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journa l homepage: www. int l .e lsev ierhea l th .com/ journa ls /cmpb

ethods toward in vivo measurement of zebrafish epithelialnd deep cell proliferation

atteo Campanaa,∗, Benoit Mauryb, Marie Dutreixc,adine Peyriérasb, Alessandro Sartia

Department of Electronics, Computer Sciences and Systems (DEIS), Bologna University, Bologna, ItalyCNRS-DEPSN, Institut de Neurobiologie Alfred Fessard, Gif sur Yvette, FranceTranslational Department, Hospital Institut Curie, Orsay, France

r t i c l e i n f o

rticle history:

eceived 4 June 2009

eceived in revised form

3 July 2009

ccepted 24 August 2009

eywords:

a b s t r a c t

We present a strategy for automatic classification and density estimation of epithelial

enveloping layer (EVL) and deep layer (DEL) cells, throughout zebrafish early embryonic

stages. Automatic cells classification provides the bases to measure the variability of rel-

evant parameters, such as cells density, in different classes of cells and is finalized to the

estimation of effectiveness and selectivity of anticancer drug in vivo. We aim at approach-

ing these measurements through epithelial/deep cells classification, epithelial area and

thickness measurement, and density estimation from scattered points. Our procedure is

utomatic cell classification

ell density

ell proliferation

iomedical image processing

based on Minimal Surfaces, Otsu clustering, Delaunay Triangulation, and Within-R cloud of

points density estimation approaches. In this paper, we investigated whether the distance

between nuclei and epithelial surface is sufficient to discriminate epithelial cells from deep

cells. Comparisons of different density estimators, experimental results, and extensively

accuracy measurements are included.

early embryonic stages. The method provides solutions to

. Introduction

echnological advances in imaging have made it feasible tocquire nondestructive in vivo images of fluorescently labeledtructures, such as cell nuclei and membranes, throughoutarly zebrafish [1] embryogenesis. Until now, these strategiesave primarily been used to discover and understand the keyegulators of embryogenesis. However, many have recognizedhat zebrafish might also provide opportunities to acceleratehe process of drug discovery [2]. In vivo image-based investi-ation provides measurements for a large number of cellular

eatures and events including nuclei movements, cells count-ng, membrane and nucleus shape changes, thereby enablinghe estimation of more significant parameters such as prolif-

∗ Corresponding author. Tel.: +39 0 547 339203; fax: +39 0 547 339208.E-mail address: m.campana@unibo.it (M. Campana).

169-2607/$ – see front matter © 2009 Elsevier Ireland Ltd. All rights resoi:10.1016/j.cmpb.2009.08.008

© 2009 Elsevier Ireland Ltd. All rights reserved.

eration rate, highly relevant for investigating anticancer drugeffects in vivo. Because of the manual nature of image analy-sis, however, these strategies suffer from low-throughput, andthus in the past have been restricted to late stage of drugdiscovery. Therefore, image processing and analysis in thisresearch area remains challenging and new automatic algo-rithms are needed to measure biological features from largetime-lapse biological dataset.

In this paper, we present an automatic algorithm to esti-mate the variation of cellular density in epithelial envelopinglayer (EVL) and deep layer (DEL) (Fig. 1) throughout zebrafish

measure features of these two classes of cells and works upontime varying three-dimensional (3D) images and clouds ofpoints, respectively depicting the embryo structures acquired

erved.

s i n

104 c o m p u t e r m e t h o d s a n d p r o g r a m

by multiphoton laser microscopy (MLSM) [3] and nuclearcenters detected by automatic image processing procedures[4]. We aim at approaching these measurements through (I)embryo outer surface reconstruction, (II) nucleus-to-surfacedistance based clustering, (III) deep cells points-based den-sity estimation, and (IV) epithelial layer thickness and densitymeasurement.

The paper is organized as follows. We start with a briefmotivation for this work. We follow with a short review ofrelated works and a discussion about the contribution of thispaper. In Section 4 we first present the data used to testthe proposed algorithms, briefly introducing the strategiesadopted for images acquisition and nuclei center detection.We follow with a description of the techniques adopted toachieve epithelial/deep cells classification and to estimate epithe-lial and deep cells density. Section 5 shows the results achievedprocessing high resolution time-lapse images of zebrafish.Section 6 presents the procedure that we designed to validateand measure the accuracy of the method. Conclusions anddirections for future work are given in Section 7.

2. Motivation

By cells classification and density estimation we expect tobe able to measure the variability of some relevant param-eters, such as proliferation rate, in different classes of cellsand between different individuals of the same species. Theseapproaches are finalized to in vivo investigation of anticancerdrug effects and measurement of the individual response totreatments. The strategy is based on the idea that embryogen-esis and cancerogenesis, under certain aspect such as the highproliferation rate of the cells, are two similar processes [5].

To decrease or block the proliferation of cancer cells, todayare available many treatments; the effectiveness of these anti-neoplastic agent is often enough to achieve tumor cell kill butoften they cause toxicity to normal tissues. The measure ofthe proliferation rate in different classes of cells (such as deepand epithelial cells) and different classes of embryo (untreatedand anticancer drug treated) is a relevant parameter for esti-

mating the effectiveness and toxicity of the treatments. Weaim at approaching these measurements through the estima-tion of EVL and DEL cell densities throughout zebrafish earlyembryonic stages.

Fig. 1 – Illustrations of the embryo from two differentpoints of view. (a) Epithelial enveloping layer (EVL) cells. (b)Deep layer (DEL) cells. EVL and DEL layers constitute theblastoderm. (c) Yolk syncytial nuclei. (d) Yolk.

b i o m e d i c i n e 9 8 ( 2 0 1 0 ) 103–117

During the blastula period changes occur in the EVL [6].At the end of the cleavage period there are more EVL cellsthan deep cells, but with successive divisions the EVL cellsbecome vastly outnumbered. The EVL flattens, its cells thin-ning and stretching markedly to form an epithelial monolayer(Fig. 1). By the blastula period, deep cells divide more rapidlythan EVL cells [7]. Moreover, EVL cell division cycles are lesssynchronous than deep cell cycles. Thus, we expect that if ananticancer drug is able to distinguish between cancer cell andnormal cells, it will in vivo differentially affect the behaviorof highly proliferative DEL cells and EVL cells characterized bylow proliferation rate. Furthermore, a measurement of the DELand EVL cells density variation provides an indirect estimationof the proliferation rate of those classes of cells, due to the factthat cellular volume decreases when cells undergo in division.

3. Background and contribution

Scientific work related to our approach can be divided into sev-eral categories. We first point out some previous approachesfor cells recognition and classification. Long et al. [8] discussed analgorithm suitable for automatic determination of cell identi-ties in a Caenorhabiditis elegans body that integrates both theabsolute and relative spatial location of cells. It uses a marker-guided, spatially constrained, two-stage bipartite matching tofind the optimal match between cells in a subject 3D confocalimage and cells in 15 template images. A classification of whiteblood cells using only their nucleus information was proposedby Theera-Umpon and Dhompongsa [9]. They investigatedwhether information about the nucleus alone is adequateto classify white blood cells in bone marrow. They proposedan algorithm based on Bayes classifiers and artificial neuralnetworks, enabling automatic classification upon single-cellimages.

Density computation is another field related to our work.Estimating the density of points in a cloud of points is a classicaltask in spatial statistics. Basic examples are the number oftrees per unit area in a forest [10] the number of galaxies perunit volume in a portion of the universe [11] or the number ofcells in the slice of an organic tissue [12].

Reconstruction of surfaces from unstructured points is alsorelated to this paper; this is a well studied problem and itscomplexity has spawned many approaches on how to gen-erate surfaces upon clouds of points with sufficient level ofcorrectness. As resumed and proposed by Papaleo [13] theexisting techniques can be grouped in two distinct classes.First, computational geometric based approaches take intoaccount the structure of the object to reconstruct and they arebased on concepts such as Voronoi Diagrams, Delaunay Tri-angulation, and Medial Axis. A second group is constituted byvolumetric based methods that build the surface by analyzingthe volume it is captured in. The representation may be a 3Dgrid of values representing the distance to the surface or it maybe a mathematical representation of the distance function.

Cell segmentation of 2D and 3D images has been covered

in a number of previous works [14–20]. Sarti et al. [17] pro-cessed confocal microscopy images to extract the shape ofnuclei. In this paper, they use partial-differential-equationbased filtering and segmentation as a preprocessing and

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c o m p u t e r m e t h o d s a n d p r o g r a m s

ost-processing strategy for computer-aided cytology. In aecent work Padfield et al. [18] describe a set of methodsesigned to automatically segment nuclei in 2D time-lapse

mages. The methods, based on level set segmentation, haveeen used to effectively extract the nuclear tracks and gen-rate a schematic representation of cell cycle phases. Anlternative strategy to identifying cell trajectories and studyhe variation of cell shape has been recently proposed by

ang et al. [19]. The algorithm performs cell segmentationnd tracking using texture-adaptative snakes and has beenested on both normal and autophagy cell image sequences.

All the developed algorithms have proved to be very use-ul for nuclei segmentation, however the reconstruction ofhe whole cell using membrane protein markers is almostn unexplored area. Ortiz et al. [20] presented a segmenta-ion algorithm based on gradient-curvature driven flow, whichs suitable for whole cell segmentation. They measured theobustness against noise and resistance to surface disconti-uities on synthetic images and demonstrated the suitabilityf the method on real cell images.

Other image processing techniques linked to our workave been summarized by Peng [21] including segmenta-ion, 3D time-varying dataset analysis, and application suchs high-throughput and high-content screening of cellularhenotypes for drug discovery. However, to the best of ournowledge no one proposed an algorithm to automaticallystimate cellular density variation in EVL and DEL embryoayers.

The main contributions of this work are: (I) to propose aethod to automatically recognize epithelial and deep cells

rom 3D images depicting zebrafish early embryonic stages,II) to estimate the variation in time of the cellular density inVL and DEL layers, (III) to measure the variation of the EVLhickness, (IV) to provide results achieved from real biologicalataset depicting untreated zebrafish embryogenesis, and (V)o propose a procedure to effectively test the accuracy of EVLells detection algorithm upon real and synthetic embryo data.

. Materials and methods

n this section, we present the detail of the methods designedo automatically measure features of EVL and DEL embryo lay-

ig. 2 – Images of the zebrafish embryo. (a) Blastoderm andolk acquired with optical microscope. Red square depictshe portion of embryo acquired by MLSM. (b and c)

embranes and nuclei image slices acquired by MLSM. (Fornterpretation of the references to color in this figure legend,he reader is referred to the web version of the article.)

i o m e d i c i n e 9 8 ( 2 0 1 0 ) 103–117 105

ers. We start with a brief introduction of the data (zebrafish 3Dimages and nuclei position) used to test the proposed meth-ods. Then we follow with a description of the approaches usedto recognize epithelial and deep cells and to measure cel-lular density in EVL and DEL layers. The methodologies weintroduce here are related to one single time step of the timedependent dataset; however, as we will present in Section 5,the algorithm can be applied to a temporal series of data inorder to estimate the variation of the features.

4.1. Image acquisition and nuclei detection

High resolution time-lapse microscopy imaging of livingorganisms is best achieved by MLSM [3]. It allows imagingthe zebrafish embryo [1] suitably engineered with distinctfluorescent proteins to highlight structure such as nuclei ormembranes throughout early embryonic stages.

Optical sections of the organism (Fig. 2) are achieved bydetecting the fluorescent radiation coming from the laserexcited focal plane. The 3D spatial sampling of the embryois achieved by changing the focal plane depth. Each acquiredvolume is defined on a grid composed by 512 voxels in x, y,directions and 164 in z; spatial resolution is 1.51 �m and tem-poral resolution is about 125 s. The acquisition of 3D imageshas been repeated throughout the early embryonic develop-ment, from 32 cells stage for 6 h [6].

The automated detection of the cells enclosed in each vol-ume is achieved first filtering the image using a so-called“geodesic mean curvature flow” (GMCF) which has beenproved to be the method that best preserves the edges simul-taneously smoothing and reducing the noise, when processingthese particular volumetric dataset [22,23,17]. Cells detectionhas been performed using an automatic nuclear centre detec-tion algorithm, called “flux-based level set centre detection”(FBLSCD) [4], based on partial-differential equations (PDE) andon a nonlinear multiscale strategy. This automatic procedureworks upon the 3D images of zebrafish nuclei and it providesclouds of points depicting the position of center of nucleifor each time step of the zebrafish time-varying dataset. Toreach that goal the algorithm uses the nuclei images as aninitial condition of a nonlinear advection-diffusion partial-differential equation which shrinks the image objects duringthe time evolution. As time is evolving it detects the posi-tions of local maxima of solution which give us the numberand positions of approximate nuclei centres. In order toprevent false negative events (due to the low intensity of somenuclei) an higher threshold is selected and consequentially anhigher number of cells is achieved. In next step, we remove thesuperfluous centres segmenting the cells by subjective surfacemethod [24,25] and removing multiple centres detected in onesingle segmented nucleus. The algorithm accuracy has beentested and measured on synthetic computer-generated andreal 2D and 3D images as presented in [4]. False positives innuclear detection were kept below 0.5%.

4.2. Epithelial and deep cells classification

The epithelial and deep cells classification procedure (Fig. 3)is based on the measurements of the distance between thenuclei and the outer embryo surface. This feature is analyzed

s i n b i o m e d i c i n e 9 8 ( 2 0 1 0 ) 103–117

Fig. 4 – (a) 2D illustration of the edge indicator g. (b) 3Drepresentation of the initial hypersurface S. (c) Slices ofmembranes image IM and of segmented outer embryoprofile SO in red. (d) 3D representation of the segmentedouter embryo surface SO. (For interpretation of thereferences to color in this figure legend, the reader is

106 c o m p u t e r m e t h o d s a n d p r o g r a m

by two distinct clustering algorithms in order to recognizeepithelial and deep nuclei. Indeed, EVL layer and deep cellslayers are located at distinct depth respect to the embryo pro-file. Thus, analyzing the distribution of the distance betweeneach nucleus and the surface, we expect to observe clusters ofcells at different distances, corresponding to the layers depth.An automatic detection of the two first clusters will allow todetermine the distance that discriminates epithelial and deepcells. The input data of this procedure are the 3D membranesimages and the set of points depicting the nuclei position. Nextparagraphs present the steps that constitute the classificationprocess (Fig. 3).

4.2.1. Embryo outer surface reconstructionThe first step of the EVL and DEL cells classification is thereconstruction of the embryo outer profile. Consider the3D image IM : (x, y, z) → IM(x, y, z) as a real positive functiondefined in some domain M ⊂ R3 and depicting the membranesstaining and thus also the embryo outer surface.

In our procedure IM is segmented by the Minimal Surfacestechnique [26,27]. As a first step of the segmentation processan initial function ˚0 is constructed in the image domain M:

˚0(x, y, z) = 1, on M \ ∂M

−1, on ∂M, ∀z > zMin(1)

where ∂M is the boundary of M, M \ ∂M is the relative com-plement of ∂M in M (M \ ∂M = {x ∈ M|x /∈ ∂M}), and zMin is theminimum value of the coordinate z (normally z = 0). Let usdefine ˚ = ˚(x, y, z, t) an evolution of ˚0, where t representsa synthetic time known in the literature as scale parameter.We point out that ˚(x, y, z, 0) = ˚0. The graph of ˚ representsa 3D manifold S = (x, y, z, ˚). The Minimal Surfaces techniqueallows to segment the objects evolving ˚ through a flow thatdepends from the characteristics of the hypersurface S andfrom the local characteristics of the image IM. The motionequation which drives the hypersurface evolution is the fol-lowing:

{˚t = gK|∇˚| + ∇g · ∇˚

K = ∇ ·( ∇˚

)(2)

˚(x, y, z, 0) = ˚0(x, y, z); |∇˚|

where the edge indicator g, defined in the domain M, is asmooth nonincreasing function of IM depicting its local struc-

Fig. 3 – Flowchart depicting the sequence of steps weundertook for EVL and DEL cells classification.

referred to the web version of the article.)

tures. In our scenario, g is defined as

g(x, y, z) ={ 1

1 + |∇G� (x, y, z) ∗ IM(x, y, z)|2 ∀z > zMin

0 z = zMin

(3)

where G� is a Gaussian kernel with standard deviation � and ∗denotes the convolution. The minima of g denote the positionof edges (Fig. 4a) and its gradient is a force field used to drivethe segmentation toward the structures boundaries.

The initial function ˚0 and the edge indicator g assumeparticular values (˚0 = 1 and g = 0) in the bottom part of theembryo (z = zMin) as illustrated in Fig. 4a and b. This ensurethat the segmented surface will reach the outer profile of theembryo, including both blastoderm and yolk (in case it hasbeen acquired), and assuming a flat shape in the regions ofcoordinate z = zMin that fall outside the embryo (Fig. 4c and d).

4.2.2. Distance based clustering algorithmsThe classification of the EVL and DEL cells is achieved ana-lyzing the distance between the nuclei and the segmentedembryo surface by automatic clustering algorithms.In orderto explain how the nucleus-to-surface distance is achieved,consider the discrete case where the final segmented outersurface SO is represented by a 3D binary image that consistsof a set of elements of a 3-grid. A value from the set {0, 1} isassigned to each i-element (voxel) of the binary image eO,i ∈ SO;Elements of value 1 correspond to the outer embryo surface(zero level set of the evolved hypersurface) and voxels equalto 0 represent the so-called “background”. Now consider theoutcome of the automatic nuclear centre detection as a cloudof points C that consists of a set of points pi ∈ C depictingthe position of nuclei centers. In order to clarify the math-ematical notation, we point out that symbol p (lower-case)always denotes a point, C (upper-case) denotes a set of points,e (lower-case) denotes a voxel, and S (upper-case) denotes a 3D

image. The nuclei-to-surface distance (Fig. 5a) is defined as theassignment to each point pi ∈ C of the euclidean distance dpi

between pi and position (represented in physical coordinates)

c o m p u t e r m e t h o d s a n d p r o g r a m s i n b

Fig. 5 – Illustrations of the outer embryo profile SO

superimposed with green spheres depicting the centers ofnuclei C. (a) 2D representation that illustrates thenucleus-to-surface distance dpi

of a generic point pi. (b) 3Drepresentation of SO and C. (For interpretation of therr

o

d

dbtpcD

D

tt

Fu

eferences to color in this figure legend, the reader iseferred to the web version of the article.)

f the closest voxel eO,i ∈ SO equal to zero (eZ,i):

pi= |pi − eZ,i|, ∀pi ∈ C (4)

Due to the fact that physical coordinates of the voxel areefined by real numbers (achieved multiplying the voxel indexy the the spatial resolution), the term |pi − eZ,i| representshe euclidean distance (non-negative real numbers). The com-utation of this distance over the entire set of points thatonstitute C (Fig. 5b), allows building the distance distribution(d):

(d) =∑

1, ∀i : dp = d (5)

i

i

hat is the number of points pi located at distance d respect tohe outer surface.

ig. 6 – Flowchart depicting the sequence of steps wendertook for deep and epithelial cell density estimation.

i o m e d i c i n e 9 8 ( 2 0 1 0 ) 103–117 107

If we consider a version of this distribution, with a reducedrange of the distance values from 0 to N (N correspondingapproximately to the depth of the second DEL layer) we expectto obtain a distribution characterized by two peaks; the firstclosed to a distance value d = 0 corresponding to the epithelialcells, and another cluster at a greater distance value, whichcorrespond to the distance between the nuclei of first layerof DEL and the outer surface. Thus, if we are able to identifyand separate these two clusters using the distance feature,we would obtain the distance T that discriminates epithelialnuclei centers CE and deep centers CD:

pi ∈ CE ∀pi : dpi≤ T (6)

pi ∈ CD ∀pi : dpi> T (7)

C = CE ∪ CD (8)

This separation procedure is basically a thresholding prob-lem and can be solved with the Otsu [28] clustering algorithms.The Otsu method obtains the threshold so as to try to makeeach cluster as tight as possible, thus minimizing their over-lap. Obviously, we cannot change the distributions, but wecan adjust where we separate the clusters (thresholding). Aswe adjust the threshold one way, we increase the spread ofone and decrease the spread of the other. The goal then is toselect the distance T that minimizes the combined spread. Wecan define the within-class variance as the weighted sum of thevariances of each cluster:

�2Within(T) = nB(T)�2

B(T) + nA(T)�2A(T) (9)

where

nB(T) =T−1∑d=0

D(d) (10)

nA(T) =N−1∑d=T

D(d) (11)

and �2A(T), �2

B(T) are respectively the variances of the pointsbelow and above the threshold, and [0, N − 1] is the range ofthe distance distribution. So, for each potential threshold Tthe within-class variance is updated; the optimal threshold isthe one that minimizes �2

Within(T).

4.3. Epithelial and deep cell density estimation

The structures of DEL and EVL layers are very different; asintroduced in the previous sections EVL and deep cells layersare located at distinct depth respect to the embryo surface.Moreover, the EVL flattens during the blastula period, its cellsthinning and stretching markedly to form an epithelial mono-layer (Fig. 1). On contrary, the deep cells constitute a multilayercloud of points that mostly cover the blastoderm volume.

Thus, different approaches (Fig. 6) have been used to computethe cellular density of these two classes of cells.

To estimate the DEL density we applied two distinct cloudsof points based density approaches (Fig. 7) to deep cells CD.

108 c o m p u t e r m e t h o d s a n d p r o g r a m s i n

Fig. 7 – Points-based methods to estimate the density of acloud of points. (a) Within-R based approach. (b) k-Nearest

neighbors method; k equal to 3.

With this methods we are able to compute the density withoutthe need to estimate the volume of the DEL.

Due to the fact that EVL is a monolayer cloud of pointsand its thickness changes throughout the embryo develop-ment, we decided to estimate explicitly the EVL density asthe ratio of the total number of epithelial cells and the EVLvolume. To achieve this, we first extract the epithelial sur-face area and we estimate the epithelial thickness over thissurface. Thus, with this technique we are able to achieve esti-mation of EVL density either per unit area and per unit volume(Fig. 6).

4.3.1. Deep cell points-based density estimationEstimating the density of points in a cloud of points is aproblem that can be solved by different approaches. Themost straightforward estimate of the density is obtained fromthe count of the number of points in a sampling windowthat cover a specific volume. We applied this approach uponthe set of deep cell centers (CD) in order to estimate theDEL density (DD). For each deep center pi ∈ CD we count thenumber of center located within a fixed distance r respectto the center pi (Fig. 7a). The deep cells density based onWithin-R based approach, DDr , is then computed as the ratioof the mean of this counting process, nr, and the volume ofthe sphere with radius r:

DDr = nr

(4/3)�r3(12)

where

nr =

∑i

∑j

w

nD∀i : pi ∈ CD, ∀j : pj ∈ CD (13)

w ={

1 if |pi − pj| ≤ r

0 if |pi − pj| > r(14)

and nD is the number of deep cells.Many alternative approaches have been proposed to esti-

mate the density upon cloud of points. A general class of

methods for estimating density is constituted of distance-based methods. The idea is to measure distances, either froma random location to the k-nearest point or from a pointto its k-nearest neighbors. The distribution of the points

b i o m e d i c i n e 9 8 ( 2 0 1 0 ) 103–117

is directly related to the intensity thus it is possible toderive the density from the distance measurements. Thesemethodologies have been applied in animal population biol-ogy to estimate the density of animals [29] and in forestry[10].

In this paper, we also provide estimation of DEL densityderived by a distance-based method. First, we measure themean distance, dk, from each point pi ∈ CD to its k-nearest neigh-bor pi,j ∈ CKi

(Fig. 7b). Then we derived the DEL density (DDk)

from the k-nearest mean distance as a function inverselyproportional to the power of three of the mean distance:

DDk= 1

dk3

(15)

where

dk =

∑i

⎛⎝∑

j

|pi − pi,j|

⎞⎠ /(k)

nD∀i, j : pi ∈ CD, pi,j ∈ CKi

(16)

Indeed, the distance measured, intuitively corresponds tothe size on of the largest bounding box that contains onlyone point. Thus, we can estimate the volume of this box asthe power of three of the mean distance the mean distancedk. The major drawback of distance based methods is thatthe distribution of distances, and consequently of the densityestimator, depends on the spatial pattern of points; this cannegatively affect the correctness of the measures.

In Section 5 we present a comparison of the accuracy of thetwo methods here described; we finally selected the Within-Rbased approach because it seems to best approximate the DELcells density.

4.3.2. Epithelial cell density estimationThe embryo outer surface SO and the EVL nuclei centers CE

allow us to compute the epithelial surface area, AE. First, wegenerate the epithelial surface SE (Fig. 8) as a binary image thatconsists of a set of elements eE,i ∈ SE; elements of value 1 depictthe epithelial surface. The idea is to create this surface startingfrom SO setting the voxels that are located far away than theepithelial cells as background elements. This is achieved iter-ating over the elements eO,i ∈ SO and measuring the euclideandistance between them physical coordinates and the nearestepithelial center pNi

∈ CE. If this distance is greater than a dis-tance value ε then the corresponding voxel is set to 0, and 1otherwise

eE,i = 1 ∀i : eO,i = 1, |eO,i − pNi| < ε (17)

As previously discussed in (4) the term |eO,i − pNi| repre-

sents the euclidean distance. Due to the fact that CE centersprogressively get close each others, we automatically com-puted ε as a function of the mean distance, �̄, between allthe epithelial centers. From experimental results we observed

that good accuracy is achieved setting ε as two times the meandistance �̄.

The epithelial surface area AE is then computed countingthe number of elements eE,i ∈ SE equal to 1 and multiplying the

c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 9 8 ( 2 0 1 0 ) 103–117 109

Fig. 8 – Illustrations of the epithelial surface (SE) in yellow,superimposed with embryo outer surface (SO) in red, andwith yellow spheres depicting the epithelial centers CE. (a)2D representation of SE and SO. (b) 3D representation of SE,SO, and CE. (For interpretation of the references to color into

ve

D

w

aetlep

tt

pwb“TacDoootp

is

Fig. 9 – (a) Epithelial centers depicted in yellow, deepcenters white, and EVL/DEL frontier points in blue. (b)Distance ti between SE (yellow) and SF (blue) surface. (c) 3Dillustration of SE and SF. (For interpretation of the referencesto color in this figure legend, the reader is referred to the

his figure legend, the reader is referred to the web versionf the article.)

alue by the voxel area AVoxel. The area AE allows achieving thepithelial density per unit area DEs :

Es = nE

AE(18)

here nE is the number of epithelial centers.A good estimate of the EVL cell density should take into

ccount also the variation of EVL thickness throughout thembryo development. To achieve such a goal, we reconstructhe surface SF depicting the frontier between the EVL and DELayers (Fig. 9c). The surface is obtained combining the detectedpithelial and deep centers. First, for each epithelial center

i ∈ CE, we generate a point pFilocated in the middle of pi and

he nearest deep center pNi∈ CD (Fig. 9a). The idea is to generate

he surface SF from the set of points pFi∈ CF.

Surface reconstruction from point clouds is a well studiedroblem and its complexity has spawned many approachesith good level of accuracy. The methods available today cane grouped, as proposed by Papaleo [13], in two main classes:Computational Geometric” and “Volumetric” approaches.he first class is constituted by algorithms that take intoccount the structure of the object to reconstruct and based onomputational geometric concept such as Voronoi Diagrams,elaunay Triangulation or Medial Axis. The volumetric meth-ds provide a representation depicting the distance to surfacer a mathematical representation of the distance function. Forur purpose we used the well-know 3D Delaunay Triangula-ions [30–32] that allows us to build the surface SF from the

oints CF.

The EVL thickness (Fig. 9b) in correspondence of the-element of the epithelial surface SE is then estimated mea-uring the euclidean distance between the position of the

web version of the article.)

i-element and the position of the nearest element eN,i of thesurface SF:

ti = |eE,i − eN,i| ∀i : eE,i ∈ SE, eE,i = 1 (19)

This allows us to compute the EVL volume VE and the EVLdensity per unit volume DE:

DE = nE

VE(20)

where

VE =∑

i

(ti · Avoxel) ∀i : eE,i ∈ SE, eE,i = 1 (21)

5. Results

We applied our method to 168 volumetric images and setsof points depicting respectively zebrafish blastoderm andnuclei centers, throughout early embryonic development from32 cells stage for 6 h. In this section we separately presentthe results achieved for EVL/ DEL cells classification anddensity computation. Performances comparisons of the dif-ferent methods discussed in the previous section are alsoincluded.

5.1. Results for epithelial and deep cells classification

The embryo outer surface SO has been automatically recon-structed for each time step of the zebrafish dataset. The

nucleus-to-surface distance measurement allowed us toachieve the distance distribution D(d) depicting the variationof EVL and DEL nuclei spatial organization throughout theembryogenesis. In Fig. 10 we illustrate the distribution D(d)

110 c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 9 8 ( 2 0 1 0 ) 103–117

Fig. 10 – Nucleus-to-surface distance distribution, D(d),obtained at time step 115 (3.2 h of development after the64/128 cells transition) and illustrated with two different

Fig. 11 – Number of EVL cells, nE, and DEL cells, nD

transition the DEs seems to decreases. This happens becauseat that stage epithelial cells thinning and stretching markedly.A good estimation of epithelia cells should take into accountalso the changes that occur in the EVL regions. For this rea-

distance scales. The line in the valley of figure (b) depict thethreshold T (6.80 �m) achieved by Otsu method.

of the nuclei at 3.2 h of development (time step 115) after the64/128 cells transition. The distribution is constituted of twoevident clusters of cells, the first closed to the outer embryosurface (2 �m) and the second at a greater distance. These twogroups of cells correspond respectively to epithelial layer andfirst level of DEL cells. Analyzing the distributions achievedat different stages of the embryo development, we observedthat clusters clearly appear after 1 h about post-64/128 cellstransition.

To automatically detect the clusters we applied the Otsuclustering method, providing the distance T (Fig. 10) that dis-criminates epithelial nuclei centers CE and deep centers CD.Fig. 11 depicts the growing of EVL and DEL cell populationsover the time and, as expected, the graph shows that DELcells become vastly outnumbered than EVL cells during theobserved embryo stages.

5.2. Results for epithelial and deep cell density

Deep cells density (DD) has been estimated upon the sets ofdeep cells points CD applying two approaches: k-nearest neigh-bors and Within-R based algorithms. Table 1 shows resultsobtained with these methods. The performances have been

analyzed on six time steps of the time varying dataset, cor-responding to different embryonic stages. For each time wefirst manually segmented the region covered by the nucleideep cells. This provided an exact estimation of the volume

identified by the Otsu method in each time step.

and, thus, also of the DEL density (see “Reference Density”in Table 1). We then computed separately the densities by k-nearest neighbors and Within-R, with different parameters inorder to find the ones that provide results that best match withthe exact density. For the Within-R algorithm we observed thatgood results can be achieved using a radius equal to 40 �m;for the k-nearest neighbors method we selected a number ofneighbors k equal to 6.

We here provide percent error measurements of the densityachieved by the two methods on the six analyzed time steps(Table 1). Results demonstrate that Within-R approach providesa density estimation much closer to the exact one than thedensity accomplished by k-nearest algorithm. Thus, deep cellsdensity has been measured in each time step by the Within-Rapproach and results are presented in Fig. 12. Due to the factthat cellular volume decreases when cells undergo in division,cells density rapidly increases throughout the embryo develop,as clearly illustrated in the graph.

In Fig. 13 we show the growing over the time of EVL sur-face density DEs (density per unit area) achieved estimatingthe epithelial surface area AE. At 3.5 h about post-64/128 cells

Fig. 12 – Growing of the deep cells density, DD, over thetime. The density has been achieved by the Within-Rapproach setting a radius r equal to 40 �m.

c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 9 8 ( 2 0 1 0 ) 103–117 111

Fig. 13 – Growing of the EVL density per unit area, DEs , overthe embryo develop time.

Fd

stiDtfpiEocvtv

Fig. 15 – Illustrations of epithelial surfaces SE at threedifferent stages of the embryo development. (a–c)Representations of SE respectively at 1.94, 3.4, and 4.9 hpost-64/128 cells transition. (d) Color mapping of thethickness. (For interpretation of the references to color in

ig. 14 – Thinning of the EVL layer throughout the embryoevelopment.

on, we automatically measured the thickness of this layerhroughout the embryo development by the method presentedn the previous section; the EVL thinning is depicted in Fig. 14.uring the first stages of development analyzed, results seem

o be spread. Indeed, epithelial cells are not clearly separatedrom the deep cells throughout early embryonic phases. At 1 host-64/128 cells transition, EVL thickness is about 20 �m and

t thinning becomes evident; at 5 h from 64/128 mitosis theVL depth is about 6.5 �m. In Fig. 15 we provide illustrationsf epithelial surfaces at three different embryo stages, with a

olor mapping that allows depicting the spatial and temporalariation of EVL thickness. The epithelial thickness allowed uso measure the variation in time of EVL cells density per unitolume (DE) depicted in Fig. 16.

Table 1 – Within-R and k-nearest methods accuracy comparison

Time step Reference density(cells/ �m3) ×10−6

Within-R density(cells/ �m3) ×10−6

64 50.02 50.0084 88.74 86.47104 122.41 122.40124 157.77 160.50144 187.38 186.40164 218.32 217.80

Error mean (%) – –

this figure legend, the reader is referred to the web versionof the article.)

6. Method accuracy

6.1. Validation

The matching between the identified cells and the imagesacquired by laser microscopy can be evaluated through thesuperimposition of the detected epithelial nuclei and themembranes images in a 3D volume rendering representation(Fig. 17) or visualizing a cutting plane of the embryo volumetricdata. Interactive tools [33,34] have been used to generate rep-resentations of the 3D biological images superimposed withthe outcome of our method. Six time steps (64, 84, 104, 124,

144, and 164) of the time varying dataset, corresponding to dif-ferent embryonic stages (1.46, 2.08, 2.78, 3.47, 4.17, and 4.86 hpost-64/128 transition) have been analyzed and mistakes,such as false positive (FP) and false negative (FN) detections,

.

k-Nearest density(cells/ �m3) ×10−6

Within-Rpercent error

k-Nearestpercent error

41.00 0.05 18.0476.90 2.56 13.34

112.40 0.01 8.18156.40 1.73 0.87197.60 0.52 5.45246.70 0.24 13.00

– 0.85 9.81

112 c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 9 8 ( 2 0 1 0 ) 103–117

Fig. 18 – Synthetic computer-generated embryo outersurfaces. (a) Low spatial resolution achieved with voxel size

Fig. 16 – EVL cells density per unit volume (DE).

have been recognized. Earlier stages of embryo developmenthave not been analyzed due to the fact that on that periodEVL structure is not completely formed, thus epithelial cellsrecognition would be difficult to achieve also by a visualinspection.

The error rate of the binary classification is depicted inTable 2. The total error rate is about 1.2%, more than 98% ofthe cells detected in the six time steps were correctly classi-fied (EVL or DEL class) and for less than 1% of cells we were notable to say which class they belong to (cells classified as NotSure). Analyzing the error rate of the classification process foreach time step it is possible to observe that mistakes mostlyoccur at earlier embryo stages. Indeed, the maximum errorrate appears in correspondence of the time step 64 and this isprobably due to the not completed formation and flattens ofepithelial layer. This implies that the distance distribution D(d)

generated at this stage results not clustered, thus not perfectcells classification is achieved.

Fig. 17 – Volume rendering representations of membranes3D images and epithelial centers CE depicted by bluespheres. Red squares highlight some region whereclassification errors, such as false positive and falsenegative, are marked with circles and cross. (a) Embryo attime step 124. (b) Time step 164. (For interpretation of thereferences to color in this figure legend, the reader isreferred to the web version of the article.)

equal to 3 �m. (b) High-resolution achieved with voxel sizeequal to 0.5 �m.

Table 2 reports also the FP and FN detections for each classof cells. Analyzing separately the EVL class and the DEL classit is possible to obtain information regarding the variation ofthe error rate and about the type of mistakes. In the earliestembryonic stage (time step 64) the major sources of misclassi-fications are epithelial false negative detections, whereas forthe last time step analyzed (164) the number of FN becomesoutnumbered and most of mistakes are due to epithelial falsepositives. A symmetric behavior of the classifier is possible toobserve in the DEL cells class, due to the fact that epithelialcells FN correspond to deep cells FP detections and epithelialFP to deep cells FN.

These results suggest that classification accuracy is influ-enced by EVL genesis and changes. Earlier stages of embryodevelopment, when EVL is not completely formed, give rise toFN epithelial classification, whereas later stages of develop-ment, characterized by EVL thinning, generate an increasingof FP epithelial detection due to the high cellular density andvicinity of EVL cells and first layer DEL cells. However, valida-tion results that we presented demonstrate that good accuracyin epithelial and deep cells classification is achieved and totalEVL/DEL classification mean error is kept below 2%.

6.2. Robustness testing

In the previous subsection we observed that in later stages ofembryo, epithelial false positives are the major source of mis-classification. As we discussed, this is due to the progressivelythinning of the EVL layer. Indeed, at the end of the observedembryo development (5 h post-64/128 transition) the epitheliallayer thickness is about 7.3 �m. The classification accuracy isinfluenced by the vicinity of epithelial cells and first layer ofDEL cells due to the fact that the two clusters of the distancedistribution get closed each other. Moreover, the degradationof the accuracy can also be justified with the spatial reso-lution of data. Comparing the final thickness value (7.3 �m)with the spatial resolution of the volumetric images (1.51 �m)it emerges the fact that only few voxels describe the EVL depthand structure.

In this subsection we investigate the accuracy and robust-ness of the classification procedure against the progressivelythinning of the epithelial layer and we analyze the algo-

rithm sensitivity to variation of the image spatial resolution.To achieve this goal we applied our method to syntheticcomputer-generated data, depicting different conditions ofepithelial thickness and image resolution.

i n b i o m e d i c i n e 9 8 ( 2 0 1 0 ) 103–117 113

fa(t((ssfcliad

dsttttsodtsddddtDetipt(tt

s

Fig. 19 – Gaussian functions depicting, at 3.6 h post-64/128cells transition, the epithelial and deep cells distance to theouter surface (�E = 2.1, �D = 12.1, �E = 1.6, �D = 2.3).Negative values stand for cells outside the reconstructed

c o m p u t e r m e t h o d s a n d p r o g r a m s

We created a synthetic embryo outer surface using a sphereunction of radius rSphere = 130 �m. The surface is depicted byvolumetric 3D binary image with physical origin coordinates

0, 0, 0) and dimension 130 �m. The sphere has been cen-ered in the point having coordinates (xSphere, ySphere, zSphere) =150, 150, 0) so that to include in the volume only half sphereFig. 18). We generated ten distinct 3D images varying the voxelize (from 3 �m to 0.5 �m) and keeping fixed the 3D image andphere dimension, so that to achieve embryo surfaces with dif-erent spatial resolution. High-resolution images (Fig. 18b) areonstituted by a larger number of voxels then the images withow spatial resolution (Fig. 18a). In the context of our sensitiv-ty test, these data represent the outcome of the segmentationlgorithm in case it is applied on embryo images acquired atifferent spatial resolutions.

In order to test the robustness of the classification proce-ure against the epithelial thinning, we generated differentets of synthetic points. Each set includes two classes of cen-er: the first class is constituted by points distributed closely tohe embryo outer surface and depicting the EVL cells, whereashe second group of points represents the cells that constitutehe first layer of the DEL. To distribute the synthetic pointsimilarly to real embryo nuclei, we analyzed the distributionf epithelial cells and deep cells detected from the zebrafishataset presented in the previous subsections. We selectedhe cells recognized at 3.6 h post-64/128 cells transition (timetep 124) and for each class (EVL and DEL) we measured theistance to the embryo outer surface in order to achieve twoistinct frequency distribution D(d) of the nuclei-to-surfaceistance. Computing separately the distance mean and stan-ard deviation values of the two classes we were able to obtainhe two Gaussian functions that better fit with the EVL andEL cells distribution (Fig. 19). At that embryonic stages thepithelial nuclei result clustered at 2.1 �m (�E) with respecto the embryo surface, whereas the first layer of deep nucleis located at 12.1 �m (�D). Analyzing the variation of thesearameters, in later embryo stages, it is possible to observehat the two clusters progressively get close to the surfacedecreasing of the Gaussian distribution mean values) and that

he distance between clusters rapidly decreases (decreasing ofhe difference between the mean value).

To recreate this behavior, we first uniformly distributed theynthetic epithelial cells over a sphere with radius rSphere − �E.

Table 2 – Misclassification rate: TP = true positive, FN = false neg

Time step EVL cells DEL cells

Cellsnum.

TP FN FP Cellsnum.

TP FN

64 130 123 95 1 964 869 184 341 338 17 1 1463 1446 1104 486 480 6 4 1,921 1,915 4124 569 563 12 3 2,405 2,393 3144 564 546 3 12 2,739 2,736 12164 688 643 2 35 3,121 3,119 35

Total 2,778 2,693 135 56 12,613 12,478 56

Percent (%) – – – – – – –

embryo profile.

The problem of evenly distributing points on a sphere can besolved using different approaches [35]. For the purpose of ourtests, we implemented a modified version of the ‘GeneralizedSpiral Points” algorithm [36]. Given a certain number of pointsand a sphere, the idea is to iteratively create points along aspiral that lay on the sphere surface. However, in a real sce-nario, the cells are not perfectly uniformly distributed overthe surface and, as illustrated in Fig. 19, they are not com-pletely concentrated at a fixed nucleus-to-surface distance.Thus, we introduced in the spiral algorithm two random Gaus-sian variables for generating perturbations that ensure notexact spherical and not exact uniform spatial placement. Foreach step of the iterative process that generates N epithelialsynthetic centers, the spatial coordinates of the generic i-pointare computed as follows:⎧

⎪⎨⎪⎩

xE = ı · cos(�) · sin(ϕ) + xSphere

yE = ı · sin(�) · sin(ϕ) + ySphere

zE = ı · cos(ϕ) + zSphere

(22)

ative, FP = false positive.

Resume

FP Total cellsnumber

Not sure False True

95 1094 6 96 99217 1804 2 18 1,784

6 2,407 2 10 2,39512 2,974 3 15 2,956

3 3,303 6 15 3,2822 3,809 10 37 3,762

135 15,391 29 191 15,171

– – 0.19 1.24 98.57

s i n b i o m e d i c i n e 9 8 ( 2 0 1 0 ) 103–117

Fig. 20 – Synthetic computer-generated epithelial (yellow)and deep cells (white) centers spatially arranged by thespiral-based approach. (a) Illustration of the ith epithelialand deep points placement. (b) Epithelial and deep pointsachieved by the spiral method (N = 200, � = 0, �E = 2.1,�D = 12.1, � = 0.15, �E = 1.6, �D = 2.3) superimposed withsynthetic embryo outer surface (red). (For interpretation ofthe references to color in this figure legend, the reader is

114 c o m p u t e r m e t h o d s a n d p r o g r a m

where

ı = rSphere − GE (23)

and

ϕ = arccos

(−1 + (2 · iG − 1)

N

)(24)

� = ϕ ·√

N · � (25)

where

iG = i + G, ∀i : zE > 0, i ∈ {1, 2, . . . , 2N} (26)

The Gaussian random variable G with mean � = 0 and stan-dard deviation � = 0.15, introduces a small variation in theindex iG (Fig. 20a). If no perturbation is added, then the coor-dinates of each point are computed with an integer value i,thus obtaining a uniform distribution of the points as achievedby the original model. On contrary, points generated with Gare placed, on the sphere surface, with a not perfect evenlydistribution. As introduced in (23), the second Gaussian ran-dom variable GE, with mean �E and standard deviation �E,is used to distribute the points over a sphere with radiusmean value ı = rSphere − �E and standard deviation �E (Fig. 20a).Thus, the computer-generated epithelial points results clus-tered at a distance �E with respect to the embryo outer surface(sphere with radius rSphere) as observed for real epithelial nuclei(Fig. 19). The constraint zE > 0 in (26) ensures to obtain centersdistributed over the semi-sphere enclosed in the synthetic 3Dvolumes depicting the embryo outer surface. Analogously tothe epithelial points, the synthetic deep cells are generated usingthe same spiral approach, introducing in the (23) an alterna-tive Gaussian random variable GD, with mean �D and standarddeviation �D:

ı = rSphere − GD (27)

that provides a good representation of the spatial distribution

of deep nuclei. For each set of points we created 200 epithe-lial cells and 200 deep cells. The resulting epithelial and deepcenters (Fig. 20b) have been marked with distinct labels sothat to easily recognize and compare them with the outcome

Table 3 – Epithelial cells detection rate (DR).

Voxel size (�m) EVL/DEL nuclei distance (�m)

2.26 2.66 3.13 3.68

3.0 0.50 0.53 0.52 0.492.5 0.52 0.51 0.49 0.502.0 0.59 0.58 0.60 0.691.5 0.61 0.70 0.69 0.821.3 0.70 0.84 0.82 0.921.0 0.81 0.87 0.89 0.880.8 0.78 0.85 0.85 0.860.7 0.81 0.85 0.84 0.870.6 0.78 0.86 0.84 0.860.5 0.79 0.83 0.82 0.85

referred to the web version of the article.)

of our clustering method. Ten different sets of points havebeen generated with the spiral-based cells placement, fixingthe standard deviation �E and �D of the two Gaussian randomvariables GE and GD, in accord with the two Gaussian distri-butions (Fig. 19) obtained from real data, and decreasing thevalue of the means �E and �D. Ten combinations of �E and

�D have been produced in order to progressively decrease theepithelial and deep nuclei mean distance (see “EVL/DEL NucleiDistance” in Tables 3 and Table 4).

4.33 5.09 5.99 7.05 8.29 9.75

0.50 0.61 0.71 0.84 0.96 0.970.64 0.79 0.88 0.96 0.99 1.000.85 0.94 0.98 0.99 1.00 1.000.91 0.96 0.98 1.00 1.00 0.980.94 0.98 0.99 1.00 0.99 0.920.94 0.97 0.98 0.99 0.96 0.920.92 0.96 0.97 0.98 0.96 0.920.92 0.95 0.97 0.98 0.95 0.900.92 0.93 0.96 0.98 0.96 0.920.92 0.93 0.96 0.97 0.96 0.89

c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 9 8 ( 2 0 1 0 ) 103–117 115

Table 4 – Epithelial cells false alarm rate (FAR).

Voxel size (�m) EVL/DEL nuclei distance (�m)

2.26 2.66 3.13 3.68 4.33 5.09 5.99 7.05 8.29 9.75

3.0 0.39 0.36 0.35 0.35 0.38 0.37 0.29 0.25 0.09 0.012.5 0.40 0.41 0.42 0.41 0.41 0.39 0.30 0.17 0.05 0.012.0 0.41 0.45 0.43 0.42 0.41 0.29 0.18 0.11 0.02 0.011.5 0.43 0.50 0.51 0.45 0.30 0.21 0.13 0.06 0.01 0.011.3 0.47 0.57 0.55 0.47 0.28 0.16 0.10 0.05 0.01 0.001.0 0.60 0.53 0.52 0.38 0.23 0.15 0.09 0.02 0.01 0.000.8 0.55 0.48 0.48 0.33 0.19 0.13 0.07 0.02 0.01 0.00

prsmafiT

pF

F(Drrm(

0.7 0.56 0.42 0.42 0.330.6 0.51 0.45 0.41 0.310.5 0.49 0.40 0.41 0.29

The accuracy tests consist of 100 experiments generatedrocessing, by epithelial and deep cells classification algo-ithm, combinations of computer-generated embryo outerurface and cells centers. The goal is to evaluate the perfor-ance of the method varying the 3D images spatial resolution

nd the EVL/DEL nuclei distance. Accuracy of a binary classi-cation test is typically expressed by the Detection Rate, DR =

P/P, where TP are the true positives, P the total number ofositives of the true class (in our case 200 cells) and by thealse Alarm Rate, FAR = FP/N, where FP are the false positives

ig. 21 – Graphs depicting the variation of accuracy rates.a) Variation of the DR over the EVL/DEL nuclei distance.ifferent lines correspond to different image spatial

esolutions. (b) Variation of the DR and FAR rates over theeduction of the voxel size. Improvement of the rates is

ore evident when dealing with small EVL/DEL distances4.33 �m).

0.18 0.12 0.05 0.02 0.01 0.000.18 0.11 0.05 0.02 0.01 0.000.16 0.11 0.04 0.02 0.01 0.00

and N the negatives of the true class (200 cells). The above tworates, in medicine field, take the name of Sensitivity (DR) andSpecificity (1 − FAR). For each experiment, comparing the syn-thetic labeled centers with the classified data achieved by ourmethod, we were able to measure the DR and the FAR rates.

Tables 3 and 4 report respectively the detection rate andthe false alarm rate of the experiments. In Fig. 21a we showthe variation of the DR over the e EVL/DEL nuclei distance withdifferent lines corresponding to different image spatial reso-lutions. It is possible to observe that, for almost all the linesdepicted in the graph, more the epithelial and deep nucleidistance is smaller and more the DR is degraded. However,experiments generated with high-resolution images (smallvoxel size) seem to be characterized by good accuracy perfor-mances. It is also evident that, the improvements achievedwith higher resolutions, are very marked in the regions of thegraph characterized by small EDL/DEL nuclei distance thatis when the epithelial layer thinning. In Fig. 21b we showthe improvements of both the DR and FAR rates, achievedprogressively decreasing the voxels size, in two cases char-acterized by different epithelial and deep nuclei distances(4.33 and 8.29 �m). Also this last graph confirms that improve-ment achieved with high-resolution images are evident whenepithelial and deep nuclei are closed each other, nevertheless,an increasing of the resolution do not provide noticeable accu-racy enhancements when we deal with lager EVL/DEL nucleidistance.

7. Conclusion and future plans

We designed an algorithm for the automatic classification anddensity measurement of EVL and DEL cells that has goodperformances on live zebrafish embryos volumetric imagesacquired by MLSM. Our procedure is based on Minimal Sur-faces geometric approach [26,27], Otsu [28] clustering method,Delaunay Triangulation [30–32] based surface reconstruction,and Within-R cloud of points density estimation.

From our experiments, it was shown that a Nucleus-to-Surface distance based classification is a robust approachfor distinguish epithelial and deep cells throughout zebrafish

early embryonic development. We used the Otsu clus-tering algorithm to automatically detect of the distancedistribution threshold that discriminates EVL from DELcells.

s i n

r

116 c o m p u t e r m e t h o d s a n d p r o g r a m

We measured the DEL cells density by cloud of points baseddensity estimators. We compared the performance achievedwith k-nearest neighbors and the Within-R approaches. Theresults demonstrate that the Within-R method provides bet-ter estimation of the DEL cell density identified from zebrafishdataset.

We also presented the strategies adopted to achieveepithelial cells density per unit volume and unit area. Wedemonstrated that with the proposed procedure we are ableto measure the thinning of the epithelial layer, thus to providean accurate measure of EVL cells density per unit volume.

We applied our algorithm on 168 time steps of a time vary-ing dataset depicting zebrafish embryogenesis (6 h of imaging)providing measurement of EVL and DEL density and thick-ness variation over the time. We validated the outcome ofsix time steps corresponding to different embryo stages Val-idation results show that misclassifying rate is about 1.3% ofthe total number of the classified cells, and that errors mostlyoccur in earlier embryonic stages when EVL layer is not com-pletely flatten and formed.

We extensively tested the robustness of the algorithmagainst the epithelial layer thinning and the sensitivity tothe variation of the image spatial resolution. To achieve sucha goal we designed a procedure to automatically generate3D embryo synthetic data and to measure the classificationaccuracy.

Improvements of the performances should be achievedin later embryo stages, when EVL thickness decreases below8 �m making difficult to discriminate the EVL cells from DELcells. The accuracy tests demonstrated that an increasing ofthe spatial resolution give rise to an enhancement of the clas-sification accuracy, especially when epithelial layer is verythin. Furthermore, an alternative clustering approach shouldbe evaluated to be used in combination with the one proposedin this work and able to reduce the epithelial false positivedetections in later embryo stages.

In future we plan to apply these methods on differentclasses of zebrafish embryo dataset, such as untreated andtreated with anticancer drugs, so that to estimate in vivo effec-tiveness and selectivity of the treatments. With these studieswe expect to measure the variability of relevant parameters,such as cells density and proliferation rate, between differentindividuals of the same species.

Acknowledgment

We thank all the members of the Embryomics and BioE-mergences projects for our very fruitful interdisciplinaryinteraction.

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