Parameter Estimates

The grey-box parameter estimates for the MM of glucose kinetics are shown in Table 9.1 for a representative NGT and IGT subject along with the standard deviations.

The apparent volume of distribution of the glucose is estimated close to 12.6 L and 13.7 L for the NGT and IGT subject, respectively.

Unlike the clamp models, the estimation of the volume V does not seem to be a problem in the MM. The values ofV for the NGT and IGT subject both seem physiological reasonable.

9.1 IVGTT Models 137

Table 9.1: MM parameter estimates for a representative NGT and IGT subject.

NGT IGT

Parameter Unit θˆ Std. dev. θˆ Std. dev.

G0 [mmol] 6.5504E+01 3.5506E+00 8.6505E+01 2.9457E+00 p1 [min⁻¹] 2.0097E−02 4.8879E−03 1.4629E−02 7.2208E−03 p2 [min⁻¹] 5.7490E−02 1.7436E−02 2.5365E−01 2.7911E−01 p3 [min⁻²pM⁻¹] 6.9959E−06 1.7469E−06 8.3331E−06 1.4697E−05 V [L] 1.2610E+01 3.9444E−01 1.3742E+01 4.1699E−01 σG [-] 9.8176E−01 3.4316E−01 5.8172E−07 2.3523E−02 σX [-] 7.9394E−09 5.3310E−06 4.5122E−03 3.6639E−03 S² [-] 7.3042E−02 2.5261E−02 3.3406E−02 1.1552E−02

AIR0−8 [pM min] 2.3265E+03 1.0320E+03

The system noise is not estimated to zero, which was the case for most of the clamp models, since the glucose and insulin measure-ments from the IVGTT are much more excited than those from the clamp study. The rather large value ofσ_G for the NGT subject in-dicates that the dynamics of the glucose is not modelled completely with the MM. The MM has not been expanded with more compart-ments since it would require the injected glucose to be labelled to be able to estimate yet another unobservable state as mentioned in Section 8.2.

The glucose effectiveness index can be calculated from the parameter estimate of p₁ from the MM. The estimated values of the glucose effectiveness index for the NGT and IGT subject are 0.020 and 0.015 min⁻¹, respectively. The glucose effectiveness is a measure of the insulin-independent ability to dispose glucose. S_G does not seem to be significantly different for NGT and IGT subjects when comparing the estimates of the two representative subjects.

The insulin sensitivity index is equal to the ratio between the esti-mated parametersp₃ and p₂ from the MM, i.e. S_I =p₃/p₂. It is a measure of the insulin-dependent ability to dispose glucose. Unlike the glucose effectiveness, the values of S_I are quite different for the two glucose tolerance groups. The estimated values are S_I = 1.217 andS_I = 0.329 for the NGT and IGT subject, respectively¹. The parameter AIR₀₋₈ is the acute insulin response which is used as a measure of the cell function, i.e. the ability of the beta-cells to produce insulin when exposed to a bolus of glucose. It is calculated as the area under the insulin curve from 0 to 8 min. using the Trapezoidal-method. The value of AIR₀₋₈ is about twice as large for the NGT subject compared with the IGT subject, which indicates that the response to the glucose bolus of the NGT subject is much larger than that of the IGT subject.

The sample mean and standard deviation of the MM parameter es-timates can be found in Appendix B.3 for the 108 NGT and 17 IGT subjects in the IVGTT. The sample mean of the system noise pa-rametersσ_Gandσ_X indicates that the MM of glucose kinetics is too simple.

9.1.3 Model Validation

Next, the ability of the MM model to predict and simulate the ob-served dynamics of the insulin/glucose system is tested. The 1-step prediction and pure simulation of the glucose concentrationC_G and the insulin action X are plotted in Figure 9.1 and Figure 9.2 for a representative NGT and IGT subject, respectively. The glucose residuals are also plotted and tested whether they can be consid-ered to be white noise using the lag-dependency function (LDF) and partial lag-dependency function (PLDF).

When comparing the time course of the measured glucose in Fig-ure 9.1(a) and FigFig-ure 9.2(a), it is seen that the disposal of glucose

1The unit ofSI is 10⁻⁴·min⁻¹pM⁻¹.

9.1 IVGTT Models 139

Figure 9.1: Measured, predicted, and simulated glucose and insulin con-centrations along with a residual analysis of glucose for a rep-resentative NGT subject.

−10 00 60 120 180

Figure 9.2: Measured, predicted, and simulated glucose and insulin con-centrations along with a residual analysis of glucose for a rep-resentative IGT subject.

9.1 IVGTT Models 141 for the IGT subject is not as fast as for the NGT subject. One hour after the glucose bolus, the glucose level of the NGT subject drops to a minimum which is below the basal glucose level, and then grad-ually returns to the level before the injection of glucose while the basal glucose level barely is reached for the IGT subject during the 180 min. of the IVGTT.

The 1-step prediction and pure simulation of the glucose concentra-tion for both the NGT and IGT subject seem to fit the measured glucose concentration nicely. Almost all of the glucose residuals plot-ted in Figure 9.1(c) and Figure 9.2(c) are within ±2σ_ε. The plots of LDF and PLDF for the NGT and IGT subjects show that the residuals are not far from being white.

The measured insulin concentration is used as an input to the model which is why it has not been predicted or simulated. The mea-sured insulin concentration is though plotted in Figure 9.1(b) and Figure 9.2(b) along with the 1-step prediction and simulation of the insulin action X to compare the time course of the two. For the NGT subject, the measured insulin concentration rises rapidly to a peak immediately after the glucose injection and drops shortly there-after to a lower level still above the basal insulin concentration. At t = 20 min., the second-phase insulin response is boosted by the tolbutamide injection to an insulin peak higher than the first-phase response which gradually drops to the basal level. The insulin peaks for the IGT subject are not as distinct as for the NGT subject and the insulin concentration does not return to the basal level before 2 hours after the glucose bolus.

The insulin action is quite different for the NGT and IGT subject.

There is an apparent delay between the measured plasma insulin and the insulin action for the NGT subject while the predicted and simulated insulin action for the IGT subject are close to zero during the whole IVGTT. This observation indicates that it is the insulin-dependent and not the insulin-ininsulin-dependent glucose uptake which is impaired for the IGT subject.