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PubMedDate not supplied

Mathematical models and their applications in medicine and health.

Mathematical models have great potentialities as regards their utility in different disciplines of medicine and health. This paper attempts to elucidate their uses in the field. A brief mention of some models has also been made. Mathematical models are useful in epidemiologic research, planning and evaluation of preventive and control programmes, clinical trials, measurement of health, cost-benefit analysis, diagnosis of patients and in maximizing effectiveness of operations aimed at attaining specified goals within existing resources.

Health Services Research↗
PubMed1998

Distributing working versions of published mathematical models for biological systems via the Internet.

Mathematical models are useful tools for investigating complex systems. By representing physiological systems as models, theories can be tested quantitatively against data from the system. Models can be used to explore new theories prior to experimentation and to design studies to optimize experimental resources. They can also be used as teaching tools to illustrate physiochemical principles. In spite of their usefulness and the time invested in developing models, published models are often underused due to the difficulty in obtaining working versions of the model. To address this problem we have designed a library for mathematical models of biological systems on the Internet. The library contains published models of biological systems in formats compatible with several modeling packages, from the fields of physiology, metabolism, endocrinology, biochemistry, and chemistry. The models can be viewed graphically, model solutions can be viewed as plots against data, and models can be downloaded to be run with software on the user's own system. The address of the library is: http://biomodel.georgetown.edu/model/ Investigators are invited to submit working versions of published models to the library. Models can be submitted electronically at the time a manuscript is accepted for publication. As journals go online, articles containing models can be linked to working versions of the models in the library. By increasing access to working versions of models, more of the investment in kinetic studies and model development can be realized.

Computer Simulation↗
PubMed1995

Psychovegetative syndrome diagnosis: an automated psychophysiological investigation and mathematical modeling approach.

1. INTRODUCTION. The main purpose of our work was to create the informational expert system of psychovegetative syndrome diagnosis by applying clinical data and estimating the functioning of the central and peripheral part of regulatory apparatus of the human organism, taking into consideration parallel and consecutive sensory, motor, associative, emotional drive systems, and internal body state. We used automatized psychophysiological investigation and mathematical models. For this purpose the following principal tasks have been prepared: the creation of database of quantifiable estimation patient state; the definition and automation of psychophysiological investigation; mathematical modeling of vegetative functions using a non-invasive sample and its connection with real psychophysiological experiment; mathematical modeling of organisms inner medium homeostasis; and the creation of an informational-expert system of psychovegetative syndrome diagnosis. 2. DATABASE OF ESTIMATION OF PATIENTS STATE. The medical records of the DB "PATIENT" contain data on patient psychic and somatoneurological status. 3. AUTOMATED PSYCHOPHYSIOLOGICAL INVESTIGATION. Psychophysiological investigation enables estimation of the functioning of several subsystems of the human organism and establishes an interrelationship between them by means of electrophysiological data and performance parameters. The study of psychophysiological provision of behavior by psychophysiological investigation enables us to get information about adaptational mechanisms of the patient under certain environmental loads. By means of special mathematical provision, the mathematical elaboration of biosignals as performance parameters has been realized; also realized were the formation of received parameters in the database, the estimation of separated parameters in the view of informativity, and the establishment of diagnostic patterns. 4. MATHEMATICAL MODELS FOR ESTIMATION INTERNAL BODY STATE. The proposed mathematical models allow investigation of homeostatic regulation in various intensities of the metabolic processes and external load. This approach in mathematical models allows us to characterize the relations between the central and peripheral parts of the regulatory mechanisms, using non-invasive samples under psychophysiological investigation and the simulation of different surroundings for brain cells functioning. 5. INFORMATION-EXPERT SYSTEM. Proceeding from the principle of psychoneural unity, we characterized the functioning mechanisms of CNS by means of automatized EEG analysis, visually evoked potential analysis, estimated psychic status, and the characteristics of neural system biochemical processes received by mathematical modeling. By using the indices of the viscero-vegetative and somatolocomotor system (as well as parameters received by automatized analysis of ECG), the EEG respiratory signal--from mathematical models of vegetative functions decision support system applied in estimation of a peripheral block of the regulatory system--is reflected in diagnosis of certain syndromes. The informational expert system, proceeding from the functioning of the human organism's regulatory apparatus, diagnosed psychovegetative syndrome and described the mechanisms of its development. 6. CONCLUSION. The informational expert system enables estimation of the functioning of a human organism as a whole and can be introduced in the sphere of practical medicine and professional orientation as well as in laboratories of experimental psychology and neurosciences.

Brain↗
PubMed1997

Compartmentalized energy transfer in cardiomyocytes: use of mathematical modeling for analysis of in vivo regulation of respiration.

The mathematical model of the compartmentalized energy transfer system in cardiac myocytes presented includes mitochondrial synthesis of ATP by ATP synthase, phosphocreatine production in the coupled mitochondrial creatine kinase reaction, the myofibrillar and cytoplasmic creatine kinase reactions, ATP utilization by actomyosin ATPase during the contraction cycle, and diffusional exchange of metabolites between different compartments. The model was used to calculate the changes in metabolite profiles during the cardiac cycle, metabolite and energy fluxes in different cellular compartments at high workload (corresponding to the rate of oxygen consumption of 46 mu atoms of O.(g wet mass)-1.min-1) under varying conditions of restricted ADP diffusion across mitochondrial outer membrane and creatine kinase isoenzyme "switchoff." In the complete system, restricted diffusion of ADP across the outer mitochondrial membrane stabilizes phosphocreatine production in cardiac mitochondria and increases the role of the phosphocreatine shuttle in energy transport and respiration regulation. Selective inhibition of myoplasmic or mitochondrial creatine kinase (modeling the experiments with transgenic animals) results in "takeover" of their function by another, active creatine kinase isoenzyme. This mathematical modeling also shows that assumption of the creatine kinase equilibrium in the cell may only be a very rough approximation to the reality at increased workload. The mathematical model developed can be used as a basis for further quantitative analyses of energy fluxes in the cell and their regulation, particularly by adding modules for adenylate kinase, the glycolytic system, and other reactions of energy metabolism of the cell.

Adenosine Diphosphate↗
PubMed2001

Mathematical modelling of physicochemical reactions and transport processes occurring around a platinum cathode during the electrochemical treatment of tumours.

The electrochemical treatment (EChT) of tumours is an anti-tumour therapy in which a continuous direct current is applied to electrodes, placed in or near a tumour. Promising results have been reported from clinical trials in China, where more than 10,000 patients have been treated with EChT during the past 10 years. Before clinical trials can be conducted outside of China, a reliable dose-planning strategy has to be developed. One approach in achieving this is the use of physicochemical simulation models. A simplified mathematical model of the physicochemical processes, occurring around a spherical platinum cathode during EChT, is developed and visualized in three steps in this paper. In the final step, tissue is treated as an aqueous solution of sodium chloride, containing a bicarbonate buffer system and organic constituents susceptible to reactions with hydroxyl ions. This model is shown to give a good description of the pH profile obtained around the cathode after EChT. The simulation results reveal a strong correlation between the pH profiles and size of experimentally measured lesions, thus indicating that it is the spreading of hydroxyl ions that determines the extent of tissue destruction around the cathode. In addition, the simulations indicate that the model could be of use in predicting the size of a lesion produced by EChT.

Animals↗
PubMed2001

Mathematical modelling of patients flow through an accident and emergency department.

OBJECTIVES: The objectives of this project; (1) to evaluate the method, (2) to assess the information required for a more detailed model, and (3) to determine if it was worthwhile to undertake the data collection needed for a more detailed model. METHODS: A mathematical model was constructed using the operational research method of discreet event simulation. The effect of different SHO shift patterns on waiting time was assessed with the model. RESULTS: The model constructed was not an accurate representation of patient flow because of the large number of assumptions that had to be made in this preliminary model. However, the model predicted that an SHO shift pattern that more closely matched the patient arrival pattern would produce shorter waiting times. CONCLUSIONS: This method can be applied to an accident and emergency department. Extension of this approach with the collection of additional data and the development of more sophisticated models seems worthwhile.

Data Collection↗
PubMed1998

Ocular fixation index and mathematical models.

Ocular fixation test and ocular fixation index (OFI) never have been interpreted in terms of mathematical models, despite their widespread diffusion. However, ocular fixation is a typical case of visual-vestibular interaction, and mathematical models have proven very helpful in interpreting some mechanisms of this interaction, e.g. those of the optokinetic-vestibular interaction. In the present paper, a first attempt is proposed toward a model interpretation of OFI. By using very simple mathematical models, the hypothesis is tested that visual suppression of vestibular nystagmus results from direct action of smooth pursuit system (SPS). The aim is to draw consequences and recognize possible limits of this hypothesis. Dependence of OFI on SPS performance is examined. Although the available experimental data are insufficient for comprehensive validation of the model, the results agree with the current interpretations. In particular, quantitative support is given to the sensitivity of OFI to central vestibular diseases. Although the interpretation of visual suppression and OFI in terms of mathematical models is still at a very preliminary stage, models may provide a theoretical reference framework for the interpretation of new experimental results and/or suggest new test protocols.

Fixation, Ocular↗
PubMed1989

A mathematical model of the kinetics of blood coagulation.

Linear mathematical models of the kinetics of blood coagulation have previously been presented (Levine, 1966, Science, N.Y. 152, 651; Martorana & Moro, 1974, Math. Biosci. 21, 77). In this paper a non-linear mathematical model of the extrinsic pathway of blood coagulation is presented to take into account a positive feedback. The feedback is due to factor Va as a co-factor involved in thrombin formation. The extrinsic pathway is shown to function as an amplifier cascade if a vessel wall injury exceeds a threshold value. For sub-threshold stimulation, the extrinsic pathway does not function.

Blood Coagulation↗
PubMed1980

Mathematical models of synaptic plasticity: I. Posttetanic potentiation.

A mathematical model of post-tetanic potentiation is proposed. The model uses differential equations and is based upon physiological postulates of the electrical, metabolic, and neuroendocrine activities that are related to synaptic connectivity. These activities may modify some important parameters in synaptic function. In the proposed model these parameters are restricted to the presynapse in view of the physiological evidence indicating that posttetanic potentiation is probably due to presynaptic mechanisms. The model takes into consideration the size of the transmitter pool available for release, the mobilization of transmitter from and to this pool, and the fraction of transmitter released. Based upon the above postulates, we have simulated different phases of the phenomenon of posttetanic potentiation, and we have presented the results of several preparations in which this event has been studied. This work represents a successful attempt to reproduce the dynamics of posttetanic potentiation based upon physiological results with a mathematical model.

Calcium↗
PubMed2001

A three-dimensional mathematical model of temporomandibular joint loading.

OBJECTIVE: A mathematical model of the temporomandibular joint was developed to study the magnitude and direction of the compressive loading experienced at the temporomandibular joint during clenching. DESIGN: The model was based on the principles of static equilibrium in three dimensions. BACKGROUND: Direct measurement of temporomandibular joint loading in humans is extremely difficult. Animal models have provided an alternative in the past. However, evidence suggests that primates are not the most accurate human analogues for temporomandibular joint studies. A mathematical model was used as an alternative to direct measurement. METHODS: The EMG activity of two masticatory muscles was combined with their cross-sectional areas to calculate the force exerted by each muscle. Experimentally determined forces were implemented into a quadratic programming model to solve for the compressive forces on the joint. Two objective functions were chosen and their ability to predict muscle and joint forces was evaluated. RESULTS: The maximum bite forces for normal men, normal women, and women with temporomandibular joint disorders were 300 N (SD 102 N), 210 N (SD 57.7 N), and 120 N (SD 77.1 N), respectively. The calculated joint force for normal males was 260 N (SD 84.1 N). Normal females and female temporomandibular joint disorder patients produced temporomandibular joint forces of 172 N (SD 37.5 N) and 152 N (SD 44.2 N), respectively.

Electromyography↗
PubMedDate not supplied

Mathematical modelling and quantitative methods.

The present review reports on the mathematical methods and statistical techniques presently available for hazard characterisation. The state of the art of mathematical modelling and quantitative methods used currently for regulatory decision-making in Europe and additional potential methods for risk assessment of chemicals in food and diet are described. Existing practices of JECFA, FDA, EPA, etc., are examined for their similarities and differences. A framework is established for the development of new and improved quantitative methodologies. Areas for refinement, improvement and increase of efficiency of each method are identified in a gap analysis. Based on this critical evaluation, needs for future research are defined. It is concluded from our work that mathematical modelling of the dose-response relationship would improve the risk assessment process. An adequate characterisation of the dose-response relationship by mathematical modelling clearly requires the use of a sufficient number of dose groups to achieve a range of different response levels. This need not necessarily lead to an increase in the total number of animals in the study if an appropriate design is used. Chemical-specific data relating to the mode or mechanism of action and/or the toxicokinetics of the chemical should be used for dose-response characterisation whenever possible. It is concluded that a single method of hazard characterisation would not be suitable for all kinds of risk assessments, and that a range of different approaches is necessary so that the method used is the most appropriate for the data available and for the risk characterisation issue. Future refinements to dose-response characterisation should incorporate more clearly the extent of uncertainty and variability in the resulting output.

Animals↗
PubMed1996

On the mathematical modelling of pain.

In this review a case is presented for the use of mathematical modelling in the study of pain. The philosophy of mathematical modelling is outlined and a recommendation is made for the use of modern nonlinear techniques and computational neuroscience in the modelling of pain. Classic and more recent examples of modelling in neurobiology in general and pain in particular, at three different levels-molecular, cellular and neural networks-are described and evaluated. Directions for further progress are indicated, particularly in plasticity and in modelling brain mechanisms. Major advantages of mathematical modelling are that it can handle extremely complex theories and it is non-invasive, and so is particularly valuable in the investigation of chronic pain.

Analgesia↗
PubMed1982

[Use of mathematical models in the analysis of gastric digestion].

Mathematical models of gastric hydrolysis of different proteins were elaborated in dogs. These models consider the spatialtemporal coordinates of distribution of pepsin, hydrogen ions and hydrolysates in the stomach, carry out the analysis of factors determining the gastric digestion. The main part belongs to topography and hydrodynamics of gastric content as well as to pepsin concentration. The concentration of "total hydrolysates" is proposed as the final criterion of the gastric digestion. An algorithm for mathematical modelling of gastric digestion is suggested.

Animals↗
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↗
PubMed1996

Sexually transmitted diseases and sexual behavior: insights from mathematical models.

The major role of mathematical models of transmission dynamics and population biology of sexually transmitted diseases is helping understand the influence of the many biologic, social, and behavioral factors that influence the incidence or prevalence of infection. Various models can examine heterogeneity in sexual behavior and determine how individual variation influences epidemiologic pattern within a population. In the cases of heterogeneity in sex acts and in sex partner numbers, heterogeneity acts to enhance the likelihood of the persistence of infection. Also important is the pattern of mixing or sexual contact within a community. Assortative mixing promotes rapid spread in high-sexual-activity classes but results in a lower endemic equilibrium state compared with random mixing. In these models, each facet of behavior is treated separately. The obvious next goal of modeling is to meld processes together into a single mathematical framework; however, quantitative epidemiologic information on each factor is still needed.

Humans↗
PubMed2002

Mathematical model to predict individual survival for patients with renal cell carcinoma.

PURPOSE: To develop a multivariate model and mathematical formula capable of calculating personalized survival for renal cell carcinoma (RCC) patients with clinically available variables. PATIENTS AND METHODS: A total of 477 patients out of 661 undergoing nephrectomy at the University of California Los Angeles between 1989 and 1999 were eligible for evaluation and formed the analyzed cohort for this retrospective study. Time to death was the primary end point assessed. Univariate analysis for 14 to 20 variables was conducted, followed by a multivariate Cox analysis. The variables that provided independent information as to the time of death for metastatic and nonmetastatic patients were coded and incorporated into a function based on the Nadas equation principle. RESULTS: For nonmetastatic patients, the significant variables in the multivariate analysis were Fuhrman's grade and Eastern Cooperative Oncology Group performance status. For the metastatic patients, Fuhrman's grade, 1997 classification T stage, number of symptoms, nodal involvement, and immunotherapy were independent predictors for survival. These variables, based on the Cox multivariate regression model, were implanted into an exponential Nadas equation. The expected survival predicted by use of the Nadas equations faithfully describes the actual survival based on Kaplan-Meier curves. CONCLUSION: We have developed mathematical equations for estimating survival after radical nephrectomy for RCC. The resulting formulas are capable of better tailoring survival estimates for a specific patient and are based on widely accepted clinical prognostic variables. On validation with external data, this type of representation can be used as a tool for the determination of personalized prognosis and may be useful for patient education and counseling.

Carcinoma, Renal Cell↗
PubMed1990

Mathematical model of chest wall mechanics: a phenomenological approach.

A mathematical model of chest wall mechanics, based on a phenomenological approach to force balances, provides a quantitative framework for analyzing many types of chest wall movements by using orthogonal displacement coordinates. The moveable components of the ventilatory system include the rib cage, diaphragm, and abdomen. A distinction is made between the lung-apposed and diaphragm-apposed actions on the rib cage. The model equations are derived from "pressure" balances and geometrical relations of the compartments; the stress-displacement relations are hyperbolic. With this model we simulated stiff and flaccid chest wall behavior under normal and constrained conditions associated with abdominal compression, a Mueller maneuver, and a diaphragmatic isometric inspiration. We also examined situations that produce paradoxical as well as orthodox inspiratory movements. The results of these simulations were quantitatively consistent with available data from the literature. A phenomenon predicted by the stiff-wall model during quasi-static inspiration is that the rib cage displacement is negligible near residual volume, but then increases dramatically with lung volume. Since this mathematical model has a sound physical basis and is more comprehensive than previous models, it can be used to predict and analyze the behavior of the chest wall under a wide variety of circumstances.

Abdominal Muscles↗
PubMed2000

Mathematical modeling of diffusion-mediated release from bulk degrading matrices.

The release of active agent from a bulk degrading matrix is formulated as a linear reaction diffusion problem. Two pools of active agent are assumed to contribute to the release: a pool of mobile active agent which readily diffuses out of the matrix upon immersion in an aqueous medium and a pool of immobilized active agent which can diffuse only after matrix degradation. Due to the linearity of our model, the dynamics of the two pools of active agent can be considered separately, for any mode of bulk degradation kinetics. For definiteness, we consider the case of first order degradation kinetics and a rectangular parallelepiped shaped matrix. A closed form solution is obtained for the release under perfect sink conditions which is then used to describe the in vitro release of the PerioChip¿trade mark omitted¿. This solution can explain the bi-phasic release profile characteristic of many hydrolytically degradable matrices. The case of mass transfer boundary conditions is solved numerically using the finite element method (FEM). This analysis indicates that under ordinary mixing conditions the diffusion layer is not rate limiting and the release is very well approximated by the analytical result for perfect sink conditions.

Aerosols↗