Albert L. Babb

The Middle Molecule Hypothesis in Perspective

The middle molecule (MM) hypothesis states that molecules in the molecular weight range of 500 to 2000 daltons/molecule accumulate in uremia and are one cause of peripheral neuropathy. Evidence for and against this hypothesis is reviewed and evaluated. The course of events in the core of early hemodialysis patients who developed neuropathy provides important support ofr the hypothesis. Failure of early peritoneal dialysis patients to develop neuropathy suggested that the peritoneum is more permeable to MMs than early hemodialysis membranes, a fact that was later hemodialysis membranes, a fact that was later confirmed by appropriate investigations. Several investigators have demonstrated that MMs actually do accumulate in uremia and disappear rapidly following a renal transplant, which suggests a high clearance by the human kidney. Retrospective and prospective studies have demonstrated a protective effect of residual renal function against MM intoxication. Our prospective studies to produce MM intoxication are reviewed and their strengths and weaknesses delineated. Similarly, the investigations of others that are cited as evidence against the MM hypothesis are reviewed. It is the opinion of hte authors that the weight of evidence supports the validity of the MM hypothesis; but that final proof still is lacking. A protocol for more definitive studies is discussed.

Modeling Soluble Gas Exchange in the Airways and Alveoli

AbstractA mathematical model of heat, water and soluble gas exchange in the airways and alveoli was used to predict the location of soluble gas exchange in the lung. A previously published model of heat, water and soluble gas exchange in the airways was improved by incorporating anatomical data on the airway wall to better describe the bronchial circulation and expanding the model to include a time varying description of soluble gas concentration in the alveoli. Next, the model was validated using two experimental data sets from the literature: (1) ethanol expirograms and (2) the uptake of seven soluble gases. Then, the model simulated the excretion of ten soluble gases whose blood:air partition coefficient λb:a, a measure of blood solubility, ranged over 5 orders of magnitude. We found that gases with λb:a < 10 exchange almost solely in the alveoli and gases with λb:a > 100 exchange almost exclusively in the airways. Gases with λb:a between 10 and 100 have significant interaction with the airways and alveoli. These results suggest that the airways play a larger role in pulmonary gas exchange than previously assumed and may require a reevaluation of pulmonary tests that involve exhaled samples of gases with λb:a > 10.

Dynamics of heat, water, and soluble gas exchange in the human airways: 1. A model study

In order to provide a means for analysis of heat, water, and soluble gas exchange with the airways during tidal ventilation, a one dimensional theoretical model describing heat and water exchange in the respiratory airways has been extended to include soluble gas exchange with the airway mucosa and water exchange with the mucous layer lining the airways. Not only do heat, water, and gas exchange occur simultaneously, but they also interact. Heating and cooling of the airway surface and mucous lining affects both evaporative water and soluble gas exchange. Water evaporation provides a major source of heat exchange. The model-predicted mean airway temperature profiles agree well with literature data for both oral and nasal breathing validating that part of the model. With model parameters giving the best fit to experimental data, the model shows: (a) substantial heat recovery in the upper airways, (b) minimal respiratory heat and water loss, and (c) low average mucous temperatures and maximal increases in mucous thickness. For resting breathing of room air, heat and water conservation appear to be more important than conditioning efficiency. End-tidal expired partial pressures of very soluble gases eliminated by the lungs are predicted to be lower than the alveolar partial pressures due to the absorption of the expired gases by the airway mucosa. The model may be usable for design of experiments to examine mechanisms associated with the local hydration and dehydration dynamics of the mucosal surface, control of bronchial perfusion, triggering of asthma, mucociliary clearance and deposition of inhaled pollutant gases.

Modeling the concentration of ethanol in the exhaled breath following pretest breathing maneuvers

A previously developed mathematical model that describes the relationship between blood alcohol (ethanol) concentration and the concentration of alcohol in the exhaled breath at end-exhalation (BrAC) has been used to quantitate the effect of pretest breathing conditios on BrAC. The model was first used to “condition” the airways with different breathing maneuvers prior to simulating a single exhalation maneuver, the maneuver used in standard breath alcohol testing. On inspiration, the alcohol in the air reaches local equilibrium with the alcohol in the bronchial capillary bed prior to entering the alveolar region. On expiration, approximately 50% of the alcohol absorbed on inspiration is desorbed back to the airways. BrAC correlates with the amount of alcohol that is desorbed to the airways. The six pretest breathing conditions and the percent change in BrAC relative to the control maneuver were: hyperventilation (−4.4%), hypoventilation (3.7%), hot-humid air (−2.9%), hot-dry air (0.66%), cold-humid air (0.13%), and cold-dry air (0.53%). The mechanism underlying these responses is not due to changes in breath temperature, but, rather to changes in the axial profile of alcohol content in the mucous lining of the airways.

Binding levels of urate ions in human serum albumin and plasma

Abstract The question of uric acid (or urate ion) binding to plasma proteins has received considerable attention in the literature. However, the actual binding level of the solute in plasma has not been satisfactorily resolved. It has now been determined that one of the major contradictions concerning reported uric acid binding levels has resulted from the use of lithium urate (prepared as a standard solution by dissolution of i g/l of uric acid in 0.6 g/l Li2CO3) instead of pure uric acid. Using a novel in vitro dynamic dialysis technique and conventional ultrafiltration techniques it was found that lithium urate exhibited binding levels of between 20–40% in 5% human serum albumin and between 35–55% in normal heparinized plasma, both at 37°. In contradistinction, binding levels of pure uric acid were about 4% in 5% human serum albumin and about 7% in normal heparinized plasma under the same conditions. This study confirms that the binding of uric acid to plasma proteins at 37° is small and probably not physiologically significant.

Dynamics of soluble gas exchange in the airways: II. Effects of breathing conditions

A mathematical model of the airways is developed which focuses on the dynamic exchange characteristics of heat, water and soluble gas. A typical airway segment is divided radially into three regions: the airway lumen, a thin mucous layer of variable thickness coating the airway wall, and an underlying nonperfused tissue layer. A bronchial circulation capillary bed lies beyond the nonperfused tissue layer. The simultaneous exchange of water, heat and soluble gas is dealt with using the model of Tsu et al. (Ann. Biomed. Eng. 16:547-571, 1988). In the case of excretion of ingested ethyl alcohol from the bronchial and pulmonary circulations, the model predicts that during inspiration, because of the alcohol flux from the airway mucosa, a concentration of alcohol in equilibrium with mucus is achieved in the inspired air before the respiratory bronchioles are reached. During exhalation, much of this alcohol redeposits on the airway surface. The net flux of alcohol from the airway surface exceeds the flux of alcohol from the mouth in the exhaled gas indicating that the exhaled alcohol comes from the airways and bronchial circulation rather than from the alveoli and the pulmonary circulation. Alcohol flux moves farther into the airways with oral breathing compared to nasal breathing. Increased ventilation shifts the alcohol flux more alveolarward. Changes in inspired air temperature and humidity have almost no effect on the distribution of alcohol flux in the airways.

Axial and radial distribution of the bronchial vasculature in sheep

A morphometric analysis was made on the bronchial vasculature of intrapulmonary airways in sheep lungs. This study provides the parameters to calculate the quantity of soluble gas diffusion between the vasculature and airways for use in a mathematical model describing heat and mass exchange in the lungs. To achieve these results, the lungs of four adult sheep (30-36 kg.) were excised, fixed, dissected and microtomed to obtain airway cross-sections for measurement. Blood vessel size and airway proximity was measured using a microscope interfaced with a computer. Distance from airway lumen to most airway vessels ranged from 30 to 270 microm. It was found that the bronchial vessels surrounding intraparenchymal airways can be described by a right-skewed distribution. Most importantly, a practical description of the bronchial capillary size and airway proximity as a function of airway diameter was found using a weighed average. This analysis facilitates calculation of soluble gas flux from the bronchial vasculature to the airway for use in a mathematical model.

On the extension of the method of moments to a cascade of well-mixed discrete stages with back-flow between stages☆

Abstract The method of moments has been applied to a system of well mixed discrete stages with backflow between adjacent stages. Both differential and difference time dependency have been treated. The recycle rate (back-flow rate) for both cases has been related to the variance of the concentration-time distributions resulting from an arbitrary input of nontransferable tracer.

Engineering Aspects of Artificial Kidney Systems

While some of the work described in the first part of this paper has appeared in medical journals from time to time, the major results are summarized here with emphasis on the engineering problems and their solutions.

OPTIMUM NUCLEAR REACTOR CONTROL THEORY.

Publisher Summary The mathematical model of the system to which the optimum control theory is applicable is based on a finite number of ordinary differential equations. A characteristic of the theory is the use made of the adjoint equations, because the problem is found to be non-self-adjoint in nature. The theory is different from the calculus of variations in its treatment of problems in classical dynamics. Dynamic programming is not thought of in the context of the calculus of variations. There is an analogos situation in the optimization of a model based on linear algebraic equations, where the calculus of maxima and minima, and linear programming could be employed. This chapter discusses the relation of dynamic programming to optimal control theory. It further discusses a generalization of the theory to encompass models of distributed rather than “point” systems, to include the usual models of nuclear reactor statics. This helps to specialize the theory and to obtain some results in reactor statics on the optimum design of systems.