Pauline Markenscoff

Computer-aided design of bioerodible devices with optimal release characteristics: a cellular automata approach

The development of a computational tool to design bioerodible devices with optimal release characteristics is presented. This computational tool uses cellular automata and parallel iterations to model and simulate the release of bioactive agents (drugs) from bioerodible matrices. The simulations can accurately model surface erosion processes in multicomponent systems of arbitrary geometry and with different dissolution rates for each component. Simulation results are analysed to show how the overall release rates are affected by the intrinsic dissolution rates, drug loading, porosity and the dispersion of the drug in the bioerodible matrix. A strongly non-linear dependence of release rates on drug loading and the intrinsic dissolution rates of the solid components is obtained and the effects of phase dispersion on the variability of release rates are elucidated. Finally, guidelines are presented for screening of alternatives to minimize the development effort and experimentation required for designing devices with desired release characteristics.

A 3D Hybrid Model for Tissue Growth: The Interplay between Cell Population and Mass Transport Dynamics

To provide theoretical guidance for the design and in vitro cultivation of bioartificial tissues, we have developed a multiscale computational model that can describe the complex interplay between cell population and mass transport dynamics that governs the growth of tissues in three-dimensional scaffolds. The model has three components: a transient partial differential equation for the simultaneous diffusion and consumption of a limiting nutrient; a cellular automaton describing cell migration, proliferation, and collision; and equations that quantify how the varying nutrient concentration modulates cell division and migration. The hybrid discrete-continuous model was parallelized and solved on a distributed-memory multicomputer to study how transport limitations affect tissue regeneration rates under conditions encountered in typical bioreactors. Simulation results show that the severity of transport limitations can be estimated by the magnitude of two dimensionless groups: the Thiele modulus and the Biot number. Key parameters including the initial seeding mode, cell migration speed, and the hydrodynamic conditions in the bioreactor are shown to affect not only the overall rate, but also the pattern of tissue growth. This study lays the groundwork for more comprehensive models that can handle mixed cell cultures, multiple nutrients and growth factors, and other cellular processes, such as cell death.

Regular Paper: Parallel Implementation of a Cellular Automaton Modeling the Growth of Three-Dimensional Tissues

A promising approach for treating tissue or organ failure involves the use of bioartificial tissue substitutes grown in scaffolds with appropriate structure and shape. Currently, however, the engineering of tissue substitutes is a long and costly process based exclusively on experimentation. Predictive computer models can greatly reduce the development costs of tissue-engineered therapies by enabling scientists to rapidly evaluate the effect of system parameters on the growth rates and quality of regenerated tissues. We report here the parallel implementation of a three-dimensional model that employs cellular automata to describe the dynamic behavior of a population of mammalian cells that migrate, interact and proliferate to generate new tissues. The simulator uses MPI for interprocessor communication and is suitable for distributed memory multi-computers. Three parallel algorithms are developed to approximate the sequential algorithm describing this dynamic process of tissue growth. The parallel algorithms progressively relax the correctness requirements using different approaches to handle the cells that either move/ divide in the boundary layers of processors or cross sub-domain boundaries. Finally, a systematic study is carried out to evaluate the accuracy and performance of these algorithms.

Scheduling a computational dag on a parallel system with communication delays and replication of node execution

The authors consider the problem of optimally scheduling the subtasks of a computational task modeled by a dag (directed acyclic graph) on parallel systems with identical processors. Execution of the subtasks (nodes) must satisfy precedence constraints that are met via data exchanges among processors which introduce communication delays. The optimization criterion used is the minimization of the processing time and the authors assume that there is no restriction on the number of processors needed and that a node may be replicated. They prove that the optimal scheduling problem can be solved in polynomial amount of time when the computational graph is a two-level dag. For a general dag they develop an algorithm that significantly reduces the search space over exhaustive search and can work very fast in many cases (the problem is NP-complete).<<ETX>>

A multiple processor system for real time control tasks

The performance of a special purpose multiple processor system with a shared bus for the transmission of output data is studied. A finite population queueing model with Poisson arrivals and services is developed and analyzed. The number of states is found to increase factorially with the number of customers. In the special case of equal arrival and service rates, the model reduces to a simpler one, whose solution is obtained by a recursive technique that reduces significantly the computation time. Under certain conditions, the simplified model provides a good approximation to the throughput predicted by the general model.

Parallel iterations and cellular automata models for simulating pore structural transformations

We develop a new class of models based on parallel iterations and cellular automata to treat pore structure transformations occurring during heterogeneous chemical reactions. Simulations on two-dimensional cellular arrays are carried out to demonstrate that the parallel iterations can accurately approximate isotropic growth of clusters (pores). This property is a necessary prerequisite for applying this approach to the study of gas-solid reactions.

Computation of tasks modeled by directed acyclic graphs on distributed computer systems: allocation without subtask replication

The problem of optimally allocating the subtasks of computational tasks modeled by directed acyclic graphs on distributed systems with identical processors is considered. Branch-and-bound and heuristic algorithms are developed for solving the optimization problem of minimizing the system response time. The heuristics attempt to minimize interprocessor communication costs while balancing the processor load. An upper bound is derived for the error in the solution computed by the heuristic algorithms, and the performance of all algorithms is evaluated. Results presented indicate that the heuristic algorithms can provide fast and accurate solution approximations.<<ETX>>

Modeling wound healing: effects of cell heterogeneity and tissue structure

Cellular automata models are developed to simulate wound healing in tissues consisting of two cell populations, each with its own distinct migratory, proliferative and death characteristics. Simulation results show that both the growth rates and the composition of regenerated tissues depend very strongly on the migration speeds and the initial spatial distribution of the cells.

Modeling the growth of three-dimensional tissues

We report the development of a model that describes the dynamic behavior of a population of cells that migrate and proliferate to fill a three-dimensional scaffold. This model is then applied to study how cell migration and the density or spatial distribution of seed cells affect the tissue growth rates.

An optimal algorithm for scheduling a computational tree on a parallel system with communication delays

We consider the problem of optimally scheduling the subtasks of a computational task modeled by a tree on parallel systems with identical processors. Execution of the subtasks must satisfy precedence constraints that are met via data exchanges among processors which introduce communication delays. The optimization criterion used is the minimization of the processing time and we assume that there is no restriction on the number of processors needed. We first show that the optimal scheduling problem can be solved in polynomial amount of time when the computational graph is a two-level tree. We then present an algorithm for the general tree that significantly reduces the search space and can work very fast in many cases. The number of processors needed for the optimal schedule is also computed.