Cancer is among the leading causes of death in the United States. Despite significant advances in drug design, the effectiveness of chemotherapeutic treatments is reduced by tumor dependent factors including heterogeneous vasculature and resistance due to drug transport. Tissue microenvironments in tumors are heterogeneous with respect to metabolic milieu, micro-vascular density and permeability, drug susceptibility of local cell populations, which directly affects chemotherapeutic efficacy. Micro-environmental physiology is characterized by oxygen limitation (hypoxia, anoxia), limited availability of key nutrients such as glucose, high lactate levels, and extracellular acidosis. Hypoxia and other microenvironmental factors have been reported to directly or indirectly impact the effectiveness of therapeutic modalities. The progression of a tumor is dependant on angiogenesis, without which small sized lesions are unable to grow beyond a size ~2 mm. Angiogenesis results in the creation of new vessels that exhibit severe structural and functional abnormalities such as being highly dilated, unusually tortuous, and containing arterio-venous shunts. This abnormal microvascular morphology results in the heterogeneous distribution of vessel diameters, intervascular distances, and nutrient and drug diffusivities across the tumor tissue.

Essential tools for tumor diagnosis and characterization are imaging techniques that allow non-invasive monitoring of tumor progression during the course of therapy and gauge the effectiveness of the therapeutic strategy. Dynamic contrast magnetic resonance imaging (DCE-MRI) is being increasingly used for the detection and diagnosis of breast cancers as alternative modality to mammography and sonography. DCE-MRI uses a low molecular weight contrast agent such as gadopentetate dimeglumine (Gd-DTPA) to produce three-dimensional spatial and temporal information that enables the estimation of vascular progression and transport characteristics in different regions of the tumor.

The present work involves the analysis of DCE-MRI images to obtain patient dependent vascular and transport characteristics for incorporation into theoretical tumor models that allow the effectiveness of different drugs and therapeutic strategies to be simulated. MRI images of breast lesions obtained from anonymous patients were provided by the MRI imaging center at Bay-State Medical Center (Springfield, MA). Each DCE-MRI data set consisted of images taken at five time points (1, 2, 3, 5 and 7 minutes) after the injection of the contrast agent. To the best of our knowledge, this study represents the first attempt to analyze DCE-MRI data with such low temporal resolution, as is typically available in the clinic. The pharmacokinetic model used for analysis consisted of three compartments: vascular, extracellular extravascular (EES), and cellular. The Matlab constrained optimization routine fmincon was used to generate local estimates of the transport coefficient between the vascular and EES compartments (K_trans ) and the vascular volume fraction (f_v).

The theoretical model was based our previous modeling efforts which integrated intracellular metabolism, nutrient and drug diffusion, cell-cycle progression, cellular drug effects, and drug pharmacokinetics ( Venkatasubramanian et al., 2006, 2007). The model was extended to account for heterogeneous vascularization and angiogenesis by utilizing tumor cords to represent individual capillaries supplying nutrients (oxygen, glucose) and chemotherapeutic drugs ( paclitaxel , 5-fluorouracil). Contrary to our previous modeling efforts focused on tumor spheroids in spherical coordinates, the present model was formulated in cylindrical coordinated to mimic tumor growth around capillaries. Local estimates of the tumor parameters (K_trans , f_v) were used to tune the tumor cord sizes and diffusion coefficients so as to capture experimentally observed heterogeneity. Simulation studies were performed to predict the impact of patient dependent tumor heterogeneity on the efficacy of various drug treatment protocols.

References

R. Venkatasubramanian , M. A. Henson, and N. S. Forbes, Incorporating Cellular Metabolism into Growth Models of Multicellular Tumor Spheriods ,Journal of Theoretical Biology, 242, 440-453 (2006).

R. Venkatasubramanian, M. A. Henson, and N. S. Forbes, Integrating Cell Cycle Progression, Drug Penetration and Metabolic Tumor Growth to Identify Optimal Therapeutic Strategies, in preparation (2007).