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Journal Club Theme of July 2009: Chemotherapeutic Drug Delivery: Understanding of Efflux Kinetics and Diffusion

Ashfaq Adnan's picture

Welcome to July 2009 issue of Journal Club Forum.  In this month, we will discuss some fundamental issues on the design and development of drug delivery systems for treating cancer related health issues.  While cancers have no known cure, some of them can be successfully treated with the combination of surgery and systematic therapy (radiation, hormone or chemo) as long as the tumor is confined within some critical area. For example, some malignant breast cancer such as ductal or lobular carcinoma can be treated with surgery followed by systematic therapy as long as their sizes are five centimeters or below. However, surgically-removed tumors often leave behind a residual cancer cell population. As a result, systemic/widespread chemotherapy is usually injected into the bloodstream to eliminate the remaining cancer cells. Unfortunately, such procedure usually imparts devastating side effects because cancer drugs are nonspecific in activity, and transporting them throughout the bloodstream further reduces their ability to target the right region. This means that they kill both healthy and unhealthy cells. Moreover, a controlled and constant release of drugs often becomes a major challenge. In most cases, a burst release of drug occurs within a short time after the device is uploaded in the body followed by a slow and ineffective amount of release.

A multiscale anatomy of carcinoma will reveal that the microstructure of cancer cells contains some characteristic elements such as specific biomarker receptors and DNA molecules that exclusively differentiate them from healthy cells. If these cancer specific ligands can be intercalated by some functional molecules supplied from an implantable device, then the device can be envisioned to serve as a complementary technology with current systemic therapy to enhance localized treatment efficiency, minimize excess injections/surgeries, and prevent tumor recurrence. Physically, it means we need to have fundamental understanding of:

      (a) Drug efflux kinetics, and

      (b) Diffusion of Drug in the body environment.

We would like to initiate our discussion based on the following articles.

1. Robert Langer, "Drug Delivery and Targeting", Nature, 392, 5-10, 1998.

2. Davis Youhanes Arifin, Lai Yeng Lee, Chi-Hwa Wang, "Mathematical Modeling and Simulation of Drug Release from Microsphere: Implications to drug delivery systems", Advanced Drug Delivery Reviews, 58: 1274-132, 2006.

3. Martin Garnett, Nanomedicine: Delivering Drugs using bottom up nanotechnology, International Journal of Nanoscience, 4, 855-861 (2005).

4. Qinghe Zhao, Bingyun Li, "pH-controlled drug loading and release from biodegradable microcapsules", Nanomedicine: Nanotechnology, Biology and Medicine, 4, 302-310, 2008.

Because of their small size (e.g. the largest dimension of doxorubicin is about 2 nm), cancer treating drug molecules are usually encapsulated with relatively "bulky" anti-inflammatory drug career (e.g. zero dimensional nanostructures) so that their "free escape" into the body can be avoided. Adsorption of drug molecules on nanoparticle careers is done via electrostatic interaction. The immediate question then follows - can we effectively control the loading and release of drug molecules by some external mechanism? Experimentally, it is observed that the salt content or pH of solution has some influence on the loading and release of drug molecules. Since pH indicates the amount of excess "effective" anions and cations of a solution, a variation in pH has direct impact on the electrostatic interactions between charged molecules. Such interactions can be addressed by so called Poisson-Boltzmann Equation

where ε(r) represents the position-dependent dielectric, Ψ(r) represents the electrostatic potential, ρf(r) represents the charge density of the solute, ci represents the concentration of the ion i at a distance of infinity from the solute, zi is the charge of the ion, q is the charge of a proton, kB is the Boltzmann constant, T is the temperature, and λ(r)is a factor for the position-dependent accessibility of position r to the ions in solution. Most cases, the distance dependent parameters (e.g. , ) can not be determined precisely. There are quite a few models available in the literatures, but none of them can quantitatively address the real situation.

Nevertheless, once drugs are released from its career, it is then important to capture their diffusion behavior through the body fluid. Naturally, an understanding of drug diffusion will allow us to understand the controllability of drug dose over time. In principle, drug diffusion is usually modeled by Fick's second law of diffusion:

Where D and C are the diffusion coefficient and drug concentration. The boundary conditions of the system are influence by the mass transfer process at the surface and the volume of the surrounding system. Moreover, the magnitude of diffusion coefficient D significantly alters as drug flows across different regimes of body matrix that makes the quantitative modeling the drug diffusion more challenging.

Apart from the limitations of these continuum models that are applied for macroscale problems, the presence of nanoscale surfaces and interfaces encounters additional problems. For instance, short ranged dispersive forces (e.g. Van der Waals force) across the drug-career-charge interface can become very significant that the electrostatic interactions described by coulombs law may not be adequate. Moreover, structure of fluid near a surface or interface often alters significantly. As a result, modeling and simulation becomes more challenging.

Comments

Hai,

  I am student of IITR, i am working on material behaviour during  defsevere plastic deformation process ,actually this is new area to me,i want your guidance how to make mathemtical modelling and solid modelling of equal channel angular pressing.please give suggestions on this topic ,expecting early reply from you.

Thanking you... 

Ashfaq Adnan's picture

I do not think there is any straight forward answer to your question. In many occasions, if your system encompasses both fluid flow and solid deformation, then it can be considered as a case of fluid-structure interaction (FSI) problem. One way to handle FSI is so called Immersed Finite Element Method (IFEM) where solids are modeled using Lagrangian scheme and fluids are modeled using Eulerian scheme. 

You may want to have a look on this method as guideline. 

Reference # 2 listed in this discussion is a nice review article that covers a wide range of mathematical modeling related to drug delivery system.

Ashfaq Adnan

Post Doctoral Fellow, Mechanical Engineering

Northwestern University, Evanston, Illinois 60208

Researchrs ID: C-4410-2008

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