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PubMed1982

An application of mathematical models in posturography.

The measurement of the horizontal displacements (HD) of the centre of mass of the human body when standing still, is often performed by means of a platform. The resulting measured HD as a function of time, both in the left-right or sinister-dexter and the posterior-anterior direction, are known as stabilograms. Such stabilograms are being more widely used to obtain the so called measured statokinesigram, similar to a Lissajous-figure, by eliminating time from the sinister-dexter stabilogram and the posterior-anterior stabilogram. It is shown that in using mathematical models of the standing person to obtained the stabilograms, the resulting statokinesigram is very different from the measured statokinesigram. It is also shown that the quantity line-integral calculated from a statokinesigram is much smaller when determined from a statokinesigram corrected by means of the mathematical models.

Humans↗
PubMed1989

Intracerebral microdialysis: II. Mathematical studies of diffusion kinetics.

The kinetics of intracerebral microdialysis are studied mathematically. In the microdialysis technique, a tubular membrane that is permeable to diffusion is implanted in the brain and perfused with an artificial cerebrospinal fluid. Molecular diffusion causes substances in the brain to enter the flowing perfusate. The perfusate is collected outside the brain and the content of various substances is determined. The mathematical problem of diffusion through the porous brain tissue into the flowing perfusate is formulated. Solutions for the concentration distributions in the brain and in the perfusate are derived. It is found that the factor limiting the transport is the diffusion through the brain and not through the membrane. A theoretical expression for the recovery ratio is also obtained. This ratio may be used to infer the extracellular concentration in the brain from the concentration in the collected perfusate.

Animals↗
PubMed1986

A mathematical model of survival kinetics. I. Theoretical basis.

A mathematical model of mortality and survival kinetics is proposed based upon the two main aspects of survival data, namely, the rate of vitality reduction with age and its statistical distribution. Certain mathematical assumptions are made on the time-course of both vitality and its distribution. Then, these two aspects are integrated in a single model which can be used to describe survivorship, cumulative mortality or dying. The model is capable of fitting empirical curves even at very advanced ages, where the widely used Gompertz law fails. Examples are provided, derived from populations having rather different lifespans such as rotifers, flies, rats and horses. The model maintains one of the most interesting characteristics of Gompertz law, namely, the possibility to estimate the 'design constant for longevity' relating maximum lifespan to one of the parameters of the model. It also has the potential characteristics enabling it to be used to judge the statistical significance of the difference between two empirical survival curves.

Aging↗
PubMedDate not supplied

A new implemented version of program MIR (MIR II): analysis and identification of mathematical models in enzyme and transport kinetic studies.

The computer program MIR previously described (R. Bianchi, G.M. Hanozet and M. Pilone Simonetta, Comput. Prog. Biomed. 16 (1983) 189) that fits trial rate laws to enzyme and transport steady-state kinetic data by the least-squares method has been enhanced. The new version MIR II is an interactive program and it consists of five major routines and a larger number of smaller program elements to perform the linear (three different functional forms) and non-linear (eleven mathematical models) regression analysis of kinetic data from enzyme and transmembrane transport experiments, also in the presence of inhibitors. Other features of the new program include a set of statistics and tests useful for the model building process, for the development of the mathematical model and for its validation and maintenance. An algorithm for fitting a straight line taking into account errors in both x and y is also provided.

Algorithms↗
PubMed1982

Mathematical processes in the evaluation of the dangerous nature of chemicals.

The present study was carried out on the basis of the question of "whether it is possible to use mathematical methods meaningfully for the evaluation of the environmental effects of chemicals." The analysis of the evaluation process showed that this may be considered as a relation between the set of test data and a target set, that of the danger classes. The very general structure of a relation considerably restricts the use of algorithms; in particular it can be shown that algorithms which would map the data directly onto the danger classes like a functional coordination are, in general, excluded. This is partly due to the highly nonhomogeneous parameter set which must be determined for evaluation purposes, and partly to the high degree of randomness or human participation in the selection of the parameters. Moreover, there was no indication whether or to what extent the parameters are interdependent, i.e., whether there are interdisciplinary regularities which could be expressed algebraically and interpreted scientifically. Questions of this kind remain components of interdisciplinary research, and they cannot be explained from a mathematical--i.e., theoretical--point of view. Considerably more empirical material needs to be available for use as the foundation for a reasonable theory.

Animals↗
PubMed1991

Enhanced right hemisphere activation in the mathematically precocious: a preliminary EEG investigation.

A preliminary electroencephalographic (EEG) investigation was conducted to determine if the pattern of hemispheric activation in mathematically precocious youth differs from that of average math ability subjects. Alpha activity at four brain sites (frontal, temporal, parietal, and occipital lobes) over the left and right cerebral hemispheres (LH/RH) was monitored while 12- to 14-year-old, right-handed males: (a) looked at a blank slide (baseline condition), (b) judged which of two chimeric faces was "happier," and (c) determined if a word was a noun or a verb. At baseline, the LH of the precocious group was found to be more active at all four brain sites relative to that of the average ability group. During chimeric face processing, the gifted subjects exhibited a significant reduction in alpha power over the RH, primarily at the temporal lobe, while no such alpha suppression was observed in the average ability subjects. For noun/verb determinations, no significant alpha power reductions were obtained for either group. These electrophysiological data generally corroborate the behavioral findings of O'Boyle and Benbow (1990a) and support their contention that enhanced RH involvement during cognitive processing may be a correlate of mathematical precocity. Moreover, the pattern of activation observed across tasks suggests that the ability to effectively coordinate LH and RH processing resources at an early age may be linked to intellectual giftedness.

Adolescent↗
PubMed1995

Photosynthetic oscillations and the interdependence of photophosphorylation and electron transport as studied by a mathematical model.

A simple mathematical model of photosynthetic carbon metabolism as driven by ATP and NADPH has been formulated to analyse photosynthetic oscillations. Two essential assumptions of this model are: (i) reduction of 3-phosphoglycerate to triosephosphate in the Clavin cycle is limited by ATP, not by NADPH, and (ii) photophosphorylation is affected by the availability of both ADP and NADP, while electron transport is limited by NADP only. The model produces oscillations of observed damping and period in ATP and NADP concentrations which are about 180 degrees out of phase, while three alternative proposals regarding coupling of electron transport and photophosphorylation do not produce oscillatory model solutions. The phases of ATP and NADPH are in reasonable agreement with the available experimental data. The model (which assumes that redox control of photophosphorylation is part of the oscillatory mechanism) is compared with an alternative proposal (that oscillations are due to interdependence of turnover of adenylates and Calvin cycle intermediates). From the similarity of the mathematical structures of both models it is inviting to speculate that both models are partial aspects of 'the oscillatory mechanism'.

Adenosine Triphosphate↗
PubMed1988

Mathematical models of the population biology of Ostertagia ostertagi and Teladorsagia circumcincta, and the economic evaluation of disease control strategies.

The construction and use of mathematical models of the population biology of Ostertagia ostertagi and Teladorsagia circumcincta is discussed. Simulated field trials implemented by deterministic mathematical models currently share with actual field trials the disadvantage that they convey no information concerning the risk associated with the net return demonstrated by the trial. This has important implications when it is necessary to rank disease control strategies in order of usefulness.

Animals↗
PubMed1991

Mathematical isolation of component spectra in HPLC/UV-vis and GC-MS. How unique are the resolved spectra?

The resolution of overlapping spectra in GC-MS and HPLC/UV-vis is fundamentally limited by the quality of the experimental data. The narrowness of the solution range depends on the degree of overlap between components. If the components are dissimilar, the solutions obtained by all mathematical methods are robust. Small perturbations in the observations do not change the calculated solution very much. Alternating regression (AR) is a useful tool in the analysis of overlapping spectra because AR can be calculated very rapidly. The robustness of the solution can be easily checked with AR. The mathematical analysis is repeated several times after adding different sets of noise. Each time different random spectra are used as a starting point. The range of solutions thus obtained reflects the quality of the data for resolution purposes.

Chemistry Techniques, Analytical↗
PubMed1991

Genomic mapping by anchoring random clones: a mathematical analysis.

A complete physical map of the DNA of an organism, consisting of overlapping clones spanning the genome, is an extremely useful tool for genomic analysis. Various methods for the construction of such physical maps are available. One approach is to assemble the physical map by "fingerprinting" a large number of random clones and inferring overlap between clones with sufficiently similar fingerprints. E.S. Lander and M.S. Waterman (1988, Genomics 2:231-239) have recently provided a mathematical analysis of such physical mapping schemes, useful for planning such a project. Another approach is to assemble the physical map by "anchoring" a large number of random clones--that is, by taking random short regions called anchors and identifying the clones containing each anchor. Here, we provide a mathematical analysis of such a physical mapping scheme.

Chromosome Mapping↗
PubMed1995

Genomic mapping by end-characterized random clones: a mathematical analysis.

Physical maps can be constructed by "fingerprinting" a large number of random clones and inferring overlap between clones when the fingerprints are sufficiently similar. E. Lander and M. Waterman (Genomics 2: 231-239, 1988) gave a mathematical analysis of such mapping strategies. The analysis is useful for comparing various fingerprinting methods. Recently it has been proposed that ends of clones rather than the entire clone be fingerprinted or characterized. Such fingerprints, which include sequenced clone ends, require a mathematical analysis deeper than that of Lander-Waterman. This paper studies clone islands, which can include uncharacterized regions, and also the islands that are formed entirely from the ends of clones.

Chromosome Mapping↗
PubMed2004

Mathematical modelling of skeletal repair.

Tissue engineering offers significant promise as a viable alternative to current clinical strategies for replacement of damaged tissue as a consequence of disease or trauma. Since mathematical modelling is a valuable tool in the analysis of complex systems, appropriate use of mathematical models has tremendous potential for advancing the understanding of the physical processes involved in such tissue reconstruction. In this review, the potential benefits, and limitations, of theoretical modelling in tissue engineering applications are examined with specific emphasis on tissue engineering of bone. A central tissue engineering approach is the in vivo implantation of a biomimetic scaffold seeded with an appropriate population of stem or progenitor cells. This review will therefore consider the theory behind a number of key factors affecting the success of such a strategy including: stem cell or progenitor population expansion and differentiation ex vivo; cell adhesion and migration, and the effective design of scaffolds; and delivery of nutrient to avascular structures. The focus will be on current work in this area, as well as on highlighting limitations and suggesting possible directions for future work to advance health-care for all.

Animals↗
PubMed2005

Mathematical approaches to differentiation and gene regulation.

We consider some mathematical issues raised by the modelling of gene networks. The expression of genes is governed by a complex set of regulations, which is often described symbolically by interaction graphs. These are finite oriented graphs where vertices are the genes involved in the biological system of interest and arrows describe their interactions: a positive (resp. negative) arrow from a gene to another represents an activation (resp. inhibition) of the expression of the latter gene by some product of the former. Once such an interaction graph has been established, there remains the difficult task to decide which dynamical properties of the gene network can be inferred from it, in the absence of precise quantitative data about their regulation. There mathematical tools, among others, can be of some help. In this paper we discuss a rule proposed by Thomas according to which the possibility for the network to have several stationary states implies the existence of a positive circuit in the corresponding interaction graph. We prove that, when properly formulated in rigorous terms, this rule becomes a theorem valid for several different types of formal models of gene networks. This result is already known for models of differential [C. Soulé, Graphic requirements for multistationarity, ComPlexUs 1 (2003) 123-133] or Boolean [E. Rémy, P. Ruet, D. Thieffry, Graphic requirements for multistability and attractive cycles in a boolean dynamical framework, 2005, Preprint] type. We show here that a stronger version of it holds in the differential setup when the decay of protein concentrations is taken into account. This allows us to verify also the validity of Thomas' rule in the context of piecewise-linear models. We then discuss open problems.

Cell Differentiation↗
PubMed2006

A mathematical model for adaptive transport network in path finding by true slime mold.

We describe here a mathematical model of the adaptive dynamics of a transport network of the true slime mold Physarum polycephalum, an amoeboid organism that exhibits path-finding behavior in a maze. This organism possesses a network of tubular elements, by means of which nutrients and signals circulate through the plasmodium. When the organism is put in a maze, the network changes its shape to connect two exits by the shortest path. This process of path-finding is attributed to an underlying physiological mechanism: a tube thickens as the flux through it increases. The experimental evidence for this is, however, only qualitative. We constructed a mathematical model of the general form of the tube dynamics. Our model contains a key parameter corresponding to the extent of the feedback regulation between the thickness of a tube and the flux through it. We demonstrate the dependence of the behavior of the model on this parameter.

Adaptation, Physiological↗
PubMed2006

The human stratum corneum as extended, covalently cross-linked biopolymer: mathematics, molecules, and medicine.

A novel mathematical and molecular hypothesis is proposed to account for the peculiar organization of human epidermis. Mathematically, the organization of the interfollicular epidermis is hypothesized to be a tetratomic identity manifesting a gravitational logic in the arrangement of its functional compartments. The squares of the natural numbers; i.e., 1, 4, 9, and 16 are taken, on empirical grounds, to correspond to the number of cell layers in the respective epidermal strata (germinativum, spinosum, granulosum, and corneum). The outer two strata, overlying the Langerhans cells, constitute the 'living' and 'dead' components of the traditional 'epidermal barrier'. Together, these two strata illustrate in their union of 9 + 16 = 25 cells, a way of conceiving the skin surface (the body-environment identity) as both closure and contact. The organization of human epidermis into functional units based on phi, the golden section ratio, builds upon this gravitational logic. Finally, the fact that the extensively cross-linked proteolipid envelope of the cornified epidermal cell is a single multi-gene molecule is deemed scientifically incontrovertible. The molecular hypothesis in need of validation and verification is whether the corneodesmosomal 'rivets' linking one corneocyte to another are covalently bonded structures. If so, the cornified scaffolding of the stratum corneum constitutes a highly organized, extended, multi-gene, polymer molecule strategically located precisely at the shared surface of the body and environment. This hypothesis places the differentiated structure of the epidermis, an ectodermal derivative like the brain, front and center in the translation of molecular biology to clinical bedside care.

Binding Sites↗
PubMed2006

Is math lateralised on the same side as language? Right hemisphere aphasia and mathematical abilities.

The main purpose of the present study was to learn how mathematical abilities are located and develop in the brain with respect to language. Mathematical abilities were assessed in six right-handed patients affected by aphasia following a lesion to their non-dominant hemisphere (crossed aphasia) and in two left-handed aphasics with a right-sided lesion. Acalculia, although in different degrees, was found in all cases. The type of acalculia depended on the type of aphasia, following patterns that have been previously observed in the most common aphasias resulting from left hemisphere lesions. No sign of right hemisphere or spatial acalculia (acalculia in left lateralised right-handed subjects) was detected. These results suggest that, as a rule, language and calculation share the same hemisphere. A primitive computational mechanism capable of recursion may be the precursor of both functions.

Aphasia↗
PubMed2006

Mathematical disabilities in children with velo-cardio-facial syndrome.

Current neurocognitive theories of number processing [Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20, 487-506] state that mathematical performance is made possible by two functionally and anatomically distinct subsystems of number processing: a verbal system located in the angular gyrus, which underlies the retrieval of arithmetic facts, and a quantity system located in the intraparietal sulcus, which subserves operations that involve semantic manipulations of quantity. According to this model, subtypes of math disability (MD) should be traceable to differential impairments in these subsystems. The present study investigated MD in children with velo-cardio-facial syndrome (VCFS) and aimed to verify which of these subsystems of number processing is impaired in these children. Eleven children with VCFS and 11 individually matched controls, selected from the same classes, completed a large battery of mathematical tests. Our data revealed that children with VCFS had preserved number reading abilities and preserved retrieval of arithmetic facts, both of which indicate that the verbal subsystem is not impaired in VCFS. By contrast, children with VCFS showed difficulties in number comparison, the execution of a calculation strategy and word problem solving, all of which involve the semantic manipulation of quantities. This provides evidence for a specific deficit in the quantity subsystem in children with VCFS, suggesting underlying abnormalities in the intraparietal sulcus.

Adolescent↗
PubMed1992

A new mathematical model to study bone turnover in growing rats.

A new mathematical model for the study of bone turnover in growing rats was developed. The model predicts a linear relationship between bone mineral content (BMC) and biochemical markers (BMK) of bone turnover assuming that rats are growing, bone turnover is profoundly affected by skeletal maturation, and resorption and formation are physiologically balanced. The model validation was performed by measuring galactosyl-hydroxylysine (GHYL) and hydroxyproline (HYP) in urines. This mathematical evidence supports our proposed use of the specific bone resorption marker GHYL to predict bone mineral content. Further studies on bone turnover will be possible by the application of the same approach.

Absorptiometry, Photon↗