Oxygen supply plays a central role in cancer cell proliferation. While vascular density increases at the early stages of carcinogenesis, mechanical solid stresses developed during growth compress tumor blood vessels and, thus, drastically reduce the supply of oxygen, but also the delivery of drugs at inner tumor regions. Among other effects, hypoxia and reduced drug delivery compromise the efficacy of radiation and chemo/nano therapy, respectively. In the present study, we developed a mathematical model of tumor growth to investigate the interconnections among tumor oxygenation that supports cancer cell proliferation, the heterogeneous accumulation of mechanical stresses owing to tumor growth, the non-uniform compression of intratumoral blood vessels due to the mechanical stresses, and the insufficient delivery of oxygen and therapeutic agents because of vessel compression. We found that the high vascular density and increased cancer cell proliferation often observed in the periphery compared to the interior of a tumor can be attributed to heterogeneous solid stress accumulation. Highly vascularized peripheral regions are also associated with greater oxygenation compared with the compressed, less vascularized inner regions. We also modeled the delivery of drugs of two distinct sizes, namely chemotherapy and nanomedicine. Model predictions suggest that drug delivery is affected negatively by vessel compression independently of the size of the therapeutic agent. Finally, we demonstrated the applicability of our model to actual geometries, employing a breast tumor model derived from MR images.

Targeting the rich extracellular matrix of desmoplastic tumors has been successfully shown to normalize collagen and hyaluronan levels and re-engineer intratumoral mechanical forces, improving tumor perfusion and chemotherapy. As far as targeting the abundant cancer-associated fibroblasts (CAFs) in desmoplastic tumors is concerned, while both pharmacologic inhibition of the sonic-hedgehog pathway and genetic depletion of fibroblasts have been employed in pancreatic cancers, the results between the two methods have been contradictory. In this study, we employed vismodegib to inhibit the sonic-hedgehog pathway with the aim to i) elucidate the mechanism of how CAFs depletion improves drug delivery, ii) extent and evaluate the potential use of sonic-hedgehog inhibitors to breast cancers, and iii) investigate whether sonic-hedgehog inhibition improves not only chemotherapy, but also the efficacy of the most commonly used breast cancer nanomedicines, namely Abraxane® and Doxil®. We found that treatment with vismodegib normalizes the tumor microenvironment by reducing the proliferative CAFs and in cases the levels of collagen and hyaluronan. These modulations re-engineered the solid and fluid stresses in the tumors, improving blood vessel functionality. As a result, the delivery and efficacy of chemotherapy was improved in two models of pancreatic cancer. Additionally, vismodegib treatment significantly improved the efficacy of both Abraxane and Doxil in xenograft breast tumors. Our results suggest the use of vismodegib, and sonic hedgehog inhibitors in general, to enhance cancer chemo- and nanotherapy.

Mechanical stretch plays an important role in regulating shape and orientation of the vascular endothelial cell. This morphological response to stretch is basic to angiogenesis, neovascularization, and vascular homeostasis, but mechanism remains unclear. To elucidate mechanisms, we used cell mapping rheometry to measure traction forces in primary human umbilical vein endothelial cells subjected to periodic uniaxial stretches. Onset of periodic stretch of 10% strain amplitude caused a fluidization response typified by attenuation of traction forces almost to zero. As periodic stretch continued, the prompt fluidization response was followed by a slow resolidification response typified by recovery of the traction forces, but now aligned along the axis perpendicular to the imposed stretch. Reorientation of the cell body lagged reorientation of the traction forces, however. Together, these observations demonstrate that cellular reorientation in response to periodic stretch is preceded by traction attenuation by means of cytoskeletal fluidization and subsequent traction recovery transverse to the stretch direction by means of cytoskeletal resolidification.

It is well documented in a variety of adherent cell types that in response to anisotropic signals from the microenvironment cells alter their cytoskeletal organization. Previous theoretical studies of these phenomena were focused primarily on the elasticity of cytoskeletal actin stress fibers (SFs) and of the substrate while the contribution of focal adhesions (FAs) through which the cytoskeleton is linked to the external environment has not been considered. Here we propose a mathematical model comprised of a single linearly elastic SF and two identical linearly elastic FAs of a finite size at the endpoints of the SF to investigate cytoskeletal realignment in response to uniaxial stretching of the substrate. The model also includes the contribution of the chemical potential energies of the SF and the FAs to the total potential energy of the SF-FA assembly. Using the global (Maxwell's) stability criterion, we predict stable configurations of the SF-FA assembly in response to substrate stretching. Model predictions obtained for physiologically feasible values of model parameters are consistent with experimental data from the literature. The model shows that elasticity of SFs alone can not predict their realignment during substrate stretching and that geometrical and elastic properties of SFs and FAs need to be included.

It is well known that substrate stretching reorganizes the actin cytoskeleton of an adherent cell. Experiments have proved that the stress fibers are reoriented into one or two distinct directions. It is further pointed out that reorientation of the stress fibers phenomena are observed with quite high strains, where linear elasticity theory is not valid. Therefore, the existing linear theories for mechanics interpretation of those phenomena are not satisfactory. The experimental evidence of the existence of two distinct directions of the reorientation indicates a co-existence of phases non-linear elastic phenomenon. Further that observation is quite strong evidence that the strain energy density function should be non-convex. The reorganization of the stress fibers under uniaxial substrate stretching is studied as a non-linear elastic stability problem. Adapting the global (Maxwell's) criterion for stability, various phenomena, concerning the reorientation of the stress fibers, are interpreted into the context of finite elasticity. The experiments demonstrate co-existence of phases phenomena that are justified in the present study. The influence of various factors like contractility and extracellular stretching is demonstrated. Furthermore, the non-convexity factor is attributed to the influence of the small GTPase Rho regulating the formation of the actin stress fibers. The predominant final stress fibers placement that is transverse to the extracellular stress direction and appears in long time after the co-existence of phases placement is also justified.