Brain, Vol. 125, No. 5, 1137-1149,
May 2002
© 2002 Guarantors of Brain
Morphometry of human superficial dorsal and dorsolateral column fibres: significance to spinal cord stimulation
1 Neuroregulation Group, Department of Neurosurgery, Leiden University Medical Centre, LUMC, 2 Institute for Biomedical Technology, University of Twente and 3 Paediatric Renal Centre, Wilhelmina Children’s Hospital, University Medical Centre, Utrecht, The Netherlands
Correspondence to: Dr H. K. P. Feirabend, Neuroregulation Group, Department of Neurosurgery, Leiden University Medical Center (LUMC), POB 9604, NL-2300 RC Leiden, The Netherlands E-mail: h.k.p.feirabend{at}lumc.nl
Received November 1, 2001. Revised December 13, 2001. Accepted January 9, 2002.
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Summary |
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In spinal cord stimulation (SCS) large diameter cutaneous (Aß) fibres in the dorsal columns (DCs) are activated and have an inhibiting effect on the transmission of pain signals by A
and C fibres from the corresponding dermatome(s). The largest Aß fibres can be activated up to a maximum depth of about 0.25 mm in the DCs. No data are available on the distribution of the large fibres in this superficial human DC layer at the common SCS levels Th10–11. Such data are indispensable to improve the predictive capability of a computer model of SCS. The whole myelinated fibre population in the superficial 300 µm of the dorsal column (DC0–300) at Th10–11 of two human subjects was morphometrically analysed. Some data was obtained from a third subject. The superficial dorsolateral column (DLC0–300) was included in this analysis because it was hypothesized that large dorsal spinocerebellar tract fibres could also be activated by SCS. Only very few fibres larger than 10.7 µm were found: a mean of 68 (0.5%) in DC0–300 and 114 (2%) in DLC0–300. Considering that the effect of SCS is primarily attributed to activation of these largest fibres, it is concluded that a surprisingly small average amount of 2.4 fibres per running 0.1 mm width and 6 fibres per segmental division of the DC is involved. Distinct mediolateral heterogeneity in fibre composition was found in both DC0–300 and DLC0–300. In the DC0–300, the mean diameter of fibres 
7.1 µm increases significantly by 5% from medial to lateral. Density (i.e. number of fibres per 1000 µm2) and frequency (i.e. percentage of a fibre size group compared to its parent population) of the large fibres increase significantly from medial to lateral in the DC0–300. For fibres 10.7 µm, these parameters increase by 200 and 269%, respectively. It is concluded that the difference in stimulation threshold of large Aß fibres in the median and lateral DC can be mainly attributed to the absence and presence, respectively, of collaterals at the stimulation site. Marked differences were found between DC0–300 and DLC0–300. The largest DLC0–300 fibres (10.7 µm) have a 320% higher frequency and a 473% higher density. Their mean diameter is, however, only 2% larger. The largest DLC0–300 fibres are not likely to be recruited by SCS, since they are not larger than their DC0–300 counterparts, they lack collaterals (which would reduce the threshold stimulus substantially) and they are more remote from the stimulation electrode. Keywords: gracile fascicle; low-thoracic spinal cord; myelinated fibres; quantitative analysis; spinal cord stimulation
Abbreviations: DC= dorsal column; DH = dorsal horn; DLC = dorsolateral column; DREZ = dorsal root entry zone; SCS = spinal cord stimulation
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Introduction |
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The management of chronic, intractable pain of neurogenic origin by electrical stimulation of the spinal cord (SCS) is a well-established clinical method (Simpson, 1994
; Barolat, 1995; North and Roark, 1995). The method is based on the ‘gate–control’ theory presented by Melzack and Wall (1965), who postulated that activity in large diameter cutaneous fibres (type Aß) inhibits the transmission of noxious information to the brain. Electrical stimulation of these large afferents by an electrode placed dorsomedially in the epidural space elicits a tingling sensation (paraesthesiae) in the corresponding dermatomes. To obtain successful treatment of chronic, neurogenic pain by SCS, the stimulation-induced paraesthesiae have to cover the pain area completely (Simpson, 1994; Barolat, 1995; North and Roark, 1995).
The dorsal columns (DCs) are the targets of SCS, because they hold Aß fibres related to all dermatomes from caudally up to the spinal segment where the electrode is situated. According to the mediolateral segmental lamination of the DC fibres (Smith and Deacon, 1984), the most caudal dermatome (S5) is represented medially in the DCs by its cutaneous afferents, followed subsequently by fibres corresponding to S4, S3, S2, S1, L5, L4, etc., in each lateral direction as shown in Fig. 1. Although dorsal root fibres are stimulated in SCS as well, they elicit paraesthesiae only in a single dermatome. This is generally insufficient since most chronic pain syndromes cover a more extensive body area.
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The stimulus amplitude needed for the activation of DC fibres is inversely related to both their diameter and their distance from the stimulating electrode, i.e. the fibre position in the DCs. To avoid motor responses and uncomfortable sensations, the stimulus amplitude for the activation of DC fibres should be less than the threshold for these side effects of SCS. Generally, the discomfort amplitude is
1.4 times the amplitude related to the initial perception of paraesthesiae. In clinical practice, paraesthesiae will thus be elicited only in those dermatomes corresponding to DC fibres requiring a stimulus below the discomfort threshold. To predict the order of DC fibre recruitment (and paraesthesiae coverage) under specified stimulation conditions by computer modelling, data on the mediolateral fibre size distribution in the human DCs are necessary (Holsheimer et al., 1991; Struijk et al., 1992; Holsheimer 1998).
Most cutaneous afferents upon entering the DCs laterally in the dorsal root entry zone (DREZ) bifurcate and leave the DCs within several segments rostrally and caudally, whereas only a fraction of the ascending fibres actually reaches the dorsal column nuclei (Horch et al., 1976; Davidoff, 1989). Due to the substantial reduction in their number, the long DC fibres are gradually displaced medially while ascending. Moreover, their diameter is reduced due to collateral branching, primarily in several segments near the DREZ (Horch et al., 1976; Fyffe, 1984). Accordingly, fibres in the lateral DCs should have a larger calibre than in the medial DCs.
Only few morphometric data on human DC fibres are available (Häggqvist, 1936; Szentagothai-Schimert, 1941; Ohnishi et al., 1976; Makino et al., 1996) and no studies have been performed in which fibre size distributions in the medial and lateral parts of the same DC segment are compared. Some data were obtained by inverse modelling of SCS (Wesselink et al., 1998). In this study CT-scan data, load impedances and stimulation amplitudes related to the initial perception of paraesthesiae in lower limb and abdominal regions of four patients treated with SCS were used to calculate the mediolateral diameter distribution of the largest DC fibres. It is suggested that the largest fibres in the lateral DCs are 30% larger than those in the median parts. Moreover, the increase in diameter of these largest fibres mainly occurred in the lateral parts of the DCs, whereas little change in diameter was seen in the median parts.
The study by Häggqvist (1936) indicates that the dorsolateral columns (DLCs) hold a substantially higher density of large fibres (up to 18 µm) than the DCs. Computer modelling predicts that these large dorsal spinocerebellar tract fibres are also likely to be activated by SCS (Holsheimer et al., 1991). Therefore, the DLC was included in the present morphometric study.
Due to the inverse relation between stimulation threshold and distance between a fibre and the electrode in the dorsal epidural space, large fibres near the dorsal boundary of the DCs will need the lowest stimulus for their activation (which most likely corresponds to the initial perception threshold of paraesthesiae). The stimulation amplitude of a fibre rises rather steeply with increasing depth in the DCs, as calculated by computer modelling (Holsheimer et al., 1991; Holsheimer, 2002). Taking into account that the maximum stimulus allowed in SCS exceeds the perception threshold by 40%, the maximum depth at which large DC fibres can be activated would be 0.2–0.25 mm.
The morphometric study presented in this paper covers a 0.3 mm thick dorsal superficial layer of both the DCs and the DLCs of the Th10–11 segments of a male and a female human subject. In addition, some data was obtained from a second male subject. Although the analysis included the full spectrum of myelinated nerve fibre diameters, the interpretation has been focused on the mediolateral distribution of the largest fibres, being most likely stimulated by SCS. Preliminary reports (Feirabend et al., 1998b, 2000) revealed that in the superficial DC and DLC these large fibres are both scant and heterogeneously distributed. For this reason, it was decided to analyse these spinal regions completely in two subjects instead of considering more limited sample areas in a larger number of subjects.
The data on the mediolateral distribution of the largest fibres will be implemented in the SCS computer model at the University of Twente, The Netherlands, to improve its predictive capability regarding DC fibre recruitment and thus paraesthesiae coverage in the management of chronic pain by SCS.
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Histology
For this study, the lower parts of two male and one female human spinal cord were available from autopsies with full consent. The male subjects were 42 and 76 years old, and the female subject was 75 years old. None of them had a history of nervous system diseases. Upon removal within 3 h post-mortem, the dissected cord was put into a modified Karnovsky fixative (Feirabend et al., 1994
, 1998a) for immersion fixation during a period of several months. The fixative was refreshed several times. The 76 years old male and the female specimen were selected for complete analysis of the superficial DC and DLC. The other male specimen was only used to provide additional data for comparison.
After identification of the cord levels, the Th10–11 segments were dissected and cut transversely on a vibratome (Bio-Rad, Veenendaal, The Netherlands) into 200 µm slices, which were stored in the same fixative. A number of slices were selected for osmication in a 1% solution of osmium tetroxide during 24 h under constant agitation. Unilateral tissue blocks containing the DC, the dorsal horn (DH) and part of the adjoining DLC were cut from the osmicated slices. At this cord level, the DC consists of the gracile fascicle only. The osmicated tissue blocks were embedded in epon (Merck, Amsterdam, The Netherlands). Semi-thin (1 µm) sections were cut using a Reichert ultramicrotome (Leica, Rijwijk, The Netherlands). The sections were stained with a 1% toluidine blue/1% borax solution. For details, see Feirabend et al. (1998a).
Microscopy and image analysis
Microscopic video images covering the dorsal superficial 300 µm white matter zone of the cord from the midline to 4 mm lateral were taken at a magnification of 40x. The areas, A(f), of all myelinated fibre profiles identifiable by light microscopy were measured (semi)automatically using a Vidas (Zeiss Kontron) image analyser (Carl Zeiss, Weesp, The Netherlands) at a magnification of 1860x in sample grids of 100 x 100 µm (Figs 2 and 3).
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The area of a fibre profile included the area of both the axon and myelin sheath profile. As fibre profiles are rarely exactly circular, the profile area is preferred over the profile diameter (Feirabend et al., 1996
). However, as the diameter is still the most common parameter for fibre size, the diameter, d(f), of the imaginary circular profile corresponding to the measured A(f) is given as well when relevant. Apart from A(f), several other measured and derived parameters (summarized in Table 1) were determined. The fibre profiles were classified into five size groups, as shown in Table 2. The minimum fibre size for recruitability was estimated to be 70 µm2; starting from this size larger fibres were classified in three arbitrary size groups, increasing in steps of 10 µm2: 70, 80 and 90 µm2. Fibres smaller than 70 µm2 were classified in two size groups with an arbitrary bound: small fibres (<40 µm2) and intermediate fibres (40–70 µm2).
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The data related to the various grids shown in Fig. 2 were combined in several ways. First, all grids in the 300 µm thick superficial layer of the dorsal (DC0–300) and dorsolateral columns (DLC0–300), respectively, were combined. Secondly, grids were combined to form three parallel 100 µm thick DC sublayers (DC0–100, DC100–200 and DC200–300) and DLC sublayers (DLC0–100, DLC100–200 and DLC200–300). Finally, adjoining parasagittal areas of
200 µm wide and 300 µm deep were composed from six grids, in both DC and DLC, so that the various parameters could be plotted as a function of the mediolateral fibre position.
Statistical evaluation
For statistical evaluation of mean values of A(f) an analysis of variance (ANOVA) was applied initially and was followed by a post hoc test according to Tukey’s least significant difference (LSD) procedure (i.e. Student’s t-test). To compare size distributions, the Kolmogorov–Smirnow test was used (Kolmogorov, 1941; Smirnow, 1948). Differences were considered significant when P < 0.05. Furthermore, linear and polynomial fitting was applied to visualize parameter fluctuations in the mediolateral plots.
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General fibre population characteristics in superficial DC and DLC
The fibre populations of the male specimen included 12 828 DC fibres and 5285 DLC fibres, taken from 81 and 24 superficial grids, respectively, as shown in Fig. 2. The populations of the female specimen included 17 447 DC fibres (83 grids) and 5680 DLC fibres (21 grids). The largest fibre profile in each specimen was never >210 µm2 (16.4 µm diameter).
Histograms of the fibre populations DC0–300 and DLC0–300 of the male and female specimens are shown in Fig. 4. This shows actual fibre size distributions, N(f), in the range 0–100 µm2 (Fig. 4A) and the relative fibre size distributions, F(f), in the ranges 0–80 µm2 (Fig. 4B), 60–140 µm2 (Fig. 4C) and 120–200 µm2 (Fig. 4D). Small fibres are by far the most frequent in both regions.
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The mean sizes A(f), densities D(f) and frequencies F(f) of the fibre profiles of the two specimens are shown in Table 3 for different size groups in both DC0–300 and DLC0–300. The values between brackets represent the percentage difference between the corresponding male and female specimen. A positive percentage indicates that the male data have a larger value than those of the corresponding female specimen and vice versa. Significant size differences between the two specimens (P < 0.05) are indicated by an asterisk.
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It appears from Table 3 that fibre profiles with A(f) <40 µm2 [d(f) <7.1 µm] are by far the most frequent. Their mean F(f) is 86.6% of all fibres in DC0–300 and 90.7% in DLC0–300. Only very few fibres are
90 µm2 [d(f) 10.7 µm], i.e. 0.5% in DC0–300 and 2.1% in DLC0–300, their densities being 0.11 and 0.63 fibres per 1000 µm2, respectively. The mean numbers of fibres N(f) of both specimens with A(f) 90 µm2 [d(f) 10.7 µm] are 68 in DC0–300 and 114 in DLC0–300. In the most superficial layer DC0–100, 63 fibres are 70 µm2, 30 fibres 80 µm2 and 15 fibres 90 µm2. For the most superficial DLC0–100, these numbers are 43, 30 and 20, respectively.
As shown in Table 3, most values of A(f), D(f) and F(f) are different in the DC0–300 and DLC0–300 of the male and female specimen. Differences in D(f) and F(f) are rather large for various size groups. In contrast, differences in A(f) are relatively small. The difference between the two specimens is significant only for the full size range (‘all’) and the size group <40 µm2 of DC0–300. For DLC0–300, significant differences in A(f) were established for all size groups except for the group 90 µm2. The corresponding size distributions of the two specimens are significantly different (P < 0.05) as well, for both DC0–300 and DLC0–300.
Differences in A(f) and size distribution among sublayers DC0–100–DC100–200–DC200–300 and DLC0–100–DLC100–200 –DLC200–300, respectively, are generally small but significant (P < 0.05) for the full size range (‘all’) and the size group <40 µm2, but not for any size group 40 µm2. Generally, the size differences among DLC sublayers are more prominent than those found between DC sublayers.
In the additional specimen, six sample areas together covering 55 200 µm2 of the superficial DC were analysed. Together these samples contained 1485 fibres with a mean A(f) of 19.19 ± 26.41 µm2 [mean d(f): 4.94 ± 5.80 µm] and a D(f) of 26.90 fibres per 1000 µm2.
Differences in superficial DC and DLC fibre population characteristics
Marked differences exist between the fibre distributions in DC0–300 and DLC0–300. In DLC0–300 small fibres (<40 µm2) are generally smaller than in DC0–300 (Table 3), whereas small and large fibres (80 µm2) are more numerous (Fig. 4). Although the mean frequencies F(f) of the small fibres (<40 µm2) in both areas differ by less than 5%, their mean density D(f) in DLC0–300 exceeds the corresponding value in DC0–300 by 38% and their mean area A(f) in DLC0–300 is 40% less than in DC0–300 (Table 3). Although the mean A(f) values of large fibres (70 µm2) in both areas differ only by 13%, the mean F(f) and D(f) of these fibres in DLC0–300 are 133% and 207% higher than in DC0–300, respectively. In the largest size group (90 µm2), this difference is even more pronounced: a 320% higher F(f) and a 473% higher D(f) in DLC0–300. In contrast, as can be computed from Table 3, the size group 40–70 µm2 in DC0–300 has a higher F(f) (123%) and D(f) (74%) than in DLC0–300. In both specimens, A(f) and size distributions of DC0–300 and DLC0–300 are significantly different (P < 0.05) for all size groups, with the exception of the group 90 µm2 for which a significant difference could not be established.
Mediolateral fibre population characteristics in superficial DC and DLC
The various parameters of the fibre populations of adjacent parasagittal areas of 200 x 300 µm were plotted as a function of their mediolateral position to characterize the mediolateral changes in the myelinated fibre population of the DC and DLC.
The mediolateral plots of mean A(f) of the full size range for both the male and the female subject, given in Fig. 5A, largely coincide. From medial to lateral, the mean A(f) in the DC first increases to a maximum at 66% of the lateral extent of the DC and then decreases towards the DREZ. On the lateral side of the latter, in the DLC, the mean A(f) is approximately the same, but increases further laterally. With only a few exceptions, full range fibre populations of both adjacent and remote parasagittal areas in either DC or DLC differ significantly from each other with respect to mean A(f) and/or size distribution. With respect to large fibres (70 µm2) much less differences are found which, moreover, only occur in the DC. According to Fig. 6, parasagittal DC areas at 1100, 1700 and 2500 µm are most frequently involved in these differences. For fibres 80 µm2, ANOVA no longer revealed significant differences in mean A(f).
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The density, D(f), of all fibres in the male specimen was smaller at all sampled distances than in the female one (Fig. 5B). The curves run largely parallel. Density is lowest at
66% of the lateral extent of the DC. Near the medial and lateral borders of the DREZ, the densities of DC and DLC are similar. At more lateral locations, the DLC D(f) decreases.
The mediolateral size, A(f), density, D(f), and frequency, F(f), plots for the larger fibre groups 40,70, 80 and 90 µm2 [d(f) 7.1, 9.4, 10.1 and 10.7 µm, respectively] in DC and DLC, based on the averaged data of the two subjects are shown in Figs. 7A, 8A and 9A, respectively. The corresponding regression lines depicted in Figs. 7B, 8B and 9B were used to estimate mediolateral parameter trends in the DC. Statistical data on the regression lines are summarized in Table 4. The A(f) plots are approximated well by a linear function (Fig. 7), whereas the D(f) and F(f) plots (Figs 8 and 9) fit well with 3rd order polynomials. Regression analysis of the DLC plots was not performed because the numbers of data points were too small.
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Dorsal column (DC)
The larger fibre groups of the DC all show a moderate, linear increase of the mean A(f) from medial to lateral (Fig. 7). According to Fig. 7B, this increase amounts 11, 10, 3 and 7% [or 5, 5, 1 and 3% of the mean d(f)] for size groups
40, 70, 80 and 90 µm2, respectively. Table 4, however, shows that, apart from the size group 40 µm2, the linear fits do not correlate well with the data (r > 0.6). This is also true when a 3rd order polynomial fit was used.
Fig. 8 shows that large fibres (70, 80 and 90 µm2) have very low densities regardless of location. According to Fig. 8B, their maximum densities, which are all present at 75% of the lateral extent of the DC, do not exceed 0.6, 0.3 and 0.15 fibres per 1000 µm2, respectively. Compared with the medial DC, these maxima correspond to an increase by 150–210%. More laterally near the DREZ, the densities of these size groups fall again to the same low medial levels. Fibres 40 µm2 have a similar mediolateral distribution and attain somewhat higher densities, but never exceed 4 fibres per 1000 µm2.
From Fig. 9, it appears that, like their densities, the frequencies of large fibres (70, 80 and 90 µm2) rise from very low values near the midline (0.25–1%) to modest maxima (0.75–3%) at 75% of the lateral extent of the DC. The increase to these maxima amounts to 200–270%. More laterally, the frequencies of fibres 80 and 90 µm2 fall to nearly the same value as in the medial DC. The frequency of fibres 70 µm2 decreases further to a level 55% lower than in the medial DC. Fibres 40 µm2 attain much higher frequencies. From the medial DC [F(f) = 11%], frequency increases to 20% at the maximum, but decreases to 3.2% towards the DREZ.
Both for D(f) and F(f), the 3rd order polynomial fits correlate significantly with the empirical data (r 0.75, P 
0.05), although r gets smaller and P gets higher with decreasing numbers of fibres (Table 4).
Dorsolateral column (DLC)
Fig. 7A shows that, in the DLC, the mean A(f) of any larger fibre size group exceeds that of its counterpart in the DC. From Table 3, it can be computed that DLC fibres 40, 70, 80 and 90 µm2 have a mean size of 24, 11, 8 and 4% larger, respectively, than DC fibres of the same size groups. Within the DLC, only moderate mediolateral changes of the mean size of these groups can be observed.
Figures 8A and 9A show that both densities and frequencies of all larger DLC fibre groups increase rapidly in a lateral direction by 85–95% and 180–210%, respectively. DLC fibres 70, 80 and 90 µm2 have a significantly higher density than their corresponding DC counterparts in all locations (Fig. 8A). The same is true for the frequency, with the exception of 3000 µm from the midline (Fig. 9A).
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Discussion |
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The probability of stimulating large fibres in DC0–300 and DLC0–300 by SCS is primarily determined by both their mediolateral position and their size. Accordingly, the two main purposes of this study were to determine the mediolateral size distribution of the largest (Aß) fibres in a 300 µm thick superficial layer of the human DC (DC0–300) and DLC (DLC0–300). This information is of major interest for a reliable calculation of the recruitment order of these fibres by computer modelling, and thus for the optimization of SCS electrodes and stimulation methods in human applications.
In the present study, the corresponding myelinated fibre populations were morphometrically analysed at cord level Th10–11, primarily focusing on fibres 70 µm2 (9.4 µm in diameter), because it is highly unlikely that smaller fibres are also activated by SCS (Holsheimer, 2002). As large fibres are both scant and heterogeneously distributed (Feirabend et al., 1998b, 2000) a deliberate choice was made to undertake a complete analysis of DC0–300 and DLC0–300 in two subjects rather than considering more limited areas in a larger number of subjects. This approach provided much more quantitative/topographical detail, which is a prerequisite for a realistic computer model. Inclusion of more subjects is not feasible due to the time-consuming semi-automatic technique applied. So far, automatic methods that are both faster and equally reliable are not available. The small number of appropriate specimens was also dictated by their limited availability. It can, moreover, be argued that more subjects are unnecessary. Data from the additional specimen and the two fully analysed specimens show a clear similarity, which supports the representativity of these subjects. The mean diameter of 4.94 ± 5.80 µm found in the additional specimen corresponds fairly well with that of the two fully analysed specimens (i.e. 5.12 ± 4.80 and 4.97 ± 4.73 µm). The density in the additional specimen was slightly higher, but remains within the range of the mediolateral fluctuation of this parameter.
Because it cannot be perfused under optimum conditions, handling human nervous tissue implies several histological disadvantages compared with animal tissue. The duration of the post mortem delay, and the fact that only immersion fixation can be applied, might interfere with the histological quality and, in turn, with the outcome of quantitative analysis of nerve fibres. Other factors including age and neurological conditions, composition of the fixative and the morphometric procedure might equally influence the morphometric result. Since these factors have so far not been studied systematically and an in vivo reference for fibre dimensions does not exist, a prerequisite for morphometric studies is the application of a standard histological technique that best preserves the fibre ultrastructure (Feirabend et al., 1994, 1998a). It appears that, in spite of diverging histological procedures in combination with different cord levels and a lacking topographic differentiation, the results of previous DC fibre measurements (Häggqvist, 1936; Szentagothai-Schimert, 1941; Onishi et al., 1976) do not differ substantially from our results. These authors give data on the fibre distribution of the gracile fascicle as a whole. The first two do not provide a mean fibre size, but we estimated these values from the data of their histograms. Data from the literature and the present results on the superficial DC, as well as our unpublished data on the deep DC in the same two human subjects are presented in Table 5. Our (unpublished) size data (in Table 5) on the deeper layers of the DC (which topographically correspond best with the DC samples analysed by the other authors) fit fairly well with data from the literature. These similarities with data from the literature and the fact that our data on superficial and deep DC fibres stem from the same specimen support the argument that the data obtained from these specimens are representative for the human population at large.
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Finally, it appeared that the variance of mean A(f) is determined mainly by the differences between fibre calibres within each subject and not by differences between subjects. It was computed that at a 95% confidence interval addition of a single subject would change the precision (i.e. 1.96 x standard error) of mean A(f) from 0.20 to 0.17 µm2. This small change is not relevant in view of the distribution of large fibres considered primarily in this paper.
Häggqvist’s observation at Th3 (Häggqvist, 1936) that large fibres are much more frequent in DLC than in DC is basically confirmed by our data (at Th10–11), although according to Häggqvist it concerns fibres 7 µm and, according to us, fibres 10.1 µm. Furthermore, the largest sizes Häggqvist observed for DC and DLC fibres (14 and 18 µm, respectively) differ from ours (16 µm in both DC0–300 and DLC0–300). The difference between the maximum size of DC fibres at low (16 µm) and high thoracic levels (14 µm) fits Szentagothai-Schimert’s observation (Szentagothai-Schimert, 1941) of a maximum size of only 9 µm at levels C2–4. Apparently, the maximum size of large DC fibres decreases in a rostral direction. This trend is also found for the mean size of all DC fibres. At Th10–11, we found a mean DC fibre diameter of 5.0 µm, whereas Ohnishi et al. (1976) reported a value of 3.2 µm at Th5.
Ohnishi et al. (1976) also presented estimates of the DC fibre density at Th5 and C3, amounting to 23 069 and 25 267 fibres/mm2, respectively. We found a density of 22 920/mm2 at Th10–11, which is slightly less than at Th5 but distinctly less than at C3. DC fibre density increases in a rostral direction and is accompanied by a reduction of the mean fibre size. In contrast, the largest fibre size in the DLC seems to increase from caudal (16 µm at Th10–11, our data in DLC0–300) to rostral [18 µm at Th3 (Häggqvist, 1936) in the dorsal spinocerebellar tract].
In the present (age-matched) material, small but significant differences in mean fibre size, A(f), and fibre distribution were observed between the two specimens. In DC0–300, these differences concern small fibres (<40 µm2) only. In DLC0–300, they also concern size groups 40, 70 and 80 µm2. The fact that significant differences could not be established for larger fibres in DC0–300 may be due to the small numbers of these fibres. The fibre density (D(f)) in the female specimen was nearly always larger than in the male specimen. The reverse was found for the frequency, F(f), of size groups. It should be stressed that all these differences may just reflect intersubject variability and are not necessarily gender-related. Data from the two subjects were averaged in further analysis.
The total number of fibres 90 µm2 (diameter 10.7 µm) in DC0–300 is small [N(f) = 68, or 0.5% of the whole fibre population]. Considering that the effect of SCS is primarily attributed to activation of this size group (Holsheimer, 2002), 2.4 fibres per running 0.1 mm width would be involved at Th10–11, or, on average, a maximum of 6 fibres per segmental division. Locally, these numbers may differ, since the actual mediolateral differences in the distribution of large fibres (see below) have not been taken into account. It was calculated that, in SCS, the segmental division recruited first (at the perception threshold of paraesthesiae) is most likely stimulated to a depth of 0.25 mm and includes about 5 fibres 10.7 µm in diameter and, in addition, a similar number of recruitable Aß fibres of 
9.4–10.7 µm (Holsheimer, 2002). In contrast, the segmental division activated last (just below the discomfort threshold) most likely includes just a single large Aß fibre 10.7 µm (in the outer 0.06 mm of the DC). The latter suggests that paraesthesiae and pain relief in a dermatome can be affected by stimulation of just a single large Aß fibre by way of its spinal collaterals.
When the mediolateral variation in fibre density of the size group 90 µm2 in DC is taken into account and, if the probability of stimulating a segmental DC division is related to the corresponding density of fibres 90 µm2, it is shown in Fig. 8B that the probability is lowest at 20%, and is three times higher at 75% of the mediolateral extent of the DC at Th10–11. When relating these data to the topographical representation of the dermatomes in the Th11 segment (Fig. 1), the sacral dermatomes would have the lowest probability, whereas the highest probability would be in and around the L1 dermatome. Apart from the fibre density, the presence of collaterals is a major factor as well (see below).
The fibre distributions of DC0–300 and DLC0–300 are distinctly different. In the latter, the number of fibres 90 µm2 (diameter 10.7 µm) is 114, resulting in 15 fibres per running 0.1 mm width (again omitting the actual mediolateral differences from consideration). Holsheimer et al. (1991) hypothesized that large DLC fibres may be a potential target for SCS in modulating dystonic and/or hyperkinetic motor impairment by activating large dorsal spinocerebellar tract (DSCT) fibres. This hypothesis was based on clinical data (Barolat, 1989) and the finding by Häggqvist (1936) that, at Th3, the largest DLC fibres were larger than those in DC (18 and 14 µm, respectively). In this study, however, we found that the largest fibres in the superficial DC and DLC have the same diameter (16 µm). Taking into account that these DLC fibres are at a larger distance from a dorsomedial epidural electrode than DC fibres and that they lack collaterals which reduce the threshold stimulus of lateral DC fibres by about 40% (Struijk et al., 1992), it is highly unlikely that, at Th10–11, DLC fibres are stimulated in SCS. Therefore, the hypothesis should be rejected for at least low thoracic stimulation.
Distinct mediolateral heterogeneity of the fibre composition was revealed in DC0–300 by regression analysis and statistical comparison of mean size, density and frequency of 200 µm wide parasagittally adjoining fibre areas. Heterogeneity of the fibre composition was also observed in DLC0–300. This phenomenon is apparently a common myeloarchitectonic feature, as it was also demonstrated in the cerebellar white matter (Feirabend et al., 1996). For this study, special attention was paid to the mediolateral heterogeneity of the size groups 40, 70, 80 and 90 µm2 in DC0–300.
A linear increase in fibre diameter up to 5% was found from medial to lateral in DC0–300, although a significant increase could only be established for fibres 40 µm2 (r = 0.89, P < 0.0001; Table 4). A mediolateral increase in the mean size is in accordance with the observation of Ohnishi et al. (1976) that DC fibres taper in a rostral direction. This implies that medial DC fibres originating from more caudal segments are smaller than more lateral ones originating from more rostral levels. Using a combination of empirical data and computer simulations, Wesselink et al. (1998) predicted a mean mediolateral increase in diameter of the largest DC fibres of 30%, which strongly exceeds the presently found, non-significant 1–5%. The explanation for this discrepancy is most likely that DC fibres have only collaterals in a few segments near their dorsal root entry zone, corresponding to the lateral part of the DC (Fyffe, 1984). It was calculated that the presence of collaterals reduces the threshold stimulus to activate DC fibres by 30–50% (Struijk et al., 1992). In the modelling study by Wesselink et al. (1998), however, both lateral and median fibres had collaterals. This implies that, for a given threshold stimulus, the diameter of a median DC fibre would have been larger without collaterals than if collaterals are present. Assuming that the largest Aß fibres in the lateral DC have a diameter of 12 µm (corresponding to the mean size of fibre group 10.7 µm), the largest median DC fibres would be 9.2 µm according to Wesselink et al. (1998). It was calculated that the threshold stimulus of the 12 µm fibre is 30% below the threshold of the 9.2 µm fibre (both with collaterals). This is within the range of threshold reductions due to the presence of collaterals (30–50%) as calculated by Struijk et al. (1992). Moreover, Wesselink et al. (1998) have shown that fibres with low thresholds are only present in the most lateral part of the DC, suggesting that Aß fibres only issue collaterals to the dorsal horn in a few segments near the entrance of the corresponding dorsal root. This seems to be in accordance with the conclusions of Brown (1981) [citing Imai and Kusama (1969), Wall and Werman (1976) and Devor et al. (1977)] that ‘cutaneous afferents distribute through axon collaterals to a rostro-caudally running column of dorsal horn of at least 10 mm and possibly up to several centimetres long’.
It is concluded that in the Th10–11 segment a significant difference in size of the largest medial and lateral fibres in DC0–300 (10.7 µm) has not been demonstrated—although the density (and frequency) of these fibres are significantly higher in the lateral DC0–300. This conclusion also suggests that a significant caudorostral tapering of large Aß fibres of lumbar and low-thoracic origin does not exist. The difference in stimulation threshold of large Aß fibres in the median and lateral DC is most probably related to the absence and presence, respectively, of collaterals at the stimulation site and not (or only marginally) to a difference in fibre size. In addition, it is unlikely that the largest DLC0–300 fibres are recruited by SCS. Although they have the same diameter (16 µm) as the largest DC0–300 fibres, they lack collaterals and are more distant from the SCS electrode than the most lateral DC fibres.
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We wish to thank Dr A. H. Zwinderman of the Department of Medical Statistics of the Leiden University Medical Centre for his readiness to advise us on statistical matters.
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