Abstract
Cells adhere to each other and to the extracellular matrix (ECM) through protein molecules on the surface of the cells. The breaking and forming of adhesive bonds, a process critical in cancer invasion and metastasis, can be influenced by the mutation of cancer cells. In this paper, we develop a nonlocal mathematical model describing cancer cell invasion and movement as a result of integrin-controlled cell-cell adhesion and cell-matrix adhesion, for two cancer cell populations with different levels of mutation. The partial differential equations for cell dynamics are coupled with ordinary differential equations describing the ECM degradation and the production and decay of integrins. We use this model to investigate the role of cancer mutation on the possibility of cancer clonal competition with alternating dominance, or even competitive exclusion (phenomena observed experimentally). We discuss different possible cell aggregation patterns, as well as travelling wave patterns. In regard to the travelling waves, we investigate the effect of cancer mutation rate on the speed of cancer invasion.
Highlights
Colloidal quantum dots (CQDs) have emerged as an attractive luminescent nanomaterial for lighting and displays, in part because of their solution processability, narrow emission linewidth and broad absorption spectra
The forward power conversion efficiency values are lower than the photoluminescence quantum yield (PLQY) because of the quantum defect and because light emitted in other directions, included light waveguided in the CQD film and the flexible glass, is not detected by the system
We have demonstrated high-speed visible light communications (VLC) using μLEDs color converted by CQDs
Summary
Colloidal quantum dots (CQDs) have emerged as an attractive luminescent nanomaterial for lighting and displays, in part because of their solution processability, narrow emission linewidth and broad absorption spectra. Blue-emitting LED chips optically excite yellow, green and/or red down-converting phosphors, eventually mixing the wavelengths to obtain light of the desired characteristics. Photodegradation starts in the samples once oxygen has permeated the epoxy sealing the edges of the flexible glass and reached the CQD films This takes between ten to more than 250 hours in our converters and during that time color conversion is stable. The forward conversion efficiency (the ratio of the power of the converted light, as measured in the forward direction by the experimental system, by the power of the bare μLED, see section 4.3) for each wavelength of color converter is consistent with the PLQY. The forward power conversion efficiency values are lower than the PLQY because of the quantum defect and because light emitted in other directions, included light waveguided in the CQD film and the flexible glass, is not detected by the system. These PL lifetime values (between 13 ns and 35 ns) are at least two orders of magnitude shorter than for conventional phosphors
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