Multiphysics models of fluid and solute transport in the microvasculature of normal and malignant breast tissues with application to the detection and treatment of breast cancer

Mary Maria Schuff, Purdue University

Abstract

The limitations of the current diagnostic and therapeutic options available for breast cancer elucidate the need for improvements to the existing methods or the introduction of novel techniques. Many of the most promising novel options for both the diagnosis and treatment of cancer involve nanoparticles. Nanoparticles have unique imaging and therapeutic possibilities arising from their small size, surface tailorability, and binding capability. If properly designed nanoparticle may exploit the disordered architecture, increased vessel density, large pores, hyperpermeability, and other abnormalities characteristic of the vasculature in tumors, and achieve increased accumulation in cancerous tissue. The efficacy of nanoparticles may be further enhanced by active targeting through chemical or biological means, e.g., using ligands that bind specifically to receptors found on cancerous cells, or physical means, e.g., application of a magnetic field to the tumor after injection of magnetic nanoparticles. In order to optimize the diagnostic and therapeutic methods, it is necessary to understand the transport processes occurring in the breast and the changes that take place with the disease. Mathematical modeling is a valuable tool which provides a conceptual framework to understand these processes. The mathematical transport models found in the literature lacked of a consistent set of governing equations suggesting limited understanding. The transport parameters reported in the literature were similarly disparate, spanning several orders of magnitude in some cases. The primary purpose of this research was to develop, calibrate, and validate a comprehensive mathematical model using mixture theory along with experimental data and parameter values available in the literature. The mixture theory formulation allowed for the application of external body forces, uptake of solutes by cells, aggregation of the solutes, and solid tissue deformation. The resulting model included a number of components not accounted for in the traditional transport equations. The dependence of the hydraulic permeability coefficient of the capillary wall on the concentration of solutes present was the most notable novel feature. A simplified version of the mixture theory model was first utilized to describe steady state blood flow in an axisymmetric microvascular geometry for the case of no solutes or solid tissue deformation. Four influential parameters were calibrated using red blood cell velocity data from the literature. The computed velocities and calibrated parameters were in good agreement with experimental data. The mixture theory model was then utilized to examine the time dependent transport of fluid and a single macromolecular solute with no active targeting. In normal tissue, the radius of the unit cell, the pressure drop along the vessel, the osmotic pressure gradient, the hydraulic permeability coefficient, the reflection coefficient of the capillary wall, and the retardation factor substantially influenced the extravascular solute transport. These parameters, as well as the extravascular pressure, were important in cancerous tissue and were calibrated using a response surface methodology and experimental data from the literature for dextrans. The calibrated parameters were within the expected ranges. The validated results showed good agreement with the experimental data for both the mean extravascular concentration as a function of time and the penetration depth of the dextrans as a function of time across a wide range of molecular weights, 3.3 to 2000 kg mol -1. For the largest solutes, the results from the mixture theory model were markedly improved compared to those of the traditional models. Subsequent to exploring influence of passive targeting, both receptor mediated and magnetic active targeting were added to the mixture theory model. Both means of active targeting increased the extravascular accumulation. The efficacy of the targeting was dependent upon a number of factors, including the solute size. The mixture theory model will be a valuable tool for further exploration of these influences.

Degree

Ph.D.

Advisors

Gore, Purdue University.

Subject Area

Biomedical engineering|Mechanical engineering|Biomechanics

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