Abstract
Muscle-selective
1 Introduction
In order to allow paraplegic patients to stand, walk and cycle, muscle activity can be elicited by stimulating either the muscle(s), or the corresponding peripheral nerve(s) or anterior roots. The question of the spatial organization of the motor fibres along the nerve trajectory is of substantial interest for the development of electrodes for stimulation and for recording of the ventral roots, if one aims at spatial selectivity at the muscle level (review in [2]). A straightforward approach for studying the spatial distribution of fibres in the profile of the peripheral nerves and spinal roots is by injecting a fluorescent tracing substance into the muscles of interest followed by visualization of the trajectory of the axonal pathways towards the primary motoneuron in histological cross-sections. Inferences for the size distribution of the labelled axons from the “size” of fluorescent patch are imprecise. However, if there is a correlation between the size of a fluorescent profile and the size of the fibre (axon + myelin sheath), a direct recalculation towards fibre size (area or diameter) from the fluorescent picture is allowed. Since the spatial distribution of the labelled axons can be investigated via the analysis of the K-function (see section 2.4), both the fibre diameters of the fluorescent-labelled axons and their spatial distribution can be studied in the same histological section. In this study we present a method for a tracer signal detection within the axonal profiles and the initial statistical analysis of the patterns of the spatial organization using the gastrocnemic muscle and the L6 ventral root of the rat as an example.
2 Methods
2.1 Animals
The gastrocnemic muscle in the rat consists of a medial and a lateral head, which are innervated by distinct branches of the tibial nerve. The motor neurons responsible for muscle innervation are located in the caudal L4 through rostral L6 segments [4]. Both medial and lateral gastrocnemic muscles of 16 rats were injected with 10 ml 4% Fluoro-Gold® (Fluorochrome Inc) after skin incision under general anaesthesia. All experiments were performed in accordance with international (EU Directive 86/609/EEC) and local laws governing the protection of animals used for experimental purposes. After 3 days of survival the rats were sacrificed and perfused transcardially with 4% paraformaldehyde in 0.1M phosphate buffer, pH 7.2. In all cases specimens of the spinal cords, ventral roots, sciatic nerves and common peroneal nerves were collected.
2.2 Tracing signal detection and measurement procedure
The collected specimens were processed separately, sectioned at 14 mm on a cryotome, cover-slipped and inspected on a Carl Zeiss Axioplan microscope equipped with CCD camera. The fluorescent signal of the axons in the ventral roots was recorded on 2 channels (DAPI filter for FG, and FITC filter for the overall morphology of the root) and used for the further image and statistical analysis. The fluorescent images were further processed by means of automatic granulometric filtering, programmed on the freeware image analysis software package ImageJ [3]. The tracing-signal containing axons were outlined and measured automatically with their locations and areas recorded in a database, followed by verification by an independent human observer. The same positive fibres (axon and myelin sheath) were identified in 3 randomly placed sample areas in a print of the analysed image and measured by a human operator. A regression line was computed for all of the matching pairs of measurements.
2.3 Spatial Statistical Analysis
The locations of the tracing signal can be represented by a “spatial point pattern” (SPP) in the plane of sectioning. Thus inferences of the spatial structure of this SPP will be valid for the underlying biological process as well. The simplest example of a SPP is the homogeneous Poisson process in the plane, which is also referred to as Completely Spatially Random (CSR). It provides the point of reference against which any other patterns can be tested [1]. The statistical test is based on the rejection of CSR, and it is performed on the base of series of independent Monte-Carlo simulations of events in random locations of the study area with the same estimated intensity, followed by calculation of Ripley’s K-function. Here we used the normalized estimator of the K-function, as calculated from the point-to-point distance matrix:
, where N denotes the number of points having dij £ h (dij – distance between each 2 points) and n –
the total number of points in the area of the study. The actual test for a
departure from the Poisson distribution, using simulated K-functions, is
performed by computation of the so called “simulation envelopes”:
(Lower simulation envelope) and
(Upper simulation envelope) [1]. Here s
denotes each simulation.
If the K-function of the real process falls below L(h), the points are more dispersed; and if the K-function of the real data rises above U(h) the data are more clustered than a Poisson process. In both cases, CSR is rejected for the interval of distances £ h [1]. All of the computational steps were programmed in Matlab 6.5.1.
3 Results
In all animals studied, the spinal cord
motoneurons in the lumbar motoneuronal columns were positive for the tracing
signal (data not shown). The fluorescent signal could successfully be
visualized and detected in cross-sections of the L6 ventral roots. Further we
exemplify the proposed method with the results of case # A1120, segment L6. The
total number of positive axons was 219 (Figure 1). For the linear regression
analysis 3 randomly placed areas were selected in the image and the positive
axons were identified in the automatic fluorescent measurements. 67% of the
matching fibres (axon + myelin sheath) could also be measured
semi-automatically on a print of the same image and their fibre diameters
distributions are represented in Fig 3. A statistically significant linear
regression relationship between the diameters of the fluorescent patches
(d[label]) and the corresponding fibre diameters (axon and myelin sheath) could
be established (N=46, R=0.368, p<0.05)(Figure 2). Separately all of the
fibres (axon + myelin sheath, d[f]) were semi-automatically measured in the
same sample areas. The resulting diameter distributions were bimodal with peaks
at 5.5 mm and 10 mm (Figure 3). On the basis of the estimated regression the predicted
fibre diameters (axon + myelin sheath) were calculated for all of the
fluorescence-positive axons and a distribution histogram was computed (Figure
3). It resulted in a unimodal distribution with a peak around 10 mm (coinciding with the Aa motor fibres), which also coincided with the
peak of the semi-automatically measured matches. The data of 300 simulations
with samples of 2000 randomly generated points are represented in Figure 4. The
K-function plots show significant departure from the CSR. The mean inter-point
distance was 144.87±72.80 mm (SD), which precedes the largest departure of the K-function from
the 
mean simulations’ value, found at 181.83 mm.
4 Discussion and Conclusions
The estimated number of the motor neurons, respectively motor axons, varies considerably in the different tracing studies with smallest estimate being 93 for the lateral gastrocnemic muscle [5] and the largest – 322 for both gastrocnemic muscles [4]. In our study the number of the motor fibres was estimated to be 219 in the L6 anterior root, which is within the range of the previous studies.
The presented method allows for the
detection of the thick myelinated motor fibres (Aa-fibres), which is important
for the applications of
The positive departures from the CSR allow for the description of the large-scale organization and presence of clustering of the Aa-fibres in the studied ventral root (Figure 4). Estimation of the locations of the possible clusters is a target of ongoing investigations (Figure 5).
References
[1] Diggle, P., Statistical analysis of spatial point patterns, 1 – 148, 1983.
[2] Prodanov, D., E. Marani, J. Holsheimer, Biomed Rev, 14: in press, 2003.
[3] Prodanov,D., http://rsb.info.nih.gov/ij/plugins/granulometry.html.
[4] Swett, J. E., R. P. Wikholm, R. H. Blanks et al., Exp. Neurol., 93: 227 – 252, 1986.
[5]
Tredici, G., C. Migliorini,
Acknowledgements
The work presented here is funded by the NeuralPRO project, EU Human Potential Project, shared cost contract No HPRN-CT-2000-00030 - Neural Prostheses.