Melvin H. Knisely

A Mathematical Simulation of Oxygen Release, Diffusion, and Consumption in the Capillaries and Tissue of the Human Brain

The purpose of this paper is to describe an attempt to obtain a better understanding of the oxygen supply to the cells of the brain by examining all phases of the release, diffusion, and consumption processes in a mathematical model. Since the original investigations of August Krogh in 1919, the mechanisms by which molecular oxygen is transported from red blood cells while they are carried in blood flowing longitudinally through capillaries, into plasma, thence radially out to and through the capillary wall into the surrounding tissues for tissue cell respiration, have been a topic of major interest. During maximal good health, and during several states of special physiology and disease states or pathologic conditions, what specific factors, or summation of factors, limit in the mathematical sense of the term the rates of oxygen supply to individual tissue cells located in individual geometric positions in the living organs? As examples, what are the effects of inhaling air containing low concentrations of oxygen, such as at high altitudes, on the individual nerve cells surrounding and all along the lengths of brain capillaries? What are the specific effects of forcibly reducing the linear rates of flow of blood through capillaries on nerve cells along the lengths of, and at various positions between, capillaries? What are the specific effects on nerve cells so located produced by the inhalation of air containing excessively high concentrations of oxygen, or of pure oxygen, perhaps under pressure such as during hyperbaric conditions?

Increased blood cell agglutination following ingestion of fat, a factor contributing to cardiac ischemia, coronary insufficiency, and anginal pain; a contribution to the biophysics of disease.

This paper has two purposes. First, to describe experiments and observations recording increased agglutination of the blood of some (but not all) human patients following the ingestion of fat-enriched meals. Second, to present a working hypothesis concerning mechanisms whereby in some (but not all) persons, the ingestion of high dietary fat is followed by agglutination of the blood, forcible reduction of blood flow through all coronary vessels, and the plugging and impaction of some, thereby producing cardiac ischemia, coronary insufficiency, and anginal pain. If the impaction of small coronary vessels is sufficiently prolonged, it should contribute to myocardial infarction. Cullen and Swank (1) demonstrated increased red cell agglutination accompanied by slowing of the circulation and at times complete cessation of blood flow in hamsters following ingestion of fat. In 1955, we reported (2) increased red cell agglutination, reduced blood flow, and transient plugging of vessels in the bulbar conjunctivae of five patients with coronary artery disease, following fat-enriched meals, and the occurrence of angina during the time of increased blood cell agglutination. Bloch (3) studied the condition of the circulating blood of patients following myocardial infarction, but he did not study dietary factors which might initiate the condition.

Concerning the geometric shapes of arteries and arterioles; a contribution to the biophysics of health, disease and death.

a long slowly tapering truncated cone? Marshall Hall, 1835, page 14 (23) pointed out that arteries &dquo;may be considered as cones.&dquo; When attempting to understand the physics or the rheology of the passage of suspensions through a series of tubes, two classes of phenomena can be investigated separately: first, the physical properties of the materials which pass through the tubes; second, the shapes and dimensions, and other physical properties such as the coefficient of elasticity, distensibility, and elastic limit of the tubes through which the moving materials pass. The main purposes of the investigations herein reported were to examine the shapes and measure the dimensions of portions of the arteries of animals and men. Progress in understanding the flow of blood in health and disease is limited in some directions by a lack of knowledge of the real shapes and dimensions of segments of the arterial system. This paper makes a preliminary statement of the problem, provides two classes of evidence that segments of arteries are actually portions of truncated cones rather than cylinders, and permits a re-analysis and re-statement of the problems as a foundation for subsequent investigations. A background of ideas pertaining to these investigations may be presented as follows:

Ante-mortem settling. Microscopic observations and analyses of the settling of agglutinated blood-cell masses to the lower sides of vessels during life: a contribution to the biophysics of disease.

For many years it has been known that after the death of a human being the blood cells settle to the lower sides of the blood vessels. It has been believed that all settling was post mortem. It is now known that in sick human beings masses of blood cells settle to the lower sides of vessels during the life of the individual. This ante-mortem settling can occur days and hours before death. (By ante-mortem settling we do not merely mean &dquo;immediately pre-agonai settling.&dquo;) Some settling is reversible. It now

KNOWLESI MALARIA IN MONKEYS II. A FIRST STEP IN THE SEPARATION OF THE MECHANICAL PATHOLOGIC CIRCULATORY FACTORS OF ONE SLUDGE DISEASE FROM POSSIBLE SPECIFIC TOXIC FACTORS OF THAT DISEASE

From the Department of Anatomy, Medical College of South Carolina, Charleston, South Carolina, and the Division of Anatomy and Preventive Medicine, University of Tennessee, Memphis, Tennessee. a The studies on which this paper is based were made possible through support given by the Tennessee Valley Authority through the Division of Preventive Medicine of the University of Tennessee, The work was aided by a grant from the Ella Sachs Plotz Fund and by United States Public Health Service Grants H-4176 and H-7114 and United States Navy Contract NONR:441. b Present address: Department of Anatomy, Medical College of South Carolina, Charleston, South Carolina. c Deceased. d Present address: Department of Anatomy, University of Colorado School of Medicine, Denver, Colorado. e Present address: Department of Anatomy, Western Reserve School of Medicine, Cleveland, Ohio. The fundamental purpose of this paper is to introduce a rigorous experimental method for separating and determining the significance of individual sets of mechanisms of the pathologic physiology of certain disease states. The first step in presenting the material is to state the contrast between the visible circulatory factors in completely healthy-normal rhesus monkeys and in monkeys which are dying of Stage III Knowlesi malaria, a condition in which the blood is very severely agglutinated 1-3 In healthy animals, including man, every formed element of the blood is separate from every other: red cells do not stick together; white cells do not stick together; platelets do not stick together; nor do any individual items of any category stick together with those of any other category. White cells and platelets do not stick to healthy-normal endothelium. Healthy small vessels do not leak microscopically detectable amounts of fluid 4~ Healthy-normal red cells are naked, i.e., uncoated by any opsonizing precipitate. They bump and slide along hepatic phagocytes and are not ingested.’ Capillaries, through which blood must pass to oxygenate and nourish the cells of each and every tissue of the body, are just wide enough to permit one, or, at most, two red cells to pass abreast. The narrowest part of the vascular system, the bottlenecks, are the terminal arterioles just at theAbstract : The fundamental purpose of this paper is to introduce a rigorous experimental method for separating and determining the significance of individual sets of mechanisms of the pathologic physiology of certain disease states. The contrast is noted between the visible circulatory factors in completely healthy-normal rhesus monkeys and in monkeys which are dying of Stage III Knowlesi malaria, a condition in which the blood is very severely agglutinated.

Alcohol, sludge, and hypoxic areas of nervous system, liver and heart

Abstract In 30 adult humans (13 females, 17 males) microscopic observations were made of blood flow and the conditions of the small vessels in the conjunctiva, and at the same time a blood sample was taken for determination of blood ethyl alcohol concentration. Ethanol concentrations ranged from zero to 328 mg/100 ml. With increasing concentrations of alcohol in the blood, the size of aggregated or agglutinated blood cell masses increased, and the forward rates of flow in small vessels decreased correspondingly. With the higher concentrations of blood alcohol and the more severe reduction in forward flow rates, the numbers of vessels in stasis, plugged, occluded, and with no flow increased significantly. Within the extreme upper concentrations of ethanol (225 and 328 mg/100 ml blood) some small vessels were ruptured, producing microscopic hemorrhages into the contiguous bulbar conjunctival tissue. No arrangement of the data, other than in ascending order of blood alcohol concentrations, has given any thus far recognizable trend of meaning. Mechanisms are described whereby reduced rates of blood flow through capillaries and the plugging of capillaries damage brain, liver, and heart.

Anti-Adhesive Drugs and Tissue Oxygenation

The intravascular agglutination of the formed elements of blood, which occurs under certain pathological conditions, results in peripheral circulation disturbances that may lead to blood flow stagnation and the plugging of small vessels with cell aggregates. [Bicher (1) and (2)] Of the blood cells involved, special attention has been given to the erythrocytes and platelets. These cells seem to possess the ability to start and accelerate the chain of events that leads to organic vessel occlusion.

A Distributed Parameter Mathematical Analysis of Oxygen Exchange from Maternal to Fetal Blood in the Human Placenta

Based on the present state of knowledge concerning the anatomy and physiology of the placenta, a theoretical analysis of the transport of oxygen from maternal to fetal blood is presented in this paper. Distributed parameter mathematical models are derived which describe the convection, diffusion and reaction processes involved in the oxygen exchange. Steady state simulations of placental oxygen transport are obtained by solving the mathematical models for two cases. Case 1 is a simulation of oxygen transport as if it occurred from maternal blood flowing concurrently to fetal blood in a straight capillary. Case 2 simulated the process as if it occurred in a multivillous flow pattern with concurrent flow characteristic of each exchange unit.

A Stochastic Model for the Transport of Oxygen to Brain Tissue

Material balances around a small, but finite volume element have formed the basis for previous mathematical models describing the transport of oxygen in the brain microcirculation. Seeking a model which would be both simple and versatile, a stochastic model was proposed based on the assumption that oxygenation of the brain can be described quantitatively by simulating the activity of only one erythrocyte and the oxygen molecules surrounding it. Compared with existing deterministic models, the capillary space-average oxygen partial pressure profiles were in close agreement. Tissue tensions were decidedly different.

Simulating Myocardium Oxygen Dynamics

A three-compartment model, consisting of erythrocytes, plasma, and tissue was simulated on a hybrid computer in the unsteady-state to predict myocardium oxygen tensions under normal and pathological conditions. The model includes nonequilibrium oxygen dissociation characteristics for the red cells with superimposed flow and metabolic rate changes. It was assumed that both flow velocity and metabolic rate varied as pure harmonic functions 180 degrees out of phase. Results indicate that under normal conditions, heart tissue tension remains essentially constant at a mean value rather than oscillating. It appears that this is primarily due to the frequency characteristics of the total physiological system and that myoglobin capacitance becomes important mainly at the lower heart rates.