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PubMed2000

Mathematical modeling for the prediction and optimization of laser hair removal.

BACKGROUND AND OBJECTIVE: The study of hair removal is a slow, tedious process. Efficacy evaluations require test-site observation for at least one complete hair cycle, a minimum of 6-8 months. In addition, tracking and counting individual hairs is extremely labor intensive. The objective of this study was to develop and evaluate a mathematical model for hair removal that could significantly speed the entire process. STUDY DESIGN/MATERIALS AND METHODS: Generally accepted kinetic and statistical modeling methods were used to develop a mathematical description of hair growth. The anagen and telogen percentages and decay times were the variables used to predict the kinetics of untreated hair. In the case that the follicles were treated, it was necessary to additionally consider the possible outcomes after treatment, making the calculations much too complicated for simple mathematical formulations. Therefore, a computerized statistical model was developed that considered the probabilities of no, partial, or complete follicular damage in addition to the untreated model variables. These models were then evaluated by comparing them to data derived from the literature and a study center. RESULTS: Values derived from the mathematical model were capable of closely approximating the experimental results of untreated (shaving) and treated (plucking, electrolysis, ruby laser, Q-switched Nd:YAG laser) hair growth kinetics. The model was also shown to be useful for optimizing the number and interval of Q-switched Nd:YAG laser treatments. CONCLUSIONS: A mathematical model can be used to reliably predict results from a variety of hair removal techniques. It also appears to be useful for optimizing a particular treatment protocol. In addition, the development of new hair removal products may be aided by using this method.

Computer Simulation↗
PubMed2000

A mathematical micturition model to restore simple flow recordings in healthy and symptomatic individuals and enhance uroflow interpretation.

We describe a model and report a new method to extract quantified data from the simple analysis of whole uroflow curves in healthy and symptomatic individuals. Recorded flow curves were compared with the curves theoretically predicted from a mathematical micturition model. This model was developed by relating each physiological event occurring during micturition to a set of mathematical equations. Due to improvements in speed of computer calculations, a very fast and adaptable mathematical micturition model became available. A total of 302 uroflow curves from 142 patients (61 men and 81 women) were studied. The control group consisted of seven men and 25 women; the symptomatic groups comprised 54 men and 56 women. The mathematical model was applied to analyze all the recorded curves. For patients with lower urinary tract symptoms, specific modelization parameters were introduced according to the clinical condition to be tested. Using two compulsory (patient sex and voided volume) and two optional parameters (clinical condition and urethral catheter size), our mathematical model was able to produce uroflow calculated curves similar to observed curves. In the control group, the calculated and recorded uroflow curves were found to superimpose with an impressive accuracy, i.e., a quadratic error <1%. Test-re-test studies gave the same determination of the specific parameters. In benign prostatic hyperplasia patients, the compressive effect on both prostatic urethra and bladder neck was separately identified. The same intra-individual values were found at 2-week intervals in the group with no treatment (P = no significance), whereas after 3 months of treatment with an alpha-blocker, a decrease in values was noted in responder patients (P < 0.001). In women with various degrees of cystocele, a constrictive effect was identified and found to be identical for successive flows during the same urodynamic testing. This large prospective study demonstrated the relevance of a sophisticated, heavily computerized micturition model, taking into account physiological voiding parameters, to the study of flow in healthy individuals and patients with benign prostatic hyperplasia or cystocele. Curve-fitting led to the determination of critical events during flow such as break point and plateau phase. Determination of these events may enhance uroflow interpretation by providing additional information on the detrusor function. Neurourol. Urodynam. 19:153-176, 2000.

Adult↗
PubMed2001

Participation in Advanced Mathematics: Do Expectation and Influence of Students, Peers, Teachers, and Parents Matter?

Using six waves of data (Grades 7 through 12) from the Longitudinal Study of American Youth (LSAY), this study investigated the effects of expectation and influence of students, peers, teachers, and parents on participation in advanced mathematics. Results of survival analysis indicated a significant decline in participation rate in the transition from Grades 11 to 12. Students with higher future expectation were more likely to participate in advanced mathematics. Peer influence and teacher expectation did not have strong effects, and the effect of student future expectation was independent of peer and teacher effects. The effect of parent expectation and parent college plan for children were strong, and in their presence, the effect of student future expectation declined. Mathematics achievement and attitude toward mathematics were the most important factors affecting participation in advanced mathematics. With control over achievement and attitude, (a) the effect of student future expectation declined, (b) the effects of peer influence and teacher expectation disappeared, and (c) the effects of parent expectation and parent college plan for children were reduced. Copyright 2001 Academic Press.

Journal Article↗
PubMed2004

A history of the study of solid tumour growth: the contribution of mathematical modelling.

A miscellany of new strategies, experimental techniques and theoretical approaches are emerging in the ongoing battle against cancer. Nevertheless, as new, ground-breaking discoveries relating to many and diverse areas of cancer research are made, scientists often have recourse to mathematical modelling in order to elucidate and interpret these experimental findings. Indeed, experimentalists and clinicians alike are becoming increasingly aware of the possibilities afforded by mathematical modelling, recognising that current medical techniques and experimental approaches are often unable to distinguish between various possible mechanisms underlying important aspects of tumour development. This short treatise presents a concise history of the study of solid tumour growth, illustrating the development of mathematical approaches from the early decades of the twentieth century to the present time. Most importantly these mathematical investigations are interwoven with the associated experimental work, showing the crucial relationship between experimental and theoretical approaches, which together have moulded our understanding of tumour growth and contributed to current anti-cancer treatments. Thus, a selection of mathematical publications, including the influential theoretical studies by Burton, Greenspan, Liotta et al., McElwain and co-workers, Adam and Maggelakis, and Byrne and co-workers are juxtaposed with the seminal experimental findings of Gray et al. on oxygenation and radio-sensitivity, Folkman on angiogenesis, Dorie et al. on cell migration and a wide variety of other crucial discoveries. In this way the development of this field of research through the interactions of these different approaches is illuminated, demonstrating the origins of our current understanding of the disease.

Cell Growth Processes↗
PubMed2005

Detection of anthelmintic resistance: a comparison of mathematical techniques.

Anthelmintic resistance has become an increasing problem particularly to gastrointestinal tract nematodes and appropriate methods are required to detect this phenomenon so the correct action can be taken. This paper compares a number of mathematical techniques that are used to analyse data. The negative binomial distribution is a mathematical distribution used to model aggregated data and hence is suitable to model the intensity of parasite burden and the magnitude of the faecal egg counts. Maximum likelihood techniques are utilised to exploit this mathematical distribution to analyse the magnitude of the faecal egg count reduction and decline in the worm burden in response to anthelmintic treatment. Data from experimental groups of sheep described in the accompanying paper are used. In addition, simulated data sets of faecal egg counts were created using a random number generator following appropriate negative binomial distributions. The results demonstrate this statistical model can detect evidence of anthelmintic resistance with a faecal egg reduction test that otherwise might require a slaughter trial to demonstrate. In addition, the simulated data sets confirm that there is a significant probability of failure to detect low anthelmintic efficacy with commonly used mathematical techniques. Consequently, the use of maximum likelihood mathematical techniques with a negative binomial statistical model would aid in the early detection of anthelmintic resistance using faecal egg count reductions and result in a lower probability of inappropriately assigning an anthelmintic as effective.

Animals↗
PubMed2002

Mathematical modelling for the new millenium: medicine by numbers.

Physicists, engineers and mathematicians are accustomed to the combination of elegance, rigour and utility that characterise mathematical models. They are familiar with the need to dip into their mathematical toolbox to select the technique of choice. However, medicine and biology have not been characterised, in general, by a mathematical formalism. The relative paucity of mathematical models in biology and medicine reflects in part the difficulty in making accurate and appropriate experimental measurements in the field. Signal noise, the lack of appropriate sensors, and uncertainty as to what constitutes the significant measurements are largely to blame for this. The purpose of this paper is to characterise a 'good' model, encourage the development and application of such models to new areas, and outline future developments in the field. It is proposed that a good model will be accurate, predictive, economical, unique and elegant. These principles will be illustrated with reference to four models: radiosensitisation of tumours, modelling solute clearance in haemodialysis, the myogenic response in reactive hyperaemia and cardiac electrical activity. It is suggested that, in the immediate future, the mathematical model will become a useful adjunct to laboratory experiment (and possibly clinical trial), and the provision of 'in silico' models will become routine.

Arrhythmias, Cardiac↗
PubMed2000

Brain biomechanics: mathematical modeling of hydrocephalus.

The considerable amount of literature on mathematical models of hydrocephalus and other brain abnormalities is critically reviewed. These models have various degrees of mathematical sophistication, and have influenced not only the diagnosis of hydrocephalus, but also its treatment with CSF shunts. The mathematical models are classified into two classes, pressure-volume models, and consolidation models. Advantages and disadvantages of both types are pointed out with a view to removing the confusion frequently generated by the technical aspects of the subject. The conclusion is reached that, while none of the current models are good enough to be of immediate use to the neurosurgeon, mathematical models are likely in the future to be a powerful tool for the understanding and the treatment of hydrocephalus, as well as other conditions related to brain biomechanics. The amount of mathematics has been kept to the absolute minimum, but it is cited and appended for those who would like to dig further into this fascinating area of research.

Biomechanical Phenomena↗
PubMedDate not supplied

Arteriovenous extracorporeal carbon dioxide removal: a mathematical model and experimental evaluation.

To explore the feasibility and operating limits of arteriovenous extracorporeal CO2 removal (AVCO2R) for support of acute respiratory failure, the authors developed a mathematical model to simulate (AVCO2R), evaluate the effects of several parameters used in its application, and predict the feasibility and necessary conditions for total CO2 removal. The mathematical model incorporated compartments representing blood, pulmonary alveoli, pulmonary capillaries, peripheral tissues and capillaries, and an extracorporeal gas exchange device. The model was validated against an animal model of extracorporeal CO2 removal. This model consisted of anesthetized and mechanically ventilated piglets. An extracorporeal CO2 removal device was placed by cannulation of a femoral artery and vein. Dynamic and steady state measurements of CO2 transfer were made and compared with simulations using the mathematical model. There was good agreement between experimental and simulated data, validating the mathematical model under a variety of conditions. The mathematical model was used to determine operating parameters for total CO2 removal. Relationships between extracorporeal blood flow, device diffusing capacity, and device gas sweep flow were established for CO2 removal at various levels of CO2 production. These simulations indicate that it is possible to achieve total CO2 removal using an extracorporeal shunt fraction of 10%-15% of cardiac output, a device diffusing capacity of 0.5 ml x min(-1) x torr(-1) (kg body weight)(-1), and a gas:blood flow of 5 or greater.

Animals↗
PubMed2001

Mathematical procedure to adjust for the healthy worker effect: the case of firefighting, diabetes, and heart disease.

This article presents a mathematical procedure to adjust for one component of the healthy worker effect (HWE), namely, the healthy hired effect, on diabetes in the case of firefighting and heart disease. Three examples from real studies are given to illustrate, step-by-step, the application of the mathematical procedure. The mathematical procedure can be applied to adjust for other components of the HWE (e.g., the low-risk hired effect on obese individuals and smokers). In such cases, additional information will be needed to use the mathematical procedure. Results of applying the mathematical procedure in the case of firefighting and heart disease revealed the rather unexpected results that adjusting for diabetes selection on hiring leads to only a 3% to 9% increase in the magnitude of ratio statistics such as the standardized mortality ratio. It might be argued that the HWE from one component such as the healthy hired effect on diabetes might be small, but together with other components, the HWE might be large. Further investigation will be needed to support this argument.

Adult↗
PubMed2006

Mathematical simulations of the effects of altered AMP-kinase activity on I and the action potential in rat ventricle.

INTRODUCTION: Alterations in the activity of a so-called "metabolic switch" enzyme, adenosine monophosphate-activated protein kinase (AMP kinase), in mammalian heart contribute to the conduction abnormalities and rhythm disturbances in the settings of Wolff-Parkinson-White syndrome and ventricular pre-excitation. A recent study by Light et al. has shown that augmented AMP kinase activity can alter the biophysical properties of mammalian cardiac sodium currents. These experiments involved an electrophysiological analysis following heterologous expression of human Na(v)1.5 in tsA201 cells. Constitutive activation of AMP kinase followed by co-transfection caused: (i) a hyperpolarizing shift in the activation curve for I(Na), (ii) a small change in the voltage dependence of steady-state inactivation, and (iii) a significant slowing in the rate of inactivation of I(Na). METHODS AND RESULTS: We have attempted to simulate these results using our mathematical model of the membrane action potential of the adult rat ventricular myocyte. The changes in I(Na) produced by AMP kinase activation and/or overexpression can be reconstructed mathematically by altering two rate constants in a Markovian model that governs the I(Na) kinetics. Simulated macroscopic I(Na) records in which a fraction (10-100%) of the Na(+) channels had the appropriate rate constants for two state-dependent transitions increased by a factor of 100-fold exhibited: (i) slowed inactivation, (ii) a shift in steady-state activation to more hyperpolarized membrane potentials, and (iii) a very small change in the voltage dependence of steady-state inactivation. SUMMARY: Thus, straightforward modifications of a previously published kinetic scheme for the time and voltage dependence of mammalian heart I(Na), when incorporated into a mathematical model for the rat ventricular action potential can reproduce the main features of these AMP kinase-induced modifications in I(Na) in mammalian ventricle. Ongoing mathematical simulations are directed toward developing formulations that mimic the molecular mechanisms for the AMP kinase effects, e.g., changes in the kinetics of I(Na) resulting from selective phosphorylation/dephosphorylation of sites on the alpha or beta subunits which comprise human Na(v)1.5. Thereafter, incorporation of these changes into a mathematical model for the action potential of the human ventricular myocyte is planned.

Action Potentials↗
PubMed2006

Development of a two-dimension manifold to represent high dimension mathematical models of the intracellular Mammalian circadian clock.

A new focus for mathematical models of the circadian pacemaker involves the encapsulation within the models of detailed biological processes responsible for generating those circadian rhythms. Representing greater biological detail requires more mathematical equations, which pose a greater challenge for the analysis of such systems. Development of a method that retains the predominant dynamics while still providing biologically detailed information is advantageous. Two high-dimension mathematical models of intracellular mammalian circadian pacemakers, Leloup-Goldbeter and Forger-Peskin, with 19 and 73 differential equations, respectively, have been published. The authors projected each of these high-dimension models onto their respective manifold using proper orthogonal functions (POFs) obtained from the empirical decomposition of the model's phase space to obtain a 2-dimension model. The resulting 2-dimension model, represented by 2 differential equations, predicts most of the salient characteristics of a biological clock including approximately 24-h oscillations, entrainment to an LD cycle, phase response curves, and the amplitude recovery dynamics that emerge following amplitude suppression. The manifold representation simplifies the mathematical analysis, since only 2 variables need to be observed and analyzed to understand the behavior of the biological clock. This reduced model derived from a model based on biological variables can be used for the development and analysis of mathematical models of the coupled mammalian oscillators to understand the dynamics of the integrated circadian pacemaker.

Animals↗
PubMed2005

Mathematical methods to assist with hospital operation and planning.

Within health Operational Research, the use of 'computer package' methods such as simulation and system dynamics is becoming so prevalent that it feels somewhat old hat to use analytical methods to develop explicit mathematical formulae or even to explore the mathematical structure of problems. This paper will discuss the use of such 'back of the envelope' analysis illustrating its usefulness. It will be shown that not only does this approach yield considerable insight, but also that it can give rise to powerful and practical solution methods. Examples of this will be discussed in relation to issues such as bed needs estimation, admissions and facilities planning. The author is Director of the Clinical Operational Research Unit (CORU) which was established in 1983, receiving core funding from the UK Department of Health. The concept of a full time university-based research unit dedicated to applying expertise in Operational Research (OR) to problems in health care provides a relatively rare research resource. Yet, the scope for such research, applied to an increasing range of health care activity, is enormous. Issues such as treatment evaluation, performance measures, clinical governance, evidence based medicine and health service delivery are all amenable to OR. Further, OR often provides an immensely cost effective alternative to traditional methods of clinical research based on randomised controlled trials or large scale epidemiological studies. The nature of OR, and one of its main strengths, is that it encompasses a wide range of analytical and scientific methods. Mathematical modeling, statistics, computer-based methods, trial design and analysis all contribute to health OR and, under both of its Directors since 1983, a conscious effort has been made within CORU to foster a diversity of research methodologies. Particular emphasis is put on developing new mathematical methods and computer software. This is somewhat at odds with what seems to be a growing trend in health OR towards researchers specialising in just one or two areas of methodology; thus Tom does queueing theory, Dick does simulation and Harry does System Dynamics. Of course there are exceptions, but for whatever reason, the trend towards specialisation seems real. In this paper, benefits of a more diverse approach to health OR is advocated, particularly the use of 'back of envelope' mathematical methods as an alternative to the use of proprietary software packages. Three case studies are described to illustrate this approach.

Biomedical Research↗
PubMed1996

Deficiencies in calculation and applied mathematics skills in pediatrics among primary care interns.

OBJECTIVE: To discover how well new house officers in primary care residency programs perform the mathematical calculations necessary to function effectively in pediatric and nursery settings. DESIGN: Criterion-referenced survey examination testing unit conversion, fluid and rehydration management, and drug-dosing skills. SETTING: Five primary care residences in family practice and pediatrics at urban and community campus sites in Illinois. PARTICIPANTS: Twenty-three family practice residents and 11 pediatric residents tested during residency orientations sessions or in conferences during the first 3 months of training. INTERVENTIONS: None. RESULTS: The mean score for all residents was 42%. Pediatric residents (mean score, 57.8%) performed significantly better than family medicine residents (mean score, 34.4%) (P = .002). Conversion from conventional to metric units was more difficult for family practice residents, but pediatric residents also made errors. Pediatric residents were significantly better than family medicine residents at calculation of fluid maintenance requirements (P < .05). Only 5 of 34 residents wrote acceptable fluid orders. Nutritional and drug therapy calculations showed fewer mathematical errors, but neither group routinely wrote medical orders that specified the drugs or formula, concentration, volume required per dose or feeding, route of administration, dosing interval, and duration of therapy. CONCLUSIONS: The potential for serious clinical errors caused by faculty calculation of dosage by house staff officers is high. New residents should have their orders for fluids and drugs double-checked by senior personnel early in their training. Residency programs should provide remedial skills training for house officers with deficiencies in applied mathematics. The medical school faculty needs to assess students' competence in mathematics before allowing independent clinical responsibility.

Clinical Competence↗
PubMed1980

A bio-physical basis of mathematics in synaptic function of the nervous system: a theory.

The purpose of this paper is to present a bio-physical basis of mathematics. The essence of the theory is that function in the nervous system is mathematical. The mathematics arises as a result of the interaction of energy (a wave with a precise curvature in space and time) and matter (a molecular or ionic structure with a precise form in space and time). In this interaction, both energy and matter play an active role. That is, the interaction results in a change in form of both energy and matter. There are at least six mathematical operations in a simple synaptic region. It is believed the form of both energy and matter are specific, and their interaction is specific, that is, function in most of the 'mind' and placed where it belongs - in nature and the synaptic regions of the nervous system; it results in both places from a precise interaction between energy (in a precise form) and matter ( in a precise structure).

Action Potentials↗
PubMed1997

Beliefs about genetic influences on mathematics achievement: a cross-cultural comparison.

The poor mathematics performance of children in the United States has become a topic of national concern. Numerous studies have shown that American children consistently perform worse than their counterparts in many parts of the world. In contrast, children in China, Japan, Taiwan, and other Asian countries consistently perform at or near the top in international comparisons. This paper examines possible causes of the poor performance of American children and the excellent performance of Asian children. Contrary to the beliefs of many Americans, the East Asian advantage in mathematics is probably not due to a genetically-based advantage in mathematics. Instead, differences in beliefs about the role of genetics may be partly responsible. Asians strongly believe that effort plays a key role in determining a child's level of achievement, whereas Americans believe that innate ability is most important. In addition, despite the relatively poor performance of their children, American parents are substantially more satisfied with their children's performance than Asian parents. The American emphasis on the role of innate ability may have several consequences for children's achievement. For example, it may lead children to fear making errors and to expend less effort on mathematics than their Asian counterparts. As research on genetic influences on behavior, traits, and abilities increases scientists should be careful to ensure that the public understands that genetics does not directly determine the exact level of a child's potential achievement.

Asia↗
PubMed2006

Working memory deficit in children with mathematical difficulties: a general or specific deficit?

This study examined whether children with mathematical difficulties (MDs) or comorbid mathematical and reading difficulties have a working memory deficit and whether the hypothesized working memory deficit includes the whole working memory system or only specific components. In the study, 31 10-year-olds with MDs and 37 10-year-olds with both mathematical and reading difficulties were compared with 47 age-matched and 50 younger controls (9-year-olds) on a number of working memory tasks. Compared with the age-matched controls, both groups of children with MDs performed worse on tasks tapping the central executive (e.g., visual matrix span) and the phonological loop (e.g., word span). More important, the MD group performed worse than the younger controls on the counting span task, whereas the group with comorbid mathematical and reading difficulties performed worse on the counting span task and the visual matrix span task. These findings provide support for the assumption that children with MDs have a working memory deficit. More specifically, children with MDs have a central executive deficit connected to concurrent processing and storage of numerical and visual information.

Child↗
PubMed2004

A theory of drug tolerance and dependence II: the mathematical model.

The preceding paper presented a model of drug tolerance and dependence. The model assumes the development of tolerance to a repeatedly administered drug to be the result of a regulated adaptive process. The oral detection and analysis of exogenous substances is proposed to be the primary stimulus for the mechanism of drug tolerance. Anticipation and environmental cues are in the model considered secondary stimuli, becoming primary in dependence and addiction or when the drug administration bypasses the natural-oral-route, as is the case when drugs are administered intravenously. The model considers adaptation to the effect of a drug and adaptation to the interval between drug taking autonomous tolerance processes. Simulations with the mathematical model demonstrate the model's behaviour to be consistent with important characteristics of the development of tolerance to repeatedly administered drugs: the gradual decrease in drug effect when tolerance develops, the high sensitivity to small changes in drug dose, the rebound phenomenon and the large reactions following withdrawal in dependence. The present paper discusses the mathematical model in terms of its design. The model is a nonlinear, learning feedback system, fully satisfying control theoretical principles. It accepts any form of the stimulus-the drug intake-and describes how the physiological processes involved affect the distribution of the drug through the body and the stability of the regulation loop. The mathematical model verifies the proposed theory and provides a basis for the implementation of mathematical models of specific physiological processes.

Adaptation, Physiological↗
PubMed1982

Mathematical ability and lateral asymmetry.

The hypothesis that special ability in mathematics is associated with a reduction in bias to dextral preference and skill was examined in several samples of students and in 97 male and 27 female teachers of mathematics, mainly in Universities and Polytechnics. The math students and math teachers differed from controls, both general and academic, in the direction predicted and several comparisons were statistically significant. Differences were in most cases clearer for males than females. An analysis of the findings in relation to the right shift (RS) theory of handedness (Annett, 1972, 1978) suggests that the incidence of left preference and skill is slightly raised in mathematicians not because of any intrinsic advantage of left preference but rather because extreme bias to the right, as expected in those carrying a hypothesised rs++ genotype, is disadvantageous for mathematical thinking. If the role of mathematics can be regarded as one of developing languages to describe those aspects of human experience which otherwise could be understood only in visuo-spatial images, it can be seen to require a coordination of those aspects of human intelligence which have been distinguished as depending differentially on the left and right cerebral hemispheres. The present findings suggest that this process might be impeded by a double dose of a gene which promotes left hemisphere language specialisation.

Adolescent↗