Algorithms for Stable Matching and Clustering in a Grid

We study a discrete version of a geometric stable marriage problem originally proposed in a continuous setting by Hoffman, Holroyd, and Peres, in which points in the plane are stably matched to cluster centers, as prioritized by their distances, so that each cluster center is apportioned a set of points of equal area. We show that, for a discretization of the problem to an $n\times n$ grid of pixels with $k$ centers, the problem can be solved in time $O(n^2 \log^5 n)$, and we experiment with two slower but more practical algorithms and a hybrid method that switches from one of these algorithms to the other to gain greater efficiency than either algorithm alone. We also show how to combine geometric stable matchings with a $k$-means clustering algorithm, so as to provide a geometric political-districting algorithm that views distance in economic terms, and we experiment with weighted versions of stable $k$-means in order to improve the connectivity of the resulting clusters.Comment: 23 pages, 12 figures. To appear (without the appendices) at the 18th International Workshop on Combinatorial Image Analysis, June 19-21, 2017, Plovdiv, Bulgari

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

Micro-Environmental Mechanical Stress Controls Tumor Spheroid Size and Morphology by Suppressing Proliferation and Inducing Apoptosis in Cancer Cells

Compressive mechanical stress produced during growth in a confining matrix limits the size of tumor spheroids, but little is known about the dynamics of stress accumulation, how the stress affects cancer cell phenotype, or the molecular pathways involved.We co-embedded single cancer cells with fluorescent micro-beads in agarose gels and, using confocal microscopy, recorded the 3D distribution of micro-beads surrounding growing spheroids. The change in micro-bead density was then converted to strain in the gel, from which we estimated the spatial distribution of compressive stress around the spheroids. We found a strong correlation between the peri-spheroid solid stress distribution and spheroid shape, a result of the suppression of cell proliferation and induction of apoptotic cell death in regions of high mechanical stress. By compressing spheroids consisting of cancer cells overexpressing anti-apoptotic genes, we demonstrate that mechanical stress-induced apoptosis occurs via the mitochondrial pathway.Our results provide detailed, quantitative insight into the role of micro-environmental mechanical stress in tumor spheroid growth dynamics, and suggest how tumors grow in confined locations where the level of solid stress becomes high. An important implication is that apoptosis via the mitochondrial pathway, induced by compressive stress, may be involved in tumor dormancy, in which tumor growth is held in check by a balance of apoptosis and proliferation

Speeding up the Consensus Clustering methodology for microarray data analysis

<p>Abstract</p> <p>Background</p> <p>The inference of the number of clusters in a dataset, a fundamental problem in Statistics, Data Analysis and Classification, is usually addressed via internal validation measures. The stated problem is quite difficult, in particular for microarrays, since the inferred prediction must be sensible enough to capture the inherent biological structure in a dataset, e.g., functionally related genes. Despite the rich literature present in that area, the identification of an internal validation measure that is both fast and precise has proved to be elusive. In order to partially fill this gap, we propose a speed-up of <monospace>Consensus</monospace> (Consensus Clustering), a methodology whose purpose is the provision of a prediction of the number of clusters in a dataset, together with a dissimilarity matrix (the consensus matrix) that can be used by clustering algorithms. As detailed in the remainder of the paper, <monospace>Consensus</monospace> is a natural candidate for a speed-up.</p> <p>Results</p> <p>Since the time-precision performance of <monospace>Consensus</monospace> depends on two parameters, our first task is to show that a simple adjustment of the parameters is not enough to obtain a good precision-time trade-off. Our second task is to provide a fast approximation algorithm for <monospace>Consensus</monospace>. That is, the closely related algorithm <monospace>FC</monospace> (Fast Consensus) that would have the same precision as <monospace>Consensus</monospace> with a substantially better time performance. The performance of <monospace>FC</monospace> has been assessed via extensive experiments on twelve benchmark datasets that summarize key features of microarray applications, such as cancer studies, gene expression with up and down patterns, and a full spectrum of dimensionality up to over a thousand. Based on their outcome, compared with previous benchmarking results available in the literature, <monospace>FC</monospace> turns out to be among the fastest internal validation methods, while retaining the same outstanding precision of <monospace>Consensus</monospace>. Moreover, it also provides a consensus matrix that can be used as a dissimilarity matrix, guaranteeing the same performance as the corresponding matrix produced by <monospace>Consensus</monospace>. We have also experimented with the use of <monospace>Consensus</monospace> and <monospace>FC</monospace> in conjunction with <monospace>NMF</monospace> (Nonnegative Matrix Factorization), in order to identify the correct number of clusters in a dataset. Although <monospace>NMF</monospace> is an increasingly popular technique for biological data mining, our results are somewhat disappointing and complement quite well the state of the art about <monospace>NMF</monospace>, shedding further light on its merits and limitations.</p> <p>Conclusions</p> <p>In summary, <monospace>FC</monospace> with a parameter setting that makes it robust with respect to small and medium-sized datasets, i.e, number of items to cluster in the hundreds and number of conditions up to a thousand, seems to be the internal validation measure of choice. Moreover, the technique we have developed here can be used in other contexts, in particular for the speed-up of stability-based validation measures.</p

In vitro calibration of a system for measurement of in vivo convective heat transfer coefficient in animals

BACKGROUND: We need a sensor to measure the convective heat transfer coefficient during ablation of the heart or liver. METHODS: We built a minimally invasive instrument to measure the in vivo convective heat transfer coefficient, h in animals, using a Wheatstone-bridge circuit, similar to a hot-wire anemometer circuit. One arm is connected to a steerable catheter sensor whose tip is a 1.9 mm × 3.2 mm thin film resistive temperature detector (RTD) sensor. We used a circulation system to simulate different flow rates at 39°C for in vitro experiments using distilled water, tap water and saline. We heated the sensor approximately 5°C above the fluid temperature. We measured the power consumed by the sensor and the resistance of the sensor during the experiments and analyzed these data to determine the value of the convective heat transfer coefficient at various flow rates. RESULTS: From 0 to 5 L/min, experimental values of h in W/(m(2)·K) were for distilled water 5100 to 13000, for tap water 5500 to 12300, and for saline 5400 to 13600. Theoretical values were 1900 to 10700. CONCLUSION: We believe this system is the smallest, most accurate method of minimally invasive measurement of in vivo h in animals and provides the least disturbance of flow

f(R) theories

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.Comment: 156 pages, 14 figures, Invited review article in Living Reviews in Relativity, Published version, Comments are welcom

Combinatorial Computational Approaches to Identify Tetracycline Derivatives as Flavivirus Inhibitors

Limited structural information of drug targets, cellular toxicity possessed by lead compounds, and large amounts of potential leads are the major issues facing the design-oriented approach of discovering new leads. In an attempt to tackle these issues, we have developed a process of virtual screening based on the observation that conformational rearrangements of the dengue virus envelope protein are essential for the mediation of viral entry into host cells via membrane fusion. Screening was based solely on the structural information of the Dengue virus envelope protein and was focused on a target site that is presumably important for the conformational rearrangements necessary for viral entry. To circumvent the issue of lead compound toxicity, we performed screening based on molecular docking using structural databases of medical compounds. To enhance the identification of hits, we further categorized and selected candidates according to their novel structural characteristics. Finally, the selected candidates were subjected to a biological validation assay to assess inhibition of Dengue virus propagation in mammalian host cells using a plaque formation assay. Among the 10 compounds examined, rolitetracycline and doxycycline significantly inhibited plaque formation, demonstrating their inhibitory effect on dengue virus propagation. Both compounds were tetracycline derivatives with IC(50)s estimated to be 67.1 µM and 55.6 µM, respectively. Their docked conformations displayed common hydrophobic interactions with critical residues that affected membrane fusion during viral entry. These interactions will therefore position the tetracyclic ring moieties of both inhibitors to bind firmly to the target and, subsequently, disrupt conformational rearrangement and block viral entry. This process can be applied to other drug targets in which conformational rearrangement is critical to function

High Interstitial Fluid Pressure Is Associated with Tumor-Line Specific Vascular Abnormalities in Human Melanoma Xenografts

PURPOSE: Interstitial fluid pressure (IFP) is highly elevated in many solid tumors. High IFP has been associated with low radiocurability and high metastatic frequency in human melanoma xenografts and with poor survival after radiation therapy in cervical cancer patients. Abnormalities in tumor vascular networks have been identified as an important cause of elevated tumor IFP. The aim of this study was to investigate the relationship between tumor IFP and the functional and morphological properties of tumor vascular networks. MATERIALS AND METHODS: A-07-GFP and R-18-GFP human melanomas growing in dorsal window chambers in BALB/c nu/nu mice were used as preclinical tumor models. Functional and morphological parameters of the vascular network were assessed from first-pass imaging movies and vascular maps recorded after intravenous bolus injection of 155-kDa tetramethylrhodamine isothiocyanate-labeled dextran. IFP was measured in the center of the tumors using a Millar catheter. Angiogenic profiles of A-07-GFP and R-18-GFP cells were obtained with a quantitative PCR array. RESULTS: High IFP was associated with low growth rate and low vascular density in A-07-GFP tumors, and with high growth rate and high vascular density in R-18-GFP tumors. A-07-GFP tumors showed chaotic and highly disorganized vascular networks, while R-18-GFP tumors showed more organized vascular networks with supplying arterioles in the tumor center and draining venules in the tumor periphery. Furthermore, A-07-GFP and R-18-GFP cells differed substantially in angiogenic profiles. A-07-GFP tumors with high IFP showed high geometric resistance to blood flow due to high vessel tortuosity. R-18-GFP tumors with high IFP showed high geometric resistance to blood flow due to a large number of narrow tumor capillaries. CONCLUSIONS: High IFP in A-07-GFP and R-18-GFP human melanoma xenografts was primarily a consequence of high blood flow resistance caused by tumor-line specific vascular abnormalities

Sustained Release of Multiple Growth Factors from Injectable Polymeric System as a Novel Therapeutic Approach Towards Angiogenesis

The aim was to investigate that a bio-degradable alginate and poly lactide-co-glycolide (PLG) system capable of delivering growth factors sequentially would be superior to single growth factor delivery in promoting neovascularization and improving perfusion