Fig. 1
Illustration of a cascade sampling design in the lung, using the estimation of the total volume of alveolar type II cells in a lung as an example. At each level, from macroscopic via light microscopic to electron microscopic, the principles of unbiased sampling, e.g. by systematic uniform random sampling, have to be applied (Step 4). At the macroscopic level, the lung is cut completely into horizontal slices of thickness t, starting at a random position between 0 and t (arrow). These slices serve two purposes: They can be used for the estimation of total lung volume by the Cavalieri estimator (Step 3) as well as for sampling of tissue blocks for light and electron microscopy (see Fig. 3). Total lung volume, V(lung), is the product of t and the total cut area of the apical side of all slices (shown in red). At a low light microscopic magnification, the volume fraction of parenchyma within lung, VV(par/lung), is estimated by point counting. The volume fraction of alveolar septum within parenchyma, VV(alvsep/par), is estimated by point counting at a medium light microscopic magnification (compare Fig. 5). The volume fraction of type II cells within alveolar septum, VV(typeII/alvsep), is estimated by point counting at a medium electron microscopic magnification. The total volume of type II cells, V(typeII), is then obtained as V(typeII) = V(lung) · VV(par/lung) · VV(alvsep/par) · VV(typeII/alvsep). Note that in this cascade sampling design, the phase of interest at one level (red) becomes the reference phase (red + green) at the next level. Modified after [34]