# Response Surface Analysis of Propofol-Remifentanil using the Curve-Fitting Toolbox

## Contents

The aim of this demo is to characterize the "complete spectrum of interaction" between opiods and hypnotics, using propofol and remifentanil as drug class prototypes [1]. 4 different surrogate drug effects measures for analgesia and hypnosis were used to understand the analgesic and sedative effects combined drug action – these are tibial pressure algometry, electrical tetany, response to laryngoscopy and an alertness/sedation score. The effects were modelled using the following drug interaction model.

References: [1] Kern SE, Xie G, White JL, Egan TD. Opioid-hypnotic synergy. Anesthesiology 2004; 100: 1373–81.

% Copyright 2009, The MathWorks, Inc. close all, clear all, clc

## Import response data

ResponseData.xls contains measures of surrogate drug effects at various concentration combinations of propofol and reminfentanil. Import the data as a dataset object.

data = dataset('xlsfile', 'ResponseData.xls');

## Characterize the response surfaces for 4 surrogate effects

Use the drug interaction model published in [1] to characterize the response surface for each of the 4 measured effects - Algometry, Tetany, Sedation and Laryingoscopy.

EffectName = {'Algometry' 'Tetany' 'Sedation' 'Laryingoscopy'}; for i = 1:length(EffectName) [fitresults(i), gof(i)] = myCreateSurfaceFit(data.Propofol, data.Remifentanil, data.(EffectName{i}), EffectName{i}) ; %#ok<SAGROW> disp([' Model for ', EffectName{i}, ' is ']) disp(fitresults{i}) disp('... and GOF is ') disp(gof(i)) end

Model for Algometry is General model: ans(x,y) = combinedEffect(x,y, IC50A, IC50B, alpha, n) Coefficients (with 95% confidence bounds): IC50A = 4.148 (4.123, 4.174) IC50B = 9.044 (8.971, 9.118) alpha = 8.501 (8.316, 8.687) n = 8.289 (8.132, 8.447) ... and GOF is sse: 0.0842 rsquare: 0.9991 dfe: 393 adjrsquare: 0.9991 rmse: 0.0146 Model for Tetany is General model: ans(x,y) = combinedEffect(x,y, IC50A, IC50B, alpha, n) Coefficients (with 95% confidence bounds): IC50A = 4.544 (4.522, 4.567) IC50B = 21.22 (21.04, 21.4) alpha = 14.94 (14.67, 15.21) n = 6.132 (6.055, 6.209) ... and GOF is sse: 0.0537 rsquare: 0.9993 dfe: 393 adjrsquare: 0.9993 rmse: 0.0117 Model for Sedation is General model: ans(x,y) = combinedEffect(x,y, IC50A, IC50B, alpha, n) Coefficients (with 95% confidence bounds): IC50A = 1.843 (1.838, 1.847) IC50B = 13.7 (13.67, 13.74) alpha = 1.986 (1.957, 2.015) n = 44.27 (42.56, 45.98) ... and GOF is sse: 0.0574 rsquare: 0.9994 dfe: 393 adjrsquare: 0.9994 rmse: 0.0121 Model for Laryingoscopy is General model: ans(x,y) = combinedEffect(x,y, IC50A, IC50B, alpha, n) Coefficients (with 95% confidence bounds): IC50A = 5.192 (5.177, 5.207) IC50B = 37.77 (37.58, 37.97) alpha = 19.67 (19.48, 19.86) n = 37 (35.12, 38.87) ... and GOF is sse: 0.1555 rsquare: 0.9982 dfe: 393 adjrsquare: 0.9982 rmse: 0.0199

## Assessment of model predictions

Evaluate the surface fit at certain characteristic drug-combination to verify that the model prediction are sensible.

valData = dataset('xlsfile', 'ValidationData.xls'); % Evaluate surface at concentration in validation data valData.Algometry = fitresults{1}(valData.Propofol, valData.Remifentanil) ; valData.Tetany = fitresults{2}(valData.Propofol, valData.Remifentanil) ; valData.Sedation = fitresults{3}(valData.Propofol, valData.Remifentanil) ; valData.Laryingoscopy = fitresults{4}(valData.Propofol, valData.Remifentanil) ; valData

valData = Propofol Remifentanil Algometry Tetany Sedation Laryingoscopy 0 0 0 0 0 0 2 0 0.0023574 0.0064788 0.97402 4.6985e-016 5 0 0.82456 0.64246 1 0.19851 10 0 0.99932 0.99213 1 1 0 1 1.1814e-008 7.3138e-009 4.6612e-051 4.4779e-059 0 2 3.6958e-006 5.1296e-007 9.8995e-038 6.1345e-048 0 4 0.0011549 3.5975e-005 2.1025e-024 8.4039e-037 2 2 0.98102 0.70638 1 0.0015253 5 2 0.99998 0.99795 1 1 10 2 1 0.99997 1 1