Simulation of intratumoral release of Etanidazole: effects of the size of surgical opening

Design of Biopolymer-Based Interstitial Therapies for the Treatment of Glioblastoma

Glioblastoma multiforme (GBM) is the most common form of primary brain cancer and has the highest morbidity rate and current treatments result in a bleak 5-year survival rate of 5.6%. Interstitial therapy is one option to increase survival. Drug delivery by interstitial therapy most commonly makes use of a polymer implant encapsulating a drug which releases as the polymer degrades. Interstitial therapy has been extensively studied as a treatment option for GBM as it provides several advantages over systemic administration of chemotherapeutics. Primarily, it can be applied behind the blood–brain barrier, increasing the number of possible chemotherapeutic candidates that can be used and reducing systemic levels of the therapy while concentrating it near the cancer source. With interstitial therapy, multiple drugs can be released locally into the brain at the site of resection as the polymer of the implant degrades, and the release profile of these drugs can be tailored to optimize combination therapy or maintain synergistic ratios. This can bypass the blood–brain barrier, alleviate systemic toxicity, and resolve drug resistance in the tumor. However, tailoring drug release requires appropriate consideration of the complex relationship between the drug, polymer, and formulation method. Drug physicochemical properties can result in intermolecular bonding with the polymeric matrix and affect drug distribution in the implant depending on the formulation method used. This review is focused on current works that have applied interstitial therapy towards GBM, discusses polymer and formulation methods, and provides design considerations for future implantable biodegradable materials.

Tumor Responsive and Tunable Polymeric Platform for Optimized Delivery of Paclitaxel to Treat Glioblastoma

Current interstitial therapies for glioblastoma can overcome the blood-brain barrier but fail to optimally release therapy at a rate that stalls cancer reoccurrence. To address this lapse, acetalated dextran (Ace-DEX) nanofibrous scaffolds were used for their unique degradation rates that translate to a broad range of drug release kinetics. A distinctive range of drug release rates was illustrated via electrospun Ace-DEX or poly(lactic acid) (PLA) scaffolds. Scaffolds composed of fast, medium, and slow degrading Ace-DEX resulted in 14.1%, 2.9%, and 1.3% paclitaxel released per day. To better understand the impact of paclitaxel release rate on interstitial therapy, two clinically relevant orthotopic glioblastoma mouse models were explored: (1) a surgical model of resection and recurrence (resection model) and (2) a distant metastasis model. The effect of unique drug release was illustrated in the resection model when a 78% long-term survival was observed with combined fast and slow release scaffolds, in comparison to a survival of 20% when the same dose is delivered at a medium release rate. In contrast, only the fast release rate scaffold displayed treatment efficacy in the distant metastasis model. Additionally, the acid-sensitive Ace-DEX scaffolds were shown to respond to the lower pH conditions associated with GBM tumors, releasing more paclitaxel in vivo when a tumor was present in contrast to nonacid sensitive PLA scaffolds. The unique range of tunable degradation and stimuli-responsive nature makes Ace-DEX a promising drug delivery platform to improve interstitial therapy for glioblastoma.

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.

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

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

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.

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.

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.

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.

Simulation of gentamicin delivery for the local treatment of osteomyelitis

In order to understand the effect of antibiotics delivery to bone tissue, by biodegradable polymeric drug disc, for the treatment of osteomyelitis, a three-dimensional simulation model is developed. The simulation investigates the effect of pressure-induced convection on drug distribution, by taking into account the pressure gradient that exists between capillaries and interstitial space, and also as a result of the surgical opening. The clotting process at the surgical opening is incorporated into the simulation, and the effect of clotting duration is investigated. The clotting duration for the baseline simulation is 2 days and it is observed that increasing this duration depresses the mean drug concentration in the marrow and cortical bone. The effect of double burst release profile is also studied and it is observed that drug concentration drops too rapidly after the first burst to provide any therapeutic effect. However, it is shown that the drug concentration after the second burst stays above the minimum inhibitory concentration of the bacteria for a longer period of time, than would have been observed for a mono-burst release. Inserting non-biodegradable polymethylmethacrylate (PMMA) beads into bone seems to cause a higher average concentration of drug in the marrow. However, this could be brought about by the difference in the geometry between the disc and the bead, and the amount of drug packed in each bead. Further simulations on the management of dead space shows the ineffectiveness of having the void filled up with surgical gel as it becomes an additional barrier to drug delivery to the infected tissues.