ODE/PDE Analysis of Multiple Myeloma

<p>Multiple myeloma is a form of bone cancer. Specifically it is a cancer of the plasma cells found in bone marrow (bone soft tissue). Normal plasma cells are an important part of the immune system.</p><p>Mathematical models for multiple myeloma based on ordinary and partial differential equations (ODE/PDEs) are presented in this book starting with a basic ODE model in Chapter 1 and concluding with a detailed ODE/PDE model in Chapter 4 that gives the spatiotemporal distribution of four dependent variable components in the bone marrow and peripheral blood: (1) protein produced by multiple myeloma cells termed the M protein (2) cytotoxic <i>T</i> lymphocytes (<i>CTL</i>s) (3) natural killer (<i>NK</i>) cells and (4) regulatory <i>T</i> cells (<i>Tregs</i>).</p><p>The computer-based implementation of the example models is presented through routines coded (programmed) in R a quality open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized e.g. no theorems and proofs. Rather the presentation is through detailed examples that the reader/researcher/analyst can execute on modest computers using the R routines that are available through a download. The PDE analysis is based on the method of lines (MOL) an established general algorithm for PDEs implemented with finite differences.</p>