Anisotropy of the ultrasonic backscatter of myocardial tissue: II. Measurements in vivo

The purpose of this investigation was to determine the angular dependence of the backscatter from canine myocardial tissue in vivo and to compare it with the variation of backscatter over the cardiac cycle that has been recognized and reported previously. The backscatter was measured from regions of left ventricular wall in canine hearts in which the fibers of the muscle lay parallel to the surface of the heart and were oriented predominantly in a circumferential fashion. Because of technical considerations, the angle of insonification was varied systematically through two cycles in which the angle relative to the muscle fiber axes ranged from 60 degrees-120 degrees. Backscatter was maximum at angles of interrogation perpendicular to the myocardial fibers and minimum at those most acute (60 degrees) relative to the orientation of the fibers. The previously observed variation of integrated backscatter over the heart cycle was evident at each angle of interrogation. At end systole, the average maximum-to-minimum angular variation of integrated backscatter as 5.0 +/- 0.4 dB. At end diastole, the average maximum-to-minimum angular variation was 3.2 +/- 0.4 dB. Thus, even though angular dependence of the backscatter from tissues with directionally oriented structures is substantial, the anisotropy does not account for cardiac-cycle-dependent variation of backscatter. Accordingly, the angular dependence should be incorporated in approaches to quantitative tissue characterization with ultrasound.     

More on betweenness-uniform graphs

We study graphs whose vertices possess the same value of betweenness centrality (which is defined as the sum of relative numbers of shortest paths passing through a given vertex). Extending previously known results of S. Gago, J. Hurajová, T. Madaras (2013), we show that, apart of cycles, such graphs cannot contain 2-valent vertices and, moreover, are 3-connected if their diameter is 2. In addition, we prove that the betweenness uniformity is satisfied in a wide graph family of semi-symmetric graphs, which enables us to construct a variety of nontrivial cubic betweenness-uniform graphs.