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BACKGROUND Lenvatinib is an oral, multitargeted tyrosine kinase inhibitor of the vascular endothelial growth factor receptors 1 through 3 (VEGFR1‐VEGFR3), fibroblast growth factor receptors 1 through 4 (FGFR1‐FGFR4), platelet‐derived growth factor receptor α (PDGFRα), ret proto‐oncogene (RET), and v‐kit Hardy‐Zuckerman 4 feline sarcoma viral oncogene homolog (KIT) signaling networks implicated in tumor angiogenesis. Positive phase 1 results in solid tumors prompted a phase 2 trial in patients with advanced, radioiodine‐refractory, differentiated thyroid cancer (RR‐DTC). METHODS Fifty‐eight patients with RR‐DTC who had disease progression during the previous 12 months received lenvatinib 24 mg once daily in 28‐day cycles until disease progression, unmanageable toxicity, withdrawal, or death. Previous VEGFR‐targeted therapy was permitted. The primary endpoint was the objective response rate (ORR) based on independent imaging review. Secondary endpoints included progression‐free survival (PFS) and safety. Serum levels of 51 circulating cytokines and angiogenic factors also were assessed. RESULTS After ≥14 months of follow‐up, patients had an ORR of 50% (95% confidence interval [CI], 37%‐63%) with only partial responses reported. The median time to response was 3.6 months, the median response duration was 12.7 months, and the median PFS was 12.6 months (95% CI, 9.9‐16.1 months). The ORR for patients who had received previous VEGF therapy (n = 17) was 59% (95% CI, 33%‐82%). Lower baseline levels of angiopoietin‐2 were suggestive of tumor response and longer PFS. Grade 3 and 4 treatment‐emergent adverse events, regardless of their relation to treatment, occurred in 72% of patients and most frequently included weight loss (12%), hypertension (10%), proteinuria (10%), and diarrhea (10%). CONCLUSIONS In patients with and without prior exposure to VEGF therapy, the encouraging response rates, median time to response, and PFS for lenvatinib have prompted further investigation in a phase 3 trial. Cancer 2015;121:2749‐2756. © 2015 American Cancer Society, This phase 2 study demonstrates that lenvatinib produces encouraging objective response and progression‐free survival rates in patients with radioiodine‐refractory, differentiated thyroid cancer and also has a well defined safety profile. Lenvatinib also exhibits activity in patients who previously received vascular endothelial growth factor/vascular endothelial growth factor receptor‐targeted therapies.

In this thesis the interaction of a normal gas dynamic shock wave with a gas containing a distribution of small solid spherical particles of two distinct radii, σ1 and σ2, is studied (1) to demonstrate that the methods of kinetic theory can be extended to treat solid particle collision phenomena in multidimensional gas-particle flows; (2) to elucidate some of the essential physical characteristics associated with particle-particle collision processes; and (3) to give some indication regarding the importance of particle collisions in particle-laden gas flows. It is assumed that upstream of the shock wave particles σ1 are uniformly distributed while particles σ2 are non-uniformly distributed parallel to the shock face and in much smaller numbers than particles σ1. Under these conditions the gas-particle σ1 flow downstream of the shock wave is very nearly one-dimensional and independent of the presence of particles σ2. The usual shock relaxation zone is established by the interaction of particles σ and the gas downstream of the shock wave. The collisional model pro- posed by Marble3 is then extended and used with a modified form of the mean free path method of kinetic theory to calculate the macroscopic distribution and velocity of particles σ2 as determined by the particle σ1- particle σ2 and particle σ2-gas interactions. Within the condition that the random velocity imparted to a particle σ2 by a collision is damped by its viscous interaction with the gas before it suffers another collision, the kinetic theory method established here may be extended to include more general particle-particle and particle-gas interaction laws than those used by Marble. However, the collisional model employed is particularly important because the criteria for its application are easy to establish and because it admits a wide class of physically interesting situations. Within the restrictions of this collision model, it is possible to analyze the macroscopic motion of particles σ2 in three important limiting cases: (σ2/σ1)2 >> ⊥,(σ2/σ1)2 << ⊥ and (σ2/σ1)2 ~ ⊥. It is found that when (σ2/σ1)2 >> ⊥ there is essentially no redistribution of particles σ2 normal to the gas flow. The only effect of particle σ1 -particle σ2 encounters is a drag force acting to slow down particles σ2. When (σ2/σ1)2 << ⊥ it is found that particles σ2. may have many collisions during their passage through the shock relaxation zone. As a consequence there may be a substantial redistribution of particles σ2 downstream of the shock wave. The physical features of this process are studied in detail together with the range of validity of this diffusion model. The case (σ2/σ1)2 ~ ⊥ is analyzed under the condition particles σ2 have at most one collision during their passage through the shock relaxation zone. It is found that when the gas or particle σ1 density is low, the single collision effects may be important even when σ2/σ1 differs significantly from unity and the particles are not very small. Under most conditions of practical significance, because there is invariably a distribution of particles sizes present in a dusty gas, the calculation of the particle distribution in the shock relaxation zone should account for the effects of particle-particle encounters. It is suggested that an experimental observation of particle size distribution in a shock relaxation zone can yield significant information on particle-particle and particle-gas interaction laws.