Estimation of length and surface of anisotropic capillaries

Surface density (SV) and length density (LV) of myocardial capillaries have hitherto been estimated from their profile boundary length (BA) and their numerical density (QA) on transverse sections by the simplifying assumptions of the Krogh model (perfectly anisotropic, straight, unbranched capillaries with constant cross-sectional area). As the capillaries actually are partially anisotropic, curved, branching cylinders with variable cross-sectional area, a geometrical bias arises from the model-reality discrepancies. We have applied and compared two methods to overcome these inconsistencies: (1) estimation of LV and SV by a more realistic model (the Dimroth-Watson distribution); (2) estimation of LV and SV from isotropic uniform random (IUR) sections. Twelve male Wistar rats were fixed by retrograde vascular perfusion. One pair of longitudinal and transverse sections, and six IUR sections per animal were selected at random from the left ventricular papillary muscles. Ultrathin sections were silver-impregnated and studied by light microscopic morphometry. Nearly identical estimates of LV and SV were found by both methods. The model-based estimation provides biologically meaningful anisotropy constants, but it presupposes knowledge of the anisotropy axis. The IUR method provides no measure of anisotropy, but it can be applied in tissues where the anisotropy axis is not known. Both methods are equally efficient and practically unbiased in SV estimation, but the model-based estimation is far more efficient in LV estimation.