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Vascularized tumor growth is characterized by both abnormal interstitial fluid flow and the associated interstitial fluid pressure (IFP). Here, we study the effect that these conditions have on the transport of therapeutic agents during chemotherapy. We apply our recently developed vascular tumor growth model which couples a continuous growth component with a discrete angiogenesis model to show that hypertensive IFP is a physical barrier that may hinder vascular extravasation of agents through transvascular fluid flux convection, which drives the agents away from the tumor. This result is consistent with previous work using simpler models without blood flow or lymphatic drainage. We consider the vascular/interstitial/lymphatic fluid dynamics to show that tumors with larger lymphatic resistance increase the agent concentration more rapidly while also experiencing faster washout. In contrast, tumors with smaller lymphatic resistance accumulate less agents but are able to retain them for a longer time. The agent availability (area-under-the curve, or AUC) increases for less permeable agents as lymphatic resistance increases, and correspondingly decreases for more permeable agents. We also investigate the effect of vascular pathologies on agent transport. We show that elevated vascular hydraulic conductivity contributes to the highest AUC when the agent is less permeable, but to lower AUC when the agent is more permeable. We find that elevated interstitial hydraulic conductivity contributes to low AUC in general regardless of the transvascular agent transport capability. We also couple the agent transport with the tumor dynamics to simulate chemotherapy with the same vascularized tumor under different vascular pathologies. We show that tumors with an elevated interstitial hydraulic conductivity alone require the strongest dosage to shrink. We further show that tumors with elevated vascular hydraulic conductivity are more hypoxic during therapy and that the response slows down as the tumor shrinks due to the heterogeneity and low concentration of agents in the tumor interior compared with the cases where other pathological effects may combine to flatten the IFP and thus reduce the heterogeneity. We conclude that dual normalizations of the micronevironment - both the vasculature and the interstitium - are needed to maximize the effects of chemotherapy, while normalization of only one of these may be insufficient to overcome the physical resistance and may thus lead to sub-optimal outcomes.

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The flow of interstitial fluid and the associated interstitial fluid pressure (IFP) in solid tumors and surrounding host tissues have been identified as critical elements in cancer growth and vascularization. Both experimental and theoretical studies have shown that tumors may present elevated IFP, which can be a formidable physical barrier for delivery of cell nutrients and small molecules into the tumor. Elevated IFP may also exacerbate gradients of biochemical signals such as angiogenic factors released by tumors into the surrounding tissues. These studies have helped to understand both biochemical signaling and treatment prognosis. Building upon previous work, here we develop a vascular tumor growth model by coupling a continuous growth model with a discrete angiogenesis model. We include fluid/oxygen extravasation as well as a continuous lymphatic field, and study the micro-environmental fluid dynamics and their effect on tumor growth by accounting for blood flow, transcapillary fluid flux, interstitial fluid flow, and lymphatic drainage. We thus elucidate further the non-trivial relationship between the key elements contributing to the effects of interstitial pressure in solid tumors. In particular, we study the effect of IFP on oxygen extravasation and show that small blood/lymphatic vessel resistance and collapse may contribute to lower transcapillary fluid/oxygen flux, thus decreasing the rate of tumor growth. We also investigate the effect of tumor vascular pathologies, including elevated vascular and interstitial hydraulic conductivities inside the tumor as well as diminished osmotic pressure differences, on the fluid flow across the tumor capillary bed, the lymphatic drainage, and the IFP. Our results reveal that elevated interstitial hydraulic conductivity together with poor lymphatic function is the root cause of the development of plateau profiles of the IFP in the tumor, which have been observed in experiments, and contributes to a more uniform distribution of oxygen, solid tumor pressure and a broad-based collapse of the tumor lymphatics. We also find that the rate that IFF is fluxed into the lymphatics and host tissue is largely controlled by an elevated vascular hydraulic conductivity in the tumor. We discuss the implications of these results on microenvironmental transport barriers, and the tumor invasive and metastatic potential. Our results suggest the possibility of developing strategies of targeting tumor cells based on the cues in the interstitial fluid.

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Inefficient vascularization hinders the optimal transport of cell nutrients, oxygen, and drugs to cancer cells in solid tumors. Gradients of these substances maintain a heterogeneous cell-scale microenvironment through which drugs and their carriers must travel, significantly limiting optimal drug exposure. In this study, we integrate intravital microscopy with a mathematical model of cancer to evaluate the behavior of nanoparticle-based drug delivery systems designed to circumvent biophysical barriers. We simulate the effect of doxorubicin delivered via porous 1000 x 400 nm plateloid silicon particles to a solid tumor characterized by a realistic vasculature, and vary the parameters to determine how much drug per particle and how many particles need to be released within the vasculature in order to achieve remission of the tumor. We envision that this work will contribute to the development of quantitative measures of nanoparticle design and drug loading in order to optimize cancer treatment via nanotherapeutics.

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OBJECTIVE: The most critical determinant of restoration of tissue structure during wound healing is the re-establishment of a functional vasculature, which largely occurs via angiogenesis, specifically endothelial sprouting from the pre-existing vasculature. MATERIALS AND METHODS: We used confocal microscopy to capture sequential images of perfused vascular segments within the injured panniculus carnosus muscle in the mouse dorsal skin-fold window chamber to quantify a range of microcirculatory parameters during the first nine days of healing. This data was used to inform a mathematical model of sequential growth of the vascular plexus. The modeling framework mirrored the experimental circular wound domain and incorporated capillary sprouting and endothelial cell (EC) sensing of vascular endothelial growth factor gradients. RESULTS: Wound areas, vessel densities and vessel junction densities obtained from the corresponding virtual wound were in excellent agreement both temporally and spatially with data measured during the in vivo healing process. Moreover, by perturbing the proliferative ability of ECs in the mathematical model, this leads to a severe reduction in vascular growth and poor healing. Quantitative measures from this second set of simulations were found to correlate extremely well with experimental data obtained from animals treated with an agent that targets endothelial proliferation (TNP-470). CONCLUSION: Our direct combination and comparison of in vivo longitudinal analysis (over time in the same animal) and mathematical modeling employed in this study establishes a useful new paradigm. The virtual wound created in this study can be used to investigate a wide range of experimental hypotheses associated with wound healing, including disorders characterized by aberrant angiogenesis (e.g., diabetic models) and the effects of vascular enhancing/disrupting agents or therapeutic interventions such as hyperbaric oxygen.

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Angiogenesis, the growth of a network of blood vessels, is a crucial component of solid tumour growth, linking the relatively harmless avascular growth phase and the potentially fatal vascular growth phase. As a process, angiogenesis is a well-orchestrated sequence of events involving endothelial cell migration, proliferation; degradation of tissue; new capillary vessel (sprout) formation; loop formation (anastomosis) and, crucially, blood flow through the network. Once there is blood flow associated with the nascent network, the subsequent growth of the network evolves both temporally and spatially in response to the combined effects of angiogenic factors, migratory cues via the extracellular matrix and perfusion-related haemodynamic forces in a manner that may be described as both adaptive and dynamic. In this paper we present a mathematical model which simultaneously couples vessel growth with blood flow through the vessels--dynamic adaptive tumour-induced angiogenesis (DATIA). This new mathematical model presents a theoretical and computational investigation of the process and highlights a number of important new targets for therapeutic intervention. In contrast to earlier flow models, where the effects of perfusion (blood flow) were essentially evaluated a posteriori, i.e. after generating a hollow network, blood flow in the model described in this paper has a direct impact during capillary growth, with radial adaptations and network remodelling occurring as immediate consequences of primary anastomoses. Capillary network architectures resulting from the dynamically adaptive model are found to differ radically from those obtained using earlier models. The DATIA model is used to examine the effects of changing various physical and biological model parameters on the developing vascular architecture and the delivery of chemotherapeutic drugs to the tumour. Subsequent simulations of chemotherapeutic treatments under different parameter regimes lead to the identification of a number of new therapeutic targets for tumour management.

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