PK/PD Models and Assumptions

The primary objective of PK/PD modelling in this thesis is to iden-tify key properties of insulin in vivo and thereby characterize and predict the insulin effect under physiologic conditions.

First of all, it is essential to identify the significance of the biologi-cal processes involved in eliciting the insulin-induced response. The delay between the plasma insulin concentration and the amount of

glucose needed to maintain a constant blood glucose concentration is illustrated through a counter-clockwise hysteresis loop in a phase-plot ofGIR vs. C_I (see Figure 6.5). The delay for treatment with insulin B is significantly larger than for insulin A but the phase-plot cannot explain whether or not the delay is due to a distributional delay or an indirect response mechanism. These two possibilities are therefore tested in an attempt to determine which model is best at describing the delay.

The effect-compartment model, where the before mentioned delay is assumed to be distributional, has previously been applied with success to clamp studies of insulin. Instead of specifying the PD parameters using in vitro data, the approach is to investigate the possibility of estimating the PK and PD simultaneously. This ap-proach seems more reasonable since the PK and PD of insulin are interdependent.

The obtained estimates of the three PD parameters are similar to those fromin vitrostudies which indicates that the simultaneous es-timation of PK and PD parameters is successful. The estimate of the maximum effectE_max for treatment with insulin A is made difficult since the observed effect of insulin A only assumes values in the linear area between 20 % and 80 % effect. To circumvent these estimation problems, the maximum effects of insulin A and B are assumed to be identical for the same subject. Since the observed effects are well below the value ofE_max, this assumption seems reasonable.

The parameter EC₅₀, which can be interpreted as the insulin con-centration producing 50 % of the maximum effect, contributes with information about the concentration needed to produce a clinical observable effect. The sample means of EC₅₀ for treatment with insulin A and B are almost equal which also is expected since the change in the primary structure of insulin B should not change the PD properties significantly but only the absorption kinetics of the molecule.

The final PD parameter which is estimated is the sigmoidicity factor

10.1 Euglycaemic Clamp Models 161 γ. The estimated value ofγ ≈2 for many of the subjects in the study is similar to the expected value from a theoretical point of view since the estimated value ofγ can be interpreted as the number of insulin molecules it takes to elicit the transport of glucose into the cells.

The derived parameters of t_max, C_max, T R_max, and R_max are esti-mated using the simulated time series of plasma insulin andGIR, re-spectively. The uncertainties of the derived parameters in this thesis are therefore much lower compared with the procedures in previous insulin studies where the derived parameters are estimated using the sparse information of only a few measurements in the determination of the maximum concentration and effect.

The drawbacks of the effect-compartment model is that several dif-ferent doses of insulin preferably should be used to validate the use of an indirect link model such as the ‘black box’ approach of the effect-compartment model. Since this information is not available for the current clamp study, the model cannot be further validated except by comparing the simulated and observed response GIR. Another problem with the effect-compartment model is that the estimated PD parameters are not reasonable for all the subjects in the study.

The doubtful estimates are investigated further by changing the ini-tial estimates but without success. The subjects with doubtful PD parameters are not removed from the study since the estimation pro-cedure seems to have converged and the simulated time series ofGIR are similar to the measurements.

Instead of ascribing the delay to be distributional in nature as in the effect-compartment model, an indirect response model where the delay is assumed to be caused by a delay downstream from the insulin receptor, is applied to the data from the clamp study. This approach is the physiological most likely but has not been used in previous clamp studies because of the experimental procedures. The variation ofGIRis quite large since the amount of glucose infused is regulated by a nurse in the attempt to keep the blood glucose concentration at the clamped level. The nurse uses the values of the measured blood glucose concentration from the previous minute to determine

how much glucose should be infused. If the nurse infuses too much glucose, the glucose will rise above the clamped level and the nurse must wait until the glucose returns to the clamped level because the GIR only assume values larger than zero since glucose cannot be withdrawn from the plasma.

When comparing the ability of the effect-compartment model and the indirect response model to predict the response to the injected insulin, it seems like it is better to use the GIR as a measure of the utilized glucose rather than trying to add a compartment for the blood glucose concentration where GIR is used as an input.

The effect-compartment model is therefore preferred compared to the indirect response model.