A theoretical study of the response of vascular tumours to different types of chemotherapy

In this paper we formulate and explore a mathematical model to study continuous infusion of a vascular tumour with isolated and combined blood-borne chemotherapies. The mathematical model comprises a system of nonlinear partial differential equations that describe the evolution of the healthy (host) cells, the tumour cells and the tumour vasculature, coupled with distribution of a generic angiogenic stimulant (TAF) and blood-borne oxygen. A novel aspect of our model is the presence of blood-borne chemotherapeutic drugs which target different aspects of tumour growth (cf. proliferating cells, the angiogenic stimulant or the tumour vasculature). We run exhaustive numerical simulations in order to compare vascular tumour growth before and following therapy. Our results suggest that continuous exposure to anti-proliferative drug will result in the vascular tumour being cleared, becoming growth-arrested or growing at a reduced rate, the outcome depending on the drug’s potency and its rate of uptake. When the angiogenic stimulant or the tumour vasculature are targeted by the therapy, tumour elimination can not occur: at best vascular growth is retarded and the tumour reverts to an avascular form. Application of a combined treatment that destroys the vasculature and the TAF, yields results that resemble those achieved following successful treatment with anti-TAF or anti-vascular therapy. In contrast, combining anti-proliferative therapy with anti-TAF or antivascular therapy can eliminate the vascular tumour. In conclusion, our results suggest that tumour growth and the time of tumour clearance are highly sensitive to the specific combinations of anti-proliferative, anti-TAF and anti-vascular drugs

A Three Species Model to Simulate Application of Hyperbaric Oxygen Therapy to Chronic Wounds

Chronic wounds are a significant socioeconomic problem for governments worldwide. Approximately 15% of people who suffer from diabetes will experience a lower-limb ulcer at some stage of their lives, and 24% of these wounds will ultimately result in amputation of the lower limb. Hyperbaric Oxygen Therapy (HBOT) has been shown to aid the healing of chronic wounds; however, the causal reasons for the improved healing remain unclear and hence current HBOT protocols remain empirical. Here we develop a three-species mathematical model of wound healing that is used to simulate the application of hyperbaric oxygen therapy in the treatment of wounds. Based on our modelling, we predict that intermittent HBOT will assist chronic wound healing while normobaric oxygen is ineffective in treating such wounds. Furthermore, treatment should continue until healing is complete, and HBOT will not stimulate healing under all circumstances, leading us to conclude that finding the right protocol for an individual patient is crucial if HBOT is to be effective. We provide constraints that depend on the model parameters for the range of HBOT protocols that will stimulate healing. More specifically, we predict that patients with a poor arterial supply of oxygen, high consumption of oxygen by the wound tissue, chronically hypoxic wounds, and/or a dysfunctional endothelial cell response to oxygen are at risk of nonresponsiveness to HBOT. The work of this paper can, in some way, highlight which patients are most likely to respond well to HBOT (for example, those with a good arterial supply), and thus has the potential to assist in improving both the success rate and hence the cost-effectiveness of this therapy

The effect of vascular endothelial growth factor in the progression of bladder cancer and diabetic retinopathy

Abstract: Bladder cancer and diabetic retinopathy is a major public health and economical burden worldwide. Despite its high prevalence, the molecular mechanisms that induce or develop bladder carcinomas and diabetic retinopathy progression are poorly understood but it might be due to the disturbance in balance between angiogenic factors such as VEGF and antiangiogenic factors such as pigment epithelium derived growth factor. VEGF is one of the important survival factors for endothelial cells in the process of normal physiological and abnormal angiogenesis and induce the expression of antiapoptotic proteins in the endothelial cells. It is also the major initiator of angiogenesis in cancer and diabetic retinopathy, where it is up-regulated by oncogenic expression and different type of growth factors. The alteration in VEGF and VEGF receptors gene and overexpression, determines a diseases phenotype and ultimately the patient's clinical outcome. However, expressional and molecular studies were made on VEGF to understand the exact mechanism of action in the genesis and progression of bladder carcinoma and diabetic retinopathy , but still how VEGF mechanism involve in such type of disease progression are not well defined. Some other factors also play a significant role in the process of activation of VEGF pathways. Therefore, further detailed analysis via molecular and therapeutic is needed to know the exact mechanisms of VEGF in the angiogenesis pathway. The detection of these types of diseases at an early stage, predict how it will behave and act in response to treatment through regulation of VEGF pathways. The present review aimed to summarize the mechanism of alteration of VEGF gene pathways, which play a vital role in the development and progression of bladder cancer and diabetic retinopathy

A theoretical study of the response of vascular tumours to different types of chemotherapy

In this paper we formulate and explore a mathematical model to study continuous infusion of a vascular tumour with isolated and combined blood-borne chemotherapies. The mathematical model comprises a system of nonlinear partial differential equations that describe the evolution of the healthy (host) cells, the tumour cells and the tumour vasculature, coupled with distribution of a generic angiogenic stimulant (TAF) and blood-borne oxygen. A novel aspect of our model is the presence of blood-borne chemotherapeutic drugs which target different aspects of tumour growth (cf. proliferating cells, the angiogenic stimulant or the tumour vasculature). We run exhaustive numerical simulations in order to compare vascular tumour growth before and following therapy. Our results suggest that continuous exposure to anti-proliferative drug will result in the vascular tumour being cleared, becoming growth-arrested or growing at a reduced rate, the outcome depending on the drug’s potency and its rate of uptake. When the angiogenic stimulant or the tumour vasculature are targeted by the therapy, tumour elimination can not occur: at best vascular growth is retarded and the tumour reverts to an avascular form. Application of a combined treatment that destroys the vasculature and the TAF, yields results that resemble those achieved following successful treatment with anti-TAF or anti-vascular therapy. In contrast, combining anti-proliferative therapy with anti-TAF or antivascular therapy can eliminate the vascular tumour. In conclusion, our results suggest that tumour growth and the time of tumour clearance are highly sensitive to the specific combinations of anti-proliferative, anti-TAF and anti-vascular drugs