PBPK model development
A whole-body PBPK model was developed using the protein base model in PK-Sim and MoBi (Open Systems Pharmacology Suite, version 8.0) [
27]. This software enables access to all relevant anatomical and physiological parameters for humans. Data such as reference organ volumes, organ densities, blood flows, blood volumes and renal function have already been incorporated based on the relevant literature [
28]. Specific physicochemical information about
68Ga-DOTATATE and relevant biological processes linked to its in vivo behavior was manually added to the PBPK model in order to eventually describe concentration–time profiles of the drug.
The following key parameters were implemented to create the in-house developed PBPK model of
68Ga-DOTATATE. Compound-specific physicochemical parameters that could be defined based on the previous literature were molecular weight, lipophilicity, fraction unbound in plasma and p
Ka values. There is limited knowledge about the metabolism and excretion of
68Ga-DOTATATE, although it is known that 12% of the administered dose is excreted unchanged in the urine within the first 4 h [
9]. Therefore, renal clearance was added to the model as a specific excretion route and was manually scaled to a predicted 12% unchanged excretion in urine.
177Lu-DOTATATE does not undergo hepatic clearance; therefore, the same is expected for
68Ga-DOTATATE [
29]. For this reason, hepatic clearance was not added to the model.
All organs were automatically included in the human model by the software, and each organ compartment was subdivided into vascular, interstitial and intracellular compartments. Distribution within these organ compartments was assumed to be homogenous. Also, the thyroid gland was added to the standardized organism using previously published data [
30]. The organs were linked by arterial and venous blood compartments, and each organ was further characterized by a specific blood flow, volume, tissue-partition coefficient and permeability [
21,
22]. Individual-specific input parameters (such as height, body weight and age) were based on the medians of the population data that were used for validation.
DOTATATE binds to the SSTRs on the cell membrane of organs and tumors, whereafter the complex is internalized into the cells [
31,
32]. To describe this physiological
68Ga-DOTATATE target accumulation, SSTR2 was added to the membrane surface of all organs that are known to express this receptor [
9,
33]. Other SSTRs and their expression profiles were neglected, because of their limited effect on overall peptide disposition due to low affinity or low expression [
34‐
36].
Passage of
68Ga-DOTATATE into the intracellular compartment was only made possible by internalization of SSTR2 into the cell after binding of the peptide to the receptor. After this internalization, SSTR2 and the radiopharmaceutical dissociate intracellularly, followed by rapid recycling of the receptor back to the cell membrane [
24,
32,
37]. Receptor recycling was added as a zero-order kinetic reaction to model.
68Ga-DOTATATE was assumed to remain intracellularly after internalization, based on evaluation of clinical PET/CT scans, but also because passive diffusion is unlikely with its high molecular weight. Intracellular
68Ga-DOTATATE degradation was added into the model as an unknown first-order reaction. For reasons of model simplicity, a fixed degradation constant was added to all compartments and no degradation products were included in the model [
16]. The internalization reaction was based on a previously published PBPK model for
90Y-DOTATATE including SSTR2 receptors [
16] and consisted of separate reactions for peptide receptor binding (nonlinear) and total internalized peptide amount. These two reactions are described as follows (with “
i” referring to a corresponding organ):
$$\frac{{{d}}}{{{{d}}t}}{{Complex}}_{i} = \frac{{k_{{{{off}}}} }}{{K_{{{D}}} }}*R_{i} *P_{i} *K_{{{{water}},i}} - k_{{{{off}}}} *{{Complex}}_{i}$$
(1)
where
koff is the dissociation rate constant of
68Ga-DOTATATE from the SSTR receptor (min
−1),
KD is the dissociation constant (nmol/L),
Ri is the SSTR2 receptor expression in the specific organ (nmol),
Pi is the interstitial peptide concentration of DOTATATE (nmol/L),
Kwater,i is the partition coefficient (water/compartment) and
Complexi is the amount of SSTR2 occupied with
68Ga-DOTATATE (nmol).
$$\frac{{\text{d}}}{{{\text{d}}t}}P_{{{\text{intracellular}}, i }} = k_{{{\text{int}}}} *{\text{Complex}}_{i} - k_{{{\text{deg}}}} *P_{i}$$
(2)
where
kint is the internalization rate constant (min
−1),
Complexi is the amount of SSTR2 bound to
68Ga-DOTATATE (nmol),
kdeg is the degradation rate constant (min
−1) and
Pi is the intracellular peptide amount of
68Ga-DOTATATE (nmol).
Model fitting and verification
Input parameters were fixed or fitted based on prior knowledge of these parameters. For model evaluation, the concentration for SSTR2 in the interstitial compartment of the organ was estimated for spleen, liver and thyroid. Model fitting was performed using a built-in Monte Carlo algorithm for parameter identification to optimize selected input parameter to describe the data best. The total model fit was evaluated based on a residual sum of squares (total error). Range for parameter fitting was 0–250 nmol/L for SSTR2 reference concentration (similar to spleen SSTR2 concentration). The SSTR2 amounts were fitted to the clinical data (peptide concentrations (µg/L)) of all 41 patients combined, and these observed scan data were assigned to whole-organ predictions including vascular, interstitial and intracellular compartments of that specific organ. All data points for the spleen, liver and thyroid were used during the model fitting of the SSTR2 concentrations. This resulted in one prediction for each organ representing this population. Ranges of SSTR2 concentrations per organ were obtained by scaling predictions to minimum and maximum observed values while also taking into account differences in administered peptide amount. This resulted in estimated population minimum and maximum SSTR2 densities per organ.
In addition, a sensitivity analysis was completed in MoBi to calculate the sensitivity of the PK model output, which was performed by alteration of input parameters with ± 10% [
38]. All input parameters were evaluated using the sensitivity analysis, and this provided understanding of critical input parameters for model output and thus predictions. The sensitivity (
Si,j) was calculated using the following equation:
$$S_{i,j} = \frac{{\Delta {{PK}}_{j} }}{{\Delta p_{i} }}*\frac{{p_{j} }}{{{{PK}}_{j} }}$$
(3)
where
PKj is the PK parameter of a certain output to an input parameter (
pj). Thus, the sensitivity for the PK parameter to that input parameter was calculated as the ratio of the relative change of that PK parameter (Δ
PKj) and the relative variation of the input parameter (Δ
pi). A sensitivity value of -1 implies that a 10% increase of the input parameter resulted in a 10% decrease of the PK parameter output.