Analysis of the dynamic behaviour of malignant tumours using mathematical models and ultrasound parameters - a survey

A miscellany of new strategies, experimental techniques and theoretical approaches are emerging in the ongoing battle against cancer. The recent explosion in the understanding of the multiple scale processes that drive the advancement of cancer is allowing useful mathematical models of the tumorigenesis to be developed. Such models have the potential to facilitate a deeper understanding of the mechanisms associated with tumor initiation and progression and can also be used to develop and test novel therapeutic approaches designed to attack this complex system at various levels. Ultrasound (US) could predict the potential for metastasis and recurrence. Colour Doppler US is able to detect tumour neovascularity and the model of the tumour vascularization. Quantitative analysis of the raising vascular signal after contrast-enhanced administration and kinetic vascular studies allow the differentiation benign malignant tumours with similar results to contrast-enhanced CT, the measure of the angiogenesis extent by the type of the tumour, the metastasis potential of the lesion and the efficacy of the treatment. A non-invasive imaging technique that could identify tumour blood flow would represent a valuable method for depiction the functional tumour status and therapy response. The progress in oncological treatment involves new strategies using tumour angiogenesis inhibitors. US would have an important role in following-up the therapeutic response. In summary, this paper illustrates how mathematical models may be used to investigate promising US techniques for an in vivo, non-invasive, globally quantification of tumour´s morphological and functional changes