Some mathematical aspects of the diagnostic process. II: A mathematical model of electrocardiographic diagnosis

In a previous paper (Bartholomay, 1971), a general mathematical model of the medical diagnostic process was described. The present paper amounts to a relization of that process in terms of conventional 12-lead electrocardiographic diagnosis as enunciated by Dr. Harold D. Levine (1966) in the course of a collaborative study by Dr. Levine and the present author at the Peter Bent Brigham Hospital of the Harvard Medical School between 1963 and 1966. The main details of the cognitive component of that model are described in detail here. The model has been programmed onto a computer system consisting of an analog-digital converter and general purpose digital computer and amounts to a simulation of Dr. Levine’s electrocardiographic analysis procedure.     

Some mathematical aspects of chemotherapy: I. One-organ models

A model of the processes occuring in the exchange of a drug between capillary plasma, extracellular space and intracellular space is developed. This leads to an interesting set of differential differences equations, one of which is an integrodifferential equation, another a partial differential equation. Under certain conditions, these may be simplified to a set of ordinary differential equations. The application of Laplace transform techniques to the solution of these equations is discussed.     

Some aspects of medical management of gastrointestinal disease. I.

Summary: Among drugs recently introduced into Canada for treatment of gastrointestinal disease are carbenoxolone sodium (used in treating gastric ulcer) and metoclopramide hydrochloride (which modifies upper gastrointestinal tract motility). A third drug, lactulose (useful in treating hepatic encephalopathy), will soon be available. Clinical experience with these drugs has been most extensive in Europe. In a new class of agents are histamine H2-receptor antagonists, which are currently under clinical trial. These drugs are the most potent inhibitors of gastric acid secretion yet investigated, and are potentially the most exciting agents to appear in many years. Part I of this paper is a review of the actions, clinical use, side effects, and dosage and administration of these new drugs.     

Outline of a new mathematical approach to general biology: I

This first part of the paper deals with the theory of organic form. By introducing a formal principle, it is possible to develop a mathematical theory of shapes of organisms, which covers both animals and plants.     

Some mathematical aspects of mapping DNA cosmids

A number of experimental and mathematical problems must be solved before high resolution physical maps of mammalian chromosomes can be reliably determined. Such a map might consist of an ordered set of nonsequenced, overlapping DNA fragments 20,000-40,000 bases long, produced by digestion of a chromosome, using two restriction enzymes. Map construction requires assigning a signature to each fragment that differentiates it unambiguously from every other fragment, and then devising a computationally efficient algorithm that will provide a unique ordering of the fragments. In the first part of this paper we present a polynomial time algorithm that yields a unique map, and is largely independent of the method for assigning signatures. In the next section we analyze the distribution of lengths of restriction digest fragments and discuss the implications for the algorithm, including the expected number of map gaps. Finally, we discuss a specific method for assigning signatures proposed by Hans Lehrach, based on which of a panel of probes binds to a given fragment. In particular we examine the effects of fragment length heterogeneity on the theoretical optimum length and number of probes, and the extent to which false signatures might be obtained by nonspecific binding. We conclude that the Lehrach strategy is effective provided the number of probes is >-150, but that each fragment will need testing with at most 25 probes.     

Some bio-sociological aspects of the mathematical theory of communication

In the first part of the paper a general discussion of the transmission of information through neural chains is given in terms of the Shannon-Weaver theory. It is pointed out that with the all-or-none law a single chain of neurons connected in series transmits one bit of information per signal. A set ofN independent parallel chains transmitsN bits per signal. If, however, the chains are interconnected, the amount of information is reduced. At the same time, however, the degree of coordination of the final neuromuscular reaction is increased. A relation between the maximum possible speed of a reaction and its degree of coordination is derived, and possible applications to spoken language are suggested. A general quantitative discussion of the relation between amount of information and amount of knowledge which an individual may obtain when confronted with the external world is made and a possible connection with new trends in logical thinking is pointed out. In the second part transmission of information through “social chains” is discussed under certain special assumptions. An expression for the “social channel noise” in terms of the length of the channel is derived. Finally an expression is given for the amount of information transmitted from one individual to another in a social group of uniform density as a function of the physical distance between the two individuals.     

Fermentation process diagnosis using a mathematical model

Summary Intriguing physiology of a solvent-producing strain ofClostridium acetobutylicum led to the synthesis of a mathematical model of the acetone-butanol fermentation process. The model presented is capable of describing the process dynamics and the culture behavior during a standard and a substandard acetone-butanol fermentation. In addition to the process kinetic parameters, the model includes the culture physiological parameters, such as the cellular membrane permeability and the number of membrane sites for active tansport of sugar. Computer process simulation studies for different culture conditions used the model, and quantitatively pointed out the importance of selected culture parameters that characterize the cell membrane behaviour and play an important role in the control of solvent synthesis by the cell. The theoretical predictions by the new model were confirmed by experimental determination of the cellular membrane permeability.     

Some remarks on the mathematical aspects of automobile driving

Some aspects which involve the interaction of the human element and of the machine element in driving are discussed. As an example a simple equation is derived for the maximum safe speed of a car on an empty road. The parameters of the equation are partly of physiological nature, partly of mechanical nature. Another example treats in a similar manner the problem of a car passing another car moving in the same direction.     

Evaluating the effectiveness of a process medical audit in a teaching general hospital.

Medical auditing has moved beyond the traditional chart review to the process audit, which identifies deficiencies in care and suggests remedies. In 1981 the audit committee of the Department of Psychiatry at Toronto General Hospital audited the use of hypnotic drugs in the inpatient unit. The audit produced two recommendations: that nursing staff record sleep graphs for inpatients more often, and that an educational program be instituted to change the physicians'' patterns of prescribing hypnotics. In 1983 the audit was repeated to test the effectiveness of the 1981 auditing process. The 1981 recommendation produced the desired improvement in recording of sleep graphs. However, the medical staff failed to change their patterns of prescribing hypnotics: oxazepam remained the preferred hypnotic. For the process audit to be effective in improving patient care those using it must ensure that the methods reflect the nature and structure of the professional group they are trying to influence.     

The effect of interfering substances on the disinfection process: a mathematical model

AIMS: To gain a greater understanding of the effect of interfering substances on the efficacy of disinfection. METHODS AND RESULTS: Current kinetic disinfection models were augmented by a term designed to quantify the deleterious effect of soils such as milk on the disinfection process of suspended organisms. The model was based on the assumption that inactivation by added soil occurred at a much faster rate than microbial inactivation. The new model, the fat-soil model, was also able to quantify the effect of changing the initial inoculum size (1 x 10(7)-5 x 10(7) ml(-1) of Staphylococcus aureus) on the outcome of the suspension tests. Addition of catalase to the disinfection of Escherichia coli by hydrogen peroxide, resulted in changes to the shape of the log survivor/time plots. These changes were modelled on the basis of changing biocide concentration commensurate with microbial inactivation. CONCLUSIONS: The reduction in efficacy of a disinfectant in the presence of an interfering substance can be quantified through the use of adaptations to current disinfection models. SIGNIFICANCE AND IMPACT OF THE STUDY: Understanding the effect of soil on disinfection efficacy allows us to understand the limitations of disinfectants and disinfection procedures. It also gives us a mechanism with which to investigate the soil tolerance of new biocides and formulations.     

Kinetics of the enzymatic hydrolysis of cellulose: 1. A mathematical model for a batch reactor process

A mathematical model for enzymatic cellulose hydrolysis, based on experimental kinetics of the process catalysed by a cellulase [see 1,4-(1,3;1,4)-β-d-glucan 4-glucanohydrolase, EC 3.2.1.4] preparation from Trichoderma longibrachiatum has been developed. The model takes into account the composition of the cellulase complex, the structural complexity of cellulose, the inhibition by reaction products, the inactivation of enzymes in the course of the enzymatic hydrolysis and describes the kinetics of d-glucose and cellobiose formation from cellulose. The rate of d-glucose formation decelerated through the hydrolysis due to a change in cellulose reactivity and inhibition by the reaction product, d-glucose. The rate of cellobiose formation decelerated due to inhibition by the product, cellobiose, and inactivation of enzymes adsorbed on the cellulose surface. Inactivation of the cellobiose-producing enzymes as a result of their adsorption was found to be reversible. The model satisfactorily predicts the kinetics of d-glucose and cellobiose accumulation in a batch reactor up to 70–80% substrate conversion on changing substrate concentration from 5 to 100 g l^?1and the concentration of the enzymic preparation from 5 to 60 g l^?1.     

Some aspects of medical management of gastrointestinal disease. Part II

Antacids are among the most frequently used drugs, yet common prescribing habits suggest that there is little familiarity with effective dosage schedules, side effects, or the differences between various antacid preparations. These factors, which are important in the choice of a specific antacid preparation, are discussed in an attempt to provide a rational basis for therapy.Corticosteroids, salicylazosulfapyridine (Salazopyrin) and diphenoxylate hydrochloride-atropine (Lomotil) are often used in treatment of inflammatory bowel disease. Recently described regimens for treating acute exacerbations and maintaining remission in patients with ulcerative colitis are reviewed, and attention is drawn to possible adverse effects of Lomotil in the treatment of colonic disease.     

A mathematical model for the leukocyte filtration process

Leukocyte filters are applied clinically to remove leukocytes from blood. In order to optimize leukocyte filters, a mathematical model to describe the leukocyte filtration process was developed by modification of a general theoretical model for depth filtration. The model presented here can be used to predict the time-dependent leukocyte filtration as a function of cell-cell interaction in the filter, filter efficiency, filter capacity, filter dimensions, and leukocyte concentration in the suspension applied to the filter. The results of different leukocyte filtration experiments previously reported in the literature could be well described by the present model. (c) 1995 John Wiley & Sons, Inc.     

A mathematical analysis of rebound in a target-mediated drug disposition model: I.Without feedback

We consider the possibility of free receptor (antigen/cytokine) levels rebounding to higher than the baseline level after one or more applications of an antibody drug using a target-mediated drug disposition model. Using geometry and dynamical systems analysis, we show that rebound will occur if and only if the elimination rate of the drug–receptor product is slower than the elimination rates of the drug and of the receptor. We also analyse the magnitude of rebound through approximations and simulations and demonstrate that it increases if the drug dose increases or if the difference between the elimination rate of the drug–receptor product and the minimum of the elimination rates of the drug and of the receptor increases.     

Nerve conduction theory: Some mathematical consequences of Bernstein's model

The generally accepted permeability theory of nerve conduction is presented in mathematical form. The resulting velocity formula is found to agree well with data on squid giant axon, but predicts velocities considerably too high in the case ofNitella. The dependence of velocity on fiber diameter is discussed for both medullated and non-medullated nerve, it being shown theoretically that velocity is proportional to the square root of diameter for non-medullated and to the diameter for medullated nerve. The equations relating the shape of the action spike to the observed permeability changes are given but are not solved.