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BACKGROUND/AIMS: The capillary bed is recognized as the site where metabolic and nutrient processes occur for living tissues at all levels. The evaluation of this vital process is a major concern in microcirculation. Unlike traditional approaches that concentrated on the extreme local properties of this process, a more global analysis toward capillary ensembles is employed here, since capillaries work as a cooperative entirety. As a first step toward ensemble analysis, the static and planar geometric parameters are investigated. Parameters such as the capillary adjacency and size information are very important in predicting and analysing certain malfunctions in the microvascular bed. METHODS/RESULTS: In order to achieve an objective and accurate analysis of these vital parameters, a computerized imaging system is proposed. Not only the number of capillaries and the capillary cross-sectional areas are important in describing the microvascular bed but the planar distribution pattern of the capillaries also carries valid information. This information, unique to the ensemble analysis, can be used to reveal, visualise and quantify the clustering of capillaries; and this information, according to the Krogh model, is fundamental in estimating the tissue oxygen supply. Two spatial models, the closest neighbor and triangulation methods, have been applied to the captured images of capillary ensembles. The closest neighbor technique generates a minimal distance map or displays a distribution, which depicts the local clustering of capillaries. The triangulation technique, on the other hand, generates a mutual distance map, which is a global description of the capillary positions. Triangulation methods have been evaluated but all except the Greedy triangulation method have been rejected due to lack of robustness and model weakness. Therefore, the capillaries are triangulated by the Greedy triangulation method, and the capillary distribution uniformity is defined as one minus the coefficient of variance of the edge lengths of the mutual distance map. CONCLUSIONS: A series of advanced image processing methods have been developed that efficiently extract the capillary position, size and distribution information from the images. These results facilitate the automatic counting of capillaries and the capillary size-related pathological analysis.

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The biological zero (BZ) problem is a critical issue inherent in laser Doppler flowmetry (LDF). It causes confusion when measuring low tissue blood flows. Many experimental studies have been done on the question of whether the BZ flux should be subtracted from the normally measured flux in various situations. However this problem can only be solved after a proper mathematical analysis. Only then can we clearly define and formulate what flux is truly meaningful in blood perfusion measurement and what movement generates the BZ flux and how can we correctly remove it. Following this motivation, the movement of moving blood cells (MBC's) is decomposed into a net translation and a random wondering based on in vivo observations. This important step leads to a clear definition of the BZ and net perfusion flux and reveals that subtraction of BZ flux from the normal flux will certainly cause an underestimation of the net flux. Using this decomposition, the relationship between the net, BZ and normal flux is established which leads to the correct formula to recover the net flux from the BZ and normal fluxes. This recovered net flux is shown to be bounded by the normal flux and the normal flux minus the BZ flux. Numerical studies, preliminary phantom model and clinical evaluations manifest that the new approach is more accurate and reasonable at measuring low net fluxes. In contrast, subtracting BZ flux causes a systematic underestimation of perfusion and is apparently inappropriate even from a methodological point of view. In addition to the novel BZ solution, a general density function of the speed of MBC's is given which is more faithful than the Maxwell density used in [4]. This general density function offers new possibilities for further theoretical developments in LDF.

We study the tunneling dynamics of dopant-induced hole polarons which are self-localized by electron-phonon coupling in a two-dimensional antiferromagnet. Our treatment is based on a path integral formulation of the adiabatic (Born-Oppenheimer) approximation, combined with manybody tight-binding, instanton, constrained lattice dynamics, and many-body exact diagonalization techniques. The applicability and limitations of the adiabatic approximation in polaron tunneling problems are discussed in detail and adiabatic results are compared to exact numerical results for a two-site polaron problem. Our results are mainly based on the Holstein-tJ and, for comparison, on the Holstein-Hubbard model. We also study the effects of 2nd neighbor hopping and long-range electron-electron Coulomb repulsion. The polaron tunneling dynamics is mapped onto an effective low-energy Hamiltonian which takes the form of a fermion tight-binding model with occupancy dependent, predominantly 2nd and 3rd neighbor tunneling matrix elements, excluded double occupancy, and an effective intersite charge interactions. Antiferromagnetic spin correlations in the original many-electron Hamiltonian are reflected by an attractive contribution to the 1st neighbor charge interaction and by Berry phase factors which determine the signs of effective polaron tunneling matrix elements. In the two-polaron case, these phase factors lead to polaron pair wave functions of either d x 2 −y 2 -wave symmetry or p-wave symmetry with zero and nonzero total pair momentum, respectively. Implications for the doping dependent isotope effect, pseudo-gap and Tc of a superconducting polaron pair condensate are discussed and compared to observed properties of the cuprate high-Tc materials. 71.38.+i, 75.10.Lp, 71.27.+a