Construction of Lp\mathcal L^p-strong Feller Processes via Dirichlet Forms and Applications to Elliptic Diffusions

We provide a general construction scheme for $\mathcal L^p$-strong Feller processes on locally compact separable metric spaces. Starting from a regular Dirichlet form and specified regularity assumptions, we construct an associated semigroup and resolvents of kernels having the $\mathcal L^p$-strong Feller property. They allow us to construct a process which solves the corresponding martingale problem for all starting points from a known set, namely the set where the regularity assumptions hold. We apply this result to construct elliptic diffusions having locally Lipschitz matrix coefficients and singular drifts on general open sets with absorption at the boundary. In this application elliptic regularity results imply the desired regularity assumptions

Cell Tracking and Therapy Evaluation of Bone Marrow Monocytes and Stromal Cells Using SPECT and CMR in a Canine Model of Myocardial Infarction

Background: The clinical application of stem cell therapy for myocardial infarction will require the development of methods to monitor treatment and pre-clinical assessment in a large animal model, to determine its effectiveness and the optimum cell population, route of delivery, timing, and flow milieu. Objectives: To establish a model for a) in vivo tracking to monitor cell engraftment after autologous transplantation and b) concurrent measurement of infarct evolution and remodeling. Methods: We evaluated 22 dogs (8 sham controls, 7 treated with autologous bone marrow monocytes, and 7 with stromal cells) using both imaging of 111Indium-tropolone labeled cells and late gadolinium enhancement CMR for up to12 weeks after a 3 hour coronary occlusion. Hearts were also examined using immunohistochemistry for capillary density and presence of PKH26 labeled cells. Results: In vivo Indium imaging demonstrated an effective biological clearance half-life from the injection site of ~5 days. CMR demonstrated a pattern of progressive infarct shrinkage over 12 weeks, ranging from 67-88% of baseline values with monocytes producing a significant treatment effect. Relative infarct shrinkage was similar through to 6 weeks in all groups, following which the treatment effect was manifest. There was a trend towards an increase in capillary density with cell treatment. Conclusion: This multi-modality approach will allow determination of the success and persistence of engraftment, and a correlation of this with infarct size shrinkage, regional function, and left ventricular remodeling. There were overall no major treatment effects with this particular model of transplantation immediately post-infarct