Penalty Ensembles for Navier-Stokes with Random Initial Conditions & Forcing

Inspired by the novel ensemble method for the Navier-Stokes equations (NSE) in 2014 \cite{Nan-Layton-ensemble}, and the work of \cite{YanLuo-ZhuWang-ensemble}, this report develops an ensemble penalty method for the NSE. In addition, the method is extended to Monte Carlo random sampling. The combination allows greater ensemble sizes with reduced complexity and thus gives a longer predictability horizon

INJECTABLE ALGINATE HYDROGELS WITH GROWTH FACTORS / LIVING STEM CELLS FOR MYOCARDIAL INFARCTION REPAIR

Myocardial infarction (MI), caused by the occlusion of the left ventricular coronary artery, may lead to massive loss of cardiomyocytes and eventually heart failure. To repair MI, one key issue is to compensate for the loss of cardiomyocytes in the MI site. Notably, cardiomyocytes are mature cells with limited proliferation capability. Another issue in MI repair is to improve the local ischemic condition at the MI site so as to provide the cells with nutrition and oxygen, where the revascularization or the renewal of the small vessels (or angiogenesis) is critical. To address the issues, the proposed study aims to develop injectable alginate hydrogels with growth factor/living cells for MI repair. To be more specific, two specific strategies were developed, which were 1) to co-deliver 6-Bromoindirubin-3-oxime (BIO) and insulin-like growth factor (IGF-1) by means of nanoparticles and 2) to encapsulate living stem cells. BIO is a small molecular drug that can promote the regeneration of cardiomyocytes and IGF-1 is able to stimulate the angiogenesis. In the development of strategy 1), both BIO and IGF-1 were encapsulated in gelatin nanoparticles, which were later cross-linked with the oxidized alginate to form a novel hybrid hydrogel system. The fabricated nanoparticles were then subjected both in vitro and in vivo characterization. The results have shown that the growth factors can continue to release over 110 hours in vitro and last for 45 days in vivo. The in vivo results have also shown that the hybrid system could enhance the proliferation of cardiomyocytes in situ and could promote revascularization around the MI sites, allowing improved cardiac function. Taken together, the strategy of co-delivering of BIO and IGF-1 is promising for MI repair. In the development of strategy 2), two types of alginate hydrogels, based on self-crosslinking (SCL) and calcium ion crosslinking (Ca2+ ), were synthesized in varying formulations; hydrogels encapsulated living muscle-derived stem cells (MDSCs) and their performance was evaluated in terms of optimizing cell viability during the injection process as well as the live/dead ratio after long-term cultivation. The morphology of the hydrogel-encapsulated cells was characterized by scanning electronic microscopy (SEM) and live/dead cells were examined using an 3-(4,5- dimethylthiazol-2-yl)- 2,5-diphenyltetrazolium bromide staining (MTT) assay. The mechanical properties of the hydrogels were also determined via a rheometer, to identify their influence on cell viability during the injection process and with respect to long-term cultivation. The results show that living cells are able to survive in both types of hydrogels and SCL hydrogel in particular is better for the living cells in long term. To sum up, this study illustrates that both strategies are promising in MI repair by presenting a non-invasive method of injecting biocompatible and biodegradable hydrogel with growth factors and living cells for supplementing cells and angiogenesis for further enhancing heart function in MI rats. These strategies could be adopted and used in clinical applications to human patients