Supplementary Data - Diabetes

SUPPLEMENTARY DATA
where I is plasma insulin concetration, n is the fractional insulin clearance rate, VI is insulin volume of
distribution and IDR is insulin delivery rate, i.e. the rate of appearance of insulin in plasma after hepatic
extraction (HE). IDR, ISR and HE are linked by the following relationship:
ISR(
t)
� IDR(
t)
HE(
t)
�
ISR(
t)
thus
ISR t � HE t �
I� ( ) � 1 � ( )
( t)
� �n
� I(
t)
�
I(
0)
� I
V
I
According to Campioni et al 2009, HE is described with a piecewise linear function:
� HE
�HEi�1
�
HE(
t)
� � t
�
�HE0
� HEb
i
i
� HE
� t
i�1
i�1
�
�t�t� i�1
t
i�1
� t � t
(A11)
©2012 American Diabetes Association. Published online at http://diabetes.diabetesjournals.org/lookup/suppl/doi:10.2337/db11-1478/-/DC1
i
b
i �1,
2,...
6
wehere HEb is the basal hepatic extraction, that can be derived from basal conncetrations:
HE
b
k
�
01
� Cb
�Vc
� k 01 � I
k � C �V
01
b
b
�V
I
(A12)
(A13)
(A14)
A table containing the definition of all the minimal model indices can be found in [Cobelli et al, Am. J.
Physiol 2007], Table 2(3).
Parameter Estimation
Oral Glucose Minimal Model was numerically identified by nonlinear least squares, implemented in
Matlab ® R2010b. Measurement error on glucose data was assumed to be independent, gaussian, with
zero mean and known standard deviation (CV = 2%). Insulin concentration is the model forcing function
and was assumed to be known without error. Model identification requires a number of assumptions
which were discussed in detail in [Dalla Man et al, IEEE Trans Biomed Eng 2002] (4). Briefly, to ensure
its a priori identifiability one has to assume values for V and SG. Here we fixed them to the median
obtained with a triple tracer method in [Dalla Man et al Am J. Physiol, 2004] (5), i.e. V=1.45 dl/kg,
SG=0.025 min -1 (median was preferred to mean values since parameters are not normally distributed).
To improve numerical identifiability of the remaining parameters p2, p3, �i (i=1..7) a gaussian bayesian
prior was considered on the square root of p2 ref (SQRp2 ref ), which is normally distributed: SQRp2 =0.11
min -1/2 , SD=10%. Finally, a constraint was imposed to guarantee that the area under the estimated Rameal
equals the total amount of ingested glucose, D, multiplied by the fraction of the ingested dose that is
actually absorbed, f (fixed to the median of reference values f=0.9): this constraint provides an
additional relationship among the unknown parameters �i, thus reducing the number of unknowns by
one.