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We propose deterministic and stochastic models for studying the pharmacokinetics of chronic myeloid leukemia (CML), upon administration of IFN-$alpha$ (the traditional treatment for CML), TKI (the current frontline medication for CML) and Wnt/$beta$-catenin signaling (the state-of-the art therapeutic breakthrough for CML). To the best of our knowledge, no mathematical model incorporating all these three therapeutic protocols are available in literature. Further, this work introduces a stochastic approach in the study of CML dynamics. The key contributions of this work are: (1) Determination of the patient condition, contingent upon the patient specific model parameters, which leads to prediction of the appropriate patient specific therapeutic dosage. (2) Addressing the question of how the dual therapy of TKI and Wnt/$beta$-catenin signaling or triple combination of all three, offers potentially improved therapeutic responses, particularly in terms of reduced side effects of TKI or IFN-$alpha$. (3) Prediction of the likelihood of CML extinction/remission based on the level of CML stem cells at detection.
The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathem
Estimating early postmortem interval EPI is a difficult task in daily forensic activity due to limitations of accurate and reliable methods. The aim of the present work is to describe a novel approach in the estimation of EPI based on quantitative ma
It is now evident that the commonly accepted strategy for treatment of HIV/AIDS by highly active antiretroviral therapy (HAART) will not lead to eradication of HIV in a reasonable time. This is straightforward from the typical exponential viral load
Until recently many studies of bone remodeling at the cellular level have focused on the behavior of mature osteoblasts and osteoclasts, and their respective precursor cells, with the role of osteocytes and bone lining cells left largely unexplored.
Tumour progression has been described as a sequence of traits or phenotypes that cells have to acquire if the neoplasm is to become an invasive and malignant cancer. Although the genetic mutations that lead to these phenotypes are random, the process