Transient interstitial fluid flow in brain tumors: Effect on drug delivery

Modeling drug transport and absorption in subcutaneous injection of monoclonal antibodies: Impact of tissue deformation, devices, and physiology

The pharmaceutical industry has experienced a remarkable increase in the use of subcutaneous injection of monoclonal antibodies (mAbs), attributed mainly to its advantages in reducing healthcare-related costs and enhancing patient compliance. Despite this growth, there is a limited understanding of how tissue mechanics, physiological parameters, and different injection devices and techniques influence the transport and absorption of the drug. In this work, we propose a high-fidelity computational model to study drug transport and absorption during and after subcutaneous injection of mAbs. Our numerical model includes large-deformation mechanics, fluid flow, drug transport, and blood and lymphatic uptake. Through this computational framework, we analyze the tissue material responses, plume dynamics, and drug absorption. We analyze different devices, injection techniques, and physiological parameters such as BMI, flow rate, and injection depth. Finally, we compare our numerical results against the experimental data from the literature.

Numerical investigation of the pharmacokinetics and pharmacodynamics of the chemotherapeutic drug in avascular and vascular stages of a brain tumor

One of the most commonly used approaches for treating solid tumors is the systemic delivery of chemotherapeutic drugs. However, our understanding of the factors influencing treatment efficacy through this method is still limited. This study presents a comprehensive and realistic mathematical model that incorporates the dynamics of tumor growth, capillary network extension, and drug delivery in a coupled and simultaneous manner. The model covers two stages of tumor growth: avascular and vascular. For tumor growth, a continuum model is employed using the phase field interface-capturing method. The neo-vascularization process is modeled using a hybrid discrete-continuum approach. Additionally, a multi-scale model is used to describe the pharmacokinetics of doxorubicin, considering various agents. The study investigates the effect of haptotaxis and reveals that a higher haptotaxis coefficient leads to faster tumor growth (up to 2.6 times) and a quicker progression to angiogenesis. The impact of tumor-related and drug-related parameters is also examined, including tumor size, tumor sensitivity to the drug, chemotherapy initialization, treatment cycle duration, drug affinity to cells, and drug dose. The findings indicate that chemotherapy is more effective during the angiogenesis stage when active loops have formed. Other clinical methods such as radiotherapy and surgery may be more appropriate during the avascular stage or the transition period between angiogenesis initialization and loop formation. The penetration depth of the drug decreases by approximately 50% with an increase in the drug binding rate to surface-cell receptors. As a result, high-associate-rate drugs are preferred for chemotherapy after active loops have formed, while low-associate-rate drugs are suitable for earlier stages.

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.

Solute Transport across the Lymphatic Vasculature in a Soft Skin Tissue

Convective transport of drug solutes in biological tissues is regulated by the interstitial fluid pressure, which plays a crucial role in drug absorption into the lymphatic system through the subcutaneous (SC) injection. In this paper, an approximate continuum poroelasticity model is developed to simulate the pressure evolution in the soft porous tissue during an SC injection. This poroelastic model mimics the deformation of the tissue by introducing the time variation of the interstitial fluid pressure. The advantage of this method lies in its computational time efficiency and simplicity, and it can accurately model the relaxation of pressure. The interstitial fluid pressure obtained using the proposed model is validated against both the analytical and the numerical solution of the poroelastic tissue model. The decreasing elasticity elongates the relaxation time of pressure, and the sensitivity of pressure relaxation to elasticity decreases with the hydraulic permeability, while the increasing porosity and permeability due to deformation alleviate the high pressure. An improved Kedem-Katchalsky model is developed to study solute transport across the lymphatic vessel network, including convection and diffusion in the multi-layered poroelastic tissue with a hybrid discrete-continuum vessel network embedded inside. At last, the effect of different structures of the lymphatic vessel network, such as fractal trees and Voronoi structure, on the lymphatic uptake is investigated. In this paper, we provide a novel and time-efficient computational model for solute transport across the lymphatic vasculature connecting the microscopic properties of the lymphatic vessel membrane to the macroscopic drug absorption.

Evaluating the reliability of tumour spheroid-on-chip models for replicating intratumoural drug delivery: considering the role of microfluidic parameters

Several tumour spheroid-on-chip models have already been proposed in the literature to conduct high throughput drug screening assays. The microfluidic configurations in these models generally depend on the strategies adopted for spheroid formation and entrapment. However, it is not clear how successful they are to mimic in vivo transport mechanisms. In this study, drug transport in different tumour spheroid-on-chip models is numerically investigated under static and dynamic conditions using porous media theory. Moreover, the treatment of a solid tumour at the initial stage of development is modelled using bolus injection and continuous infusion methods. Then, the results of tumour spheroid-on-chip, including drug concentration, cell viability, as well as pressure and fluid shear stress distributions, are compared with those of the solid tumour, assuming identical transport properties in all models. Finally, a new configuration of the microfluidic device along with the optimal drug concentrations is proposed, which can well imitate a given in vivo situation.

Lymphatic uptake of biotherapeutics through a 3D hybrid discrete-continuum vessel network in the skin tissue

Subcutaneous administration is a common approach for the delivery of biotherapeutics, which is achieved mainly through the absorption across lymphatic vessels. In this paper, the drug transport and lymphatic uptake through a three-dimensional hybrid discrete-continuum vessel network in the skin tissue are investigated through high-fidelity numerical simulations. We find that the local lymphatic uptake through the explicit vessels significantly affects macroscopic drug absorption. The diffusion of drug solute through the explicit vessel network affects the lymphatic uptake after the injection. This effect, however, cannot be captured using previously developed continuum models. The lymphatic uptake is dominated by the convection due to lymphatic drainage driven by the pressure difference, which is rarely studied in experiments and simulations. Furthermore, the effects of injection volume and depth on the lymphatic uptake are investigated in a multi-layered domain. We find that the injection volume significantly affects the rate of lymphatic uptake through the heterogeneous vessel network, while the injection depth has little influence, which is consistent with the experimental results. At last, the binding and metabolism of drug molecules are studied to bridge the simulations to the drug clearance experients. We provide a new approach to study the diffusion and convection of drug molecules into the lymphatic system through the hybrid vessel network.

Does the Extracellular Matrix Support Cell-Cell Communication by Elastic Wave Packets?

The extracellular matrix (ECM) is a fibrous network supporting biological cells and provides them a medium for interaction. Cells modify the ECM by applying traction forces, and these forces can propagate to long ranges and establish a mechanism of mechanical communication between neighboring cells. Previous studies have mainly focused on analysis of static force transmission across the ECM. In this study, we explore the plausibility of dynamic mechanical interaction, expressed as vibrations or abrupt fluctuations, giving rise to elastic waves propagating along ECM fibers. We use a numerical mass-spring model to simulate the longitudinal and transversal waves propagating along a single ECM fiber and across a 2D random fiber network. The elastic waves are induced by an active contracting cell (signaler) and received by a passive neighboring cell (receiver). We show that dynamic wave propagation may amplify the signal at the receiver end and support up to an order of magnitude stronger mechanical cues and longer-ranged communication relative to static transmission. Also, we report an optimal impulse duration corresponding to the most effective transmission, as well as extreme fast impulses, in which the waves are encaged around the active cell and do not reach the neighboring cell, possibly due to the Anderson localization effect. Finally, we also demonstrate that extracellular fluid viscosity reduces, but still allows, dynamic propagation along embedded ECM fibers. Our results motivate future biological experiments in mechanobiology to investigate, on the one hand, the mechanosensitivity of cells to dynamic forces traveling and guided by the ECM and, on the other hand, the impact of ECM architecture and remodeling on dynamic force transmission and its spectral filtering, dispersion, and decay.

Music improves the therapeutic effects of bevacizumab in rats with glioblastoma: Modulation of drug distribution to the brain

Background

The development of new methods for modulation of drug distribution across to the brain is a crucial step in the effective therapies for glioblastoma (GBM). In our previous work, we discovered the phenomenon of music-induced opening of the blood-brain barrier (OBBB) in healthy rodents. In this pilot study on rats, we clearly demonstrate that music-induced BBB opening improves the therapeutic effects of bevacizumab (BZM) in rats with GBM via increasing BZM distribution to the brain along the cerebral vessels.

Methods

The experiments were performed on Wistar male rats (200–250 g, n=161) using transfected C6-TagRFP cell line and the loud rock music for OBBB. The OBBB was assessed by spectrofluorometric assay of Evans Blue (EB) extravasation and confocal imaging of fluorescent BZM (fBZM) delivery into the brain. Additionally, distribution of fBZM and Omniscan in the brain was studied using fluorescent and magnetic resonance imaging (MRI), respectively. To analyze the therapeutic effects of BZM on the GBM growth in rats without and with OBBB, the GBM volume (MRI scans), as well as immunohistochemistry assay of proliferation (Ki67 marker) and apoptosis (Bax marker) in the GBM cells were studied. The Mann–Whitney–Wilcoxon test was used for all analysis, the significance level was p < 0.05, n=7 in each group.

Results

Our finding clearly demonstrates that music-induced OBBB increases the delivery of EB into the brain tissues and the extravasation of BZM into the brain around the cerebral vessels of rats with GBM. Music significantly increases distribution of tracers (fBZM and Omniscan) in the rat brain through the pathways of brain drainage system (perivascular and lymphatic), which are an important route of drug delivery into the brain. The music-induced OBBB improves the suppressive effects of BZM on the GBM volume and the cellular mechanisms of tumor progression that was accompanied by higher survival among rats in the GBM+BZM+Music group vs. other groups.

Conclusion

We hypothesized that music improves the therapeutic effects of BZM via OBBB in the normal cerebral vessels and lymphatic drainage of the brain tissues. This contributes better distribution of BZM in the brain fluids and among the normal cerebral vessels, which are used by GBM for invasion and co-opt existing vessels as a satellite tumor form. These results open the new perspectives for an improvement of therapeutic effects of BZM via the music-induced OBBB for BZM in the normal cerebral vessels, which are used by GBM for migration and progression.

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.

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.

Transport and Lymphatic Uptake of Biotherapeutics Through Subcutaneous Injection

Drug transport and uptake in the subcutaneous tissue receives increasing attention in biomechanical and pharmaceutical researches, as subcutaneous administration becomes a common approach for the delivery of biotherapeutics, such as monoclonal antibodies. In this paper, high-fidelity numerical simulations are used to investigate the mechanisms governing drug transport and absorption in the subcutaneous tissue, which is expressed as a porous medium modeled by Darcy's law. The effects of tissue properties (permeability and porosity), the injection flow rate, and the vascular permeability of lymphatic vessels on the lymphatic uptake are studied. Additionally, an empirical formula for the lymphatic uptake during the injection is developed based on the numerical results. The roles of lymphatic drainage, blood perfusion, osmotic pressure, and the drug binding to the cells and the extracellular matrix in the lymphatic uptake are systematically studied. Furthermore, the drug distribution and absorption in a multi-layered porous medium are investigated to illustrate the effect of heterogeneity of permeability, as the permeability varies over a wide range in different layers of the tissue (such as dermis, subcutaneous tissue, muscle). While the interstitial pressure plays an essential role in the mechanisms regulating the absorption of free monoclonal antibodies, the binding and metabolism of drug proteins also affect the drug absorption by reducing the total free monoclonal antibodies.

Utilizing Dynamic Contrast-Enhanced Magnetic Resonance Imaging (DCE-MRI) to Analyze Interstitial Fluid Flow and Transport in Glioblastoma and the Surrounding Parenchyma in Human Patients

Background: Glioblastoma (GBM) is the deadliest and most common brain tumor in adults, with poor survival and response to aggressive therapy. Limited access of drugs to tumor cells is one reason for such grim clinical outcomes. A driving force for therapeutic delivery is interstitial fluid flow (IFF), both within the tumor and in the surrounding brain parenchyma. However, convective and diffusive transport mechanisms are understudied. In this study, we examined the application of a novel image analysis method to measure fluid flow and diffusion in GBM patients. Methods: Here, we applied an imaging methodology that had been previously tested and validated in vitro, in silico, and in preclinical models of disease to archival patient data from the Ivy Glioblastoma Atlas Project (GAP) dataset. The analysis required the use of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), which is readily available in the database. The analysis results, which consisted of IFF flow velocity and diffusion coefficients, were then compared to patient outcomes such as survival. Results: We characterized IFF and diffusion patterns in patients. We found strong correlations between flow rates measured within tumors and in the surrounding parenchymal space, where we hypothesized that velocities would be higher. Analyzing overall magnitudes indicated a significant correlation with both age and survival in this patient cohort. Additionally, we found that neither tumor size nor resection significantly altered the velocity magnitude. Lastly, we mapped the flow pathways in patient tumors and found a variability in the degree of directionality that we hypothesize may lead to information concerning treatment, invasive spread, and progression in future studies. Conclusions: An analysis of standard DCE-MRI in patients with GBM offers more information regarding IFF and transport within and around the tumor, shows that IFF is still detected post-resection, and indicates that velocity magnitudes correlate with patient prognosis.

Image-based spatio-temporal model of drug delivery in a heterogeneous vasculature of a solid tumor - Computational approach

The solute transport distribution in a tumor is an important criterion in the evaluation of the cancer treatment efficacy. The fraction of killed cells after each treatment can quantify the therapeutic effect and plays as a helpful tool to evaluate the chemotherapy treatment schedules. In the present study, an image-based spatio-temporal computational model of a solid tumor is provided for calculation of interstitial fluid flow and solute transport. Current model incorporates heterogeneous microvasculature for angiogenesis instead of synthetic mathematical modeling. In this modeling process, a comprehensive model according to Convection-Diffusion-Reaction (CDR) equations is employed due to its high accuracy for simulating the binding and the uptake of the drug by tumor cells. Based on the velocity and the pressure distribution, transient distribution of the different drug concentrations (free, bound, and internalized) is calculated. Then, the fraction of killed cells is obtained according to the internalized concentration. Results indicate the dependence of the drug distribution on both time and space, as well as the microvasculature density. Free and bound drug concentration have the same trend over time, whereas, internalized and total drug concentration increases over time and reaches a constant value. The highest amount of concentration occurred in the tumor region due to the higher permeability of the blood vessels. Moreover, the fraction of killed cells is approximately 78.87% and 24.94% after treatment with doxorubicin for cancerous and normal tissues, respectively. In general, the presented methodology may be applied in the field of personalized medicine to optimize patient-specific treatments. Also, such image-based modeling of solid tumors can be used in laboratories that working on drug delivery and evaluating new drugs before using them for any in vivo or clinical studies.

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.

Mathematical modeling of intraperitoneal drug delivery: simulation of drug distribution in a single tumor nodule

The intraperitoneal (IP) administration of chemotherapy is an alternative treatment for peritoneal carcinomatosis, allowing for higher intratumor concentrations of the cytotoxic agent compared to intravenous administration. Nevertheless, drug penetration depths are still limited to a few millimeters. It is thus necessary to better understand the limiting factors behind this poor penetration in order to improve IP chemotherapy delivery. By developing a three-dimensional computational fluid dynamics (CFD) model for drug penetration in a tumor nodule, we investigated the impact of a number of key parameters on the drug transport and penetration depth during IP chemotherapy. Overall, smaller tumors showed better penetration than larger ones, which could be attributed to the lower IFP in smaller tumors. Furthermore, the model demonstrated large improvements in penetration depth by subjecting the tumor nodules to vascular normalization therapy, and illustrated the importance of the drug that is used for therapy. Explicitly modeling the necrotic core had a limited effect on the simulated penetration. Similarly, the penetration depth remained virtually constant when the Darcy permeability of the tissue changed. Our findings illustrate that the developed parametrical CFD model is a powerful tool providing more insight in the drug transport and penetration during IP chemotherapy.

Mathematical modeling and optimal control problems in brain tumor targeted drug delivery strategies

In this paper, we present a mathematical model that describes tumor-normal cells interaction dynamics focusing on role of drugs in treatment of brain tumors. The goal is to predict distribution and necessary quantity of drugs delivered in drug-therapy by using optimal control framework. The model describes interactions of tumor and normal cells using a system of reactions–diffusion equations involving the drug concentration, tumor cells and normal tissues. The control estimates simultaneously blood perfusion rate, reabsorption rate of drug and drug dosage administered, which affect the effects of brain tumor chemotherapy. First, we develop mathematical framework which models the competition between tumor and normal cells under chemotherapy constraints. Then, existence, uniqueness and regularity of solution of state equations are proved as well as stability results. Afterwards, optimal control problems are formulated in order to minimize the drug delivery and tumor cell burden in different situations. We show existence and uniqueness of optimal solution, and we derive necessary conditions for optimality. Finally, to solve numerically optimal control and optimization problems, we propose and investigate an adjoint multiple-relaxation-time lattice Boltzmann method for a general nonlinear coupled anisotropic convection–diffusion system (which includes the developed model for brain tumor targeted drug delivery system).

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

PURPOSE

Convection enhanced delivery (CED) is a promising method of anticancer treatment to bypass the blood-brain barrier. This paper is aimed to study drug transport under different CED operating conditions.

METHODS

The convection enhanced delivery of chemotherapeutics to an intact and a remnant brain tumour after resection is investigated by means of mathematical modelling of the key physical and physiological processes of drug transport. Realistic models of brain tumour and its holding tissue are reconstructed from magnetic resonance images. Mathematical modelling is performed for the delivery of carmustine and paclitaxel with different infusion rates, solution concentrations and locations of infusion site.

RESULTS

Modelling predications show that drug penetration can be improved by raising the infusion rate and the infusion solution concentration. The delivery of carmustine with CED is highly localised. High drug concentration only can be achieved around the infusion site. The transport of paclitaxel is more sensitive to CED-enhanced interstitial fluid as compared to carmustine, with deeper penetration into tumour interior. Infusing paclitaxel in the upstream of interstitial fluid flow leads to high spatial averaged concentration and relatively uniform distribution.

CONCLUSION

Results obtained in this study can be used to guide the design and optimisation of CED treatment regimens.

Convection-enhanced Delivery of Therapeutics for Malignant Gliomas

Convection-enhanced delivery (CED) circumvents the blood–brain barrier by delivering agents directly into the tumor and surrounding parenchyma. CED can achieve large volumes of distribution by continuous positive-pressure infusion. Although promising as an effective drug delivery method in concept, the administration of therapeutic agents via CED is not without challenges. Limitations of distribution remain a problem in large brains, such as those of humans. Accurate and consistent delivery of an agent is another challenge associated with CED. Similar to the difficulties caused by immunosuppressive environments associated with gliomas, there are several mechanisms that make effective local drug distribution difficult in malignant gliomas. In this review, methods for local drug application targeting gliomas are discussed with special emphasis on CED. Although early clinical trials have failed to demonstrate the efficacy of CED against gliomas, CED potentially can be a platform for translating the molecular understanding of glioblastomas achieved in the laboratory into effective clinical treatments. Several clinical studies using CED of chemotherapeutic agents are ongoing. Successful delivery of effective agents should prove the efficacy of CED in the near future.

Towards an integrated systems-based modelling framework for drug transport and its effect on tumour cells

Background

A systematic understanding of chemotherapeutic influence on solid tumours is highly challenging and complex as it encompasses the interplay of phenomena occurring at multiple scales. It is desirable to have a multiscale systems framework capable of disentangling the individual roles of multiple contributing factors, such as transport and extracellular factors, and purely intracellular factors, as well as the interactions among these factors. Based on a recently developed systems-based modelling framework, we have developed a coupled system in order to further elucidate the role of drug transport, and its interplay with cellular signalling by incorporating intra- and extra-vascular drug transport in tumour, dynamic descriptions of intracellular signalling and tumour cell density dynamics.

Results

Different aspects of the interaction between transport and cell signalling and the effects of transport parameters have been investigated in silico. Limited drug penetration is found to be a major constraint in inducing drug effect; many aspects of the interaction of transport with cell signalling are independent of the details of cell signalling. A sensitivity analysis indicates that the effect of drug diffusivity depends on the balance between interstitial drug transport and the specific requirement for triggering apoptosis (governed by highly nonlinear signalling networks), suggesting that the effect of drug diffusivity in such cases must be considered in conjunction with descriptions of cellular dynamics.

Conclusions

The modelling framework developed in this study provides qualitative and mechanistic insights into the effect of drug on tumour cells. It provides an in silico experimental platform to investigate the interplay between extracellular factors (e.g. transport) and intracellular factors. Such a platform is essential to understanding the individual and combined effects of transport and cellular factors in solid tumour.

Modeling mass transfer from carmustine-loaded polymeric implants for malignant gliomas

Significant advances in the encapsulation and release of drugs from degradable polymers have led to the Food and Drug Administration approval of Gliadel wafers for controlled local delivery of the chemotherapeutic drug carmustine to high-grade gliomas following surgical resection. Due to the localized nature of the delivery method, no pharmacokinetic measurements have been taken in humans. Rather, pharmacokinetic studies in animals and associated modeling have indicated the capability of carmustine to be delivered in high concentrations within millimeters from the implant site over approximately 5 days. Mathematical models have indicated that diffusion has a primary role in transport, which may be complemented by enhanced fluid convection from postsurgical edema in the initial 3 days following implantation. Carmustine's penetration distance is also presumably limited by its lipophilicity and permeability in the capillaries. This review discusses the mathematical models that have been used to predict the release and distribution of carmustine from a polymeric implant. These models provide a theoretical framework for greater understanding of systems for localized drug delivery while highlighting factors that should be considered in clinical applications. In effect, Gliadel wafers and similar drug delivery implants can be optimized with reduction in required time and resources with such a quantitative and integrative approach.

Effect of tumor shape and size on drug delivery to solid tumors

: Tumor shape and size effect on drug delivery to solid tumors are studied, based on the application of the governing equations for fluid flow, i.e., the conservation laws for mass and momentum, to physiological systems containing solid tumors. The discretized form of the governing equations, with appropriate boundary conditions, is developed for predefined tumor geometries. The governing equations are solved using a numerical method, the element-based finite volume method. Interstitial fluid pressure and velocity are used to show the details of drug delivery in a solid tumor, under an assumption that drug particles flow with the interstitial fluid. Drug delivery problems have been most extensively researched in spherical tumors, which have been the simplest to examine with the analytical methods. With our numerical method, however, more complex shapes of the tumor can be studied. The numerical model of fluid flow in solid tumors previously introduced by our group is further developed to incorporate and investigate non-spherical tumors such as prolate and oblate ones. Also the effects of the surface area per unit volume of the tissue, vascular and interstitial hydraulic conductivity on drug delivery are investigated.

Use of mathematical models to understand anticancer drug delivery and its effect on solid tumors

The transport of anticancer drugs and their effect on tumor cells involve a number of physical and biochemical processes. Mathematical modeling provides a tool to help us understand the interaction of these complex processes, thereby contributing to the improvement and optimization of drug delivery. This article starts with a discussion of the biological and physiological properties of tumors, which are often found as barriers to anticancer drug transport and effect. A broad spectrum of mathematical models is reviewed to give an overview of the current state of modeling approaches and different categories of models are outlined. These include pharmacokinetic and transport-based models for the prediction of temporal and temporal-spatial profiles of antidrug concentrations, as well as empirical or deterministic models to describe the effect of drug. We conclude that the systematic elucidation and integration of cellular signal transduction with the biophysical aspects of drug transport will lead to a better understanding of the entire drug-delivery process.

A systems-based mathematical modelling framework for investigating the effect of drugs on solid tumours

Background

Elucidating the effects of drugs on solid tumours is a highly challenging multi-level problem, since this involves many complexities associated with transport and cellular response, which in turn is characterized by highly non-linear chemical signal transduction. Appropriate systems frameworks are needed to seriously address the sources of these complexities, especially from the cellular side.

Results

We develop a skeletal modelling framework incorporating interstitial drug transport, intracellular signal processing and cell population descriptions. The descriptions aim to appropriately capture the nature of information flow. The model is deliberately formulated to start with simple intracellular descriptions so that additional features can be incorporated in a modular fashion. Two kinds of intracellular signalling modules which describe the drug effect were considered, one a monostable switch and the other a bistable switch. Analysis of our model revealed how different drug stimuli can lead to cell killing in the tumour. Interestingly both modules considered exhibited similar trends. The effects of important parameters were also studied.

Conclusions

We have created a predictive systems platform integrating drug transport and cellular response which can be systematically augmented to include additional layers of cellular complexity. Our results indicate that intracellular signalling models which are qualitatively different can give rise to similar behaviour to simple (and typical) stimuli, and that validating intracellular descriptions must be performed with care by considering a variety of drug stimuli.

Numerical modeling of fluid flow in solid tumors

A mathematical model of interstitial fluid flow is developed, based on the application of the governing equations for fluid flow, i.e., the conservation laws for mass and momentum, to physiological systems containing solid tumors. The discretized form of the governing equations, with appropriate boundary conditions, is developed for a predefined tumor geometry. The interstitial fluid pressure and velocity are calculated using a numerical method, element based finite volume. Simulations of interstitial fluid transport in a homogeneous solid tumor demonstrate that, in a uniformly perfused tumor, i.e., one with no necrotic region, because of the interstitial pressure distribution, the distribution of drug particles is non-uniform. Pressure distribution for different values of necrotic radii is examined and two new parameters, the critical tumor radius and critical necrotic radius, are defined. Simulation results show that: 1) tumor radii have a critical size. Below this size, the maximum interstitial fluid pressure is less than what is generally considered to be effective pressure (a parameter determined by vascular pressure, plasma osmotic pressure, and interstitial osmotic pressure). Above this size, the maximum interstitial fluid pressure is equal to effective pressure. As a consequence, drugs transport to the center of smaller tumors is much easier than transport to the center of a tumor whose radius is greater than the critical tumor radius; 2) there is a critical necrotic radius, below which the interstitial fluid pressure at the tumor center is at its maximum value. If the tumor radius is greater than the critical tumor radius, this maximum pressure is equal to effective pressure. Above this critical necrotic radius, the interstitial fluid pressure at the tumor center is below effective pressure. In specific ranges of these critical sizes, drug amount and therefore therapeutic effects are higher because the opposing force, interstitial fluid pressure, is low in these ranges.

Mathematical modeling and simulation of drug release from microspheres: Implications to drug delivery systems

This article aims to provide a comprehensive review of existing mathematical models and simulations of drug release from polymeric microspheres and of drug transport in adjacent tissues. In drug delivery systems, mathematical modeling plays an important role in elucidating the important drug release mechanisms, thus facilitating the development of new pharmaceutical products by a systematic, rather than trial-and-error, approach. The mathematical models correspond to the known release mechanisms, which are classified as diffusion-, swelling-, and erosion-controlled systems. Various practical applications of these models which explain experimental data are illustrated. The effect of gamma-irradiation sterilization on drug release mechanism from erosion-controlled systems will be discussed. The application of existing models to nanoscale drug delivery systems specifically for hydrophobic and hydrophilic molecules is evaluated. The current development of drug transport modeling in tissues utilizing computational fluid dynamics (CFD) will also be described.