Supplemental Material

The following five supplements are provided as further background as mentioned in the principal paper:

1) Neuron density in Conel: provides a comparison of calculations of neuron populations as described in this paper and the methods used in the Shankle, et al., CYBERCHILD database.

2) A Cautionary Tale: provides a model for what Conel was measuring in his developmental brain atlases, which has implications for interpretation of that data.

3) Relational graphs and maximal cliques for K-2 and K-4 to K-7: provides the corresponding graphs to Figures 5 and 7 for the k-clusters not described in detail in the principal paper, which focused on K-1 and K-3.

4) Nomenclature in Conel: provides a complete list of the verbal descriptions employed by Conel in his atlases, which was based on von Economo, compared to the Brodmann Area references employed in the principal paper.

5) MATLAB m-files: provides the MATLAB code necessary to implement Equations 1 and 3, as well as the Monte Carlo surrogate data used to calculate the random graph surrogate and corresponding p-value for Figure 4.


Neuron density in Conel

As noted in the principal article, Shankle, et al., also used Conel’s neuron density data, and have also made Conel’s data available on-line in the CYBERCHILD database. Here we show how Conel’s data is listed in CYBERCHILD, illustrating with the information on layer thicknesses for BA 4L (FAγ – L in Conel’s nomenclature). We then explain our comment in Methods that our raw population calculations differ from Shankle, et al. for 72 months and for Layer V at all ages.

Figure D1 shows a portion of the data from CYBERCHILD for cortical layer depth. The yellow areas are identical to the entries from Conel’s atlases. The remaining entries are calculated based on Conel’s input data. Shankle, et al., used the same pro rata method for deriving sublayer depths and neuron densities, which we will examine in a moment.

Figure D1. Cortical layer depth in CYBERCHILD. This reproduces the cortical layer depth data (in mm) from CYBERCHILD for BA 4L (FAgl in CYBERCHILD’s abbreviation and FAγ for the leg in Conel). Conel’s data is highlighted in yellow. Conel did not publish sub-layer depths. Each of the values in CYBERCHILD for a sublayer is consequently a pro rata share of the value for the entire layer. Consequently, the sum of 3.1 to 3.3 is the total in 3; the sum of 5.15 to 5.27 is the total in 5; and the sum of 6.13 to 6.24 is the total in 6. Abbreviations: Sm = small neuron, Lg = large neuron, XL = extra-large neuron, Sp = spindle neuron, Py = pyramidal neuron

For Layer III, Conel distinguished three sublayers in his neuron data: IIIa, b, and c respectively. He also distinguished two sublayers for Layer V and Layer VI: Va, Vb, VIa, and VIb, respectively. The abbreviations Sm = small neuron, Lg = large neuron, XL = extra-large neuron, Sp = spindle neuron, Py = pyramidal neuron, appeared to us to pertain to neuron descriptions and not to sublayers. This affects the neuron density data displayed in Figure D2.

Figure D2. Neuron density in CYBERCHILD. Data from Conel’s tables are highlighted in yellow. The remaining values are interpolations. The neuron densities for 72 months are means taken over both left and right hemispheres for the respective layer. Conel published three sets of densities and did not publish a mean so no highlights are used in that column. Abbreviations: Sm = small neuron, Lg = large neuron, XL = extra-large neuron, Sp = spindle neuron, Py = pyramidal neuron

Our value for ν(l, b, t) uses the product of layer depth and mean neuron density, adjusted for scale, since the density is calculated on Conel based on a 100µm3 cube. For Figures D1 and D2, our calculations and the CYBERCHILD results from multiplying layer_code 1 to 4 for both data types are identical for Layer I to Layer IV. However, the results are not the same for Layer V. We interpreted Conel’s abbreviations to apply to neuron types within the sublayers and consequently calculated the mean neuron density for Layer V as the sum of all the small, large and extra-large neurons in sublayers a and b, divided by two. This is depicted in Figure D3.

Figure D3. Mean neuron density in Layer V using our method. Conel’s data is highlighted in yellow. Our calculations are highlighted in blue. The mean density in line V is the average of the sublayer totals in Va and Vb.

Correcting for scale, the CYBERCHILD Layer V population result for the first column (Birth) would be 0.530 x 10 x 38.8 = 205.64 (the 10 corrects for the mm scale for the layer depth). Our calculation for that population is 0.530 x 10 x 97 = 514.1.

This effect does not occur for Layer VI. Conel reported only a single number of neurons for each sublayer in Layer VI while he distinguished the somal size data for spindle and pyramidal cells in his tables. CYBERCHILD assigns the single number to both cell types, which cancels the effects of dividing the total Layer VI depth by four rather than two.

For 72 month neuron populations, we used only left hemisphere data, as all prior Conel data had only pertained to the left hemisphere. This leads to the adjustments for this same Brodmann Area detailed in Figure D4. With the exception of Layer V, this adjustment to CYBERCHILD data matched our outputs.

Figure D4. Conel’s left-hemisphere neuron density data for 72 months. Case numbers appear in the first row for the three subjects detailed in Conel’s data. Conel’s data is highlighted in yellow.


A Cautionary Tale: A Model for What Conel Measured

Conel identified a large number of relevant and measurable aspects of the human brain. For each of 54 observational units, Conel obtained measurements on most of these aspects. In some cases, raw measures were converted to derived measures such as densities. Let p be the number of measures of interest, whether raw or derived. In the following I will represent the data on the ith individual as Xi1, Xi2, … ,Xip. If the jth measurement on the ith individual was not obtained, I will say Xij = NA.

With each observational unit is associated an integer in the set


{0,1,3,6,15,24,48,72}

corresponding to the closest number of months of the age of the individual; hence, we may represent the jth measurement on the ith individual as .

Our model, whatever its specific form, involves an average value of each of p aspects of interest as

a function of time, µ1(t), µ2(t), … , µp(t).

The objective is to learn how the µj change in time. This is a multivariate function of t, and the relation between the changes in time of µj1 and the changes of µj2 is likely to be very complicated.

Now, what kind of data would be necessary to analyze this model? Clearly the finer the time scale the better.

An important issue is whether we can obtain repeated measures on an individual, so as to reduce experimental error. (``Experimental error'' means simply the random variation among observational units that are otherwise identical; that is, have identical relevant characteristics. The only relevant characteristic in this study is age.)

Conel's measurements were destructive; that is, repeated measures were not possible.

Our inference on µj(t) must be made from all available measures that correspond to µj(t). These are all measurements Xij() such that ≈ t.

In Conel's dataset, for any given t there was a small number (5 to 9) of Xij() available for inference on µj(t), and inferences on µj(t1) - µj(t2) must be made from data from different observational units.

The analysis problem that this presents can be compared to the problem of trying to model the physical growth of children. Say we are interested only in how height and weight change up to age 6. We measure 7 children who are “1 year old” (that is, their age is between 9 and 15 months), and we measure 6 other children who are “2 years old”, and so on, using 54 different children each measured once. There are obviously all kinds of sources of error here. We could, of course, make many more measurements on each child and get a very large dataset. The only ways to decrease the experimental error, however, would be to measure a lot more children at each age, to refine the time scale, and to measure the same child at multiple times (which, of course, we could not do if the child has to be dead for us to measure it). The experimental error (and so the width of ``confidence intervals'') would be very great in such a study.

Continuing with this example, suppose that all of the 54 children just happened to have the same height and weight at age 6. That does not mean that the measurement on one at age 2 had a strong relationship to another one at age 3.

This analogy is important to bear in mind as we proceed to make inferences from Conel's data.


Relational graphs and maximal cliques for K-2, and K-4 to K-7

This supplement contains the relational graphs and depictions of maximal cliques for the five remaining k-clusters in Table 3 of the principal article. K-1 and K-3 (corresponding to 72 months and 15 months, respectively) were analyzed in the principal article in Figures 5 to 8.

Figure S1. Relational graph and maximal clique for K-2 for D < 0.1. The addresses in K-2 are arrayed around the graph in the order they are listed in Conel, citing the respective Brodmann Area and cortical layer. In Table 3 of the principal article, K-2 has 2 maximal cliques of size 6, with C(l, b, t) maxima for the members occurring at 1 month. Common members of the maximal cliques are: BA 46 LIV, BA 45r LV, BA 40 LIII, BA 37 LI and BA 42 LIII with mutual correlated change relationships depicted as red solid lines. Each of these also has a change relationship where D < 0.1 with BA 41 LIII (blue) and BA 10 LIII (green), constituting two overlapping maximal cliques. All other relationships with D < 0.1 are indicated by dashed lines. No address in this k-cluster has a statistically significant change magnitude (i.e., C(l, b, t) > 3.9). In BA 45r, r = rostral.

Figure S2. Relational graph and maximal clique for K-4 for D < 0.1. The addresses in K-4 are arrayed around the graph in the order they are listed in Conel, citing the respective Brodmann Area and cortical layer. In Table 3 of the principal article, K-4 has 1 maximal clique of size 4, with C(l, b, t) maxima for the members occurring at 48 months. Common members of the maximal cliques are: BA 7 LIII, BA 40 LIV, BA 22 LIV, and BA 21 LVI with mutual correlated change relationships depicted as red solid lines. All other relationships with D < 0.1 are indicated by dashed lines. No address in this k-cluster has a statistically significant change magnitude (i.e., C(l, b, t) > 3.9).

Figure S3. Relational graph and maximal clique for K-5 for D < 0.1. The addresses in K-5 are arrayed around the graph in the order they are listed in Conel, citing the respective Brodmann Area and cortical layer. In Table 3 of the principal article, K-5 has 3 maximal cliques of size 4, with C(l, b, t) maxima for the members occurring at 6 months. The only common member of the maximal cliques is BA 29 LVI. It has a change relationship where D < 0.1 with BA 37 LII, BA 17 LI and BA 17 LIV (green; Group 1 in Table 3) and a similar change relationship with BA 45r LVI, BA 7 LII and BA 14 LIII (red; Group 2 in Table 3). Finally, Group 3 (with additional relationships depicted in blue) contains BA 29 LVI, BA 45r LVI (from Group 3) and BA 17 LI and BA 17 LIV (from Group 2), constituting three overlapping maximal cliques. All other relationships with D < 0.1 are indicated by dashed lines. BA 29 LVI and BA 17 LI have a statistically significant change magnitude (i.e., C(l, b, t) > 3.9).


Figure S4. Relational graph and maximal clique for K-6 for D < 0.1. The addresses in K-6 are arrayed around the graph in the order they are listed in Conel, citing the respective Brodmann Area and cortical layer. In Table 3 of the principal article, K-6 has 2 maximal cliques of size 4, with C(l, b, t) maxima for the members occurring at 24 months. The two maximal cliques have no common members. The first maximal clique contains: BA 44 LIV, BA 45 LVI, BA 42 LVI and BA 13 LI with mutual correlated change relationships depicted as red solid lines. The second maximal clique contains: BA 41 LV, BA 38 LVI, BA 14 LI and BA 4P LI (in green). All other relationships with D < 0.1 are indicated by dashed lines. BA 42 LVI and BA 14 LI have a statistically significant change magnitude (i.e., C(l, b, t) > 3.9). P = paracentral lobule.


Figure S5. Relational graph and maximal clique for K-7 for D < 0.1. The addresses in K-7 are arrayed around the graph in the order they are listed in Conel, citing the respective Brodmann Area and cortical layer. In Table 3 of the principal article, K-7 has 2 maximal cliques of size 6, with C(l, b, t) maxima for the members occurring at 3 months. Common members of the maximal cliques are: BA 6 LIII, BA 6 LV, BA 39 LIV, BA 38 LI and BA 13 LIV with mutual correlated change relationships depicted as red solid lines. Each of these also has a change relationship where D < 0.1 with BA 44 LII (blue) and BA 39 LVI (green), constituting two overlapping maximal cliques. All other relationships with D < 0.1 are indicated by dashed lines. BA 38 LI has a statistically significant change magnitude (i.e., C(l, b, t) > 3.9).