# Population Pharmacokinetic Modelling of the Complex Release Kinetics of Octreotide LAR: Defining Sub-Populations by Cluster Analysis

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. PK Data

^{®}LAR Depot (octreotide acetate for injectable suspension, Novartis Pharmaceuticals UK Limited, London, UK), under fasting conditions, as part of a phase 1, single dose PK study. A single dose of deep intramuscular injection was given on Day 0. A pre-dose serum sample was collected on Day 0 and 36 more samples were collected at the following times after administration: 0.5, 1, 1.5, 2, 3, 4, 6, 10, 24, 48, 72, 96, 144, 192, 240, 288, 336, 384, 432, 480, 528, 576, 624, 672, 720, 768, 816, 864, 912, 1008, 1176, 1344, 1512, 1680, 1848 and 2088 h. Two subjects were removed according to the clinical protocol and a dataset was constructed including patients from the reference arm for the population PK analysis purpose. Demographic data, comprising body weight, height, BMI, age, gender and ethnicity were also provided. The study was conducted according to the guidelines of the Declaration of Helsinki and approved by the Jordan Food and Drug Administration (IRB#: TRI-80818). The bioanalysis was carried out by a validated LCMSMS method by Triumpharma CRO (Amman, Jordan). Briefly, the method used a Triple Quad LCMSMS instrument from SCIEX (Framingham, MA, USA) and a ZORBAX SB-C8 column from Agilent Technologies (Santa Clara, CA, USA), with length 100 mm, inner diameter 4.6 mm and particle size 3.5 µm mL, using Octreotide-D8 as internal standard. Linearity was established by preparing an eight-point standard calibration curve in K3EDTA human plasma, covering the Octreotide concentration range 8.835 pg/mL to 4010.010 pg/mL.

#### 2.2. Data Analysis

#### 2.2.1. Clustering

^{3}, would roughly assign the same importance to the horizontal (time) offsets and the vertical offsets. This approach allowed the identification of different patterns in release kinetics, without the influence of apparent clearance and, consequently, total exposure.

#### 2.2.2. Population Pharmacokinetic Modeling

#### 2.2.3. Structural PK Model

_{j}stands for the fraction of the dose delivered by the transit process j and TRANSIT

_{j}is the function of the j

_{ith}rate of input component, as the following:

_{j}), which correspond to the three parallel transit processes, to be put in sequential order, as following:

#### 2.2.4. Variability Model

_{1}was constrained to 300 h, by applying a logit-normal generalization, where the logit term is constraint between 0 and 1:

_{j}indicate the fraction of the bioavailable dose that is released through a process with defined delay and shape. One should not confuse it with F, the absolute bioavailability parameter, which is not identifiable. Thus, the apparent clearance CL/F and the apparent volume of distribution V/F are estimated, and these apparent values are implied everywhere in the text. Therefore, the fraction parameters (f

_{j}) have individual values between 0 and 1, with sums adding up to 1. The logistic-normal transformation described in the article of Tsamandouras et al. [13] was applied to constrain the parameters to the above conditions, so that:

_{i}:

_{pop}is the population mean parameter value and η

_{i}is the normally distributed deviation with zero mean and ω

^{2}variance. IIV was reported as a CV (%) in the original scale, using the equation CV (%) = √(ω^2) × 100%. The variance-covariance matrix Ω was estimated, including the diagonal and the non-diagonal terms, in order to identify correlations in random effects, in the key-models for model-building and the final model. The additive, proportional and combined error model, were tested to describe the residual variability.

#### 2.2.5. Model Evaluation

## 3. Results

#### 3.1. Clustering

^{6}pg × h/mL vs. 0.94 × 10

^{6}pg × h/mL, and maximum concentration Cmax, 5034.8 vs. 1433.3 pg/mL, so modelling with respect to this sub-population is important to appropriately predict these measures (Table 1).

#### 3.2. Population PK Model

#### 3.3. Modeling the Sub-Populations of Cluster Analysis

#### 3.4. Bioequivalence Metrics Evaluation

## 4. Discussion

_{i}and the number of transit compartments N

_{i}, parameters. The rich PK dataset allowed the estimation of IIV for all the model parameters with low uncertainty. The final population PK model we developed, which incorporates sub-populations, describing well the octreotide PK course in both the individual and population level, and the PK metrics of AUC and Cmax.

_{j}

_{,i}) to one, and at the same time maintaining 0 ≤ f

_{j}

_{,i}≤ 1 was conducted with the use of the multivariate logistic-normal distribution. The aforementioned components of the model were crucial regarding the successful convergence of the estimation methods, reasonable computation time and precise estimates.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Stueven, A.K.; Kayser, A.; Wetz, C.; Amthauer, H.; Wree, A.; Tacke, F.; Wiedenmann, B.; Roderburg, C.; Jann, H. Somatostatin analogues in the treatment of neuroendocrine tumors: Past, present and future. Int. J. Mol. Sci.
**2019**, 20, 3049. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Comets, E.; Mentré, F.; Kawai, R.; Nimmerfall, F.; Marbach, P.; Vonderscher, J. Modeling the Kinetics of Release of Octreotide from Long-Acting Formulations Injected Intramuscularly in Rabbits. J. Pharm. Sci.
**2000**, 89, 1123–1133. [Google Scholar] [CrossRef] - Park, K.; Skidmore, S.; Hadar, J.; Garner, J.; Park, H.; Otte, A.; Soh, B.K.; Yoon, G.; Yu, D.; Yun, Y.; et al. Injectable, long-acting PLGA formulations: Analyzing PLGA and understanding microparticle formation. J. Control. Release
**2019**, 304, 125–134. [Google Scholar] [CrossRef] [PubMed] - Zhou, H.; Chen, T.-L.; Marino, M.; Lau, H.; Miller, T.; Kalafsky, G.; McLeod, J.F. Population PK and PK/PD modelling of microencapsulated octreotide acetate in healthy subjects. Br. J. Clin. Pharmacol.
**2000**, 50, 543–552. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Genolini, C.; Ecochard, R.; Benghezal, M.; Driss, T.; Andrieu, S.; Subtil, F. KmlShape: An efficient method to cluster longitudinal data (Time-Series) according to their shapes. PLoS ONE
**2016**, 11, e0150738. [Google Scholar] [CrossRef] - Bauer, R.J. NONMEM Tutorial Part I: Description of Commands and Options, With Simple Examples of Population Analysis. CPT Pharmacomet. Syst. Pharmacol.
**2019**, 8, 525–537. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Bauer, R.J. NONMEM Tutorial Part II: Estimation Methods and Advanced Examples. CPT Pharmacomet. Syst. Pharmacol.
**2019**, 8, 538–556. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Gibiansky, L.; Gibiansky, E.; Bauer, R. Comparison of Nonmem 7.2 estimation methods and parallel processing efficiency on a target-mediated drug disposition model. J. Pharmacokinet. Pharmacodyn.
**2012**, 39, 17–35. [Google Scholar] [CrossRef] [PubMed] - Keizer, R.J.; Karlsson, M.O.; Hooker, A. Modeling and simulation workbench for NONMEM: Tutorial on Pirana, PsN, and Xpose. CPT Pharmacomet. Syst. Pharmacol.
**2013**, 2, e50. [Google Scholar] [CrossRef] [PubMed] - Lindbom, L.; Ribbing, J.; Jonsson, E.N. Perl-speaks-NONMEM (PsN)—A Perl module for NONMEM related programming. Comput. Methods Programs Biomed.
**2004**, 75, 85–94. [Google Scholar] [CrossRef] [PubMed] - Savic, R.M.; Jonker, D.M.; Kerbusch, T.; Karlsson, M.O. Implementation of a transit compartment model for describing drug absorption in pharmacokinetic studies. J. Pharmacokinet. Pharmacodyn.
**2007**, 34, 711–726. [Google Scholar] [CrossRef] [PubMed] - Shivva, V.; Korell, J.; Tucker, I.G.; Duffull, S.B. An approach for identifiability of population pharmacokinetic- pharmacodynamic models. CPT Pharmacomet. Syst. Pharmacol.
**2013**, 2, 1–9. [Google Scholar] [CrossRef] [PubMed] - Tsamandouras, N.; Wendling, T.; Rostami-Hodjegan, A.; Galetin, A.; Aarons, L. Incorporation of stochastic variability in mechanistic population pharmacokinetic models: Handling the physiological constraints using normal transformations. J. Pharmacokinet. Pharmacodyn.
**2015**, 42, 349–373. [Google Scholar] [CrossRef] [PubMed] - Nguyen, T.H.T.; Mouksassi, M.S.; Holford, N.; Al-Huniti, N.; Freedman, I.; Hooker, A.C.; John, J.; Karlsson, M.O.; Mould, D.R.; Perez Ruixo, J.J.; et al. Model evaluation of continuous data pharmacometric models: Metrics and graphics. CPT Pharmacomet. Syst. Pharmacol.
**2017**, 6, 87–109. [Google Scholar] [CrossRef] - Kim, H.; Han, S.; Cho, Y.-S.; Yoon, S.-K.; Bae, K.-S. Development of R packages: ‘NonCompart’ and ‘ncar’ for noncompartmental analysis (NCA). Transl. Clin. Pharmacol.
**2018**, 26, 10. [Google Scholar] [CrossRef] [Green Version] - European Medicines Agency. EMA/MB/69923/2010—Annual Report of the European Medicines Agency 2009. Available online: https://www.ema.europa.eu/en/documents/scientific-guideline/octreotide-acetate-depot-powder-solvent-suspension-injection-10-mg-20-mg-30-mg-product-specific_en.pdf (accessed on 30 March 2021).
- Shivva, V.; Korell, J.; Tucker, I.G.; Duffull, S.B. Parameterisation affects identifiability of population models. J. Pharmacokinet. Pharmacodyn.
**2014**, 41, 81–86. [Google Scholar] [CrossRef] [PubMed] - Jaber, M.M.; Al-Kofahi, M.; Sarafoglou, K.; Brundage, R.C. Individualized Absorption Models in Population Pharmacokinetic Analyses. CPT Pharmacomet. Syst. Pharmacol.
**2020**, 9, 307–309. [Google Scholar] [CrossRef] [PubMed] - Hadar, J.; Skidmore, S.; Garner, J.; Park, H.; Park, K.; Wang, Y.; Qin, B.; Jiang, X. Characterization of branched poly(lactide-co-glycolide) polymers used in injectable, long-acting formulations. J. Control. Release
**2019**, 304, 75–89. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**Graphical representation of the pharmacokinetic model which describes octreotide LAR pharmacokinetics. The drug is released from the depot to the muscle through four empirical processes with different kinetic characteristics and is then absorbed to the systematic circulation.

**Figure 2.**Two sub-populations were identified by the cluster analysis. The clusters are depicted with the different colour and the “mean typical profiles” are drawn with the bold line. Concentrations were normalized with the average concentration per subject to return the shape of exposure, therefore normalized concentrations on the y-axis are unitless.

**Figure 3.**Individual plots of Observations vs PRED and IPRED showing the flexibility of the PPK model to predict for four representative subjects. Solid line and dashed line indicate IPRED and PRED, respectively.

**Figure 4.**Visual Predictive Checks of the base model (

**a**) and the final model (

**b**). The median, 5th and 95th percentiles of the observations (lines) are compared with the corresponding 95% confidence intervals of the 1000 simulated datasets (shaded areas).

**Figure 5.**Visual Predictive Checks of the final model, stratified on cluster, (

**a**) for cluster 1 and (

**b**) for cluster 2.

**Figure 6.**VPC plots for PK metrics in the base and final model. Black lines denote the median, 10th and 90th percentiles of the observations. The shaded areas and coloured lines represent the medians and 95% CI of the 1000 simulated datasets for the corresponding statistic measures of the observations. The five panels correspond respectively to the following PK parameters: AUC (0–t), AUC (0–28 days), AUC (28–56 days), AUC (0–24 h) and Cmax.

Demographics | Median (Q1–Q3) |
---|---|

Subjects, n | 118 |

Age, years | 28 (23–37) |

Height, cm | 175 (170–178) |

Weight, kg | 75 (66–86) |

BMI, kg/m^{2} | 24.75 (22.4–27.7) |

Clustering | |

Cluster 1, n | 103 |

Cluster 2, n | 15 |

Non-Compartmental Analysis | Mean (±SD) |

AUC_{0–t} (pg × h/mL) | 988.7 × 10^{3} (±327.9 × 10^{3}) |

Cluster 1 | 944.0 × 10^{3} (±284.0 × 10^{3}) |

Cluster 2 | 1295.2 × 10^{3} (±442.1 × 10^{3}) |

Cmax (pg/mL) | 1891.1 (±1622.6) |

Cluster 1 | 1433.3 (±497.4) |

Cluster 2 | 5034.8 (±2840.6) |

**Table 2.**Parameter estimates of the final model and the corresponding inter-individual variability. Relative standard errors and bootstrap confidence intervals are also provided.

Parameter | Estimate (RSE%) | Bootstrap | Workflow Bootstrap | ||||
---|---|---|---|---|---|---|---|

Median | 95% CI | RSE (%) | Median | 95% CI | RSE (%) | ||

k_{a} | 0.27 (2.2) | 0.27 | 0.26–0.28 | 2 | 0.27 | 0.26–0.28 | 2 |

V | 15.3 (7.7) | 15.1 | 13.5–16.8 | 6 | 15.1 | 13.6–17.1 | 6 |

CL Cluster effect: | 32.7 (5.8) −8.61 (34) | 32.7 −9.32 | 31.0–34.4 −14.32 to −3.66 | 3 48 | 32.6 −9.24 | 30.8–34.8 −13.95 to −3.57 | 3 38 |

Y_{F1} | −5.18 (1.8) | −5.19 | −5.24 to −5.11 | 1 | −5.19 | −5.24 to −5.11 | 1 |

Y_{F2}Cluster effect: | −3.36 (7.9) 3.06 (33) | −3.35 3.01 | −3.62 to −3.03 2.52–3.46 | 4 8 | −3.34 3.02 | −3.69 to −3.02 2.02–3.55 | 5 14 |

Y_{F3}Cluster effect: | −1.54 (2.8) −0.523 (26.8) | −1.54 −0.468 | −1.64 to −1.42 −0.704 to −0.291 | 4 22 | −1.55 −0.47 | −1.65 to −1.44 −0.715–0.01 | 4 35 |

Y_{MTT1} | −0.421 (21.8) | −0.41 | −0.554 to −0.244 | 20 | −0.41 | −0.562 to −0.253 | 20 |

MTT2 | 181 (3.3) | 180 | 166–191 | 5 | 179 | 167–191 | 4 |

MTT3 | 506 (3.8) | 508 | 486–530 | 4 | 508 | 481–534 | 3 |

N1 | 3.42 (15) | 3.43 | 2.67–4.07 | 10 | 3.44 | 2.80–4.10 | 9 |

N2 | 17.9 (6) | 18.0 | 15.1–20.2 | 7 | 18.0 | 15.9–20.3 | 7 |

N3 | 5.08 (5) | 5.00 | 4.57–5.62 | 5 | 5.03 | 4.58–5.57 | 5 |

Proportional Residual Error | 0.143 (1.3) | 0.143 | 0.128–0.155 | 5 | 0.14 | 0.127–0.156 | 5 |

Additive Residual Error | 28.4 (3.7) | 28.2 | 22.9–33.8 | 10 | 28.8 | 23.6–35.2 | 10 |

Inter-Individual Variability | Estimate (RSE%) [Shrinkage %] | Median | 95% CI | RSE (%) | Median | 95% CI | RSE (%) |

IIV_{V} | 39.4 (13) [16.3] | 39.9 | 33.4–46.5 | 17 | 39.7 | 32.1–46.1 | 13 |

IIV_{CL} | 28.2 (8) [1] | 28.3 | 24.2–34.6 | 30 | 28.3 | 23.4–32.7 | 22 |

IIV_{YF1} | 28.9 (7) [3.4] | 25.8 | 14.1–50.1 | 65 | 28.1 | 13.9–48.2 | 50 |

IIV_{YF2} | 128.8 (16) [4] | 128.4 | 112.5–141.3 | 6 | 129.2 | 110.9–143.7 | 6 |

IIV_{YF3} | 20.5 (18) [30.3] | 21.0 | 13.1–35.0 | 30 | 21.1 | 14.1–37.2 | 25 |

IIV_{YMTT1} | 60.1 (12) [12] | 59.6 | 48.5–70.7 | 10 | 60.6 | 49.5–73.6 | 10 |

IIV_{MTT2} | 17.3 (20) [17.6] | 18.2 | 14.4–26.3 | 68 | 18.7 | 14.3–28.8 | 50 |

IIV_{MTT3} | 20.2 (9) [1.7] | 20.7 | 16.9–31.2 | 74 | 20.6 | 16.6–30.0 | 54 |

IIV_{N1} | 71.2 (10) [22] | 70.2 | 36.0–101.5 | 25 | 69.2 | 36.0–106.1 | 23 |

IIV_{N2} | 26.2 (21) [31.2] | 26.3 | 16.0–33.6 | 32 | 26.5 | 16.9–34.1 | 26 |

IIV_{N3} | 31.4 (12) [9.3] | 29.7 | 24.0–41.5 | 14 | 31 | 24.2–42.2 | 14 |

_{Fi}, normal variable associated with the fraction of the i

_{th}transit process; MTT

_{i}, mean transit time of the i

_{th}process; YMTT1, normal variable associated with MTT1; Ni, number of transit compartments for the i

_{th}process.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kapralos, I.; Dokoumetzidis, A.
Population Pharmacokinetic Modelling of the Complex Release Kinetics of Octreotide LAR: Defining Sub-Populations by Cluster Analysis. *Pharmaceutics* **2021**, *13*, 1578.
https://doi.org/10.3390/pharmaceutics13101578

**AMA Style**

Kapralos I, Dokoumetzidis A.
Population Pharmacokinetic Modelling of the Complex Release Kinetics of Octreotide LAR: Defining Sub-Populations by Cluster Analysis. *Pharmaceutics*. 2021; 13(10):1578.
https://doi.org/10.3390/pharmaceutics13101578

**Chicago/Turabian Style**

Kapralos, Iasonas, and Aristides Dokoumetzidis.
2021. "Population Pharmacokinetic Modelling of the Complex Release Kinetics of Octreotide LAR: Defining Sub-Populations by Cluster Analysis" *Pharmaceutics* 13, no. 10: 1578.
https://doi.org/10.3390/pharmaceutics13101578