(T0930-09-59) Population Balance Modeling of Aggregation in Long-Acting Injectable Formulations Integrated with PBPK

Purpose: Long-acting injectable (LAI) formulations are critical for sustained drug delivery in a multitude of applications for birth control, psychological disorders, human immunodeficiency virus (HIV), and cancer. The complex interaction of the body’s immune response at the injection site and the formulation’s properties including active pharmaceutical ingredient (API) solubility, particle size, injection volume, viscosity, and excipients all combine to form a complex system. An example of such interaction is particle aggregation at the depot site. Studies have observed aggregation of particles in vivo after intramuscular injection¹. Simulating aggregation dynamics is essential for understanding the difficult-to-observe in vivo formulation behavior at the injection site. This would potentially help to optimize formulation design. The objective of this study is to develop a population balance model (PBM) to describe in vivo API aggregation of once-monthly extended-release LAI suspension of Invega Sustenna® (paliperidone palmitate) and integrate it with a physiologically based pharmacokinetic (PBPK) model to predict the in vivo performance of Invega Sustenna®.

Methods: A population balance model to calculate particle aggregation was implemented within GastroPlus Version 9.8.3 (Simulations Plus, Inc.).  The model is based on a finite difference solution of the discrete population balance equation of Smoluchowski².  The fixed pivot method was utilized to solve the system of aggregation equations and conserve mass and particle number³. Multiple aggregation kernels were implemented including uniform, sum of sizes, and Brownian motion.  The model is coupled to the full dissolution equations in the intramuscular depot volume.  As drug dissolves it can partition into the muscle tissue and be taken up into systemic circulation where the full PBPK model in GastroPlus describes systemic pharmacokinetics.  A perfusion-limited PBPK model was calibrated against Paliperidone IV administration⁴. The default Lukacova method was utilized to compute the partition coefficients.

Results: The calculated volume of distribution was 122 L.  Total clearance of 4.418 L/hr was fit to the observed IV data with 79.2% of the clearance being attributed to kidney clearance⁵. The model was then utilized to predict paliperidone palmitate exposure after intramuscular administration in the deltoid assuming the palmitate ester is converted to paliperidone before reaching systemic circulation⁶.  Pharmacokinetics of intramuscular injection were simulated with the Johnson dissolution model with mean particle size of 0.359 µm with a standard deviation of 1.4 µm based on measured particle size^7,8.  The simulation results performed with and without the population balance model are shown in Figure 1.  The default model without aggregation greatly mispredicted the observed plasma concentration data (Fig 1.A). This is because the API immediately reaches saturated solubility in the depot volume for 25, 50, 100, and 150 mg doses causing constant and flat absorption profile.  Alternatively, the population balance model allows the particles to increase in size over time as shown in Figure 2 for the 50 mg model with sum of sizes kernel.  The particle size grows from the initial mean value of 0.359 µm to an average of 110 µm by 2000 hours post dose.   This slows the dissolution rate over time resulting in the correct profile shape (Fig 1 B-D). The kernel rate constant or scaler was fit to values of 1 (unitless), 4x10^-11 mg²/s, and 2x10^-10 mg²/s for the Brownian motion, uniform, and sum of sizes kernel, respectively.  The rate of collisions predicted based on Brownian motion kernel accurately predicted the aggregation without adjustment indicating that theoretical diffusional collision rates may be the correct mechanism.  The accuracy of the predictions with respect to Cmax, Tmax, and AUCinf are shown in Table 1.  The 25, 50 and 150 mg dose have a Cmax error range for all population balance kernels of -22.7 to 10.4% while the 100 mg dose model has a Cmax error range of 60 to 64.3%.  It is unknown as to why the 100 mg dose does not seem to follow dose proportional pharmacokinetics while the 25, 50 and 150 mg doses can be modeled with the same parameters.  One theory is that some amount of the dose gets into the subcutaneous and that differences between injections could cause variability in the results⁹.

Conclusion: The population balance model with aggregation enables prediction of the correct dissolution and absorption dynamics within the intramuscular depot volume when coupled with the PBPK model. When dissolution is predicted based on observed particle size, dissolution is too fast resulting in a non-sink situation where the depot volume is saturated at the API solubility leading to constant absorption and flat plasma concentration profiles.  The incorporation of the population balance model and particle aggregation allows the dissolution rate to change over time leading to conditions where the depot volume isn’t saturated and releases drug more slowly over longer time periods which agrees with the observed in vivo for paliperidone palmitate. Future work on additional compounds such as aripiprazole lauroxil is ongoing and will be utilized to validate the population balance approach.

References: 1. Darville, Nicolas, et al. "Intramuscular administration of paliperidone palmitate extended-release injectable microsuspension induces a subclinical inflammatory reaction modulating the pharmacokinetics in rats." Journal of pharmaceutical sciences 103.7 (2014): 2072-2087.
2. Smoluchowski, Marian (1916). "Drei Vorträge über Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen". Phys. Z. (in German). 17: 557–571, 585–599.
3. Kumar, Sanjeev, and Doraiswami Ramkrishna. "On the solution of population balance equations by discretization—I. A fixed pivot technique." Chemical Engineering Science 51.8 (1996): 1311-1332.
4. Samtani, Mahesh N., An Vermeulen, and Kim Stuyckens. "Population pharmacokinetics of intramuscular paliperidone palmitate in patients with schizophrenia: a novel once-monthly, long-acting formulation of an atypical antipsychotic." Clinical pharmacokinetics 48 (2009): 585-600.
5. Vermeir M, Naessens I, Remmerie B, Mannens G, Hendrickx J, Sterkens P, Talluri K, Boom S, Eerdekens M, van Osselaer N, Cleton A. Absorption, metabolism, and excretion of paliperidone, a new monoaminergic antagonist, in humans. Drug Metab Dispos. 2008 Apr;36(4):769-79
6. Darville, Nicolas, et al. "The effect of macrophage and angiogenesis inhibition on the drug release and absorption from an intramuscular sustained-release paliperidone palmitate suspension." Journal of Controlled Release 230 (2016): 95-108.
7. Shi, Junfeng, et al. "Comparison of paliperidone palmitate from different crystallization processes and effect on formulations in vitro and in vivo." Pharmaceutics 14.5 (2022): 1094.

Acknowledgements: This research project is supported by the Food and Drug Administration (FDA) of the U.S. Department of Health and Human Services (HHS) as part of a financial assistance award U01FD008304 totaling $800,000 with 100 percent funded by FDA/HHS. The contents are those of the author(s) and do not necessarily represent the official views of, nor an endorsement, by FDA/HHS, or the U.S. Government.

Figure 1: Observed and simulated results for 25-150 mg IM injection of paliperidone palmitate with A) no agglomeration model, B) Brownian motion kernel aggregation, C) uniform kernel aggregation, and D) sum of sizes kernel aggregation.

Figure 2: Simulated particle size vs. time for 50 mg paliperidone palmitate IM injection.

Table 1: Observed and simulated results and prediction error for Cmax, Tmax, and AUC for 25-150 mg IM injection of paliperidone palmitate with and without aggregation including Brownian motion, uniform, and sum of sizes collision kernel.