A mathematical model of polymeric controlled drug release and transport in the brain

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.

Predictive models for pressure-driven fluid infusions into brain parenchyma

Direct infusions into brain parenchyma of biological therapeutics for serious brain diseases have been, and are being, considered. However, individual brains, as well as distinct cytoarchitectural regions within brains, vary in their response to fluid flow and pressure. Further, the tissue responds dynamically to these stimuli, requiring a nonlinear treatment of equations that would describe fluid flow and drug transport in brain. We here report in detail on an individual-specific model and a comparison of its prediction with simulations for living porcine brains. Two critical features we introduced into our model-absent from previous ones, but requirements for any useful simulation-are the infusion-induced interstitial expansion and the backflow. These are significant determinants of the flow. Another feature of our treatment is the use of cross-property relations to obtain individual-specific parameters that are coefficients in the equations. The quantitative results are at least encouraging, showing a high fraction of overlap between the computed and measured volumes of distribution of a tracer molecule and are potentially clinically useful. Several improvements are called for; principally a treatment of the interstitial expansion more fundamentally based on poroelasticity and a better delineation of the diffusion tensor of a particle confined to the interstitial spaces.

Rigorous mathematical modeling techniques for optimal delivery of macromolecules to the brain

Several treatment modalities for neurodegenerative diseases or tumors of the central nervous system involve invasive delivery of large molecular weight drugs to the brain. Despite the ample record of experimental studies, accurate drug targeting for the human brain remains a challenge. This paper proposes a systematic design method of administering drugs to specific locations in the human brain based on first principles transport in porous media. The proposed mathematical framework predicts achievable treatment volumes in target regions as a function of brain anatomy and infusion catheter position. A systematic procedure to determine the optimal infusion and catheter design parameters that maximize the penetration depth and volumes of distribution will be discussed. The computer simulations are validated with agarose gel phantom experiments and rat data. The rigorous computational approach will allow physicians and scientists to better plan the administration of therapeutic drugs to the central nervous system.

Prediction of convection-enhanced drug delivery to the human brain

The treatment for many neurodegenerative diseases of the central nervous system (CNS) involves the delivery of large molecular weight drugs to the brain. The blood brain barrier, however, prevents many therapeutic molecules from entering the CNS. Despite much effort in studying drug dispersion with animal models, accurate drug targeting in humans remains a challenge. This article proposes an engineering approach for the systematic design of targeted drug delivery into the human brain. The proposed method predicts achievable volumes of distribution for therapeutic agents based on first principles transport and chemical kinetics models as well as accurate reconstruction of the brain geometry from patient-specific diffusion tensor magnetic resonance imaging. The predictive capabilities of the methodology will be demonstrated for invasive intraparenchymal drug administration. A systematic procedure to determine the optimal infusion and catheter design parameters to maximize penetration depth and volumes of distribution in the target area will be discussed. The computational results are validated with agarose gel phantom experiments. The methodology integrates interdisciplinary expertise from medical imaging and engineering. This approach will allow physicians and scientists to design and optimize drug administration in a systematic fashion.

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

The efficacy of radiotherapy can be enhanced by the delivery of radiosensitizer (Etanidazole) to brain tumor from biodegradable polymer implants. This process is investigated by simulation carried out at a cut section of tumor with polymeric wafers of Etanidazole loading implanted in the resected cavity. The coupled mass and momentum equations are solved to obtain the transient solution of the drug distribution in the tumor. The polymeric delivery shows high therapeutic index, indicating the wafers' success in delivering more drugs to the tumor rather than to the tissue. The penetration distance of Etanidazole was found to decrease from 14 mm (at 5th/40th day after implantation) to 6.5 mm (at 30th/75th day), suggesting an initial high burst of drug release which cause nearby tissue toxicity and a low effective drug delivery towards the later stages. The short penetration depth is due to Etanidazole having low interstitial Peclet number and high elimination/diffusion modulus. Edema causes the interstitial pressure, velocity, and concentration to increase in all domains, and leads to enhanced convection and a lowering of therapeutic index. Simulations on the open tumor geometry show significantly lower efficacy of the drug delivery due to the uneven distribution of drug in the tumor zone.

A finite element model for predicting the distribution of drugs delivered intracranially to the brain

Drug therapy to the central nervous system is complicated by the presence of the blood-brain barrier. The development of new drug delivery techniques to overcome this obstacle will be aided by a clear understanding of the transport processes in the brain. A rigorous theoretical framework of the transport of drugs delivered locally to the parenchyma has been developed using the finite element method. Magnetic resonance imaging has been used to track the transport of paramagnetic contrast markers in the brain. The information obtained by postprocessing spin-echo, T1-weighted, and proton density images has been used to refine the mathematical model that includes realistic brain geometry and salient anatomic features and allows for two-dimensional transport of chemical species, including both diffusive and convective contributions. In addition, the effects of regional differences in tissue properties, ventricular boundary, and edema on the transport have been considered. The model has been used to predict transport of interleukin-2 in the brain and study the major determinants of transport, at both early and late times after drug delivery.