Laplace Transform Based Modeling of Drug Delivery with Reversible Drug Binding in a Multilayer Tissue.

OBJECTIVE: Drug delivery from a drug-loaded device into an adjacent tissue is a complicated process involving drug transport through diffusion and advection, coupled with drug binding kinetics responsible for drug uptake in the tissue. This work presents a theoretical model to predict drug delivery from a device into a multilayer tissue, assuming linear reversible drug binding in the tissue layers. METHODS: The governing mass conservation equations based on diffusion, advection and drug binding in a multilayer cylindrical geometry are written, and solved using Laplace transformation. The model is used to understand the impact of various non-dimensional parameters on the amounts of bound and unbound drug concentrations as functions of time. RESULTS: Good agreement for special cases considered in past work is demonstrated. The effect of forward and reverse binding reaction rates on the multilayer drug binding process is studied in detail. The effect of the nature of the external boundary condition on drug binding and drug loss is also studied. For typical parameter values, results indicate that only a small fraction of drug delivered binds in the tissue. Additionally, the amount of bound drug rises rapidly with time due to early dominance of the forward reaction, reaches a maxima and then decays due to the reverse reaction. CONCLUSIONS: The general model presented here can account for other possible effects such as drug absorption within the device. Besides generalizing past work on drug delivery modeling, this work also offers analytical tools to understand and optimize practical drug delivery devices.

Performance of drug-coated balloons in coronary and below-the-knee arteries: Anatomical, physiological and pathological considerations.

Below-the-knee (infrapopliteal) atherosclerotic disease, which presents as chronic limb-threatening ischemia (CLTI) in nearly 50% of patients, represents a treatment challenge when it comes to the endovascular intervention arm of management. Due to reduced tissue perfusion, patients usually experience pain at rest and atrophic changes correlated to the extent of the compromised perfusion. Unfortunately, the prognosis remains unsatisfactory with 30% of patients requiring major amputation and a mortality rate of 25% within 1 year. To date, randomized multicentre trials of endovascular intervention have shown that drug-eluting stents (DES) increase patency rate and lower target lesion revascularization rate compared to plain balloon angioplasty and bare-metal stents. The majority of these trials recruited patients with focal infrapopliteal lesions, while most patients requiring endovascular intervention have complex and diffuse atherosclerotic disease. Moreover, due to the nature of the infrapopliteal arteries, the use of long DES is limited. Following recent results of drug-coated balloons (DCBs) in the treatment of femoropopliteal and coronary arteries, it was hoped that similar effective results would be achieved in the infrapopliteal arteries. In reality, multicentre trials have failed to support the proposed hypothesis and no advantage was found in using DCBs in comparison to plain balloon angioplasty. This review aims to explore anatomical, physiological and pathological differences between lesions of the infrapopliteal and coronary arteries to explain the differences in outcome when using DCBs.

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.

Genomic structural variation: A complex but important driver of human evolution.

Structural variants (SVs)-including duplications, deletions, and inversions of DNA-can have significant genomic and functional impacts but are technically difficult to identify and assay compared with single-nucleotide variants. With the aid of new genomic technologies, it has become clear that SVs account for significant differences across and within species. This phenomenon is particularly well-documented for humans and other primates due to the wealth of sequence data available. In great apes, SVs affect a larger number of nucleotides than single-nucleotide variants, with many identified SVs exhibiting population and species specificity. In this review, we highlight the importance of SVs in human evolution by (1) how they have shaped great ape genomes resulting in sensitized regions associated with traits and diseases, (2) their impact on gene functions and regulation, which subsequently has played a role in natural selection, and (3) the role of gene duplications in human brain evolution. We further discuss how to incorporate SVs in research, including the strengths and limitations of various genomic approaches. Finally, we propose future considerations in integrating existing data and biospecimens with the ever-expanding SV compendium propelled by biotechnology advancements.

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.

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.

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.

Mathematical modelling of endovascular drug delivery: Balloons versus stents.

The most common treatment for obstructive coronary artery disease (CAD) is the implantation of a permanent drug-eluting stent (DES). Not only has this permanency been associated with delayed healing of the artery, but it also poses challenges when treating subsequent re-narrowing due to in-stent restenosis (ISR). Drug-coated balloons (DCBs) provide a potential solution to each of these issues. While their use has been primarily limited to treating ISR, in recent years, DCBs have emerged as an attractive potential alternative to DESs for the treatment of certain de novo lesions. However, there remain a number of concerns related to the safety and efficacy of these devices. Firstly, unlike DESs, DCBs necessitate a very short drug delivery window, favouring a higher drug loading. Secondly, while the majority of coronary DCBs in Europe are coated with paclitaxel, the potential mortality signal raised with paclitaxel DCBs in peripheral interventions has shifted efforts towards the development of limus-eluting balloons. The purpose of this paper is to provide a computational model that allows drug delivery from DCBs and DESs to be investigated and compared. We present a comprehensive computational framework that employs a 2D-axisymmetric geometry, incorporates two nonlinear phases of drug binding (specific and non-specific) and includes the influence of diffusion and advection, within a multilayer arterial wall. We utilise this framework to (i) simulate drug delivery from different types of balloon platform; (ii) explore the influence of DCB application time; (iii) elucidate the importance on release kinetics of elevated pressure during DCB application; (iv) compare DCB delivery of two different drugs (sirolimus and paclitaxel) and; (v) compare simulations of DESs versus DCBs. Key measures of comparison are related to safety (drug content in tissue, DC) and efficacy (specific binding site saturation, %SBSS) markers. Our results highlight the pros and cons of each device in terms of DC and %SBSS levels achieved and, moreover, indicate the potential for designing a DCB that gives rise to sufficiently similar safety and efficacy indicators as current commercial DESs.

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.

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.

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.

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.

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.

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.

How does stent expansion alter drug transport properties of the arterial wall?

Stents have become the most successful device to treat advanced atherosclerotic lesions. However, one of the main issues with these interventions is the development of restenosis. The coating of stents with antiproliferative substances to reduce this effect is now standard, although such drugs can also delay re-endothelialization of the intima. The drug release strategy is therefore a key determinant of drug-eluting stent efficacy. Many mathematical models describing drug transport in arteries have been developed and, usually separately, models describing the mechanics of arterial tissue have been devised. However, the literature is lacking a comprehensive model that adequately takes into account both the mechanical deformation of the porous arterial wall and the resulting impact on drug transport properties. In this paper, we provide the most comprehensive study to date of the effect of stent mechanical expansion on the drug transport properties of a three-layer arterial wall. Our model incorporates the state-of-the art description of the mechanical properties of arterial tissue though an anisotropic, hyperelastic material model and includes a nonlinear saturable binding model to describe drug transport in the arterial wall. We establish relationships between mechanical force generated through device expansion and alteration in diffusion within the arterial wall and perform simulations to elucidate the impact of such alterations in spatio-temporal drug release and tissue uptake. Mechanical deformation of the arterial wall results in modified drug transport properties and tissue drug concentrations, highlighting the importance of coupling solid mechanics with drug transport.