Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Mathematical Concepts”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 901 records · Page 50Linked to original sources
PubMed2002

A new hypothesis (concept) of diagnosing Alzheimer's disease.

The diagnosis of dementia has proven problematic due to different criteria. Even neuropathological changes are arbitrarily defined. A mathematical model is proposed that may standardize diagnosis of dementia, and Alzheimer's disease was used as an example. The model suggests that there are cognitive decline curves that represent the rate of natural attrition for neurons in the cerebral cortex. In normal aging, each individual will lose neurons along one curve. Individuals with higher brain reserve will start off at a higher percentile. An accelerated loss of neurons (dementia) is depicted as a deviation from the natural cognitive decline curve. This model may differentiate age-related cognitive decline from dementia or preclinical dementia. Furthermore, it may allow dementia to be diagnosed earlier, hence earlier treatment. Comparison of data may be easier and more valid if the diagnosis of dementia is standardized under this model. Advantages and challenges of this concept are further discussed.

Age Factors↗
PubMed1981

The relationship between therapist-client interpersonal compatibility, sex of therapist, and therapeutic outcome.

Explored the relationship between therapist-client interpersonal compatibility, sex of therapist, and psychotherapeutic outcome. The research sample consisted of 48 therapist-client dyads. The therapists were all graduate students enrolled in an individual therapy practicum, while the client sample was composed of 48 undergraduate female (mean age 19.3 years). The interpersonal compatibility of the dyads was determined from the FIRO-B results for each of the members' using a modification of Schutz's (1966) original mathematical schema. Therapy outcome was determined from pretherapy and posttherapy testing with the Tennessee Self Concept Scale and Mooney Problem Check List. A 3 X 2 research design with one concomitant variable (pretest) was used and data were analyzed using an analysis of covariance procedure. Results suggested that among this sample the sex of therapist did not have a significant differential effect. There was also a consistent lack of interaction effects between dyadic compatibility and sex of therapist. However, significant differences in therapeutic outcome across the levels of compatibility were observed.

Adjustment Disorders↗
PubMed2000

Metabolic control of contractile performance in isolated perfused rat heart. Analysis of experimental data by reaction:diffusion mathematical model.

The intracellular mechanisms of regulation of energy fluxes and respiration in contracting heart cells were studied. For this, we investigated the workload dependencies of the rate of oxygen consumption and metabolic parameters in Langendorff-perfused isolated rat hearts.(31)P NMR spectroscopy was used to study the metabolic changes during transition from perfusion with glucose to that with pyruvate with and without active creatine kinase system. The experimental results showed that transition from perfusion with glucose to that with pyruvate increased the phosphocreatine content and stability of its level at increased workloads. Inhibition of creatine kinase reaction by 15-min infusion of iodoacetamide decreased the maximal developed tension and respiration rates by a factor of two.(31)P NMR data were analyzed by a mathematical model of compartmentalized energy transfer, which is independent from the restrictions of the classical concept of creatine kinase equilibrium. The analysis of experimental data by this model shows that metabolic stability-constant levels of phosphocreatine, ATP and inorganic phosphate-at increased energy fluxes is an inherent property of the compartmentalized system. This explains the observed substrate specificity by changes in mitochondrial membrane potential. The decreased maximal respiration rate and maximal work output of the heart with inhibited creatine kinase is well explained by the rise in myoplasmic ADP concentration. This activates the adenylate kinase reaction in the myofibrillar space and in the mitochondria to fulfil the energy transfer and signal transmission functions, usually performed by creatine kinase. The activity of this system, however, is not sufficient to maintain high enough energy fluxes. Therefore, there is a kinetic explanation for the decreased maximal respiration rate of the heart with inhibited creatine kinase: i.e. a kinetically induced switch from an efficient energy transfer pathway (PCr-CK system) to a non-efficient one (myokinase pathway) within the energy transfer network of the cell under conditions of low apparent affinity of mitochondria to ADP in vivo. This may result in a significant decrease in the thermodynamic affinity of compartmentalized ATPase systems and finally in heart failure.

Animals↗
PubMed1981

Hierarchical organization, integrations in biology and cancer, balance loss, and a question on modernism.

The hierarchical organization of biological processes is considered in the light of universal interrelationships of each and every factor affecting open systems such as human life. The maintenance of health and/or the production of disease are viewed at different levels of biological organization as related to the dualistic concept. The relative effects of environmental versus genetic tendencies in the pathogenesis of "disease" are mathematically formulated as related to time and location. Psychological determinants are considered as cause and as consequence of the onset of somatic disease. The multifactorial aspects of chronic pathology are seen in relation to dominant tendencies in life and in medical sciences, as well as to individual factors. The "non-specificity" of some aspects of cancer as related to "Adaptation" is advanced. Doubts are raised regarding the ultimate value of modern technological achievements and overspecialization per se, as well as on the lines followed by modern trends in the organization of cancer research. Finally, the increasing need for progressive thoughtful integration versus increasing specialization is stressed.

Disease↗
PubMed1995

G explained.

This paper presents the hypothesis that the general factor, g, which emerges from psychometric batteries and which has been equated with general intelligence, is the result of a physical brain feature which enhances neural network efficiency and is determined for the brain in general. This conception of intelligence provides a resolution of the unity-versus-modularity debate in the intelligence field and yields specific predictions as to the nature and kind of brain features that will be found to provide a physical explanation for g. To avoid nosological confusion, it is suggested that 'n' be used to represent the neurological concept of general intelligence while 'g' should continue to denote the general factor emerging from mathematical analyses of mental test batteries.

Animals↗
PubMed1985

Theorems on log-convex disposition curves in drug and tracer kinetics.

Conventionally, analysis of the dynamic behaviour of substances in the whole organism is based on the multiexponential paradigm (compartmental model). Alternatively the use of power functions has been proposed. In this paper a unified view is developed investigating the implications of observed log-convexity of disposition (clearance) curves. Using a non-compartmental approach it is proved that the disposition residence time distribution corresponding to a log-convex impulse response (blood concentration-time curve) belongs to the DFR (decreasing failure rate) class, implying that (1) the disposition curve has an exponential tail and (2) the relative dispersion of residence times is greater than or equal to one. This class of disposition curves includes multiexponential and power functions as special cases. In terms of the underlying biophysical principles the DFR property is discussed as a consequence of a dominant role of passive distribution processes of particles in the organism. The paper also deals with the corresponding properties of a recirculatory model using renewal theoretic concepts.

Diagnostic Uses of Chemicals↗
PubMed2006

A non-invasive tissue-specific molecular delivery method of cancer gene therapy.

A Japanese word, monozukuri (literally translated "making things") is the philosophy of first having the idea and then the faith in the technical expertise and experience to accomplish the result. We believe that the concept of engineering is monozukuri. Through the process of monozukuri, engineered natural science based on mathematics and physics has been developed. Medicine is the field of study which has been developed for maintaining daily healthy life with diagnosis, treatment, examination, and protection. Biomedical engineering is the interdisciplinary study of engineering and medicine, and should be developed based on monozukuri. In this particular research, we have developed a physical molecular delivery method for cancer gene therapy using nano/microbubbles and ultrasound. First, the behavior of cavitation bubbles and subsequent shock wave phenomena involved in the mechanism of molecular delivery were analyzed, combining theory and computer simulation. In a second step, the methodology was optimized in vitro and in vivo. Finally, the therapeutic potential of the method in pre-clinical models was evaluated using transgenes relevant to cancer gene therapy instead of reporter genes, and whole body, non-invasive imaging using single photon emission computed tomography (SPECT/CT) was used to evaluate the selectivity of gene delivery in vivo.

Animals↗
PubMed2001

An information-based sequence distance and its application to whole mitochondrial genome phylogeny.

MOTIVATION: Traditional sequence distances require an alignment and therefore are not directly applicable to the problem of whole genome phylogeny where events such as rearrangements make full length alignments impossible. We present a sequence distance that works on unaligned sequences using the information theoretical concept of Kolmogorov complexity and a program to estimate this distance. RESULTS: We establish the mathematical foundations of our distance and illustrate its use by constructing a phylogeny of the Eutherian orders using complete unaligned mitochondrial genomes. This phylogeny is consistent with the commonly accepted one for the Eutherians. A second, larger mammalian dataset is also analyzed, yielding a phylogeny generally consistent with the commonly accepted one for the mammals. AVAILABILITY: The program to estimate our sequence distance, is available at http://www.cs.cityu.edu.hk/~cssamk/gencomp/GenCompress1.htm. The distance matrices used to generate our phylogenies are available at http://www.math.uwaterloo.ca/~mli/distance.html.

Animals↗
PubMed2001

A unified formalism using effective surface permittivity to study acoustic waves in various anisotropic and piezoelectric multilayers.

A unified formalism is presented that uses the effective surface permittivity (ESP) to study surface acoustic waves (SAW) in layered substrates and guided waves in layered plates. Based on known mathematical tools, such as ordinary differential equation and transfer matrix, a generalized surface impedance (GSI) concept is developed and exploited to investigate the acoustic propagation in various anisotropic and piezoelectric layered structures. The ESP function, originally defined for the surface of a homogeneous and semi-infinite piezoelectric substrate, is extended to both the top surface of and an interface in a layered half space, as well as to either surface of a finite-thickness plate. General ESP expressions for all mentioned configurations are derived in terms of an equivalent GSI matrix. It is shown that, when using the appropriate GSI matrices, the same form of the ESP expressions applies no matter whether the structure is a homogeneous half space alone or coated with a layered plate or a layered plate alone. GSI matrices are explicitly given in terms of the bulk partial mode solutions for a substrate and via the transfer matrix for a plate. Modified GSI matrices for structures consisting of both a plate and a substrate are also specified. Analytical development is fully detailed to suit program implementation. To illustrate its versatility, the formalism is also applied to two-substrate configurations, allowing one to analyze guided waves in a plate sandwiched between and interfacial waves existing along the boundary of two different media. Numerical examples are given to illustrate the spectrum features that the ESP shows for various structures. Deduced ESP expressions allow one to locate directly all piezoelectrically active waves in any structure including at least one piezoelectric layer. Acoustic modes that are not piezoelectrically active and those in non-piezoelectric materials can be also obtained by using the intermediate results, such as derived GSI matrices.

Journal Article↗
PubMed2003

Perspective: repression of competition and the evolution of cooperation.

Repression of competition within groups joins kin selection as the second major force in the history of life shaping the evolution of cooperation. When opportunities for competition against neighbors are limited within groups, individuals can increase their own success only by enhancing the efficiency and productivity of their group. Thus, characters that repress competition within groups promote cooperation and enhance group success. Leigh first expressed this idea in the context of fair meiosis, in which each chromosome has an equal chance of transmission via gametes. Randomized success means that each part of the genome can increase its own success only by enhancing the total number of progeny and thus increasing the success of the group. Alexander used this insight about repression of competition in fair meiosis to develop his theories for the evolution of human sociality. Alexander argued that human social structures spread when they repress competition within groups and promote successful group-against-group competition. Buss introduced a new example with his suggestion that metazoan success depended on repression of competition between cellular lineages. Maynard Smith synthesized different lines of thought on repression of competition. In this paper, I develop simple mathematical models to illustrate the main processes by which repression of competition evolves. With the concepts made clear, I then explain the history of the idea. I finish by summarizing many new developments in this subject and the most promising lines for future study.

Animals↗
PubMed2000

Nonlinear EEG analysis and its potential role in epileptology.

Deterministic chaos offers a striking explanation for apparently irregular behavior of the brain that is evidenced in the EEG. Recent developments in the physical-mathematical framework of the theory of nonlinear dynamics (colloquially often termed chaos theory) provide new concepts and powerful algorithms to analyze such time series. Because of its high versatility, nonlinear time series analysis has already gone beyond the physical sciences and, at present, is being successfully applied in a variety of disciplines, including cardiology, neurology, psychiatry, and epileptology. However, it is well known that different influencing factors limit the use of nonlinear measures to characterize EEG dynamics in a strict sense. Nevertheless, when interpreted with care, relative estimates of, e.g., the correlation dimension or the Lyapunov exponents, can reliably characterize different states of normal and pathologic brain function. In epileptology, extraction of nonlinear measures from the intracranially recorded EEG promises to be important for clinical practice. In addition to an immense reduction of information content of long-lasting EEG recordings, previous studies have shown that these measures enable (a) localization of the primary epileptogenic area in different cerebral regions during the interictal state, (b) investigations of antiepileptic drug effects, (c) analyses of spatio-temporal interactions between the epileptogenic zone and other brain areas, and (d) detection of features predictive of imminent seizure activity. Nonlinear time series analysis provides new and supplementary information about the epileptogenic process and thus contributes to an improvement in presurgical evaluation.

Brain Mapping↗
PubMed2006

Towards a theory of a solution space for the biplane imaging geometry problem.

Biplane angiographic imaging is a primary method for visual and quantitative assessment of the vasculature. In order to reliably reconstruct the three-dimensional (3D) position, orientation, and shape of the vessel structure, a key problem is to determine the rotation matrix R and the translation vector t which relate the two coordinate systems. This so-called Imaging Geometry Determination problem is well studied in the medical imaging and computer vision communities and a number of interesting approaches have been reported. Each such technique determines a solution which yields 3D vasculature reconstructions with errors comparable to other techniques. From the literature, we see that different techniques with different optimization strategies yield reconstructions with equivalent errors. We have investigated this behavior, and it appears that the error in the input data leads to this equivalence effectively yielding what we call the solution space of feasible geometries, i.e., geometries which could be solutions given the error or uncertainty in the input image data. In this paper, we lay the theoretical framework for this concept of a solution space of feasible geometries using simple schematic constructions, deriving the underlying mathematical relationships, presenting implementation details, and discussing implications and applications of the proposed idea. Because the solution space of feasible geometries encompasses equivalent solutions given the input error, the solution space approach can be used to evaluate the precision of calculated geometries or 3D data based on known or estimated uncertainties in the input image data. We also use the solution space approach to calculate an imaging geometry, i.e., a solution.

Algorithms↗
PubMed2000

Population preventable fraction of bicycle related head injuries.

OBJECTIVE: This study analyzes the population attributable fraction (PAF) of bicycle head injuries due to non-helmet use. METHODS: The concept of the PAF and Levin's formula for its calculation were used to develop mathematical models for estimation of: (i) attributable fraction of bicycle related head injuries in the population due to non-helmet use, (ii) expected proportion of helmeted cases among all head injuries, and (iii) estimate of the helmet use rate in the population based on patient case information. The PAF was calculated for a sample of injuries from Stavanger, Norway. RESULTS: Levin's formula was used to calculate the PAF. Two additional mathematical models were developed for calculating the expected proportion of helmeted cases and the estimation of the helmet use rate in the population. The P calculation examples for all models were is shown. It was estimated that 133 out of 210 injuries could have been avoided in Stavanger between 1990 and 1996 if all children aged 0-14 had used helmets. CONCLUSIONS: If applied correctly, the PAF is a valid and useful indicator for the population effects of bicycle helmets. The models developed in this study may help to better interpret and predict the population effects of helmet promotion interventions.

Adolescent↗
PubMed2005

A brief conceptual tutorial on multilevel analysis in social epidemiology: interpreting neighbourhood differences and the effect of neighbourhood characteristics on individual health.

STUDY OBJECTIVE: Using a conceptual rather than a mathematical approach, this article proposed a link between multilevel regression analysis (MLRA) and social epidemiological concepts. It has been previously explained that the concept of clustering of individual health status within neighbourhoods is useful for operationalising contextual phenomena in social epidemiology. It has been shown that MLRA permits investigating neighbourhood disparities in health without considering any particular neighbourhood characteristic but only information on the neighbourhood to which each person belongs. This article illustrates how to analyse cross level (neighbourhood-individual) interactions, how to investigate associations between neighbourhood characteristics and individual health, and how to use the concept of clustering when interpreting those associations and geographical differences in health. DESIGN AND PARTICIPANTS: A MLRA was performed using hypothetical data pertaining to systolic blood pressure (SBP) from 25 000 subjects living in the 39 neighbourhoods of an imaginary city. Associations between individual characteristics (age, body mass index (BMI), use of antihypertensive drug, income) or neighbourhood characteristic (neighbourhood income) and SBP were analysed. RESULTS: About 8% of the individual differences in SBP were located at the neighbourhood level. SBP disparities and clustering of individual SBP within neighbourhoods increased along individual BMI. Neighbourhood low income was associated with increased SBP over and above the effect of individual characteristics, and explained 22% of the neighbourhood differences in SBP among people of normal BMI. This neighbourhood income effect was more intense in overweight people. CONCLUSIONS: Measures of variance are relevant to understanding geographical and individual disparities in health, and complement the information conveyed by measures of association between neighbourhood characteristics and health.

Antihypertensive Agents↗
PubMed1990

Measurement of free hormones in blood.

The binding by serum proteins of circulating thyroid and steroid hormones is a phenomenon whose physiological significance is still not understood, and the validity of the free hormone hypothesis remains in doubt. Indeed, even the most basic physicochemical consequences of these proteins' presence within the microcirculation continue to generate controversy, reflecting disagreement of the rate-limiting effects of hormone-protein interactions on hormone efflux from protein-containing fluid compartments. My colleagues and I have claimed, in particular, that the observations on which Pardridge and coworkers' current ideas crucially depend are entirely explicable using a relatively simple mathematical model of hormone efflux from tissue capillaries differing from the even simpler model relied on by these authors only in that it takes basic hormone-binding kinetics into consideration. The necessity to postulate the local hormone release mechanisms that Pardridge et al. propose in order to account for their observations is thus obviated. Though this conclusion continues to be contested by Pardridge et al. (on the grounds that our own model is invalid), the controversy demonstrates the crucial importance in this area of sound mathematical analysis and the great danger of misinterpreting experimental data by reliance on oversimple theoretical concepts. In reality, the effects of intracapillary protein-binding reactions on target-tissue hormone uptake are of considerably greater complexity than are encompassed in the simple model which is sufficient to explain the observation of Pardridge et al. (1). In particular the assumption made by a number of workers that intracapillary hormone dissociation from binding proteins does not limit the rate of tissue uptake if the latter is substantially less than the intracapillary free hormone generation rate is demonstrably invalid, being incorrectly based on the kinetics of homogeneous (liquid-phase) reactions. By making this assumption, false conclusions may be drawn regarding the kinetics of hormone transport to target tissues, and hence of the effects of the changes in binding protein concentrations that occur in a variety of pathophysiological states. Relying on more detailed analysis, my colleagues and I have suggested that it is plausible, purely on physicochemical grounds, that the characteristic changes in binding protein levels seen in pregnancy serve to redistribute hormone throughout the body, specifically (in the case of the thyroid hormones) directing T4 to the feto-placental unit. Though difficult to verify directly (and perhaps invalid), this proposition has refocused attention on the fetal needs for T4 before the development of the fetal thyroid gland, and on the possible effects on neurological development of an inadequate maternal T4 supply.(ABSTRACT TRUNCATED AT 400 WORDS)

Blood Proteins↗
PubMed2000

[Information for fuzzy sets in disease diagnosis].

The mathematics offers the formal models in which variables and parameters can have the different interpretation. The application of formal model is then in the hands of experience and mostly also of knowledge, out of the mathematical way. Hence it followed that in the case, when the function of certain model is ensured by the software of computer, the everybody user to have know of a structure of mathematical models, their sense and possibilities. For example we have any object the role of fuzzy--mathematics in the one medical diagnostic situation. We shall attempt to show that the fundamental concepts of the theory of semantic information can be defined in a very straightforward way on the basis of the theory of fuzzy semantic information that has been recently developed by Zadeh and Shannon.

Diagnosis, Computer-Assisted↗
PubMedDate not supplied

[Realization of the morphogenetic potential of plants: hormonal-genetic approach].

The basic principles of a model describing the hormonal control of the genome expression are stated, and its graphical interpretation is presented. The expression and evolution of the genetic information of organisms are regarded as an universal process of redifferentiation. The possibility is considered to represent the genome as a dynamic system. The study of the morphogenetic potential of organisms is based on the approach worked out by E. Cartan to the description of dynamic systems. A concept of morphogenetic potential is introduced, and its relation to genome states is shown. A mathematical model describing the expression of the morphogenetic potential is proposed. The mathematical formalism developed can be helpful for the solution of a great variety of tasks.

Gene Expression Regulation, Plant↗
PubMed1991

[The prediction of the toxic effect of chemical substances].

On the basis of general conception of the toxicity mechanism of chemical substances the authors worked out a conceptual and mathematical model of intoxication within a range from subtle effects and up to lethal cases. The tests of this model were made on the basis of carbon oxide action. The model gives the possibility to elaborate practical methods for prognostication and realization of health service measures in case of large-scale chemical catastrophes.

Accidents, Occupational↗