Mass transport is a fundamental process in living organisms, responsible for the delivery of oxygen, nutrients, and drugs from blood vessels to tissues, as well as the removal of waste products back to the vascular and lymphatic systems. This exchange occurs across various biological barriers, including blood vessel walls and cellular membranes, and involves complex mechanical and biochemical interactions. Traditional experimental and clinical methods have provided valuable insights into mass transport, but due to the complexity and heterogeneity of biological systems, computational models are essential for deeper understanding. Here, we give a brief review of a smeared modeling concept, termed the Kojic Transport Model (KTM), for gradient-driven physical fields within composite media such as biological tissue. The basic idea of the KTM is the formulation of the composite smeared finite element (CSFE). This element is composed of volumetric domains with different physical fields that are coupled by connectivity elements at each FE node representing biological barriers. The domains include 1D fields represented by 3D continuum form by formulation of the consistent transport tensors The KTM has been implemented in our finite element package PAK and demonstrated to be accurate and robust in modeling. We have selected models of mass transport (diffusion and perfusion) in the liver, pancreas, and tumor which grows over time.
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