A general model of coupled drug release and tissue absorption for drug delivery devices

Polymeric nanocarriers delivery systems in ischemic stroke for targeted therapeutic strategies

Ischemic stroke is a complex, high-mortality disease with multifactorial etiology and pathogenesis. Currently, drug therapy is mainly used treat ischemic stroke in clinic, but there are still some limitations, such as limited blood-brain barrier (BBB) penetration efficiency, a narrow treatment time window and drug side effects. Recent studies have pointed out that drug delivery systems based on polymeric nanocarriers can effectively improve the insufficient treatment for ischemic stroke. They can provide neuronal protection by extending the plasma half-life of drugs, enhancing the drug's permeability to penetrate the BBB, and targeting specific structures and cells. In this review, we classified polymeric nanocarriers used for delivering ischemic stroke drugs and introduced their preparation methods. We also evaluated the feasibility and effectiveness and discussed the existing limitations and prospects of polymeric nanocarriers for ischemic stroke treatment. We hoped that this review could provide a theoretical basis for the future development of nanomedicine delivery systems for the treatment of ischemic stroke.

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.

Computational modeling of in-stent restenosis: Pharmacokinetic and pharmacodynamic evaluation

Persistence of the pathology of in-stent restenosis even with the advent of drug-eluting stents warrants the development of highly resolved in silico models. These computational models assist in gaining insights into the transient biochemical and cellular mechanisms involved and thereby optimize the stent implantation parameters. Within this work, an already established fully-coupled Lagrangian finite element framework for modeling the restenotic growth is enhanced with the incorporation of endothelium-mediated effects and pharmacological influences of rapamycin-based drugs embedded in the polymeric layers of the current generation drug-eluting stents. The continuum mechanical description of growth is further justified in the context of thermodynamic consistency. Qualitative inferences are drawn from the model developed herein regarding the efficacy of the level of drug embedment within the struts as well as the release profiles adopted. The framework is then intended to serve as a tool for clinicians to tune the interventional procedures patient-specifically.

Quantitative Systems Pharmacology and Machine Learning: A Match Made in Heaven or Hell?

As pharmaceutical development moves from early-stage in vitro experimentation to later in vivo and subsequent clinical trials, data and knowledge are acquired across multiple time and length scales, from the subcellular to whole patient cohort scale. Realizing the potential of this data for informing decision making in pharmaceutical development requires the individual and combined application of machine learning (ML) and mechanistic multiscale mathematical modeling approaches. Here we outline how these two approaches, both individually and in tandem, can be applied at different stages of the drug discovery and development pipeline to inform decision making compound development. The importance of discerning between knowledge and data are highlighted in informing the initial use of ML or mechanistic quantitative systems pharmacology (QSP) models. We discuss the application of sensitivity and structural identifiability analyses of QSP models in informing future experimental studies to which ML may be applied, as well as how ML approaches can be used to inform mechanistic model development. Relevant literature studies are highlighted and we close by discussing caveats regarding the application of each approach in an age of constant data acquisition. SIGNIFICANCE STATEMENT: We consider when best to apply machine learning (ML) and mechanistic quantitative systems pharmacology (QSP) approaches in the context of the drug discovery and development pipeline. We discuss the importance of prior knowledge and data available for the system of interest and how this informs the individual and combined application of ML and QSP approaches at each stage of the pipeline.

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.

Channeling is a distinct class of dissolution in complex porous media

The traditional model of solid dissolution in porous media consists of three dissolution regimes (uniform, compact, wormhole)-or patterns-that are established depending on the relative dominance of reaction rate, flow, and diffusion. In this work, we investigate the evolution of pore structure using numerical simulations during acid injection on two models of increasing complexity. We investigate the boundaries between dissolution regimes and characterize the existence of a fourth dissolution regime called channeling, where initially fast flow pathways are preferentially widened by dissolution. Channeling occurs in cases where the distribution in pore throat size results in orders of magnitude differences in flow rate for different flow pathways. This focusing of dissolution along only dominant flow paths induces an immediate, large change in permeability with a comparatively small change in porosity, resulting in a porosity-permeability relationship unlike any that has been previously seen. This work suggests that the traditional conceptual model of dissolution regimes must be updated to incorporate the channeling regime for reliable forecasting of dissolution in applications like geothermal energy production and geologic carbon storage.

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.

Transdermal Drug Delivery: Determining Permeation Parameters Using Tape Stripping and Numerical Modeling

The function of transdermal drug delivery (TDD) systems is complex due to the multiple layers necessary for controlling the rate of drug release and the interaction with the patient’s skin. In this work, we study a particular aspect of a TDD system, that is, the parameters that describe the drug permeation through the skin layers. Studies of the diffusion of two compounds were carried out and supported by tape stripping and numerical modeling. The experimental studies are carried out for porcine skin in a Franz diffusion cell and tape stripping is used to quantify the concentration of drug in the stratum corneum. A multi-layered numerical model, based on Fickian diffusion, is used to determine the unknown parameters that define the skin’s permeability, such as the partition between layers and the mass transfer coefficients due to the surface barrier. A significant correlation was found between the numerical modeling and experimental results, indicating that the partition and mass transfer effects at the interlayer boundary are accurately represented in the numerical model. We find that numerical modeling is essential to fully describe the diffusion characteristics.

An Overview of In Vitro Drug Release Methods for Drug-Eluting Stents

The drug release profile of drug-eluting stents (DESs) is affected by a number of factors, including the formulation, design, and physicochemical properties of the utilized material. DES has been around for twenty years and despite its widespread clinical use, and efficacy in lowering the rate of target lesion restenosis, it still requires additional development to reduce side effects and provide long-term clinical stability. Unfortunately, for analyzing these implants, there is still no globally accepted in vitro test method. This is owing to the stent's complexity as well as the dynamic arterial compartments of the blood and vascular wall. The former is the source of numerous biological, chemical, and physical mechanisms that are more commonly observed in tissue, lumen, and DES. As a result, universalizing bio-relevant apparatus, suitable for liberation testing of such complex implants is difficult. This article aims to provide a comprehensive review of the methods used for in vitro release testing of DESs. Aspects related to the correlation of the release profiles in the cases of in vitro and in vivo are also addressed.

Super-swelling Hydrogel-forming Microneedle based Transdermal Drug Delivery: Mathematical Modelling, Simulation and Experimental Validation

Super-swelling hydrogel-forming microneedles (HFMNs) based transdermal drug delivery (TDD) is gaining significant interest due to their non-invasiveness and ability to deliver a wide range of drugs. The HFMNs swell by imbibing interstitial skin fluid (ISF), and they facilitate drug transport from the reservoir attached at the base into the skin without polymer dissolution. To develop HFMNs for practical applications, a complete understanding of the drug transport mechanism is required, allowing for controlled TDD and geometrical optimisation. A three-phase system consisting of a reservoir, microneedle, and skin is considered. A mathematical model is developed to incorporate the drug binding within the matrix of the compartment, which was not considered earlier. Super-swelling nature of the HFMNs is incorporated through the swelling ratio obtained experimentally for a polymer. The results are validated with in vitro diffusion studies of ibuprofen sodium (IBU) across excised porcine skin, showing that around 20% of the loaded IBU in lyophilised wafer was delivered in 24 hours. It was observed that increasing IBU solubility in reservoir can achieve high drug transport across the skin. The developed model is shown to be in good agreement with the experimental data. It is concluded that the proposed model can be considered a tool with predictive design and development of super-swelling HFMNs based TDD 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.

An unsteady analysis of two-phase binding of drug in an asymmetric stenosed vessel

In this paper, we investigate endovascular delivery to get a step ahead of the pharmacological limitations it has due to the complexity of dealing with a patient-specific vessel through a mathematical model. We divide the domain of computation into four sub-domains: the lumen, the lumen-tissue interface, the upper tissue and the lower tissue which are extracted from an asymmetric atherosclerotic image derived by the intravascular ultrasound (IVUS) technique. The injected drug at the luminal inlet is transported with the streaming blood which is considered Newtonian. An irreversible uptake kinetics of the injected drug at the lumen-tissue interface from the luminal side to the tissue domains is assumed. Subsequently, the drug is dispersed within the tissue followed by its retention in the extracellular matrix (ECM) and by receptor-mediated binding. The Marker and Cell (MAC) method has been leveraged to get a quantitative insight into the model considered. The effect of the wall absorption parameter on the concentration of all drug forms (free as well as two-phase bound) has been thoroughly investigated, and some other important factors, such as the averaged concentration, the tissue content, the fractional effect, the concentration variance and the effectiveness of drug have been graphically analyzed to gain a clear understanding of endovascular delivery. The simulated results predict that with increasing values of the absorption parameter, the averaged concentrations of all drug forms do decrease. An early saturation of binding sites takes place for smaller values of the absorption parameter, and also rapid saturation of ECM binding sites occurs as compared to receptor binding sites. Results also predict the influence of surface roughness as well as asymmetry of the domain about the centerline on the distribution and retention of drug. A thorough sensitivity analysis has been carried out to determine the influence of some parameters involved.

Mathematical modelling of drug-diffusion from multi-layered capsules/tablets and other drug delivery devices

In this paper, two mathematical models have been formulated by extending the basic reaction-diffusion model, along with suitable initial and boundary conditions to study the drug delivery and its diffusion in biological tissues from multi-layered capsules/tablets and other drug delivery devices (DDDs), respectively. These devices are either taken orally or through other drug-administration routes. The formulated models are solved using the variational finite element method followed by the fundamental matrix method, to study the drug delivery and its diffusion more efficiently. The main aim of this work is to provide an effective model, using optimal mathematical techniques to help researchers and biologists in medicine in decreasing the endeavours and expenses in designing DDDs. The outcomes obtained are compared with the experimental data to demonstrate the validity and the feasibility of the proposed work.

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.

Specific and nonspecific binding of drug eluted from a half-embedded stent in presence of atherosclerotic plaque

This study is dealt with the two-phase binding (specific and nonspecific) of drug eluted from a half- embedded drug-eluting stent in presence of atherosclerotic plaque. The specific binding due to the interaction of drug molecules with specific receptors and nonspecific binding caused by the trapping of drug in the extra-cellular matrix have been paid due attention. An idealised wall consisting of a plaque and a healthy tissue region has been considered. Moreover, a Dirichlet release condition is imposed on the strut surface. In this investigation, a two-dimensional model governing drug transport and its two-phase binding in cylindrical polar coordinate system has been solved numerically by a finite-difference method. Our simulation predicts that plaque behaves like a physical barrier in two types of the binding process and there is an inverse relationship between bound drug concentration and plaque thickness. Simulations show that a single peak profile of drug is noted when the struts are situated one-strut radius apart and as the inter-strut distance increases, the peak concentration falls and distinct peak profiles over each strut are visualised. The model also reveals that in the region downstream of a strut, the concentration of both bound drug forms in the plaque and healthy regions increases, and eventually, the saturation length of binding sites increases. Predicted results show for smaller Damköhler number, the rapid saturation of binding sites takes place and the stent having thinner strut may perform well in terms of effectiveness as well as efficacy in the stent-based delivery.

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.

Mathematical modelling of drug delivery from pH-responsive nanocontainers

Targeted drug delivery systems represent a promising strategy to treat localised disease with minimum impact on the surrounding tissue. In particular, polymeric nanocontainers have attracted major interest because of their structural and morphological advantages and the variety of polymers that can be used, allowing the synthesis of materials capable of responding to the biochemical alterations of the environment. While experimental methodologies can provide much insight, the generation of experimental data across a wide parameter space is usually prohibitively time consuming and/or expensive. To better understand the influence of varying design parameters on the release profile and drug kinetics involved, appropriately-designed mathematical models are of great benefit. Here, we developed a continuum-scale mathematical model to describe drug transport within, and release from, a hollow nanocontainer consisting of a core and a pH-responsive polymeric shell. Our two-layer mathematical model accounts for drug dissolution and diffusion and includes a mechanism to account for trapping of drug molecules within the shell. We conduct a sensitivity analysis to assess the effect of varying the model parameters on the overall behaviour of the system. To demonstrate the usefulness of our model, we focus on the particular case of cancer treatment and calibrate the model against release profile data for two anti-cancer therapeutical agents. We show that the model is capable of capturing the experimentally observed pH-dependent release.

Designing Better Cardiovascular Stent Materials - A Learning Curve

Cardiovascular stents are life-saving devices and one of the top 10 medical breakthroughs of the 21st century. Decades of research and clinical trials have taught us about the effects of material (metal or polymer), design (geometry, strut thickness, and the number of connectors), and drug-elution on vasculature mechanics, hemocompatibility, biocompatibility, and patient health. Recently developed novel bioresorbable stents are intended to overcome common issues of chronic inflammation, in-stent restenosis, and stent thrombosis associated with permanent stents, but there is still much to learn. Increased knowledge and advanced methods in material processing have led to new stent formulations aimed at improving the performance of their predecessors but often comes with potential tradeoffs. This review aims to discuss the advantages and disadvantages of stent material interactions with the host within five areas of contrasting characteristics, such as 1) metal or polymer, 2) bioresorbable or permanent, 3) drug elution or no drug elution, 4) bare or surface-modified, and 5) self-expanding or balloon-expanding perspectives, as they relate to pre-clinical and clinical outcomes and concludes with directions for future studies.

Assessing the influence of atherosclerosis on drug coated balloon therapy using computational modelling

Interventional therapies such as drug-eluting stents (DES) and drug-coated balloons (DCB) have significantly improved the clinical outcomes of patients with coronary occlusions in recent years. Despite this marked improvement, ischemic cardiovascular disease remains the most common cause of death worldwide. To address this, research efforts are focused on improving the safety and efficacy of the next generation of these devices. However, current experimental methods are unable to account for the influence of atherosclerotic lesions on drug uptake and retention. Therefore, in this study, we used an integrated approach utilizing both in vitro and in silico methods to assess the performance of DCB therapy. This approach was validated against existing in vivo results before being used to numerically estimate the effect of the atheroma. A bolus release of sirolimus was observed with our coating matrix. This, coupled with the rapid saturation of specific and non-specific binding sites observed in our study, indicated that increasing the therapeutic dose coated onto the balloons might not necessarily result in greater uptake and/or retention. Additionally, our findings alluded to an optimal exposure time, dependent on the coating matrix, for the DCBs to be expanded against the vessel. Moreover, our findings suggest that a biphasic drug release profile might be beneficial for establishing and maintaining the saturation of bindings sites within severely occluded vessels. Ultimately, we have demonstrated that computational methods may be capable of assessing the efficacy of DCB therapy as well as predict the influence of atherosclerotic lesions on said efficacy.

Strategies for antimicrobial peptide coatings on medical devices: a review and regulatory science perspective

Indwelling and implanted medical devices are subject to contamination by microbial pathogens during surgery, insertion or injection, and ongoing use, often resulting in severe nosocomial infections. Antimicrobial peptides (AMPs) offer a promising alternative to conventional antibiotics to reduce the incidence of such infections, as they exhibit broad-spectrum antimicrobial activity against Gram-negative and Gram-positive bacteria, microbial biofilms, fungi, and viruses. In this review-perspective, we first provide an overview of the progress made in this field over the past decade with an emphasis on the local release of AMPs from implant surfaces and immobilization strategies for incorporating these agents into a wide range of medical device materials. We then provide a regulatory science perspective addressing the characterization and testing of AMP coatings based on the type of immobilization strategy used with a focus on the US market regulatory niche. Our goal is to help narrow the gulf between academic studies and preclinical testing, as well as to support a future literature base in order to develop the regulatory science of antimicrobial coatings.

A Langevin dynamics approach for multi-layer mass transfer problems

We use Langevin dynamics simulations to study the mass diffusion problem across two adjacent porous layers of different transport properties. At the interface between the layers, we impose the Kedem-Katchalsky (KK) interfacial boundary condition that is well suited in a general situation. A detailed algorithm for the implementation of the KK interfacial condition in the Langevin dynamics framework is presented. As a case study, we consider a two-layer diffusion model of a drug-eluting stent. The simulation results are compared with those obtained from the solution of the corresponding continuum diffusion equation, and an excellent agreement is shown.

Modeling diffusion-based drug release inside a nerve conduit in vitro and in vivo validation study

The objective of this work was to develop a model and understand the diffusion of a drug into and throughout a drug delivering nerve conduit from a surrounding reservoir through a hole in the wall separating the lumen of the conduit and the reservoir. A mathematical model based on Fick's law of diffusion was developed using the finite difference method to understand the drug diffusion and the effect of varying device parameters on the concentration of drug delivered from a hole-based drug delivery device. The mathematical model was verified using a physical microfluidic (μFD) model and an in vitro/in vivo release test using prototype devices. The results of the mathematical model evaluation and microfluidic device testing offered positive insight into the reliability and function of the reservoir and hole-based drug delivering nerve conduit. The mathematical model demonstrated how changing device parameters would change the drug concentration inside the device. It was observed that the drug release in the conduit could be tuned by both concentration scaling and changing the hole size or number of holes. Based on the results obtained from the microfluidic device, the error in the mathematical drug release model was shown to be less than 10% when comparing the data obtained from mathematical model and μFD model. The data highlights the flexibility of having a hole-based drug delivery system, since the drug release can be scaled predictably by changing the device parameters or the concentration of the drug in the reservoir. Graphical abstract .

Effect of tissue permeability and drug diffusion anisotropy on convection-enhanced delivery

Although convection-enhanced delivery (CED) can successfully facilitate a bypass of the blood brain barrier, its treatment efficacy remains highly limited in clinic. This can be partially attributed to the brain anisotropic characteristics that lead to the difficulties in controlling the drug spatial distribution. Here, the responses of six different drugs to the tissue anisotropy are examined through a parametric study performed using a multiphysics model, which considers interstitial fluid flow, tissue deformation and interlinked drug transport processes in CED. The delivery outcomes are evaluated in terms of the penetration depth and delivery volume for effective therapy. Simulation results demonstrate that the effective penetration depth in a given direction can be improved with the increase of the corresponding component of anisotropic characteristics. The anisotropic tissue permeability could only reshape the drug distribution in space but has limited contribution to the total effective delivery volume. On the other hand, drugs respond in different ways to the anisotropic diffusivity. The large delivery volumes of fluorouracil, carmustine, cisplatin and doxorubicin could be achieved in relatively isotropic tissue, while paclitaxel and methotrexate are able to cover enlarged regions into anisotropic tissues. Results obtained from this study serve as a guide for the design of CED treatments.

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.

The need for mathematical modelling of spatial drug distribution within the brain

The blood brain barrier (BBB) is the main barrier that separates the blood from the brain. Because of the BBB, the drug concentration-time profile in the brain may be substantially different from that in the blood. Within the brain, the drug is subject to distributional and elimination processes: diffusion, bulk flow of the brain extracellular fluid (ECF), extra-intracellular exchange, bulk flow of the cerebrospinal fluid (CSF), binding and metabolism. Drug effects are driven by the concentration of a drug at the site of its target and by drug-target interactions. Therefore, a quantitative understanding is needed of the distribution of a drug within the brain in order to predict its effect. Mathematical models can help in the understanding of drug distribution within the brain. The aim of this review is to provide a comprehensive overview of system-specific and drug-specific properties that affect the local distribution of drugs in the brain and of currently existing mathematical models that describe local drug distribution within the brain. Furthermore, we provide an overview on which processes have been addressed in these models and which have not. Altogether, we conclude that there is a need for a more comprehensive and integrated model that fills the current gaps in predicting the local drug distribution within the brain.

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.

Improving the Prediction of Local Drug Distribution Profiles in the Brain with a New 2D Mathematical Model

The development of drugs that target the brain is very challenging. A quantitative understanding is needed of the complex processes that govern the concentration–time profile of a drug (pharmacokinetics) within the brain. So far, there are no studies on predicting the drug concentration within the brain that focus not only on the transport of drugs to the brain through the blood–brain barrier (BBB), but also on drug transport and binding within the brain. Here, we develop a new model for a 2D square brain tissue unit, consisting of brain extracellular fluid (ECF) that is surrounded by the brain capillaries. We describe the change in free drug concentration within the brain ECF, by a partial differential equation (PDE). To include drug binding, we couple this PDE to two ordinary differential equations that describe the concentration–time profile of drug bound to specific as well as non-specific binding sites that we assume to be evenly distributed over the brain ECF. The model boundary conditions reflect how free drug enters and leaves the brain ECF by passing the BBB, located at the level of the brain capillaries. We study the influence of parameter values for BBB permeability, brain ECF bulk flow, drug diffusion through the brain ECF and drug binding kinetics, on the concentration–time profiles of free and bound drug.

Predicting patient exposure to nickel released from cardiovascular devices using multi-scale modeling

Many cardiovascular device alloys contain nickel, which if released in sufficient quantities, can lead to adverse health effects. However, in-vivo nickel release from implanted devices and subsequent biodistribution of nickel ions to local tissues and systemic circulation are not well understood. To address this uncertainty, we have developed a multi-scale (material, tissue, and system) biokinetic model. The model links nickel release from an implanted cardiovascular device to concentrations in peri-implant tissue, as well as in serum and urine, which can be readily monitored. The model was parameterized for a specific cardiovascular implant, nitinol septal occluders, using in-vitro nickel release test results, studies of ex-vivo uptake into heart tissue, and in-vivo and clinical measurements from the literature. Our results show that the model accurately predicts nickel concentrations in peri-implant tissue in an animal model and in serum and urine of septal occluder patients. The congruity of the model with these data suggests it may provide useful insight to establish nickel exposure limits and interpret biomonitoring data. Finally, we use the model to predict local and systemic nickel exposure due to passive release from nitinol devices produced using a wide range of manufacturing processes, as well as general relationships between release rate and exposure. These relationships suggest that peri-implant tissue and serum levels of nickel will remain below 5 μg/g and 10 μg/l, respectively, in patients who have received implanted nitinol cardiovascular devices provided the rate of nickel release per device surface area does not exceed 0.074 μg/(cm² d) and is less than 32 μg/d in total.

STATEMENT OF SIGNIFICANCE

The uncertainty in whether in-vitro tests used to evaluate metal ion release from medical products are representative of clinical environments is one of the largest roadblocks to establishing the associated patient risk. We have developed and validated a multi-scale biokinetic model linking nickel release from cardiovascular devices in-vivo to both peri-implant and systemic levels. By providing clinically relevant exposure estimates, the model vastly improves the evaluation of risk posed to patients by the nickel contained within these devices. Our model is the first to address the potential for local and systemic metal ion exposure due to a medical device and can serve as a basis for future efforts aimed at other metal ions and biomedical products.

Mechanistic modelling of drug release from multi-layer capsules

We propose a novel in silico model for computing drug release from multi-layer capsules. The diffusion problem in such heterogeneous layer-by-layer composite medium is described by a system of coupled partial differential equations, which we solve analytically using separation of variables. In addition to the conventional partitioning and mass transfer interlayer conditions, we consider a surface finite mass transfer resistance, which corresponds to the case of a coated capsule. The drug concentration in the core and through all the layers, as well as in the external release medium, is given in terms of a Fourier series that we compute numerically to describe and characterize the drug release mechanism.

Modelling chemistry and biology after implantation of a drug-eluting stent. Part I: Drug transport

Drug-eluting stents have been used widely to prevent restenosis of arteries following percutaneous balloon angioplasty. Mathematical modelling plays an important role in optimising the design of these stents to maximise their efficiency. When designing a drug-eluting stent system, we expect to have a sufficient amount of drug being released into the artery wall for a sufficient period to prevent restenosis. In this paper, a simple model is considered to provide an elementary description of drug release into artery tissue from an implanted stent. From the model, we identified a parameter regime to optimise the system when preparing the polymer coating. The model provides some useful order of magnitude estimates for the key quantities of interest. From the model, we can identify the time scales over which the drug traverses the artery wall and empties from the polymer coating, as well as obtain approximate formulae for the total amount of drug in the artery tissue and the fraction of drug that has released from the polymer. The model was evaluated by comparing to in-vivo experimental data and good agreement was found.

Mechanisms Underlying Drug Delivery to Peripheral Arteries

Delivery of drugs onto arterial targets via endovascular devices commands several principles: dissolution, diffusion, convection, drug binding, barriers to absorption, and interaction between the drug, delivery vehicle, and accepting arterial wall. The understanding of drug delivery in the coronary vasculature is vast; there is ongoing work needed in the peripheral arteries. There are differences that account for some failures of application of coronary technology into the peripheral vascular space. Breakthroughs in peripheral vascular interventional techniques building on current technologies require investigators willing to acknowledge the similarities and differences between these different vascular territories, while developing technologies adapted for peripheral arteries.

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.