Identification of Living OligodendrocyteDevelopmental Stages by Fractal Analysis ofCell Morphology

Frederic Bernard,1 Jean-Louis Bossu,2 and Stephane Gaillard1*1Laboratoire de Neurobiologie du Developpement et de la Regeneration, CNRS, Centre de Neurochimie,Strasbourg, France2Laboratoire de Neurotransmission et Secretion Neuroendocrine, CNRS, Centre de Neurochimie,Strasbourg, France

The Mandelbrot’s fractal dimension (D), a measure ofshape complexity, has been used to quantify the com-plex morphology of living cells. Previous studies on glialcells have shown that as cells increase in morphologicalcomplexity, their “D” value increases, suggesting that“D” could be used to estimate their stage of differentia-tion. In the present study the box-counting method wasused to calculate the “D” values of rat cerebellar oligo-dendrocytes during their differentiation in primary cul-ture. These values were correlated with the immunore-activity of cells to antigenic markers commonly used forassessing their stages of differentiation: A2B5, O4 andanti-galactocerebroside (Gal-C). Our results show thatchanges of the fractal dimension during differentiationfollow the well known pattern of markers expression bythese cells. These results demonstrate that A2B5-, O4-,and Gal-C-expressing oligodendrocytes can be confi-dently estimated from their respective fractal dimensionvalues. Based on this immunocytochemical calibration,the calculation of “D” allows an easy and fast determi-nation of the developmental stage of living (unstained)oligodendrocytes before the study of their physiologicalcharacteristics. Using this method we precisely identifiedliving oligodendrocyte progenitors and early pro-oligodendrocytes expressing voltage-activated sodiumcurrents that is a common characteristic of these twoimmature developmental stages (Sontheimer et al.[1989b] Neuron 2:1135–1145). J. Neurosci. Res. 65:439–445, 2001. © 2001 Wiley-Liss, Inc.

Key words: oligodendroglia; morphology; fractal dimen-sion; development

Many physiological characteristics depend on thedifferentiation stage of the cells studied. In neurons forinstance, it is well established that the appearance of thevarious ionic conductances follows a sequential timing(Spitzer, 1979). More recently, a similar successive appear-ance of ionic channels has also been reported duringoligodendrocyte differentiation (Kettenmann et al., 1991).

Most of the models used in developmental physiol-ogy (such as cell culture systems) contain unsynchronized

cells. It is thus essential to assess the exact developmentalstage of a given cell before the study of its physiologicalproperties. The pattern of oligodendrocyte differentiationhas been well studied by using antibodies directed againstvarious stage-specific markers such as A2B5 (Raff et al.,1983), anti-GD3 (Levi et al., 1987), O4 and anti-galactocerebroside O1 (Sommer and Schachner, 1981).The corresponding developmental stages (oligodendrocyteprogenitor, pro-oligodendrocyte, immature and matureoligodendrocyte) have been characterized in dissociatedcell culture systems (Levi et al., 1987), in tissue sections(Reynolds and Wilkin, 1988) and also in vivo (Curtis etal., 1988).

Although such immunocytological methods are themost rigorous in establishing the developmental stage ofoligodendrocytes, they are difficult to combine with phys-iological analysis carried out on living cells. Thus, theidentification of cellular developmental stages is usuallymade by using morphological criteria.

The complex morphology of oligodendrocytes is noteasily quantified using classical measures such as length,diameter or surface. Complex morphology of natural ob-jects could, however, be successfully quantified by usingthe statistical self-similarity concept of the fractal geometryintroduced by Mandelbrot (1983). This approach, inde-pendent of the visual estimation of the morphologicalcomplexity, allows one to quantify objectively the com-plexity of a shape border by measuring its fractal dimen-sion (D) (see Material and Methods section). A high “D”value indicates a higher degree of complexity.

Previous studies have demonstrated that fractal anal-ysis was suitable for quantifying the complex morphologyof oligodendrocytes (Smith et al., 1989, 1991; McKinnonet al., 1993), and that the fractal dimension of these cells

*Correspondence to: Stephane Gaillard, Laboratoire de Neurobiologie duDeveloppement et de la Regeneration, CNRS, Centre de Neurochimie, 5,rue Blaise Pascal, 67084 Strasbourg, France.E-mail: sgaillard@neurochem.u-strasbg.fr

Received 13 November 2000; Revised 26 April 2001; Accepted 28 April2001

Journal of Neuroscience Research 65:439–445 (2001)

© 2001 Wiley-Liss, Inc.

increases during their development in culture (Smith et al.,1989; Smith and Behar, 1994). Furthermore, it was dem-onstrated that mature oligodendrocytes, positively stainedwith O1 antibody, have a higher fractal dimension thanoligodendroglial precursor cells, immunostained withA2B5 antibody (Kreider et al., 1996). These results havesuggested that the fractal dimension of a given oligoden-drocyte could be potentially used to estimate its develop-mental stage. A strong correlation between “D” values andthe expression by a given cell type of specific develop-mental antigens must however, be established as a prelim-inary; this is the aim of the present report.

We computed the fractal dimension of individualcells positively stained with A2B5, O4 and anti-Gal-Cantibodies. Late mature cells with processes ending in largemembranous patches are not fractal objects and were notincluded in the present study.

We observed a tight correlation between the varia-tion in the fractal dimension of the different populations ofcells and their respective immuno cytochemical character-istics. This observation demonstrates that the fractaldimension can be used to confidently estimate the devel-opmental stage of oligodendrocyte progenitors, pro-oligodendrocytes, immature and early mature oligoden-drocytes. This was further confirmed by using “D” toidentify the developmental stage of living cells expressingthe voltage activated sodium current in unstained cultures.The expression of this current has been found previouslyonly in early immature cells (Sontheimer et al., 1989b;Barres et al., 1990). Our results agree well with thesestudies because we recorded sodium currents in cells char-acterized by a fractal dimension corresponding to A2B51

and early O41 cells.

MATERIAL AND METHODSCell Culture

Primary cultures of newborn rat cerebellar oligodendro-cytes were prepared as described previously (Boussouf et al.,1997). Briefly, the cells were mechanically dissociated and platedat a concentration of about 105 cells per 35 mm culture dish inDulbecco’s modified Eagle’s medium (DMEM, Gibco, GrandIsland, NY) supplemented with sodium bicarbonate (25 mM),insulin (0.5 mM), gentamicin (0.05 mg/ml) and 10% decomple-mented horse serum. Cells were incubated at pH 7.40 at 37°Cin a humidified incubator equilibrated with 95% air/5% CO2.Two days after plating, the cells were rinsed and exposed to aserum-free chemically defined medium consisting of DMEMsupplemented with sodium bicarbonate (25 mM), bovine serumalbumin (100 mg/ml), human transferrin (100 mg/ml), proges-terone (20 nM), insulin (0.5 mM), putrescine (100 mM), tri-iodothyronine (10 nM), sodium selenite (30 nM), penicillin(50 UI/ml) and streptomycin (50 mg/ml) (Gaillard and Bossu,1995). All reagents were from Sigma Chemical Company (St.Louis, MO). The medium was completely renewed every 4days.

Immunostaining

In order to detect surface markers, immunocytochemicalstainings were carried out at room temperature on plastic culture

dishes according to the following protocols: after fixation inparaformaldehyde (4%), cells were rinsed with phosphate buff-ered saline (PBS) (three times) and incubated for 60 min with10% goat serum in PBS to block unspecific antigenic sites. Cellswere then incubated for 60 min with one of the followingprimary antibodies diluted in PBS: Anti-Gal-C (mouse IgG,5 mg/ml, Boehringer-Mannheim Biochemicals, Indianapolis,IN); A2B5 (mouse IgM, 10 mg/ml, Boehringer-Mannheim);O4 (mouse IgM, 10 mg/ml, Boehringer). After washing them inPBS, cells were incubated for 60 min with Alexa Fluor 488-(Molecular Probes, Eugene, OR) or CY3- (Jackson Immu-noResearch Laboratories, Inc., West Grove, PA) conjugatedgoat anti mouse IgG or IgM, (1/400). After washing them inPBS, cells were then mounted with Vectashield (Vector Labo-ratories, Burlingame, CA) under a glass coverslip for micro-scopic observation. This study was carried out on cells after 2 tomore than 10 days in primary culture, to cover a broader rangeof morphological and physiological differentiation stages.

Image Capture and Analysis

All immunopositive cells were selected for image capturewith the only condition that they were isolated, without contactor interweaving with neighboring cells. Only highly maturecells were discarded because the presence of myelin-like mem-branous sheets convey to these cells a morphology devoid of theself-similarity characteristic of fractal objects.

Cell images were captured with a cooled CCD digitalcamera (KX 85, Apogee Instruments Inc., Tucson, AZ) con-nected to the photomicrographic attachment of an invertedmicroscope equipped for epifluorescence analysis (OlympusIMT2). Cells were observed with a 340 oil objective (n.a.0.85). Original images were stored as TIFF format for furtheranalysis. The original images (Fig. 1A) were binarized by select-ing a suitable threshold allowing to save most of the finestprocesses of the cell (Fig. 1B). In some cases, various artifacts(fragments of dead cells or processes belonging to other cells)were deleted from the binary image to save the morphology ofa single isolated cell (Fig. 1C). The skeleton of the cell was thencomputed using a thinning algorithm (Fig. 1D). All these stepswere carried out by using the Scion Image program (that is thePC version of the popular NIH Image program, originallywritten at the National Institute of Health. Scion Image can befreely downloaded at: http://www.scioncorp.com).

Fractal Dimension Calculation

The methods most commonly used for measuring thefractal dimension of a given object in a plane are length-related(Smith et al., 1996). Among the several approaches for measur-ing length-related fractal dimension, the box-counting methodhas been shown to be relevant for computing the fractal dimen-sion of cultured oligodendrocytes (Smith et al., 1991) and wasused in the present study. This method consists of superimposingsuccessive grids with boxes of different sizes on the skeleton ofthe considered cell. The box-counting fractal dimension (Db)was then calculated from the slope of the linear regressionbetween the log of the number of occupied boxes and the log ofthe corresponding boxes’ size. Owing to the actual size of theoligodendrocytes in culture, the boxes’ sizes were set from1–20 mm (Takeda et al., 1992). In the present study, the fractal

440 Bernard et al.

dimension of the cells was computed by using the Benoitsoftware (TruSoft International Inc., St. Petersburg, FL).

Fractal Nature of Oligodendrocytes

Several reports from Smith and Behar (1994) demon-strated that oligodendrocytes in primary culture display mor-phologies with self-similarity properties, which is a definingcharacteristic of fractal objects. Because oligodendrocytes mor-phology could depend on culture medium, tissue origin or celladhesion characteristics (Szuchet, 1995), we first verified theself-similarity property of oligodendrocytes in our culture con-ditions. This was carried out by comparing the fractal dimensioncalculated from the integrality of a single cell with those calcu-lated from smaller parts of the same cell. A typical result of suchan analysis is shown on Figure 2. The similarity of Db valuesfrom the whole cell and from smaller parts of this cell confirmedthe self-similarity property of oligodendrocytes in our cultureconditions and thus strengthened the quantification of theirmorphology with fractal analysis.

The fractal property of objects is also evidenced by a highvalue for the correlation coefficient of the linear regression ofthe log/log plot (Reichenbach et al., 1992; Takeda et al., 1992).For all the cells studied in the present report (n 5 741) thesecorrelation coefficients were always greater than 20.993.

Electrophysiology

The culture medium was replaced with a solution con-taining in mM: NaCl 137.0, KCl 5.4, CaCl2 1.0, MgCl2 1.0,MgSO4 0.8, HEPES 20, and BaCl2 1.0 to block inward recti-fying potassium currents; pH adjusted to 7.40 with NaOH.Culture dishes were then transferred on the stage of a NikonDiaphot 300 microscope (Tokyo, Japan). Patch-clamp record-ings were carried out under voltage clamp (at 20°C) in thewhole-cell configuration of the patch-clamp recording methodusing an Axopatch 200 B amplifier (Axon Instruments, FosterCity, CA). Pipettes of 4 MV were pulled from borosilicate glasscapillaries and filled with a solution containing in mM: CsCl2130, EGTA/CsOH 1, MgCl2 2, NaCl 2, HEPES/CsOH 10,MgATP 2, and GTP 0.5. The pH was adjusted to 7.2 withCsOH. Gigaohm seals between the pipette and the cell wereobtained and capacitance transients were minimized. After goinginto the whole-cell recording configuration, the cell wasvoltage-clamped at 280 mV and the series resistance and cellmembrane capacitance measured using a step of 610 mV werecompensated. Voltage commands (duration 10 msec, step of5 mV) were generated using the Pclamp6 software (Axon In-struments, Burlingame, CA). The resulting current traces (dig-itized at 5 kHz) were corrected for linear leak by subtracting

Fig. 1. Illustration of the successivesteps of image analysis exemplifiedwith an O4 positive cell. A: Imagesof fluorescent cells were capturedand saved as 8 bits gray levels nu-meric images. B: The original imagewas then binarized using a suitablethreshold. When present in the field,large artifacts (arrows) were manu-ally deleted, although small oneswere automatically eliminated usingerosion algorithms to save the mor-phology of a single cell (C). D: Theskeleton of the cell was finally ob-tained using a thinning algorithm.

Fractal Dimension and Oligodendrocyte Differentiation 441

after appropriate scaling the average current response to fourvoltage steps of one-fourth the amplitude of the test pulse andstored for off line analysis on a IBM PC computer using thePclamp6 software.

RESULTSFractal Dimension of Cells

The ranges of fractal dimension for cells immuno-stained with the different antibodies are illustrated in Fig-ure 3. The actual minimum and maximum values for thefollowing antibodies are: A2B5, 1.053 – 1.468; O4: 1.233– 1.721 and anti-Gal-C: 1.326 – 1.713 respectively. Itshould be noted that the fractal dimension of objects in atwo-dimensional image necessarily lies between 1 (for aline) and 2 (for a surface) (Smith et al., 1996).

The existence of A2B51/Gal-C1 immature oligo-dendrocytes has been reported (Levi et al., 1986). From

our data, an overlapping of Db values for A2B51 cells on onehand and Gal-C1 cells on the other hand is observed (Fig. 3).The population covered by these values (from 1.326 – 1.468)could conceivably correspond to the immature oligodendro-cytes cited above that actually express both antigens at thesame time. To verify this hypothesis, a double staining withA2B5 and anti Gal-C antibodies was carried out. The pres-ence of A2B51/Gal-C1 immature oligodendrocytes wasalso observed in our culture conditions (not illustrated), andthe minimal and maximal values of Db for these doublestained cells were 1.322 and 1.480 respectively.

The use of fractal dimension on living (unstained)cells implies that the whole morphology of the cell couldbe observed under phase contrast optics, with no loss offine details. This was ascertained in this study by compar-ing the values of “D” calculated from the phase contrastand the fluorescence images of the same cell. A typicalresult obtained from a Gal-C1 oligodendrocyte is illus-trated on Figure 4 and shows that both images give rise toalmost identical fractal dimension. Similar results were alsoobtained with A2B51 and O41 cells (not illustrated).

Sodium Current ExpressionA transient sodium current was recorded on cells

characterized by a fractal dimension ranging from 1.027–1.395 (n 5 71). These values correspond to oligodendro-cyte progenitors and early pro-oligodendrocytes. Thevoltage-gated sodium current had a peak ranging from219 to 2586 pA (mean 2166 6 14 pA, n 5 71). Typicalrecordings of these currents are illustrated in Figure 5C,D.More mature cells were also selected for patch-clamprecordings, no sodium current was observed on cells witha fractal dimension greater than 1.395 (37 cells recorded,with “Db” extending to 1.647). To further study thisdevelopmentally regulated expression of the sodium cur-

Fig. 3. Extent of fractal dimension for A2B5 (n 5 142), O4 (n 5 279)and Gal-C (n 5 187) positive cells.

Fig. 2. Self-similarity of oligoden-drocytes exemplified with a Gal-Cpositive cell. The fractal dimensioncalculated on the whole cell (769 3870 pixels, corresponding to anoriginal size of 113 3 128 mm) isvery close to those calculated onsmaller parts of the cell (287 3 440pixels for an original size of 42 365 mm in A and 180 3 208 pixelsfor an original size of 26 3 31 mmin B).

442 Bernard et al.

rent, its density (calculated from the ratio of its maximumamplitude to the capacitance of the corresponding cell)was plotted against the fractal dimension of the cell. Theresults of this analysis are illustrated in Figure 6 and showthat current density decreased with progenitor differenti-ation, when developmental stages are defined by the fractaldimension of cells.

DISCUSSION

It has been well demonstrated that the magnitude of“D” is mainly weighted by two distinct characteristics ofcell morphology: the profuseness of branching and theruggedness of the border (Smith et al., 1996). The fractaldimension of cultured oligodendrocytes is mainly influ-

Fig. 4. Gal-C positive cell viewedunder fluorescent (A) and phasecontrast (B) optics. The fractal di-mensions calculated from both im-ages were almost identical: 1.662 inA and 1.667 in B.

Fig. 5. An oligodendrocyte progenitor, viewed under phase contrastoptics (A), was identified by its fractal dimension (1.063). The mem-brane capacitance of this cell was 7.4 pF and the sodium currentrecorded (C, lower trace) had a peak amplitude of 2430 pA corre-sponding to a current density of 58.1 pA/pF. In a more mature

pre-oligodendrocyte (B), identified by a fractal dimension of 1.279, asmaller sodium current with a peak at 277 pA was recorded (D, lowertrace). The capacitance of the cell shown in B was 19.8 pF, corre-sponding to a current density of 3.9 pA/pF. Upper traces in C and Dillustrated the voltage-step protocol used to reveal the sodium currents.

Fractal Dimension and Oligodendrocyte Differentiation 443

enced by their extent of process branching and thus, “D”has been shown to correlate with degrees of oligodendro-cyte maturation (Smith and Behar, 1994; Kreider et al.,1996). Our results are consistent with these previous stud-ies because we show that the fractal dimension of oligo-dendrocytes increases as cells grow and differentiate inculture (Fig. 3). It is well established that at early stages inculture, oligodendrocyte progenitors are immunopositivefor A2B5 antibody but not to other antibodies known tolabel immature or mature oligodendrocytes such as O4and anti Gal-C (Levi et al., 1987). Our results demonstratethat the fractal dimension can be used to identify theseprogenitors because immuno-positive cells for A2B5 ex-hibited a lower fractal dimension value. Furthermore, itshould be noted that the shape of a small, bipolar immaturecell recognized by A2B5 antibody is close to a line whenskeletonized and the actual lower limit of 1.053, we mea-sured for A2B51 cells, is also close to 1,000, which is thetheoretical fractal dimension of a line (Smith et al., 1996).

The timing of marker expression during oligoden-drocyte differentiation has been extensively studied. It isparticularly well established that A2B5 positive cells be-come O4 positive before expressing Gal-C (Levi et al.,1987). Once again, calculation of the fractal dimensionallows us to identify these A2B51, O41, Gal-C2 pro-oligodendrocytes because the minimal value of the fractaldimension calculated for O41 cells (1.233) is lower thanthe minimal value calculated for Gal-C1 cells (1.326).Levi et al. (1987) also reported that Gal-C1, O42 cellswere never observed, and that after becoming Gal-C1, thecells lose the surface antigen binding A2B5 antibody butkeep the antigen binding O4 antibody. As illustrated onFigure 3, the fractal dimension of cells immuno-stained bythese antibodies strongly reflects this timing of markerexpression.

An intermediate A2B51, Gal-C1 stage has beenidentified both in situ (Reynolds and Wilkin, 1988) and inprimary culture (Saneto and De Vellis, 1985; Levi et al.,

1987). This developmental stage was clearly identified onthe basis of the fractal dimension. These cells correspondto the population located between the lower value ofGal-C1 cells (Db 5 1.326) and the higher value of A2B51

cells (Db 5 1.468). This range established on the basis ofsingle staining experiments was well confirmed by thedouble staining results. Fractal dimensions of A2B51,Gal-C1 double-stained cells extended from 1.322–1.480,values that are very close to those calculated for singlestaining.

Our results demonstrate that the morphological dif-ferentiation of oligodendrocytes, as quantified by theirfractal dimension, well matches the timing of biochemicalmarker expression (gangliosides, sulfatides, galactocerebro-side).

Applying this immunological calibration, we identifyby their fractal dimension the developmental stages of cellsexpressing voltage-activated sodium current. This currentwas found in all cells characterized by a fractal dimensioncorresponding to A2B51, O42 progenitors and in 16 outof 53 cells characterized by a fractal dimension of earlyO41 pro-oligodendrocytes. These observations agree wellwith previous reports showing that a sodium current withsimilar characteristics was developmentally regulated byoligodendrocytes because it was recorded in all A2B5antigen-positive and in only a minority of O4 antigen-positive cells, but was no longer observed in differentiatedO1 and O10 antigen-positive oligodendrocytes (Sonthei-mer et al., 1989b; Barres et al., 1990, Borges et al., 1995).The sodium current-expressing cells characterized by afractal dimension smaller than 1.053 (that is the lower“Db” value found for A2B51 cells) probably corre-sponded to the population of vim1, PSA N-CAM1,A2B52 pre-progenitors well characterized by Grinspanand Franceschini (1995).

The decrease of sodium current density with advanc-ing differentiation stages, quantified by “Db”, described inthis study is very similar to the results of Glassmeier andJeserich (1995) for the expression of the same voltage-gated sodium current by trout oligodendrocytes. Thisfurther illustrates that fractal dimension is an efficientcriterion for assessing the developmental stages of un-stained cells in culture. A decrease of current density withmaturation of mice oligodendrocytes has also been re-ported for the proton-activated sodium channel (Sonthei-mer et al., 1989a).

A rapid characterization of the developmental stagesof living cells could be useful in studies on the effects ofgrowth factors on cell development. In the oligodendro-cyte lineage, two proliferative stages (A2B51, O42 andA2B51, O41, Gal-C2) have been identified on the basisof their mitogenic response to type-1 astrocytes, menin-geal cells and cerebellar interneuron conditioned media(Gard and Pfeiffer, 1990). These two populations areclearly distinguishable by their maximal value of fractaldimension: 1.233 for A2B51, O42 and 1.326 for A2B51,O41, Gal-C2 (Fig. 3).

Fig. 6. Sodium current densities in oligodendrocytes as a function offractal dimensions (mean 6 SEM, the number of recorded cells is givenfor each class).

444 Bernard et al.

The actual values of fractal dimensions reported inthe present study are relevant only for the culture condi-tions we used and must not be considered as a paradigm.The correlation between “D” values and the expression ofany given developmental marker must be made for anyother culture system because both can be modified byculture medium composition, tissue origin or cell adhe-sion characteristics (Szuchet, 1995).

ACKNOWLEDGMENTSWe acknowledge Drs. A. Deruyver and Y. Hode for

their contributions on the early stages of this work. Wealso thank Dr. J. Garwood, Cathy and Suzy for correctingthe article.

REFERENCESBarres BA, Koroshetz WJ, Swartz KJ, Chun LLY, Corey DP. 1990. Ion

channel expression by white matter glia: the O-2A glial progenitor cell.Neuron 4:507–524.

Borges K, Wolswijk G, Ohlemeyer C, Kettenmann H. 1995. Adult ratoptic nerve oligodendrocyte progenitor cells express a distinct repertoireof voltage- and ligand-gated ion channels. J Neurosci Res 40:591–605.

Boussouf A, Lambert RC, Gaillard S. 1997. Voltage-dependent Na1-HCO3

2 cotransporter and Na1/H Na1 exchanger are involved in in-tracellular pH regulation of cultured mature rat cerebellar oligodendro-cytes. Glia 19:74–84.

Curtis R, Cohen J, Fok-Seang J, Hanley MR, Gregson NA, Reynolds R,Wilkin GP. 1988. Development of macroglial cells in rat cerebellum. I.Use of antibodies to follow early in vivo development and migration ofoligodendrocytes. J Neurocytol 17:43–54.

Gaillard S, Bossu JL. 1995. Voltage-gated ionic currents in mature oligo-dendrocytes isolated from rat cerebellum. Neurosci Lett 190:191–194.

Gard AL, Pfeiffer SE. 1990. Two proliferative stages of the oligodendrocytelineage (A2B51O42 and O41GalC2) under different mitogenic control.Neuron 5:615–625.

Glassmeier G, Jeserich G. 1995. Changes in ion channel expression duringin vitro differentiation of trout oligodendrocyte precursor cells. Glia15:83–93.

Grinspan JB, Franceschini B. 1995. Platelet-derived growth factor is asurvival factor for PSA-NCAM1 oligodendrocyte pre-progenitor cells.J Neurosci Res 41:540–551.

Kettenmann H, Blankenfeld GV, Trotter J. 1991. Physiological propertiesof oligodendrocytes during development. Ann NY Acad Sci 633:64–77.

Kreider BQ, Morley M, Burns MM, Lavy LA, Pleasure D. 1996. Com-plexity analysis of oligodendroglial processes expressing myelin-associatedglycoprotein. J Neurosci Res 44:459–470.

Levi G, Aloisi F, Wilkin GP. 1987. Differentiation of cerebellar bipotentialglial precursors into oligodendrocytes in primary culture: developmentalprofile of surface antigens and mitotic activity. J Neurosci Res 18:407–417.

Levi G, Gallo V, Ciotti MT. 1986. Bipotential precursors of putativefibrous astrocytes and oligodendrocytes in rat cerebellar cultures expressdistinct surface features and “neuron-like” g-aminobutyric acid transport.Proc Natl Acad Sci USA 83:1504–1508.

Mandelbrot BB. 1983. The fractal geometry of nature. New-York: WHFreeman. p 468.

McKinnon RD, Smith C, Behar T, Smith T, Dubois-Dalcq M. 1993.Distinct effects of bFGF and PDGF on oligodendrocyte progenitor cells.Glia 7:245–254.

Raff MC, Miller RH, Noble M. 1983. A glial progenitor cell that developsin vitro into an astrocyte or an oligodendrocyte depending on culturemedium. Nature 303:390–396.

Reichenbach A, Siegel A, Senitz D, Smith TG Jr. 1992. A comparativefractal analysis of various mammalian astroglial cell types. Neuroimage1:69–77.

Reynolds R, Wilkin GP. 1988. Development of macroglial cells in ratcerebellum. II. An in situ immunohistochemical study of oligodendrogliallineage from precursor to mature myelinating cell. Development 102:409–425.

Saneto RP, De Vellis J. 1985. Characterization of cultured rat oligoden-drocytes proliferating in a serum-free, chemically defined medium. ProcNatl Acad Sci USA 82:3509–3513.

Smith TG Jr, Behar TN. 1994. Comparative fractal analysis of cultured gliaderived from optic nerve and brain demonstrate different rates of mor-phological differentiation. Brain Res 634:181–190.

Smith TG Jr, Behar TN, Lange GD, Marks WB, Sheriff WH Jr. 1991. Afractal analysis of cultured rat optic nerve glial growth and differentiation.Neuroscience 41:159–166.

Smith TG Jr, Lange GD, Marks WB. 1996. Fractal methods and results incellular morphology—dimensions, lacunarity and multifractals. J Neuro-sci Meth 69:123–136.

Smith TG Jr, Marks WB, Lange GD, Sheriff WH Jr, Neale EA. 1989. Afractal analysis of cell images. J Neurosci Meth 27:173–180.

Sommer I, Schachner M. 1981. Monoclonal antibodies (O1 to O4) tooligodendrocyte cell surfaces: an immunocytological study in the centralnervous system. Dev Biol 83:311–327.

Sontheimer H, Perouansky M, Hoppe D, Lux HD, Grantyn R, Ketten-mann H. 1989a. Glial cells of the oligodendrocyte lineage express proton-activated Na1 channels. J Neurosci Res 24:496–500.

Sontheimer H, Trotter J, Schachner M, Kettenmann H. 1989b. Channelexpression correlates with differentiation stage during the development ofoligodendrocytes from their precursor cells in culture. Neuron 2:1135–1145.

Spitzer NC. 1979. Ion channels in development. Ann Rev Neurosci2:363–397.

Szuchet S. 1995. The morphology and ultrastructure of oligodendrocytesand their functional implications. In: Kettenmann H, Ransom BR, edi-tors. New York: Oxford University Press. p 23–43.

Takeda T, Ishikawa A, Ohtomo K, Kobayashi Y, Matsuoka T. 1992.Fractal dimension of dendritic tree of cerebellar Purkinje cell during onto-and phylogenetic development. Neurosci Res 13:19–31.

Fractal Dimension and Oligodendrocyte Differentiation 445