Investigating the effect of drug release on in-stent restenosis: A hybrid continuum - agent-based modelling approach

BACKGROUND AND OBJECTIVE

In-stent restenosis (ISR) following percutaneous coronary intervention with drug-eluting stent (DES) implantation remains an unresolved issue, with ISR rates up to 10%. The use of antiproliferative drugs on DESs has significantly reduced ISR. However, a complete knowledge of the mechanobiological processes underlying ISR is still lacking. Multiscale agent-based modelling frameworks, integrating continuum- and agent-based approaches, have recently emerged as promising tools to decipher the mechanobiological events driving ISR at different spatiotemporal scales. However, the integration of sophisticated drug models with an agent-based model (ABM) of ISR has been under-investigated. The aim of the present study was to develop a novel multiscale agent-based modelling framework of ISR following DES implantation.

METHODS

The framework consisted of two bi-directionally coupled modules, namely (i) a drug transport module, simulating drug transport through a continuum-based approach, and (ii) a tissue remodelling module, simulating cellular dynamics through an ABM. Receptor saturation (RS), defined as the fraction of target receptors saturated with drug, is used to mediate cellular activities in the ABM, since RS is widely regarded as a measure of drug efficacy. Three studies were performed to investigate different scenarios in terms of drug mass (DM), drug release profiles (RP), coupling schemes and idealized vs. patient-specific artery geometries.

RESULTS

The studies demonstrated the versatility of the framework and enabled exploration of the sensitivity to different settings, coupling modalities and geometries. As expected, changes in the DM, RP and coupling schemes illustrated a variation in RS over time, in turn affecting the ABM response. For example, combined small DM - fast RP led to similar ISR degrees as high DM - moderate RP (lumen area reduction of ∼13/17% vs. ∼30% without drug). The use of a patient-specific geometry with non-equally distributed struts resulted in a heterogeneous RS map, but did not remarkably impact the ABM response.

CONCLUSION

The application to a patient-specific geometry highlights the potential of the framework to address complex realistic scenarios and lays the foundations for future research, including calibration and validation on patient datasets and the investigation of the effects of different plaque composition on the arterial response to DES.

Modelling smart drug release with functionally graded materials

Functionally graded materials (FGMs), possessing properties that vary smoothly from one region to another, have been receiving increasing attention in recent years, particularly in the aerospace, automotive and biomedical sectors. However, they have yet to reach their full potential. In this paper, we explore the potential of FGMs in the context of drug delivery, where the unique material characteristics offer the potential of fine-tuning drug-release for the desired application. Specifically, we develop a mathematical model of drug release from a thin film FGM, based upon a spatially-varying drug diffusivity. We demonstrate that, depending on the functional form of the diffusivity (related to the material properties) a wide range of drug release profiles may be obtained. Interestingly, the shape of these release profiles are not, in general, achievable from a homogeneous medium with a constant diffusivity.

Controlling release from encapsulated drug-loaded devices: insights from modeling the dissolution front propagation

Dissolution of drug from its solid form to a dissolved form is an important consideration in the design and optimization of drug delivery devices, particularly owing to the abundance of emerging compounds that are extremely poorly soluble. When the solid dosage form is encapsulated, for example by the porous walls of an implant, the impact of the encapsulant drug transport properties is a further confounding issue. In such a case, dissolution and diffusion work in tandem to control the release of drug. However, the interplay between these two competing processes in the context of drug delivery is not as well understood as it is for other mass transfer problems, particularly for practical controlled-release considerations such as an encapsulant layer around the drug delivery device. To address this gap, this work presents a mathematical model that describes controlled release from a drug-loaded device surrounded by a passive porous layer. A solution for the drug concentration distribution is derived using the method of eigenfunction expansion. The model is able to track the dissolution front propagation, and predict the drug release curve during the dissolution process. The utility of the model is demonstrated through comparison against experimental data representing drug release from a cylindrical drug-loaded orthopedic fixation pin, where the model is shown to capture the data very well. Analysis presented here reveals how the various geometrical and physicochemical parameters influence drug dissolution and, ultimately, the drug release profile. It is found that the non-dimensional initial concentration plays a key role in determining whether the problem is diffusion-limited or dissolution-limited, whereas the nature of the problem is largely independent of other parameters including diffusion coefficient and encapsulant thickness. We expect the model will prove to be a useful tool for those designing encapsulated drug delivery devices, in terms of optimizing the design of the device to achieve a desired drug release profile.

Solute transport with Michaelis-Menten kinetics for in vitro cell culture

A traditional method of in vitro cell culture involves a monolayer of cells at the base of a petri dish filled with culture medium. While the primary role of the culture medium is to supply nutrients to the cells, drug or other solutes may be added, depending on the purpose of the experiment. Metabolism by cells of oxygen, nutrients and drug is typically governed by Michaelis-Menten (M-M) kinetics. In this paper, a mathematical model of solute transport with M-M kinetics is developed. Upon non-dimensionalization, the reaction/diffusion system is re-characterized in terms of Volterra integral equations, where a parameter $\beta $, the ratio of the initial solute concentration to the M-M constant, proves important: $\beta \ll 1$ is relevant to drug metabolism for the liver, whereas $\beta \gg 1$ is more appropriate in the case of oxygen metabolism. Regular perturbation expansions for both cases are obtained. A small-time expansion and steady-state solution are also presented. All results are compared against the numerical solution of the Volterra integral equations, and excellent agreement is found. The utility of the model and analytical solutions are discussed in the context of assisting experimental researchers to better understand the environment within in vitro cell culture experiments.

Modeling Dual Drug Delivery from Eluting Stents: The Influence of Non-Linear Binding Competition and Non-Uniform Drug Loading

OBJECTIVE

There is increasing interest in simultaneous endovascular delivery of more than one drug from a drug-loaded stent into a diseased artery. There may be an opportunity to obtain a therapeutically desirable uptake profile of the two drugs over time by appropriate design of the initial drug distribution in the stent. Due to the non-linear, coupled nature of diffusion and reversible specific/non-specific binding of both drugs as well as competition between the drugs for a fixed binding site density, a comprehensive numerical investigation of this problem is critically needed.

METHODS

This paper presents numerical computation of dual drug delivery in a stent-artery system, accounting for diffusion as well as specific and non-specific reversible binding. The governing differential equations are discretized in space, followed by integration over time using a stiff numerical solver. Three different cases of initial dual drug distribution are considered.

RESULTS

For the particular case of sirolimus and paclitaxel, results show that competition for a limited non-specific binding site density and the significant difference in the forward/backward reaction coefficients play a key role in determining the nature of drug uptake. The nature of initial distribution of the two drugs in the stent is also found to influence the binding process, which can potentially be used to engineer a desirable dual drug uptake profile.

CONCLUSIONS

These results help improve the fundamental understanding of endovascular dual drug delivery. In addition, the numerical technique and results presented here may be helpful for designing and optimizing other drug delivery problems as well.

Optimization of Initial Drug Distribution in Spherical Capsules for Personalized Release

OBJECTIVE

Customization of the rate of drug delivered based on individual patient requirements is of paramount importance in the design of drug delivery devices. Advances in manufacturing may enable multilayer drug delivery devices with different initial drug distributions in each layer. However, a robust mathematical understanding of how to optimize such capabilities is critically needed. The objective of this work is to determine the initial drug distribution needed in a spherical drug delivery device such as a capsule in order to obtain a desired drug release profile.

METHODS

This optimization problem is posed as an inverse mass transfer problem, and optimization is carried out using the solution of the forward problem. Both non-erodible and erodible multilayer spheres are analyzed. Cases with polynomial forms of initial drug distribution are also analyzed. Optimization is also carried out for a case where an initial burst in drug release rate is desired, followed by a constant drug release rate.

RESULTS

More than 60% reduction in root-mean-square deviation of the actual drug release rate from the ideal constant drug release rate is reported. Typically, the optimized initial drug distribution in these cases prevents or minimizes large drug release rate at early times, leading to a much more uniform drug release overall.

CONCLUSIONS

Results demonstrate potential for obtaining a desired drug delivery profile over time by carefully engineering the drug distribution in the drug delivery device. These results may help engineer devices that offer customized drug delivery by combining advanced manufacturing with mathematical optimization.

An intricate interplay between stent drug dose and release rate dictates arterial restenosis

Since the introduction of percutaneous coronary intervention (PCI) for the treatment of obstructive coronary artery disease (CAD), patient outcomes have progressively improved. Drug eluting stents (DES) that employ anti-proliferative drugs to limit excess tissue growth following stent deployment have proved revolutionary. However, restenosis and a need for repeat revascularisation still occurs after DES use. Over the last few years, computational models have emerged that detail restenosis following the deployment of a bare metal stent (BMS), focusing primarily on contributions from mechanics and fluid dynamics. However, none of the existing models adequately account for spatiotemporal delivery of drug and the influence of this on the cellular processes that drive restenosis. In an attempt to fill this void, a novel continuum restenosis model coupled with spatiotemporal drug delivery is presented. Our results indicate that the severity and time-course of restenosis is critically dependent on the drug delivery strategy. Specifically, we uncover an intricate interplay between initial drug loading, drug release rate and restenosis, indicating that it is not sufficient to simply ramp-up the drug dose or prolong the time course of drug release to improve stent efficacy. Our model also shows that the level of stent over-expansion and stent design features, such as inter-strut spacing and strut thickness, influence restenosis development, in agreement with trends observed in experimental and clinical studies. Moreover, other critical aspects of the model which dictate restenosis, including the drug binding site density are investigated, where comparisons are made between approaches which assume this to be either constant or proportional to the number of smooth muscle cells (SMCs). Taken together, our results highlight the necessity of incorporating these aspects of drug delivery in the pursuit of optimal DES design.

Drug diffusion and release from a bioerodible spherical capsule

Controlled release of a drug contained in a spherical polymer capsule is of significant interest in many fields of medicine. There is growing interest in tailoring the erosion properties of the drug to help control and optimize the drug release process. Theoretical understanding of the nature of drug release from a bioerodible capsule is, therefore, important for designing effective drug delivery systems. While drug release from a fixed-radius capsule is relatively easier to model, the shrinking nature of a bioerodible capsule due to surface erosion presents several difficulties in theoretical modeling. This work presents a closed-form solution for the drug concentration distribution and drug delivery characteristics from a spherical capsule undergoing linear surface erosion. This problem is solved by a transformation that converts the moving boundary problem into a fixed boundary problem. For uniform initial drug distribution, the solution is shown to depend on a single non-dimensional parameter. The theoretical model is used to develop an understanding of the impact of varying the drug diffusion coefficient and rate of erosion on drug delivery characteristics. It is found that, in general, the nature of drug release in a bioerodible sphere is determined by a delicate balance between two simultaneously occurring processes - erosion and diffusion. This work improves the theoretical understanding of diffusion in drug delivery systems by accounting for the practical erosion phenomena, and may contribute towards the design and optimization of drug delivery systems.

How Does Fluid Flow Influence Drug Release from Drug Filled Implants?

Drug-filled implants (DFIs) have emerged as an innovative approach to control the delivery of drugs. These devices contain the drug within the structure of the implant itself and avoid the need to include additional drug carrier materials such as a polymers, which are often associated with inflammation and delayed healing/tissue regeneration at the implant site. One common feature of in vitro experiments to generate drug release profiles is stirring or agitation of the release medium. However, the influence of the resulting fluid flow on the rate of drug release from DFIs has yet to be quantified. In this paper we consider two DFIs, which although similar in shape and size, employ different strategies to control the release of drug: a porous pin with pores on the order of μm and a pin drilled with orifices of the order of mm. We develop a multiphysics mathematical model of drug release from these DFIs, subject to fluid flow induced through stirring and show that fluid flow greatly influences the drug release profile for the orifice pin, but that the porous pin drug release profile is relatively insensitive to flow. We demonstrate that drug release from the porous pin may adequately be described through a simplified radial 1D dissolution-diffusion model, while a 3D dissolution-advection-diffusion model is required to describe drug release from the orifice pin. A sensitivity analysis reveals that that the balance of reaction-advection-diffusion in terms of key nondimensional numbers governs the overall drug release. Our findings potentially have important implications in terms of devising the most relevant experimental protocol for quantifying drug release from DFIs.

3D modelling of drug-coated balloons for the treatment of calcified superficial femoral arteries

Background/Objectives

Drug-coated balloon therapy for diseased superficial femoral arteries remains controversial. Despite its clinical relevance, only a few computational studies based on simplistic two-dimensional models have been proposed to investigate this endovascular therapy to date. This work addresses the aforementioned limitation by analyzing the drug transport and kinetics occurring during drug-coated balloon deployment in a three-dimensional geometry.

Methods

An idealized three-dimensional model of a superficial femoral artery presenting with a calcific plaque and treated with a drug-coated balloon was created to perform transient mass transport simulations. To account for the transport of drug (i.e. paclitaxel) released by the device, a diffusion-reaction equation was implemented by describing the drug bound to specific intracellular receptors through a non-linear, reversible reaction. The following features concerning procedural aspects, pathologies and modelling assumptions were investigated: (i) balloon application time (60–180 seconds); (ii) vessel wall composition (healthy vs. calcified wall); (iii) sequential balloon application; and (iv) drug wash-out by the blood stream vs. coating retention, modeled as exponential decay.

Results

The balloon inflation time impacted both the free and specifically-bound drug concentrations in the vessel wall. The vessel wall composition highly affected the drug concentrations. In particular, the specifically-bound drug concentration was four orders of magnitude lower in the calcific compared with healthy vessel wall portions, primarily as a result of reduced drug diffusion. The sequential application of two drug-coated balloons led to modest differences (~15%) in drug concentration immediately after inflation, which became negligible within 10 minutes. The retention of the balloon coating increased the drug concentration in the vessel wall fourfold.

Conclusions

The overall findings suggest that paclitaxel kinetics may be affected not only by the geometrical and compositional features of the vessel treated with the drug-coated balloon, but also by balloon design characteristics and procedural aspects that should be carefully considered.

Do we really understand how drug eluted from stents modulates arterial healing?

The advent of drug-eluting stents (DES) has revolutionised the treatment of coronary artery disease. These devices, coated with anti-proliferative drugs, are deployed into stenosed or occluded vessels, compressing the plaque to restore natural blood flow, whilst simultaneously combating the evolution of restenotic tissue. Since the development of the first stent, extensive research has investigated how further advancements in stent technology can improve patient outcome. Mathematical and computational modelling has featured heavily, with models focussing on structural mechanics, computational fluid dynamics, drug elution kinetics and subsequent binding within the arterial wall; often considered separately. Smooth Muscle Cell (SMC) proliferation and neointimal growth are key features of the healing process following stent deployment. However, models which depict the action of drug on these processes are lacking. In this article, we start by reviewing current models of cell growth, which predominantly emanate from cancer research, and available published data on SMC proliferation, before presenting a series of mathematical models of varying complexity to detail the action of drug on SMC growth in vitro. Our results highlight that, at least for Sodium Salicylate and Paclitaxel, the current state-of-the-art nonlinear saturable binding model is incapable of capturing the proliferative response of SMCs across a range of drug doses and exposure times. Our findings potentially have important implications on the interpretation of current computational models and their future use to optimise and control drug release from DES and drug-coated balloons.

Influence of vessel curvature and plaque composition on drug transport in the arterial wall following drug-eluting stent implantation

In the last decade, many computational models have been developed to describe the transport of drug eluted from stents and the subsequent uptake into arterial tissue. Each of these models has its own set of limitations: for example, models typically employ simplified stent and arterial geometries, some models assume a homogeneous arterial wall, and others neglect the influence of blood flow and plasma filtration on the drug transport process. In this study, we focus on two common limitations. Specifically, we provide a comprehensive investigation of the influence of arterial curvature and plaque composition on drug transport in the arterial wall following drug-eluting stent implantation. The arterial wall is considered as a three-layered structure including the subendothelial space, the media and the adventitia, with porous membranes separating them (endothelium, internal and external elastic lamina). Blood flow is modelled by the Navier-Stokes equations, while Darcy's law is used to calculate plasma filtration through the porous layers. Our findings demonstrate that arterial curvature and plaque composition have important influences on the spatiotemporal distribution of drug, with potential implications in terms of effectiveness of the treatment. Since the majority of computational models tend to neglect these features, these models are likely to be under- or over-estimating drug uptake and redistribution in arterial tissue.

Unexpected Role of Nonimmune Cells: Amateur Phagocytes

Effective and efficient efferocytosis of dead cells and associated cellular debris are critical to tissue homeostasis and healing of injured tissues. This important task was previously thought to be restricted to professional phagocytes (PPs). However, accumulating evidence has revealed another type of phagocyte, the amateur phagocyte (AP), which can also participate in efferocytosis. APs are non-myeloid progenitor/nonimmune cells that include differentiated cells (e.g., epithelial cells, fibroblasts, and endothelial cells [ECs]) and stem cells (e.g., neuronal progenitor cells and mesenchymal cells) and can be found throughout the human body. Studies have shown that APs have two prominent roles: identifying and removing dead cells presumably before PPs reach the site of injury and assisting PPs in the removal of cell corpses and the resolution of inflamed tissue. With respect to the engulfment and degradation of dead cells, APs are slower and less efficient than PPs. However, APs are fundamental to preventing the spread of inflammation over a large area. In this review, we present the diversity and characteristics of healthy and non-neoplastic APs in mammals. We also propose a hypothetical mechanism of the efferocytosis of immunoglobulin G (IgG)-opsonized myelin debris by ECs (APs). Furthermore, the ingestion and clearance of dead cells can induce proinflammatory or anti-inflammatory cytokine production, endothelial activation, and cellular fate transition, which contribute to the progression of disease. An understanding of the role of APs is necessary to develop effective intervention strategies, including potential molecular targets for clinical diagnosis and drug development, for inflammation-related diseases.

Macrophage membrane functionalized biomimetic nanoparticles for targeted anti-atherosclerosis applications

Atherosclerosis (AS), the underlying cause of most cardiovascular events, is one of the most common causes of human morbidity and mortality worldwide due to the lack of an efficient strategy for targeted therapy. In this work, we aimed to develop an ideal biomimetic nanoparticle for targeted AS therapy. Methods: Based on macrophage "homing" into atherosclerotic lesions and cell membrane coating nanotechnology, biomimetic nanoparticles (MM/RAPNPs) were fabricated with a macrophage membrane (MM) coating on the surface of rapamycin-loaded poly (lactic-co-glycolic acid) copolymer (PLGA) nanoparticles (RAPNPs). Subsequently, the physical properties of the MM/RAPNPs were characterized. The biocompatibility and biological functions of MM/RAPNPs were determined in vitro. Finally, in AS mouse models, the targeting characteristics, therapeutic efficacy and safety of the MM/RAPNPs were examined. Results: The advanced MM/RAPNPs demonstrated good biocompatibility. Due to the MM coating, the nanoparticles effectively inhibited the phagocytosis by macrophages and targeted activated endothelial cells in vitro. In addition, MM-coated nanoparticles effectively targeted and accumulated in atherosclerotic lesions in vivo. After a 4-week treatment program, MM/RAPNPs were shown to significantly delay the progression of AS. Furthermore, MM/RAPNPs displayed favorable safety performance after long-term administration. Conclusion: These results demonstrate that MM/RAPNPs could efficiently and safely inhibit the progression of AS. These biomimetic nanoparticles may be potential drug delivery systems for safe and effective anti-AS applications.

Mathematical modelling of fluid flow and solute transport to define operating parameters for in vitro perfusion cell culture systems

In recent years, there has been a move away from the use of static in vitro two-dimensional cell culture models for testing the chemical safety and efficacy of drugs. Such models are increasingly being replaced by more physiologically relevant cell culture systems featuring dynamic flow and/or three-dimensional structures of cells. While it is acknowledged that such systems provide a more realistic environment within which to test drugs, progress is being hindered by a lack of understanding of the physical and chemical environment that the cells are exposed to. Mathematical and computational modelling may be exploited in this regard to unravel the dependency of the cell response on spatio-temporal differences in chemical and mechanical cues, thereby assisting with the understanding and design of these systems. In this paper, we present a mathematical modelling framework that characterizes the fluid flow and solute transport in perfusion bioreactors featuring an inlet and an outlet. To demonstrate the utility of our model, we simulated the fluid dynamics and solute concentration profiles for a variety of different flow rates, inlet solute concentrations and cell types within a specific commercial bioreactor chamber. Our subsequent analysis has elucidated the basic relationship between inlet flow rate and cell surface flow speed, shear stress and solute concentrations, allowing us to derive simple but useful relationships that enable prediction of the behaviour of the system under a variety of experimental conditions, prior to experimentation. We describe how the model may used by experimentalists to define operating parameters for their particular perfusion cell culture systems and highlight some operating conditions that should be avoided. Finally, we critically comment on the limitations of mathematical and computational modelling in this field, and the challenges associated with the adoption of such methods.

Penetration of the blood-brain barrier and the anti-tumour effect of a novel PLGA-lysoGM1/DOX micelle drug delivery system

Effective treatment of glioma and other central nervous system (CNS) diseases is hindered by the presence of the blood-brain barrier (BBB). A novel nano-delivery vehicle system composed of PLGA-lysoGM1/DOX micelles was developed to cross the BBB for CNS treatment. We have shown that doxorubicin (DOX) as a model drug encapsulated in PLGA-lysoGM1 micelles can achieve up to 3.8% loading efficiency and 61.6% encapsulation efficiency by the orthogonal test design. Our in vitro experiments demonstrated that PLGA-lysoGM1/DOX micelles had a slow and sustainable drug release under physiological conditions and exhibited a high cellular uptake through the macropinocytosis and the autophagy/lysosomal pathways. In vivo experimental studies in zebrafish and mice confirmed that PLGA-lysoGM1/DOX micelles could cross the BBB and be specifically accumulated in the brain. Moreover, an excellent anti-glioma effect was observed in intracranial glioma-bearing rats. Therefore, PLGA-lysoGM1/DOX micelles not only effectively can cross the BBB, but our results also suggest that they have great potential for anti-glioma therapy and other central nervous system diseases.

Covalent immobilization of biomolecules on stent materials through mussel adhesive protein coating to form biofunctional films

It is widely accepted that surface biofunctional modification may be an effective approach to improve biocompatibility and confer new bioactive properties on biomaterials. In this work, mussel adhesive protein (MAP) was applied as a coating on 316 L stainless steel substrates (316 L SS) and stents, and then either immobilized VEGF or CD34 antibody were added to create biofunctional films. The properties of the MAP coating were characterized by scanning electron microscope (SEM), atomic force microscope (AFM) and a water contact angle test. Universal tensile testing showed that the MAP coating has adequate adhesion strength on a 316 L stainless steel material surface. Subsequent cytotoxicity and hemolysis rate tests showed that the MAP coatings have good biocompatibility. Moreover, using N-(3-Dimethylaminopropyl)-N'-ethylcarbodiimide hydrochloride and N-hydroxysulfosussinimide (EDC/NHS) chemistry, VEGF and CD34 antibody were immobilized on the MAP coatings. The amount and immobilized yield of VEGF on the MAP coatings were analyzed by enzyme-linked immuno-assays (ELISA). Finally, an endothelial cells culture showed that the VEGF biofunctional film can promote the viability and proliferation of endothelial cells. An in vitro CD34⁺ cells capturing test also verified the bioactive properties of the CD34 antibody coated stents. These results showed that the MAP coatings allowed effective biomolecule immobilization, providing a promising platform for vascular device modification.

Mathematical modelling of the restenosis process after stent implantation

The stenting procedure has evolved to become a highly successful technique for the clinical treatment of advanced atherosclerotic lesions in arteries. However, the development of in-stent restenosis remains a key problem. In this work, a novel two-dimensional continuum mathematical model is proposed to describe the complex restenosis process following the insertion of a stent into a coronary artery. The biological species considered to play a key role in restenosis development are growth factors, matrix metalloproteinases, extracellular matrix, smooth muscle cells and endothelial cells. Diffusion-reaction equations are used for modelling the mass balance between species in the arterial wall. Experimental data from the literature have been used in order to estimate model parameters. Moreover, a sensitivity analysis has been performed to study the impact of varying the parameters of the model on the evolution of the biological species. The results demonstrate that this computational model qualitatively captures the key characteristics of the lesion growth and the healing process within an artery subjected to non-physiological mechanical forces. Our results suggest that the arterial wall response is driven by the damage area, smooth muscle cell proliferation and the collagen turnover among other factors.

Modelling phase separation in amorphous solid dispersions

Much work has been devoted to analysing thermodynamic models for solid dispersions with a view to identifying regions in the phase diagram where amorphous phase separation or drug recrystallization can occur. However, detailed partial differential equation non-equilibrium models that track the evolution of solid dispersions in time and space are lacking. Hence theoretical predictions for the timescale over which phase separation occurs in a solid dispersion are not available. In this paper, we address some of these deficiencies by (i) constructing a general multicomponent diffusion model for a dissolving solid dispersion; (ii) specializing the model to a binary drug/polymer system in storage; (iii) deriving an effective concentration dependent drug diffusion coefficient for the binary system, thereby obtaining a theoretical prediction for the timescale over which phase separation occurs; (iv) calculating the phase diagram for the Felodipine/HPMCAS system; and (iv) presenting a detailed numerical investigation of the Felodipine/HPMCAS system assuming a Flory-Huggins activity coefficient. The numerical simulations exhibit numerous interesting phenomena, such as the formation of polymer droplets and strings, Ostwald ripening/coarsening, phase inversion, and droplet-to-string transitions. A numerical simulation of the fabrication process for a solid dispersion in a hot melt extruder was also presented. STATEMENT OF SIGNIFICANCE: Solid dispersions are products that contain mixtures of drug and other materials e.g. polymer. These are liable to separate-out over time - a phenomenon known as phase separation. This means that it is possible the product differs both compositionally and structurally between the time of manufacture and the time it is taken by the patient, leading to poor bioavailability and so ultimately the shelf-life of the product has to be reduced. Theoretical predictions for the timescale over which phase separation occurs are not currently available. Also lacking are detailed partial differential equation non-equilibrium models that track the evolution of solid dispersions in time and space. This study addresses these issues, before presenting a detailed investigation of a particular drug-polymer system.

Development of an in vitro media perfusion model of Leishmania major macrophage infection

Background

In vitro assays are widely used in studies on pathogen infectivity, immune responses, drug and vaccine discovery. However, most in vitro assays display significant differences to the in vivo situation and limited predictive properties. We applied medium perfusion methods to mimic interstitial fluid flow to establish a novel infection model of Leishmania parasites.

Methods

Leishmania major infection of mouse peritoneal macrophages was studied within the Quasi Vivo QV900 macro-perfusion system. Under a constant flow of culture media at a rate of 360μl/min, L. major infected macrophages were cultured either at the base of a perfusion chamber or raised on 9mm high inserts. Mathematical and computational modelling was conducted to estimate medium flow speed, shear stress and oxygen concentration. The effects of medium flow on infection rate, intracellular amastigote division, macrophage phagocytosis and macropinocytosis were measured.

Results

Mean fluid speeds at the macrophage cell surface were estimated to be 1.45 x 10⁻⁹ m/s and 1.23 x 10⁻⁷ m/s for cells at the base of the chamber and cells on an insert, respectively. L. major macrophage infection was significantly reduced under both media perfusion conditions compared to cells maintained under static conditions; a 85±3% infection rate of macrophages at 72 hours in static cultures compared to 62±5% for cultures under slow medium flow and 55±3% under fast medium flow. Media perfusion also decreased amastigote replication and both macrophage phagocytosis (by 44±4% under slow flow and 57±5% under fast flow compared with the static condition) and macropinocytosis (by 40±4% under slow flow and 62±5% under fast flow compared with the static condition) as measured by uptake of latex beads and pHrodo Red dextran.

Conclusions

Perfusion of culture medium in an in vitro L. major macrophage infection model (simulating in vivo lymphatic flow) reduced the infection rate of macrophages, the replication of the intracellular parasite, macrophage phagocytosis and macropinocytosis with greater reductions achieved under faster flow speeds.

A mathematical model of sonoporation using a liquid-crystalline shelled microbubble

In recent years there has been a great deal of interest in using thin shelled microbubbles as a transportation mechanism for localised drug delivery, particularly for the treatment of various types of cancer. The technique used for such site-specific drug delivery is sonoporation. Despite there being numerous experimental studies on sonoporation, the mathematical modelling of this technique has still not been extensively researched. Presently there exists a very small body of work that models both hemispherical and spherical shelled microbubbles sonoporating due to acoustic microstreaming. Acoustic microstreaming is believed to be the dominant mechanism for sonoporation via shelled microbubbles. Rather than considering the shell of the microbubble to be composed of a thin protein, which is typical in the literature, in this paper we consider the shell to be a liquid-crystalline material. Up until now there have been no studies reported in the literature pertaining to sonoporation of a liquid-crystalline shelled microbubble. A mathematical expression is derived for the maximum wall shear stress, illustrating its dependency on the shell's various material parameters. A sensitivity analysis is performed for the wall shear stress considering the shell's thickness; its local density; the elastic constant of the liquid-crystalline material; the interfacial surface tension and; the shell's viscoelastic properties. In some cases, our results indicate that a liquid-crystalline shelled microbubble may yield a maximum wall shear stress that is two orders of magnitude greater than the stress generated by commercial shelled microbubbles that are currently in use within the scientific community. In conclusion, our preliminary analysis suggests that using liquid-crystalline shelled microbubbles may significantly enhance the efficiency of site-specific drug delivery.

Biomimetic Nanotherapies: Red Blood Cell Based Core-Shell Structured Nanocomplexes for Atherosclerosis Management

Cardiovascular disease is the leading cause of mortality worldwide. Atherosclerosis, one of the most common forms of the disease, is characterized by a gradual formation of atherosclerotic plaque, hardening, and narrowing of the arteries. Nanomaterials can serve as powerful delivery platforms for atherosclerosis treatment. However, their therapeutic efficacy is substantially limited in vivo due to nonspecific clearance by the mononuclear phagocytic system. In order to address this limitation, rapamycin (RAP)-loaded poly(lactic-co-glycolic acid) (PLGA) nanoparticles are cloaked with the cell membrane of red blood cells (RBCs), creating superior nanocomplexes with a highly complex functionalized bio-interface. The resulting biomimetic nanocomplexes exhibit a well-defined "core-shell" structure with favorable hydrodynamic size and negative surface charge. More importantly, the biomimetic nature of the RBC interface results in less macrophage-mediated phagocytosis in the blood and enhanced accumulation of nanoparticles in the established atherosclerotic plaques, thereby achieving targeted drug release. The biomimetic nanocomplexes significantly attenuate the progression of atherosclerosis. Additionally, the biomimetic nanotherapy approach also displays favorable safety properties. Overall, this study demonstrates the therapeutic advantages of biomimetic nanotherapy for atherosclerosis treatment, which holds considerable promise as a new generation of drug delivery system for safe and efficient management of atherosclerosis.

Combining mathematical modelling with in vitro experiments to predict in vivo drug-eluting stent performance

In this study, we developed a predictive model of in vivo stent based drug release and distribution that is capable of providing useful insights into performance. In a combined mathematical modelling and experimental approach, we created two novel sirolimus-eluting stent coatings with quite distinct doses and release kinetics. Using readily measurable in vitro data, we then generated parameterised mathematical models of drug release. These were then used to simulate in vivo drug uptake and retention. Finally, we validated our model predictions against data on drug kinetics and efficacy obtained in a small in vivo evaluation. In agreement with the in vivo experimental results, our mathematical model predicted consistently higher sirolimus content in tissue for the higher dose stents compared with the lower dose stents. High dose stents resulted in statistically significant improvements in three key efficacy measures, providing further evidence of a basic relationship between dose and efficacy within DES. However, our mathematical modelling suggests a more complex relationship is at play, with efficacy being dependent not only on delivering an initial dose of drug sufficient to achieve receptor saturation, but also on the consequent drug release rate being tuned to ensure prolonged saturation. In summary, we have demonstrated that our combined in vitro experimental and mathematical modelling framework may be used to predict in vivo DES performance, opening up the possibility of an in silico approach to optimising the drug release profile and ultimately the effectiveness of the device.

In vitro Liver Zonation of Primary Rat Hepatocytes

The ability of the liver to simultaneously carry out multiple functions is dependent on the metabolic heterogeneity of hepatocytes spatially located within a liver lobule spanning from the portal triad to the central vein. This complex zonal architecture of the liver, however, makes accurate in vitro modeling a challenge and often standard culture systems assume a homogenous model which may lead to inaccurate translatability of results. Here, we use a combination of mathematical modeling and experimental data to demonstrate a readily constructible in vitro flow system capable of liver zonation in primary rat hepatocytes. We show the differential expression of zonation markers, enhanced functionality when compared to standard static cultures and zone-specific metabolism and cell damage in the presence of paracetamol, a known zone-specific toxin. This type of advanced system provides a more in-depth and essential understanding of liver physiology and pathophysiology as well as the accurate evaluation of pharmacological interventions at a zone-specific level.

Modelling drug release from polymer-free coronary stents with microporous surfaces

Traditional coronary drug-eluting stents (DES) are made from metal and are coated with a permanent polymer film containing an anti-proliferative drug. Subsequent to stent deployment in a diseased coronary artery, the drug releases into the artery wall and helps prevent restenosis by inhibiting the proliferation of smooth muscle cells. Although this technology has proven to be remarkably successful, there are ongoing concerns that the presence of a polymer in the artery can lead to deleterious medical complications, such as late stent thrombosis. Polymer-free DES may help overcome such shortcomings. However, the absence of a rate-controlling polymer layer makes optimisation of the drug release profile a particular challenge. The use of microporous stent surfaces to modulate the drug release rate is an approach that has recently shown particularly promising clinical results. In this study, we develop a mathematical model to describe drug release from such stents. In particular, we develop a mathematical model to describe drug release from microporous surfaces. The model predicts a two-stage release profile, with a relatively rapid initial release of most of the drug, followed by a slower release of the remaining drug. In the model, the slow release phase is accounted for by an adsorption/desorption mechanism close to the stent surface. The theoretical predictions are compared with experimental release data obtained in our laboratory, and good agreement is found. The valuable insights provided by our model will serve as a useful guide for designing the enhanced polymer-free stents of the future.

Assessing the potential of mathematical modelling in designing drug-releasing orthopaedic implants

Orthopaedic implants have been the subject of intense research in recent years, with academics, clinicians and industrialists seeking to broaden our understanding of their function and potential consequences within the human body. Current research is focussed on ways to improve the integration of an orthopaedic device within the body, whether it be to encourage better osseointegration, combat possible infection or stem the foreign body response. A key emerging strategy is the controlled delivery of therapeutics from the device, which may take the form of, for example, antibiotics, analgesics, anti-inflammatories or growth factors. However, the optimal device design that gives rise to the desired controlled release has yet to be defined. There are many examples in the literature of experimental approaches which attempt to tackle this issue. However, the necessity of having to conduct multiple experiments to test different scenarios is a major drawback of this approach. So enter stage left: mathematical modelling. Using a mathematical modelling approach can provide much more than experiments in isolation. For instance, a mathematical model can help identify key drug release mechanisms and uncover the rate limiting processes; allow for the estimation of values of the parameters controlling the system; quantify the effect of the interaction with the biological environment; and aid with the design of optimisation strategies for controlled drug release. In this paper we review current experimental approaches and some relevant mathematical models and suggest the future direction of such approaches in this field.

Modeling bispecific monoclonal antibody interaction with two cell membrane targets indicates the importance of surface diffusion

We have developed a mathematical framework for describing a bispecific monoclonal antibody interaction with two independent membrane-bound targets that are expressed on the same cell surface. The bispecific antibody in solution binds either of the two targets first, and then cross-links with the second one while on the cell surface, subject to rate-limiting lateral diffusion step within the lifetime of the monovalently engaged antibody-antigen complex. At experimental densities, only a small fraction of the free targets is expected to lie within the reach of the antibody binding sites at any time. Using ordinary differential equation and Monte Carlo simulation-based models, we validated this approach against an independently published anti-CD4/CD70 DuetMab experimental data set. As a result of dimensional reduction, the cell surface reaction is expected to be so rapid that, in agreement with the experimental data, no monovalently bound bispecific antibody binary complexes accumulate until cross-linking is complete. The dissociation of the bispecific antibody from the ternary cross-linked complex is expected to be significantly slower than that from either of the monovalently bound variants. We estimate that the effective affinity of the bivalently bound bispecific antibody is enhanced for about 4 orders of magnitude over that of the monovalently bound species. This avidity enhancement allows for the highly specific binding of anti-CD4/CD70 DuetMab to the cells that are positive for both target antigens over those that express only one or the other We suggest that the lateral diffusion of target antigens in the cell membrane also plays a key role in the avidity effect of natural antibodies and other bivalent ligands in their interactions with their respective cell surface receptors.

Modelling the Impact of Atherosclerosis on Drug Release and Distribution from Coronary Stents

Although drug-eluting stents (DES) are now widely used for the treatment of coronary heart disease, there remains considerable scope for the development of enhanced designs which address some of the limitations of existing devices. The drug release profile is a key element governing the overall performance of DES. The use of in vitro, in vivo, ex vivo, in silico and mathematical models has enhanced understanding of the factors which govern drug uptake and distribution from DES. Such work has identified the physical phenomena determining the transport of drug from the stent and through tissue, and has highlighted the importance of stent coatings and drug physical properties to this process. However, there is limited information regarding the precise role that the atherosclerotic lesion has in determining the uptake and distribution of drug. In this review, we start by discussing the various models that have been used in this research area, highlighting the different types of information they can provide. We then go on to describe more recent methods that incorporate the impact of atherosclerotic lesions.

Some design considerations for polymer-free drug-eluting stents: a mathematical approach

In this paper we provide the first model of drug elution from polymer-free arterial drug-eluting stents. The generalised model is capable of predicting drug release from a number of polymer-free systems including those that exhibit nanoporous, nanotubular and smooth surfaces. We derive analytical solutions which allow us to easily determine the important parameters that control drug release. Drug release profiles are provided, and we offer design recommendations so that the release profile may be tailored to achieve the desired outcome. The models presented here are not specific to drug-eluting stents and may also be applied to other biomedical implants that use nanoporous surfaces to release a drug.

Release mechanism and parameter estimation in drug-eluting stent systems: analytical solutions of drug release and tissue transport

Drug-eluting stents have significantly improved the treatment of coronary artery disease. They offer reduced rates of restenosis compared with their bare-metal predecessors and are the current gold standard in percutaneous coronary interventions. Drug-eluting stents have been approved for use in humans since 2002 and yet, despite the intensive research activity over the past decade, the drug release mechanism(s) and the uptake into the arterial wall are still poorly understood. While stent manufacturers have focussed primarily on empirical methods, several mathematical models have appeared in the literature considering the release problem, the uptake problem and also the coupled problem. However, two significant challenges that remain are in understanding the drug release mechanism(s) and also the determination of the various parameters characterizing the system. These include drug diffusion coefficients and dissolution constants in the stent polymer coating as well as drug diffusion coefficients, binding/uptake rates and the magnitude of the transmural convection in the arterial wall. In this paper we attempt to address these problems. We provide analytical solutions which, when compared with appropriate experiments, may allow the various parameters of the system to be estimated via the inverse problem. The analytical solutions which we provide here for drug release in vitro may thus be used as a tool for providing insights into the mechanism(s) of release.