Background: The size of lipoprotein particles is relevant to the risk of coronary artery disease (CAD). Methods: We investigated the feasibility of atomic force microscopy (AFM) for evaluating the size of large low-density lipoprotein (LDL) and small dense LDL (sd-LDL) separated by ultracentrifugation. The measurements by AFM in tapping mode were compared to those by electron microscopy (EM).Results: There was a significant difference in particle sizes determined by AFM between large LDL (20.6 AE 1.9 nm, mean AE SD) and sd-LDL (16.2 AE 1.4 nm) obtained from six healthy volunteers (P < 0.05). The particle sizes determined by EM for the same samples were 23.2 AE 1.4 nm for large LDL and 20.4 AE 1.4 nm for sd-LDL. The difference between large LDL and sd-LDL detected by EM was also statistically significant (P < 0.05). In addition, the particle sizes of each lipoprotein fraction were significantly different between AFM and EM: P < 0.05 for large LDL and P < 0.05 for sd-LDL. Conclusions: AFM can differentiate between sd-LDL and large LDL particles by their size, and might be useful for evaluating risk for CAD.
Let A be a plane region inside an outer rectangle with r rectangular obstacles, and let k terminal pairs lie on the boundaries of the outer rectangle and one of the obstacles. This paper presents an efficient algorithm which finds "non-crossing" rectilinear paths in the plane region A, each connecting a terminal pair without passing through any obstacles, and whose total length is minimum. Non-crossing paths may share common points or line segments but do not cross each other in the plane. The algorithm takes time O(n log n) where n = k + r.
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