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Biomedical subjects

S Torquato

Publications and source records attributed to S Torquato.

At least 19 recordsLinked to original sources
PubMed2001

Pattern of self-organization in tumour systems: complex growth dynamics in a novel brain tumour spheroid model.

We propose that a highly malignant brain tumour is an opportunistic, self-organizing and adaptive complex dynamic biosystem rather than an unorganized cell mass. To test the hypothesis of related key behaviour such as cell proliferation and invasion, we have developed a new in vitro assay capable of displaying several of the dynamic features of this multiparameter system in the same experimental setting. This assay investigates the development of multicellular U87MGmEGFR spheroids in a specific extracellular matrix gel over time. The results show that key features such as volumetric growth and cell invasion can be analysed in the same setting over 144 h without continuously supplementing additional nutrition. Moreover, tumour proliferation and invasion are closely correlated and both key features establish a distinct ratio over time to achieve maximum cell velocity and to maintain the system's temporo-spatial expansion dynamics. Single cell invasion follows a chain-like pattern leading to the new concept of a intrabranch homotype attraction. Since preliminary studies demonstrate that heterotype attraction can specifically direct and accelerate the emerging invasive network, we further introduce the concept of least resistance, most permission and highest attraction as an essential principle for tumour invasion. Together, these results support the hypothesis of a self-organizing adaptive biosystem.

Adaptation, Biological↗
PubMed2000

Emergence of a subpopulation in a computational model of tumor growth.

Malignant brain tumors consist of a number of distinct subclonal populations. Each of these subpopulations may be characterized by its own behaviors and properties. These subpopulations arise from the constant genetic and epigenetic alteration of existing cells in the rapidly growing tumor. However, since each single-cell mutation only leads to a small number of offspring initially, very few newly arisen subpopulations survive more than a short time. The present work quantifies "emergence", i.e. the likelihood of an isolated subpopulation surviving for an extended period of time. Only competition between clones is considered; there are no cooperative effects included. The probability that a subpopulation emerges under these conditions is found to be a sigmoidal function of the degree of change in cell division rates. This function has a non-zero value for mutations which confer no advantage in growth rate, which represents the emergence of a distinct subpopulation with an advantage that has yet to be selected for, such as hypoxia tolerance or treatment resistance. A logarithmic dependence on the size of the mutated population is also observed. A significant probability of emergence is observed for subpopulations with any growth advantage that comprise even 0.1% of the proliferative cells in a tumor. The impact of even two clonal populations within a tumor is shown to be sufficient such that a prognosis based on the assumption of a monoclonal tumor can be markedly inaccurate.

Brain Neoplasms↗
PubMed2000

Simulated brain tumor growth dynamics using a three-dimensional cellular automaton.

We have developed a novel and versatile three-dimensional cellular automaton model of brain tumor growth. We show that macroscopic tumor behavior can be realistically modeled using microscopic parameters. Using only four parameters, this model simulates Gompertzian growth for a tumor growing over nearly three orders of magnitude in radius. It also predicts the composition and dynamics of the tumor at selected time points in agreement with medical literature. We also demonstrate the flexibility of the model by showing the emergence, and eventual dominance, of a second tumor clone with a different genotype. The model incorporates several important and novel features, both in the rules governing the model and in the underlying structure of the model. Among these are a new definition of how to model proliferative and non-proliferative cells, an isotropic lattice, and an adaptive grid lattice.

Algorithms↗
PubMed2000

Is random close packing of spheres well defined?

Despite its long history, there are many fundamental issues concerning random packings of spheres that remain elusive, including a precise definition of random close packing (RCP). We argue that the current picture of RCP cannot be made mathematically precise and support this conclusion via a molecular dynamics study of hard spheres using the Lubachevsky-Stillinger compression algorithm. We suggest that this impasse can be broken by introducing the new concept of a maximally random jammed state, which can be made precise.

Journal Article↗
PubMed2000

Cellular automaton of idealized brain tumor growth dynamics.

A novel cellular automaton model of proliferative brain tumor growth has been developed. This model is able to simulate Gompertzian tumor growth over nearly three orders of magnitude in radius using only four microscopic parameters. The predicted composition and growth rates are in agreement with a test case pooled from the available medical literature. The model incorporates several new features, improving previous models, and also allows ready extension to study other important properties of tumor growth, such as clonal competition.

Algorithms↗
PubMed2000

Comment on "Walker diffusion method for calculation of transport properties of composite materials"

In a recent paper [C. DeW. Van Siclen, Phys. Rev. E 59, 2804 (1999)], a random-walk algorithm was proposed as the best method to calculate transport properties of composite materials. It was claimed that the method is applicable both to discrete and continuum systems. The limitations of the proposed algorithm are analyzed. We show that the algorithm does not capture the peculiarities of continuum systems (e.g., "necks" or "choke points") and we argue that it is the stochastic analog of the finite-difference method.

Journal Article↗
PubMed2000

Stochastic reconstruction of sandstones

A simulated annealing algorithm is employed to generate a stochastic model for a Berea sandstone and a Fontainebleau sandstone, with each a prescribed two-point probability function, lineal-path function, and "pore size" distribution function, respectively. We find that the temperature decrease of the annealing has to be rather quick to yield isotropic and percolating configurations. A comparison of simple morphological quantities indicates good agreement between the reconstructions and the original sandstones. Also, the mean survival time of a random walker in the pore space is reproduced with good accuracy. However, a more detailed investigation by means of local porosity theory shows that there may be significant differences of the geometrical connectivity between the reconstructed and the experimental samples.

Journal Article↗
PubMed2000

Towards a quantification of disorder in materials: distinguishing equilibrium and glassy sphere packings

This paper examines the prospects for quantifying disorder in simple molecular or colloidal systems. As a central element in this task, scalar measures for describing both translational and bond-orientational order are introduced. These measures are subsequently used to characterize the structures that result from a series of molecular-dynamics simulations of the hard-sphere system. The simulation results can be illustrated by a two-parameter ordering phase diagram, which indicates the relative placement of the equilibrium phases in order-parameter space. Moreover, the diagram serves as a useful tool for understanding the effect of history on disorder in nonequilibrium structures. Our investigation provides fresh insights into the types of ordering that can occur in equilibrium and glassy systems, including quantitative evidence that, at least in the case of hard spheres, contradicts the notion that glasses are simply solids with the "frozen in" structure of an equilibrium liquid. Furthermore, examination of the order exhibited by the glassy structures suggests, to our knowledge, a new perspective on the old problem of random close packing.

Journal Article↗
PubMed1997

Reconstruction of the Structure of Dispersions

To what extent can the structure of a disordered heterogeneous material be reconstructed using limited but essentially exact structural information about the original system? We formulate a methodology based on simulated annealing to reconstruct both equilibrium and non-equilibrium dispersions of particles based only on correlation functions which statistically characterize the system. To test this method, we reconstruct dispersions from the radial distribution function (RDF) associated with the original system. Other statistical correlation functions are evaluated to compare how well the reconstructed system matches the original system. We show that for low-density systems or high-density systems with little particle aggregation, our reconstruction from the RDF reproduces the system fairly well. However, for dense systems with extensive clustering, RDF information is somewhat inadequate in being able to reconstruct the original system. We also show that one can produce a system with an RDF that is similar to the reference system, but with appreciably different structure. Finally, system-size effects are analyzed analytically.

Journal Article↗