This thesis describes the use of mathematical modelling to analyse the treatment of patients with immune disorders; namely, Multiple Myeloma, a cancer of plasma cells that create excess monoclonal antibody; and kidney transplants, where the immune system produces polygonal antibodies against the implanted organ. Linear and nonlinear compartmental models play an important role in the analysis of biomedical systems; in this thesis several models are developed to describe the in vivo kinetics of the antibodies that are prevalent for the two disorders studied. These models are validated against patient data supplied by clinical collaborators. Through this validation process important information regarding the dynamic properties of the clinical treatment can be gathered. In order to treat patients with excess immune antibodies the clinical staff wish to reduce these high levels in the patient to near healthy concentrations. To achieve this they have two possible treatment modalities: either using artificial methods to clear the material, a process known as apheresis, or drug therapy to reduce the production of the antibody in question. Apheresis techniques differ in their ability to clear different immune complexes; the effectiveness of a range of apheresis techniques is categorised for several antibody types and antibody fragments. The models developed are then used to predict the patient response to alternative treatment methods, and schedules, to find optimal combinations. In addition, improved measurement techniques that may offer an improved diagnosis are suggested. Whilst the overall effect of drug therapy is known, through measuring the concentration of antibodies in the patient’s blood, the short-term relationship between drug application and reduction in antibody synthesis is still not well defined; therefore, methods to estimate the generation rate of the immune complex, without the need for invasive procedures, are also presented
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