Multiphysics Modeling and Simulation of Subcutaneous Injection and Absorption of Biotherapeutics: Sensitivity Analysis

A multi-scale numerical study of monoclonal antibodies uptake by initial lymphatics after subcutaneous injection

This paper studies the transport of monoclonal antibodies through skin tissue and initial lymphatics, which impacts the pharmacokinetics of monoclonal antibodies. Our model integrates a macroscale representation of the entire skin tissue with a mesoscale model that focuses on the papillary dermis layer. Our results indicate that it takes hours for the drugs to disperse from the injection site to the papillary dermis before entering the initial lymphatics. Additionally, we observe an inhomogeneous drug distribution in the interstitial space of the papillary dermis, with higher drug concentrations near initial lymphatics and lower concentrations near blood capillaries. To validate our model, we compare our numerical simulation results with experimental data, finding a good alignment. Our parametric studies on the drug molecule properties and injection parameters suggest that a higher diffusion coefficient increases the transport and uptake rate while binding slows down these processes. Furthermore, shallower injection depths lead to faster lymphatic uptake, whereas the size of the injection plume has a minor effect on the uptake rate. These findings advance our understanding of drug transport and lymphatic absorption after subcutaneous injection, offering valuable insights for optimizing drug delivery strategies and the design of biotherapeutics.

Multiphysics Simulation of Local Transport and Absorption Coupled with Pharmacokinetic Modeling of Systemic Exposure of Subcutaneously Injected Drug Solution

INTRODUCTION

Subcutaneous (SC) injectables have become more acceptable and feasible for administration of biologics and small molecules. However, efficient development of these products is limited to costly and time-consuming techniques, partially because absorption mechanisms and kinetics at the local site of injection remain poorly understood.

OBJECTIVE

To bridge formulation critical quality attributes (CQA) of injectables with local physiological conditions to predict systemic exposure of these products.

METHODOLOGY

We have previously developed a multiscale, multiphysics computational model to simulate lymphatic absorption and whole-body pharmacokinetics of monoclonal antibodies. The same simulation framework was applied in this study to compute the capillary absorption of solubilized small molecule drugs that are injected subcutaneously. Sensitivity analyses were conducted to probe the impact by key simulation parameters on the local and systemic exposures.

RESULTS

This framework was capable of determining which parameters had the biggest impact on small molecule absorption in the SC. Particularly, membrane permeability of a drug was found to have the biggest impact on drug absorption kinetics, followed by capillary density and drug diffusivity.

CONCLUSION

Our modelling framework proved feasible in predicting local transport and systemic absorption from the injection site of small molecules. Understanding the effect of these properties and how to model them may help to greatly expedite the development process.

MPET2: a multi-network poroelastic and transport theory for predicting absorption of monoclonal antibodies delivered by subcutaneous injection

Subcutaneous injection of monoclonal antibodies (mAbs) has attracted much attention in the pharmaceutical industry. During the injection, the drug is delivered into the tissue producing strong fluid flow and tissue deformation. While data indicate that the drug is initially uptaken by the lymphatic system due to the large size of mAbs, many of the critical absorption processes that occur at the injection site remain poorly understood. Here, we propose the MPET² approach, a multi-network poroelastic and transport model to predict the absorption of mAbs during and after subcutaneous injection. Our model is based on physical principles of tissue biomechanics and fluid dynamics. The subcutaneous tissue is modeled as a mixture of three compartments, i.e., interstitial tissue, blood vessels, and lymphatic vessels, with each compartment modeled as a porous medium. The proposed biomechanical model describes tissue deformation, fluid flow in each compartment, the fluid exchanges between compartments, the absorption of mAbs in blood vessels and lymphatic vessels, as well as the transport of mAbs in each compartment. We used our model to perform a high-fidelity simulation of an injection of mAbs in subcutaneous tissue and evaluated the long-term drug absorption. Our model results show good agreement with experimental data in depot clearance tests.

A biomimetic chip to assess subcutaneous bioavailability of monoclonal antibodies in humans

Subcutaneous (subQ) injection is a common route for delivering biotherapeutics, wherein pharmacokinetics is largely influenced by drug transport in a complex subQ tissue microenvironment. The selection of good drug candidates with beneficial pharmacokinetics for subQ injections is currently limited by a lack of reliable testing models. To address this limitation, we report here a Subcutaneous Co-Culture Tissue-on-a-chip for Injection Simulation (SubCuTIS). SubCuTIS possesses a 3D coculture tissue architecture, and it allows facile quantitative determination of relevant scale independent drug transport rate constants. SubCuTIS captures key in vivo physiological characteristics of the subQ tissues, and it differentiates the transport behavior of various chemically distinct molecules. We supplemented the transport measurements with theoretical modeling, which identified subtle differences in the local absorption rate constants of seven clinically available mAbs. Accounting for first-order proteolytic catabolism, we established a mathematical framework to assess clinical bioavailability using the local absorption rate constants obtained from SubCuTIS. Taken together, the technology described here broadens the applicability of organs-on-chips as a standardized and easy-to-use device for quantitative analysis of subQ drug transport.

SubQ-Sim: A Subcutaneous Physiologically Based Biopharmaceutics Model. Part 1: The Injection and System Parameters

PURPOSE

To construct a detailed mechanistic and physiologically based biopharmaceutics model capable of predicting 1) device-formulation-tissue interaction during the injection process and 2) binding, degradation, local distribution, diffusion, and drug absorption, following subcutaneous injection. This paper is part of a series and focusses on the first aspect.

METHODS

A mathematical model, SubQ-Sim, was developed incorporating the details of the various substructures within the subcutaneous environment together with the calculation of dynamic drug disposition towards the lymph ducts and venous capillaries. Literature was searched to derive key model parameters in healthy and diseased subjects. External factors such as body temperature, exercise, body position, food or stress provide a means to calculate the impact of "life events" on the pharmacokinetics of subcutaneously administered drugs.

RESULTS

The model predicts the tissue backpressure time profile during the injection as a function of injection rate, volume injected, solution viscosity, and interstitial fluid viscosity. The shape of the depot and the concentrations of the formulation and proteins in the depot are described. The model enables prediction of formulation backflow following premature needle removal and the resulting formulation losses. Finally, the effect of disease (type 2 diabetes) or the presence of recombinant human hyaluronidase in the formulation on the injection pressure, are explored.

CONCLUSIONS

This novel model can successfully predict tissue back pressure, depot dimensions, drug and protein concentration and formulation losses due to incorrect injection, which are all important starting conditions for predicting drug absorption from a subcutaneous dose. The next article will describe the absorption model and validation against clinical data.

A Perspective on Model-Informed IVIVC for Development of Subcutaneous Injectables

Subcutaneously administered drugs are growing in popularity for both large and small molecule drugs. However, development of these systems - particularly generics - is slowed due to a lack of formal guidance regarding preclinical testing and in vitro - in vivo correlations (IVIVC). Many of these methods, while appropriate for oral drugs, may not be optimized for the complex injection site physiologies, and release rate and absorption mechanisms of subcutaneous drugs. Current limitations for formulation design and IVIVC can be supported by implementing mechanistic, computational methods. These methods can help to inform drug development by identifying key drug and formulation attributes, and their effects on drug release rates. This perspective, therefore, addresses current guidelines in place for oral IVIVC development, how they may differ for subcutaneously administered compounds, and how modeling and simulation can be implemented to inform design of these products. As such, integration of modeling and simulation with current IVIVC systems can help in driving the development of subcutaneous injectables.

Multiphysics modeling and simulation of local transport and absorption kinetics of intramuscularly injected lipids nanoparticles

Recent clinical applications of mRNA vaccines highlight the critical role of drug delivery, especially when using lipid nanoparticles (LNPs) as the carrier for genetic payloads. However, kinetic and transport mechanisms for locally injected LNPs, such as lymphatic or cellular uptake and drug release, remain poorly understood. Herein, we developed a bottom-up multiphysics computational model to simulate the injection and absorption processes of LNPs in muscular tissues. Our purpose was to seek underlying connections between formulation attributes and local exposure kinetics of LNPs and the delivered drug. We were also interested in modeling the absorption kinetics from the local injection site to the systemic circulation. In our model, the tissue was treated as the homogeneous, poroelastic medium in which vascular and lymphatic vessel densities are considered. Tissue deformation and interstitial fluid flow (modeled using Darcy's Law) were also implemented. Transport of LNPs was described based on diffusion and advection; local disintegration and cellular uptake were also integrated. Sensitivity analyses of LNP and drug properties and tissue attributes were conducted using the simulation model. It was found that intrinsic tissue porosity and lymphatic vessel density affect the local transport kinetics; diffusivity, lymphatic permeability, and intracellular update kinetics also play critical roles. Simulated results were commensurate with experimental observations. This study could shed light on the development of LNP formulations and enable further development of whole-body pharmacokinetic models.

Lymphatic uptake of biotherapeutics through a 3D hybrid discrete-continuum vessel network in the skin tissue

Subcutaneous administration is a common approach for the delivery of biotherapeutics, which is achieved mainly through the absorption across lymphatic vessels. In this paper, the drug transport and lymphatic uptake through a three-dimensional hybrid discrete-continuum vessel network in the skin tissue are investigated through high-fidelity numerical simulations. We find that the local lymphatic uptake through the explicit vessels significantly affects macroscopic drug absorption. The diffusion of drug solute through the explicit vessel network affects the lymphatic uptake after the injection. This effect, however, cannot be captured using previously developed continuum models. The lymphatic uptake is dominated by the convection due to lymphatic drainage driven by the pressure difference, which is rarely studied in experiments and simulations. Furthermore, the effects of injection volume and depth on the lymphatic uptake are investigated in a multi-layered domain. We find that the injection volume significantly affects the rate of lymphatic uptake through the heterogeneous vessel network, while the injection depth has little influence, which is consistent with the experimental results. At last, the binding and metabolism of drug molecules are studied to bridge the simulations to the drug clearance experients. We provide a new approach to study the diffusion and convection of drug molecules into the lymphatic system through the hybrid vessel network.

Understanding Formulation and Temperature Effects on Dermal Transport Kinetics by IVPT and Multiphysics Simulation

PURPOSE

It is often unclear how complex topical product formulation factors influence the transport kinetics through skin tissue layers, because of multiple confounding attributes. Environmental factors such as temperature effect are also poorly understood. In vitro permeation testing (IVPT) is frequently used to evaluate drug absorption across skin, but the flux results from these studies are from a combination of mechanistic processes.

METHOD

Two different commercially available formulations of oxybenzone-containing sunscreen cream and continuous spray were evaluated by IVPT in human skin. Temperature influence between typical skin surface temperature (32°C) and an elevated 37°C was also assessed. Furthermore, a multiphysics-based simulation model was developed and utilized to compute the flux of modeled formulations.

RESULTS

Drug transport kinetics differed significantly between the two drug products. Flux was greatly influenced by the environmental temperature. The multiphysical simulation results could reproduce the experimental observations. The computation further indicated that the drug diffusion coefficient plays a dominant role in drug transport kinetics, influenced by the water content which is also affected by temperature.

CONCLUSION

The in vitro testing and bottom-up simulation shed insight into the mechanism of dermal absorption kinetics from dissimilar topical products.

Role of Tissue Hydraulic Permeability in Convection-Enhanced Delivery of Nanoparticle-Encapsulated Chemotherapy Drugs to Brain Tumour

PURPOSE

Tissue hydraulic permeability of brain tumours can vary considerably depending on the tissue microstructure, compositions in interstitium and tumour cells. Its effects on drug transport and accumulation remain poorly understood.

METHODS

Mathematical modelling is applied to predict the drug delivery outcomes in tumours with different tissue permeability upon convection-enhanced delivery. The modelling is based on a 3-D realistic tumour model that is extracted from patient magnetic resonance images.

RESULTS

Modelling results show that infusing drugs into a permeable tumour can facilitate a more favourable hydraulic environment for drug transport. The infused drugs will exhibit a relatively uniform distribution and cover a larger tumour volume for effective cell killing. Cross-comparisons show the delivery outcomes are more sensitive to the changes in tissue hydraulic permeability and blood pressure than the fluid flow from the brain ventricle. Quantitative analyses demonstrate that increasing the fluid gain from both the blood and brain ventricle can further improve the interstitial fluid flow, and thereby enhance the delivery outcomes. Furthermore, similar responses to the changes in tissue hydraulic permeability can be found for different types of drugs.

CONCLUSIONS

Tissue hydraulic permeability as an intrinsic property can influence drug accumulation and distribution. Results from this study can deepen the understanding of the interplays between drug and tissues that are involved in the drug delivery processes in chemotherapy.

Multiscale pharmacokinetic modeling of systemic exposure of subcutaneously injected biotherapeutics

Subcutaneously injected formulations have been developed for many biological products including monoclonal antibodies (mAbs). A knowledge gap nonetheless remains regarding the absorption and catabolism mechanisms and kinetics of a large molecule at the administration site. A multiscale pharmacokinetic (PK) model was thus developed by coupling multiphysics simulations of subcutaneous (SC) absorption kinetics with whole-body pharmacokinetic (PK) modeling, bridged by consideration of the presystemic clearance by the initial lymph. Our local absorption simulation of SC-injected albumin enabled the estimation of its presystemic clearance and led to the whole-body PK modeling of systemic exposure. The local absorption rate of albumin was found to be influential on the PK profile. Additionally, nineteen mAbs were explored via this multiscale simulation and modeling framework. The computational results suggest that stability propensities of the mAbs are correlated with the presystemic clearance, and electrostatic charges in the complementarity-determining region influence the local absorption rate. Still, this study underscores a critical need to experimentally determine various biophysical characteristics of a large molecule and the biomechanical properties of human skin tissues.