Numerical Modeling of Drug Delivery to Solid Tumor Microvasculature

Modeling interstitial fluid flow involves processes such as fluid diffusion, convective transport in the extracellular matrix, and extravasation from blood vessels. In all of these processes, computational fluid dynamics can play a crucial role in elucidating the mechanisms of fluid flow in solid tumors and surrounding tissues. To date, microvasculature flow modeling has been most extensively studied with simple tumor shapes and their capillaries at different levels and scales. With our proposed numerical model, however, more complex and realistic tumor shapes and capillary networks can be studied. First, 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. Simulations of interstitial fluid transport in a homogeneous solid tumor demonstrate that, in a uniformly perfused tumor, i.e., one with no necrotic region, the interstitial pressure distribution results in a non-uniform distribution of drug particles. Pressure distribution for different values of necrotic radii is examined, and two new parameters, the critical tumor radius and critical necrotic radius, are defined. In specific ranges of these critical dimensions the interstitial fluid pressure is relatively lower, which in turn leads to a diminished opposing force against drug movement and a subsequently higher drug concentration and potentially enhanced therapeutic effects. In this work, the numerical model of fluid flow in solid tumors is further developed to incorporate and investigate non-spherical tumor shapes such as prolate and oblate ones. Using this enhanced model, tumor shape and size effects on drug delivery to solid tumors are then studied. Based on the assumption that drug particles flow with the interstitial fluid, the pressure and velocity maps of the latter are used to illustrate the drug delivery pattern in a solid tumor. Additionally, the effects of the surface area per unit volume of the tissue, as well as vascular and interstitial hydraulic conductivity on drug delivery efficiency, are investigated. Using a tumor-induced microvasculature architecture instead of a uniform distribution of vessels provides a more realistic model of solid tumors. To this end, continuous and discrete mathematical models of angiogenesis were utilized to observe the effect of matrix density and matrix degrading enzymes on capillary network formation in solid tumors. Additionally, the interactions between matrix-degrading enzymes, the extracellular matrix and endothelial cells are mathematically modeled. Existing continuous and discrete models of angiogenesis were modified to impose the effect of matrix density on the solution. The imposition has been performed by a specific function in movement potential. Implementing realistic boundary and initial conditions showed that, unlike in previous models, the endothelial cells accelerate as they migrate toward the tumor. Now, the tumor-induced microvasculature network can be applied to the model developed in Chapters 2 and 3. Once the capillary network was set up, fluid flow in normal and cancerous tissues was numerically simulated under three conditions: constant and uniform distribution of intravascular pressure in the whole domain, a rigid vascular network, and an adaptable vascular network. First, governing equations of sprouting angiogenesis were implemented to specify the different domains for the network and interstitium. Governing equations for flow modeling were introduced for different domains. The conservation laws for mass and momentum, Darcy’s equation for tissue, and a simplified Navier Stokes equation for blood flow through capillaries were then used for simulating interstitial and intravascular flows. Finally, Starling’s law was used to close this system of equations and to couple the intravascular and extravascular flows. The non-continuous behavior of blood and the adaptability of capillary diameter to hemodynamics and metabolic stimuli were considered in blood flow simulations through a capillary network. This approach provided a more realistic capillary distribution network, very similar to that of the human body. This work describes the first study of flow modeling in solid tumors to realistically couple intravascular and extravascular flow through a network generated by sprouting angiogenesis, consisting of one parent vessel connected to the network. Other key factors incorporated in the model for the first time include capillary adaptation, non-continuous viscosity blood, and phase separation of blood flow in capillary bifurcation. Contrary to earlier studies which arbitrarily assumed veins and arteries to operate on opposite sides of a tumor network, the present approach requires the same vessel to run and from the network. Expanding the earlier models by introducing the outlined components was performed in order to achieve a more-realistic picture of blood flow through solid tumors. Results predict an almost doubled interstitial pressure and are in better agreement with human biology compared to the more simplified models generally in use today

The role of the microvascular network structure on diffusion and consumption of anticancer drugs

We investigate the impact of microvascular geometry on the transport of drugs in solid tumors, focusing on the diffusion and consumption phenomena. We embrace recent advances in the asymptotic homogenization literature starting from a double Darcy—double advection-diffusion-reaction system of partial differential equations that is obtained exploiting the sharp length separation between the intercapillary distance and the average tumor size. The geometric information on the microvascular network is encoded into effective hydraulic conductivities and diffusivities, which are numerically computed by solving periodic cell problems on appropriate microscale representative cells. The coefficients are then injected into the macroscale equations, and these are solved for an isolated, vascularized spherical tumor. We consider the effect of vascular tortuosity on the transport of anticancer molecules, focusing on Vinblastine and Doxorubicin dynamics, which are considered as a tracer and as a highly interacting molecule, respectively. The computational model is able to quantify the treatment performance through the analysis of the interstitial drug concentration and the quantity of drug metabolized in the tumor. Our results show that both drug advection and diffusion are dramatically impaired by increasing geometrical complexity of the microvasculature, leading to nonoptimal absorption and delivery of therapeutic agents. However, this effect apparently has a minor role whenever the dynamics are mostly driven by metabolic reactions in the tumor interstitium, eg, for highly interacting molecules. In the latter case, anticancer therapies that aim at regularizing the microvasculature might not play a major role, and different strategies are to be developed

Numerical simulation of solid tumor blood perfusion and drug delivery during the “vascular normalization window” with antiangiogenic therapy

This Article is provided by the Brunel Open Access Publishing Fund - Copyright @ 2011 Hindawi PublishingTo investigate the influence of vascular normalization on solid tumor blood perfusion and drug delivery, we used the generated blood vessel network for simulations. Considering the hemodynamic parameters changing after antiangiogenic therapies, the results show that the interstitial fluid pressure (IFP) in tumor tissue domain decreases while the pressure gradient increases during the normalization window. The decreased IFP results in more efficient delivery of conventional drugs to the targeted cancer cells. The outcome of therapies will improve if the antiangiogenic therapies and conventional therapies are carefully scheduled

A Review of Mathematical Models for the Formation of\ud Vascular Networks

Mainly two mechanisms are involved in the formation of blood vasculature: vasculogenesis and angiogenesis. The former consists of the formation of a capillary-like network from either a dispersed or a monolayered population of endothelial cells, reproducible also in vitro by specific experimental assays. The latter consists of the sprouting of new vessels from an existing capillary or post-capillary venule. Similar phenomena are also involved in the formation of the lymphatic system through a process generally called lymphangiogenesis.\ud \ud A number of mathematical approaches have analysed these phenomena. This paper reviews the different modelling procedures, with a special emphasis on their ability to reproduce the biological system and to predict measured quantities which describe the overall processes. A comparison between the different methods is also made, highlighting their specific features

Modelling of combination therapy using implantable anticancer drug delivery with thermal ablation in solid tumor.

Local implantable drug delivery system (IDDS) can be used as an effective adjunctive therapy for solid tumor following thermal ablation for destroying the residual cancer cells and preventing the tumor recurrence. In this paper, we develop comprehensive mathematical pharmacokinetic/pharmacodynamic (PK/PD) models for combination therapy using implantable drug delivery system following thermal ablation inside solid tumors with the help of molecular communication paradigm. In this model, doxorubicin (DOX)-loaded implant (act as a transmitter) is assumed to be inserted inside solid tumor (acts as a channel) after thermal ablation. Using this model, we can predict the extracellular and intracellular concentration of both free and bound drugs. Also, Impact of the anticancer drug on both cancer and normal cells is evaluated using a pharmacodynamic (PD) model that depends on both the spatiotemporal intracellular concentration as well as characteristics of anticancer drug and cells. Accuracy and validity of the proposed drug transport model is verified with published experimental data in the literature. The results show that this combination therapy results in high therapeutic efficacy with negligible toxicity effect on the normal tissue. The proposed model can help in optimize development of this combination treatment for solid tumors, particularly, the design parameters of the implant

Multiphase modeling and qualitative analysis of the growth of tumor cords

In this paper a macroscopic model of tumor cord growth is developed, relying on the mathematical theory of deformable porous media. Tumor is modeled as a saturated mixture of proliferating cells, extracellular fluid and extracellular matrix, that occupies a spatial region close to a blood vessel whence cells get the nutrient needed for their vital functions. Growth of tumor cells takes place within a healthy host tissue, which is in turn modeled as a saturated mixture of non-proliferating cells. Interactions between these two regions are accounted for as an essential mechanism for the growth of the tumor mass. By weakening the role of the extracellular matrix, which is regarded as a rigid non-remodeling scaffold, a system of two partial differential equations is derived, describing the evolution of the cell volume ratio coupled to the dynamics of the nutrient, whose higher and lower concentration levels determine proliferation or death of tumor cells, respectively. Numerical simulations of a reference two-dimensional problem are shown and commented, and a qualitative mathematical analysis of some of its key issues is proposed.Comment: 34 pages, 18 figure