Computer simulation of the delivery of etanidazole to brain tumor from PLGA wafers: comparison between linear and double burst release systems

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.

Computational Modeling of Interstitial Fluid Pressure and Velocity in Head and Neck Cancer Based on Dynamic Contrast-Enhanced Magnetic Resonance Imaging: Feasibility Analysis

We developed and tested the feasibility of computational fluid modeling (CFM) based on dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) for quantitative estimation of interstitial fluid pressure (IFP) and velocity (IFV) in patients with head and neck (HN) cancer with locoregional lymph node metastases. Twenty-two patients with HN cancer, with 38 lymph nodes, underwent pretreatment standard MRI, including DCE-MRI, on a 3-Tesla scanner. CFM simulation was performed with the finite element method in COMSOL Multiphysics software. The model consisted of a partial differential equation (PDE) module to generate 3D parametric IFP and IFV maps, using the Darcy equation and Ktrans values (min⁻¹, estimated from the extended Tofts model) to reflect fluid influx into tissue from the capillary microvasculature. The Spearman correlation (ρ) was calculated between total tumor volumes and CFM estimates of mean tumor IFP and IFV. CFM-estimated tumor IFP and IFV mean ± standard deviation for the neck nodal metastases were 1.73 ± 0.39 (kPa) and 1.82 ± 0.9 × (10⁻⁷ m/s), respectively. High IFP estimates corresponds to very low IFV throughout the tumor core, but IFV rises rapidly near the tumor boundary where the drop in IFP is precipitous. A significant correlation was found between pretreatment total tumor volume and CFM estimates of mean tumor IFP (ρ = 0.50, P = 0.004). Future studies can validate these initial findings in larger patients with HN cancer cohorts using CFM of the tumor in concert with DCE characterization, which holds promise in radiation oncology and drug-therapy clinical trials.

Evaluation of inverse methods for estimation of mechanical parameters in solid tumors

To treat cancer, knowledge of mechanical parameters can be essential. This study proposes a new approach for estimating hydraulic conductivity (k) and hydraulic conductivity ratio (α) of a living tissue, based on inverse methods, allowing tissue parameter estimation using only a limited set of measurements. First, two population-based algorithms (Levenberg-Marquardt (LM) method and conjugate gradient (CG) method) and two gradient-based algorithms (genetic algorithm (GA) and particle swarm optimization (PSO) algorithm) are considered, and a comparative study between these different inverse methods is performed to determine which methods have a good performance in terms of convergence rate and stability. CG method is shown to perform well in the case of noise-free input data; however, in the case of noisy input data, it fails to converge. The other three methods (LM, GA, and PSO) converge with estimation errors <10% in both noise-free and noisy input data, suggesting their utility to tackle this problem. In the second part, the effectiveness and good accuracy of these robust algorithms (LM, GA, and PSO) are validated with experimental results. The hydraulic conductivity and hydraulic conductivity ratio of a specific living tumor tissue are then estimated for mammary adenocarcinoma (R3230AC). Moreover, assuming measurement of only one-point interstitial pressure inside the tumor, the effect of the location of this one-point on estimation accuracy of hydraulic conductivity is investigated. We show that estimation errors for points measured near the surface and center of the tumor are greater than at other points.

Effects of Focused-Ultrasound-and-Microbubble-Induced Blood-Brain Barrier Disruption on Drug Transport under Liposome-Mediated Delivery in Brain Tumour: A Pilot Numerical Simulation Study

Focused ultrasound (FUS) coupled with microbubbles (MB) has been found to be a promising approach to disrupt the blood-brain barrier (BBB). However, how this disruption affects drug transport remains unclear. In this study, drug transport in combination therapy of liposomes and FUS-MB-induced BBB disruption (BBBD) was investigated based on a multiphysics model. A realistic 3D brain tumour model extracted from MR images was applied. The results demonstrated the advantage of liposomes compared to free doxorubicin injection in further improving treatment when the BBB is opened under the same delivery conditions using burst sonication. This improvement was mainly due to the BBBD-enhanced transvascular transport of free doxorubicin and the sustainable supply of the drug by long-circulating liposomes. Treatment efficacy can be improved in different ways. Disrupting the BBB simultaneously with liposome bolus injection enables more free drug molecules to cross the vessel wall, while prolonging the BBBD duration could accelerate liposome transvascular transport for more effective drug release. However, the drug release rate needs to be well controlled to balance the trade-off among drug release, transvascular exchange and elimination. The results obtained in this study could provide suggestions for the future optimisation of this FUS-MB–liposome combination therapy against brain cancer.

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.

Modelling drug transport during intraperitoneal chemotherapy

Despite a strong rationale for intraperitoneal (IP) chemotherapy, the actual use of the procedure is limited by the poor penetration depth of the drug into the tissue. Drug penetration into solid tumours is a complex mass transport process that involves multiple parameters not only related to the used cytotoxic agent but also to the tumour tissue properties and even the therapeutic setup. Mathematical modelling can provide unique insights into the different transport barriers that occur during IP chemotherapy as well as offer the possibility to test different protocols or drugs without the need for in vivo experiments. In this work, a distinction is made between three different types of model: the lumped parameter model, the distributed model and the cell-based model. For each model, we discuss which steps of the transport process are included and where assumptions are made. Finally, we focus on the advantages and main limitations of each category and discuss some future perspectives for the modelling of IP chemotherapy.

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.

Effect of fluid friction on interstitial fluid flow coupled with blood flow through solid tumor microvascular network

A solid tumor is investigated as porous media for fluid flow simulation. Most of the studies use Darcy model for porous media. In Darcy model, the fluid friction is neglected and a few simplified assumptions are implemented. In this study, the effect of these assumptions is studied by considering Brinkman model. A multiscale mathematical method which calculates fluid flow to a solid tumor is used in this study to investigate how neglecting fluid friction affects the solid tumor simulation. The mathematical method involves processes such as blood flow through vessels and solute and fluid diffusion, convective transport in extracellular matrix, and extravasation from blood vessels. The sprouting angiogenesis model is used for generating capillary network and then fluid flow governing equations are implemented to calculate blood flow through the tumor-induced capillary network. Finally, the two models of porous media are used for modeling fluid flow in normal and tumor tissues in three different shapes of tumors. Simulations of interstitial fluid transport in a solid tumor demonstrate that the simplifications used in Darcy model affect the interstitial velocity and Brinkman model predicts a lower value for interstitial velocity than the values that Darcy model predicts.

Effect of tumor shape, size, and tissue transport properties on drug delivery to solid tumors

Background

The computational methods provide condition for investigation related to the process of drug delivery, such as convection and diffusion of drug in extracellular matrices, drug extravasation from microvessels or to lymphatic vessels. The information of this process clarifies the mechanisms of drug delivery from the injection site to absorption by a solid tumor. In this study, an advanced numerical method is used to solve fluid flow and solute transport equations simultaneously to investigate the effect of tumor shape and size on drug delivery to solid tumor.

Methods

The advanced mathematical model used in our previous work is further developed by adding solute transport equation to the governing equations. After applying appropriate boundary and initial conditions on tumor and surrounding tissue geometry, the element-based finite volume method is used for solving governing equations of drug delivery in solid tumor. Also, the effects of size and shape of tumor and some of tissue transport parameters such as effective pressure and hydraulic conductivity on interstitial fluid flow and drug delivery are investigated.

Results

Sensitivity analysis shows that drug delivery in prolate shape is significantly better than other tumor shapes. Considering size effect, increasing tumor size decreases drug concentration in interstitial fluid. This study shows that dependency of drug concentration in interstitial fluid to osmotic and intravascular pressure is negligible.

Conclusions

This study shows that among diffusion and convection mechanisms of drug transport, diffusion is dominant in most different tumor shapes and sizes. In tumors in which the convection has considerable effect, the drug concentration is larger than that of other tumors at the same time post injection.

Evaluation of a voxelized model based on DCE-MRI for tracer transport in tumor

Recent advances in the treatment of cancer involving therapeutic agents have shown promising results. However, treatment efficacy can be limited due to inadequate and uneven uptake in solid tumors, thereby making the prediction of drug transport important for developing effective therapeutic strategies. In this study, a patient-specific computational porous media model (voxelized model) was developed for predicting the interstitial flow field and distribution of a systemically delivered magnetic resonance (MR) visible tracer in a tumor. The benefits of a voxel approach include less labor and less computational time (approximately an order of magnitude reduction compared to the traditional computational fluid dynamics (CFD) approach developed earlier by our group). The model results were compared with that obtained from a previous approach based on unstructured meshes along with MR-measured tracer concentration data within tumors, using statistical analysis and qualitative representations. The statistical analysis indicated the similarity between the structured and unstructured models' results with a low root mean square error (RMS) and a high correlation coefficient. The voxelized model captured features of the flow field and tracer distribution such as high interstitial fluid pressure inside the tumor and the heterogeneous distribution of the tracer. Predictions of tracer distribution by the voxelized approach also resulted in low RMS error when compared with MR-measured data over a 1 h time course. The similarity in the voxelized model results with experiment and the nonvoxelized model predictions were maintained across three different tumors. Overall, the voxelized model serves as a reliable and swift alternative to approaches using unstructured meshes in predicting extracellular transport within tumors.

Numerical Modeling of Interstitial Fluid Flow Coupled with Blood Flow through a Remodeled Solid Tumor Microvascular Network

Modeling of interstitial fluid flow involves processes such as fluid diffusion, convective transport in extracellular matrix, and extravasation from blood vessels. To date, majority of microvascular flow modeling has been done at different levels and scales mostly on simple tumor shapes with their capillaries. However, with our proposed numerical model, more complex and realistic tumor shapes and capillary networks can be studied. Both blood flow through a capillary network, which is induced by a solid tumor, and fluid flow in tumor’s surrounding tissue are formulated. First, governing equations of angiogenesis are implemented to specify the different domains for the network and interstitium. Then, governing equations for flow modeling are introduced for different domains. The conservation laws for mass and momentum (including continuity equation, Darcy’s law for tissue, and simplified Navier–Stokes equation for blood flow through capillaries) are used for simulating interstitial and intravascular flows and Starling’s law is used for closing this system of equations and coupling the intravascular and extravascular flows. This is the first study of flow modeling in solid tumors to naturalistically couple intravascular and extravascular flow through a network. This network is generated by sprouting angiogenesis and consisting of one parent vessel connected to the network while taking into account the non-continuous behavior of blood, adaptability of capillary diameter to hemodynamics and metabolic stimuli, non-Newtonian blood flow, and phase separation of blood flow in capillary bifurcation. The incorporation of the outlined components beyond the previous models provides a more realistic prediction of interstitial fluid flow pattern in solid tumors and surrounding tissues. Results predict higher interstitial pressure, almost two times, for realistic model compared to the simplified model.

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.

Local drug delivery strategies for cancer treatment: gels, nanoparticles, polymeric films, rods, and wafers

Polymer-based drug delivery depots have been investigated over the last several decades as a means to improve upon the lack of tumor targeting and severe systemic morbidities associated with intravenous chemotherapy treatments. These localized therapies exist in a variety of form factors designed to facilitate the delivery of drug directly to the site of disease in a controlled manner, sparing off-target tissue toxicities. Many of these depots are biodegradable and designed to maintain therapeutic concentrations of drug at the tumor site for a prolonged period of time. Thus a single implantation procedure is required, sometimes coincident with tumor excision surgery, and thereby biodegrading following complete release of the loaded active agent. Even though localized polymer depot delivery systems have been investigated, a surprisingly small subset of these technologies has demonstrated potentially curative preclinical results for cancer applications, and fewer have progressed toward commercialization. The aims of this article are to review the most well-studied and efficacious local polymer delivery systems from the last two decades, to examine the rationale for utilizing drug-eluting polymer implants in cancer patients, and to identify the patient cohorts that could most benefit from localized therapy. Finally, a discussion of the physiological barriers to localized therapy (i.e. drug penetration, transport), technical hurdles, and future outlook of the field is presented.

Sensitivity analysis of an image-based solid tumor computational model with heterogeneous vasculature and porosity

An MR image-based computational model of a murine KHT sarcoma is presented that allows the calculation of plasma fluid and solute transport within tissue. Such image-based models of solid tumors may be used to optimize patient-specific therapies. This model incorporates heterogeneous vasculature and tissue porosity to account for nonuniform perfusion of an MR-visible tracer, gadolinium-diethylenetriamine pentaacetic acid (Gd-DTPA). Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) was conducted following intravenous infusion of Gd-DTPA to provide 1 h of tracer-concentration distribution data within tissue. Early time points (19 min) were used to construct 3D K(trans) and porosity maps using a two-compartment model; tracer transport was predicted at later time points using a 3D porous media model. Model development involved selecting an arterial input function (AIF) and conducting a sensitivity analysis of model parameters (tissue, vascular, and initial estimation of solute concentration in plasma) to investigate the effects on transport for a specific tumor. The developed model was then used to predict transport in two additional tumors. The sensitivity analysis suggests that plasma fluid transport is more sensitive to parameter changes than solute transport due to the dominance of transvascular exchange. Gd-DTPA distribution was similar to experimental patterns, but differences in Gd-DTPA magnitude at later time points may result from inaccurate selection of AIF. Thus, accurate AIF estimation is important for later time point prediction of low molecular weight tracer or drug transport in smaller tumors.

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.

Modeling doxorubicin transport to improve intratumoral drug delivery to RF ablated tumors

A mathematical model of drug transport provides an ideal strategy to optimize intratumoral drug delivery implants to supplement radiofrequency (RF) ablation for tumor treatment. To simulate doxorubicin transport in non-ablated and ablated liver tumors, a one-dimensional, cylindrically symmetric transport model was generated using a finite element method (FEM). Parameters of this model, the diffusion (D) and elimination (gamma) coefficients for doxorubicin, were estimated using drug distributions measured 4 and 8 days after placing biodegradable implants in non-ablated and ablated rabbit VX2 liver carcinomas. In non-ablated tumor, values of diffusion and elimination parameters were 25% and 94% lower than normal liver tissue, respectively. In ablated tumor, diffusion near the ablation center was 75% higher than non-ablated tumor but decreased to the non-ablated tumor value at the ablation periphery. Drug elimination in ablated tumor was zero for the first four days, but by day 8 returned to 98% of the value for non-ablated tumor. Three-dimensional (3-D) simulations of drug delivery from implants with and without RF thermal ablation underscore the benefit of using RF ablation to facilitate local drug distribution. This study demonstrates the use of computational modeling and optimal parameter estimation to predict local drug pharmacokinetics from intratumoral implants after ablation.

Effect of heterogeneous vasculature on interstitial transport within a solid tumor

Novel strategies for cancer treatment involving macromolecular therapeutic agents have been recently developed and show promising results. Inadequate and heterogeneous uptake in tumor tissue has been shown to be a major obstacle for these compounds in clinical cancer therapy. Such distributions have been difficult to account for in predictive models. A three-dimensional computational model was developed to investigate the role of heterogeneous vasculature on interstitial transport within a murine sarcoma. The model accounts for extravasation and extracellular transport in a porous media. Spatial variation of fluid filtration rate per unit volume of tissue and vascular permeability were estimated from a dynamic contrast-enhanced (DCE)-MRI data set. Fluid filtration (L(p)S/V) and permeability (PS/V) maps were embedded in a model of tumor tissue and used to predict interstitial fluid pressure (IFP) and fluid flow. As in previous studies, pressure profiles were predicted to be elevated within the tumor. The model predicted boundary-dependent variation in outwardly directed interstitial velocity with lower velocities predicted near the skin boundary. Simulated tissue distribution of a macromolecular albumin tracer (MW approximately 60 kDa) was found to be heterogeneous with lower concentrations predicted in certain central regions. Simulated distributions of Gd-DTPA tracer (MW approximately 0.57 kDa) were less heterogeneous than albumin tracer. In sensitivity analysis, predicted tracer uptake was enhanced by increasing vascular leakiness. Increasing the interstitial hydraulic conductivity relative to the surrounding tissue reduced the overall drug uptake.

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.

A model to simulate tumour oxygenation and dynamic [18F]-Fmiso PET data

The microenvironment of a tumour, in particular its hypoxic status, is a crucial factor in its response to radiotherapy. Conventional techniques for measuring hypoxia are either invasive or follow surgical intervention, and thus not ideal. Positron emission tomography allows the non-invasive pre-surgical assessment of oxygen status by measuring the spatiotemporal distribution of hypoxia-specific tracers. However, the relationship between levels of uptake and the underlying oxygen tension are yet to be elucidated. Furthermore, it is not fully understood how changes in the underlying physiology affect the appearance of uptake. This paper presents a modular simulation of the tumour microenvironment, underpinned by a probability density function (PDF) to model the vasculature. The model is solved numerically, to simulate both the steady-state oxygenation of a tumour and the spatiotemporal distribution of the hypoxia-specific tracer, [18F]-fluoromisonidazole (Fmiso), in a 2D environment. The results show that using a PDF to represent the vasculature effectively captures the 'hypoxic island' appearance of oxygen-deficient tissues seen ex vivo. Simulated tissue activity curves (TACs) demonstrate the general two-stage trend of empirical data, with an initial perfusion-dominated uptake, followed by hypoxia-specific binding. In well-perfused tissue, activity follows plasma levels in early stages, with binding of Fmiso only becoming apparent at a later stage. In structurally hypoxic tissue, a more gradual initial increase in activity is observed, followed by the same accumulation slope. We demonstrate the utility of theoretical modelling of tracer uptake, by quantifying the changes in TAC structure that arise as a result of altering key physiological characteristics. For example, by decreasing either the proximity of tissue to the vasculature, or the effective diffusion coefficient of Fmiso, we can observe a shift of TAC structure from corresponding to well-perfused to avascular regions, despite wholly different underlying causes.

Local controlled drug delivery to the brain: mathematical modeling of the underlying mass transport mechanisms

The mass transport mechanisms involved in the controlled delivery of drugs to living brain tissue are complex and yet not fully understood. Often the drug is embedded within a polymeric or lipidic matrix, which is directly administered into the brain tissue, that is, intracranially. Different types of systems, including microparticles and disc- or rod-shaped implants are used to control the release rate and, thus, to optimize the drug concentrations at the site of action in the brain over prolonged periods of time. Most of these dosage forms are biodegradable to avoid the need for the removal of empty remnants after drug exhaustion. Various physical and chemical processes are involved in the control of drug release from these systems, including water penetration, drug dissolution, degradation of the matrix and drug diffusion. Once the drug has been released from the delivery system, it has to be transported through the living brain tissue to the target site(s). Again, a variety of phenomena, including diffusion, drug metabolism and degradation, passive or active uptake into CNS tissue and convection can be of importance for the fate of the drug. An overview is given of the current knowledge of the nature of barriers to free access of drug to tumour sites within the brain and the state of the art of: (i) mathematical modeling approaches describing the physical transport processes and chemical reactions which can occur in different types of intracranially administered drug delivery systems, and of (ii) theories quantifying the mass transport phenomena occurring after drug release in the living tissue. Both, simplified as well as complex mathematical models are presented and their major advantages and shortcomings discussed. Interestingly, there is a significant lack of mechanistically realistic, comprehensive theories describing both parts in detail, namely, drug transport in the dosage form and in the living brain tissue. High quality experimental data on drug concentrations in the brain tissue are difficult to obtain, hence this is itself an issue in testing mathematical approaches. As a future perspective, the potential benefits and limitations of these mathematical theories aiming to facilitate the design of advanced intracranial drug delivery systems and to improve the efficiency of the respective pharmacotherapies are discussed.

Barriers to carrier mediated drug and gene delivery to brain tumors

Brain tumor patients face a poor prognosis despite significant advances in tumor imaging, neurosurgery and radiation therapy. Potent chemotherapeutic drugs fail when used to treat brain tumors because biochemical and physiological barriers limit drug delivery into the brain. In the past decade a number of strategies have been introduced to increase drug delivery into the brain parenchyma. In particular, direct drug administration into the brain tumor has shown promising results in both animal models and clinical trials. This technique is well suited for the delivery of liposome and polymer drug carriers, which have the potential to provide a sustained level of drug and to reach cellular targets with improved specificity. We will discuss the current approaches that have been used to increase drug delivery into the brain parenchyma in the context of fluid and solute transport into, through and from the brain, with a focus on liposome and polymer drug carriers.