Mathematical modeling of the human body during water replacement and dehydration: body water changes.

A model of the human body that integrates the variables involved in temperature regulation and blood gas transport within the cardiovascular and respiratory systems is presented here. It expands upon previous work to describe the competition between skin and muscles when both require increased blood flows during exercise and/or heat stress. First, a detailed study of the control relations used to predict skin blood flow was undertaken. Four other control relations employed in the model were also examined and modified as indicated by empirical results found in literature. Internal responses to exercise and/or heat stress can affect both thermoregulation and the cardiorespiratory system. Dehydration was studied in addition to complete water replacement during similar environmental and exercise situations. Control relations for skin blood flow and evaporative heat loss were modified and a water balance was added to study how the loss of water through sweat can be limiting. Runoff from sweating as a function of relative humidity was introduced along with evaporation, and these results were compared to data to validate the model.

Human water, sodium, and calcium regulation during space flight and exercise.

When one is exposed to microgravity, fluid which is normally pooled in the lower extremities is redistributed headward and weight bearing bones begin to demineralize due to reduced mechanical stresses. The kidney, which is the primary regulator of body fluid volume and composition, responds to the fluid shift and bone demineralization by increasing the urinary output of water, sodium, and calcium. This research involves developing a mathematical description of how water and electrolytes are internally redistributed and exchanged with the environment during space flight. This model consequently involves kidney function and the associated endocrine system. The model agrees well with actual data, including that a low sodium diet can prevent bone demineralization. Therefore, assumptions made to develop the model are most likely valid. Additionally, various levels of activity are also considered in the model since exercise may help to eliminate some of the undesired effects of space flight such as muscle atrophy and bone demineralization.

An information theoretic approach for combining neural network process models.

Typically neural network modelers in chemical engineering focus on identifying and using a single, hopefully optimal, neural network model. Using a single optimal model implicitly assumes that one neural network model can extract all the information available in a given data set and that the other candidate models are redundant. In general, there is no assurance that any individual model has extracted all relevant information from the data set. Recently, Wolpert (Neural Networks, 5(2), 241 (1992)) proposed the idea of stacked generalization to combine multiple models. Sridhar, Seagrave and Barlett (AIChE J., 42, 2529 (1996)) implemented the stacked generalization for neural network models by integrating multiple neural networks into an architecture known as stacked neural networks (SNNs). SNNs consist of a combination of the candidate neural networks and were shown to provide improved modeling of chemical processes. However, in Sridhar's work SNNs were limited to using a linear combination of artificial neural networks. While a linear combination is simple and easy to use, it can utilize only those model outputs that have a high linear correlation to the output. Models that are useful in a nonlinear sense are wasted if a linear combination is used. In this work we propose an information theoretic stacking (ITS) algorithm for combining neural network models. The ITS algorithm identifies and combines useful models regardless of the nature of their relationship to the actual output. The power of the ITS algorithm is demonstrated through three examples including application to a dynamic process modeling problem. The results obtained demonstrate that the SNNs developed using the ITS algorithm can achieve highly improved performance as compared to selecting and using a single hopefully optimal network or using SNNs based on a linear combination of neural networks.

Human water, sodium, and calcium regulation during space flight and exercise.

When one is exposed to microgravity, fluid which is normally pooled in the lower extremities is redistributed headward and weight bearing bones begin to demineralize due to reduced mechanical stresses. The kidney, which is the primary regulator of body fluid volume and composition, responds to the fluid shift and bone demineralization by increasing the urinary output of water, sodium, and calcium. This research involves developing a mathematical description of how water and electrolytes are internally redistributed and exchanged with the environment during space flight. This model consequently involves kidney function and the associated endocrine system. The model agrees well with actual data, including that a low sodium diet can prevent bone demineralization. Therefore, assumptions made to develop the model are most likely valid. Additionally, various levels of activity are also considered in the model since exercise may help to eliminate some of the undesired effects of space flight such as muscle atrophy and bone demineralization.

Predicting insensible water loss in premature neonates.

The insensible water loss from the skin of premature neonates in various environments can be estimated by modeling the skin as a composite membrane and applying Fick's law to each layer. Studies involving human skin development have made it possible to apply the proposed model to predict an infant's insensible water loss as a function of gestational age and postnatal age. However, the model tends to overestimate the insensible water loss particularly for gestational ages over 28 weeks. Values used in the model for the diffusivity of water through the stratum corneum were determined from adult skin rather than neonatal skin, which may be a factor in the overestimation.

Effects of dietary fat on cholesterol movement between tissues in CBA/J and C57BR/cdJ mice.

Differences in dietary fats cause differences in cholesterol metabolism in mice. CBA/J mice are resistant to diet-induced hypercholesterolemia and atherosclerosis; they adjust hepatic hydroxymethyl-glutaryl-CoA reductase activity (HMGR) to maintain homeostasis; C57BR/cdJ mice are susceptible, but young animals are thought to maintain homeostasis by changing fecal excretion of sterols. Compartmental modelling of movement of [4-14C]cholesterol was used to analyze movement of cholesterol between serum and liver, heart, and carcass in mice fed 40 en% fat, polyunsaturated to saturated fatty acid ratio (P/S) = 0.24 (US74) or 30 en% fat, P/S = 1 (MOD). Dietary effects were quite pronounced, while strain effects were more subdued. The C57/cdJ animals appear to regulate the overall cholesterol balance by reducing synthesis, as do the CBA/J animals, even though synthesis is not reduced to the same degree as in the CBA/J animals. Both diet and strain influence the whole-animal turnover rate, with slower turnover occurring for C57BR/cdJ animals and animals fed the US74 diet.

The energetics of embryonic growth and development. I. Oxygen consumption, biomass growth, and heat production.

A quantitative phenomenological model to describe the relationships between biomass growth rate, oxygen consumption, and heat production in developing embryos has been developed and tested using a wide range of experimental data. The model employs generalized material and energy balances, principles of enzyme kinetics, and an overall metabolic model scheme based on known biochemical principles. The phosphorylation concentration ratio of ATP and ADP occurs naturally and becomes a significant parameter in the analysis. The model is applied to the growth of Escherichia coli, Oryzias latipes, chick spinal cord, and whole chicken eggs. Excellent agreement between the model and the experimental data is obtained. In a succeeding paper (Part II) environmental effects and growth efficiency are discussed.

Effect of temperature on the myoglobin-facilitated transport of oxygen in skeletal muscle.

An analysis of thermal effects on the facilitative transport of oxygen in skeletal muscle fibers is presented. Steady-state mass and energy transport balances are written and solved analytically or numerically using a finite-difference procedure. It is shown that no significant spatial thermal gradients exist due to internal reactions or bulk conduction effects across a muscle fiber. At typical muscle conditions, it is predicted that increased global temperature reduces the fraction of oxygenated myoglobin, increases local oxygen concentrations, and increases the percentage of oxygen flux attributed to oxy-myoglobin. The maximum supportable oxygen consumption rate, mO2max, is defined as the highest consumption rate sustainable without developing anoxic regions at the center of the fiber. By considering only temperature sensitive effects within fibers, mO2max is found to increase slightly with temperature at low temperatures. This increase is due to thermal effects on the diffusion coefficients as opposed to effects associated with the kinetics of the myoglobin-oxygen reaction. If the simulations include the temperature effect associated with oxygen solubility in blood plasma, mO2max decreases with temperature. A sensitivity analysis was performed by varying the values of relevant parameters. The maximum consumption rate was least affected by parameters associated with the kinetic and equilibrium constants and most affected by the diffusion coefficients and the concentration of myoglobin.

Modelling heat and mass exchange of buried avian eggs.

The eggs of the Megapodiidae are incubated while buried in a substrate with which they exchange heat and water. The eggs may be buried in sand or in a mound composed in part or totally of organic material. We have analyzed the heat and water exchange of these buried eggs by constructing egg heat and mass balances. The equations are used to examine changes in egg temperature and water exchange during incubation in different environments. The thermal conductivities of the substrates are likely to vary by a factor of 5 to 10, with sand having the greatest thermal conductivity and organic litter the smallest. We predict that eggs incubated in sand will increase in temperature by 1 degree C or less, whereas eggs incubated in organic material will increase in temperature by 4 degrees C or more. Mound temperatures should remain low (less than 35 degrees C) to prevent overheating of eggs and hatchlings. Eggs can be incubated in sand at higher temperatures with less risk of overheating. Egg water loss in mounds is likely to be variable depending on mound humidity and considerably greater than 0 even in very high humidities. We expect that the rate of water loss by the eggs will increase many fold during incubation because of the low thermal conductivity of the mound material and the consequent increase in egg temperature.

Energy transformation and entropy production in living systems I. Applications to embryonic growth.

Generalized material and energy balances are presented for biological systems that experience negligible kinetic, elastic, and potential energy changes. The balances are used to characterize the mass changes and energy transformations that occur in the developing avian embryo, using as an example a consistent set of data for the chicken egg. It is shown that the rate of total chemical energy turnover by the embryo is a quantity of interest and that this rate is not necessarily equivalent to the metabolic rate that is predicted from heat transfer measurements or oxygen consumption rates. The energy required for evaporative water loss is accounted for in the overall energy balance. Using the results of the energy calculations and a generalized expression for the rates of internal and total entropy production, the Prigogine-Wiame hypothesis is examined for the developing embryo with two different assumptions regarding the efficiency of biomass conversion. An order of magnitude analysis of the internal heat-conduction term is performed to show that the chemical reaction term dominates the entropy production relation. The constant efficiency case is shown to be in agreement with the Prigogine-Wiame hypothesis for the data used in the analysis.

Ventilation-perfusion ratio obtained by a noninvasive frequency response technique.

Results of animal experiments using sinusoidal changes in inspired halothane concentration showed that the ratio of variation in end-expired concentration to the variation in inspired concentration reached a plateau in the Bode diagram. With the help of an uptake and distribution model, the interpretation of the results showed that the level of the plateau is determined by the overall ventilation-perfusion ratio. With a good selection of input frequency, tracer agent, and known ventilation, the ventilation-perfusion ratio and the lung perfusion can be consequently obtained noninvasively. Mean ventilation-perfusion ratio was determined with 20 human voluteers. At rest a mean ratio was found of 0.87 +/- 0.28 (SD). At a work load of 90 W a mean ratio was found of 1.19 +/- 0.19 (SD). In two individuals reproducibility and influence of CO2 was studied. At rest without additional CO2 the ventilation-perfusion ratio was 0.71 +/- 0.06 (SD) obtained with a constant breathing rate of 10/min. At an end-expired CO2 level of 6% the ventilation-perfusion ratio was increased almost 2.5 times. The calculated perfusion with and without increased end-expired CO2 levels under the same work load were well reproducible.

Canine hyperthermia with cerebral protection.

Extreme whole-body hyperthermia was achieved without lasting side effects in canines by elevating body core temperature to 42 degrees C, using a warm water bath. Cold water irrigation of the nasal alar fold permitted an additional core temperature elevation of 0.5-1.0 degrees C above brain temperature for periods up to 1.5 h. The brain-core temperature differential was maintained by a physiological arteriovenous heat exchanger located at the base of the brain. The maximum tolerable core temperature for the 21 nonirrigated dogs was 42 degrees C for 60-90 min, whereas that for the 28 irrigated dogs was 42.5-43 degrees C for similar time intervals. A mathematical model of the total heat transfer system described the observed dynamic temperature responses. It was the solution of a differential equation which fit the normalized experimental data points and predicted reasonable values for known and unknown experimental parameters.