Concentration-Dependent Diffusion of Monoclonal Antibodies: Underlying Mechanisms of Anomalous Diffusion.

The development, storage, transport, and subcutaneous delivery of highly concentrated monoclonal antibody formulations pose significant challenges due to the high solution viscosity and low diffusion of the antibody molecules in crowded environments. These issues often stem from the self-associating behavior of the antibody molecules, potentially leading to aggregation. In this work, we used a dissipative particle dynamics-based coarse-grained model to investigate the diffusion behavior of IgG1 antibody molecules in aqueous solutions with 15 and 32 mM NaCl and antibody concentrations ranging from 10 to 400 mg/mL. We determined the coarse-grained interaction parameters by matching the calculated structure factor with the computational and experimental data from the literature. Our results indicate Fickian diffusion for antibody concentrations of 10 and 25 mg/mL and anomalous diffusion for concentrations exceeding 50 mg/mL. The anomalous diffusion was observed for ∼0.33 to 0.4 µs, followed by Fickian diffusion for all antibody concentrations. We observed a strong linear correlation between the diffusion behavior of the antibody molecules (diffusion coefficient D and anomalous diffusion exponent α) and the amount of aggregates present in the solution and between the amount of aggregates and the Coulomb interaction energy. The investigation of underlying mechanisms for anomalous diffusion revealed that in crowded environments at high antibody concentrations, the attractive interaction between electrostatically complementary regions of the antibody molecules could further bring the neighboring molecules closer to one another, ultimately resulting in aggregate formation. Further, the Coulomb attraction can continue to draw more molecules together, forming larger aggregates.

Inverse resolution of spatially varying diffusion coefficient using Physics-Informed neural networks.

Resolving the diffusion coefficient is a key element in many biological and engineering systems, including pharmacological drug transport and fluid mechanics analyses. Additionally, these systems often have spatial variation in the diffusion coefficient which must be determined, such as for injectable drug-eluting implants into heterogeneous tissues. Unfortunately, obtaining the diffusion coefficient from images in such cases is an inverse problem with only discrete data points. The development of a robust method that can work with such noisy and ill-posed datasets to accurately determine spatially-varying diffusion coefficients is of great value across a large range of disciplines. Here, we developed an inverse solver that uses physics informed neural networks (PINNs) to calculate spatially-varying diffusion coefficients from numerical and experimental image data in varying biological and engineering applications. The residual of the transient diffusion equation for a concentration field is minimized to find the diffusion coefficient. The robustness of the method as an inverse solver was tested using both numerical and experimental datasets. The predictions show good agreement with both the numerical and experimental benchmarks; an error of less than 6.31% was obtained against all numerical benchmarks, while the diffusion coefficient calculated in experimental datasets matches the appropriate ranges of other reported literature values. Our work demonstrates the potential of using PINNs to resolve spatially-varying diffusion coefficients, which may aid a wide-range of applications, such as enabling better-designed drug-eluting implants for regenerative medicine or oncology fields.

Rheology of bi-disperse dense fiber suspensions.

While significant progress has been made in the modeling and simulation of uniform fiber suspensions, no existing model has been validated for industrially-relevant concentrated suspensions containing fibers of multiple aspect ratios. In the present work, we investigate bi-disperse suspensions with two fiber populations in varying aspect ratios in a steady shear flow using direct numerical simulations. Moreover, we measure the suspension viscosity by creating a controlled length bidispersity for nylon fibers suspended in a Newtonian fluid. The results showed good agreement between the experimentally measured and numerically predicted viscosity for bi-disperse suspensions. The ratio between the aspect ratio of large to small fibers (size ratio) and the volume fraction of large fibers (composition) in bi-disperse systems strongly affected the rheological behavior of the suspension. The increment of relative viscosity associated with size ratio and composition can be explained by the decrease in the maximum flowable limit or jamming volume fraction. Moreover, the relative viscosity of bi-disperse suspensions collapses, when plotted against the reduced volume fraction, demonstrating the controlling influence of the jamming fraction in bi-disperse fiber suspensions.

A compartment model for subcutaneous injection of monoclonal antibodies.

Despite the growing popularity of subcutaneous (SC) administration for monoclonal antibodies (mAbs), there remains a limited understanding of the significance of mAb transport rate constants within the interstitial space and the lymphatic system on their pharmacokinetics. To bridge this knowledge gap, we introduce a compartmental model for subcutaneously administered mAbs. Our model differentiates FcRn-expressing cells across various sites, and the model predictions agree with experimental data from both human and rat studies. Our findings indicate that the time to reach the maximum mAb concentration in the plasma, denoted by Tmax, displays a weak positive correlation with mAb half-life and a negligible correlation with bioavailability. In contrast, the half-life of mAbs exhibits a strong positive correlation with bioavailability. Moreover, the rate of mAb transport from lymph to plasma significantly affects the mAb half-life. Increasing the transport rates of mAbs from the injection site to the lymph or from lymph to plasma enhances bioavailability. These insights, combined with our compartmental model, contribute to a deeper understanding of the pharmacokinetics of subcutaneously administered mAbs.

Computational modeling of the effect of skin pinch and stretch on subcutaneous injection of monoclonal antibodies using autoinjector devices.

Subcutaneous injection of monoclonal antibodies (mAbs) has experienced unprecedented growth in the pharmaceutical industry due to its benefits in patient compliance and cost-effectiveness. However, the impact of different injection techniques and autoinjector devices on the drug's transport and uptake is poorly understood. Here, we develop a biphasic large-deformation chemomechanical model that accounts for the components of the extracellular matrix that govern solid deformation and fluid flow within the subcutaneous tissue: interstitial fluid, collagen fibers and negatively charged proteoglycan aggregates. We use this model to build a high-fidelity representation of a virtual patient performing a subcutaneous injection of mAbs. We analyze the impact of the pinch and stretch methods on the injection dynamics and the use of different handheld autoinjector devices. The results suggest that autoinjector base plates with a larger device-skin contact area cause significantly lower tissue mechanical stress, fluid pressure and fluid velocity during the injection process. Our simulations indicate that the stretch technique presents a higher risk of intramuscular injection for autoinjectors with a relatively long needle insertion depth.

Numerical studies of the lymphatic uptake rate.

Lymphatic uptake is essential for transporting nutrients, wastes, immune cells, and therapeutic proteins. Despite its importance, the literature lacks a quantitative analysis of the factors that affect lymphatic uptake, including interstitial pressure, downstream pressure, and tissue deformation. In this paper, we present a coupled model of a poroelastic tissue with initial lymphatics and quantify the impact of these factors on the rate of lymphatic uptake. Our results indicate that the lymphatic uptake increases with the amplitude of the oscillating downstream pressure when the amplitude exceeds a threshold. Additionally, the cross-sectional area of initial lymphatics increases with the volumetric strain of the tissue, while the interstitial pressure increases when the strain rate becomes negative. Therefore, the lymphatic uptake reaches its maximum when the tissue has positive volumetric strain while being compressed. We have also investigated the effect of intersection angles and positions of two initial lymphatics and concluded that they have minor impacts on lymphatic uptake. However, the lymphatic uptake per unit length of initial lymphatics decreases with their total length. These findings advance our understanding of lymphatic uptake and can guide the development of strategies to accelerate the transport of therapeutics.

Stress and stretching regulate dispersion in viscoelastic porous media flows.

In this work, we study the role of viscoelastic instability in the mechanical dispersion of fluid flow through porous media at high Péclet numbers. Using microfluidic experiments and numerical simulations, we show that viscoelastic instability in flow through a hexagonally ordered (staggered) medium strongly enhances dispersion transverse to the mean flow direction with increasing Weissenberg number (Wi). In contrast, preferential flow paths can quench the elastic instability in disordered media, which has two important consequences for transport: first, the lack of chaotic velocity fluctuations reduces transverse dispersion relative to unstable flows. Second, the amplification of flow along preferential paths with increasing Wi causes strongly-correlated stream-wise flow that enhances longitudinal dispersion. Finally, we illustrate how the observed dispersion phenomena can be understood through the lens of Lagrangian stretching manifolds, which act as advective transport barriers and coincide with high stress regions in these viscoelastic porous media flows.

Solute Transport across the Lymphatic Vasculature in a Soft Skin Tissue.

Convective transport of drug solutes in biological tissues is regulated by the interstitial fluid pressure, which plays a crucial role in drug absorption into the lymphatic system through the subcutaneous (SC) injection. In this paper, an approximate continuum poroelasticity model is developed to simulate the pressure evolution in the soft porous tissue during an SC injection. This poroelastic model mimics the deformation of the tissue by introducing the time variation of the interstitial fluid pressure. The advantage of this method lies in its computational time efficiency and simplicity, and it can accurately model the relaxation of pressure. The interstitial fluid pressure obtained using the proposed model is validated against both the analytical and the numerical solution of the poroelastic tissue model. The decreasing elasticity elongates the relaxation time of pressure, and the sensitivity of pressure relaxation to elasticity decreases with the hydraulic permeability, while the increasing porosity and permeability due to deformation alleviate the high pressure. An improved Kedem-Katchalsky model is developed to study solute transport across the lymphatic vessel network, including convection and diffusion in the multi-layered poroelastic tissue with a hybrid discrete-continuum vessel network embedded inside. At last, the effect of different structures of the lymphatic vessel network, such as fractal trees and Voronoi structure, on the lymphatic uptake is investigated. In this paper, we provide a novel and time-efficient computational model for solute transport across the lymphatic vasculature connecting the microscopic properties of the lymphatic vessel membrane to the macroscopic drug absorption.

Mechanistic Computational Modeling of Implantable, Bioresorbable Drug Release Systems.

Implantable, bioresorbable drug delivery systems offer an alternative to current drug administration techniques; allowing for patient-tailored drug dosage, while also increasing patient compliance. Mechanistic mathematical modeling allows for the acceleration of the design of the release systems, and for prediction of physical anomalies that are not intuitive and may otherwise elude discovery. This study investigates short-term drug release as a function of water-mediated polymer phase inversion into a solid depot within hours to days, as well as long-term hydrolysis-mediated degradation and erosion of the implant over the next few weeks. Finite difference methods are used to model spatial and temporal changes in polymer phase inversion, solidification, and hydrolysis. Modeling reveals the impact of non-uniform drug distribution, production and transport of H+ ions, and localized polymer degradation on the diffusion of water, drug, and hydrolyzed polymer byproducts. Compared to experimental data, the computational model accurately predicts the drug release during the solidification of implants over days and drug release profiles over weeks from microspheres and implants. This work offers new insight into the impact of various parameters on drug release profiles, and is a new tool to accelerate the design process for release systems to meet a patient specific clinical need.

Hydrodynamic considerations for spring-driven autoinjector design.

In recent years, significant progress has been made in the studies of the spring-driven autoinjector, leading to an improved understanding of this device and its interactions with tissue and therapeutic proteins. The development of simulation tools that have been validated against experiments has also enhanced the prediction of the performance of spring-driven autoinjectors. This paper aims to address critical hydrodynamic considerations that impact the design of spring-driven autoinjectors, with a specific emphasis on sloshing and cavitation. Additionally, we present a framework that integrates simulation tools to predict the performance of spring-driven autoinjectors and optimize their design. This work is valuable to the pharmaceutic industry, as it provides crucial insights into the development of spring-driven autoinjectors and therapeutic proteins. This work can also enhance the efficacy and safety of the delivery of therapeutic proteins, ultimately improving patient outcomes.

Rheology of 3D printable ceramic suspensions: effects of non-adsorbing polymer on discontinuous shear thickening.

Concentrated suspensions of particles at volume fractions (ϕ) ≥ 0.5 often exhibit complex rheological behavior, transitioning from shear thinning to shear thickening as the shear stress or shear rate is increased. These suspensions can be extruded to form 3D structures, with non-adsorbing polymers often added as rheology modifiers to improve printability. Understanding how non-adsorbing polymers affect the suspension rheology, particularly the onset of shear thickening, is critical to the design of particle inks that will extrude uniformly. In this work, we examine the rheology of concentrated aqueous suspensions of colloidal alumina particles and the effects of adding non-adsorbing polyvinylpyrrolidone (PVP). First, we show that suspensions with ϕalumina = 0.560-0.575 exhibited discontinuous shear thickening (DST), where the viscosity increased by up to two orders of magnitude above an onset stress (τmin). Increasing ϕalumina from 0.550 to 0.575 increased the viscosity and yield stress in the shear thinning regime and decreased τmin. Next, PVP was added at concentrations within the dilute and semi-dilute non-entangled regimes of polymer conformation (ϕPVP = 0.005-0.050) to suspensions with constant ϕalumina = 0.550. DST was observed in all cases and increasing ϕPVP increased the viscosity and yield stress. Interestingly, increasing ϕPVP also increased τmin. We posit that the free PVP chains act as lubricants between alumina particles, increasing the stress needed to induce thickening. Finally, we demonstrate through direct comparisons of suspensions with and without PVP how non-adsorbing polymer addition can extend the extrusion processing window due to the increase in τmin.

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.

Investigation of macromolecular transport through tunable collagen hyaluronic acid matrices.

Therapeutic macromolecules possess properties such as size and electrostatic charge that will dictate their transport through subcutaneous (SC) tissue and ultimate bioavailability and efficacy. To improve therapeutic design, platforms that systematically measure the transport of macromolecules as a function of both drug and tissue properties are needed. We utilize a Transwell chamber with tunable collagen-hyaluronic acid (ColHA) hydrogels as an in vitro model to determine mass transport of macromolecules using non-invasive UV spectroscopy. Increasing hyaluronic acid (HA) concentration from 0 to 2 mg/mL within collagen gels decreases the mass transport of five macromolecules independent of size and charge and results in a maximum decrease in recovery of 23.3% in the case of bovine immunoglobulin G (IgG). However, in a pure 10 mg/mL HA solution, negatively-charged macromolecules bovine serum albumin (BSA), ß-lactoglobulin (BLg), dextran (Dex), and IgG had drastically increased recovery by 20-40% compared to their performance in ColHA matrices. This result was different from the positively-charged macromolecule Lysozyme (Lys), which, despite its small size, showed reduced recovery by 3% in pure HA. These results demonstrate two distinct regimes of mass transport within our tissue model. In the presence of both collagen and HA, increasing HA concentrations decrease mass transport; however, in the absence of collagen, the high negative charge of HA sequesters and increases residence time of positively-charged macromolecules and decreases residence time of negatively-charged macromolecules. Through our approach, ColHA hydrogels serve as a platform for the systematic evaluation of therapeutic macromolecule transport as a function of molecular characteristics.

Lagrangian stretching reveals stress topology in viscoelastic flows.

Viscoelastic flows are pervasive in a host of natural and industrial processes, where the emergence of nonlinear and time-dependent dynamics regulates flow resistance, energy consumption, and particulate dispersal. Polymeric stress induced by the advection and stretching of suspended polymers feeds back on the underlying fluid flow, which ultimately dictates the dynamics, instability, and transport properties of viscoelastic fluids. However, direct experimental quantification of the stress field is challenging, and a fundamental understanding of how Lagrangian flow structure regulates the distribution of polymeric stress is lacking. In this work, we show that the topology of the polymeric stress field precisely mirrors the Lagrangian stretching field, where the latter depends solely on flow kinematics. We develop a general analytical expression that directly relates the polymeric stress and stretching in weakly viscoelastic fluids for both nonlinear and unsteady flows, which is also extended to special cases characterized by strong kinematics. Furthermore, numerical simulations reveal a clear correlation between the stress and stretching field topologies for unstable viscoelastic flows across a broad range of geometries. Ultimately, our results establish a connection between the Eulerian stress field and the Lagrangian structure of viscoelastic flows. This work provides a simple framework to determine the topology of polymeric stress directly from readily measurable flow field data and lays the foundation for directly linking the polymeric stress to flow transport properties.

Modeling large-volume subcutaneous injection of monoclonal antibodies with anisotropic porohyperelastic models and data-driven tissue layer geometries.

Subcutaneous injection of therapeutic monoclonal antibodies (mAbs) has become one of the fastest-growing fields in the pharmaceutical industry. The transport and mechanical processes behind large volume injections are poorly understood. Here, we leverage a large-deformation poroelastic model to study high-dose, high-speed subcutaneous injection. We account for the anisotropy of subcutaneous tissue using of a fibril-reinforced porohyperelastic model. We also incorporate the multi-layer structure of the skin tissue, generating data-driven geometrical models of the tissue layers using histological data. We analyze the impact of handheld autoinjectors on the injection dynamics for different patient forces. Our simulations show the importance of considering the large deformation approach to model large injection volumes. This work opens opportunities to better understand the mechanics and transport processes that occur in large-volume subcutaneous injections of mAbs.

Multi-feature-Based Robust Cell Tracking.

Cell tracking algorithms have been used to extract cell counts and motility information from time-lapse images of migrating cells. However, these algorithms often fail when the collected images have cells with spatially and temporally varying features, such as morphology, position, and signal-to-noise ratio. Consequently, state-of-the-art algorithms are not robust or reliable because they require manual inputs to overcome the cell feature changes. To address these issues, we present a fully automated, adaptive, and robust feature-based cell tracking algorithm for the accurate detection and tracking of cells in time-lapse images. Our algorithm tackles measurement limitations twofold. First, we use Hessian filtering and adaptive thresholding to detect the cells in images, overcoming spatial feature variations among the existing cells without manually changing the input thresholds. Second, cell feature parameters are measured, including position, diameter, mean intensity, area, and orientation, and these parameters are simultaneously used to accurately track the cells between subsequent frames, even under poor temporal resolution. Our technique achieved a minimum of 92% detection and tracking accuracy, compared to 16% from Mosaic and Trackmate. Our improved method allows for extended tracking and characterization of heterogeneous cell behavior that are of particular interest for intravital imaging users.

Characterizing viral samples using machine learning for Raman and absorption spectroscopy.

Machine learning methods can be used as robust techniques to provide invaluable information for analyzing biological samples in pharmaceutical industries, such as predicting the concentration of viral particles of interest in biological samples. Here, we utilized both convolutional neural networks (CNNs) and random forests (RFs) to predict the concentration of the samples containing measles, mumps, rubella, and varicella-zoster viruses (ProQuad®) based on Raman and absorption spectroscopy. We prepared Raman and absorption spectra data sets with known concentration values, then used the Raman and absorption signals individually and together to train RFs and CNNs. We demonstrated that both RFs and CNNs can make predictions with R2 values as high as 95%. We proposed two different networks to jointly use the Raman and absorption spectra, where our results demonstrated that concatenating the Raman and absorption data increases the prediction accuracy compared to using either Raman or absorption spectrum alone. Additionally, we further verified the advantage of using joint Raman-absorption with principal component analysis. Furthermore, our method can be extended to characterize properties other than concentration, such as the type of viral particles.

The role of liquid rheological properties on the injection process of a spring-driven autoinjector.

Accurate injection time prediction is essential in developing spring-driven autoinjector devices since the drug delivery is expected to finish within seconds to bring convenience, reduce the risk for early lift-off, and provide a consistent experience to users. The Carreau model captures the liquid's shear-dependent viscosity measured in our experiments. Thus, a quasi-steady model, which uses the Carreau model to describe the liquid's viscosity, is developed to predict the injection time of spring-driven autoinjectors. Analytical relations between the flow rate and the pressure drop in the needle are also obtained. The Carreau number in the spring-driven autoinjector is greater than one and smaller than a critical value; in this region, using the power-law model to describe the liquid viscosity accurately predicts the injection time, which agrees with the current literature findings. Additionally, a force threshold is identified for the friction force between the plunger and the syringe barrel, beyond which the injection time is infinite. Appreciation of this force threshold can help avoid device stalling and reduce the risk of underdosing. Moreover, the role of liquid's shear-thinning index on the injection time of spring-driven autoinjectors is quantified. Understanding the shear-thinning index allows formulators to experiment with excipients and pH to enhance confidence in drug/device combination product design and integration. Our experimental and theoretical results can help drug product and device developers with integrated product design and improve the patient experience.

The air entrainment and hydrodynamic shear of the liquid slosh in syringes.

Understanding the interface motion and hydrodynamic shear induced by the liquid sloshing during the insertion stage of an autoinjector can help improve drug product administration. We perform experiments to investigate the interfacial motion and hydrodynamic shear due to the acceleration and deceleration of syringes. The goal is to explore the role of fluid properties, air gap size, and syringe acceleration on the interface dynamics caused by autoinjector activation. We used a simplified autoinjector platform to record the syringe and liquid motion without any view obstruction. Water and silicone oil with the same viscosity are used as the model fluids. Particle Image Velocimetry (PIV) is employed to measure the velocity field. Simultaneous shadowgraph visualization captures the air entrainment. Our in-house PIV and image processing algorithms are used to quantify the hydrodynamic stress and interfacial area to investigate the effects of various autoinjector design parameters and fluid types on liquid sloshing. The results indicate that reducing the air gap volume and syringe acceleration/deceleration mitigate the interface area and effective shear. Moreover, the interfacial area and induced hydrodynamic stress decrease with the Fr=U/aD, where U is the interface velocity, a is the maximum syringe acceleration, and D is the syringe diameter.

Transport and distribution of biotherapeutics in different tissue layers after subcutaneous injection.

The subcutaneous injection is the main route of administration for monoclonal antibodies (mAbs) and several other biotherapeutics due to the patient comfort and cost-effectiveness. However, their transport and distribution after subcutaneous injection is poorly understood. Here, we exploit a three-dimensional poroelastic model to find the biomechanical response of the tissue, including interstitial pressure and tissue deformation during the injection. We quantify the drug concentration inside the tissue. We start with a single-layer model of the tissue. We show that during the injection, the difference between the permeability of the solvent and solute will result in a higher drug concentration proportional to the inverse permeability ratio. Then we study the role of tissue layered properties with primary layers, including epidermis, dermis, subcutaneous (SQ), and muscle layers, on tissue biomechanical response to injection and drug transport. We show that the drug will distribute mainly in the SQ layer due to its lower elastic moduli. Finally, we study the effect of secondary tissue elements like the deep fascia layer and the network of septa fibers inside the SQ tissue. We use the Voronoi tessellation algorithm to create random geometry of the septa network. We show how drugs accumulate around these tissue components as observed in the experimental SQ injection. Next, we study the effect of injection rate on drug concentration. We show how higher injection rates will slightly increase the drug concentration around septa fibers. Finally we demonstrate how the concentration dependent viscosity will increase the concentration of biotherapeutics in the direction of septa fibers.