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Multiple myeloma (MM) is a genetically complex hematological cancer that is characterized by proliferation of malignant plasma cells in the bone marrow. MM evolves from the clonal premalignant disorder monoclonal gammopathy of unknown significance (MGUS) by sequential genetic changes involving many different genes, resulting in dysregulated growth of multiple clones of plasma cells. The migration, survival, and proliferation of these clones require the direct and indirect interactions with the non-hematopoietic cells of the bone marrow. We develop a hybrid discrete-continuous model of MM development from the MGUS stage. The discrete aspect of the model is observed at the cellular level: cells are represented as individual objects which move, interact, divide, and die by apoptosis. Each of these actions is regulated by intracellular and extracellular processes as described by continuous models. The hybrid model consists of the following submodels that have been simplified from the much more complex state of evolving MM: cell motion due to chemotaxis, intracellular regulation of plasma cells, extracellular regulation in the bone marrow, and acquisition of mutations upon cell division. By extending a previous, simpler model in which the extracellular matrix was considered to be uniformly distributed, the new hybrid model provides a more accurate description in which cytokines are produced by the marrow microenvironment and consumed by the myeloma cells. The complex multiple genetic changes in MM cells and the numerous cell-cell and cytokine-mediated interactions between myeloma cells and their marrow microenviroment are simplified in the model such that four related but evolving MM clones can be studied as they compete for dominance in the setting of intraclonal heterogeneity. [ABSTRACT FROM AUTHOR]

Human Immunodeficiency Virus (HIV) infection of humans represents a complex biological system and a great challenge to public health. Novel approaches for the analysis and prediction of the infection dynamics based on a multi-scale integration of virus ontogeny and immune reactions are needed to deal with the systems' complexity. The aim of our study is: (1) to formulate a multi-scale mathematical model of HIV infection; (2) to implement the model computationally following a hybrid approach; and (3) to calibrate the model by estimating the parameter values enabling one to reproduce the "standard"observed dynamics of HIV infection in blood during the acute phase of primary infection. The modeling approach integrates the processes of infection spread and immune responses in Lymph Nodes (LN) to that observed in blood. The spatio-temporal population dynamics of T lymphocytes in LN in response to HIV infection is governed by equations linking an intracellular regulation of the lymphocyte fate by intercellular cytokine fields. We describe the balance of proliferation, differentiation and death at a single cell level as a consequence of gene activation via multiple signaling pathways activated by IL-2, IFNa and FasL. Distinct activation thresholds are used in the model to relate different modes of cellular responses to the hierarchy of the relative levels of the cytokines. We specify a reference set of model parameter values for the fundamental processes in lymph nodes that ensures a reasonable agreement with viral load and CD4+ T cell dynamics in blood. [ABSTRACT FROM AUTHOR]