# Areas and slopes

Abstract

It is frequently necessary to estimate areas, slopes, arc lengths, averages, lag times or asymptotes in circumstances where the data are too noisy to fit a deterministic equation or where a mathematical model cannot be derived and an empirical equation or numerical procedure has to be used. Use program AVERAGE to estimate areas, averages and fractions above and below thresholds by the trapeziodal method or use COMPARE with splines under tension if this is preferred. program INRATE estimates initial and final rates, lag times and areas using empirical equations, while program QNFIT uses a deterministic model.

Details

If a process can be described by a mathematical equation then this can be fitted to a data set and the best fit model can then be used to estimate areas and derivatives, etc. Program QNFIT in the SIMFIT package can be used for this purpose. Frequently the exact model may be unknown or too complicated to be used in this way or the data may be too noisy. In such cicumstances the noisy data may be used without correction, as in the trapezoidal method for estimating area under curves or perhaps joining up the early points to define initial rates, but in many instances data smoothing and use of an empirical model may be preferred.

Data smoothing

This process is the use of empirical equations to fit noisy data sets in order to use all the data to estimate parameters that characterise the underlying process. Choosing the correct smoothing technique is not always easy and requires care.

Program AVERAGE (Trapezoidal method)

This accepts curve fit files and joins the points (or means of if replicates are supplied) by straight lines. These are used as a robust method to calculate AUC, time above threshold or average concentrations in pharmacokinetic studies.

Program INRATE (Polynomials, exponentials and power laws)

This can fit lines, quadratics, exponentials, Hill equations or lag time equations. It is used for enzyme catalysed initial rates, emptying of vesicles, diffusion into cells, etc. It is very important to use the correct type of model with INRATE.

Programs CALCURVE, COMPARE and SPLINE (splines)

These use cubic splines to fit arbitrary curves. They are most useful with complicated wavy curves where it is required to estimate derivatives, areas and arc lengths. Care is needed to check plots to ensure that best fit splines are not too wavy.

Back to Help Menu or End Help