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Journal of Neuroscience Methods 163 (2007) 24–30

A fast and accurate procedure for deriving the Sholl profilein quantitative studies of neuronal morphology

Humberto Gutierrez ∗, Alun M. DaviesSchool of Biosciences, Cardiff University, Museum Avenue, P.O. Box 911, Cardiff CF10 3US, Wales, United Kingdom

Received 16 November 2006; received in revised form 3 February 2007; accepted 6 February 2007

bstract

The growth and elaboration of neural processes underpins the establishment of neural architecture during development and is a key facet ofeural plasticity throughout life. Sholl analysis is a valuable and widely used method for quantifying the extent and complexity of neural processesn the vicinity of the neuronal soma, such as the dendritic arbors of individual neurons in vivo and neuritic arbors of individual neurons in vitro. Itonsists of tracing a series of concentric rings with regular radial increments centred in the neuronal soma and counting the number Xi of processesntersecting each ring. This is a laborious and time-consuming procedure that consequently can only be applied to relatively small numbers ofeurons. We propose a simpler and accurate method for deriving exactly the same information based only on the relative position, with respecto the cell soma, of the bifurcation (Bi) and terminal points (Ti) of processes. By means of the iterative equation Xi = Xi−1 + Bi − Ti, it is possibleo automatically reconstruct the complete pattern of intersections between neurites and the concentric rings. We compared our method with the

onventional Sholl analysis and found that our simplified procedure is approximately five times faster permitting numerically larger samples to benalyzed. We further tested the sensitivity of our method of analysis by looking at the effect of preventing NF-�B signaling on BDNF-dependenteuritic growth in sensory neurons. 2007 Elsevier B.V. All rights reserved.

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eywords: Sholl analysis; Morphology; Dendritic arbor; Pyramidal neurons; S

. Introduction

The pattern of growth and elaboration of neural processess critical for the establishment of a functional nervous systemuring development and is an integral feature of the changesn neural architecture that contribute to plasticity in the matureervous system. Sholl analysis (Sholl, 1953) is a widely usedethod for quantifying and graphically representing the charac-

eristic morphology of neuritic arbors (Caserta et al., 1995; Duant al., 2003; Pante et al., 2005; Gutierrez et al., 2004, 2005; Haast al., 2006; Ip et al., 2002; Isaacs et al., 1998; Kheirandish et al.,005; Libersat and Duch, 2002; Lowndes et al., 1990; Mizrahnd Libersat, 2002; Neale et al., 1993; Ristanovic et al., 2006;hi et al., 2004; Robinson and Kolb, 1997; Spires et al., 2004;

ood et al., 2004; Zagrebelsky et al., 2005). In the basic pro-

edure, the number of intersections of neuritic processes withings of increasing radii centred in the cell soma are counted.

∗ Corresponding author. Tel.: +44 29 2087 51 76.E-mail address: gutierrezh@cf.ac.uk (H. Gutierrez).

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165-0270/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.jneumeth.2007.02.002

y neuron

he Sholl profile is obtained by plotting the number of intersec-ions versus the radial distance from the cell soma (Sholl, 1953;ig. 1B). Whether manually or computer assisted, this is a time-onsuming procedure that consequently can only be applied toelatively small numerical samples of neurons. In the case ofomputer-assisted systems, this is due to strict requirements inhe image quality needed for their automatic processing. This inurn requires extensive editing or laborious separate tracing ofeural processes in order to obtain the well-segmented, noise-ree images needed. Here we describe a simpler method foreriving the same information based on fewer input data: theumber of processes emerging from the cell soma and relativeositions, with respect to the cell soma, of bifurcation points androcess terminals (Fig. 1B). This results in a considerable simpli-cation in data acquisition and analysis, thereby facilitating thetudy of larger numbers of neurons with a more robust statisticalreatment of the data. To demonstrate this, we directly compared

ur simplified procedure with conventional Sholl analysis. Weurther tested our method of analysis by looking at the effect oflocking NF-�B signaling on the size and complexity of neuriterbors growing from cultured sensory neurons.

H. Gutierrez, A.M. Davies / Journal of Neuroscience Methods 163 (2007) 24–30 25

Fig. 1. Schematic representation comparing the basic layout used in the conventional Sholl analysis and the simplified method described here. (A) For the classicSholl analysis, a number of concentric rings with regular radial increments centred in the neuronal soma are traced and the number Xi of neurites intersecting eachring of increasing radii is counted (open circles). These data averaged over a population of sampled neurons and plotted vs. radial distance result in the characteristicS ed fro( 0).

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holl profile (inset). (B) In the simplified method, the entire Sholl profile is deriv‘t’ points in panel B) and the number of processes emerging from the soma (X

. Methods

A schematic representation of the basic layout used in theonventional Sholl analysis is shown in Fig. 1A. For any givenell, the Sholl profile is expressed by the list of values X1, X2,3. . ., representing the number of intersections of neurites withoncentric ring of increasing radii. After averaging over a num-er of sampled neurons and plotting the number of intersectionser ring as a function of radial distance, the characteristic Shollrofile (see inset in Fig. 1) of a given set of neurons is obtained.n the simplified method we propose, the list of values Xi cane derived by taking only into account the relative position oferminal and branching points relative to the cell soma (Fig. 1B).he method is based on the following principle.

Let X(r) be the number of intersections occurring betweeneuritic segments and a circle of arbitrary radius r centered inhe cell soma. Empirically, the function X(r) shows initially aapid increase with r, reaching a maximum value at some point,nd from there X(r) decreases down to zero at a distance fromhe soma at which no more neuritic segments are to be foundsee inset in Fig. 1A). Variations in X(r) are only due to twoinds of discreet events: (a) branching events taking place at aarticular distance r from the soma, resulting in an increase of(r) and (2) process termination, resulting in a decrease of X(r).

In other words:

dX

dr= B(r) − T (r). (1)

here B(r) is the number of branching or bifurcation eventsccurring at distance r, and T(r) is the number of terminationsccurring at the same distance.

Expressing (1) in its discreet form and equating �r to anitary interval we get:

i = Xi−1 + Bi − Ti. (2)

here Xi is the number of intersections occurring at the ithnterval boundary (ith ring), and Bi and Ti are, respectively, the

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m the radial distance to bifurcations (‘b’ points in panel B) and terminal points

umber of bifurcation and termination events occurring in theth interval.

Thus, by simply knowing the relative position of branchingnd termination events, the entire set X of intersections can beerived by iteration of Eq. (2).

The first step of the routine consists then in obtaining the listsf values T and B. This can be implemented manually or assistedy computer.

If the procedure is implemented manually, a template ofoncentric rings at regular intervals can be superimposed tohe images of neurons previously acquired. Instead of countingntersections per ring, only terminal segments and bifurcations

ust be counted per inter-ring interval, as well as the number ofeural processes emerging directly from the cell soma (primaryeurites, X0 in Figs. 1 and 2). This will result in the list of val-es B1, B2, B3. . ., representing bifurcation points per inter-ringnterval and the list T1, T2, T3. . ., for terminal points per inter-ing interval (see example in Fig. 2A). It is important to notehat Eq. (2) assumes binary trees; that is, only binary branchingvents take place. This means that a trifurcation or, in the generalase, an n-furcation, should be regarded as consisting of n − 1inary branching events and should be counted accordingly.

This part of the procedure can also be implemented by meansf a simple computer program. In this case no tracing of con-entric circles is necessary. By using the computer mouse theoma center is marked followed by marking terminal segmentsrst and then bifurcation points. The scale bar of the images cane used to derive the radial distances t1, t2, t3. . ., tn from theoma to terminal points and the radial distances b1, b2, b3. . .,m from the soma to bifurcation points. Once a maximum num-er of rings and the radial increment D are arbitrarily decided,ranching point or terminal segment are ascribed to their cor-esponding intervals as follows: if bi is the radial distance to a

iven branching point, the corresponding interval for that pointill be the integer part of bi/D. The list of values B1, B2, B3. . .,

s then obtained by automatically counting the occurrence ofalues representing each interval. Following the exact same pro-

26 H. Gutierrez, A.M. Davies / Journal of Ne

Fig. 2. Basic principle for the derivation of the Sholl profile based only onthe relative location of terminal and bifurcation points. (A) The list of valuesT1, T2, T3. . ., etc., is obtained by counting the number of terminal points ateach interval (black triangles), where T1 is the number of terminal points in thefirst interval, T2 is the number of terminals in the 2nd interval, etc. Followingexactly the same procedure the values B1, B2, B3. . . can be obtained, listingthe number of bifurcations found at each interval (asterisks). X0 is the numberof primary neurites coming directly from the soma, in this example X = 1. (B)Using the lists of values B and T plus the value of X0 previously obtained, thelist of values X1, X2, X3. . . can then be generated by means of the iterativeequation shown. Thus, in this example: X1 = X0 + Bl − T1 = 1 + 0 − 0 = 1. Next,Xw

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2 = X1 + B2 − T2 = 1 + 1 − 0 = 2, etc. Note that the resulting vector X coincidesith the Sholl pattern of intersections sought for this neuron.

edure, values T1, T2, T3. . ., can be obtained listing the numberf terminal segments found at each interval.

The second step consists in reconstructing the entire inter-ection pattern. Fig. 2B illustrates the basic algorithm. Like inhe conventional procedure, intersections will be representedy the list of values X1, X2, X3. . ., which in this case will beenerated by iteratively applying Eq. (2) to the lists of val-es Ti and Bi previously obtained. Although this can also bealculated manually, the basic principle can easily be imple-ented in any programming platform (a simple Matlab script

ncluding a routine for image display and sampling of terminalnd branching points is freely available on request). The initial0 value, necessary for calculating X1, is the number of pro-esses emerging directly from the soma. In the example shownn Fig. 2, X0 = 1. Therefore, X1 = X0 + (number of bifurcationsound in the first interval) − (number of terminal segments foundn the first interval), that is X1 = 1 + 0 + 0 = 1. X2 = X1 + (numberf bifurcations in the 2nd interval) − (terminal segments in thend interval) = 1 + 1 + 0 = 2, etc. (Fig. 2B). The resulting list ofalues Xi is the Sholl profile sought for this neuron.

.1. Dissociated neuronal cultures

Dissociated cultures of nodose neurons were set up from new-orn mice obtained from of CD1 mice. Dissected ganglia wererypsinized (0.05% trypsin for 25 min at 37 ◦C) and dissociated

y trituration. The neurons were plated in defined, serum-freeedium on a poly-ornithine/laminin substratum in 35 mm tis-

ue culture dishes (Davies et al., 1993) and incubated in theresence of BDNF (R&D, 10 ng/ml). For the blockade of NF-

Fera

uroscience Methods 163 (2007) 24–30

B signaling, the NF-�B inhibitor SN50 (Calbiochem, 10 �M)as added 3 h after plating along with BDNF. Neuronal culturesere incubated during 24 h and then fluorescently labeled with

he vital dye Calcein AM (Invitrogen). Images encompassinghe whole neuritic arbors of individual neurons were digitallyrabbed in a standard inverted fluorescence microscope. Pair-ise comparisons were made using the student T-test. Forultiple comparisons ANOVA was performed followed by Fish-

rs post-hoc test.

. Results

In order to validate the method, a comparison between theonventional measurement of the Sholl profile (C. Sholl) andhe simplified estimation described here (Fast Sholl) was car-ied out. Nodose neurons were cultured for 24 h and stainedith Calcein AM. Images of 64 cells were grabbed and ana-

yzed using two separate procedures. For the conventional Shollnalysis, concentric circles were digitally traced at 30 �m inter-als. By means of the computer mouse the intersections betweeneurites and the rings were marked, counted and the data auto-atically stored. The time spent in the analysis of each individual

mage was recorded. For the simplified method described herehe centre of the soma was marked as well as the terminalsnd branching points. By means of a simple computer pro-ram the radial distances were calculated and the corresponding0 �m intervals assigned to each branching and/or terminaloint. The time spent on the analysis of each individual imageas again recorded. Fig. 3A shows the resulting Fast Sholl pro-le compared to the directly measured one (C. Sholl). An almostomplete overlapping of both curves was obtained illustrating anfficient estimation of the Sholl profile obtained by our method.

complementary way of comparing both methods consists inomparing the cumulative number of intersections obtained perell across the entire set of concentric rings. Fig. 3B compares theverage total number of intersections obtained by each method.he average value obtained from the conventional Sholl was1.2 ± 5.0, compared to 49.8 ± 4.5 obtained from our simplifiedethod.To quantify the actual efficiency of our method, a statistical

orrelation of the cumulative number of intersections per cell asssessed by the two methods was carried out. As can be seen inig. 3C a slope of 0.991 was obtained with R2 = 0.95, indicat-

ng and almost complete statistical identity between the valuesbtained by both methods. As mentioned before, Sholl analy-is tends to be a laborious and time-consuming procedure foruantifying neuritic morphology. The direct counting of inter-ections between neurites and the concentric rings generallynvolves a large number of counting events. By contrast, ourimplified method relies in the counting of a much more reducedet of items, i.e., terminals and branching points. As a result, themount of time spent acquiring and analyzing the data is con-iderably reduced, especially with more complex neurite arbors.

ig. 3D shows the average analysis time spent per neuron usingach different method. Fast Sholl profiling resulted in over 78%eduction in analysis time when compared to the conventionalnalysis.

H. Gutierrez, A.M. Davies / Journal of Neuroscience Methods 163 (2007) 24–30 27

Fig. 3. Comparison between the direct measurement of the Sholl profile and the simplified method described here. Nodose neurones were cultured for 24 h andstained with Calcein AM. Images of 64 cells were grabbed and analyzed using two separate procedures. For the conventional Sholl analysis, concentric circles weredigitally traced at 30 �m intervals. By means of the computer mouse the intersections between neurites and the rings were manually marked, counted and the dataautomatically stored. For the simplified method, the centre of the soma was marked as well as the terminal and branching points. By means of a simple computerprogram, the radial distances were calculated and the corresponding 30 �m intervals assigned to each branching and/or terminal point. Panel A shows the derivedS l). (Br ethodt

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dneuritic trees in experimental samples of neurons.

In order to illustrate the sensitivity of the method in an experi-mental setting, we analyzed the effect of blocking nuclear factor�B (NF-�B) signaling on the growth of neuritic arbors of nodose

Fig. 4. Correlation between the total estimated intersections per cell obtainedby the Fast Sholl and the total length in micrometers of the neuritic arbors percell as estimated by independent neurite tracing. Thirty individual neurons weresampled across the entire range of morphologies and the total number of esti-

holl profile (Fast Sholl) compared to the conventional measurement (C. Sholegression of the total number of intersections per cell as assessed by the two mime spent per neuron ± SEM using each different method.

Sholl profiling rests on the spatial distribution of intersectionsetween a set of concentric rings and the neuritic arbor of a neu-on. If the rings were infinitesimally spaced and an infinite setf rings was traced, intersecting points would actually samplehe entire length of the neuritic arbor. In other words, the totalumber of intersections (i.e., the area under the Sholl curve) isirectly proportional to the total metric length of the neuriticrbor. In order to further confirm the reliability of our Sholl pro-le estimation, a statistical correlation was carried out between

he estimated cumulative number of intersections and the actualength of the neuritic arbors as measured by independent neuriteracing. To this end, 30 individual neurons were sampled acrosshe entire range of morphologies and the total number of esti-

ated intersections derived according to the simplified methodescribed here (horizontal axis). Inter-ring intervals were setgain at 30 �m. Total neurite length was measured by directracing of the neurites (vertical axis). As shown in Fig. 4, theorresponding linear regression shows a very strong correlationR2 = 0.981, p < 0.0001) between actual length and the total num-er of intersections as estimated by our method. The slope ofhe function (33.928) reveals the average length in micrometersf a neurite segment between two adjacent circles. The value of

he function at the origin (21.304) reflects the fact that neuronsith short processes that do not cross the first ring still have an

verage length of 21.304 �m as assessed by direct tracing. Theesulting linear equation can subsequently be used as a stan-

matce

) Comparison of the average total number of intersections ± SEM. (C) Linears, note the close agreement between both measurements. (D). Average analysis

ard curve to derive the total (metric) length in micrometers of

ated intersections derived according to the method described here (horizontalxis). Total neuritic length was measured by direct tracing of the neurites (ver-ical axis). The resulting linear equation can subsequently be used as a standardurve to calculate the total (metric) length in micrometers of neuritic arbors inxperimental samples of neurons.

28 H. Gutierrez, A.M. Davies / Journal of Neuroscience Methods 163 (2007) 24–30

Fig. 5. Effect of blocking NF-�B signaling on the growth of sensory neurons. Neonatal nodose neurones were cultured in the presence of BDNF alone (control) orBDNF plus SN50, an NF-�B signaling inhibitor. 24 h later, the cultures were stained with Calcein AM and 40 neurones were randomly sampled per group. Imageswere digitally grabbed and analyzed according to the method described here. (A) Fast Sholl analysis comparing the overall growth profile of control and SN50-treatedt ated nS and Sa

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reated neurons. (B) Photomicrographs of representative control and SN50-treN50-treated cells. (D) Corresponding metric length in micrometers of controlnd D represent the mean values ± SEM. Scale bar: 50 �m. *p < 0.05.

anglion neurons cultured with brain-derived neurotrophic fac-or (BDNF). NF-�B is a ubiquitously expressed transcriptionactor that has recently been shown to regulate the growth of neu-al processes in the developing peripheral and central nervousystem (Gutierrez et al., 2005).

Neonatal nodose neurones were grown in low-density disso-iated cultures either in the presence of BDNF alone (control)r BDNF plus the NF-�B nuclear translocation inhibitor SN50.4 h later, the cultures were stained with Calcein AM, and 40eurones were randomly sampled per group. Images were dig-tally grabbed and analyzed. Radial increments for the Shollnalysis were set again at 30 �m. Fig. 5A shows the derivedholl analysis comparing the overall neurite morphology ofontrol and SN50-treated neurons. An overall reduction in thepatial complexity of the neuritic arbors was detected in theN50-treated group. NF-�B blockade resulted in a statisticallyignificant reduction in the number of bifurcations when com-ared to the control group (see Fig. 5C). By means of the standardurve described above, the corresponding metric length for eachroup was determined based on the estimated total (cumulative)umber of intersections. The result showed a clear and statisti-ally significant reduction in the total length and total number ofranching points of the neuritic arbor of SN50-treated cells when

ompared to the control condition (Fig. 5D). These results aren complete agreement with published data showing that pre-enting NF-�B activation or inhibiting NF-�B transcriptionalctivity reduces process growth and complexity in nodose neu-

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eurons. (C) Total number of bifurcations or branching points of control andN50-treated nodose neurons derived by the method described here. Bars in C

ons (Gutierrez et al., 2005). This results shows that our methods sensitive to morphological differences resulting from differentxperimental manipulations.

. Discussion

Sholl analysis (Sholl, 1953) is a widely used method for quan-ifying the characteristic scaling properties of dendritic arborsn vivo and neuritic arbors in vitro (Caserta et al., 1995; Daviest al., 1993; Duan et al., 2003; Pante et al., 2005; Gutierrezt al., 2004, 2005; Haas et al., 2006; Ip et al., 2002; Isaacs etl., 1998; Kheirandish et al., 2005; Libersat and Duch, 2002;owndes et al., 1990; Mizrah and Libersat, 2002; Neale et al.,993; Ristanovic et al., 2006; Shi et al., 2004; Robinson andolb, 1997; Spires et al., 2004; Wood et al., 2004; Zagrebelskyt al., 2005). This analysis describes the distribution of neu-itic segments at different distances from the cell body. Despitets long established utility in quantifying changes in neuronal

orphology occurring during development and under partic-lar experimental conditions, Sholl analysis suffers from therawback of being a very time-consuming method as it involvesathering the complete set of neurite intersection points inseries of concentric circles centred on the cell soma. This

mposes practical constrains on the sample size of neurons thatan be conveniently analyzed and consequently on the statisti-al treatment that can be applied to the data. To circumvent thisrawback of Sholl analysis, we have developed an alternative,

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H. Gutierrez, A.M. Davies / Journal of

fficient method of obtaining the entire Sholl profile of a popula-ion of neurons from a much more reduced set of sampled pointsbifurcations and terminal points). This results in a considerableimplification and reduction in the analysis time, thereby allow-ng for numerically larger samples of neurons to be includedithin a study, with resultant more reliable statistical treatmentf the data.

The resolution of the Sholl analysis ultimately depends on theensity of the sampling of intersections. That is, the number andpacing of concentric circles. The greater the number of con-entric circles and the smaller the intercircle intervals, the morerecise the analysis. However, since the cumulative number ofntersection points, the actual counted items, depends linearly onhe number of concentric rings, increasing the number of con-entric circles results in a proportional increase in the workloadf the analysis. In marked contrast, the entire information of theholl analysis in our method is contained in an invariant set ofounted points, namely, terminal and bifurcation points. Fromhe point of view of this method the number of concentric circleso be included in the analysis is completely inconsequential. Inther words, a high-resolution Sholl analysis using an arbitrar-ly large number of circles with short intercircle intervals canqually be derived from the same reduced and constant set ofampled points with no additional work. We demonstrate thatur method permits an accurate estimation of the total numberf intersections without the direct counting used in the conven-ional Sholl analysis. Furthermore, by means of a standard curve,he total length of the neuritic arbor can be easily calculated fromur data set.

In estimating the pattern of intersections, the robustness ofur simplified method clearly rests on the larger size of sam-les. Thus, for instance, for individual meandering processeshat intersect the same ring more than once (or even extendack towards the soma), our simplified method may result in alight underestimation of the number of intersections for thosearticular processes. However, the statistical impact of suchvents on the overall pattern of growth is clearly negligiblehen larger numbers of neurons are included in the analysis

see Figs. 3 and 4). This is particularly true for dendritic treess well as for neuritic arbors of neurons in culture. Althoughhese and other events add to the error of the method, the facthat larger samples can be analyzed greatly minimizes the con-ribution of those events to the expected levels of noise in theata.

It is worth noticing that, since our method takes direct accountf the relative position, with respect to the cell soma, of bifur-ation and terminal points, novel and convenient morphologicalarameters can also be derived directly from the spatial distri-ution of these points.

Although automated systems for conducting Sholl analysisre available, they impose strict requirements in the qualityf the images (see, for instance, http://wwwbiology.ucsd.edu/abs/ghosh/software/index.html). This in turn demands either

xtensive editing or separate manual tracing in order to obtainhe final high contrast, noise-free images to be used in the analy-is. Although the automatic analysis itself can be carried out veryapidly, preparation of images is time consuming and tedious,

I

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oscience Methods 163 (2007) 24–30 29

mposing again practical restrictions on the numerical size of theampled population of neurons. In the method described here,simple and direct visual inspection of the images permits the

mmediate marking and counting of the bifurcation and terminaloints without highly stringent requirements in the quality of themages and without any need of separate tracing of the neuriticrocesses. This is particularly useful in the case of preparationsf Golgi impregnated neurons or fluorescently labeled neuronsn organotypic cultures where wide variations in intensity andackground noise make the direct use of automatic systemsmpossible unless a separate tracing of neurons is carried outsee, for instance, Gutierrez et al., 2004, 2005; Zagrebelsky etl., 2005).

In order to illustrate the sensitivity of the method in an exper-mental setting we analyzed the effect of blocking nuclear factorB (NF-�B) on the development of the neuritic arbour of nodoseeurons. Consistent with reported data (Gutierrez et al., 2005),ur fast analysis method revealed a clear and statistically signif-cant reduction in the overall size, total length and total numberf branching points of the neuritic arbour of SN50-treated cellshen compared to the control condition. This result demon-

trates that the method presented here is sensitive enough to besed in the context of experimental manipulations resulting inhanges in neuritic morphology.

In conclusion, the simplified method presented seems to behighly efficient, rapid and inexpensive way of deriving the

ame spatial information resulting from the conventional Shollnalysis. The method can be easily implemented and permitsarger samples of cells to be analyzed, allowing a more robusttatistical treatment in the study of neuronal morphology.

cknowledgement

This work was supported by a grant from the Wellcome Trust.

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