Fig. 3

Estimation of the volume of the fixed lung (Step 3) according to the Cavalieri estimator and subsequent sampling. a The lung is embedded in agar and cut into slices of equal thickness t, with a random start in the agar outside the lung, thus following the principles of systematic uniform random sampling (SURS). Slice thickness t is adjusted to obtain around 8–10 slices. b The slices are placed on a tray with a consistent orientation, e.g. all apical surfaces upwards. The total volume of the lung, V, is calculated as the sum of the cut surface areas, A, of all slices (indicated in red in a) multiplied by the slice thickness t: V = ΣA·t. The cut surface areas, A, are estimated by counting points, P, hitting the cut surface areas using a grid with a known area per point, a(p), as: V = ΣP·a(p)·t. A constant definition for a point “hit”, P, is needed, e.g. the upper right corner of the crosses that symbolize the test points (indicated by red arrow). Based on this definition, correct point counts are shown in red. Note that in this example, where the slices are oriented with their apical side upwards, the first slice does not contain an apical cut surface and thus does not contribute any point counts. Accordingly, the uncut pleura at the lateral sides, here visible on the first four slices when viewed from above (grey), is also excluded (black test points) whereas the cut pleura at the apical surfaces (black) is included (red test points). c This collection of fixed lung slices can also be used as the starting point for SURS (Step 4). For example, if 3 different embedding protocols shall be used in the study (e.g. embedding in glycol methacrylate for light microscopic stereology, embedding in paraffin for immunohistochemistry and embedding of smaller subsamples in epon for electron microscopy), the slices are randomly assigned to these 3 protocols with a constant sampling interval (here 3). Thus, slices 1, 4 and 7 will be embedded according to protocol 1, slices 2, 5 and 8 will be embedded according to protocol 2 and slices 3, 6 and 9 will be embedded according to protocol 3. Note that all slices have to be sampled for embedding, even those who had to be excluded from the Cavalieri estimator (here slice 1). Also note that each of these 3 subsamples obtained by SURS constitutes a fraction of 1/3 of the whole lung. They can therefore also be used as starting point for fractionator sampling. d The principle of SURS consists of a random component (the selection of the first sample) and a systematic uniform component (the constant sampling interval for the selection of all other samples). SURS also applies to the subsequent stages of the sampling sequence, such as the selection of smaller subsamples (e.g. for electron microscopy) or the selection of fields of view on histologic sections from an embedded lung slice. The sampling interval is adjusted to achieve the desired number of samples