Anaesthetic trainees often have enormous trouble understanding the quantitative aspects of the basic sciences underlying clinical anaesthetic practice. The subjects of pharmokinetics and statistics are often unpopular with trainees, and studied with little enthusiasm. In spite of their reluctance, this is an area that they are required to study and understand as a core part of their training for postgraduate exams. Mathematics and statistics for anaesthetists presents simple mathematical ideas, and explains how these can be used to model and understand problems which arise in clinical anaesthesia. The common features of the underlying mathematics are emphasised through a pictorial/graphical approach, in preference to vast amounts of algebra. The book presents statistics in an informal and less intimidating style that most standard statistical texts, incorporating illustrations and cartoons throughout. The book will be valuable to anaesthetists, in guiding them through what can be an intimidating part of their training.
Steven Cruickshank, Consultant Anaesthetist, Department of Anaesthesia, Newcastle General Hospital, Newcastle-upon-Tyne
Section 1 Physiological and pharmacological modelling Introduction The input-output principle Steady-states: Alveolar ventillation & PaCO2 Gas laws Flux & the Fick principle Fick & cardiac output; dilution methods Fick & cerebral blood flow Apnoeic oxygenation Nitrogen washout and preoxygeneration Time constants Step change in ventilation Air embolism Pharmacokinetic models Drug-receptor interaction Drug antagonism Oscillating systems Damped oscillations Forced oscillation Modelling arterial pressure waves Section 2 - Mathematical background Numbers Functions Pattern functions & transformation Constant function Linear Rectangular hyperbolic functions Polynomial functions Inverse functions Exponential & logarithmic functions Sinusoidal functions Functions of more than one variable The derivative & differentiation Maxima & minima Integration Differential equations Numerical methods for differential equations Section 3 - Probability & statistics Probability models and simulation Waiting times in a Poisson process Passing the fellowship; the binomial distribution Measuring SVP; the normal distribution Modelling with random variables Sums of random variables Probability Conditional probability & Bayes theorem Summary measures; location and dispersion The normal distribution Statistical inference Sample mean. Estimation & confidence Sample variance Significance testing Samples of unknown mean and variance Categorial data Related variables; linear regression Related variables; correlation Distribution-free methods Stochastic IOP. Queues Bibliography Index
