Hemispheric surface area measures

Surface area measures of the cortex are important because they reflect cytoarchitectural organisation. Current thinking attributes the size of the cortical surface mainly to the growth of the neocortex due to expansion of its neuropil (Armstrong et al.,1991 & 1995). In ontogeny and phylogeny, this expansion is limited very largely to a tangential direction by replication of a basic columnar multicellular element, which is repeated and locally elaborated rather than fundamentally changed (Richman et al.,1975; Rockel et al.,1980; Rakic, 1995): there is hardly any increase in cortical thickness even across species (Welker, 1990). Cortical folding allows a large surface area to be contained in a comparatively small volume and is an efficient organisation (Ruppin et al.,1993). As a consequence of this organisation, the surface density of neurons in the cortex has been postulated to be constant, so that determination of a cortical surface area measure might provide a means of

estimating total and regional neuronal numbers and function- specific neuronal proportions (see 1.4).

For reasons given in section 3.13, the cortical surface area measure used was the SM surface, a boundary created by the spatial dominance of intergyral arcuate (or "U" fibres) and aggregating projectional fibres passing through this interface. Such projectional fibres are most plentiful in the walls and at the crowns of gyri and least numerous in the depths of the sulci (Welker, 1990).

The white matter cores within gyri, underlying the crown and walls, increase SM surface area significantly more than they increase its volume. Measurement of the surface area of a block of SM before and after arbitrary but defined pruning supports this proposition: the removal of all protruding white matter cores 3mm or less in diameter leads to a large loss of surface area, but significantly less volume loss. The observed loss of surface area correlates significantly with the calculated extra surface area of the block generated by its surface folding. That the observed loss and calculated extra surface area are not identical may simply be because an arbitrary (though defined) white matter core size of 3mm was specified; real gyral cores have various diameters and shapes, and a more sophisticated method might have been to remove cores depending on individual brain size. The aim, however, was to demonstrate a principle, which is also supported by the

finding that the ratio of extra SM area to the total SM area (the ratio E^/SM^) is high. The experiment shows that E^, the extra surface area generated by folding of the SM, may also be taken as an estimate of the surface area of the gyral cores, that is the area directly overlain by cortical grey matter in gyral crowns and walls rather than in sulcal depths. Both E;^ and SMa correlate, in normal brains, with GM volume, and thus with total neuronal number (Braendgaard et al.,1990). However, given the nonuniform density of projectional (afferent and efferent) fibres crossing the grey-white interface, E^^ better

reflects projectional axon numbers than does the total SM area, SM^, and may be considered to be more biologically relevant (Sisodiya et al.,1996) . In brains where, for example, the cortex is pathologically thickened (for example as a result of lissencephaly), may be a better measure of projectional axonal numbers that either SM^, grey matter volume (Haug, 1987; Braendgaard et al.,1990) or even the free GM surface (Rockel et al.,1980).

The surface area derivatives quantify mean structural properties of entire hemispheres. The parameters assess the relationship between the extra SM area, and GM and SM volume and CCA. These ratios are independent of brain size and may identify changes in structural proportions even though the underlying variables (surface areas and volumes) fall within the normal range. Values all fall within three standard deviations of the mean for control subjects, suggesting that there is order in normal cerebral structure. In patients, small areas of disproportion, due to structural abnormality, may be averaged out by larger areas of proportion (structural normality) within the same hemisphere. If abnormal values for these parameters are found, then the pathological process present in the hemisphere must be quantitatively dominant.

The ratio ECC is perhaps most simply interpreted. In control subjects, E^^ is a measure of the number of projectional axons and the amount of neuropil/neuron causing tangential growth of the neocortex (Fig 5.1) . CCA is a measure of the number of interhemispheric fibres (Tomasch, 1954; Aboitiz et al.,1992). ECC is a function of these quantities. An increase in ECC implies either (1) that the proportion of

(noninterhemispheric) projectional axons is increased and the proportion of interhemispheric fibres is reduced (or that they are thinner on average) or (2) that the mean amount of neuropil/neuron is increased (or some combination of these findings) . In any case, there must be an alteration in the normal pattern of interneuronal connectivity (as mediated by

Figure 5.1

Schematic demonstration of generation of SM surface. In t h e t o p f i g u r e , t h e predominantly outer folded line represents the real SM surface in cross-section; the circular outline encompasses the same area but is unfolded; the difference in the perimeters of the two regions is the extra length (area in three dimensions) generated by the folding of the surface of the SM. This is termed E^, the extra area and is defined by:

Ea = SM^ - 4rr(3SMV/4n)2/3

where SM^ is the measured SM surface area and SMV the measured SM v o l u m e .

The bottom figure represents a single gyrus; the outer thick line is the grey-CSF surface, the inner thick line is the GM- SM interface. The numerous thin lines are projectional axons. Note their density is highest at the gyral crown and lowest at the gyral base; in the sulcus, they form U fibres

(marked T ) • The base of the white matter core of the gyrus (shaded grey) is composed of projectional axons; these are separated in the body of the gyrus by the growth of the neuropil (represented by the squares) . E& is a measure of the inner thick line, ie the surface of gyral white matter cores, and is therefore generated by both projectional axons and neuropil growth (see text). A fixed proportion of projectional axons pass through t h e c o r p u s c a l l o s u m (represented in cross-section and not to scale), the cross- sectional area of which is proportional to the number of fibres passing through it.

axons, synapses and dendrites), given that the proportion of neurons belonging to a given functional class is thought to be fixed (Winfield et al., 1980) and that the mean amount of neuropil/neuron in normal brains is also relatively constant (see above). The specific nature of average changes in cortical structure probably cannot be determined solely from a change in ECC, but a better idea might be gained if changes in EGM, ESM and hemispheric volumes were also taken into account. A reduction in ECC has the converse implications with respect to changes in cerebral structure, and also implies extensive alteration in averaged interneuronal connectivity.

EGM is a function of E^ as above and GM volume. GM volume depends on neuronal numbers and, predominantly, on neuropil volume (Haug, 1956) , gross gliosis being excluded in this study by the negative Tg findings (see section 3.3). Any change in neuropil is equivalent to a change in connectivity; changes in neuronal numbers, given the finite volume of the GM and that all neurons have neuropil, must be accompanied by neuropil volume change and therefore alteration in connectivity. A reduction in EGM therefore implies (some combination of) either (1) a reduction in the mean amount of neuropil/neuron or the proportion of projectional axons or (2) a disproportionate increase in the GM volume, that again necessitates a fall in projectional axon number.

Geometrically, grey matter volume is a function of grey matter surface area and thickness. Changes in grey matter thickness are very limited (Rakic, 1995; and section 4.6). It has been suggested that this is because of biophysical constraints acting on the apical dendrites of pyramidal cells (Prothero and Sundsten, 1984) . An equally valid reason may be that if an abnormal number of neurons are stacked vertically and yet maintain normal dendritic expansions, then the tangential area available for the passage of the increased number of afferent and efferent axons required to keep the increased number of neurons connected is, perversely, reduced.

limiting the number of neurons that can be supported in such a stack. This is essentially a more pial and smaller scale application of the gyral window concept of Prothero and Sundsten (1984) . Therefore in abnormally thick cortex, if the number of neurons is increased, then the proportion of axons that cross the grey-white interface must be reduced; if the number of neurons is unchanged or reduced, then in the absence of gross gliosis (normal T^ findings), the mean amount of neuropil per neuron must increase. Abnormal cortical thickness therefore implies that connectivity within it is likely to be abnormal.

ESM is a function of and SM volume. The biological correlate of SM volume is the product of the number of all extracortical projectional axons of various diameters and the mean volume of axons of a given diameter. If ESM is increased, then either E^ must be disproportionately large (ie. there are more projectional axons, demanding a reduced mean volume per axon in the SM, or more neuropil/neuron - but this cannot be associated with increased extracortical projection as then SM volume would rise - so that local connectivity, without axons entering and contributing to the SM, must rise), or there is simply reduced volume per axon in the SM (with or without a reduction in their number) . In either case (or with some combination of the two possibilities), the reduced mean volume per projectional axon implies altered connectivity as axons must be shorter and/or thinner than normal: the latter possibility is likely to be associated with reduced terminal arborization of the axon (Mitchison, 1991). Shorter axons would suggest a tendency to increased local connectivity at the expense of more distant connectivity. In this group of patients, if ESM is abnormal, it is always increased. In no case is an increase in ESM associated with an abnormally high value of E^ itself; indeed, in one case, an abnormally high ESM is associated with an abnormally low E^ (patient 7) .