Drug-coated balloons (DCBs) are used commonly for delivering drug into diseased arteries. When applied on the inner surface of an artery, drug is transported from the balloon into the multilayer arterial wall through diffusion and advection, where it is ultimately absorbed through binding reactions. Mathematical modeling of these mass transport processes has the potential to help understand and optimize balloon-based drug delivery, thereby ensuring both safety and efficacy. The present work derives a closed-form solution for the multilayer cylindrical convection-diffusion-reaction (CDR) transport problem that occurs in balloon-based endovascular drug delivery. The model is presented for an arbitrary number of layers, and accounts for various transport processes in terms of relevant non-dimensional numbers. Quasi-orthogonality for this multilayer problem is derived. Closed-form expressions for the amounts of drug delivered by the balloon, bound in each arterial layer and lost from the external surfaces are derived. It is shown that only a small fraction of drug from the balloon is actually delivered into the artery during the short exposure time, which is influenced strongly by the diffusion coefficient of the inner-most layer. Further, binding of the drug is found to depend strongly on the reaction coefficient, expressed in terms of the Damköhler number. It is shown that boundary conditions on the inner and outer surfaces, expressed in terms of Sherwood numbers, play a role in drug uptake over a longer time period. The model is general enough to be applicable for a wide variety of scenarios and operational conditions, including an arbitrary number of layers. Results from this work provide fundamental insights into drug transport and uptake processes. In addition, these results may help improve the safety and efficacy of balloon-based drug delivery.

Controlled drug delivery from a multilayer spherical capsule is used for several therapeutic applications. Developing a theoretical understanding of mass transfer in the multilayer capsule is critical for understanding and optimizing targeted drug delivery. This paper presents an analytical solution for the mass transport problem in a general multilayer sphere involving diffusion as well as drug immobilization in various layers due to binding reactions. An eigenvalue-based solution for this multilayer diffusion-reaction problem is derived in terms of various non-dimensional quantities including Sherwood and Damköhler numbers. It is shown that unlike diffusion-reaction problems in heat transfer, the present problem does not admit imaginary eigenvalues. The effect of binding reactions represented by the Damköhler numbers and outer surface boundary condition represented by the Sherwood number on drug delivery profile is analyzed. It is shown that a low Sherwood number not only increases drug delivery time, but also reduces the total mass of drug delivered. The mass of drug delivered is also shown to reduce with increasing Damköhler number. The impact of shell thickness is analyzed. The effect of a thin outer coating is accounted for by lumping the mass transfer resistance in series with convective boundary resistance, and a non-dimensional number involving the thickness and diffusion coefficient of the coating is shown to govern its impact on drug delivery characteristics. The analytical model presented here improves the understanding of mass transfer in a multilayer spherical capsule in presence of binding reactions, and may help design appropriate experiments for down-selecting candidate materials and geometries for drug delivery applications of interest.

Usually, clinicians assess the correct hemodynamic behavior and fetal wellbeing during the gestational age thanks to their professional expertise, with the support of some indices defined for Doppler fetal waveforms. Although this approach has demonstrated to be satisfactory in the most of the cases, it can be largely improved with the aid of more advanced techniques, i.e. numerical analysis and simulation. Another key aspect limiting the analysis is that clinicians rely on a limited number of Doppler waveforms observed during the clinical examination. Moreover, the use of simple velocimetric indicators for deriving possible malfunctions of the fetal cardiovascular system can be misleading, being the fetal assessment based on a mere statistical analysis (comparison with physiological ranges), without any deep physiopathological interpretations of the observed hemodynamic changes. The use of a lumped mathematical model, properly describing the entire fetal cardiovascular system, would be absolutely helpful in this context: by targeting physiological model parameters on the clinical reliefs, we could gain deep insights of the full system. The calibration of model parameters may also help in formulating patient-specific early diagnosis of fetal pathologies. In the present work, we develop a robust parameter estimation algorithm based on two different optimization methods using synthetic data. In particular, we deal with the inverse problem of recognizing the most significant parameters of a lumped fetal circulation model by using time tracings of fetal blood flows and pressures obtained by the model. This represents a first methodological work for the assessment of the accuracy in the identification of model parameters of an algorithm based on closed-loop mathematical model of fetal circulation and opens the way to the application of the algorithm to clinical data.

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.

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.

The present paper represents a first methodological work for the construction of a robust and accurate algorithm for the solution of an inverse problem given by the identification of the parameters of a lumped mathematical model of fetal circulation introduced by G. Pennati et al. (1997). The underlying estimation techniques here applied are two global search meth- ods, respectively a Parameter Space Investigation (PSI) and the Ensemble Kalman Filter (EnKF), with a refinement performed with a local search method, i.e. Levenberg- Marquardt method (LM). The results here presented show the soundness of our methodology and opens the possibility to apply these techniques for the parameter identification of waveforms obtained from Doppler clinical measurements in the next future. Our final goal is to build a non-invasive simulation tool for the description of the circulation of fetuses in the context of a patient-specific model in order to help clinicians in early diagnosis of pathologies like cardiac distress or growth retardation.

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.

We present a mechanistic model of drug release from a multiple emulsion into an external surrounding fluid. We consider a single multilayer droplet where the drug kinetics are described by a pure diffusive process through different liquid shells. The multilayer problem is described by a system of diffusion equations coupled via interlayer conditions imposing continuity of drug concentration and flux. Mass resistance is imposed at the outer boundary through the application of a surfactant at the external surface of the droplet. The two-dimensional problem is solved numerically by finite volume discretization. Concentration profiles and drug release curves are presented for three typical round-shaped (circle, ellipse, and bullet) droplets and the dependency of the solution on the mass transfer coefficient at the surface analyzed. The main result shows a reduced release time for an increased elongation of the droplets.

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.

The migration of endothelial cells (ECs) is critical for various processes including vascular wound healing, tumor angiogenesis, and the development of viable endovascular implants. Recent observations (time-lapse imaging over 12hr periods) in our laboratory of ECs cultured on line patterns - surfaces where cellular adhesion is limited to 15 ?m wide lines - have demonstrated the presence of three distinct migration phenotypes: a) running - cells are polarized and migrate continuously and persistently on the adhesive lines with possible directional changes, b) undecided - cells are elongated and exhibit periodic changes in the direction of their polarization and minimal net migration, and c) tumbling-like - cells migrate persistently for a certain amount of time but then stop and round up for a few hours before spreading again and resuming migration. Because EC migration is regulated by intracellular ATP levels and cellular elongation induced ATP release, we hypothesize that the three migration phenotypes on line patterns, which translate into different cell length variations in time, are related to different intracellular ATP profiles. Thus, we have developed a mathematical model to provide a description of the complex interactions between cell length, cytoskeletal (F-actin) organization, and intracellular ATP concentration. To identify the parameters that reproduce the experimental observations, we have implemented an optimization procedure that yields the parameter values that best fit the experimental data on cell lengths. The results show that depending on the parameter values adopted for the simulations, the different ATP profiles can indeed be obtained. Future work will focus on providing experimental evidence for the involvement of intracellular ATP in determining the three types of migration behavior.

Drug releasing capsules and droplets are largely used in biomedical applications. Such vehicles consist of a drug-loaded core surrounded by a thin semi-permeable layer. Diffusion is by far the dominant mechanism in drug delivery, beside other physico-chemical factors, such as osmosis, drug dissolution, polymer swelling and degradation. We upgrade existing mechanistic models by extending their applications to the composite structures, and characterize the kinetics of the drug eluted from the vehicle into the external targeted medium. We develop a theoretical and computational study aimed at modelling the drug release from a composite spherical core-shell capsule or a double emulsion having either a protective coating or a surfactant, under the assumption of radial symmetry. The problem of release from such a layer-by-layer composite systems is described by a system of coupled partial differential equations, which we solve analytically in terms of Fourier series or using numerical solutions. In addition to the conventional partitioning and interlayer conditions, we consider a finite mass transfer coefficient, to model the resistance at the surface. Expressions for the concentration and the cumulative mass in all layers are given to show the dependence and sensitivity to parameters, such as diffusivity, permeability and partition coefficients. The release curve characterizes the drug transport mechanism and suggests how to guarantee a controlled release. The proposed model constitutes a simple tool to predict the release from composite materials that, measuring their performance or comparing different configurations, can help in designing novel drug delivery systems.

The migration of endothelial cells (ECs) is critical for various processes including vascular wound healing, tumor angiogenesis, and the development of viable endovascular implants. EC migration is regulated by intracellular ATP and recent observations in our laboratory on ECs cultured on line patterns - surfaces where cellular adhesion is limited to 15 m-wide lines that physically confine the cells - have demonstrated very different migration behavior from cells on control unpatterned surfaces. Specifically, while ECs on unpatterned surfaces exhibit random motion in the absence of flow and persistent directed motion under flow, cells on line patterns both in the presence and absence of flow exhibit three distinct migration phenotypes: a) running- cells are polarized and migrate continuously and persistently on the adhesive lines with possible directional changes, b) undecided- cells are elongated and exhibit periodic changes in the direction of their polarization and minimal net migration, and c) tumbling-like - cells migrate persistently for a certain amount of time but then stop and round up for a few hours before spreading again and resuming migration. We hypothesize that the three migration phenotypes on patterns reflect differences in intracellular ATP profiles. Specifically, we propose that running ECs have sufficiently high ATP concentrations at all time in order to elongate, polarize, and migrate. In contrast, we suggest that undecided ECs have an intermediate level of ATP concentration that is sufficiently high for cell spreading but not for sustained polarization and migration. Finally, tumbling-like cells are thought to have low levels of intracellular ATP during the rounding-up phase but manage to "recharge their batteries" so that ATP levels recover sufficiently for the cells to eventually elongate, polarize, and migrate. To test this hypothesis, we have developed a mathematical model that describes the time evolution of intracellular ATP concentration. The computations provide the time dynamics of both EC length and intracellular ATP concentration. The results demonstrate that depending on the parameter values adopted for the simulations, the different hypothesized intracellular ATP profiles can indeed be obtained. Thus, for certain parameter values, we observe a rapid and sustained increase in ATP concentration, corresponding to the hypothesized behavior for running cells. For other parameter values, the ATP concentration remains within an intermediate range throughout, presumably reflecting undecided cells. Finally, for part of the parameter space, we obtain an initial drop in the concentration followed by recovery, as suggested for tumbling-like cells. The results are consistent with the notion that changes in intracellular ATP modulate the phenotype of EC migration on line patterns.

The migration of endothelial cells (ECs) is critical for various processes including vascular wound healing, tumor angiogenesis, and the development of viable endovascular implants. EC migration is regulated by intracellular ATP; thus, elucidating the dynamics of intracellular ATP concentration is important. Recent observations (time-lapse imaging over 12-hr periods) in our laboratory on ECs cultured on line patterns - surfaces where cellular adhesion is limited to 15 ?m-wide lines that physically confine the cells - have demonstrated very different migration behavior from cells on control unpatterned surfaces. Specifically, while ECs on unpatterned surfaces exhibit random motion in the absence of flow and persistent directed motion under flow, cells on line patterns both in the presence and absence of flow exhibit three distinct migration phenotypes (Fig. 1): a) running - cells are polarized and migrate continuously and persistently on the adhesive lines with possible directional changes, b) undecided - cells are elongated and exhibit periodic changes in the direction of their polarization and minimal net migration, and c) tumbling-like - cells migrate persistently for a certain amount of time but then stop and round up for a few hours before spreading again and resuming migration. We hypothesize that the three migration phenotypes on line patterns reflect differences in intracellular ATP profiles. Specifically, we propose that running ECs have sufficiently high ATP concentrations at all time in order to elongate, polarize, and migrate. In contrast, we suggest that undecided ECs have an intermediate level of ATP concentration that is sufficiently high for cell spreading but not for sustained polarization and migration. Finally, tumbling-like cells are thought to have low levels of intracellular ATP during the rounding-up phase but manage to "recharge their batteries" so that ATP levels recover sufficiently for the cells to eventually elongate, polarize, and migrate. To test this hypothesis, we have developed a mathematical model that describes the time evolution of intracellular ATP concentration.

We present a general mechanistic model of mass diffusion for a composite sphere placed in a large ambient medium. The multi-layer problem is described by a system of diffusion equations coupled via interlayer boundary conditions such as those imposing a finite mass resistance at the external surface of the sphere. While the work is applicable to the generic problem of heat or mass transfer in a multi-layer sphere, the analysis and results are presented in the context of drug kinetics for desorbing and absorbing spherical microcapsules. We derive an analytical solution for the concentration in the sphere and in the surrounding medium that avoids any artificial truncation at a finite distance. The closed-form solution in each concentric layer is expressed in terms of a suitably-defined inverse Laplace transform that can be evaluated numerically. Concentration profiles and drug mass curves in the spherical layers and in the external environment are presented and the dependency of the solution on the mass transfer coefficient at the surface of the sphere analyzed.

In this paper, we consider a multi-layer diffusion model of drug release from a composite spherical microcapsule into an external surrounding medium. Based on this model, we present two approaches for estimating the release time, i.e. the time required for the drug-filled capsule to be depleted. Both approaches make use of temporal moments of the drug concentration at the centre of the capsule, which provide useful insight into the timescale of the process and can be computed exactly without explicit calculation of the full transient solution of the multi-layer diffusion model. The first approach, which uses the zeroth and first temporal moments only, provides a crude approximation of the release time taking the form of a simple algebraic expression involving the various parameters in the model (e.g. layer diffusivities, mass transfer coefficients, partition coefficients) while the second approach yields an asymptotic estimate of the release time that depends on consecutive higher moments. Through several test cases, we show that both approaches provide a computationally- cheap and useful tool to quantify the release time of composite microcapsule configurations.

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.

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.

Predicting the release performance of a drug delivery device is an important challenge in pharmaceutics and biomedical science. In this paper, we consider a multi-layer diffusion model of drug release from a composite spherical microcapsule into an external surrounding medium. Based on this model, we present two approaches for estimating the release time, i.e. the time required for the drug-filled capsule to be depleted. Both approaches make use of temporal moments of the drug concentration at the centre of the capsule, which provide useful insight into the timescale of the process and can be computed exactly without explicit calculation of the full transient solution of the multi-layer diffusion model. The first approach, which uses the zeroth and first temporal moments only, provides a crude approximation of the release time taking the form of a simple algebraic expression involving the various parameters in the model (e.g. layer diffusivities, mass transfer coefficients, partition coefficients) while the second approach yields an asymptotic estimate of the release time that depends on consecutive higher moments. Through several test cases, we show that both approaches provide a computationally-cheap and useful tool to quantify the release time of composite microcapsule configurations.