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PubMed1989

Transport rates of proteins in porous materials with known microgeometry.

Many biological and biotechnological systems involve the diffusion of macromolecules through complicated macroporous (pore size on the order of 10-100 microns) environments. In this report, we present and evaluate an experimental system for measuring the rate of protein transport in an inert, macroporous membrane. For this particular membrane system, the microgeometry was characterized in terms of distribution of pore size, position, and orientation. Although the rate of protein desorption was much less than expected based on continuum diffusion models, we demonstrate that the measured transport rates are consistent with diffusion of protein in a complex, interconnected network of water-filled pores. The porous systems exhibit transitional behavior in quantitative agreement with the behavior of percolation lattices (mean square error 7%, n = 29). Predictive mathematical models of the diffusion process were developed: these models used percolation concepts to describe pore topology, continuum models of diffusion/dissolution to describe protein movement at each single pore, and measured pore size distributions. Effective diffusion coefficients for protein transport in aqueous, constricted macropores were predicted by this technique. Predicted diffusion coefficients, based on measured and derived microstructural parameters, agree with experimentally measured diffusion coefficients within a factor of 2. This approach may be useful in the design of porous polymer systems for biological applications and for evaluating other biological systems where conduction of mass, heat, momentum, or charge occurs in a heterogeneous environment.

Kinetics↗
PubMed1993

[Is the new chaos- and fractal research of importance to medical science?].

Living systems are characterized by a complexity of structure and function which goes well beyond the descriptive capacity of classical physical and mathematical methods. During the latest decade, the development of non-linear dynamics has introduced a series of new concepts and tools to describe even extremely complex systems. This has led to a better understanding of the processes through which complex structures can arise from very simple interactions. The present and a following paper will give a brief introduction to some concepts and methods of this new science.

Biological Evolution↗
PubMed1982

The quantitative nutrient-response relationship.

A quantitative mathematical model for the description of nutrientresponse relationships can be derived by the application of the concepts of a) specific nutrient-macromolecular interaction, b) response proportional to the extent of this interaction, c) law of mass action and d) saturation kinetics. This model can be used to produce the four-parameter mathematical model for physiological responses. The possible uses of the model are discussed, an idealized example is given, and the model is applied to the interpretation and description of a growth experiment in which male, weanling Sprague-Dawley rats are fed diets varying in concentration of an amino acid mixture.

Animals↗
PubMed2006

Statistical genetics concepts and approaches in schizophrenia and related neuropsychiatric research.

Statistical genetics is a research field that focuses on mathematical models and statistical inference methodologies that relate genetic variations (ie, naturally occurring human DNA sequence variations or "polymorphisms") to particular traits or diseases (phenotypes) usually from data collected on large samples of families or individuals. The ultimate goal of such analysis is the identification of genes and genetic variations that influence disease susceptibility. Although of extreme interest and importance, the fact that many genes and environmental factors contribute to neuropsychiatric diseases of public health importance (eg, schizophrenia, bipolar disorder, and depression) complicates relevant studies and suggests that very sophisticated mathematical and statistical modeling may be required. In addition, large-scale contemporary human DNA sequencing and related projects, such as the Human Genome Project and the International HapMap Project, as well as the development of high-throughput DNA sequencing and genotyping technologies have provided statistical geneticists with a great deal of very relevant and appropriate information and resources. Unfortunately, the use of these resources and their interpretation are not straightforward when applied to complex, multifactorial diseases such as schizophrenia. In this brief and largely nonmathematical review of the field of statistical genetics, we describe many of the main concepts, definitions, and issues that motivate contemporary research. We also provide a discussion of the most pressing contemporary problems that demand further research if progress is to be made in the identification of genes and genetic variations that predispose to complex neuropsychiatric diseases.

Chromosome Mapping↗
PubMedDate not supplied

A mathematical model for time perception with experimentally obtained subjective time scales for humans and rats.

The concept of sensation measurement with the entailing subjective scales is explained. It is shown that linearity between, e.g. sensation halving values and standard values implies that subjective sensation (output) grows as a power function of the physical measure of the stimulus (input). This outcome can be used in the scaling of subjective duration, based on reproduction experiments, i.e., experiments in which the participants are required to reproduce given time intervals, e.g., indicated by noise. It will be shown that what is reproduction for the participant is halving for the experimenter, making it possible to determine the parameters of the power function. The model is confirmed experimentally for humans and rats, the rats having a lower exponent than adults. In a recent experiment it was shown that the reproduced durations differ between female and male observers as well as for different sound intensities. These differences could be attributed to differences in parameter values. An interesting observation is that almost all power functions exhibit a discontinuity, possibly indicating a switch between different neural loops as the durations become longer.

Animals↗
PubMedDate not supplied

[Mathematical model of the sarcomagenic action of osteotropic alpha emitters].

A model for osteosarcoma induction by alpha-emitters is proposed which is based on a well-known conception on the mechanisms of radiation-induced cancer, the processes of bone tissue regeneration, and the kinetics of cells subjected to carcinogenic risk. The main mathematical relations of the proposed model are presented. The dose-effect relationship of the model is compared with the epidemiological data available on the development of osteosarcoma in patients affected by long-lived radium isotopes.

Alpha Particles↗
PubMed1986

Digital signal processing in studies of animal acoustical communication, including human speech.

The study of animal acoustical communication and other biological signals like cardiopulmonary cycles and neurological waves has advanced rapidly in the last few years. Progress has been stimulated by dramatic improvements in transducers, recorders, computers, and digital signal processing (DSP) techniques. Nevertheless, many biologists cannot take advantage of these new techniques and technology because mainframe computer usage is expensive and DSP theory is buried in highly technical engineering and mathematical journals. Recently, new developments in microcomputer hardware and commercially available DSP software have greatly improved this picture. Nevertheless, DSP theory remains largely inaccessible to the non-specialist. In this paper, selected areas of DSP theory are surveyed in relation to a common biological signal processing problem, namely, the analysis of animal acoustical signals. Signal digitization techniques are described, including the concepts of word-width, sample rate, and data encoding. An overview of the mathematical models developed for human speech encoding and analysis is presented. Finally, selected DSP techniques used in the time and frequency domains, including digital filtering, spectral analysis, and dynamic time warping are reviewed.

Animals↗
PubMed1999

A new concept for a metacarpophalangeal prosthesis: consequence on joint biomechanics.

OBJECTIVE: The purpose of this work was to establish whether surface replacement non-constrained prostheses can duplicate the normal biomechanics of the metacarpophalangeal joint. DESIGN: A series of mathematical models. BACKGROUND: A non-constrained prostheses has been designed for the replacement of the metacarpophalangeal joint. It uses the concept of surface replacement in that it attempts to replicate the anatomy of the original cartilage surfaces. The centre of rotation of the prosthesis is also sited at the same position as in the natural joint to maintain the balance between the flexor and extensor tendon forces, such that the prosthesis duplicates the biomechanics of the normal joint. Due to the unique dimensions of each joint that may present for surgery, the four sizes of prosthesis that are available for implantation may not always produce an exact replication of the joint kinematics. These situations were examined to establish whether the biomechanics of the joint can indeed be restored. METHODS: Mathematical models for each size of prosthesis implanted into a range of different sized metacarpophalangeal joints were developed. The prosthetic and cartilage surface profiles were compared and the balance between the tendon forces was examined. RESULTS: Differences in size that may occur between the surface profiles of the normal joint and prosthesis, together with any relocation of the centre of rotation, would have negligible effects on the normal joint biomechanics. CONCLUSIONS: All four sizes of the non-constrained prosthesis can duplicate the normal biomechanics of the joint and hence provide normal function.

Biomechanical Phenomena↗
PubMed1999

Revisiting the epidemiological standard of preeclampsia: primigravidity or primipaternity?

Pregnancy-induced hypertensive disorders, and especially preeclampsia, are documented to occur primarily in first pregnancies and rarely in subsequent pregnancies. Therefore, the concept of primigravidity is the epidemiological cornerstone of this disease. The authors propose a concept in which preeclampsia is a disease of new couples, especially after a short period of sexual cohabitation, and explore if this alternative primipaternity model, as compared with the primigravidity concept, provides a better fit with well-known epidemiologic descriptions. First, the primipaternity model provides a mathematical modelling which may explain the prevalence of approximately 10% in long-term monogamic populations. Further, it proposes explanations for many epidemiological descriptions which were previously difficult to understand and assemble in a single concept.

Cultural Characteristics↗
PubMed2005

Thoughts about the ventricular gradient and its current clinical use (Part I of II).

The concept of the ventricular gradient was conceived in the mind of Frank Wilson in the early 1930s. Wilson, a mathematical genius, believed that the calculation of the ventricular gradient yielded information that was not otherwise obtainable. The method of analysis was not utilized by clinicians at large because the concept was not easy to understand and because the method used to compute the direction of the ventricular gradient was so time consuming that clinicians could not use it. Grant utilized the concept to create vector electrocardiography, but he believed that if his method of analysis was used, it was not often necessary to compute the direction of the ventricular gradient. He did, however, describe an easy way to compute the direction of the ventricular gradient. The current major clinical use of the ventricular gradient is to identify primary and secondary T-wave abnormalities in an electrocardiogram showing left or right ventricular hypertrophy or left or right ventricular conduction abnormalities. In addition, the author uses the term ventricular time gradient instead of ventricular gradient in an effort to clarify the concept. Finally, the author discusses the possible clinical significance of a normally directed but shorter than normal ventricular time gradient, an attribute that has not been emphasized previously.

Action Potentials↗
PubMed1992

Perceptual and academic patterns of learning-disabled/gifted students.

This research explored ways gifted children with learning disabilities perceive and recall auditory and visual input and apply this information to reading, mathematics, and spelling. 24 learning-disabled/gifted children and a matched control group of normally achieving gifted students were tested for oral reading, word recognition and analysis, listening comprehension, and spelling. In mathematics, they were tested for numeration, mental and written computation, word problems, and numerical reasoning. To explore perception and memory skills, students were administered formal tests of visual and auditory memory as well as auditory discrimination of sounds. Their responses to reading and to mathematical computations were further considered for evidence of problems in visual discrimination, visual sequencing, and visual spatial areas. Analyses indicated that these learning-disabled/gifted students were significantly weaker than controls in their decoding skills, in spelling, and in most areas of mathematics. They were also significantly weaker in auditory discrimination and memory, and in visual discrimination, sequencing, and spatial abilities. Conclusions are that these underlying perceptual and memory deficits may be related to students' academic problems.

Achievement↗
PubMed1980

On a mathematical relationship between growth rate and life span.

Using the Principles of Similitude a relation between the life span of an organism and its growth rate, ageing rate and initial weight is derived. It is shown that considerations based only on dimensional homogeneity allow us to make non-trivial assertions about the form of the equation of state. Closely related to these considerations is the specification of dimensionless numbers which we defined in the Concept of Vitality.

Animals↗
PubMed2006

Performance analysis of LVQ algorithms: a statistical physics approach.

Learning vector quantization (LVQ) constitutes a powerful and intuitive method for adaptive nearest prototype classification. However, original LVQ has been introduced based on heuristics and numerous modifications exist to achieve better convergence and stability. Recently, a mathematical foundation by means of a cost function has been proposed which, as a limiting case, yields a learning rule similar to classical LVQ2.1. It also motivates a modification which shows better stability. However, the exact dynamics as well as the generalization ability of many LVQ algorithms have not been thoroughly investigated so far. Using concepts from statistical physics and the theory of on-line learning, we present a mathematical framework to analyse the performance of different LVQ algorithms in a typical scenario in terms of their dynamics, sensitivity to initial conditions, and generalization ability. Significant differences in the algorithmic stability and generalization ability can be found already for slightly different variants of LVQ. We study five LVQ algorithms in detail: Kohonen's original LVQ1, unsupervised vector quantization (VQ), a mixture of VQ and LVQ, LVQ2.1, and a variant of LVQ which is based on a cost function. Surprisingly, basic LVQ1 shows very good performance in terms of stability, asymptotic generalization ability, and robustness to initializations and model parameters which, in many cases, is superior to recent alternative proposals.

Algorithms↗
PubMed1991

[The energetics and economics of the cardiac pump function].

In anesthesiology and intensive care medicine it is often necessary to treat disorders involving cardiac failure or low-output syndrome. However, in patients who are endangered by ischemic heart disease, any pharmacologic therapy with positive inotropic agents should improve cardiac output without increasing myocardial oxygen demand significantly: the heart should perform its task as efficiently as possible. In the present study a mathematical model of myocardial efficiency was developed. The implications of this theoretical concept of myocardial efficiency were evaluated in animal experiments. THEORETICAL MODEL. Cardiac efficiency is predominantly dependent on preload, afterload, and inotropic state. Quantitatively, it can be calculated from end-diastolic volume, left ventricular systolic pressure (Psyst), stroke volume (SV), and ejection time. The implications of the theoretical analysis are: (1) the inotropic state, which leads to optimal myocardial efficiency, is specifically determined by preload and afterload: for each preload and afterload one matched inotropic state is necessary to achieve optimal efficiency; (2) an increase in blood pressure leads to a decrease in myocardial efficiency even if the inotropic state is optimally matched to preload and afterload; and (3) an increase in end-diastolic volume improves the efficiency of myocardial pump work. ANIMAL EXPERIMENTS. The validity of the theoretical model was studied in animal experiments with emphasis on the following items: (1) is theoretically optimal efficiency of myocardial pump work achieved by physiologic regulation of myocardial performance? (2) how does sympathetic stimulation influence myocardial efficiency? and (3) how do cardiodepressive agents such as beta-blockers or volatile anesthetics influence myocardial efficiency? METHODS. Experiments were performed on nine mongrel dogs after induction of piritramide--nitrous oxide anesthesia. Standard hemodynamics: heart rate, Psyst, maximum left ventricular pressure rise (dP/dtmax), and SV (thermodilution) as well as coronary blood flow (pressure difference catheter) and myocardial oxygen consumption (Fick principle) were measured. In order to create a broad range of different hemodynamic settings, blood withdrawal and retransfusion of blood and/or colloid osmotic solutions were used to modify intravascular volume. Additionally, the inotropic state was varied by infusion of catecholamines (isoproterenol 0.4-0.8 microgram.kg-1.min-1 or norepinephrine 1-2 micrograms.kg-1.min-1). Experimental myocardial failure was induced by adding halothane (0.8-1.5 MAC) to the basic anesthesia, beta-blockade with propranolol (125-250 micrograms.kg-1), and combination of beta-blockade with a pressure load imposed on the myocardium (propranolol 125-250 micrograms.kg-1 + norepinephrine 1-2 micrograms.kg-1.min-1). RESULTS. During variation of the intravascular blood volume by normo-, hypo-, and hypervolemia, the myocardial efficiency very closely matched the theoretically predicted values of optimal efficiency: the average observed efficiency was 98.8% of predicted optimal efficiency. Increasing afterload with norepinephrine did not alter this close relationship, although absolute values of efficiency decreased as predicted by the theoretical model. Application of isoproterenol resulted in SVs that exceeded optimal values by 41.5%. In contrast, during experimental myocardial failure SVs were too small to achieve the necessary values for optimal pump work; observed myocardial efficiency was therefore significantly lower than optimal efficiency. CONCLUSIONS. For pharmacological interventions, it can be concluded that maximal efficiency of cardiac pump work requires maximal end-diastolic filling in combination with minimal afterload. (ABSTRACT TRUNCATED AT 400 WORDS)

Anesthesia, Inhalation↗
PubMed1979

A computer program for simulating a distributed metabolic system. Distribution volumes in a simulated organism.

A metabolite or hormone is distributed with non-uniform concentration throughout some volume within an intact organism. Various methods involving radioactive tracers are used to estimate the total mass of the metabolite and its volume of distribution. The calculations of mass and volume are based on very simple models, and cannot usually be validated by measurements on the real animal. Hence we have developed a computer program for simulating a metabolic system with convective and diffusive transport. The tracer experiments can be simulated by solving the differential equations for convective diffusion by finite element methods. Thus the total metabolic mass and distribution volume can be both 'measured' and calculated by all the standard techniques. In this way some mathematical methods currently in general use can be seen to be patently incorrect, and others quite acceptable. The concept of a metabolic doublet was introduced, by analogy with an electrical dipole.

Biological Transport↗
PubMed2006

Subitizing, magnitude representation, and magnitude retrieval in deaf and hearing adults.

This study examines basic number processing (subitizing, automaticity, and magnitude representation) as the possible underpinning of mathematical difficulties often evidenced in deaf adults. Hearing and deaf participants completed tasks to assess the automaticity with which magnitude information was activated and retrieved from long-term memory (using a Stroop-like paradigm to assess congruity effects), the representational format of magnitude information (by analysis of distance and Spatial Numerical Association of Response Codes effects), and the ability to rapidly enumerate small sets (subitizing). Both groups showed distance effects taken to indicate the use of a visual-spatial analog number line representing approximate quantity. Furthermore, both groups showed similar patterns of performance on the subitizing tasks and showed similar amounts of interference in an analysis of congruity effects. This is taken as evidence against the notion that idiosyncratic differences in basic number processing account for mathematical difficulties experienced by deaf individuals.

Adolescent↗
PubMed2002

Effects of coding dictionary on signal generation: a consideration of use of MedDRA compared with WHO-ART.

To support signal generation a terminology should facilitate recognition of medical conditions by using terms which represent unique concepts, providing appropriate, homogeneous grouping of related terms. It should allow intuitive or mathematical identification of adverse events reaching a threshold frequency or with disproportionate incidence, permit identification of important events which are commonly drug-related, and support recognition of new syndromes. It is probable that the Medical Dictionary for Regulatory Activities (MedDRA) preferred terms (PTs) or high level terms (HLTs) will be used to represent adverse events for the purposes of signal generation. A comparison with 315 WHO Adverse Reaction Terminology (WHO-ART) PTs showed that for about 72% of WHO-ART PTs, there were one or two corresponding MedDRA PTs. However, there were instances where there were many MedDRA PTs corresponding to single WHO-ART PTs. In many cases, MedDRA HLTs grouped large numbers of PTs and sometimes there could be problems when a single HLT comprises PTs which represent very different medical concepts, or conditions which differ greatly in their clinical importance. Further studies are needed to compare the way in which identical data sets coded with MedDRA and with other terminologies actually function in generating and exploring signals using the same methods of detection and evaluation.

Adverse Drug Reaction Reporting Systems↗
PubMed1975

Gamma-ray spectrometry data collection and reduction by simple computing systems.

The review summarizes the present state of the involvement of relatively small computing devices in the collection and processing of gamma-ray spectrum data. An economic and utilitarian point of view has been chosen with regard to data collection in order to arrive at practically valuable conclusions in terms of feasibility of possible configurations with respect to their eventual application. A unified point of view has been adopted with regard to data processing by developing an information theoretical approach on a more or less intuitive level in an attempt to remove the largest part of the virtual disparity between the several processing methods described in the literature. A synoptical introduction to the most important mathematical methods has been incorporated, together with a detailed theoretical description of the concept gamma-ray spectrum. In accordance with modern requirements, the discussions are mainly oriented towards high-resolution semiconductor detector-type spectra. The critical evaluation of the processing methods reviewed is done with respect to a set of predefined criteria. Smoothing, peak detection, peak intensity determination, overlapping peak resolving and detection and upper limits are discussed in great detail. A preferred spectrum analysis method combining powerful data reduction properties with extreme simplicity and speed of operation is suggested. The general discussion is heavily oriented towards activation analysis application, but other disciplines making use of gamma-ray spectrometry will find the material presented equally useful. Final conclusions are given pointing to future developments and shifting their centre of gravity towards improving the quality of the measurements rather than expanding the use of tedious and sophisticated mathematical techniques requiring the limits of available computational power.

Activation Analysis↗