#### 4. Inconsistencies and misleading claims

**A. GLI, volume fraction and stereology**

First, authors keep claiming that “GLI is a well-established stereological parameter”. In fact, **it** **has very little to do with stereology. **Stereology is a science of calculation a three-dimensional value from measurements made on two-dimensional planar sections. For example, the 3-D **volume** of an object can be determined from the 2-D **areas** of its plane sections; the **length** of some morphological structure in 3D can be determined from counting the **number** of its sections in 2D, etc. The technique for determining volume fraction in 3D from area fraction on infinitely-thin sections of “spatially homogenous” samples (polished surfaces of non-transparent materials) is well known as Delesse’s principle, as it was first described by geologist A. E. Delesse in 1843. So, constantly repeating that “areal fraction is an estimate of the volume density of cell bodies” seems not only misleading, but simply wrong, because **area fraction measured in microscopic sections is not equal to volume fraction**. Moreover, the same authors (A. Schleicher and K. Zilles) quite clearly demonstrated with A. Wree in 1982 (the paper was described above) the **difference** between these two values. It **is small **enough **only** if the section thickness is **between 4.6 and 5.6 μk**. The exact quotation from this paper (with my underlining), section “Estimation of volume fraction by GLI measurement”, page 38, is quite clear: “a section thickness from 4.6 μk could be defined (Fig. 4a) as permitting measurement of the GLI representing an estimate of volume fractions of all grisea with a tolerable error of about ± 15%. If another section thickness is used, the measured data have to be corrected with a factor that can be ascertained from Fig. 4a.” The referenced image, taken from 1990’s paper of A. Schlicher and K. Zilles is below (I could not use A.Wree’s paper due to the poor quality of available copy).

Looking at this picture we can see quite clearly that GLI value (~35%) is close enough to the volume density for sections from 4 to 6 mkm. For 20 micron thick sections GLI value is about ~65%, which roughly gives 86% relative error (or from 78% to 390% for different structures, according to Wree et all.). Clearly, it is not a good match to unbiased values obtained from 1-mkm thick sections. In other words, by claiming that “areal fraction is an estimate of the volume density of cell bodies” the **authors ignore their own results** **published ****earlier, **which quite clearly demonstrate the opposite: **in 20 micron-thick sections area fraction is VERY POOR estimate of volume density**.

Unfortunately, this problem is not just an academic question. Correction for the section thickness might be very important, and the lack of thereof might artificially bias many results, including the increase of inter-subject variability, especially when tissue processing conditions of different brains vary. Differences in postmortem delay, time of fixation and fixative (Bodian, formalin), as, for example is described in paper “Cytoarchitectonic mapping of the human dorsal exastriate cortex” (M. Kujovic, at all, Brain Struct. Funct. 218:157-182, 2013), might have significant effect on variation of morphometric value measured in a section plane, even if the expected section thickness supposed to be the same (in this case – 20 μk ) in all measured brains.

I honestly tried to find out how the abovementioned correction of GLI is done, and was it done at all, looking in all publications of A. Schleicher and K. Zilles that followed 1982’s paper. Finally, in 2000’s paper I found direct admission: “**GLI values are biased volume density estimates**“. So, later claim by group, that include same authors, that GLI “profiles reflect laminar fluctuations of cells density” (S. Lorenz et all, “Two new cytoarchitectonic areas of human mid-fusiform gyrus”, Cerebral Cortex, 2015, 1-13) is quite misleading again, and contradicts earlier statement that “GLI differs from the estimation of numerical densities (number of objects per volume unit of reference space).”