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PubMed1976

[Use of computers and mathematical methods in epidemiological work. V. Assessment of infection morbidity using standardized indices].

The paper treats of the method of obtaining special and generalized indices on the computer M-222 to be used for the analysis of infectious morbidity under the automatic control system conditions. Assessment of significance of the differences between the actual number of diseases and the "usual" morbidity level characteristic of the given territory and the time of the year lies at the basis of the calculation of the standardized indices. Complex evaluation of the epidemiological condition of the controlled district was carried out according to the data of the official monthly and annual sanitary-epidemiological report forms No. 85.

Computers↗
PubMed1976

Changes in the shape of the developing vertebrate nervous system analyzed experimentally, mathematically and by computer simulation.

Two forces are necessary and sufficient to produce the transformation of the newt neural plate from a hemispheric sheet of cells one cell thick to a keyhole shape. These forces are: (1) a regionally programmed shrinkage of the surface of the neural plate (accomplished by contraction of the apical surfaces of the neural plate cells and elongation of these cells perpendicular to the plate); and (2) displacement of the whole sheet caused by elongation of either the notochord or the overlying neural plate cells in the antero-posterior direction. A computer simulation and mathematical analysis ("morphodynamics"), together with experiments and observations on embryos, were used to deduce the morphogenesis of the neural plate from these forces.

Animals↗
PubMed2004

Mathematical and computational techniques to deduce complex biochemical reaction mechanisms.

Time series data can now be routinely collected for biochemical reaction pathways, and recently, several methods have been proposed to infer reaction mechanisms for metabolic pathways and networks. In this paper we provide a survey of mathematical techniques for determining reaction mechanisms for time series data on the concentration or abundance of different reacting components, with little prior information about the pathways involved.

Algorithms↗
PubMed2005

Mathematical and computational modelling of spatio-temporal signalling in rod phototransduction.

Rod photoreceptors are activated by light through activation of a cascade that includes the G protein-coupled receptor rhodopsin, the G protein transducin, its effector cyclic guanosine monophosphate (cGMP) phosphodiesterase and the second messengers cGMP and Ca2+. Signalling is localised to the particular rod outer segment disc, which is activated by absorption of a single photon. Modelling of this cascade has previously been performed mostly by assumption of a well-stirred cytoplasm. We recently published the first fully spatially resolved model that captures the local nature of light activation. The model reduces the complex geometry of the cell to a simpler one using the mathematical theories of homogenisation and concentrated capacity. The model shows that, upon activation of a single rhodopsin, changes of the second messengers cGMP and Ca2+ are local about the particular activated disc. In the current work, the homogenised model is computationally compared with the full, non-homogenised one, set in the original geometry of the rod outer segment. It is found to have an accuracy of 0.03% compared with the full model in computing the integral response and a 5200-fold reduction in computation time. The model can reconstruct the radial time-profiles of cGMP and Ca2+ in the interdiscal spaces adjacent to the activated discs. Cellular electrical responses are localised near the activation sites, and multiple photons sufficiently far apart produce essentially independent responses. This leads to a computational analysis of the notion and estimate of 'spread' and the optimum distribution of activated sites that maximises the response. Biological insights arising from the spatio-temporal model include a quantification of how variability in the response to dim light is affected by the distance between the outer segment discs capturing photons. The model is thus a simulation tool for biologists to predict the effect of various factors influencing the timing, spread and control mechanisms of this G protein-coupled, receptor-mediated cascade. It permits ease of simulation experiments across a range of conditions, for example, clamping the concentration of calcium, with results matching analogous experimental results. In addition, the model accommodates differing geometries of rod outer segments from different vertebrate species. Thus it represents a building block towards a predictive model of visual transduction.

Animals↗
PubMed1976

[Use of a computer and mathematical methods in epidemiological work. Report 3. Experience with the operational tracing of infectious morbidity using an automic self-service information unit].

The authors describe their experience in the elaboration and introduction into practice of epidemiological service of the system of operative tracing of infectious morbidity at the level of the central sanitary-epidemiological station under conditions of automatic control system. Data on improvement of information supply and logic analysis of the information with the aid of Minsk-22 computer are presented. Forms of documents are considered. Experience in the use of this system for two years pointed to its expediency.

Communicable Diseases↗
PubMed1994

Classroom attributes and achievement test scores for deaf and hard of hearing students.

This study examined reading comprehension and mathematics computation achievement of deaf and hard-of-hearing students in a variety of school settings. Data were collected by Gallaudet University's Center for Assessment and Demographic Studies during its 1990 standardization of the 8th Edition Stanford Achievement Test. Descriptive and inferential statistical methods were used to analyze the relationships among achievement scores, classroom attributes, and demographic factors associated with achievement. Based on the results of this study, inclusion with hearing students in regular classrooms is related to a variety of demographic factors. When reading comprehension and mathematics computation scores are adjusted for these factors, they are higher for the deaf and hard-of-hearing students in regular classrooms. However, it is not known whether the higher achievement is due to inclusion or whether students were selected for inclusion due to their higher achievement levels.

Achievement↗
PubMed1995

The maintenance of self-replicating plasmids in Saccharomyces cerevisiae: mathematical modelling, computer simulations and experimental tests.

A distributive model has been constructed to describe the maintenance of the native 2 microns and 2 micron-based plasmids in the yeast Saccharomyces cerevisiae. This model includes elements which represent the influence of selection, segregation, replication and amplification on plasmid stability. A computer program has been written in TURBO PASCAL to implement the model and a number of simulation experiments have been carried out. These simulations permitted the choice of a form of the model which is compatible with the available experimental evidence. The form chosen involves an amplification system in which the RAF gene product binds to the Rep1/Rep2 dimer to prevent the latter acting to repress the activity of the FLP gene. At the same time an upper limit (or 'ceiling') was imposed on the number of plasmid molecules able to replicate. Maternal bias was accommodated by 'tagging' a small proportion of molecules for inheritance by the mother nucleus and these tags being removed (or 'cleared') by the Rep1/Rep2 dimers. This final form of the model makes specific predictions about the stability of 2 microns and YEp plasmids in yeast populations and about the distribution of plasmid copy number between cells in such populations. The predictions on stability have been subjected to experimental test and results provide good support for the model.

Cell Division↗
PubMed1981

A posteriori time-varying filtering of averaged evoked potentials. II. Mathematical and computational aspects.

The problem of estimating an unknown transient signal, given an ensemble of waveforms, in which this signal appears as a nonrandom component in the presence of additive noise is considered. This problem is solved by generalizing the method of "a posteriori 'Wiener' filtering". In the new method, the ensemble average is filtered by a time-varying system which is based on estimated time-varying power spectra of signal and noise. The nature of this system, and the computational procedures involved, are discussed in detail. A software package for time-varying filtering is briefly described. Application of the method is illustrated by a simulation example, which also provides a comparison to time-invariant a posteriori "Wiener" filtering.

Brain↗
PubMed2003

Defining forces that are associated with shoulder dystocia: the use of a mathematic dynamic computer model.

OBJECTIVE: A computer model was modified to study the impact of maternal endogenous and clinician-applied exogenous delivery loads on the contact force between the anterior fetal shoulder and the maternal symphysis pubis. STUDY DESIGN: Varying endogenous and exogenous loads were applied, and the contact force was determined. Experiments also examined the effect of pelvic orientation and the direction of load application on contact force behind the symphysis pubis. RESULTS: Exogenous loading forces (50-100 N) resulted in anterior shoulder contact forces of 107 to 127 N, with delivery accomplished at 100 N of applied load. Higher contact forces (147-272 N) were noted for endogenously applied loads (100-400 N), with delivery occurring at 400 N of maternal force. Pelvic rotation from lithotomy to McRoberts' positioning resulted in reduced contact forces. Downward lateral flexion of the fetal head led to little difference in contact force but required 30% more exogenous load to achieve delivery. CONCLUSION: Compared with clinician-applied exogenous force, larger maternally derived endogenous forces are needed to clear the impacted anterior fetal shoulder. This is associated with >2 times more contact force by the obstructing symphysis pubis. McRoberts' positioning reduces shoulder-symphysis pubis contact force. Lateral flexion of the fetal head results in the larger forces that are needed for delivery but has little effect on contact force. Model refinements are needed to examine delivery forces and brachial plexus stretching more specifically.

Delivery, Obstetric↗
PubMed2003

Steps toward building mathematical and computer models from cognitive task analyses.

Typically, detailed quantitative and computer models of human operators performing real world tasks cannot easily be developed. We propose a technique that more easily allows for that development. We propose that when a cognitive task analysis has been carried out, a computer simulation model useful for approximations of task completion time is often within reach. The first step is to construct an activity network or order-of-processing diagram from the task analysis. Second, activity durations are found in the literature or approximated through multidimensional scaling. Finally, equations are written for calculating task completion time, or a program is written for simulations to estimate this time. Resulting models can be useful for optimizing system design. The approach is illustrated with an activity network by W. D. Gray, B. E. John, and M. E. Atwood (1993) for a telephone operator task. Simulations demonstrate the feasibility of using multidimensional scaling to obtain approximate activity durations. The approach is also illustrated with an order-of-processing diagram representing drivers reading roadside message displays. We point out that if a more detailed picture of unobservable mental processes in a task is needed, techniques have been developed for this through analysis of response times. Actual or potential applications of this research include system design, human-computer interaction, message comprehension, and simulation of information-processing tasks.

Cognition↗
PubMed1999

A perspective on standardizing the predictive power of noninvasive cardiovascular tests by likelihood ratio computation: 1. Mathematical principles.

The current practice of reporting positive and negative predictive value (PV), sensitivity (Se), and specificity (Sp) as measures of the power of noninvasive cardiovascular tests has significant limitations. A test result's PV and its comparison with other test results are highly dependent on the pretest disease prevalence at which it is determined; the citation of sensitivity and specificity provides no succinct or explicit quantitation of the rule-in and rule-out power of a test. This article presents a rationale for the use of an alternative standard for expressing predictive power in the form of positive and negative likelihood ratios, (+)LR and (-)LR. The likelihood ratios are composite expressions of test power, which incorporate the Se and Sp and their respective complements [(1 - Se) and (1 - Sp)], thus yielding single unambiguous measures of positive and negative predictive power. The likelihood ratios are calculated as follows: (+)LR = Se/(1 - Sp) and (-)LR = Sp/(1 - Se). On analysis of the predictive value equations, the likelihood ratios equal the quotients of the posttest predictive value odds to the pretest prevalence odds for disease and no disease, respectively, as follows: (+)LR = (+)PVOd/POD and (-)LR = (-)PVOn/PON, where (+)PVOd is positive predictive value odds for disease, POD is prevalence odds for disease, (-)PVOn is negative predictive value odds for no disease, and PON is prevalence odds for no disease. Thus, the likelihood ratios are measures of the odds advantage in posttest probability of disease or no disease relative to pretest probability, independent of disease prevalence in the tested population. The quotients of the (+)LR or the (-)LR among test results studied in a common population are direct expressions of their relative predictive power in that population. The likelihood ratio principle is applicable to the evaluation of the predictive power of multiple tests performed in a common population and to estimating predictive power at multiple test thresholds.

Confidence Intervals↗
PubMed2006

Re-engineering Colles: form, function and fragility fractures.

Of the twenty nine anatomy professors in the Royal College of Surgeons in Ireland, primus inter pares is Abraham Colles. In his 1811 book A Treatise on Surgical Anatomy he revolutionised the subject by teaching it topographically, seeking "to describe the relative position of the parts and to point out the subservience of anatomical knowledge to surgical practice". Today we have extended this to 'clinical practice' and, in the Anatomy Room, students are guided through each region by clinically trained staff, from surface anatomy via three-dimensional dissection to radiological images. This is augmented by online histology and radiology courses and DVDs in which dissection footage, edited by a content analysis engine, is used to preview and review practical classes. In the same book, Colles also wrote that 'the fixed and immutable laws of mathematics are little applicable to the science of medicine'. Computer-aided learning argues against this. So does research which links fatigue microdamage to bone remodelling and the development of algorithms to predict, and thus prevent, osteoporotic fractures. Mechanical principles are being used to develop scaffolds for tissue engineering and to optimise the mechanical environment of seeded mesenchymal stem cells. While Colles' teaching approach holds true, in biomechanics, tissue engineering and computing, mathematical laws are now being successfully applied to medical science.

Anatomy↗