Numerical Modeling of Fluid Flow in Solid Tumors

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. The discretized form of the governing equations, with appropriate boundary conditions, is developed for a predefined tumor geometry. The interstitial fluid pressure and velocity are calculated using a numerical method, element based finite volume. Simulations of interstitial fluid transport in a homogeneous solid tumor demonstrate that, in a uniformly perfused tumor, i.e., one with no necrotic region, because of the interstitial pressure distribution, the distribution of drug particles is non-uniform. Pressure distribution for different values of necrotic radii is examined and two new parameters, the critical tumor radius and critical necrotic radius, are defined. Simulation results show that: 1) tumor radii have a critical size. Below this size, the maximum interstitial fluid pressure is less than what is generally considered to be effective pressure (a parameter determined by vascular pressure, plasma osmotic pressure, and interstitial osmotic pressure). Above this size, the maximum interstitial fluid pressure is equal to effective pressure. As a consequence, drugs transport to the center of smaller tumors is much easier than transport to the center of a tumor whose radius is greater than the critical tumor radius; 2) there is a critical necrotic radius, below which the interstitial fluid pressure at the tumor center is at its maximum value. If the tumor radius is greater than the critical tumor radius, this maximum pressure is equal to effective pressure. Above this critical necrotic radius, the interstitial fluid pressure at the tumor center is below effective pressure. In specific ranges of these critical sizes, drug amount and therefore therapeutic effects are higher because the opposing force, interstitial fluid pressure, is low in these ranges

The air quality impacts of road closures associated with the 2004 Democratic National Convention in Boston

BACKGROUND: The Democratic National Convention (DNC) in Boston, Massachusetts in 2004 provided an opportunity to evaluate the impacts of a localized and short-term but potentially significant change in traffic patterns on air quality, and to determine the optimal monitoring approach to address events of this nature. It was anticipated that the road closures associated with the DNC would both influence the overall air pollution level and the distribution of concentrations across the city, through shifts in traffic patterns. METHODS: To capture these effects, we placed passive nitrogen dioxide badges at 40 sites around metropolitan Boston before, during, and after the DNC, with the goal of capturing the array of hypothesized impacts. In addition, we continuously measured elemental carbon at three sites, and gathered continuous air pollution data from US EPA fixed-site monitors and traffic count data from the Massachusetts Highway Department. RESULTS: There were significant reductions in traffic volume on the highway with closures north of Boston, with relatively little change along other highways, indicating a more isolated traffic reduction rather than an across-the-board decrease. For our nitrogen dioxide samples, while there was a relatively small change in mean concentrations, there was significant heterogeneity across sites, which corresponded with our a priori classifications of road segments. The median ratio of nitrogen dioxide concentrations during the DNC relative to non-DNC sampling periods was 0.58 at sites with hypothesized traffic reductions, versus 0.88 for sites with no changes hypothesized and 1.15 for sites with hypothesized traffic increases. Continuous monitors measured slightly lower concentrations of elemental carbon and nitrogen dioxide during road closure periods at monitors proximate to closed highway segments, but not for PM(2.5 )or further from major highways. CONCLUSION: We conclude that there was a small but measurable influence of DNC-related road closures on air quality patterns in the Boston area, and that a low-cost monitoring study combining passive badges for spatial heterogeneity and continuous monitors for temporal heterogeneity can provide useful insight for community air quality assessments

A tumor cord model for Doxorubicin delivery and dose optimization in solid tumors

<p>Abstract</p> <p>Background</p> <p>Doxorubicin is a common anticancer agent used in the treatment of a number of neoplasms, with the lifetime dose limited due to the potential for cardiotoxocity. This has motivated efforts to develop optimal dosage regimes that maximize anti-tumor activity while minimizing cardiac toxicity, which is correlated with peak plasma concentration. Doxorubicin is characterized by poor penetration from tumoral vessels into the tumor mass, due to the highly irregular tumor vasculature. I model the delivery of a soluble drug from the vasculature to a solid tumor using a tumor cord model and examine the penetration of doxorubicin under different dosage regimes and tumor microenvironments.</p> <p>Methods</p> <p>A coupled ODE-PDE model is employed where drug is transported from the vasculature into a tumor cord domain according to the principle of solute transport. Within the tumor cord, extracellular drug diffuses and saturable pharmacokinetics govern uptake and efflux by cancer cells. Cancer cell death is also determined as a function of peak intracellular drug concentration.</p> <p>Results</p> <p>The model predicts that transport to the tumor cord from the vasculature is dominated by diffusive transport of free drug during the initial plasma drug distribution phase. I characterize the effect of all parameters describing the tumor microenvironment on drug delivery, and large intercapillary distance is predicted to be a major barrier to drug delivery. Comparing continuous drug infusion with bolus injection shows that the optimum infusion time depends upon the drug dose, with bolus injection best for low-dose therapy but short infusions better for high doses. Simulations of multiple treatments suggest that additional treatments have similar efficacy in terms of cell mortality, but drug penetration is limited. Moreover, fractionating a single large dose into several smaller doses slightly improves anti-tumor efficacy.</p> <p>Conclusion</p> <p>Drug infusion time has a significant effect on the spatial profile of cell mortality within tumor cord systems. Therefore, extending infusion times (up to 2 hours) and fractionating large doses are two strategies that may preserve or increase anti-tumor activity and reduce cardiotoxicity by decreasing peak plasma concentration. However, even under optimal conditions, doxorubicin may have limited delivery into advanced solid tumors.</p

Fiscal Multipliers and Public Debt Dynamics in Consolidations

The success of a consolidation in reducing the debt ratio depends crucially on the value of the multiplier, which measures the impact of consolidation on growth, and on the reaction of sovereign yields to such a consolidation. We present a theoretical framework that formalizes the re spo nse of the public debt ratio to fiscal consolidations in relation to the value of fiscal multipliers, the starting debt level and the cyclical elasticity of the budget balance. We also assess the role of markets confidence to fiscal consolidations under al ternative scenarios. We find that with high levels of public debt and sizeable fiscal multipliers , debt ratios are likely to increase in the short term in response to fiscal consolidations. Hence, the typical horizon for a consolidation during crises episo des to reduce the debt ratio is two - three years , although this horizon depends critically on the size and persistence of fiscal multipliers and the reaction of financial markets. Anyway, such undesired debt responses are mainly short - lived. This effect is very unlikely in non - crisis times, as it requires a number of conditions difficult to observe at the same time , especially high fiscal multipliers

Effects of Anti-VEGF on Predicted Antibody Biodistribution: Roles of Vascular Volume, Interstitial Volume, and Blood Flow

BACKGROUND: The identification of clinically meaningful and predictive models of disposition kinetics for cancer therapeutics is an ongoing pursuit in drug development. In particular, the growing interest in preclinical evaluation of anti-angiogenic agents alone or in combination with other drugs requires a complete understanding of the associated physiological consequences. METHODOLOGY/PRINCIPAL FINDINGS: Technescan™ PYP™, a clinically utilized radiopharmaceutical, was used to measure tissue vascular volumes in beige nude mice that were naïve or administered a single intravenous bolus dose of a murine anti-vascular endothelial growth factor (anti-VEGF) antibody (10 mg/kg) 24 h prior to assay. Anti-VEGF had no significant effect (p>0.05) on the fractional vascular volumes of any tissues studied; these findings were further supported by single photon emission computed tomographic imaging. In addition, apart from a borderline significant increase (p = 0.048) in mean hepatic blood flow, no significant anti-VEGF-induced differences were observed (p>0.05) in two additional physiological parameters, interstitial fluid volume and the organ blood flow rate, measured using indium-111-pentetate and rubidium-86 chloride, respectively. Areas under the concentration-time curves generated by a physiologically-based pharmacokinetic model changed substantially (>25%) in several tissues when model parameters describing compartmental volumes and blood flow rates were switched from literature to our experimentally derived values. However, negligible changes in predicted tissue exposure were observed when comparing simulations based on parameters measured in naïve versus anti-VEGF-administered mice. CONCLUSIONS/SIGNIFICANCE: These observations may foster an enhanced understanding of anti-VEGF effects in murine tissues and, in particular, may be useful in modeling antibody uptake alone or in combination with anti-VEGF

Academic and social integration and study progress in problem based learning

The present study explores the effects of problem-based learning (PBL) on social and academic integration and study progress. Three hundred and five first-year students from three different psychology curricula completed a questionnaire on social and academic integration. Effects of a full-fledged PBL environment were compared to (1) effects of a conventional lecture-based learning environment, and (2) effects of a learning environment that combined lectures and other methods aimed at activating students. Lisrel analyses show direct positive effects of the learning environment on study progress: students in PBL obtained more credits compared to students in more conventional curricula. Moreover, the levels of social and academic integration were also higher among students in the PBL curriculum. The links between integration and study progress were less straightforward. Formal social integration positively affected study progress, but informal academic integration was negatively related to study progress

Convection and Retro-Convection Enhanced Delivery: Some Theoretical Considerations Related to Drug Targeting

Delivery of drugs and macromolecules into the brain is a challenging problem, due in part to the blood–brain barrier. In this article, we focus on the possibilities and limitations of two infusion techniques devised to bypass the blood–brain barrier: convection enhanced delivery (CED) and retro-convection enhanced delivery (R-CED). CED infuses fluid directly into the interstitial space of brain or tumor, whereas R-CED removes fluid from the interstitial space, which results in the transfer of drugs from the vascular compartment into the brain or tumor. Both techniques have shown promising results for the delivery of drugs into large volumes of tissue. Theoretical approaches of varying complexity have been developed to better understand and predict brain interstitial pressures and drug distribution for these techniques. These theoretical models of flow and diffusion can only be solved explicitly in simple geometries, and spherical symmetry is usually assumed for CED, while axial symmetry has been assumed for R-CED. This perspective summarizes features of these models and provides physical arguments and numerical simulations to support the notion that spherical symmetry is a reasonable approximation for modeling CED and R-CED. We also explore the potential of multi-catheter arrays for delivering and compartmentalizing drugs using CED and R-CED

A Systems Approach for Tumor Pharmacokinetics

Recent advances in genome inspired target discovery, small molecule screens, development of biological and nanotechnology have led to the introduction of a myriad of new differently sized agents into the clinic. The differences in small and large molecule delivery are becoming increasingly important in combination therapies as well as the use of drugs that modify the physiology of tumors such as anti-angiogenic treatment. The complexity of targeting has led to the development of mathematical models to facilitate understanding, but unfortunately, these studies are often only applicable to a particular molecule, making pharmacokinetic comparisons difficult. Here we develop and describe a framework for categorizing primary pharmacokinetics of drugs in tumors. For modeling purposes, we define drugs not by their mechanism of action but rather their rate-limiting step of delivery. Our simulations account for variations in perfusion, vascularization, interstitial transport, and non-linear local binding and metabolism. Based on a comparison of the fundamental rates determining uptake, drugs were classified into four categories depending on whether uptake is limited by blood flow, extravasation, interstitial diffusion, or local binding and metabolism. Simulations comparing small molecule versus macromolecular drugs show a sharp difference in distribution, which has implications for multi-drug therapies. The tissue-level distribution differs widely in tumors for small molecules versus macromolecular biologic drugs, and this should be considered in the design of agents and treatments. An example using antibodies in mouse xenografts illustrates the different in vivo behavior. This type of transport analysis can be used to aid in model development, experimental data analysis, and imaging and therapeutic agent design.National Institutes of Health (U.S.) (grant T32 CA079443