Mathematical models and their applications in medicine

This paper emphasises the fact that mathematical modelling techniques have important applications in routine medical practice and medical education. It is argued that the development of mathematical models should be more closely linked to experimentation and that techniques based on computer simulation can extend the range of applicable models to models based on nonlinesr differential equations which are the largest class of models in biological work. Model have an important role in hypothesis testing and in the development of indirect methods for measuring physiological quantities. The important of model validation is stressed

Investigation of respiratory controller function based on simulation studies

The paper describes work in progress on dynamic aspects of the physiological system concerned with chemical control of respiration in man. The immediate objective of the study is an improved understanding of the influence of the dynamic aspects of various subsystems on measures of controller function used in current clinical tests. A longer term aim involves development of improved tests for clinical investigation of control system performance. The paper presents preliminary results of simulation studies on a dynamic model of the system, including a parameter sensitivity analysis of the control loop involving the central chemoreceptors

The measurement of lung volume by a self-adaptive modelling technique

This article describes a method for estimation of lung volume that is based on the use of adaptive modelling principles, involving continuous parameter adjustment through the use of sensitivity functions. The technique is implemented using an analog computer. Measurements of lung volume obtained using this approach have been compared with results found by more conventional methods in a group of normal subjects

Computer models of gas exchange processes in pulmonary ventilation

This chapter describes approaches to the modelling of respiratory gas exchange processes. Steady-state and dynamic models are considered and issues associated with experimental validation of proposed models are addressed. Adaptive modelling concepts are also introduced and applied to indirect estimation of model parameters, including the volume of the alveolar compartment

Application of mathematical models in respiratory medicine

The techniques of dynamic analysis are used frequently in the study of physical systems but rarely in the experimental or routine study of physiological systems. Sucdh techniques considerably extend conventional methods of investigation in this area and provide a convenient means of quantifying a system's performance. Such quantification would represent useful information for the clinician. The study of respiratory gas exchange is suited to this approach. Both lumped and distributed parameter models have been investigated. Lumped parameter models with associated parameter estimation techniques should lead to new non-invasive methods of measurement, suited to use in clinical practice. Distributed models of the type described increase the detailed understanding of gas transport in the lung and the probable effects of disease in this process. It is suggested that there is a general need for increased collaboration between physical scientists and mathematically trained clinicians

Simulation in the teaching of concepts of respiratory gas exchange

The study of pulmonary gas exchange involves understanding factors which influence the performance of a complex nonlinear system. Experimentation with a realistic simulation gives the student insight which is very difficult to obtain by conventional teaching methods. A dynamic model of carbon dioxide transport has been developed and implemented on both a special purpose analog computer and a digital computer. The special purpose analog computer has significant advantages for this application

Estimation of the parameters of a lung model with clinical applications

In a mathematical representation of a physiological system variables of the model usually correspond to particular physiological variables, and model paraemters can be associated with specific quantities in the real system. This paper discusses the application of system identification and parameter estimatiion techniques for estimation of parameters of a lung model. Experimental aspects are outlined and potential clinical applications discussed

Genetic correlation analysis suggests association between increased self reported sleep duration in adults and schizophrenia and type 2 diabetes

Study Objectives: We sought to examine how much of the heritability of self-report sleep duration is tagged by common genetic variation in populations of European ancestry and to test if the common variants contributing to sleep duration are also associated with other diseases and traits. Methods: We utilized linkage disequilibrium (LD)-score regression to estimate the heritability tagged by common single nucleotide polymorphisms (SNPs) in the CHARGE consortium genome-wide association study (GWAS) of self-report sleep duration. We also used bivariate LD-score regression to investigate the genetic correlation of sleep duration with other publicly available GWAS datasets. Results: We show that 6% (SE = 1%) of the variance in self-report sleep duration in the CHARGE study is tagged by common SNPs in European populations. Furthermore, we find evidence of a positive genetic correlation (rG) between sleep duration and type 2 diabetes (rG = 0.26, P = 0.02), and between sleep duration and schizophrenia (rG = 0.19, P = 0.01). Conclusions: Our results show that increased sample sizes will identify more common variants for self-report sleep duration; however, the heritability tagged is small when compared to other traits and diseases. These results also suggest that those who carry variants that increase risk to type 2 diabetes and schizophrenia are more likely to report longer sleep duration