Breast cancer is the most common type of cancer among women and despite recent advances in the medical field, there are still some inherent limitations in the currently used screening techniques. The radiological interpretation of X-ray mammograms often leads to over-diagnosis and, as a consequence, to unnecessary traumatic and painful biopsies. First we use the 1D Wavelet Transform Modulus Maxima (WTMM) method to reveal changes in skin temperature dynamics of women breasts with and without malignant tumor. We show that the statistics of temperature temporal fluctuations about the cardiogenic and vasomotor perfusion oscillations do not change across time-scales for cancerous breasts as the signature of homogeneous monofractal fluctuations. This contrasts with the continuous change of temperature fluctuation statistics observed for healthy breasts as the hallmark of complex multifractal scaling. When using the 2D WTMM method to analyze the roughness fluctuations of X-ray mammograms, we reveal some drastic loss of roughness spatial correlations that likely results from some deep architectural change in the microenvironment of a breast tumor. This local breast disorganisation may deeply affect heat transfer and related thermomechanics in the breast tissue and in turn explain the loss of multifractal complexity of temperature temporal fluctuations previously observed in mammary glands with malignant tumor. These promising findings could lead to the future use of combined wavelet-based multifractal processing of dynamic IR thermograms and X-ray mammograms to help identifying women with high risk of breast cancer prior to more traumatic examinations. Besides potential clinical impact, these results shed a new light on physiological changes that may precede anatomical alterations in breast cancer development.[-]

Therapy resistance and tumour relapse after drug therapy are commonly explained by Darwinian selection of pre-existing drug-resistant, often stem-like cancer cells resulting from random mutations. However, the ubiquitous nongenetic heterogeneity and plasticity of tumour cell phenotype raises the question: are mutations really necessary and sufficient to promote cell phenotype changes during tumour progression? Tumorigenesis is a dynamic biological process that involves distinct cancer cell subpopulations proliferating at different rates and interconverting between them. Cancer therapy inevitably spares some cancer cells, even in the absence of resistant mutants. Accumulating observations suggest that the non-killed, residual tumour cells actively acquire a new phenotype simply by exploiting their developmental potential. These surviving cells are stressed by the cytotoxic treatment, and owing to phenotype plasticity, exhibit a variety of responses. By entering such stem-like, stress-response states, the surviving cells strengthen their capacity to cope with future noxious agents. Considering nongenetic cell state dynamics and the relative ease with which surviving but stressed cells can be tipped into latent attractors of the gene regulatory network provides a foundation for exploring new therapeutic approaches that seek not only to kill cancer cells but also to avoid promoting resistance and relapse that are inherently linked to the attempts to kill them.[-]

The emergence of drug-resistance is a major challenge in chemotherapy. In this talk we will present our recent mathematical models for describing the dynamics of drug-resistance in solid tumors. Our models follow the dynamics of the tumor, assuming that the cancer cell population depends on a phenotype variable that corresponds to the resistance level to a cytotoxic drug. We incorporate the dynamics of nutrients and two different types of drugs: a cytotoxic drug, which directly impacts the death rate of the cancer cells, and a cytostatic drug that reduces the proliferation rate. Through analysis and simulations, we study the impact of spatial and phenotypic heterogeneity on the tumor growth under chemotherapy. We demonstrate that heterogeneous cancer cells may emerge due to the selection dynamics of the environment. Our models predict that under certain conditions, multiple resistant traits emerge at different locations within the tumor. We show that a higher dosage of the cytotoxic drug may delay a relapse, yet, when this happens, a more resistant trait emerges. Moreover, we estimate the expansion rate of the tumor boundary as well as the time of relapse, in terms of the resistance trait, the level of the nutrient, and the drug concentration. Finally, we propose an efficient drug schedule aiming at minimizing the growth rate of the most resistant trait. By combining the cytotoxic and cytostatic drugs, we demonstrate that the resistant cells can be eliminated.[-]

How combination therapies can reduce the emergence of cancer resistance? Can we exploit intra-tumoral competition to modify the effectiveness of anti-cancer treatments?
Bearing these questions in mind, we present a mathematical model of cancer-immune competition under therapies. The model consists of a system of differential equations for the dynamics of two cancer clones and T-cells. Comparisons with experimental data and clinical protocols for non-small cell lung cancer have been performed.
In silico experiments confirm that the selection of proper infusion schedules plays a key role in the success of anti-cancer therapies. The outcomes of protocols of chemotherapy and immunotherapy (separately and in combination) differing in doses and timing of the treatments are analyzed.
In particular, we highlight how exploiting the competition between cancer populations seems to be an effective recipe to limit the insurgence of resistant populations. In some cases, combination of low doses therapies could yield a substantial control of the total tumor population without imposing a massive selective pressure that would suppress the sensitive clones leaving unchecked the clonal types resistant to therapies.[-]

Cell-extracellular matrix interaction and the mechanical properties of cell nucleus have been demonstrated to play a fundamental role in cell movement across fibre networks and micro-channels and then in the spread of cancer metastases. The lectures will be aimed at presenting several mathematical models dealing with such a problem, starting from modelling cell adhesion mechanics to the inclusion of influence of nucleus stiffness in the motion of cells, through continuum mechanics, kinetic models and individual cell-based models.[-]

Irreversible electroporation (IRE) is the sole physical ablative technology inducing tumorous cell death by process unrelated to thermal effect. This characteristic makes the technique suitable for the treatment of subtypes of liver tumors especially hepatocellular carcinoma (HCC) located next to critical structures leading to contraindications to thermal ablation like radiofrequency, microwave or cryotherapy. However, while IRE appears safe in such assumed challenging cases for thermal techniques, several issues remain to be addressed to make its use easier and more effective in clinical practice. First of all, tissue changes induced by IRE must be assessed keeping in mind that conversely to thermal techniques its efficacy is not limited to observable coagulative necrotic component of treatment zone. In addition, IRE which is multibipolar ablative technology requires meticulous demanding electrodes positioning to ensure proper magnitude of electric fields between each dipole. Finally, numerical simulations of IRE are mandatory to ease the setting of electrical pulses parameters to improve predictability of treatment in each individual case. In this setting of continue efforts to improve practicability of IRE the technique is routinely used in our institution since several years for the treatment of patients bearing early and locally advanced HCC not amenable to resection or thermal ablation. All along our experience with IRE, imaging appeared as a key point for addressing the specific issues listed above. For the 58 first patients 92% of complete ablation were achieved while the one-year local tumor progression free survival was 70% (95% CI: 56%, 81%). Indeed, despite the need of improvements IRE appears right now as a unique opportunity to achieve complete sustained local tumor control for patient bearing early or locally advanced HCC not amenable to other curative treatments.[-]