A simple mathematical modeling of the growth of microorganism colonies

The growth rates of aspergillus, fusarium, and penicillium microorganism colonies in Czapex Dox Agar as a feed material, under room conditions, are observed to be linear. This phenomenon is mathematically modeled and exactly predicted on the basis of the exponential growth assumption of a single microorganism. The approach allows an easy determination of the multiplication constant of a had microorganisms been allowed to grow freely microorganism, in given conditions.     

The diffusion process approach to one-compartmental stochastic models: A mathematical note

We consider the one-dimension (one-compartment) exponential model using a diffusion process approach. In particular, we summarize the known results in the case where the stochastic component of the model is a Gaussian white noise process with mean zero and variance σ². Finally, we briefly illustrate a number of cases where similar forms of model arise.     

Dry-heat destruction of lipopolysaccharide: mathematical approach to process evaluation.

A mathematical model was developed to estimate the number of logarithmic cycles (LDec) of lipopolysaccharide concentration destroyed by a dry-heat sterilization process. The LDec values calculated from the mathematical model agreed well with those obtained from the destruction of lipopolysaccharide by a dry-heat treatment. A discussion of how the mathematical model may be used to evaluate a dry-heat sterilization cycle is presented. This mathematical model and the dry-heat destruction curves indicated existence of a maximum LDec value at each temperature. The implications of this finding are discussed.     

Dry-heat destruction of lipopolysaccharide: mathematical approach to process evaluation.

A mathematical model was developed to estimate the number of logarithmic cycles (LDec) of lipopolysaccharide concentration destroyed by a dry-heat sterilization process. The LDec values calculated from the mathematical model agreed well with those obtained from the destruction of lipopolysaccharide by a dry-heat treatment. A discussion of how the mathematical model may be used to evaluate a dry-heat sterilization cycle is presented. This mathematical model and the dry-heat destruction curves indicated existence of a maximum LDec value at each temperature. The implications of this finding are discussed.     

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.     

Quantitative analysis of electrophoretograms: A mathematical approach to super-resolution

A mathematical method is presented for the quantitative analysis of overlapping spots or bands taken from digitized gel patterns. The procedure is applied to both one- and two-dimensional gel electrophoretic separations.     

A mathematical model for the freezing process in biological tissue

A mathematical model has been developed to study the process of freezing in biological organs. The model consists of a repetitive unit structure comprising a cylinder of tissue with an axial blood vessel (Krogh cylinder) and it is analysed by the methods of irreversible thermodynamics. The mathematical simulation of the freezing process in liver tissue compares remarkably well with experimental data on the structure of tissue frozen under controlled thermal conditions and the response of liver cells to changes in cooling rate. The study also supports the proposal that the damage mechanism responsible for the lack of success in attempts to preserve tissue in a frozen state, under conditions in which cells in suspension survive freezing, is direct mechanical damage caused by the formation of ice in the vascular system.     

Effects of clot contraction on clot degradation: A mathematical and experimental approach

Thrombosis, resulting in occlusive blood clots, blocks blood flow to downstream organs and causes life-threatening conditions such as heart attacks and strokes. The administration of tissue plasminogen activator (t-PA), which drives the enzymatic degradation (fibrinolysis) of these blood clots, is a treatment for thrombotic conditions, but the use of these therapeutics is often limited due to the time-dependent nature of treatment and their limited success. We have shown that clot contraction, which is altered in prothrombotic conditions, influences the efficacy of fibrinolysis. Clot contraction results in the volume shrinkage of blood clots, with the redistribution and densification of fibrin and platelets on the exterior of the clot and red blood cells in the interior. Understanding how these key structural changes influence fibrinolysis can lead to improved diagnostics and patient care. We used a combination of mathematical modeling and experimental methodologies to characterize the process of exogenous delivery of t-PA (external fibrinolysis). A three-dimensional (3D) stochastic, multiscale model of external fibrinolysis was used to determine how the structural changes that occur during the process of clot contraction influence the mechanism(s) of fibrinolysis. Experiments were performed based on modeling predictions using pooled human plasma and the external delivery of t-PA to initiate lysis. Analysis of fibrinolysis simulations and experiments indicate that fibrin densification makes the most significant contribution to the rate of fibrinolysis compared with the distribution of components and degree of compaction (p < 0.0001). This result suggests the possibility of a certain fibrin density threshold above which t-PA effective diffusion is limited. From a clinical perspective, this information can be used to improve on current therapeutics by optimizing timing and delivery of lysis agents.     

A note on the survival of Legionella pneumophila in stagnant tap water

Tap water, from an experimental hot water system, containing a known virulent strain of Legionella pneumophila was stored in screw-capped bottles for 14 months. Viable counts showed survival of L. pneumophila and at least three other bacterial species. This reinforces the view that L. pneumophila can survive in stagnant water foatively long periods of time.     

A note on the survival of Legionella pneumophila in stagnant tap water

Tap water, from an experimental hot water system, containing a known virulent strain of Legionella pneumophila was stored in screw-capped bottles for 14 months. Viable counts showed survival of L. pneumophila and at least three other bacterial species. This reinforces the view that L. pneumophila can survive in stagnant water for relatively long periods of time.     

A note on a possible mathematical approach to the theory of individual freedom

As suggested in previous publications, freedom may be defined quantitatively as a restriction upon the choice of a number of activities. If the choice is determined by maximizing the satisfaction function, it is suggested that freedom may be defined in terms of the satisfaction function. If an individual is isolated and no physical restrictions limit his choice of activities, he is free to choose any activity in an amount which maximizes his satisfaction. This isolated state may be considered therefore as that of maximum freedom. If the individual interacts with another, he will choose different amounts of his object of satisfaction depending on whether he behaves egoistically or altruistically. But in either case the value chosen will not maximize his satisfaction function considered alone. A simple analytical expression is suggested as a measure of freedom in this case, and some problems which arise from this suggestion are mentioned.     

A mathematical approach to the analysis of diversity in antibody gene families

In this article, we develop a mathematical approach for the analysis of diversity in antibody gene families. This approach is arrived at by examining two general questions about protein populations: (1) What is a relative measure of the diversity exhibited by one protein family when compared with a second? (2) What is the probability that two protein populations were derived from a single common population? These quantitative approaches permit a variety of precise evolutionary, genetic, and developmental questions to be asked of antibody gene families. Using this methodology, we demonstrate that the diversity in mouse κ-immunoglobulin chains is considerably greater than in their human κ counterparts. We also show that the variable (V_L) regions of light chains associated with IgG and IgA immunoglobulins in the mouse appear to have been derived from a common population of V_L genes. This approach also can be used to analyse sequence data from other informational multigene families.     

A kinetic model of growth and product formation of the anaerobic microorganism Thermoanaerobacter thermohydrosulfuricus

A model is developed to describe the growth, product formation and enzyme synthesis of the microorganism Thermoanaerobacter thermohydrosulfuricus. It differentiates between extracellular enzymatic starch degradation and the microorganism's constant specific growth rate, combined with the ingestion of maltose and maltotriose (the products of starch cleavage). The formation of growth dependent products like ethanol, acetate and the synthesis of the cell-associated enzyme, amylopullulanase, are formulated with constant yield coefficients. In contrast, both the non-growth dependent product lactate, and extracellular enzyme activity are linked to an intracellular substrate concentration. Most of the parameters used in the model are evaluated from batch culture or literature. The calculated results are compared with experimental data. Keywords: Continuous culture; Thermoanaerobacter thermohydrosulfuricus; Starch; Model     

Some mathematical aspects of the medical diagnostic process. I: a general mathematical model

Making a medical diagnosis consists of correlating knownpatterns of disease with the various classes of clinical data elicited from the history, physical examination, and batteries of tests relative to the diagnostic dynamics symbolized by atree branching into the various possible diagnostic decisions. In this paper a relational mathematical model of the reasoning aspects of the conventional medical diagnostic process is suggested as a way of extracting a general, formal concept of medical diagnosis. Computer implementation of the model is discussed briefly.     

The comparability of pharmacokinetics of creatinine in rabbit and man: A mathematical approach

A model simulating the kinetics of creatinine displacement in rabbit is investigated. The model is validated by comparing the predicted renal clearance and production rate constant with observed values and those reported previously in the literature. By applying steady state conditions to the model, a simple equation for prediction of creatinine clearance from serum creatinine is obtained. This is the first equation for predicting clearance which is not based on empirical relationships. The equation is then tested on a set of data from 61 patients with various degrees of renal impairment and a wide variation in weights and ages. It is found that good correlation (r = 0·93) exists between predicted and observed creatinine clearances. This comparability is attributed to the similarities in disposition of a non-threshold substance, like creatinine, in rabbits and man. Thus, it is suggested that more confidence can be placed on the use of rabbit as animal model in creatinine investigations.