An integrated model of Plasmodium falciparum dynamics

The within-host and between-host dynamics of malaria are linked in myriad ways, but most obviously by gametocytes, the parasite blood forms transmissible from human to mosquito. Gametocyte dynamics depend on those of non-transmissible blood forms, which stimulate immune responses, impeding transmission as well as within-host parasite densities. These dynamics can, in turn, influence antigenic diversity and recombination between genetically distinct parasites. Here, we embed a differential-equation model of parasite-immune system interactions within each of the individual humans represented in a discrete-event model of Plasmodium falciparum transmission, and examine the effects of human population turnover, parasite antigenic diversity, recombination, and gametocyte production on the dynamics of malaria. Our results indicate that the local persistence of P. falciparum increases with turnover in the human population and antigenic diversity in the parasite, particularly in combination, and that antigenic diversity arising from meiotic recombination in the parasite has complex differential effects on the persistence of founder and progeny genotypes. We also find that reductions in the duration of individual human infectivity to mosquitoes, even if universal, produce population-level effects only if near-absolute, and that, in competition, the persistence and prevalence of parasite genotypes with gametocyte production concordant with data exceed those of genotypes with higher gametocyte production. This new, integrated approach provides a framework for investigating relationships between pathogen dynamics within an individual host and pathogen dynamics within interacting host and vector populations.     

A mathematical model of blood,cerebrospinal fluid and brain dynamics

Using first principles of fluid and solid mechanics a comprehensive model of human intracranial dynamics is proposed. Blood, cerebrospinal fluid (CSF) and brain parenchyma as well as the spinal canal are included. The compartmental model predicts intracranial pressure gradients, blood and CSF flows and displacements in normal and pathological conditions like communicating hydrocephalus. The system of differential equations of first principles conservation balances is discretized and solved numerically. Fluid–solid interactions of the brain parenchyma with cerebral blood and CSF are calculated. The model provides the transitions from normal dynamics to the diseased state during the onset of communicating hydrocephalus. Predicted results were compared with physiological data from Cine phase-contrast magnetic resonance imaging to verify the dynamic model. Bolus injections into the CSF are simulated in the model and found to agree with clinical measurements.

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An integrated model of cardiac mitochondrial energy metabolism and calcium dynamics

We present an integrated thermokinetic model describing control of cardiac mitochondrial bioenergetics. The model describes the tricarboxylic acid (TCA) cycle, oxidative phosphorylation, and mitochondrial Ca(2+) handling. The kinetic component of the model includes effectors of the TCA cycle enzymes regulating production of NADH and FADH(2), which in turn are used by the electron transport chain to establish a proton motive force (Delta mu(H)), driving the F(1)F(0)-ATPase. In addition, mitochondrial matrix Ca(2+), determined by Ca(2+) uniporter and Na(+)/Ca(2+) exchanger activities, regulates activity of the TCA cycle enzymes isocitrate dehydrogenase and alpha-ketoglutarate dehydrogenase. The model is described by twelve ordinary differential equations for the time rate of change of mitochondrial membrane potential (Delta Psi(m)), and matrix concentrations of Ca(2+), NADH, ADP, and TCA cycle intermediates. The model is used to predict the response of mitochondria to changes in substrate delivery, metabolic inhibition, the rate of adenine nucleotide exchange, and Ca(2+). The model is able to reproduce, qualitatively and semiquantitatively, experimental data concerning mitochondrial bioenergetics, Ca(2+) dynamics, and respiratory control. Significant increases in oxygen consumption (V(O(2))), proton efflux, NADH, and ATP synthesis, in response to an increase in cytoplasmic Ca(2+), are obtained when the Ca(2+)-sensitive dehydrogenases are the main rate-controlling steps of respiratory flux. These responses diminished when control is shifted downstream (e.g., the respiratory chain or adenine nucleotide translocator). The time-dependent behavior of the model, under conditions simulating an increase in workload, closely reproduces experimentally observed mitochondrial NADH dynamics in heart trabeculae subjected to changes in pacing frequency. The steady-state and time-dependent behavior of the model support the hypothesis that mitochondrial matrix Ca(2+) plays an important role in matching energy supply with demand in cardiac myocytes.     

An integrated scheduling and control model for multi-mode projects

In today’s highly competitive uncertain project environments, it is of crucial importance to develop analytical models and algorithms to schedule and control project activities so that the deviations from the project objectives are minimized. This paper addresses the integrated scheduling and control in multi-mode project environments. We propose an optimization model that models the dynamic behavior of projects and integrates optimal control into a practically relevant project scheduling problem. From the scheduling perspective, we address the discrete time/cost trade-off problem, whereas an optimal control formulation is used to capture the effect of project control. Moreover, we develop a solution algorithm for two particular instances of the optimal project control. This algorithm combines a tabu search strategy and nonlinear programming. It is applied to a large scale test bed and its efficiency is tested by means of computational experiments. To the best of our knowledge, this research is the first application of optimal control theory to multi-mode project networks. The models and algorithms developed in this research are targeted as a support tool for project managers in both scheduling and deciding on the timing and quantity of control activities.     

A mathematical treatment of integrated Ca dynamics within the ventricular myocyte

We have developed a detailed mathematical model for Ca2+ handling and ionic currents in the rabbit ventricular myocyte. The objective was to develop a model that: 1), accurately reflects Ca-dependent Ca release; 2), uses realistic parameters, particularly those that concern Ca transport from the cytosol; 3), comes to steady state; 4), simulates basic excitation-contraction coupling phenomena; and 5), runs on a normal desktop computer. The model includes the following novel features: 1), the addition of a subsarcolemmal compartment to the other two commonly formulated cytosolic compartments (junctional and bulk) because ion channels in the membrane sense ion concentrations that differ from bulk; 2), the use of realistic cytosolic Ca buffering parameters; 3), a reversible sarcoplasmic reticulum (SR) Ca pump; 4), a scheme for Na-Ca exchange transport that is [Na]i dependent and allosterically regulated by [Ca]i; and 5), a practical model of SR Ca release including both inactivation/adaptation and SR Ca load dependence. The data describe normal electrical activity and Ca handling characteristics of the cardiac myocyte and the SR Ca load dependence of these processes. The model includes a realistic balance of Ca removal mechanisms (e.g., SR Ca pump versus Na-Ca exchange), and the phenomena of rest decay and frequency-dependent inotropy. A particular emphasis is placed upon reproducing the nonlinear dependence of gain and fractional SR Ca release upon SR Ca load. We conclude that this model is more robust than many previously existing models and reproduces many experimental results using parameters based largely on experimental measurements in myocytes.     

A mathematical model of brain glucose homeostasis

Background  

The physiological fact that a stable level of brain glucose is more important than that of blood glucose suggests that the ultimate goal of the glucose-insulin-glucagon (GIG) regulatory system may be homeostasis of glucose concentration in the brain rather than in the circulation.     

An integrated mathematical model for co-composting of agricultural solid wastes with industrial wastewater

An integrated model for the composting process was developed. The structure of the model is such that it can be implemented in any mixture of different substrates, even in the case of co-composting of a solid waste with industrial wastewater. This paper presents a mathematical formulation of the physicochemical and biological principles that govern the composting process. The model of the co-composting ecosystem included mass transfer, heat transfer and biological processes. The biological processes included in the model were hydrolysis of particulate substrates, microbial growth and death. Two microbial populations (bacteria and fungi) were selected using Monod kinetics. Growth limiting functions of inhibitory factors, moisture and dissolved oxygen were added in the Monod kinetics. The bacteria were considered to utilise the easy biodegradable carbon hydrolysis product, fungi the difficult one, while both could degrade the carbon of wastewater. The mass balances of the most important nutrients, nitrogen and phosphorous, were also included in this approach. Model computer simulations provided results that fitted satisfactory the experimental data. Conclusively, the model could be a useful tool for the prediction of the co-composting process performance in the future and could be used to assist in the operation of co-composting plants.     

Diuresis and its hormonal control in butterflies

The sudden weight loss after eclosion in the butterflies Acraea horta, Danaus chrysippus and Papilio demodocus is largely due to diuresis. The potassium concentration of the haemolymph is approximately halved as a result, and extensive diuresis leads to increases in sodium concentration and total osmolarity. The isolated Malpighian tubules of all three species are stimulated to fast rates of fluid secretion by cyclic AMP and by homogenates of the brains and corpora cardiaca. The tubules of Papilio lose their sensitivity to stimulation after the first day of adult life, and ingestion of a large volume of artificial nectar by this butterfly does not cause diuresis.     

Nutritional and hormonal control of glucose and fructose utilization by lung

Whereas glucose is a major substrate for pulmonary lipid synthesis, fructose has also been suggested as a potential substrate. In vivo pulmonary fatty acid synthesis is depressed in hormonally deprived conditions, such as diabetes, and this can be modified by fructose feeding, but not by glucose feeding. In this study the glucose and fructose utilizations were compared in normal, diabetic and fasting states using isolated perfused rat lungs. When (U-14C)- or (5-3H)-glucose was used as substrate, glucose utilization by lung was reduced by 50% in both the fasting and diabetic animals compared to the normal controls. Using (U-14C)-glucose as substrate, the incorporation of (14C)-label in various metabolites of glucose was significantly depressed. For example, this reduction was 50% in lactate, pyruvate and CO2, 15% in ethanol-insoluble fraction, 65% in neutral lipids, 75% in phospholipids, 80% in fatty acid moiety, 40% in deacylated fraction and 10% in the polysaccharide fractions. Refeeding the fasted animals or insulin treatment to the diabetic animals restored these depressed (14C)-recoveries to the normal levels. Fructose utilization was less than 10% of glucose utilization, but remained unaffected by fasting and diabetic states. In addition, pulmonary hexokinase enzyme activity was lowered significantly in fasting and diabetic animals, whereas fructokinase enzyme activity was not altered. Despite the low rate of fructose utilization, these results suggest that fructose may serve as an alternative substrate for pulmonary phospholipid synthesis when glucose utilization is significantly depressed.     

A mathematical model of the dynamics of granulocytopoiesis in mammals

A mathematical model has been developed for the dynamics of granulocytopoiesis in mammals subjected to chronic irradiation. The model involves a chalones mechanism of haemopoiesis regulation and comprises 12 nonlinear differential equations. The simulation results agree with the experimental data concerning the dynamics of granulocytopoiesis in rats affected by radiation within a wide range of dose rates.     

A mathematical model of the dynamics of odontogenic cyst growth

OBJECTIVE: To formulate a mathematical model of odontogenic cyst growth and establish the dynamics of cyst enlargement and role of osmotic pressure forces throughout its growth. STUDY DESIGN: The model assumed a spherical cyst with a semipermeable lining of living cells and a core consisting of degraded cellular material, including generic osmotic material, fed by the continuous death of epithelial cells in the lining. The lining cells were assumed to have both elastic and viscous properties, reflecting the action of physical stresses by the surrounding cyst capsule, composed of fibroblasts and collagen fibers. The model couples the cyst radius and osmotic pressure differences resulting in a system of 2 nonlinear ordinary differential equations. RESULTS: The model predicts that in all parameter regimens the long-time behavior of the cyst is the same and that linear radial expansion results. CONCLUSION: In the early and intermediate stages of cystic growth, osmotic pressure differences play an important role; however, in very large cysts, this role becomes negligible, and cell birth in the lining dominates growth.     

A mathematical model for the population dynamics of army ants

A stochastic cellular automata model for the population dynamics of the army antEciton burchelli on Barro Colorado Island in Panama is set up. It is simulated on the computer and shown to give good agreement with biological data. It is analysed using two approximations akin to the mean field approximation in statistical mechanics, and good agreement with the simulations is obtained. Finally, the role of distance between successive statary phase bivouacs is discussed with regard to the rate of colony growth. There are two aspects of the biological system studied here that make it of general importance. First, the population is structured, since the size of each colony of army ants is crucial. Second, the spatial behaviour of the population, as in many others, is not diffusion-like, although it is random. This has implications for the kind of model that is chosen.     

A mathematical model for the decay of conserved blood

In the present paper a simple model is presented by means of which a decay of stored blood can be predicted. The following factors are incorporated in the calculation: The relation of the depot stock to the average number of cross matchings per day, the probability of transfusions, the time reserved for crossed stored blood and that which is not transfused as well as the percentage of stored blood already reserved when arriving at the depot.     

A mathematical model for dynamics of CD40 clustering

Ligand bound-receptors in a signalosome complex trigger signals to determine cellular functions. Upon ligand binding, the ligand–receptor complexes form clusters on cell membrane. Guided by the previous experimental reports on the cluster formation of CD40, a trans membrane receptor for CD40-ligand, we built a minimal model of the receptor cluster formation. In this model, we studied co-operative and non-co-operative clustering of a maximum of four CD40 molecules assuming a positive mediator of clustering such as cholesterol to be present in both cases. We observed that co-operative interactions between CD40 molecules resulted in more of the largest CD40 clusters than that observed with the non-co-operatively interacting CD40 molecules. We performed global sensitivity analysis on the model parameters and the analyses suggested that cholesterol influenced only the initial stage of the co-operatively clustering CD40 molecules but it affects both the initial and the final stages in case of the non-co-operatively clustering CD40 molecules. Robustness analyses revealed that in both co-operative and non-co-operative interactions, the higher order clusters beyond a critical size are more robust with respect to alterations in the environmental parameters including the cholesterol. Thus, the role of co-operative and non-co-operative interactions in environment-influenced receptor clustering is reported for the first time.     

Analysis of the nonlinear heart rate dynamics by two-contour mathematical model

Using a two-contour mathematical model, changes in the degree of heart rate variability induced by an increased extracardial impulsation in the sinoatrial node have been studied. The model is based on quantitative characteristics of impulse conduction in the cardiac conduction system. A mathematical and computer modeling revealed the following three regimes of heart rate variability: linear dynamics, the 1st-degree chaos, and the 2nd-degree chaos. Transitions between these regimes have been studied. A comparative analysis of the one- and two-contour models of heart rate regulation has been performed.     

An age-dependent feedback control model of calcium dynamics in yeast cells

The functional decline of selected proteins or organelles leads to aging at the intracellular level. Identification of these proteins or organelles is usually challenging to traditional single-factor approaches since these factors are inter-connected via feedback or feedforward controls. Establishing a feedback control model to simulate the interactions of multiple factors is an insightful approach to guide the search for proteins involved in aging. However, there are only a few mathematical models describing the age-dependent accumulation of DNA mutations, which are directly or indirectly induced by deterioration of the intracellular environment including alteration of calcium homeostasis, a contributor of aging. Thus, based on Cui and Kaandorp’s model, we develop an age-dependent mathematical model for the calcium homeostasis in budding yeast Saccharomyces cerevisiae. Our model contains cell cycle-dependent aging factors and can qualitatively reproduce calcium shocks and calcium accumulations in cells observed in experiments. Using this model, we predict calcium oscillations in wild type, pmc1Δ, and pmr1Δ cells. This prediction suggests that Pmr1p plays a major role in regulating cytosolic calcium. Combining the model with our experimental lifespan data, we predict an upper-limit of cytosolic calcium tolerance for cell survival. This prediction indicates that, for aged cells (>35 generations), no pmr1 Δ can tolerate the cytosolic calcium concentration of 0.1 μM while a very small fraction (1%) of aged wild type cells (>50 generations) can tolerate a high cytosolic calcium concentration of 0.5 μM.     

An integrated model of thermodynamic-hemodynamic-pharmacokinetic system and its application on decoupling control of intracranial temperature and pressure in brain hypothermia treatment

Brain hypothermia treatment (BHT) is an intensive care characterized by simultaneous managements of various vital signs, such as intracranial temperature (ICT) and pressure (ICP), of the severe neuropatient. Medical treatments including therapeutic ambient cooling and diuresis are separately carried out based on the experience of the medical staff involved in the clinical management of various pathophysiological processes, such as thermodynamics, hemodynamics and pharmacokinetics. However, no special attention has been paid to the interactions among these subsystems in therapeutic hypothermia because of the lack of theoretical knowledge. Therefore, quantitative analyses using an integrated model of various physiological processes and their interactions are of pressing need. In the present paper, we propose a general compartmental model to describe the pathophysiological processes of the three aforementioned dynamics, on account of the dynamical analogy of temperature, pressure and concentration. The model is verified by the agreement of model-based simulation results with clinical evidence. Based on responses of the integrated model to various stimuli, a transfer function matrix is identified to linearly approximate the characteristic interrelationships between medical treatments (ambient cooling and diuresis) and the vital signs (ICT and ICP). Then a controller that decouples ambient cooling and diuresis is proposed for efficient management of ICT and ICP, enhancement of hypothermic decompression and reduction of diuretic dosage. Decoupling control simulation indicates that ICT and ICP of the integrated model, representing a patient under BHT, can be simultaneously regulated by a single PID controller for ambient cooling and another for diuresis. The proposed decoupler effectively establishes hypothermic decompression, reduces the dosage of diuretic and improves ICP management. Theoretical analyses of the integrated model and decoupling control of ICT and ICP provide insights into the intensive care of various pathophysiological processes in patients undergoing BHT.