Flow correlated percolation during vascular network formation in tumors

A theoretical model based on the molecular interactions between a growing tumor and a dynamically evolving blood vessel network describes the transformation of the regular vasculature in normal tissues into a highly inhomogeneous tumor specific capillary network. The emerging morphology, characterized by the compartmentalization of the tumor into several regions differing in vessel density, diameter and necrosis, is in accordance with experimental data for human melanoma. Vessel collapse due to a combination of severely reduced blood flow and solid stress exerted by the tumor, leads to a correlated percolation process that is driven towards criticality by the mechanism of hydrodynamic vessel stabilization.Comment: 4 pages, 3 figures (higher resolution at http://www.uni-saarland.de/fak7/rieger/HOMEPAGE/flow.eps

Fragmentation pathways of nanofractal structures on surface

We present a detailed systematical theoretical analysis of the post-growth processes occurring in nanofractals grown on surface. For this study we developed a method which accounts for the internal dynamics of particles in a fractal. We demonstrate that particle diffusion and detachment controls the shape of the emerging stable islands on surface. We consider different scenarios of fractal post-growth relaxation and analyze the time evolution of the island's morphology. The results of our calculations are compared with available experimental observations, and experiments in which the post-growth relaxation of deposited nanostructures can be probed are suggested.Comment: 34 pages, 11 figure

Mathematical modeling of the metastatic process

Mathematical modeling in cancer has been growing in popularity and impact since its inception in 1932. The first theoretical mathematical modeling in cancer research was focused on understanding tumor growth laws and has grown to include the competition between healthy and normal tissue, carcinogenesis, therapy and metastasis. It is the latter topic, metastasis, on which we will focus this short review, specifically discussing various computational and mathematical models of different portions of the metastatic process, including: the emergence of the metastatic phenotype, the timing and size distribution of metastases, the factors that influence the dormancy of micrometastases and patterns of spread from a given primary tumor.Comment: 24 pages, 6 figures, Revie

High Acute Myeloid Leukemia derived VEGFA levels are associated with a specific vascular morphology in the leukemic bone marrow

Acute Myeloid Leukemia (AML) bone marrow biopsies at diagnosis display enhanced angiogenesis and increased VEGFA expression. In a xenograft mouse model it was described that availability of free VEGFA versus bound VEGFA is related to different vascular morphology. In this study we investigate the relationship between vascular morphology within AML bone marrow biopsies and AML derived VEGFA levels. Vessel count and surface area (Chalkley count) were calculated in AML bone marrow biopsies at diagnosis (n = 32), at remission (n = 8) and Normal Bone Marrow (n = 32) using immunohistochemical staining for FVIII, CD31, CTIV, SMA and VEGFA. VEGFA protein levels were measured. High vessel count was associated with an immature vessel status. Combining vessel count and Chalkley count different vessel morphology patterns were quantified within AML bone marrow biopsies. Three different subgroups could be distinguished. The subgroup (37.5% of the samples) exhibiting a high vessel count and vessels with predominantly large lumen (normal Chalkley count) was associated with high secreted VEGFA protein levels. Different vasculature patterns are seen in AML bone marrow biopsies, defined by combining number and size of vessel. These quantified morphology patterns, combined with VEGFA levels, might be of value in the success of VEGF/VEGFR-signaling interference approaches

Predicting drug pharmacokinetics and effect in vascularized tumors using computer simulation

In this paper, we investigate the pharmacokinetics and effect of doxorubicin and cisplatin in vascularized tumors through two-dimensional simulations. We take into account especially vascular and morphological heterogeneity as well as cellular and lesion-level pharmacokinetic determinants like P-glycoprotein (Pgp) efflux and cell density. To do this we construct a multi-compartment PKPD model calibrated from published experimental data and simulate 2-h bolus administrations followed by 18-h drug washout. Our results show that lesion-scale drug and nutrient distribution may significantly impact therapeutic efficacy and should be considered as carefully as genetic determinants modulating, for example, the production of multidrug-resistance protein or topoisomerase II. We visualize and rigorously quantify distributions of nutrient, drug, and resulting cell inhibition. A main result is the existence of significant heterogeneity in all three, yielding poor inhibition in a large fraction of the lesion, and commensurately increased serum drug concentration necessary for an average 50% inhibition throughout the lesion (the IC50 concentration). For doxorubicin the effect of hypoxia and hypoglycemia (“nutrient effect”) is isolated and shown to further increase cell inhibition heterogeneity and double the IC50, both undesirable. We also show how the therapeutic effectiveness of doxorubicin penetration therapy depends upon other determinants affecting drug distribution, such as cellular efflux and density, offering some insight into the conditions under which otherwise promising therapies may fail and, more importantly, when they will succeed. Cisplatin is used as a contrast to doxorubicin since both published experimental data and our simulations indicate its lesion distribution is more uniform than that of doxorubicin. Because of this some of the complexity in predicting its therapeutic efficacy is mitigated. Using this advantage, we show results suggesting that in vitro monolayer assays using this drug may more accurately predict in vivo performance than for drugs like doxorubicin. The nonlinear interaction among various determinants representing cell and lesion phenotype as well as therapeutic strategies is a unifying theme of our results. Throughout it can be appreciated that macroscopic environmental conditions, notably drug and nutrient distributions, give rise to considerable variation in lesion response, hence clinical resistance. Moreover, the synergy or antagonism of combined therapeutic strategies depends heavily upon this environment

Self-organization of developing embryo using scale-invariant approach

<p>Abstract</p> <p>Background</p> <p>Self-organization is a fundamental feature of living organisms at all hierarchical levels from molecule to organ. It has also been documented in developing embryos.</p> <p>Methods</p> <p>In this study, a scale-invariant power law (SIPL) method has been used to study self-organization in developing embryos. The SIPL coefficient was calculated using a centro-axial skew symmetrical matrix (CSSM) generated by entering the components of the Cartesian coordinates; for each component, one CSSM was generated. A basic square matrix (BSM) was constructed and the determinant was calculated in order to estimate the SIPL coefficient. This was applied to developing <it>C. elegans </it>during early stages of embryogenesis. The power law property of the method was evaluated using the straight line and Koch curve and the results were consistent with fractal dimensions (fd). Diffusion-limited aggregation (DLA) was used to validate the SIPL method.</p> <p>Results and conclusion</p> <p>The fractal dimensions of both the straight line and Koch curve showed consistency with the SIPL coefficients, which indicated the power law behavior of the SIPL method. The results showed that the ABp sublineage had a higher SIPL coefficient than EMS, indicating that ABp is more organized than EMS. The fd determined using DLA was higher in ABp than in EMS and its value was consistent with type 1 cluster formation, while that in EMS was consistent with type 2.</p

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

Consensus guidelines for the use and interpretation of angiogenesis assays

The formation of new blood vessels, or angiogenesis, is a complex process that plays important roles in growth and development, tissue and organ regeneration, as well as numerous pathological conditions. Angiogenesis undergoes multiple discrete steps that can be individually evaluated and quantified by a large number of bioassays. These independent assessments hold advantages but also have limitations. This article describes in vivo, ex vivo, and in vitro bioassays that are available for the evaluation of angiogenesis and highlights critical aspects that are relevant for their execution and proper interpretation. As such, this collaborative work is the first edition of consensus guidelines on angiogenesis bioassays to serve for current and future reference