The important part of the Fractionator approach to Systematic Random Sampling (SRS) is that the Area Sampling Fraction (ASF) remains constant throughout all of the sections that are counted. The ASF is the ratio between the area of one counting frame and the area of one space of the SRS grid, and therefore is completely independent of the size and shape of your region of interest. As long as you only count cells which are within the portion of the counting frame that is inside the region of interest your results will remain unbiased.

“Variation of fractionator estimates and its prediction” (1998 Schmitz, C. in Anat Embryol (Berl), 198 371-97, see Fig. 9) examines this question in greater detail by performing two separate calculations of the Volume Fraction (VF) and comparing them. First, they calculate the VF by taking the ratio of the area of one counting frame to the area of one SRS grid space. Then, they calculate the VF by breaking each counting frame into 1000 pieces and directly summing only those pieces that fall over the area of interest, and they divide this area by the volume of the region, measured directly. They find that the two separate VF calculations agree, and therefore the final estimate of the total number of cells within the region of interest will not differ significantly based on which method for VF calculation is chosen. Since the first method is much faster it is used for calculating the VF.

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