Quantitative neurite outgrowth measurement based on image segmentation with topological dependence



The study of neuronal morphology and neurite outgrowth has been enhanced by the combination of imaging informatics and high content screening, in which thousands of images are acquired using robotic fluorescent microscopy. To understand the process of neurite outgrowth in the context of neuroregeneration, we used mouse neuroblastoma N1E115 as our model neuronal cell. Six-thousand cellular images of four different culture conditions were acquired with two-channel widefield fluorescent microscopy. We developed a software package called NeuronCyto. It is a fully automatic solution for neurite length measurement and complexity analysis. A novel approach based on topological analysis is presented to segment cells. The detected nuclei were used as references to initialize the level set function. Merging and splitting of cells segments were prevented using dynamic watershed lines based on the constraint of topological dependence. A tracing algorithm was developed to automatically trace neurites and measure their lengths quantitatively on a cell-by-cell basis. NeuronCyto analyzes three important biologically relevant features, which are the length, branching complexity, and number of neurites. The application of NeuronCyto on the experiments of Toca-1 and serum starvation show that the transfection of Toca-1 cDNA induces longer neurites with more complexities than serum starvation. © 2008 International Society for Advancement of Cytometry

Cellular morphogenesis and its relationship with cell functions are significant and critical in many biological studies. Advances in digital microscopy and robotic techniques in cell cultures have enabled thousands of cell images to be acquired through high-content screenings. Manual processing of those images is subjective, labor intensive, and inaccurate. Automatic analysis and extracting quantitative information are challenging, but vital for inferring new biological insights.

Neurites, including axons and dendrites, are a unique feature of neurons that allow formation and maintenance of the nervous system. Understanding the process of neurite outgrowth is important for neuroregeneration strategies in the treatment of diseases, such as Alzheimer's disease and Parkinson's. In this article, N1E115 cells are used as our model to follow neurite outgrowth. N1E115 mouse neuroblastoma cells have been used as a model neuronal cell for a number of years. N1E115 cells grow as round cells and upon serum starvation (or cDNA transfection) produce neurites and a neuronal morphology.

Transducer of cdc42-dependent actin-1 assembly (Toca-1) is a protein that has three distinct domains; F-BAR, Cdc42 binding site, and SH3 domain. The F-BAR domain can deform membranes while the SH3 domain binds N-WASP, linking to actin polymerization. The domain structure of Toca-1 is very similar to the Insulin Receptor Substrate 53 kDa (IRSp53) and both proteins induce the formation of filopodia (complexity) and neurites in N1E115 (1). In the present study, we used Toca-1 to induce neurite outgrowth, neurite branching and complexity of N1E115 cells and compared the results quantitatively with serum starvation.

Neurite outgrowth is also stimulated by, for example, GAP-45 (2), conditioned medium (3), calcium (4), and adhesion molecules (5). Ecdysteroid enhances neurite branching by altering growth cone structure and function (6).

In parallel to the neurite outgrowth studies, progress has been made to analyze cellular images automatically where nuclei are used as references for cell segmentation. Different nuclei finding methods have been reported, such as simple thresholding (7), watershed algorithm (8, 9), iterative morphology methods (10), level set boundary searching approach based on gradient flow (11), and flexible contour model for overlapping and closely packed nuclei (12). Other related research can be found in Refs. 13–15.

The watershed approach has been widely applied for cell segmentation (9–10, 16, 17). However, one major problem with the watershed approach is over-segmentation (17) and some methods have been proposed to solve this problem, e.g., rule-based merging (18) and marker-controlled watershed correction based on Voronoi diagram (19). Watershed segmentation is integrated with the level set formulation to segment the cells in (16). Similar cell segmentation approach based on found nuclei in (17) uses one level set function for individual corresponding cell to prevent the merging of different cells. Some approaches, which combined watershed and level set, also address the problem of over-segmentation, such as marker-controlled level set (16) and preserving topology by simple point concept (20).

After the cellular images are accurately segmented, measuring the length of neurites on a cell-by-cell basis is thus feasible. Studies on neurite tracing have been reported. NeuronJ is a semi-automatic neurite tracing technique (21), which is very easy to use, however semi-automatic technique would be time consuming for high content screening experiments. Some automatic approaches are proposed too, such as automatic tracing of dye-injected neurons (22), EM-based local estimation of neuron filament (23), automatic tracing of the neurite from 3D microscopy images (24), and rapid automated three-dimensional tracing of neurons (25). Xiong et al. proposed a hysteresis filter and break linking approach to compensate the discontinuities of the neurite outgrowth (26). Recently, HCA-vision (27) is presented, which is a fast, sensitive, reliable, and fully automatic algorithm for neurite tracing. It also can analyze the branching complexities. Our approach will segment the neural cells first, such that more information can be extracted, for example, the cell shape (not only the cell body sizes). We also developed a fully automatic tracing algorithm with comparable accuracy.

In this study, the N1E115 cells are induced to form neurites under four different culture conditions and more than 6000 cellular images are acquired. We developed software package called NeuronCyto to analyze the acquired images. In our NeuronCyto, a new segmentation algorithm based on topological analysis is proposed to segment the cells. Thereafter, we designed an automatic function for NeuronCyto to quantitatively measure the length, branching complexity,1 and number of neurites. Finally, we assessed these features to determine under which conditions the N1E115 cells have more and longer neurites.


Image Acquiring and Objective

In our experiments, N1E115 cells were grown in 18 × 18 glass coverslip maintained at 37°C and 5% CO2 is supplied. The culture medium is Dulbecco's Modified Eagle's medium with 4500 mg/ml glucose and 1% pencillin-streptomycin as antibiotic. The cells in the laminin coated glass coverslip were serum starved for 48 h. Cells that are grown on coverslips are used only for the purpose of fixation and immunolabelling. For normal culture though, no enzyme is used. At last, cells are aspirated with fresh warm medium and resuspended in appropriate densities.

The images of our study are acquired from fixed N1E115 cells stained by DAPI and FITC-phalloidin. DAPI stains the nucleus; FITC-phallodin stains the abundant endogeneous filamentous actin. The cells are counted, seeded, and resuspended into monolayer on the coverslips with an appropriate density, about 50–70% confluency. The seeding procedure guarantees that nuclei do not overlap with each other, since we want cells to be well separated such that morphology of individual cells can be observed. Images were acquired using a wide-field fluorescent microscope with filters for DAPI and FITC stains. The original images were acquired at 20× magnification with 1366 × 1020 pixels of 12 bits accuracy and the resolution is 0.31 μm/pixel. Cellular images were acquired under four different culture conditions (i) serum starvation with 50,000 cells/slide, (ii) serum starvation with 30,000 cells/slide, (iii) Toca-1 transfected with 50,000 cells/slide, and (iv) Toca-1 transfected with 30,000 cells/slide. About 1500 images were acquired under each condition.

To formalize the segmentation problem, cellular images are defined on a subset in two-dimensional space Ω ⊂ R2. We use fn(x,y): Ω → R and fc(x,y): Ω → R to represent the image intensities of DAPI and FITC at pixel (x, y). In this article, the superscripts “n” and “c” represent the “nucleus” and “cell,” respectively. All images are normalized such that fn(x,y) ∈ [0,1] and fc(x,y) ∈ [0,1]. The segmented regions of fn represent nuclei segments, denoted by ωmath image for i = 1,2, …L, where L is the number of detected nuclei. Similarly, the segmented regions of fc are cell segments, denoted by ωmath image for i = 1,2,…L. The numbers of nuclei segments and cell segments should be the same. Both ωmath image and ωmath image form connected regions in Ω. Because of the limitation of space, only a simple statement defines the connected region.

Connected region

A set of points π ⊆ R2 form a connected region if ∀ (x1, y1) ∈ π and ∀ (x2, y2) ∈ π, ∃ a path Γ ⊆ R2 connecting (x1, y1) and (x2, y2) such that Γ ⊆ π.

Level Set Method and Mumford-Shah Model

The Mumford-Shah model is region-based, robust to noise and suitable for segmenting objects with complex morphology. We use Chan-Vese's formulation for two-phase segmentation, which is in Refs. 28, 29:

equation image(1)

where u(x,y) is the image intensity. μ, υ, λ1, and λ2 are the weights of contour length, area, foreground, and background, respectively. c1 and c2 are constants, which are the mean values of the background and foreground. Here, the length and area parameters μ and υ are set to zero to allow irregular contours and varying sizes of nuclei and cells. Optimizing the Mumford-Shad model leads to the Euler-Lagrange equation, which is an iterative procedure:

equation image(2)

where δε is a regularized Dirac delta function (29). We set λ1 = 1 and λ2 = 50 for the cell segmentation to emphasis importance of the background such that we may preserve the continuity of weak neurites. We choose ε = 1 and Δt = 10. The parameter selection for λ, λ2, and Δt will be discussed in more detail in the Results section.

Three acquired images are shown in Figure 1. Low level preprocesses, such as de-noise (30) and removal of nonuniform background (30), are needed to improve the image quality. The preprocessing step of the images in our NeuronCyto is critical for the further analysis.

Figure 1.

Cell images with detected nuclei. Neurites and cell bodies are manually annotated by arrows; outline of the cell body is illustrated by yellow line. Detected seeds are outlined in blue and geometric centers are marked by red dots.

In our study, nuclei are segmented first and serve as references for the cell segmentation. To segment the nuclei, we initialize the level set function ϕn,t(x,y) as:

equation image(3)

Substitute u(x,y) by fn(x,y) and evolve ϕn,t(x,y) according to Eq. (2) till convergence to obtain the nuclei segments ωmath image, i = 1,2,…L. Nuclei segments are called seeds in our work. Each ωmath image forms a connected region and is labeled by a unique integer, indicated by the subscript i = 1,2,…L. The background is labeled by 0. ωmath image are illustrated by blue outlines in Figure 1.

The evolution of level set function for cell segmentation is slightly different since we should use the information of ωmath image. We transform fc(x,y) using the information of ωmath image:

equation image(4)

Note that equation image(x,y) ∈ [0,1], since fc(x,y) ∈ [0,1]. The purpose of this transformation is to ensure that the cell segments ωmath image always entirely contain a nucleus ωmath image. The level set function for cell segmentation is initialized as:

equation image(5)

We substitute u(x,y) by fc(x,y) in Eq. (2) and then evolve ϕn,t using Eq. (2). Unlike the works in (17) where each individual cell has one corresponding level set function, we use only one level set function to segment all cells to achieve better computational efficiency.

Instead of using distance function (17, 20, 28, 29), we initialize the level set function for cell segmentation according to Eq. (5). Such initialization ensures that the zero level sets start from the seeds and evolve outwards with a speed related with the image intensity, e.g., brighter regions will be segmented as foreground earlier.

Preservation of Topological Dependence

To prevent merging of different segments during the evolution of ϕc,t, a dynamic watershed scheme is applied based on the concept of topological dependence.

Topological dependence

A set of connected regions πi (i = 1,2,…L) is said to be topologically dependent with another set of connected regions θi (i = 1,2,…L) if:

equation image(6)

Because we initialize the level set function for cell segmentation according to Eq. (5), ωmath image = ωmath image (i = 1,2,…L) when t = 0. Thus ωmath image (i = 1,2,…L) is topologically dependent with ωmath image (i = 1,2,…L). To preserve topological dependence, we calculate the watershed lines Wt at each time step t when Eq. (6) is satisfied. The definition of Wt is:

equation image(7)

where dmin[(x,y)|ωmath image] is given by:

equation image(8)

Watershed lines defined in Eq. (8) is also known as equal distance lines in other literature (17). According to its definition, if (x,y) ∈ ωmath image, then dmin[(x,y)|ωmath image] = 0. A point on the watershed line is illustrated by a brown dot in Figure 2a.

Figure 2.

Illustration of dynamic watershed lines and preservation of the topological dependence. A point of the watershed line is illustrated by the brown dot in Figure 2a. Labels of different regions at different time are indicated by random colors. The level set function evolves from t in (a) to t + Δt in (b). Thereafter, re-labeling is carried out in (c) and (d) to eliminate the residual regions and preserve the topological dependence.

Figure 3.

Results of parameter tuning for differentiation cell body and neurite. Morphology operation, closing, is applied using disk structural elements of different radius (rd = 2,5,8,11, and 14 pixels). Twenty images, totally 1861 cells, are random selected for this procedure. The numbers of cells with accepted cell body and neurite of different parameters are shown. According to the result, we choose rd = 5 for the closing operation to distinguish the neurites from the cell bodies. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Evolving the level set functions from t to t + Δt may cause the connected regions to split or merge, resulting in the violation of the topological dependence with ωmath image. Splitting is easier to deal with. Any connected regions that do not contain a nucleus are removed at every iteration, for example, the gray region in Figure 2b. Merging can be prevented at t + Δt using Wt. After removing the split regions, if the remaining connected regions are topological dependent to the nucleus segments ωmath image, then these regions will take the labels of ωmath image and we denoted them by ωmath image.

If the topological dependence is violated, preserving the topological dependence and recovering the correct segmentation ωmath image consist of a series of re-labeling steps. First, we label the remaining connected regions as “unknown” and the background as 0. Then, we obtain the intersection of the remaining connected regions and Wt, which form a set of common boundaries {Smath image, Smath image, … Smath image}, where M is the number of common boundaries. Two examples of such common boundaries are illustrated by Smath image and Smath image in Figure 2b. The regions separated by the common boundaries are considered as different connected regions. Thus, we obtain a new set of connected regions, denoted by βmath image (k = 1,2,…K). If βmath image contains a nuclei, e.g., ωmath image ⊆ βmath image, we use the label of ωmath image to label βmath image. The remaining unlabeled residual regions, such as βmath image, βmath image, and βmath image in Figure 2c are handled by an iterative procedure as follows.

Re-labeling of the residual regions

Any residual region must be created by some common boundaries. One side of those common boundaries must be adjacent to this given residual region and the other side is adjacent to some other region that may or may not be successfully re-labeled previously. Each unlabeled residual region will take the label of the adjacent region that shares the longest common boundary, which is denoted by Smath image. If all regions adjacent to this given residual region are “unknown,” then this residual region cannot be re-labeled in the current iteration. Iterate this procedure until all “unknown” residual regions are re-labeled.

In Figure 2c, βmath image is an unknown residual region and separated from βmath image and βmath image by common boundaries Smath image and Smath image. Since Smath image is longer than Smath image (see Fig. 2c), e.g., Smath image is Smath image, we re-labeled βmath image with the label of βmath image, instead of βmath image. Labeling the unknown residual regions according to the longest common boundary is to integrate the geometrical information in the cell segmentation. After all the residual regions are re-labeled, we obtain the connected regions ωmath image, which are topological dependent with ωmath image. Finally, the watershed lines Wtt is updated using Eq. (7), shown in Figure 2d.

In the segmentation step of our NeuronCyto, both the variation of fc(x,y) and the geometrical information are essential. The speed of the level set evolution depends on the variation of cell image intensity; brighter regions will be segmented as foreground earlier. The Watershed lines in our approach depend strongly on the level set function. It is critical that we evolve the watershed lines with the level set based on topological dependence such that the geometrical knowledge are integrated in cell segmentation at every iteration. Re-labeling residual regions according to the longest common boundary utilizes geometrical information, thus both the variation of the image intensity and the geometrical information are combined to achieve better results. We will validate the segmentation function of NeuronCyto and compare its accuracy with other popular software packages in the section of results.

Quantitative Measurement of Neurite Length

After NeuronCyto segment the cells, we need to distinguish the neurites from the cell body before the measurement. We apply a parameter tuning procedure to distinguish cell bodies and neurites. A disk structure with radius rd is applied for closing morphological operation (Erosion followed by dilation). Thereafter, we overlay the cell body with the skeleton of the segmentation (30) to obtain the neurites.

Twenty images, containing 1861 cells, were randomly selected. We calculate the cell bodies with rd = 2, 5, 8, 11, and 14 pixels. Cell bodies with errors are manually counted. As shown in Figure 3, the disk structure with radius rd = 5 pixel achieved the best accuracy, which is about 99%. Therefore, NeuronCyto use rd = 5 pixels to differentiate the neurites from the cell bodies.

Our software, NeuronCyto, has a neurite tracing function, which is developed to analyze the neurites quantitatively. The algorithm traces around the perimeter of each cell body. When it encounters a neurite, it will automatically trace neurites and quantitatively measure the lengths of its branches. Information, such as number of branching points and number of cell per image, are extracted through the tracing algorithm. Because of the limitation of space, we can only provide limited details of our tracing algorithm in the Supporting Information.


Segmentation Results Comparison

To assure an accurate segmentation results using NeuronCyto, it is important to determine a suitable time step Δt for the evolution of the level set function. We choose a big time step Δt = 10 to compromise between the accuracy and computation. To verify that using Δt = 10 does not introduce significant numerical errors, we performed our segmentations on eight randomly selected images with three different time steps Δt = 1, 5, and 10. The adjusted rand index (31) between Δt = 1 and Δt = 10 is 0.9944 ± 0.0025 and between Δt = 5 and Δt = 10 is 0.9952 ± 0.0024. This shows that using a big time step does not introduce significant numerical errors.

We compare the segmentation results of our software, NeuronCyto, with CellProfiler (32) and MetaMorph. CellProfiler is one of the most popular cellular image analysis freeware developed by the Broad Institute of Harvard and MIT. MetaMorph is commercial software and developed by MDS for cellular image analysis. The parameters of CellProfiler were suggested by the software developers and a service engineer from MDS fine tuned the parameters for Metamorph. One hundred images containing 4916 cells were randomly selected. They are processed by CellProfiler, MetaMorph, and NeuronCyto to generate 300 segmentations (100 for each approach). The segmentations were then divided into 15 sets of 20 each and randomly shuffled. Two reviewers manually scored these segmented images without knowing which approach was applied. The reviewers counted the cells that are segmented incorrectly. The results are shown in Table 1a.

Table 1. Comparisons of segmentations and neurite length measurements
  1. (a) The segmentation accuracies of MetaMorph, CellProfiler, and our method (NeuronCyto) show that NeuronCyto achieved the best segmentation results based on 100 random selected images. (b) The comparisons of neurite length measurements based on the 16 neurites show that the measurements are consistent among NeuronJ, HCA-vision, and NeuronCyto. For each row, we choose two approaches from the three methods and calculate the mean percentage difference of the lengths using the later approach as a reference.

(a)Mean accuracy
MetaMorph74.16 ± 1.02%
CellProlifier90.85 ± 0.56%
NeuronCyto93.25 ± 0.57%
(b)Mean difference
NeuronCyto vs. NeuronJ4.85 ± 2.81%
HCA-vision vs. NeuronJ3.20 ± 2.74%
NeuronCyto vs. HCA-vision2.70 ± 3.87%

NeuronCyto achieved the best performance, which is about 2.5% better than CellProfiler and much higher than MetaMorph. CellProfiler can segment the cell well, however, it over-segments the cells when the shapes of the nucleus and cells are irregular. Furthermore, it does not have the functionality to measure the neurite length and analyze its branching. Metamorph has the functionality of measuring the length of neurites, but it cannot analyze the branching of the neurites. It also fails to detect some fine neurite structures. Since segmentation results of Metamorph are not acceptable, the measurement of neurite length on a cell-by-cell basis is not reliable.

Automatic Measurement of the Neurite Outgrowth

The segmentation results of the images in Figure 1 are shown in Figure 4a, 4c and 4e, where each cell is labeled by different integer and illustrated by random colors. The final results of the cell bodies and neurite tracing are shown in Figure 4b, 4d, and 4f.

Figure 4.

Segmentation of the neural cells and final results. In the segmentation results, nuclei are outlined by blue line and their geometrical centers are shown by red dots. Cells are labeled by different integer and illustrated by random colors. In the final results, a few cells with long neurite outgrowth are highlighted by the yellow legends, where “CellLength” is the cell body length.

Neurite outgrowth is an essential parameter for assessing not only a unique characteristic of neurons but also as a measure of the ability of drugs, proteins, or chemicals to stimulate neuroregeneration. In addition to neurite length, other important features of neurons include: complexity of neurite branching, number of cell extensions per cell, and number of neurites per cell. The complexity of neurite branching is defined as the number of sub-branches of a neurite divided by the length of that neurite.

To validate the neurite length measurements of NeuronCyto, we selected seven images and chose 16 neurites. They are processed by NeuronJ, HCA-vision, and NeuronCyto. This result is shown in Table 1b. For each row in Table 1b, we choose two approaches from the above three methods and calculate the mean difference (%) of neurite length using the later approach as a reference. For example, mean difference of NeuronCyto versus NeuronJ is equation image, where lmath image is the length of ith neurite and the subscript indicates the approach. We can see that the measurements of NeuronJ, HCA-vision, and NeuronCyto are consistent.

We trace and analyze the neurites according to the final results, shown in Figure 4b, 4d and 4f. The measurements of neurite length are shown in Figure 5a. We can see that the neurite length of Toca-1 transfected cells (50,000 cells/coverslip) is longer than the other three conditions. The complexities of neurites are shown in Figure 5b. Toca-1 (50,000 cells/coverslip) induces more complexity than the other three conditions. The number of cell extensions per cell is shown in Figure 5c. We can see that serum starvation induced more short cell extensions than Toca-1. We averaged the cell body length over all the cells in the four conditions and used 1.5 times this mean value as a threshold to define the neurite outgrowth. The number of neurites per cell is shown in Figure 5d, which clearly shows that Toca-1 (50,000 cells/coverslip) induced more outgrowth than serum starvation. This result also confirms the unpublished work done by Sohail et al. from Institute of Medical Biology.

Figure 5.

Evaluation and analysis of neurites. (a) The neurite length of Toca-1 cells (50,000 cells/coverslip) are longer than the other three conditions; (b) Toca-1 cells (50,000 cells/coverslip) have a tendency to be more complicated (more branches/length); (c) Serum starvation results in more but shorter cell extensions than Toca-1 cells; (d) Toca-1 cells (50,000 cells/coverslip) induced more neurites/cell than the other three conditions.


Many segmentation algorithms could not properly segment cells that are clumpy and touches each other, especially when the intensity contrast at the boundaries is low and their geometrical shapes are highly variable. We proposed a novel segmentation approach for cellular images. Our NeuronCyto combines the advantages of level set and watershed in a novel way based on the concept of topology dependence. The speed of the level set evolution depends on the variation of cell image intensity, since we initialize the level set function for cell segmentation according to Eq. (5) instead of using traditional distance function. Another novelty of our segmentation method is that the watershed lines evolve dynamically, which is essential to preserve the known topology of the found seeds. This constraint of topology dependence also solved the over-segmentation problem of watershed approach. We applied our approach on more than 6000 acquired cellular images. According to the validation of 100 randomly selected images containing 4916 cells, our segmentation method achieved better performance than CellProfiler and MetaMorph. We used only one level set function to segment all the cells in an image, hence, our algorithm is more efficient than the work in Ref. 17 where each cell is associated with an individual level set function. Our segmentation approach is developed based on images acquired by two-channel microscopy, however, it can be easily generalized and applied to cellular images of multi-channel microscopy when the nuclei are acquired by one of the channels. Our software, NeuronCyto, is available at http://neuroncyto.bii.a-star.edu.sg. The Matlab source codes, executable binary files and a web-based demonstration are available in above URL.

Quantitative information is needed to understand the process of neurite outgrowth. CellProfiler can segment the cells reasonably well, but it does not have the functionality to measure the neurite lengths and analyze their branching/complexity; Metamorph has the functionality to measure the neurite length without analyzing the branching, but its segmentation results are not acceptable. We proposed an automatic approach to differentiate the neurites from cells using NeuronCyto. It allows three important morphological features of neurites, e.g., length, branching complexity, and number, to be scored and this has relevance to drug discovery for neuroregeneration. NeuronCyto is applied on one experimental dataset and observed that serum starvation yields more but short cell extensions, whereas Toca-1 induced more long neurites with more complexity than serum starvation as scored manually.


The authors thank Dr. Anne Carpenter's help by providing the parameters for CellProfiler. They also thank Dr. Tanavde Vivek for his valuable comments on the manuscript.

  • 1

    Branching complexity is defined by the number of the branches divided by the length of the neurite.