Mathematical Modelling of Convection Enhanced Delivery of Carmustine and Paclitaxel for Brain Tumour Therapy

Mathematical modelling of microneedle-mediated transdermal delivery of drug nanocarriers into skin tissue and circulatory system

Microneedle-mediated transdermal delivery using nanocarriers can successfully overcome the barrier of the stratum corneum and protect drugs from elimination in skin tissues. However, the effectiveness of drug delivery to different layers of skin tissues and the circulatory system varies considerably, subject to the properties of the drug delivery system and delivery regime. How to maximise delivery outcomes remains unclear. In this study, mathematical modelling is employed to investigate this transdermal delivery under various conditions, using the skin model that is reconstructed based on the realistic skin anatomical structure. Treatment efficacy is evaluated in terms of drug exposure over time. The modelling results demonstrate the complex dependence of drug accumulation and distribution on the nanocarrier properties, microneedle properties and environment in different skin layers and blood. Specifically, delivery outcomes in the entire skin and blood can be improved by increasing the loading dose and reducing microneedle spacing. However, several parameters need to be optimised with respect to the specific location of the target site in the tissue for better treatment; these include the drug release rate, nanocarrier diffusivity in microneedle and skin tissue, nanocarrier transvascular permeability, nanocarrier partition coefficient between tissue and microneedle, microneedle length, wind speed and relative humidity. The delivery is less sensitive to the diffusivity and physical degradation rate of free drugs in microneedle, and their partition coefficient between tissue and microneedle. Results obtained from this study can be used to improve the design of the microneedle-nanocarrier combined drug delivery system and delivery regime.

Convection-Enhanced Delivery of Antiangiogenic Drugs and Liposomal Cytotoxic Drugs to Heterogeneous Brain Tumor for Combination Therapy

Simple Summary

Although developed anticancer drugs have shown desirable effects in preclinical trials, the clinical efficacy of chemotherapy against brain cancer remains disappointing. One of the important obstacles is the highly heterogeneous environment in tumors. This study aims to evaluate the performance of an emerging treatment using antiangiogenic and cytotoxic drugs. Our mathematical modelling confirms the advantage of this combination therapy in homogenizing the intratumoral environment for better drug delivery outcomes. In addition, the effects of local microvasculature and cell density on this therapy are also discussed. The results would contribute to the development of more effective treatments for brain cancer.

Abstract

Although convection-enhanced delivery can successfully bypass the blood-brain barrier, its clinical performance remains disappointing. This is primarily attributed to the heterogeneous intratumoral environment, particularly the tumor microvasculature. This study investigates the combined convection-enhanced delivery of antiangiogenic drugs and liposomal cytotoxic drugs in a heterogeneous brain tumor environment using a transport-based mathematical model. The patient-specific 3D brain tumor geometry and the tumor’s heterogeneous tissue properties, including microvascular density, porosity and cell density, are extracted from dynamic contrast-enhanced magnetic resonance imaging data. Results show that antiangiogenic drugs can effectively reduce the tumor microvascular density. This change in tissue structure would inhibit the fluid loss from the blood to prevent drug concentration from dilution, and also reduce the drug loss by blood drainage. The comparisons between different dosing regimens demonstrate that the co-infusion of liposomal cytotoxic drugs and antiangiogenic drugs has the advantages of homogenizing drug distribution, increasing drug accumulation, and enlarging the volume where tumor cells can be effectively killed. The delivery outcomes are susceptible to the location of the infusion site. This combination treatment can be improved by infusing drugs at higher microvascular density sites. In contrast, infusion at a site with high cell density would lower the treatment effectiveness of the whole brain tumor. Results obtained from this study can deepen the understanding of this combination therapy and provide a reference for treatment design and optimization that can further improve survival and patient quality of life.

Application of a multicomponent model of convectional reaction-diffusion to description of glucose gradients in a neurovascular unit

A supply of glucose to a nervous tissue is fulfilled by a cerebrovascular network, and further diffusion is known to occur at both an arteriolar and a microvascular level. Despite a direct relation, a blood flow dynamic and reaction-diffusion of metabolites are usually considered separately in the mathematical models. In the present study they are coupled in a multiphysical approach which allows to evaluate the effects of capillary blood flow changes on near-vessels nutrient concentration gradients evidently. Cerebral blood flow (CBF) was described by the non-steady-state Navier-Stokes equations for a non-Newtonian fluid whose constitutive law is given by the Carreau model. A three-level organization of blood–brain barrier (BBB) is modelled by the flux dysconnectivity functions including densities and kinetic properties of glucose transporters. The velocity of a fluid flow in brain extracellular space (ECS) was estimated using Darcy’s law. The equations of reaction-diffusion with convection based on a generated flow field for continues and porous media were used to describe spatial-time gradients of glucose in the capillary lumen and brain parenchyma of a neurovascular unit (NVU), respectively. Changes in CBF were directly simulated using smoothing step-like functions altering the difference of intracapillary pressure in time. The changes of CBF cover both the decrease (on 70%) and the increase (on 50%) in a capillary flow velocity. Analyzing the dynamics of glucose gradients, it was shown that a rapid decrease of a capillary blood flow yields an enhanced level of glucose in a near-capillary nervous tissue if the contacts between astrocytes end-feet are not tight. Under the increased CBF velocities the amplitude of glucose concentration gradients is always enhanced. The introduced approach can be used for estimation of blood flow changes influence not only on glucose but also on other nutrients concentration gradients and for the modelling of distributions of their concentrations near blood vessels in other tissues as well.

Convection-Enhanced Delivery In Silico Study for Brain Cancer Treatment

Brain cancer therapy remains a formidable challenge in oncology. Convection-enhanced delivery (CED) is an innovative and promising local drug delivery method for the treatment of brain cancer, overcoming the challenges of the systemic delivery of drugs to the brain. To improve our understanding about CED efficacy and drug transport, we present an in silico methodology for brain cancer CED treatment simulation. To achieve this, a three-dimensional finite element formulation is utilized which employs a brain model representation from clinical imaging data and is used to predict the drug deposition in CED regimes. The model encompasses biofluid dynamics and the transport of drugs in the brain parenchyma. Drug distribution is studied under various patho-physiological conditions of the tumor, in terms of tumor vessel wall pore size and tumor tissue hydraulic conductivity as well as for drugs of various sizes, spanning from small molecules to nanoparticles. Through a parametric study, our contribution reports the impact of the size of the vascular wall pores and that of the therapeutic agent on drug distribution during and after CED. The in silico findings provide useful insights of the spatio-temporal distribution and average drug concentration in the tumor towards an effective treatment of brain cancer.

Role of Tissue Hydraulic Permeability in Convection-Enhanced Delivery of Nanoparticle-Encapsulated Chemotherapy Drugs to Brain Tumour

PURPOSE

Tissue hydraulic permeability of brain tumours can vary considerably depending on the tissue microstructure, compositions in interstitium and tumour cells. Its effects on drug transport and accumulation remain poorly understood.

METHODS

Mathematical modelling is applied to predict the drug delivery outcomes in tumours with different tissue permeability upon convection-enhanced delivery. The modelling is based on a 3-D realistic tumour model that is extracted from patient magnetic resonance images.

RESULTS

Modelling results show that infusing drugs into a permeable tumour can facilitate a more favourable hydraulic environment for drug transport. The infused drugs will exhibit a relatively uniform distribution and cover a larger tumour volume for effective cell killing. Cross-comparisons show the delivery outcomes are more sensitive to the changes in tissue hydraulic permeability and blood pressure than the fluid flow from the brain ventricle. Quantitative analyses demonstrate that increasing the fluid gain from both the blood and brain ventricle can further improve the interstitial fluid flow, and thereby enhance the delivery outcomes. Furthermore, similar responses to the changes in tissue hydraulic permeability can be found for different types of drugs.

CONCLUSIONS

Tissue hydraulic permeability as an intrinsic property can influence drug accumulation and distribution. Results from this study can deepen the understanding of the interplays between drug and tissues that are involved in the drug delivery processes in chemotherapy.

Effect of Particle Size and Surface Charge on Nanoparticles Diffusion in the Brain White Matter

Purpose

Brain disorders have become a serious problem for healthcare worldwide. Nanoparticle-based drugs are one of the emerging therapies and have shown great promise to treat brain diseases. Modifications on particle size and surface charge are two efficient ways to increase the transport efficiency of nanoparticles through brain-blood barrier; however, partly due to the high complexity of brain microstructure and limited visibility of Nanoparticles (NPs), our understanding of how these two modifications can affect the transport of NPs in the brain is insufficient.

Methods

In this study, a framework, which contains a stochastic geometric model of brain white matter (WM) and a mathematical particle tracing model, was developed to investigate the relationship between particle size/surface charge of the NPs and their effective diffusion coefficients (D) in WM.

Results

The predictive capabilities of this method have been validated using published experimental tests. For negatively charged NPs, both particle size and surface charge are positively correlated with D before reaching a size threshold. When Zeta potential (Zp) is less negative than -10 mV, the difference between NPs’ D in WM and pure interstitial fluid (IF) is limited.

Conclusion

A deeper understanding on the relationships between particle size/surface charge of NPs and their D in WM has been obtained. The results from this study and the developed modelling framework provide important tools for the development of nano-drugs and nano-carriers to cure brain diseases.

Insights into Infusion-Based Targeted Drug Delivery in the Brain: Perspectives, Challenges and Opportunities

Targeted drug delivery in the brain is instrumental in the treatment of lethal brain diseases, such as glioblastoma multiforme, the most aggressive primary central nervous system tumour in adults. Infusion-based drug delivery techniques, which directly administer to the tissue for local treatment, as in convection-enhanced delivery (CED), provide an important opportunity; however, poor understanding of the pressure-driven drug transport mechanisms in the brain has hindered its ultimate success in clinical applications. In this review, we focus on the biomechanical and biochemical aspects of infusion-based targeted drug delivery in the brain and look into the underlying molecular level mechanisms. We discuss recent advances and challenges in the complementary field of medical robotics and its use in targeted drug delivery in the brain. A critical overview of current research in these areas and their clinical implications is provided. This review delivers new ideas and perspectives for further studies of targeted drug delivery in the brain.

Mathematical modelling of nanoparticle-mediated topical drug delivery to skin tissue

Nanoparticles have been extensively studied to improve drug delivery outcomes, however, their use in topical delivery remains controversial. Although the feasibility to cross the human skin barrier has been demonstrated in experiments, the risk of low drug concentration in deep tissue still limits the application. In this study, mathematical modelling is employed to examine the performance of nanoparticle-mediated topical delivery for sending drugs into the deep skin tissue. The pharmacokinetic effect is evaluated based on the drug exposure over time. As compared to the delivery using plain drugs, nanoparticle-mediated topical delivery has the potential to significantly improve the drug exposure in deep skin tissue. Modelling predictions denote that the importance of sufficient long-term drug-skin contact in achieving effective drug deposition in the deep skin tissue. The delivery outcomes are highly sensitive to the release rate. Accelerating the release from nanoparticles in stratum corneum is able to improve the drug exposure in stratum corneum and viable epidermis while resulting in the reductions in dermis and blood. The release rate in stratum corneum and viable epidermis should be well-designed below a threshold for generating effective drug accumulation in dermis and blood. A more localised drug accumulation can be achieved in the capillary-rich region of dermis by increasing the local release rate. The release rate in dermis needs to be optimised to increase the drug exposure in the dermis region where there are fewer blood and lymphatics capillaries. Results from this study can be used to improve the regimen of topical delivery for localised treatment.

A numerical study of the distribution of chemotherapeutic drug carmustine in brain glioblastoma

To cure the illness in the brain glioblastoma, the Gliadel wafer, as the first FDA-approved chemotherapy, was available on the market since 1997. Due to the complex studies in vivo, more and more researchers have paid their attention to investigate the dynamic process in the brain by numerical methods. This study aimed to simulate the drug concentration in the cavity after drug releases from Gliadel wafers into the brain tumor by a two-dimensional simulation. The government equations, the parameters, and corresponding initial and boundary conditions are specified. Then the models are discretized and solved by finite element method (FEM) and finite difference method (FDM) based on C++ library Adaptive Finite Element Package (AFEPack) and MATLAB, respectively. First of all, the numerical convergence of the method is studied by numerical results represented in several successively refined meshes, which shows the reliability of our method. In the results from FEM, a steady state of the pressure in the normal tissue can be simulated. As for FDM, the changes of drug concentration are displayed at six different times. The numerical method in this paper is an effective tool for the numerical study on drug release from polymers. Additionally, convection is a critical factor in drug transportation. Moreover, the simulation approach can be used as the guild for remedy optimization and dynamic analysis of other drugs (paclitaxel) for tumor treatment in the clinic. This mathematical model has wide applications about drug release in multiple dosage forms, such as long sustained release microspheres, oral extended release hydrophilic matrix tablets, hydrogel, and sustained release topical rings.

Unveiling a key role of oxaloacetate-glutamate interaction in regulation of respiration and ROS generation in nonsynaptic brain mitochondria using a kinetic model

Glutamate plays diverse roles in neuronal cells, affecting cell energetics and reactive oxygen species (ROS) generation. These roles are especially vital for neuronal cells, which deal with high amounts of glutamate as a neurotransmitter. Our analysis explored neuronal glutamate implication in cellular energy metabolism and ROS generation, using a kinetic model that simulates electron transport details in respiratory complexes, linked ROS generation and metabolic reactions. The analysis focused on the fact that glutamate attenuates complex II inhibition by oxaloacetate, stimulating the latter's transformation into aspartate. Such a mechanism of complex II activation by glutamate could cause almost complete reduction of ubiquinone and deficiency of oxidized form (Q), which closes the main stream of electron transport and opens a way to massive ROS generating transfer in complex III from semiquinone radicals to molecular oxygen. In this way, under low workload, glutamate triggers the respiratory chain (RC) into a different steady state characterized by high ROS generation rate. The observed stepwise dependence of ROS generation on glutamate concentration experimentally validated this prediction. However, glutamate's attenuation of oxaloacetate's inhibition accelerates electron transport under high workload. Glutamate-oxaloacetate interaction in complex II regulation underlies the observed effects of uncouplers and inhibitors and acceleration of Ca2+ uptake. Thus, this theoretical analysis uncovered the previously unknown roles of oxaloacetate as a regulator of ROS generation and glutamate as a modifier of this regulation. The model predicted that this mechanism of complex II activation by glutamate might be operative in situ and responsible for excitotoxicity. Spatial-time gradients of synthesized hydrogen peroxide concentration, calculated in the reaction-diffusion model with convection under a non-uniform local approximation of nervous tissue, have shown that overproduction of H2O2 in a cell causes excess of its level in neighbor cells.

Patient specific, imaging-informed modeling of rhenium-186 nanoliposome delivery via convection-enhanced delivery in glioblastoma multiforme

Convection-enhanced delivery of rhenium-186 (¹⁸⁶Re)-nanoliposomes is a promising approach to provide precise delivery of large localized doses of radiation for patients with recurrent glioblastoma multiforme. Current approaches for treatment planning utilizing convection-enhanced delivery are designed for small molecule drugs and not for larger particles such as¹⁸⁶Re-nanoliposomes. To enable the treatment planning for¹⁸⁶Re-nanoliposomes delivery, we have developed a computational fluid dynamics approach to predict the distribution of nanoliposomes for individual patients. In this work, we construct, calibrate, and validate a family of computational fluid dynamics models to predict the spatio-temporal distribution of¹⁸⁶Re-nanoliposomes within the brain, utilizing patient-specific pre-operative magnetic resonance imaging (MRI) to assign material properties for an advection-diffusion transport model. The model family is calibrated to single photon emission computed tomography (SPECT) images acquired during and after the infusion of¹⁸⁶Re-nanoliposomes for five patients enrolled in a Phase I/II trial (NCT Number NCT01906385), and is validated using a leave-one-out bootstrapping methodology for predicting the final distribution of the particles. After calibration, our models are capable of predicting the mid-delivery and final spatial distribution of¹⁸⁶Re-nanoliposomes with a Dice value of 0.69 ± 0.18 and a concordance correlation coefficient of 0.88 ± 0.12 (mean ± 95% confidence interval), using only the patient-specific, pre-operative MRI data, and calibrated model parameters from prior patients. These results demonstrate a proof-of-concept for a patient-specific modeling framework, which predicts the spatial distribution of nanoparticles. Further development of this approach could enable optimizing catheter placement for future studies employing convection-enhanced delivery.

Multiphysics Modeling and Simulation of Subcutaneous Injection and Absorption of Biotherapeutics: Model Development

PURPOSE

Many monoclonal antibodies (mAbs) are administered via subcutaneous (SC) injection. Local transport and absorption kinetics and mechanisms, however, remain poorly understood. A multiphysics computational model was developed to simulate the injection and absorption processes of a protein solution in the SC tissue.

METHODS

Quantitative relationships among tissue properties and transport behaviors of an injected solution were described by respective physical laws. SC tissue was treated as a 3-dimensional homogenous, poroelastic medium, in which vasculatures and lymphatic vessels were implicitly treated. Tissue deformation was considered, and interstitial fluid flow was modeled by Darcy's law. Transport of the drug mass was described based on diffusion and advection, which was integrated with tissue mechanics and interstitial fluid dynamics.

RESULTS

Injection and absorption of albumin and IgG solutions were simulated. Upon injection, a sharp rise in tissue pressure, porosity, and fluid velocity could be observed at the injection tip. Largest tissue deformation appeared at the model surface. Transport of drug mass out of the injection zone was minimal. Absorption by local lymphatics was found to last several weeks.

CONCLUSIONS

A bottom-up method was developed to simulate drug transport and absorption of protein solutions in skin tissue base on physical principles. The results appear to match experimental observations.

Addressing BBB Heterogeneity: A New Paradigm for Drug Delivery to Brain Tumors

Effective treatments for brain tumors remain one of the most urgent and unmet needs in modern oncology. This is due not only to the presence of the neurovascular unit/blood-brain barrier (NVU/BBB) but also to the heterogeneity of barrier alteration in the case of brain tumors, which results in what is referred to as the blood-tumor barrier (BTB). Herein, we discuss this heterogeneity, how it contributes to the failure of novel pharmaceutical treatment strategies, and why a "whole brain" approach to the treatment of brain tumors might be beneficial. We discuss various methods by which these obstacles might be overcome and assess how these strategies are progressing in the clinic. We believe that by approaching brain tumor treatment from this perspective, a new paradigm for drug delivery to brain tumors might be established.

A 3D brain unit model to further improve prediction of local drug distribution within the brain

The development of drugs targeting the brain still faces a high failure rate. One of the reasons is a lack of quantitative understanding of the complex processes that govern the pharmacokinetics (PK) of a drug within the brain. While a number of models on drug distribution into and within the brain is available, none of these addresses the combination of factors that affect local drug concentrations in brain extracellular fluid (brain ECF). Here, we develop a 3D brain unit model, which builds on our previous proof-of-concept 2D brain unit model, to understand the factors that govern local unbound and bound drug PK within the brain. The 3D brain unit is a cube, in which the brain capillaries surround the brain ECF. Drug concentration-time profiles are described in both a blood-plasma-domain and a brain-ECF-domain by a set of differential equations. The model includes descriptions of blood plasma PK, transport through the blood-brain barrier (BBB), by passive transport via paracellular and transcellular routes, and by active transport, and drug binding kinetics. The impact of all these factors on ultimate local brain ECF unbound and bound drug concentrations is assessed. In this article we show that all the above mentioned factors affect brain ECF PK in an interdependent manner. This indicates that for a quantitative understanding of local drug concentrations within the brain ECF, interdependencies of all transport and binding processes should be understood. To that end, the 3D brain unit model is an excellent tool, and can be used to build a larger network of 3D brain units, in which the properties for each unit can be defined independently to reflect local differences in characteristics of the brain.

Electrokinetic Convection-Enhanced Delivery of Solutes to the Brain

Pressure-induced infusion of solutions into brain tissue is used both in research and in medicine. In medicine, convection enhanced delivery (CED) may be used to deliver agents to localized areas of the brain, such as with gene therapy to functional targets or with deep tumors not readily amenable to resection. However, clinical trials have demonstrated mixed results from CED. CED is limited by a lack of control of the infusion flow path and may cause damage or even neurological deficits due to neuronal distortion. In laboratory research, infusions may be achieved using pressure or using brief bursts of electrical current in iontophoresis. Electrokinetic convection enhanced delivery (ECED) has the potential to deliver drugs and other bioactive substances to local regions in the brain with improved control and lower applied pressures than pressure-based CED. ECED improves control over the infusion profile because the fluid follows the electrical current path and thus can be directed. Both small molecules and macromolecules can be delivered. Here we demonstrate proof-of-principal that electrokinetic (electroosmosis and electrophoresis) convection-enhanced delivery is a viable means for delivering solutes to the brain. We assessed the volume of tissue exposed to the infusates tris(2,2'-bipyridine)ruthenium(II) and fluorescent dextrans. Control of the direction of the transport was also achieved over distances ranging from several hundred micrometers to more than 4 mm. Electrokinetic delivery has the potential to improve control over infusions.

Polymeric Biomaterial Scaffolds for Tumoricidal Stem Cell Glioblastoma Therapy

Glioblastoma (GBM) is the most common primary brain tumor and has a poor prognosis; as such, there is an urgent need to develop innovative new therapies. Tumoricidal stem cells are an emerging therapy that has the potential to combat limitations of traditional local and systemic chemotherapeutic strategies for GBM by providing a source for high, sustained concentrations of tumoricidal agents locally to the tumor. One major roadblock for tumoricidal stem cell therapy is that the persistence of tumoricidal stem cells injected as a cell suspension into the GBM surgical resection cavity is limited. Polymeric biomaterial scaffolds have been utilized to enhance the delivery of tumoricidal stem cells in the surgical resection cavity and extend their persistence in the brain, ultimately increasing their therapeutic efficacy against GBM. In this review, we examine three main scaffold categories explored for tumoricidal stem cell therapy: microcapsules, hydrogels, and electrospun scaffolds. Furthermore, considering the significant impact of surgery on the brain and recurrent GBM, we survey a brief history of orthotopic models of GBM surgical resection.

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.

Application of Transmural Flow Across In Vitro Microvasculature Enables Direct Sampling of Interstitial Therapeutic Molecule Distribution

In vitro prediction of physiologically relevant transport of therapeutic molecules across the microcirculation represents an intriguing opportunity to predict efficacy in human populations. On-chip microvascular networks (MVNs) show physiologically relevant values of molecular permeability, yet like most systems, they lack an important contribution to transport: the ever-present fluid convection through the endothelium. Quantification of transport through the MVNs by current methods also requires confocal imaging and advanced analytical techniques, which can be a bottleneck in industry and academic laboratories. Here, it is shown that by recapitulating physiological transmural flow across the MVNs, the concentration of small and large molecule therapeutics can be directly sampled in the interstitial fluid and analyzed using standard analytical techniques. The magnitudes of transport measured in MVNs reveal trends with molecular size and type (protein versus nonprotein) that are expected in vivo, supporting the use of the MVNs platform as an in vitro tool to predict distribution of therapeutics in vivo.

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.

An on-chip model of protein paracellular and transcellular permeability in the microcirculation

Recent therapeutic success of large-molecule biologics has led to intense interest in assays to measure with precision their transport across the vascular endothelium and into the target tissue. Most current in vitro endothelial models show unrealistically large permeability coefficients due to a non-physiological paracellular transport. Thus, more advanced systems are required to better recapitulate and discern the important contribution of transcellular transport (transcytosis), particularly of pharmaceutically-relevant proteins. Here, a robust platform technology for the measurement of transport through a human endothelium is presented, which utilizes in vitro microvascular networks (MVNs). The self-assembled MVNs recapitulate the morphology and junctional complexity of in vivo capillaries, and express key endothelial vesicular transport proteins. This results in measured permeabilities to large molecules comparable to those observed in vivo, which are orders of magnitude lower than those measured in transwells. The permeability of albumin and immunoglobulin G (IgG), biopharmaceutically-relevant proteins, is shown to occur primarily via transcytosis, with passage of IgG regulated by the receptor FcRn. The physiological relevance of the MVNs make it a valuable tool to assess the distribution of biopharmaceuticals into tissues, and may be used to prioritize candidate molecules from this increasingly important class of therapeutics.

Design of diffusion-controlled drug delivery devices for controlled release of Paclitaxel

Controlled drug delivery devices were predicted in a reverse engineering framework for the controlled release of Paclitaxel, an anti-cancer drug, widely used in the treatment of solid tumors. Using quantitative structure-property relationship models for mutual diffusion coefficients of the drug in biocompatible and biodegradable polymers and partition coefficients of the drug between polymers and blood, a framework was developed to predict optimal drug delivery devices for desired dosage regimens. The validation of the predicted mutual diffusion and partition coefficients using experimental data was reported in previous studies. Optimal design parameters along with selection of most appropriate polymers suitable for different dosage regimens, selected based on current clinical practice, were predicted for maximum bioavailability of the drug while maintaining the released drug concentration in blood within the therapeutic range. Reservoir and monolithic type of diffusion-controlled drug delivery devices of different shapes and sizes were predicted with different initial drug loadings and bioavailability for different dosage regimens. The effects of the released Paclitaxel from these devices on the tumor growth were also modeled using a previously reported mathematical pharmacokinetic-pharmacodynamic model. The proposed approach can easily be used to design other diffusion-controlled drug delivery devices.

Convection enhanced delivery of liposome encapsulated doxorubicin for brain tumour therapy

Convection enhanced delivery is promising to overcome the blood brain barrier. However, the treatment is less efficient in clinic due to the rapid elimination of small molecular drugs in brain tumours. In this study, numerical simulation is applied to investigate the convection enhanced delivery of liposome encapsulated doxorubicin under various conditions, based on a 3-D brain tumour model that is reconstructed from magnetic resonance images. Treatment efficacy is evaluated in terms of the tumour volume where the free doxorubicin concentration is above LD90. Simulation results denote that intracerebral infusion is effective in increasing the interstitial fluid velocity and inhibiting the fluid leakage from blood around the infusion site. Comparisons with direct doxorubicin infusion demonstrate the advantages of liposomes in enhancing the doxorubicin accumulation and penetration in the brain tumour. Delivery outcomes are determined by both the intratumoural environment and properties of therapeutic agents. The treatment efficacy can be improved by either increasing the liposome solution concentration and infusion rate, administrating liposomes in the tumour with normalised microvasculature density, or using liposomes with low vascular permeability. The delivery is less sensitive to liposome diffusivity in the examined range (E-11~E-7 cm²/s) as convective transport is dominative in determining the liposome migration. Drug release rate is able to be optimised by keeping a trade-off between enhancing the drug penetration and providing sufficient free doxorubicin for effective cell killing. Results from this study can be used to improve the regimen of CED treatments.

Computational modelling of drug delivery to solid tumour: Understanding the interplay between chemotherapeutics and biological system for optimised delivery systems

Drug delivery to solid tumour involves multiple physiological, biochemical and biophysical processes taking place across a wide range of length and time scales. The therapeutic efficacy of anticancer drugs is influenced by the complex interplays among the intrinsic properties of tumours, biophysical aspects of drug transport and cellular uptake. Mathematical and computational modelling allows for a well-controlled study on the individual and combined effects of a wide range of parameters on drug transport and therapeutic efficacy, which would not be possible or economically viable through experimental means. A wide spectrum of mathematical models has been developed for the simulation of drug transport and delivery in solid tumours, including PK/PD-based compartmental models, microscopic and macroscopic transport models, and molecular dynamics drug loading and release models. These models have been used as a tool to identify the limiting factors and for optimal design of efficient drug delivery systems. This article gives an overview of the currently available computational models for drug transport in solid tumours, together with their applications to novel drug delivery systems, such as nanoparticle-mediated drug delivery and convection-enhanced delivery.

Magnetic Oleosome as a Functional Lipophilic Drug Carrier for Cancer Therapy

In the present study, we fabricated magnetic oleosomes functionalized with recombinant proteins as a new carrier for oil-based lipophilic drugs for cancer treatment. The bioengineered oleosome is composed of neutral lipids surrounded by a phospholipid monolayer with embedded oleosin fusion proteins. The oleosin was genetically fused to a nanobody of a green fluorescent protein (GFP). A recombinant protein consisting of immunoglobulin-binding protein LG fused to GFP was used to couple the oleosome to an antibody for targeted delivery to breast cancer cells. The lipid core of the oleosome was loaded with magnetic nanoparticles and carmustine as the lipophilic drug. The magnetic oleosome was characterized using transmission electron microscopy and dynamic light scattering. Moreover, the specific delivery of oleosome into the target cancer cell was investigated via confocal microscopy. To examine the cell viability of the delivered oleosome, a conventional 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide assay was carried out. Furthermore, an animal study was conducted to confirm the effect resulting from the delivery of the anticancer drug-loaded oleosomes. Taken together, the fabricated lipophilic drug-loaded magnetic oleosome can be a powerful tool for oil-based drug delivery agent for cancer therapy.

Convection enhanced delivery of chemotherapeutic drugs into brain tumour

Convection enhanced delivery (CED) of chemotherapeutic drugs can successfully bypass the blood-brain barrier (BBB). However, the treatment efficacy is significantly variable in clinic owing to the absence of proper drugs and the lack of understanding on the local drug transport. In this study, mathematical modelling is employed to investigate the suitability of six chemotherapeutic drugs from the perspective of intratumoural transport, including fluorouracil, carmustine, cisplatin, methotrexate, doxorubicin and paclitaxel. The convection/diffusion/reaction model coupled with Darcy's law is applied to a 3-D realistic brain tumour model that is extracted from magnetic resonance (MR) images. The modelling demonstrates the advantages of CED in enhancing the convective flow of interstitial fluid and reducing the drug concentration dilution caused by the fluid loss from blood stream in the tumour region around the infusion site. The delivery outcomes of the drug in CED treatments are strongly dependent on its physicochemical properties. Convection is more effective in determining the transport of paclitaxel and methotrexate in brain tumour. Paclitaxel exhibits its superiority in drug penetration and accumulation, resulting in the largest effective delivery volume as compared to the other studied drugs. Nanocarrier and diagnostic ultrasound are able to enhance the drug penetration for achieving improved delivery outcomes. Results obtained in this study can serve as a guide for optimising CED treatment regimens.