(588f) Model Generation for Distributed Systems in Life-Sciences and Biology

Mathematical models for reaction and transport phenomena of interest in chemical engineering lead to partial differential equations (PDE). Examples include momentum transport in computational fluid mechanics, chemical kinetics, species transport and mass transfer in pharmacokinetics and detailed distributed reaction mechanisms for invasive drug delivery in the central nervous systems.

While numerous commercial tools are available for the numerical solution of PDEs, few features offer computer-aided support for the consistent formulation of distributed systems models. Existing CFD tools provide static interfaces to merely select specific problem types or among a given set of boundary conditions. In addition, the core equation can often be altered to some degree with user-defined functions. For example, user-defined functions permit the integration of custom-defined sink or source terms to model reaction rates. Despite the ability to parameterize problems, designers are limited to a static problem library with little freedom to create truly novel applications. Yet, especially in life-science and biological systems modeling, there is a growing need to set up and solve novel formulations currently not offered by existing software tools. A big gap also exists in design optimization of distributed systems, because the black-box PDE solutions cannot readily be integrated with mathematical programming algorithms.

This overview presentation will highlight emerging new modeling patters for distributed systems in biomedical applications. We will introduce a model generation framework, which produces symbolic equation sets that can be solved with multiple algorithms, that can be combined among each other and supplied with arbitrary boundary conditions and that can be integrated with mathematical programming techniques with relative ease. Novel applications include the definition of tensors capable of defining anisotropic and heterogeneous field properties such as the tensor fields for molecular diffusivity, hydraulic conductivity and shear modulus frequently occurring in biological tissues. We will also demonstrate a novel dual mesh technique to capture the multi-scale phenomena of pulsating vasculature embedded in porous tissue. This technique allows even on coarse meshes for consistent momentum and mass exchange between multiple physiological compartments with different spatial and temporal resolutions such as soft tissue perfused by a pulsating vasculature. Two large scale inversion problems for distributed systems will be introduced. The first one allows the discovery of unknown physical properties from medical image data; the second example showing an optimal distributed design problem with PDE constraints solves the optimal placement of a infusion catheter for the most effective treatment of glioma. The modeling concepts our group developed over the last decade will be introduced in the context of case studies in life-sciences and biology.