First-line therapy in HER2 positive metastatic breast cancer. Is the mosaic fully completed or are we missing additional pieces?

The discovery of human epidermal growth factor receptor 2 (HER2) and its role in the biology of breast cancer and the subsequent development of HER2-targeted therapies, have dramatically improved clinical outcomes for women with early-stage and advanced HER2-positive breast cancer (BC). HER-2 targeted therapies represent a major step forward in achieving the goal of delivering individualized targeted therapy for BC, and trastuzumab was the first anti-HER-2 strategy to be approved for treatment of HER-2 positive BC. This review discusses the treatment of metastatic HER2-positive BC and describes efficacy and safety of novel anti-HER2 target therapies in first-line metastatic settings and the future challenges include refining such treatments, reducing toxicity and simultaneously developing innovative therapies. Furthermore, combinations of trastuzumab and drugs targeting the downstream pathway are described. In the next future will be possible to use an ample armamentarium of combination therapies directed against HER2 and key signaling components integrated in the HER network. This approach will allow clinicians to tailor the management of the individual patient on the basis of tumor- specific biomarker profiles. There is an urgent need for prospective biomarker-driven trials to identify patients for whom targeting is cost-effective

Aggregative movement and front propagation for bi-stable population models

Front propagation for the aggregation-diffusion-reaction equation is investigated, where f is a bi-stable reaction-term and D(v) is a diffusion coefficient with changing sign, modeling aggregating-diffusing processes. We provide necessary and sufficient conditions for the existence of traveling wave solutions and classify them according to how or if they attain their equilibria at finite times. We also show that the dynamics can exhibit the phenomena of finite speed of propagation and/or finite speed of saturation

Diffusion-aggregation processes with mono-stable reaction terms

This paper analyses front propagation of the equation $u_\tau=[D(u)v_x]_x +f(v) \;\;\; \tau < 0, x \in \mathbb{R}$ where $f$ is a monostable (ie Fisher-type) nonlinear reaction term and $D(v)$ changes its sign once, from positive to negative values,in the interval $v \in[0,1]$ where the process is studied. This model equation accounts for simultaneous diffusive and aggregative behaviors of a population dynamic depending on the population density $v$ at time $\tau$ and position $x$. The existence of infinitely many travelling wave solutions is proven. These fronts are parametrized by their wave speed and monotonically connect the stationary states u = 0 and v = 1. In the degenerate case, i.e. when D(0) and/or D(1) = 0, sharp profiles appear, corresponding to the minimum wave speed. They also have new behaviors, in addition to those already observed in diffusive models, since they can be right compactly supported, left compactly supported, or both. The dynamics can exhibit, respectively, the phenomena of finite speed of propagation, finite speed of saturation, or both

Guiding-like functions for semilinear evolution equations with retarded nonlinearities

The paper deals with a semilinear evolution equation in a reflexive and separable Banach space. The non-linear term is multivalued, upper Caratheodory and it depends on a retarded argument. The existence of global almost exact, i.e. classical, solutions is investigated. The results are based on a continuation principle for condensing multifields and the required transversalities derive from the introduction of suitable generalized guiding functions. As a consequence, the equation has a bounded globally viable set.The results are new also in the lack of retard and in the single valued case. A brief discussion of a non-local diffusion model completes this investigation

Guiding-like functions for semilinear evolution equations with retarded nonlinearities

The paper deals with a semilinear evolution equation in a reflexive and separable Banach space. The non-linear term is multivalued, upper Caratheodory and it depends on a retarded argument. The existence of global almost exact, i.e. classical, solutions is investigated. The results are based on a continuation principle for condensing multifields and the required transversalities derive from the introduction of suitable generalized guiding functions. As a consequence, the equation has a bounded globally viable set. The results are new also in the lack of retard and in the single valued case. A brief discussion of a non-local diffusion model completes this investigation

Activity of eribulin mesylate in brain metastasis from breast cancer. a stone in a pond?

Background: Brain metastases develop in approximately 10-25% of patients with metastatic breast cancer (MBC) and are associated with a very poor prognosis. Case Report: We report the case of a 40-year-old woman with MBC and associated lung, bone, liver, and brain metastases, who experienced a time to progression of several months with eribulin after whole-brain radiotherapy (WBRT), 2 lines of chemotherapy, and 1 line of hormonal therapy, maintaining a good toxicity profile. Discussion: Eribulin, in association with local treatment such as WBRT, can be well tolerated and effective in achieving a long progression-free survival and a good control of brain metastases in patients with MBC who have received multiple lines of treatment. The vascular remodeling properties of eribulin, combined with brain radiotherapy, might facilitate the passage of eribulin across the blood brain barrier, improving brain response. Conclusion: Our anecdotal experience suggests that eribulin may have a potentially beneficial effect on brain metastases while maintaining a good systemic control of the disease in patients with MBC

Strictly localized bounding functions and Floquet boundary value problems

Semilinear multivalued equations are considered, in separable Banach spaces with the Radon-Nikodym property. An effective criterion for the existence of solutions to the associated Floquet boundary value problem is showed. Its proof is obtained combining a continuation principle with a Liapunov-like technique and a Scorza-Dragoni type theorem. A strictly localized transversality condition is assumed. The employed method enables to localize the solution values in a not necessarily invariant set; it allows also to introduce nonlinearities with superlinear growth in the state variable

Strictly localized bounding functions and Floquet boundary value problems

Semilinear multivalued equations are considered, in separable Ba-nach spaces with the Radon-Nikodym property. An effective criterion for the existence of solutions to the associated Floquet boundary value problem is showed. Its proof is obtained combining a continuation principle with a Liapunov-like technique and a Scorza-Dragoni type theorem. A strictly localized transversality condition is assumed. The employed method enables to localize the solution values in a not necessarily invariant set; it allows also to introduce nonlinearities with superlinear growth in the state variable