Pattern analysis of chronic liver diseases from the viewpoint of structural connectivity

On microscopic picture of cirrhosis and allied disorders, "degree of nodular separation" rho theta was established to measure the advancement of cirrhotic change. Based on mathematical treatment of the curvature of linear boundaries between the parenchymal and interstitial areas, rho theta is defined as: rho theta = theta A (net)/theta A (abs) (-1 smaller than or equal to rho theta smaller than or equal to +1) where theta A (net) is the net sum and theta A (abs) the absolute sum of the angles subtended by the boundaries in an area A, provided that plus and minus angles are distinguished according to whether the curvature is convex or concave toward the interstitium. rho theta = +1 when all nodules are round and completely separated, and diminishes with advancing internodular coalescence, finally to a negative value when the interstitium is disconnected to separate parts by nodular joining. The parameter thus describes patterns of different connectivity, serving as a measure of architectural disorganization. rho theta is easily determined by tangent counting on histological picture. The method was applied to 70 autopsy cases including cirrhosis and chronic hepatitis, and the results were related to the hepatic weight, development of hepatoma, and so on.