Anuraag R. Kansal

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.

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.

Nonequilibrium hard-disk packings with controlled orientational order

This paper addresses one of the fundamental questions in the theory of hard-disk packings—how order within a system relates to packing density. The algorithm presented is a seed-based, growth protocol in which new disks are added sequentially to the surface of a growing cluster. The angular position of the new disk is chosen based on the minimization of an objective function designed to control order, as measured by the global bond-orientational order parameter ψ6, which varies between 0 and 1 (with 1 indicating perfect hexagonal close-packed order). Modifying the objective function allows the final packing fraction to be biased while maintaining tight control over ψ6. Inside of the range 0⩽ψ6⩽0.70, the targeted order parameter ψ6 is achieved to within two decimal places of accuracy. Furthermore, it is found that random structures (ψ6∼0.01) can be generated with packing fractions in the range 0.40⩽η⩽0.77. Interestingly, the algorithm can produce nonequilibrium hard-disk configurations that are considerabl...

A Cellular Automaton Model of Brain Tumor Treatment and Resistance

We have extended an automaton model of brain tumor growth to study the effects of treatment. By varying three treatment parameters, we can simulate tumors that display clinically plausible survival times. Much of our work is dedicated to heterogeneous tumors with both treatment-sensitive and treatment-resistant cells. First, we investigate two-strain systems in which resistant cells are initialized within predominantly sensitive tumors. We find that when resistant cells are not confined to a particular location, they compete more effectively with the sensitive population. Moreover, in this case, the fraction of resistant cells within the tumor is a less important indicator of patient prognosis when compared to the case in which the resistant cells are scattered throughout the tumor. In additional simulations, we investigate tumors that are initially monoclonal and treatment-sensitive, but that undergo resistance-mutations in response to treatment. Here, the tumors with both very frequent and very infrequent mutations develop with more spherical geometries. Tumors with intermediate mutational responses exhibit multi-lobed geometries, as mutant strains develop at localized points on the tumors’ surfaces.

Prediction of trapping rates in mixtures of partially absorbing spheres

The combined effects of diffusion and reaction in heterogeneous media govern the behavior of a wide variety of physical and biological phenomena, including the consumption of nutrients by cells and the study of magnetic relaxation in tissues. We have considered the so-called “trapping problem,” in which diffusion takes place exterior to a collection of fixed traps while reaction occurs at their surface. A simulation technique for predicting the overall trapping rate for systems of partially absorbing spherical traps based on the first-passage spheres method is presented. Using data obtained by applying this simulation technique, we then consider the problem of mixtures of partially absorbing traps. By hypothesizing a method for reducing a general mixture of traps to a mixture of perfect absorbers and perfect reflectors (i.e., reducing the dimensionality of the space of variables), we are able to accurately predict the effective surface rate constant and the trapping rate for an arbitrary mixture of partially absorbing traps. Remarkably, we find that a single, nearly universal curve allows accurate predictions to be made over a wide range of trap volume fractions and even for different trap distributions.

Globally and locally minimal weight spanning tree networks

The competition between local and global driving forces is significant in a wide variety of naturally occurring branched networks. We have investigated the impact of a global minimization criterion versus a local one on the structure of spanning trees. To do so, we consider two spanning tree structures—the generalized minimal spanning tree (GMST) defined by Dror et al. (Eur. J. Oper. Res. 120 (2000) 583) and an analogous structure based on the invasion percolation network, which we term the generalized invasive spanning tree (GIST). In general, these two structures represent extremes of global and local optimality, respectively. Structural characteristics are compared between the GMST and GIST for a fixed lattice. In addition, we demonstrate a method for creating a series of structures which enable one to span the range between these two extremes. Two structural characterizations, the occupied edge density (i.e., the fraction of edges in the graph that are included in the tree) and the tortuosity of the arcs in the trees, are shown to correlate well with the degree to which an intermediate structure resembles the GMST or GIST. Both characterizations are straightforward to determine from an image and are potentially useful tools in the analysis of the formation of network structures.