Platelets, 2013: Fractal and Euclidean descriptors of platelet shape

http://informahealthcare.com/pltISSN: 0953-7104 (print), 1369-1635 (electronic)

Platelets, Early Online: 1–11! 2013 Informa UK Ltd. DOI: 10.3109/09537104.2013.842639

METHOD ARTICLE

Fractal and Euclidean descriptors of platelet shape

Max-Joseph Kraus1,2, Heiko Neeb2,3, & Erwin F. Strasser4

1Geiselgasteig Ambulance, Grunwald, Munich, Germany, 2Institute for Medical Engineering and Information Processing, University of Koblenz,

Koblenz, Germany, 3Koblenz University of Applied Sciences, Multimodal Imaging Physics Group, Koblenz, Germany, and 4Transfusion and

Haemostaseology Department, University Hospital of Erlangen, Erlangen, Germany

Abstract

Platelet shape change is a dynamic membrane surface process that exhibits remarkablemorphological heterogeneity. Once the outline of an irregular shape is identified andsegmented from a digital image, several mathematical descriptors can be applied to numericalcharacterize the irregularity of the shapes surface. 13072 platelet outlines (PLO) weresegmented automatically from 1928 microscopic images using a newly developed algorithmfor the software product Matlab R2012b. The fractal dimension (FD), circularity, eccentricity,area and perimeter of each PLO were determined. 972 PLO were randomly assigned forcomputer-assisted manual measurement of platelet diameter as well as number, width andlength of filopodia per platelet. FD can be used as a surrogate parameter for determining theroughness of the PLO and circularity can be used as a surrogate to estimate the number andlength of filopodia. The relationship between FD and perimeter of the PLO reveals the existenceof distinct groups of platelets with significant structural differences which may be caused byplatelet activation. This new method allows for the standardized continuous numericalclassification of platelet shape and its dynamic change, which is useful for the analysis ofaltered platelet activity (e.g. inflammatory diseases, contact activation, drug testing).

Keywords

Fractal analysis, geometry, PRP,quantification, shape change,standardization

History

Received 16 May 2013Revised 29 July 2013Accepted 5 September 2013Published online 4 November 2013

Introduction

The improvements in digital imaging and computer-basedanalysis, as well as advances in new mathematical methodssuch as fractal geometry [1], are enabling new approaches to thegeometrical description of platelet shape change (PSC).

Fractal analysis is being increasingly applied to a variety ofbiological questions [2–10], and has proven useful in the analysisof cellular and subcellular systems [6, 8, 10]. With the introduc-tion of fractal geometries in the early 1980s a new parameter, theso-called fractal dimension (FD), was defined. The FD essentiallymeasures the irregularity or roughness of a shape or surface. Losaet al. have shown that the pericellular membranes of peripheralblood mononuclear cells have an irregular membrane contourwith self-similar behavior, and that FD is a quantitative descriptorof the actual geometrical cell shape [6]. They note that thedetermination of the FD of cell outlines enables the attribution of‘‘numerical values to peculiar qualitative features of spatialstructures such as irregularity, morphologic complexity androughness, which can be used to characterize cells of differentorigins or in different functional and/or pathologic states’’[5].

This article describes an automated and thus standardizedapproach for the quantification of PSC. It is based on acombination of computer-based tools for image analysis andpattern recognition. In this study, images were acquired usingdark field light microscopy, which provides excellent contrast forthe recognition of platelet surface structures [11]. Outlines ofplatelets were automatically segmented from digital images

using a newly developed algorithm. Geometrical parameters ofplatelet shape were then prospectively evaluated; this includedthe determination of the FD, the calculation of shape descrip-tors such as circularity and eccentricity as well as the deter-mination of Euclidean measures such as platelet outline perimeterand area.

We provide detailed quantitative information on the geomet-rical features of platelets, describing for the first time therelationship between the perimeter, FD and circularity of plateletoutlines – useful parameters for the automated, standardized andreproducible description of PSC.

Methods

Sample preparation and image acquisition

In a first experiment, 5ml of platelet rich plasma (PRP) from sixanonymized samples of anticoagulated whole blood (3.2%buffered sodium-citrate 0.105 M) were prepared as describedpreviously [11, 12]. Microscopy was performed using a 100:1 oilimmersion objective (Leitz Wetzlar Germany, *160/0.17, PLFluotar, 100/1.32-0.60 Oil) and digital images of unstained andnon-fixed platelets were acquired using a Canon 600 D reflexcamera (Canon Inc., Tokyo, Japan) adapted through a digitalcamera adapter (MICROS Produktions & Handels GmbH,Austria) to the c-mount of a dark field light microscope. Imageacquisition was performed immediately after preparation. Thetable was moved in meandering loops from the lower left to theupper right edge of the microscope slide and an image was takenat each table position. Image acquisition took approximately15 min per slide.

Correspondence: Dr. Dr. Max-Joseph Kraus, Geiselgasteig Ambulance,Robert-Koch-Str. 9, 82031 Grunwald, Munich, Germany. Tel: +49 8964954228. Fax: +49 89 64963485. E-mail: mjk@praxis-geiselgasteig.de

For the platelet activation tests, blood samples were drawn atminimal stasis from the left antecubital vein of a healthy volunteerusing a butterfly device with a 21-gauge needle. Blood was drawndirectly into standard vacutainer siliconized glass tubes contain-ing 3.2% tri-natrium citrate 0.105 M (BD� Vacutainer No.367714, BD Medical, Heidelberg). The first sample was discardedto remove tissue fragments. Immediately after blood withdrawalthe samples were centrifuged at 160 g for 12 min at roomtemperature. The PRP was removed with a pipette (VitrexMedical, Herlev, Denmark) and 1 ml of PRP was placed into aclean 1.5 ml polypropylene vial (Eppendorf safe-lock tubes,Eppendorf AG, Hamburg) and immersed in a 37 �C water bath.Thirty minutes after PRP preparation, aliquots of 180ml PRP werepipetted into vials containing either 20 ml of 200mMol ADP or150mMol TRAP (Molab GmbH, Langenfeld, Germany) pre-warmed to 37 �C. The resulting concentration in the sample was20mMol ADP and 15 mMol TRAP. After gentle mixture thesamples were incubated for 10 min at 37 �C. After incubation200ml of prewarmed 0.4% HEPES-buffered formaldehyde (1 partformaldehyde 4%, Otto Fischar GmbH & Co. KG, Saarbrucken,Germany, in 9 parts HEPES buffer solution, 238 g/L, Sigma-Aldrich GmbH, Steinheim, Germany) was added to each sampleand after gently mixing the samples were incubated for anadditional 30 min at 37 �C.

From each of the two samples, five specimens were prepared.For specimen preparation, 5 ml of fixed ADP- or TRAP-preactivated PRP was pipetted onto a microscope slide andcarefully covered with a high precision coverslip (Precision coverglass No. 1.5H, 22� 22 mm, 170� 5mm thickness, PaulMarienfeld GmbH & Co. KG, Lauda-Konigshofen, Germany).Platelets were allowed to settle to the microscope slide for120 min before microscopic examination. For image acquisitionthe microscope table was moved in meandering loops from thelower left to the upper right side of the specimen. One image wastaken every 5 s for 250 s. Accordingly, 250 images were takeneach for ADP- and TRAP-activated platelet specimen.

For timelapse imaging, 5ml of unfixed PRP was pipetted ontoa microscope slide. The specimen was carefully covered with acoverslip and microscopy was started immediately. Focus was setto the middle of the specimen and the table remained fixed in thesame position during the entire procedure. One picture was takenfrom the same region of the slide every 5 seconds for 43 m35 s (i.e. 500 images in total). Focus was manually adjustedduring the procedure.

Image analysis

For further computational analysis, platelet-like structures have tobe identified on the digital image. Accordingly, images must besegmented into regions containing relevant foreground pixels.Image segmentation was performed using a newly developedalgorithm for the automated detection of platelet outlines ondigital images [13]. A fully automated process chain (Figure 1)was implemented using Matlab R2012b (MathWorks Inc.,Natwick, USA) [14]. Technical details on the image segmentationprocess are provided in the supplementary material.

In the first experiment, 6476 image segments were segmentedautomatically from 928 digital pictures. For platelet activationtests 3916 platelet outlines were segmented automatically from atotal of 500 images. For timelapse imaging analysis, sixindividual platelets were controlled for 43m35s. A total of 2680platelet outlines were segmented from 500 images.

Each image segment represents the outline of an individualplatelet or aggregate of platelets and is called a platelet outline(PLO). A randomized sample of PLOs from the first experimentwas prepared for additional manual measurement. Therefore, a

number between 0 and 1 was randomly sampled from a uniformdistribution for each segment. If the number was �0.15, thesegment was chosen, resulting in 15% selection probability.In total, 972 segments were chosen from the total pool ofsegments (15.1%). For manual measurements the segmentedarea of the original image was displayed centered on a400� 400 pixel image scaled to 10 pixels per mm.Furthermore, images were loaded in a combined stack, showingthe segment of the original image on the left and thecorresponding outline on the right (Figure 2). The accuracyand conformance of the automatically detected outline to theouter membrane of the corresponding platelet were graded from1 (‘‘excellent’’) to 6 (‘‘very poor’’).

Fully automated measurements (FAM)

For each PLO, the following shape parameters were determinedusing Matlab R2012b (Figure 3).Perimeter (P): The length of the outline in mm.Area (A): The region enclosed by the outline in mm2.Fractal dimension: FD was used as a measure for the roughness ofplatelet surfaces, i.e. the spatial heterogeneity of their outline.Classically, FD is strictly defined only for self-similar objects thatexhibit the same structure at different length scales. Differentapproaches to measure FD exist. Here, the box-counting methodwas applied, which works as follows: (1) The 400� 400 pixelimage containing the outline of a single segmented platelet wasdivided into disjunct rectangular boxes with an edge length of rk

(2) the number Nk of boxes that contain a surface element of theplatelet was determined. The approach was then repeated 400times for different length scales, starting at r1 ¼ 1 pixel andstopping at r400 ¼ 400 pixel, i.e. a single box covering the wholeimage. For perfectly self-similar objects, the scatter plot of log rk

versus log Nk is is a straight line. In this case, the FD is givenby the negative slope of the corresponding line. However, as it isnot evident a priori that platelet surfaces are really self-similar,the first 5 and the last 3 points were omitted from the fit of thedata (Figure 4). The curve indeed exhibited a nonlinear trend inthat regime, which is characteristic for non-perfect fractalbehavior.Circularity (C): The circularity measures the ‘‘roundness’’ of anobject by relating the measured area, A, to the area of a circlewhich has the same perimeter, P, as the segmented platelet,C ¼ 4�A

Eccentricity ("): This parameter measures the eccentricity of anellipse that has the same second-moments along its major axis asthe outline of the platelet segment. Here, the eccentricity of anellipse measures the ratio of the distance between its two foci andthe major axis length. Larger values therefore represent morecigar-shaped objects, whereas an eccentricity of zero is observedfor circular objects.MajorAxisL: The length (in mm) of the major axis of the ellipsethat has the same normalized second central moments as theregion.MinorAxisL: The length (in mm) of the minor axis of the ellipsethat has the same normalized second central moments as theregion.

Computer-assisted manual measurements

The following parameters were manually determined (Figure 3)by visual inspection of the individual image segments, employingthe image annotation features of ImageJ software (NIH ImageJ,Version 1.42-l) as described in [11, 12]:Diameter (d): the largest diameter of the platelet in mm.Number of filopodia per platelet: the number Nðf Þ of filopodiaper platelet.

2 M.-J. Kraus et al. Platelets, Early Online: 1–11

Length of filopodia: The length yi in mm of any protrusionextending from the platelet’s outer membrane, measured from theedge of the membrane to the end of the filopodium. The index iruns over all Nðf Þ filopodia identified for each platelet.The resulting parameter is the average filopodia length perplatelet �y ¼

Pyi=Nðf Þ

Width of filopodia base: The width in mm of the filopodium at thebase of the membrane protrusion, ai was determined for eachfilopodium. The resulting parameter is the average width of thefilopodia base per platelet a¼

Pai=Nðf Þ

Width of filopodia apex: The width in mm of the membraneprotrusion at the most distant part of the filopodium, ei wasdetermined. The resulting parameter is the average width of thefilopodia apex per platelet e¼

Pei=Nðf Þ.

Statistical analysis

First, all variables were tested for normal distribution using theKolmogorov–Smirnov test. All tested variables exhibited a non-normal distribution (p50.05). Thus, a non-parametric test fornon-normally distributed samples was used. For two independentsamples, we used the Mann–Whitney U-test, and for three or moregroups, we used the Kruskal–Wallis test. The correlation betweentwo variables was calculated with Spearman Rho (�). Thecategorized data, by contrast, were evaluated by means of chisquare tests, for which all requirements were fulfilled. For alltests, differences were considered significant when p values were

less than 0.05 (p50.05), and highly significant when p valueswere less than 0.001 (p50.001). The continuous variables werepresented as means and medians, while standard deviations andquartiles were chosen as a measure of dispersion. Statisticalanalysis was performed using SPSS Statistics 20.0 (IBM Corp.,Armonk, NY).

Results

The first experiment was performed to evaluate the basicprinciples of the new measurement approach. The scatter diagramof FD vs. perimeter (Figure 5) revealed the existence of threeclearly distinct groups of data. This phenomenon was reprodu-cible and seen in all of the analyzed specimens. A group IDbetween 1 and 3 was assigned to each segment based on itslocation in the scatter diagram. Distributions and median valuesfor almost all measured parameters differed significantly betweenthe three groups (Table I, Figures 6 and 7). Figure 6 shows thesuperimposition of all platelet outlines (PLO) differentiated bygroup. One can see that group 1 (G1) consists of smaller, rounderand more homogeneous platelets, whereas group 2 (G2) containslarger and more heterogeneous platelets with longer filopodia.By contrast, Group 3 (G3) is made up of very large platelets oraggregates of platelets with high outer membrane heterogeneity.The image segments belonging to each of the groups werecarefully analyzed by inspecting the associated digital images.We observed that G1 contained mostly floating, not yet adherent

Figure 1. Schematic representation of the basic workflow for a fully automated platelet segmentation. Starting from a digitized RGB color image (I1),the image is first transferred into a grey scale image (I2) by combining information from different channels. The corresponding image is then de-noisedand corrected for the background bias field, which is estimated as shown in the shaded area in the bottom of the figure (I3). Image I3 is binarized (I4)and connected components are determined (I5). Small and large connected components are removed from the image (I6) and the border of theremaining segments is determined (I7). Using the border information, the segments are shrunken to be less sensitive to the image resolution dependentsmearing off the objects (I8). Finally, segments that are located at the border of the image are removed, resulting in the final segmented image. Thebias field estimation works iteratively and is based on the filtered original gray scale image (I3). In the first iteration, the full image I3 is considered torepresent the bias field. From I3, all pixels with grey value larger than a given threshold, which is based on the maximum grey value in that image, areset to zero (B1). B1 is then smoothed by a local median filter (B2) and pixels with zero grey value are filled with the average grey value of the image(B3). The whole procedure is repeated Niter times to result in the final estimation of the smoothly varying bias field.

DOI: 10.3109/09537104.2013.842639 Fractal and Euclidean geometry of platelet shape 3

platelets, whereas G2 was dominated by platelets alreadyspreading on the microscope slide and G3 contained mostlyaggregates of platelets.

There was a significant negative correlation (�¼�0.644,p50.001) between circularity and the number of filopodia perplatelet. Circularity was highly significant different for plateletswith (C¼ 0.688� 0.230) and without (C¼ 0.991� 0.211) filo-podia, as well as for platelets with different number of filopodiaper platelet (Figure 7). FD was only slightly correlated to thenumber of filopodia per platelet (�¼ 0.139, p50.001). Figure 8shows platelet outlines with identical values for area(A¼ 34.34 mm2), perimeter (P¼ 23.38mm) and circularity

(C¼ 0.79), but different values for FD (FD 1.21 vs. 1.47). Thisillustrates that the value of FD is influenced by irregularities inthe outline structure that are not directly evident to the human eye.To better visualize different values of FD, platelet outlines withidentical perimeter and area values but different FD values weresuperimposed. Figure 9 illustrates that FD is indeed a propermeasure for the irregularity of the platelet outline.

During manual measurements the accuracy and conformanceof the platelet outline was assessed. In 89.88% of cases, theaccuracy and conformance of the automatically detected outlineto the outer membrane of the corresponding platelet was graded‘‘good’’ or ‘‘excellent.’’ Automated and manual measurementsshowed a significant correlation for parameters that measure

Figure 2. Original pictures of platelets (left) and their automaticallydetected outlines (right) as an example for the accuracy of automatedoutline detection. Mathematical descriptors of the outlines are given foreach platelet in the upper left edge. The inner circle of the coordinateplane has a radius of 2.5mm, the outer circle has a radius of 5mm.

Figure 4. Scatter plot of the edge length of disjunct rectangular boxescompletely covering the entire image logrk vs. the number of boxescontaining a surface element of the platelet logNk for a randomly selectedplatelet outline (continuous curve). Results from a linear fit of thecorresponding data, after removing the first 5 and the last 3 points,are also illustrated (dashed curve). The fractal dimension of the outline isthen given by the negative slope of the dashed curve.

Figure 3. Images of shape changed platelets from the same specimen atthe same time point after preparation (Dark field light microscopy,Objective: PL Fluotar 100/1.32–0.60 OIL; Leitz, Wetzlar, Germany).Original: the image as taken. CAM: computer-assisted manual measure-ments. The measured regions of interest are shown. FAM: fullyautomated measurements. Outlines have been detected fully automatedusing a newly developed algorithmic approach for Matlab R2012b.

Figure 5. Scatter diagrams for perimeter vs. fractal dimension of platelet outlines for three different experiments. Left above: 6476 outlines fromnon-fixed platelets activated through contact to glass. Left below: 2680 outlines from six individual platelets followed over 43 min. Right: 3916platelets fixed after 10 min preactivation with 15 mmol TRAP or 20mmol ADP. While the individual parameters are distributed continuously, therelationship between perimeter vs. fractal dimension reveals the existence of at least four clearly distinct groups of data. Group was assignedautomatically to each segment based on its location in the scatter diagram. The corresponding platelets exhibit significant structural differences(see Tables I, III and Figure 6). G0 consists of small and round platelets, G1 contains larger platelets forming some relatively short and thin filopodia,G2 is made up of large platelets forming longer and broader pseudopodia and G3 consists of aggregates of platelets or very large platelets. For plateletspreactivated with TRAP there is a significant shift toward G2 and G3 as compared to platelets preactivated with the weaker agonist ADP. However, alsothe outlines of single platelets during timelapse imaging are classified into the same groups. Only the scatter plots that contained the fractal dimensionas one parameter showed clustering into distinct groups.

Table I. Fully automated (FAM) and computer-assisted manual (CAM) measurements of platelet shape.

All Group1 Group 2 Group3 p(G1-G2) p(G1-G3) p(G2-G3)

FAMN(FAM) 6.476 (100.0%) 3.739 (57.7%) 2.511 (38.8%) 226 (3.5%)A (mm2) 24.98 (15.50–42.36) 16.78 (12.97–22.64) 45.10 (33.88–60.82) 131.13 (99.82–147.85) 50.001 50.001 50.001

35.10� 32.19 18.59� 7.00 49.74� 22.54 145.66� 64.37P (mm) 20.65 (15.71–28.05) 16.36 (13.90–19.22) 29.09 (25.07–35.33) 63.44 (54.29–80.13) 50.001 50.001 50.001

24.18� 13.26 16.73� 3.64 31.16� 8.35 69.95� 22.17FD 1.296 (1.244–1.362) 1.331 (1.276–1.393) 1.257 (1.218–1.302) 1.245 (1.211–1.290) 50.001 50.001 0.002

1.306� 0.079 1.337� 0.075 1.264� 0.061 1.250� 0.059C 0.770 (0.573–0.973) 0.875 (0.684–1.031) 0.661 (0.491–0.850) 0.395 (0.295–0518) 50.001 50.001 50.001

0.770� .262 0.857� .237 0.672� .242 0.411� 0.173" 0.69 (0.57–0.81) 0.65 (0.52–0.76) 0.75 (0.63–0.85) 0.87 (0.57–0.81) 50.001 50.001 50.001

0.67� 0.17 0.64� 0.16 0.72� 0.16 0.82� 0.13

CAMN(CAM) 972 (100%) 561 (57.7%) 383 (39.4%) 28 (2.9%)N(F) 1.50� 0.05 1.07� 0.44 1.96� 0.09 3.75� 0.64 50.001 50.001 0.004�y (mm) 1.37 (1.03–1.89) 1.16 (0.88–1.59) 1.66 (1.22–2.23) 1.71 (1.48–2.81) 50.001 50.001 0.233

1.53� 0.73 1.26� 0.50 1.82� 0.82 2.03� 0.83a (mm) 0.77 (0.60–0.97) 0.72 (0.58–0.90) 0.81 (0.66–1.04) 0.92 (0.77–0.99) 50.001 0.008 0.563

0.81� 0.30 0.75� 0.25 0.88� 0.33 0.87� 0.21e (mm) 0.41 (0.33–0.50) 0.38 (0.30–0.48) 0.43 (0.35–0.53) 0.43 (0.38–0.54) 50.001 0.013 0.495

0.44� 0.18 0.41� 0.18 0.47� 0.19 0.48� 0.16d (mm) 5.07 (3.90–6.83) 4.09 (3.45–4.89) 7.04 (5.95–8.45) 12.95 (12.18–15.64) 50.001 50.001 50.001

5.78� 2.87 4.25� 1.07 7.38� 2.22 14.59� 6.20

Distributions and median values for almost all measured parameters differed significantly between the three groups assigned based on the location inthe P-FD scatter diagram (Figure 5).

similar aspects of platelet shape. The parameter most similar tothe manual measured largest diameter of platelets is MajorAxisL(Figure 10). It is correlated with diameter by �¼ 0.908(p50.001).

In a second experiment platelets were preactivated either withADP or TRAP. The values for all automatically distinguishedparameters were significantly different (Table II). The outlines ofTRAP platelets were larger and less rounded and had a reducedmembrane roughness compared to the ADP platelet outlines.Again, the scatter diagram of perimeter vs. FD showed theexistence of clearly distinct subgroups of data. As in the firstexperiment, the algorithm for platelet segmentation was set toexclude all elements with an area5 10 mm2, and platelets with adiameter less than 3.5mm were not segmented. Therefore, thisparameter was now corrected to an area 5 5mm2. This changeexplains the appearance of a new group of platelet outlines withsmall perimeter values and high FD values on the left side of thescatter diagram (Figure 5). In the following discussion, this newgroup is called group 0 (G0). G0 consists of small and roundplatelet outlines with high circularity values (C¼ 1.298� 0.262)

and small values for eccentricity ("¼ 0.574� 0.179), area(A¼ 7.01� 1.46 mm2) and perimeter (P¼ 8.32� 1.11 mm). Thediameter can be estimated as D¼P/�¼ 2.65� 0.35 mm.G0 platelets presumably form the group of least activatedplatelets. Again, the values of almost all measured parameterswere different between the four groups with a high level ofsignificance (Table III).

In the P-FD scatter diagram the platelet outlines of the ADPand TRAP activated platelets could be subdivided into the exactsame four groups. However, the numerical distribution of theoutlines between groups was significantly different (Figure 11).Therefore, after activation with either agonist, similar morpho-logical platelet shapes were found. However, in the case of TRAPplatelets we observed larger platelets and the formation of moreand longer filopodia (G2) as well as the increased formation ofaggregates (G3) when compared to ADP. It is remarkable thatdespite activation with both agonists, most of the platelet outlinesare found in G1, a group that consists of rather small plateletswith few morphological signs of activation.

For timelapse imaging, the same central region of themicroscope slide was continuously kept in focus for 43 min. Sixindividual platelets (Figure 12) were observed from their attach-ment to the slide to the subsequent change of their outlinemorphology [15]. At the beginning, two platelets (No. 4 and No.6) had already attached to the glass of the microscope slide andshow no more lateral movement. 2m50s after coverslipping, athird platelet (No. 3) attached to the slide. Attachment of theremaining platelets was observed at 3m55s (No. 2), 6m15s (No. 1)and at 7m00s (No. 5). While platelets No. 1, 2, 3 and 5 began

Figure 7. There is a significant (p50.001, **) negative correlationbetween the circularity of the platelet outline and the number and length(not shown) of filopodia per platelet. Once the outline of the platelet issegmented successfully from the digital image, circularity can be used asan easy to calculate surrogate parameter for the numerical description offilopodia number and length per platelet.

Figure 8. Original image (left), segment (middle) and outline (right) oftwo platelets with identical values for area, perimeter, circularity andeccentricity but different values for fractal dimension (above: FD 1.47,below: FD 1.21). This illustrates that the value of fractal dimension isinfluenced by tiny irregularities in the platelet outline not directly evidentto the human eye.

Figure 6. The outlines of all segments corresponding to the groupsdefined in the P-FD scatter diagram (Figure 5, left above) weresuperimposed into a single image. This illustrates the significantstructural differences between the three groups. Only scatter diagramsthat contained the fractal dimension as one parameter showed subdivisioninto three different groups. Left: Group 1, n¼ 3739. Middle: Group 2,n¼ 2511. Right: Group 3, n¼ 226.

Figure 9. The superimposition of 10 platelet outlines for platelets withidentical values for perimeter and area, but different values for fractaldimension (left: FD 1.10, middle: FD 1.25, right: FD 1.40). Thisillustrates that FD is indeed a suitable measure for the irregularity of theplatelet outline.

forming several pseudopodia within seconds after attachment tothe slide, platelet No. 4 did not develop relevant pseudopodiaduring the entire observation period. Platelet outline No. 6represented a small aggregate of two platelets, as a second plateletattached at 3m55s in the same region of the image and clearlycame in contact to the primary attached platelet. Despite the factthat only single platelets and one single small aggregate (No. 6)were examined, the P-FD scatter diagram once again revealedthe separation of the platelet outlines into distinct subgroups(Figure 5). As no larger aggregates formed on the slide, there wereno observations for G3.

Figure 13 demonstrates how the values of area and circularitychanged for platelet No. 1 during the observation period. It shouldbe noted that the group ID was assigned automatically and wasonly determined based on the values for the platelet outline in theP-FD scatter diagram. In Figure 13A, a small and round platelet(G0) attaches to the slide. Immediately after attachment severalsmall filopodia form (G1, Figure 13B). Moving forward in time,two larger pseudopodia begin to spread out. At this time point(14m55s after preparation) the outline of this platelet is now T

.01�

Figure 10. The parameter most similar to the manually measured largestdiameter d of the platelets is the automatically determined MajorAxisL,i.e. the major axis of an ellipse that has the same normalized secondcentral moments as the respective platelet outline. This illustrates that theparameters automatically determined in the current work are highlycorrelated with the corresponding manual measurements.

Table II. Automated detected platelet outlines from 250 images each forplatelets either preactivated for 10 min with 20mmol ADP or 15mmolTRAP.

ADP TRAP p (ADP-TRAP)

N(Images) 250 250N(PLO) 2066 1850A (mm2) 13.01 (8.34–21.42) 15.15 (9.12–27.25) 50.001

18.08� 17.09 23.83� 27.22P (mm) 12.53 (9.47–17.20) 13.60 (10.13–20.00) 50.001

14.65� 7.88 17.22� 12.08FD 1.304 (1.242–1.405) 1.292 (1.240–1.381) 50.001

1.331� 0.109 1.317� 0.103C 1.102 (0.848–1.290) 1.065 (0.784–1.254) 50.001

1.068� 0.325 1.026� 0.330" 0.644 (0.500–0.789) 0.666 (0.515–0.804) 0.003

0.634� 0.188 0.651� 0.186

Platelets preactivated with TRAP had significantly higher values for area,perimeter and eccentricity, and lower values for circularity and fractaldimension than platelets preactivated with ADP.

categorized under G2 (Figure 13C). At the end of the observationperiod, the larger pseudopodia retract and the group assignmentreverts to G1 (Figure 13D). Similar behavior was observed in allfour platelets that formed filopodia. However, one platelet (No. 4)did not show filopodia formation during the entire observationperiod, but instead a more homogeneous spreading of thehyalomer on the slide. Accordingly, there was no change ingroup assignment during the observation period for this platelet,and it remained in G1 the entire time (Figure 14).

Discussion

This prospectively designed pilot study presents results obtainedusing a new method for the mathematical description andstatistical analysis of the geometrical features of blood platelets.Microscopic images of fixed and unfixed, non-stained plateletsfrom PRP were examined. Platelet outlines were detected througha newly developed pattern analysis approach. The automaticallydetermined platelet shape parameters were highly correlated with

the corresponding manual measurements (Figure 10). As well, thevisual inspection of the detected outlines confirmed a highconsistency with the visually observed outer membranes of theplatelet (Figure 2). Both observations show that the automatedapproach works efficiently and that the parameters derived can beused for the assessment of the geometrical structure of platelets.This represents an important step forward, as it enables theanalysis of large numbers of platelets. Studies relying on large-scale platelet measurement are not otherwise feasible, due to thetime consuming task of manual measurement.

The scatter diagram for perimeter vs. FD of platelet outlinesshowed the clear clustering of platelets into distinct groups(Figure 5). The clustering in the P-FD scatter diagram into similargroups was observed when examining individual platelets duringtimelapse imaging as well as when examining thousandsof platelets after activation. However, it should be noted thatonly the scatter plots that contained the FD as one parametershowed clustering into distinct groups. This corroborates theobservations of LOSA et al. [6] and MASHIAH et al. [8], whoexamined the FDs of pericellular membranes in leukemic andlymphoblastic cells. Both authors report significantly differentFD ranges for different biochemical and structurally definedsubgroups of lymphocytes.

A more detailed evaluation of the groups identified by theP-FD scatter diagram revealed highly significant differences foralmost all of the measured parameters (Tables I and III). Thisimplies that structurally different groups of platelets can beidentified based on the relationship between perimeter and FD.We identified a group 0 (G0) consisting of small and roundedplatelets that did not form filopodia. We suspect that theseplatelets represent the least activated platelets. However, accord-ing to their high values for circularity and relatively low values foreccentricity, these platelets were no longer discoid, but hadalready undergone disc-to-sphere transformation. By contrast,group 1 (G1) consisted of already slightly enlarged platelets thathad formed some short filopodia. According to the morphologicalclassification proposed by ROSENSTEIN [15] and ALLEN [16],this group corresponds to the early spheroidal stage (stage 2).Group 2 (G2) contained large and more heterogeneous plateletswith long and broad filopodia. This group included the plateletsthat had undergone the greatest shape change, and corresponded

Figure 11. Shows the numerical distribution of platelet outlines between the four groups defined in the P-FD scatter diagram (Figure 5, right) fromplatelets either activated with TRAP or ADP. For platelets activated with the stronger agonist TRAP, significantly more platelet outlines are found inthe P-FD scatter groups 2 and 3. These groups represent platelets with stronger signs of activation, i.e. the formation of larger and broader filopodia(G2) or the formation of aggregates (G3).

Figure 12. One image out of a series of 500 images taken from the sameregion of the microscope slide. Six individual platelets were followedfrom their attachment to the slide to subsequent change in their outlinemorphology. The outlines of the platelets were detected automaticallyusing a newly developed algorithm for Matlab. The entire image seriescan be downloaded as a timelapse video from informahealthcare.com/plt.Please see description following the Reference section.

Figure 13. Shows change in area (above) and circularity (below) for a single platelet (Platelet 1 in Figure 12) during the first 2500 s (43m35s) afterpreparation. One image was taken every 5 s and the outline of the same platelet was segmented from each image. Each point in the scatter diagramshows the area and circularity of the automatically segmented platelet outline at a given time point. Platelets were automatically assigned to a groupbased on their position in the P-FD scatter diagram (Figure 5, left below). The segmented outlines of this platelet at four time points are shown on theright. The outer circle of the coordinate plane has a diameter of 5 mm. At time point A the platelet attaches as a small and round platelet to the slide(Group G0). It has a small area and a high value for circularity. Immediately after attachment, the formation of several relatively short and thin filopodiabegins (B, Group G1). The circularity of the outline decreases dramatically and the area increases. At point C two larger pseudopodia begin to spreadout. The group assignment changes to G2. At point D, the larger pseudopodia are retracted for approximately 5 min and the group changes back to G1.

to ROSENSTEIN’s and ALLEN’s late pseudopodial stage. Thethird group (G3) consisted of platelet aggregates and very largeplatelets. Whereas the difference between aggregates and singleplatelets with respect to perimeter and FD was obvious, thesubdivision of platelets into distinct groups (G0, G1 and G2)requires further exploration. This subdivision could potentiallybe related to the different mechanisms of platelet activationdescribed by HARTWIG, who reports on ‘‘drastically differentmechanisms of cytoskeleton reorganization’’ mediated by dif-ferent cell signaling pathways with a view to the formation ofthin filopodia during platelet activation and the formation ofbroad and large lamellopodia during platelet spreading [17]. It isremarkable that FD was so strongly associated with differentactivation states, despite FD not being directly correlated to thenumber, length or width of filopodia. Accordingly, plateletsurface structure and roughness seem to play a crucial role inplatelet function.

Platelets preactivated with TRAP had significantly highervalues for area, perimeter and eccentricity, and lower valuesfor circularity and FD than platelets preactivated with ADP(Table II). This confirms that the applied method is suitable fordetecting platelets at different stages of activation. In the P-FDscatter diagram, we observed a significant shift toward G2 and G3for platelets preactivated with TRAP as compared to plateletspreactivated with the weaker agonist ADP. This means that forTRAP, more platelets showed morphological signs of consider-able shape change and that more aggregates were formed incomparison to ADP preactivated platelets. Hence, all four groupswere observed in ADP as well as in TRAP-activated platelets,the majority of platelets were found in G1, a group that showsonly slight morphological signs of platelet activation. As plateletswere fixed with formaldehyde prior to preparation in thisexperiment, these observations should not have been influencedby platelet activation on glass, and should reflect the activationstatus caused solely by the different agonists.

The image sequence acquired during timelapse imagingfurther illustrates the meaning of the observed grouping in the

P-FD scatter diagram. The continuing shape change witnessed inthe six individual unfixed platelets after attachment to the glassof the microscope slide was documented and analyzed asdescribed in detail above. The group ID automatically assignedduring the segmentation and analysis process was directlyassociated to the morphological changes in the platelet outline.While small and round platelets were assigned to G0, plateletsdeveloping small and short filopodia were assigned to G1. Afterformation of large and broad pseudopodia, the platelets areclassified under G2. Platelet outline No. 6 highlights a limitationin our method, as it was a small aggregate of two platelets.Currently, we have no means to automatically distinguishbetween the outline of a single large platelet and the outlineof a small aggregate of platelets.

Timelapse imaging also illustrated that circularity is directlycorrelated to the number of filopodia per platelet (Figure 13,below). With the increasing formation of filopodia, there is asignificant decline in the value of circularity. Circularity variedat a high level of significance in relation to the number offilopodia per platelet. This is a crucial insight, as circularity is ameasure that can be easily calculated once the platelets aresegmented and identified on digital images. By contrast, theaccurate automated detection of filopodia is much morecomplicated and requires more complicated algorithmic meth-ods. However, as can be seen in Figure 7, there is also aconsiderable overlap in interquartile ranges for circularity inrelation to the number of filopodia per platelet. Accordingly,current means make it impossible to directly predict the exactnumber of filopodia per platelet based on circularity alone. Theexact prediction of filopodia number would require a morecomplicated approach that takes multiple measures like circu-larity, eccentricity and FD into account.

To summarize, by measuring FD, circularity and eccentricity,we have shown that platelets with the same area, the sameperimeter or the same diameter can exhibit highly heterogeneousoutline structures. Indeed, platelet outline structure is the mostimportant parameter in the qualitative morphological classifica-tion of PSC [15, 16]. We quantitatively described the differencesin number, length and width of filopodia per platelet. We showedthat platelets in different functional states exhibited significantdifferences in our automatically measured parameters.Additionally, we documented and numerically evaluated theprocess of filopodia formation after attachment to the microscopeslide. We showed that FD can be used as a surrogate parameter forthe determination of the roughness of the platelet outline.Furthermore, we introduced circularity as a simple means ofestimating the length and number of filopodia per platelet.Finally, we showed that the relation between FD vs. perimeter isassociated with distinct subgroups of platelets in vitro, whichallows the classification of a platelet population into groups withdifferent morphological states.

We hypothesize that with this method for the sensitivequantitative analysis of platelet shape, potential differences inplatelet shape and the dynamics of its change can now benumerical evaluated in different physiological and pathophysio-logical conditions. This will improve our understanding of therole of platelets in the development of illness that is accompaniedby increased platelet activity, such as inflammatory diseases.The precise quantitative evaluation of platelet shape is of interestin the evaluation of platelet-active drugs and in plateletcytoskeleton, as well as in materials research. Future investiga-tions should seek to precisely evaluate the influence of agonistsand antagonists about platelet surface interaction with a focus onthe newly described descriptors of platelet shape to explore therelationships between platelet shape and its physiological andpathophysiological conditions.

Figure 14. Shows change in area for a single platelet (Platelet 4 inFigure 12) over the first 2500 s (43m35s) after preparation. One imagewas taken every 5 s and the outline of the same platelet was segmentedfrom each image. Each point in the scatter diagram shows the area of theautomated segmented platelet outline at a given time point. The plateletwas automatically assigned to a group according to the values in the P-FDscatter diagram (Figure 5, left below). This platelet does not showrelevant filopodia formation during the entire observation period. Incontrast to the platelet diagrammed in Figure 13, there is no relevantchange in the group assignment.

Acknowledgements

The authors would like to thank Tanja Kottmann for valuable assistancewith the statistical analysis. Additional thanks goes to Lucais Sewell forrevising the article.

Declaration of interest

The authors report no conflicts of interest. The authors alone areresponsible for the content and writing of this article.

References

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2. Havlin S, Buldyrev SV, Goldberger AL, Mantegna RN, OssadnikSM, Peng CK, Simons M, Stanley HE. Fractals in biology andmedicine. Chaos Solitons Fractals 1995;6:171–201.

3. Goldberger AL, West BJ. Fractals in physiology and medicine. YaleJ Biol Med 1987;60:421–435.

4. Losa GA. The fractal geometry of life. Rivista di Biologia 2009;102:29–59.

5. Losa GA. Fractal morphometry of cell complexity. Rivista diBiologia 2002;95:239–258.

6. Losa GA, Baumann G, Nonnenmacher TF. Fractaldimension of pericellular membranes in human lymphocytesand lymphoblastic leukemia cells. Pathol, Res Pract 1992;188:680–686.

7. Martin-Garin B, Lathuiliere B, Verrecchia E, Geister J. Use offractal dimensions to quantify coral shape. Coral Reefs 2007;26:541–550.

8. Mashiah A, Wolach O, Sandbank J, Uziel O, Raanani P, Lahav M.Lymphoma and leukemia cells possess fractal dimensions that

correlate with their biological features. Acta Haematol 2008;119:142–150.

9. Chakrabarty RK, Moosmuller H, Garro MA, Arnott WP, Walker J,Susott RA, Babbitt RE, Wold CE, Lincoln EN, Hao WM. Emissionsfrom the laboratory combustion of wildland fuels: Particle morph-ology and size. J Geophys Res 2006;111:D07204:1–16.

10. Wang X, Becker FF, Gascoyne PR. The fractal dimension of cellmembrane correlates with its capacitance: A new fractal single-shellmodel. Chaos 2010;20:043133:1–7.

11. Kraus MJ, Strasser EF, Eckstein R. A new method for measuring thedynamic shape change of platelets. Transfus Med Hemother 2010;37:306–310.

12. Kraus MJ; Kraus, Max-Joseph, Dr. med., 82031 (DE), assignee.Messung der Dynamik der Anderungen von Blutplattchen. PatentDE102009059274.2011.

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14. Neeb H, Kraus MJ. 2013 Grunwald Remagen Opensource UnifiedPlatelet-Identification Tracker (GROUP-IT). Available from: http://platelets.praxis-geiselgasteig.de/group_it.zip.

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Supplementary material available online

1). This video shows six individual human blood platelets from their attachment to the microscope slide to subsequent change in their outlinemorphology for 43 minutes. The outlines of the platelets were detected automatically using a newly developed algorithm for Matlab. Figures 5, 13 and14 show details for the mathematical descriptors derived from the detected outlines. 5ml of unfixed PRP was pipetted onto a microscope slide.The specimen was carefully covered with a coverslip and microscopy (Dark field light microscopy, Objective: PL Fluotar 100/1.32–0.60 OIL;Leitz, Wetzlar, Germany) was started immediately. Focus was set to the middle of the specimen and the table remained fixed in the same positionduring the entire procedure. One picture was taken from the same region of the slide every 5 seconds for 43m35s (500 images). Focus was manuallyadjusted during the procedure. The video displays at 7 frames per second. Original images are shown on the left, an overlay of the detected outlines isshown on the right.

2). Technical details on the image segmentation process.

Platelets, 2013: Fractal and Euclidean descriptors of platelet shape

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