. The approach consisted in coupling three models, the seneque model for upstream sub-basins, the ProSe model for the Seine river and main tributaries and finally the s i am1d model for the downstream estuary. After consistency verification, the integrated model was applied to scenarios proposed by the Seine-Normandie Water Agency. As a result of improvement in the nitrogen treatment by waste water treatment plants, the annual load of ammonia at the basin scale will be reduced by 65%. The oxygen and ammonia criteria in the estuary will improve from “bad” to “good”. However the nitrate criteria will remain “poor”, given the strong influence of non-point sources. Despite a 70–75% drop of the point orthophosphate loads, the criteria for this variable will also remain “poor”. The nutrient levels will be high enough to maintain eutrophication in the system; a general trend to a shift from N-limitation to P-limitation will be accentuated.     

Mathematical modelling of primary production in Green Bay (Lake Michigan,USA), a phosphorus-and light-limited system

Application of mathematical models in the design and evaluation of lake restoration programmes must include due consideration of three basic concepts of model development; 1) that the model framework is appropriately matched to the intended management use, 2) that selection of the proper degree of model complexity is fundamental to the achievement of model credibility and 3) that field and laboratory studies must be designed and interpreted with the aid of the model to insure development of a comprehensive, integrated tool.These concepts are demonstrated for the case of lake restoration efforts in Green Bay (Lake Michigan, USA). Striking gradients in water quality (transparency, algal standing crop, hypolimnetic oxygen depletion) and trophic state occur along the major axis of the bay in response to phosphorus loaded from the Fox River. A simple model for gross primary production is developed to permit calculation of the relative importance of internal carbon production to the total organic carbon budget of the bay. Primary production varies from high rates over a limited photic depth in the turbid, phosphorus-rich waters of the eutrophic portions of the bay to low rates over an extensive photic depth in the transparent, phosphoruspoor reaches of the oligotrophic regions. Internal production accounts for approximately 90% of the total organic carbon loaded to the system over the summer growing season. Water quality management strategies must address the stimulation of primary production by phosphorus loaded from the Fox River in any attempt to lower the standing crop of nuisance algae, improve water clarity, and reduce rates of hypolimnetic oxygen depletion in Green Bay.     

Different modelling tools of aquatic ecosystems: A proposal for a unified approach

Over the last few decades, several modelling tools have been developed for the simulation of hydrodynamic and biogeochemical processes in aquatic ecosystems. Until late 70's, coupling hydrodynamic models to biogeochemical models was not common and today, problems linked to the different scales of interest remain. The time scale of hydrodynamic phenomena in coastal zone (minutes to hours) is much lower than that of biogeochemistry (few days). Over the last years, there has been an increasing tendency to couple hydrodynamic and biogeochemical models in a clear recognition of the importance of incorporating in one model the feedbacks between physical, chemical and biological processes. However, different modelling teams tend to adopt different modelling tools, with the result that benchmarking exercises are sometimes difficult to achieve in projects involving several institutions. Therefore, the objectives of this paper are to provide a quick overview of available modelling approaches for hydrodynamic and biogeochemical modelling, to help people choose among the diversity of available models, as a function of their particular needs, and to propose a unified approach to allow modellers to share software code, based on the object oriented programming potentiality. This approach is based on having object dynamic link libraries that may be linked to different model shells. Each object represents different processes and respective variables, e.g. hydrodynamic, phytoplankton and zooplankton objects. Some simple rules are proposed to link available objects to programs written in different source codes.     

On the mathematical modelling of pain

In this review a case is presented for the use of mathematical modelling in the study of pain. The philosophy of mathematical modelling is outlined and a recommendation is made for the use of modern nonlinear techniques and computational neuroscience in the modelling of pain. Classic and more recent examples of modelling in neurobiology in general and pain in particular, at three different levels—molecular, cellular and neural networks—are described and evaluated. Directions for further progress are indicated, particularly in plasticity and in modelling brain mechanisms. Major advantages of mathematical modelling are that it can handle extremely complex theories and it is non-invasive, and so is particularly valuable in the investigation of chronic pain. Special issue dedicated to Dr. Herman Bachelard     

TRAP: a modelling approach to below-ground carbon allocation in temperate forests

Tree root systems, which play a major role in below-ground carbon (C) dynamics, are one of the key research areas for estimating long-term C cycling in forest ecosystems. In addition to regulating major C fluxes in the present conditions, tree root systems potentially hold numerous controls over forest responses to a changing environment. The predominant contribution of tree root systems to below-ground C dynamics has been given little emphasis in forest models. We developed the TRAP model, i.e. Tree Root Allocation of Photosynthates, to predict the partitioning of photosynthates between the fine and coarse root systems of trees among series of soil layers. TRAP simulates root system responses to soil stress factors affecting root growth. Validation data were obtained from two Belgian experimental forests, one mostly composed of beech (Fagus sylvatica L.) and the other of Scots pine (Pinus sylvestris L.). TRAP accurately predicted (R = 0.88) night-time CO₂ fluxes from the beech forest for a 3-year period. Total fine root biomass of beech was predicted within 6% of measured values, and simulation of fine root distribution among soil layers was accurate. Our simulations suggest that increased soil resistance to root penetration due to reduced soil water content during summer droughts is the major mechanism affecting the distribution of root growth among soil layers of temperate Belgian forests. The simulated annual rate of C input to soil litter due to the fine root turnover of the Scots pine was 207 g C m^–2 yr^–1. The TRAP model predicts that fine root turnover is the single most important source of C to the temperate forest soils of Belgium.     

The dynamics of T-cell fratricide: application of a robust approach to mathematical modelling in immunology

Fratricide between CD8(+) T lymphocytes is known to occur in HTLV-I and possibly HSV-1 and HIV-1 infection. However it is not known what effect, if any, T-cell fratricide has on the course of infection. Here we present simple mathematical techniques to investigate T-cell fratricide with particular reference to HTLV-I infection. Using a general model we predict the qualitative and quantitative effect of fratricide on HTLV-I equilibrium proviral load. We also investigate the effect of fratricide on the probability of viral clearance. We show that, surprisingly, fratricide can lead either to an increase or a decrease in equilibrium proviral load. We derive the conditions necessary for fratricide to cause a decrease in load and deduce that, for the five HTLV-I-positive patients considered here, fratricide has probably caused an increase in equilibrium load. We also estimate the percentage increase in load that is attributable to fratricide and determine the parameters that should be measured in order to improve this estimate. Finally, we show that fratricide reduces the probability of viral clearance. Mathematical modelling of HTLV-I infection, as is often the case in biology, is severely hampered by a lack of experimental data. Consequently it is difficult to know what functional form a model should take. The behaviour of complex nonlinear systems is highly model-dependent. Predictions based on theoretical models are therefore sensitive to the choice of model; this is a very severe problem that undermines and limits the success of the application of mathematics to immunology. In this paper we reduce the model dependency of the results in two ways-by considering (analytically) a general model with a minimal number of assumptions and, where this is not possible, by checking (numerically) that a wide range of models yield the same results. We therefore begin to develop two practical methods for dealing with the problem of robustness in mathematical models of the immune system.     

Current status of immunology research in India

Rudimentary studies on aspects of biochemistry in India date back to 1927. But, in the field of Immunology, such studies were started by scholars only during early 1970s at the All India Institute of Medical Sciences, New Delhi, India. Science and Technology was not an immediate priority until 1961 due to domestic and political conditions in the country. We were then 11 years old since independence and our focus was on economic and social developments. Gradually, improvements were made in the field and now we have 15 to 20 major groups (small in size) of immunologists in the country, who have made significant contribution in the field during the last 8 to 10 years. Hence, we anticipate improvements in manpower and infrastructure in the near future.     

Constitutive modelling of brain tissue: Experiment and theory

Recent developments in computer-integrated and robot-aided surgery—in particular, the emergence of automatic surgical tools and robots—as well as advances in virtual reality techniques, call for closer examination of the mechanical properties of very soft tissues (such as brain, liver, kidney, etc.). The ultimate goal of our research into the biomechanics of these tissues is the development of corresponding, realistic mathematical models. This paper contains experimental results of in vitro, uniaxial, unconfined compression of swine brain tissue and discusses a single-phase, non-linear, viscoelastic tissue model. The experimental results obtained for three loading velocities, ranging over five orders of magnitude, are presented. The applied strain rates have been much lower than those applied in previous studies, focused on injury modelling. The stress-strain curves are concave upward for all compression rates containing no linear portion from which a meaningful elastic modulus might be determined. The tissue response stiffened as the loading speed increased, indicating a strong stress-strain rate dependence. The use of the single-phase model is recommended for applications in registration, surgical operation planning and training systems as well as a control system of an image-guided surgical robot. The material constants for the brain tissue are evaluated. Agreement between the proposed theoretical model and experiment is good for compression levels reaching 30% and for loading velocities varying over five orders of magnitude.     

A primer on cancer immunology and immunotherapy

The role of immunity in cancer has been abundantly demonstrated in murine tumor models as well as in man. Induction of clinically effective antitumor immune responses, based on this information, in patients with cancer however, remains elusive. This is not because tumors lack recognizable antigens [in fact there is evidence that there are thousands of potential novel targets in each tumor cell] but rather due to the fact that the induction of responses is not adequate nor particularly well understood. Tumors seem to be rather effective at limiting immune responses. Many of the molecularly defined antigens that have been detected on tumor cells are derived from self-proteins and as such are subject to tolerizing mechanisms. Such tumors have also developed escape mechanisms capable of evading or suppressing immune responses. Understanding the role of dendritic cells during the effector phase of the immune response and the complex interactions of stromal, immune, and tumor cells in the tumor microenvironment represent the next challenges to be understood for tumor immunology.This is a summary of the work presented at the First Cancer Immunology and Immunotherapy Summer School, 8–13 September 2003, Ionian Village, Peloponnese, Greece     

An ecophysiological approach to modelling resource fluxes in competing plants

A conceptual model of resource acquisition and allocation within a generalized, individual plant growing vegetatively in competition with others is presented. The model considers C and N acquisition, synthesis of assimilates and their transport and partitioning, growth of new tissues, reserve formation and recycling, and losses due to root exudation and respiration. These processes are regulated by the relative size of the C and N substrate pools in shoot and roots, in relation to meristematic sink strength. Translocation and allocation patterns are represented according to the Minchin phloem transport model. The current model is used to consider the impact of competition on resource acquisition and allocation, first by considering a plant growing in isolation and its response to manipulation of light, CO2 and N supplies. Secondly, competitive plants are introduced and the direct effects on plant responses in terms of resource depletion are considered separately from indirect effects such as potential changes in the quality of resources available (e.g. light quality or soil N sources). In the past, many studies of plant competition have not established the importance of these indirect effects because they have not established all the processes involved in competition. This model can be used to interpret responses of whole plants to their neighbours in terms of the relative importance of both the direct and indirect effects of competition.     

An algorithmic approach to modelling the retinal receptor topography

Based on published research results on the structure of the human retina and the initial assumption of tight hexagonal packing of cones, the mean cone-distance function is derived. Disorder in the cone lattice is explained as the superposition of increasing topological distortion in the hexagonal lattice (providing a possible explanation for observed systematic lattice distortions) and local jitter of neighbor-toneighbor distances, for which a simple statistical model is provided. These individual results are incorporated into a proposed algorithm for simulating the cone receptors' topography in 3D-space. Finally, possible software and hardware applications of the algorithmically defined retina model are briefly touched.     

Modelling the Human Immune System by Combining Bioinformatics and Systems Biology Approaches

Over the past decade a number of bioinformatics tools have been developed that use genomic sequences as input to predict to which parts of a microbe the immune system will react, the so-called epitopes. Many predicted epitopes have later been verified experimentally, demonstrating the usefulness of such predictions. At the same time, simulation models have been developed that describe the dynamics of different immune cell populations and their interactions with microbes. These models have been used to explain experimental findings where timing is of importance, such as the time between administration of a vaccine and infection with the microbe that the vaccine is intended to protect against. In this paper, we outline a framework for integration of these two approaches. As an example, we develop a model in which HIV dynamics are correlated with genomics data. For the first time, the fitness of wild type and mutated virus are assessed by means of a sequence-dependent scoring matrix, derived from a BLOSUM matrix, that links protein sequences to growth rates of the virus in the mathematical model. A combined bioinformatics and systems biology approach can lead to a better understanding of immune system-related diseases where both timing and genomic information are of importance.     

Anhydrobiosis quotient: a novel approach to evaluate stability in desiccated bacterial cells

Aim:  The major objective of this study was the development of a methodology to quantify the anhydrobiotic ability of bacteria and its application to evaluate the stability of desiccated bacterial cells using the biocontrol agent Tsukamurella paurometabola C-924 as a model of anhydrobiote.
Methods and Results:  Tsukamurella paurometabola C-924 was desiccated by spray-drying. Samples of desiccated cells were stored at several temperatures and viability and residual moisture were measured at different intervals of time. The term anhydrobiosis quotient (ε) was defined, and a scale of anhydrobiotic ability for classifying micro-organisms in terms of tolerance to desiccation was established (1 ≤  ε  ≤ 15). The anhydrobiosis quotient was used to evaluate the stability of the anhydrobiotic cells. As a main result, changes in the anhydrobiosis quotient at several temperatures were fitted using a reparameterized Weibull model, which was found to be robust for the prediction of the stability at 4°C.
Conclusions:  A novel methodology was developed to evaluate the desiccated state in bacteria. The anhydrobiosis quotient allows the quantitative estimation of the anhydrobiotic ability, and the mathematical model developed allows the prediction of the desiccated state of bacterial populations.
Significance and Impact of the Study:  The new methodology could be applied in studying the anhydrobiosis state of bacterial populations as a predictive tool for industrial and environmental microbiology.