Acute leukemia and chemotherapy: A modeling viewpoint

Invariance-based analysis of cancer chemotherapy

“…Thus, the control goal is to steer the tumor at an admissible size at the end of the therapy, by holding the normal cells above the admitted level which is representative of an healthy condition of the patient. We consider the mathematical model used in [1], [17] that models the interaction between tumoral and normal cells and the effect of chemotherapy drug. This low dimensional model has been used by many researches in the past to reproduce and simulate the cancer brain dynamic.…”

“…Thus, several scientific researchers and doctors have been attracted to work on this topic, in order to help the patients who suffer from this disease. In the literature, several mathematical models to stimulate the evolution of the cancer cells have appeared in the last decades, some of them are based on the evolution of the different cells, see [1], [7], [12], [17]. Such models may incorporate the effect of external drugs on the evolution of the cancer, as chemotherapy and immunotherapy drug or their combination.…”

“…In the recent years, mathematical models of cancer have been widely used also for control-based tumoral therapy design, applying optimal control [6], [14], or feedback control, see [2], [5]. Our work in this paper is based on the model inspired by the work of [1], [17]. It represents the evolution of normal and tumor cells, taking into account the effect of chemotherapy drug.…”

“…It represents the evolution of normal and tumor cells, taking into account the effect of chemotherapy drug. In [1], this model is used to represent the evolution of acute myeloblastic leukemia (AML) and in [17] it has been used to simulate the cancer evolution. The normal cells represent a part of the innate immune system of the human body and can be interpreted as the aggregation of NK cells, CD8+ cells and a circulating lymphocytes (or white blood cells) as defined in [5].…”

Chemotherapy of vascularised tumours: Role of vessel density and the effect of vascular “pruning”

“…Chemotherapy has a clinical role so important that in the common usage of many languages the word chemotherapy nowadays uniquely denotes anti-tumour chemotherapy. A huge corpus of experimental and clinical literature has been produced in the last 60 years, but chemotherapy also triggered the production of a large amount of theoretical researches due to its apparently simple translation into mathematical models (Skipper 1986, Wheldon 1988, Cojocaru and Agur 1992, Afenya 1996, Swierniak et al 1996, Panetta 1997, Ledzewicz and Schättler 2006, Simeoni et al 2004 A c c e p t e d m a n u s c r i p t Ribba et al 2005). Quite interestingly, and unlike from other fields of biomedicine, here there has been a limited but important interplay between theoretical and experimental-clinical scientists (Goldie and Coldman 1979, Norton and Simon 1986, Panetta et al 2008, Ubezio and Cameron 2008.…”