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PubMed1998

Statistical quality control methods in infection control and hospital epidemiology, part I: Introduction and basic theory.

This article is the first in a two-part series discussing and illustrating the application of statistical process control (SPC) to processes often examined by hospital epidemiologists. The basic philosophical and theoretical foundations of statistical quality control and their relation to epidemiology are emphasized in order to expand mutual understanding and cross-fertilization between these two disciplines. Part I provides an overview of quality engineering and SPC, illustrates common types of control charts, and provides references for further information or statistical formulae. Part II discusses statistical properties of control charts, issues of chart design and optimal control limit widths, alternate possible SPC approaches to infection control, some common misunderstandings, and more advanced issues. The focus of both articles is mostly non-mathematical, emphasizing important concepts and practical examples rather than academic theory and exhaustive calculations.

Humans↗
PubMed1981

Identifying and remediating specific deficiencies of entering medical students.

For many reasons some entering medical students have specific deficiencies in substantive areas. This study describes a methodology used successfully in the areas of anatomy terminology, behavioral science concepts, and applied mathematics both to identify students with these deficiencies and to provide the required remediation. The methodology involves empirical identification of what students need to know, the use of specially constructed criterion-referenced tests, and "stand-alone" instructional materials. Benefits of the methodology include assurance that all students have certain minimal skills and competencies, specification for faculty of the students' skills and knowledge, and a reported increase in student confidence in the areas covered.

Anatomy↗
PubMed2007

The reinfection threshold regulates pathogen diversity: the case of influenza.

The awareness that pathogens can adapt and evolve over relatively short time-scales is changing our view of infectious disease epidemiology and control. Research on the transmission dynamics of antigenically diverse pathogens is progressing and there is increasing recognition for the need of new concepts and theories. Mathematical models have been developed considering the modelling unit in two extreme scales: either diversity is not explicitly represented or diversity is represented at the finest scale of single variants. Here, we use an intermediate approach and construct a model at the scale of clusters of variants. The model captures essential properties of more detailed systems and is much more amenable to mathematical treatment. Specificities of pathogen clusters and the overall potential for transmission determine the reinfection rates. These are, in turn, important regulators of cluster dynamics. Ultimately, we detect a reinfection threshold (RT) that separates different behaviours along the transmissibility axis: below RT, levels of infection are low and cluster substitutions are probable; while above RT, levels of infection are high and multiple cluster coexistence is the most probable outcome.

Animals↗
PubMed2000

On imputing function to structure from the behavioural effects of brain lesions.

What is the link, if any, between the patterns of connections in the brain and the behavioural effects of localized brain lesions? We explored this question in four related ways. First, we investigated the distribution of activity decrements that followed simulated damage to elements of the thalamocortical network, using integrative mechanisms that have recently been used to successfully relate connection data to information on the spread of activation, and to account simultaneously for a variety of lesion effects. Second, we examined the consequences of the patterns of decrement seen in the simulation for each type of inference that has been employed to impute function to structure on the basis of the effects of brain lesions. Every variety of conventional inference, including double dissociation, readily misattributed function to structure. Third, we tried to derive a more reliable framework of inference for imputing function to structure, by clarifying concepts of function, and exploring a more formal framework, in which knowledge of connectivity is necessary but insufficient, based on concepts capable of mathematical specification. Fourth, we applied this framework to inferences about function relating to a simple network that reproduces intact, lesioned and paradoxically restored orientating behaviour. Lesion effects could be used to recover detailed and reliable information on which structures contributed to particular functions in this simple network. Finally, we explored how the effects of brain lesions and this formal approach could be used in conjunction with information from multiple neuroscience methodologies to develop a practical and reliable approach to inferring the functional roles of brain structures.

Behavior↗
PubMed2001

Stress, strain, and mechanotransduction in cells.

It is widely accepted that numerous cell types respond to mechanical stimuli, yet there is no general agreement as to whether particular cells respond directly to stress, strain, strain-rate, strain-energy, or other mechanical quantities. By recalling the definitions of the mathematical (not physical) concepts of stress and strain, it is suggested herein that cells cannot respond directly to these continuum metrics or to quantities derived from them--mechanistic models will need to be based on more fundamental quantities, as, for example, inter-atomic forces or conformational changes of the appropriate molecules. Nonetheless, the concepts of stress and strain should continue to play an important role in mechanobiology, both in the identification of empirical correlations and in the development of phenomenological constitutive models, each of which can contribute to our basic understanding as well as help in the design of future experiments and some clinical interventions. It is important to remember, therefore, that empirical correlations and most constitutive relations in continuum mechanics do not seek to model the actual physics--rather, their utility is in their predictive capability, which is often achieved via different relations in terms of different metrics for the same material under different conditions. Hence, with regard to quantifying cellular responses to mechanical stimuli, we must delineate between the identification of fundamental mechanisms and the formulation of phenomenological correlations, the latter of which only requires convenient metrics that need not be unique or physical.

Biomechanical Phenomena↗
PubMed1997

Regression towards the mean, historically considered.

The simple yet subtle concept of regression towards the mean is reviewed historically. Verbal, geometric, and mathematical expressions of the concept date to the discoverer of the concept, Francis Galton. That discovery and subsequent understanding (and misunderstanding) of the concept are surveyed.

Biometry↗
PubMed1973

Task analysis in curriculum design: a hierarchically sequenced introductory mathematics curriculum.

A method of systematic task analysis is applied to the problem of designing a sequence of learning objectives that will provide an optimal match for the child's natural sequence of acquisition of mathematical skills and concepts. The authors begin by proposing an operational definition of the number concept in the form of a set of behaviors which, taken together, permit the inference that the child has an abstract concept of "number". These are the "objectives" of the curriculum. Each behavior in the defining set is then subjected to an analysis that identifies hypothesized components of skilled performance and prerequisites for learning these components. On the basis of these analyses, specific sequences of learning objectives are proposed. The proposed sequences are hypothesized to be those that will best facilitate learning, by maximizing transfer from earlier to later objectives. Relevant literature on early learning and cognitive development is considered in conjunction with the analyses and the resulting sequences. The paper concludes with a discussion of the ways in which the curriculum can be implemented and studied in schools. Examples of data on individual children are presented, and the use of such data for improving the curriculum itself, as well as for examining the effects of other treatment variables, is considered.

Journal Article↗
PubMedDate not supplied

[A stochastic approach to solving the problem of sensory system thresholds].

On the basis of an analysis of mathematical models realizing concept of discrete and signal detection probability of the threshold it is shown that utilization for describing the discrete model concepts of probability and the apparatus of Dirac delta functions and root-mean-square of noise distribution being reduced to zero in the continuous model the analytical expressions of the models are identical. The evidence obtained shows inner unity of the examined thresholds models and universal nature of the thresholds model of Swets, Tanner and Birdsall built on the basis of the statistical theory of signal detectability. It provides solution of one of the central problems of psychophysics--that of the threshold of the sensory systems.

Models, Theoretical↗
PubMedDate not supplied

Attention, the intersection of cost and quality in health care.

A method for assessing health care technology that models the demand on the clinician's attention exerted by patients' data (diagnostic and therapeutic) can provide a means for simultaneously reducing the cost and improving the quality of health care. The attentional demand exerted by patients' data can be measured by the amount of uncertainty in the data. Uncertainty can be expressed mathematically by the concept of entropy in information theory.

Health Services Needs and Demand↗
PubMedDate not supplied

High-dose-rate afterloading and the LQ-model--evaluation of efficacy in cervix cancer therapy.

For short-time afterloading with high dose rates at irradiation treatment of gynecological tumors an adequate fractioning with reduced total dose is necessary considering the basically changed dose-time relation opposite to the common long-time brachytherapy. In addition to the careful clinical control of empiric found fractioning regimes for the primary and postoperative intrauterine and intravaginal afterloading therapy in cervix carcinoma and endometrium carcinoma, at which the surroundings reactions of the urine bladder, rectum and sheath, and also the tumor regression and relapses were investigated, a calculation of equivalent doses seems to be recommendable by means of mathematically formulated model conception according to the NSD formula and the LQ model. Changed exponents p for the fractioning rate N depending on the total treatments time were used for the rate calculations at slowly fractionated small-volume irradiation opposite to a higher fractionated percutaneous great-volume irradiation NSD conception was developed for. In LQ-model calculation changed coefficients mu for the repair half-life-time T in connection to the changed repair capacity in small volume brachytherapy were used. Knowing the compatibility and tumor efficiency of the rate-values and the alpha/beta-ratio for different fraction regimes were calculated and compared concerning their radiobiological equivalence and practical use. The calculations show a good clinical correspondence for single and total dosage in fractionated high dose rate afterloading of gynecological tumors.

Brachytherapy↗
PubMed1994

Computer modelling of processes in ecosystems--general principles.

Concept of the mathematical modelling of ecosystems is presented, starting with a set of variables and a set of relations. Examples are given for the models of plant populations in terrestrial ecosystems. The differences between well-structured and ill-structured problems are shown with some methodological consequences for strategy of applications of computer models.

Computer Simulation↗
PubMedDate not supplied

A unique vascular graft concept for coronary and peripheral applications.

Synthetic vascular grafts for coronary bypass (3-4 mm inner diameter [ID], 40-100 ml/min) continue to fail despite success in high flow peripheral applications. A unique method is presented that uses a fluid dynamic approach to improve patency. A large diameter graft (5-6 mm ID) is used with an arteriovenous (AV) shunt to create a high flow rate (350-650 ml/min); a Venturi flow resistance controls the AV shunt and provides high pressure to the coronary arteries. The resulting graft can supply as many coronary arteries as required by means of side to side anastomoses upstream from the Venturi resistance. The concept was studied in a mock circulation system to analyze fluid dynamics under pulsatile flow. Mathematical models were used to study laminar and turbulent shear stresses and flow distributions over the physiologic range of Reynolds numbers. In vitro testing demonstrated little bovine red blood cell (RBC) hemolysis (0.249 mg Hb/min) compared with other devices. In vivo testing in sheep showed no significant acute changes in pulse rate or blood pressure in response to the shunt. The fluid and mathematical modeling of this concept has additional application in the study of flow past stenoses.

Animals↗
PubMed1994

New concepts in the study of tissue vascularization: a mathematical model of skin vascularization.

A preliminary study demonstrated the existence of a fractal structure for perforator arterial vessels of the skin and proved to be a useful tool to compare vascular trees on the basis of their complexity. Fractal analysis of axial-perforator arteriovenous vascular trees was performed on the skin of mice after injection of the arterial network by india ink. Fractal analysis was performed by box counting. Fractal dimension D was determined for 35 venous and 31 arterial perforator vessels (D = 1.302 and 1.264, respectively) and 5 venous and 3 arterial axial vessels (D = 1.374 and 1.328, respectively) (r2 > or = 0.985). All vascular networks show a fractal structure, characterized by a specific D. These values are relatively constant; D is a function of the anatomic and physiologic characteristics. There was no significant difference between venous and arterial networks, nor was there between axial and perforator networks (p < 0.05); this demonstrates a similar efficacy in terms of perfusion of the skin. A computer simulation based on fractal theory has been developed to reproduce the two kinds of vascular networks. Fractals are the result of a construction procedure that is repeated and repeated so that the iteration of a very simple rule can produce seemingly complex shapes, such as vascular networks. The basic module that is repeated in the whole structure is Y-shaped and is termed the generator; this generator is applied to a basic structure, called the initiator. After a few iterations, a vascular network is obtained. The difference between axial and perforator vascular networks is the choice of the initiator, whereas the generator is identical.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗
PubMed1989

Towards the development of a mathematical model for acupuncture meridians.

Traditional concepts of classical acupuncture and Chinese medicine come from a culture which is very different from ours, and there has been considerable problems in their accurate presentation. Our approach is to attempt the development of a mathematical language that links these traditional concepts theoretically to models that can be experimentally tested. We first review some of Manaka's findings, confirmed also by our results, having to do with low intensity stimuli. In particular, Manaka applied polarized agents such as Cu(+) and Zn(-) to nonacupuncture points on a meridian and to the so called "mother and child" points on a meridian. In both cases he observed the pressure pain reaction which increased for one orientation of Cu and Zn on the meridian and decreased for the opposite orientation. Note that in the case of "mother and child" points the observed reaction was in agreement with the so called "five phase (five element)" theory. Also, in the case of the "mother and child" points the effect usually lasted considerably longer than in the case of nonacupuncture points on a meridian. Taking into account the connection between Manaka's results and skin electrical measurements by some electrodermal diagnostic instruments such as Motoyama's AMI, we discuss some equivalent electric circuits for a single meridian and relate them to the nervous system response. In particular, an electrical circuit model similar to the synapse membrane with two ionic channels seems to be especially useful when we try to explain Manaka's clinical results and Motoyama's results on the velocity of propagation of electrical impulses along meridians. We also develop a mathematical model in the form of a linear five dimensional dynamical system of the so called "five phase (five element)" laws such as "creative" cycle, "controlling" cycle, etc., in the case of a single meridian. We connect this model with the membrane type model mentioned above by assuming a simple mass action law, for the dependence of the conductances in the ionic channels on the input signals. This combined model is used to describe the development of a "disease" and its treatment according to the "five phase" theory. Here we interpret the "disease" as a blockage in a meridian, while the treatment initiates the unblocking process.

Acupuncture Therapy↗
PubMed1993

A multidimensional model of the effect of gravity on the spatial orientation of the monkey.

A "sensory conflict" model of spatial orientation was developed. This mathematical model was based on concepts derived from observer theory, optimal observer theory, and the mathematical properties of coordinate rotations. The primary hypothesis is that the central nervous system of the squirrel monkey incorporates information about body dynamics and sensory dynamics to develop an internal model. The output of this central model (expected sensory afference) is compared to the actual sensory afference, with the difference defined as "sensory conflict." The sensory conflict information is, in turn, used to drive central estimates of angular velocity ("velocity storage"), gravity ("gravity storage"), and linear acceleration ("acceleration storage") toward more accurate values. The model successfully predicts "velocity storage" during rotation about an earth-vertical axis. The model also successfully predicts that the time constant of the horizontal vestibulo-ocular reflex is reduced and that the axis of eye rotation shifts toward alignment with gravity following postrotatory tilt. Finally, the model predicts the bias, modulation, and decay components that have been observed during off-vertical axis rotations (OVAR).

Animals↗
PubMed1998

Structure, use, and validation of the IEUBK model.

The potential impact of the effects of lead in children is a major concern. Although measurements of lead concentration can be made in a geographic area, it is difficult to predict the effects of this exposure that involve complicated biologic functions. Dynamic mathematical models that can be simulated on a digital computer provide one method of analysis to facilitate the prediction process. The integrated exposure uptake biokinetic (IEUBK) model is a dynamic mathematical model that has been discretized for execution on a digital computer. This paper is concerned with the general difficulties in validating a dynamic model of this type. A number of the general pitfalls of validating a model of this type are presented. The illustrations are of a general nature not requiring an understanding of the physiologic effects of lead on children. The concept of validating a model by comparing results to historical data is discussed. A comparison is made with traditional modeling efforts having this form of dynamic model. Also included are general mathematic concepts illustrating potential difficulties with intuitive analyses in calibrating a dynamic model.

Animals↗
PubMed1994

Information and clonal concepts in ageing.

A model based on information theory and one based on somatic mutation in an expanding pool of cells are combined to give a theory of ageing. A mathematical formula, based on concepts from information theory, gives a close fit to the age incidence of mortality and disease in middle and old age. The basic concept is that biological systems process information and make decisions to maintain their integrity. But the decision process is fallible and significant errors could lead to disease or death. Decay in the components of the system will lead to a rising error rate with age and the form of the curve will be influenced by redundancy which is a fundamental property of information systems. In addition it is suggested that an important part of the decay in the decision process is due to a subset of mutant stem cells which have a proliferative advantage and slowly expand in number throughout life. This idea is derived from application of a model of somatic mutation in expanding cells to data in cancer and on the increase of dominant mutations with paternal age. This composite view explains why ageing is less subject to the vagaries of the extrauterine environment than suggested by the simple information model and points to a significant role for the intrauterine environment in the ageing process.

Aging↗