# MF2C3: Multi-Feature Fuzzy Clustering to Enhance Cell Colony Detection in Automated Clonogenic Assay Evaluation

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## Abstract

**:**

## 1. Introduction

## 2. Background

## 3. Materials and Methods

#### 3.1. Cell Lines

#### 3.2. Cell Colony Feature Extraction

- $p(\cdot )$ is the normalized gray level histogram counts for the current sliding window ${\mathcal{W}}_{ij}$ (obtained from the native RGB color space using the rgb2gray MatLab built-in function);
- $M$ and $N$ are the dimensions of the pixel matrix ${\mathcal{I}}_{\mathrm{well}}$ ($M=N$, considering that the well, automatically detected, is circular);
- $\mathcal{L}$ is the number of gray levels considered after the quantization (in our case, $\mathcal{L}=256$);
- ${\mu}_{{\mathcal{W}}_{ij}}={\displaystyle \sum}_{l=0}^{\mathcal{L}-1}p\left(l\right)\cdot l$ is the local mean considering a sliding window of size $\omega \times \omega \text{}$.

#### 3.3. Circle Hough Transform

^{®}Inc., Corning, NY, USA). In this specific study, the experiments were performed only on 6-well plates, where each well has a diameter of 34.80 mm. Regardless of the number of wells, the image acquisitions on the scanner are always performed in the same way, in terms of both focal distance and resolution, so that the zoom factor does not change. The circle candidates are produced by voting in the parameter space center points $c$, and then the local maxima are selected in the accumulator matrix. Formally, each point $\left({x}_{c},{y}_{c}\right)\text{}$ in the parameter space, representing a circle center, must meet conditions in Equation (4), where $\theta $ is the angular coordinate with respect to the positive x-axis, by using a polar coordinate system [45]:

#### 3.4. Spatial FCM Clustering

- $m$ is the fuzzification constant (weighting exponent: $1\le m<\infty $) that determines the fuzziness degree of the classification process. If $m=1$, the FCM algorithm approximates hard K-means. In general, the higher the $m$ value, the greater the fuzziness degree will be (the most common choice is $m=2$);
- $U$ is the fuzzy $C$-partition of the data matrix $X$;
- ${d}_{ik}=\parallel {x}_{k}-{v}_{i}\parallel {}^{2}$ is the squared distance between ${x}_{k}$ and ${v}_{i}$, computed through an induced norm $\parallel \text{}\xb7\text{}\parallel $ on ${\mathbb{R}}^{n}$ (usually the Euclidean ${\ell}_{2}$ norm).

#### 3.5. Surviving Fraction Quantification

- The Plating Efficiency (η) represents the fraction of colonies formed from cells that were not exposed to the treatment, considering the number of grown colonies and the number of plated cells, and must be determined for each experiment;
- The Survival Fraction (SF) represents the surviving fraction of cells after any treatment (i.e., irradiation or cytotoxic agent), calculated taking into account the PE of untreated cells, the number of colonies grown after treatment and the number of plated cells.

#### 3.6. MF2C3 Parameter Settings

## 4. The Proposed Multi-Feature Automatic Clustering Approach

^{®}development environment (The MathWorks, Natick, MA, USA) version 2016b. The Graphical User Interface (GUI) exploited the built-in MatLab GUI Development Environment (GUIDE).

## 5. Experimental Results

_{%Area}) versus the manual colony counts (SF

_{Manual}). Each diagram shows the correlation coefficients obtained on MCF7, MCF10, T98G, and U251MG cell cultures (by exploiting 79, 40, 40, and 40 samples, respectively) treated with different doses of radiation or cytotoxic agent. The experimental findings, in terms of $r$ coefficient values, showed a high level of correlation between multi-feature automatic approach and manual cell colony quantification for all the analyzed cell lines. More specifically: Figure 8a shows excellent results; in Figure 8b, the equality straight-line reveals a positive offset in the SF

_{%Area}measurements, by slightly over-estimating the manual colony counts SF

_{Manual}(in approximately 52% of the cases for SF

_{%Area}> 0.40); on the contrary, Figure 8c is characterized by a moderate negative offset in the SF

_{%Area}measurements for 60% of the samples; considering SF

_{%Area}< 0.45, the results automatically obtained by MF2C3 on the U251MG cell line (Figure 8d) slightly over-estimate the manual measurements in about 62% of the samples. We can conclude that, considering the four different experimental data, no systematic error is found in terms of under-/over-estimation.

## 6. Discussion and Comparisons

- Fully automatic approach that does not require any human intervention, allowing for eliminating the subjectivity of the quantification;
- No need for specific hardware during the images acquisition phase. Since just a general-purpose flat-bed scanner is required, every laboratory can use our approach, without having to acquire any additional hardware;
- Using a multi-feature local descriptor as input of the sFCM clustering algorithm for cell colony detection. This novel approach, exploiting entropy and SD, was tested on four human cell lines and obtained excellent results.

## 7. Conclusions

_{%Area}) showed high correlation values against the manual colony counting measurements (SF

_{Manual}) on the MCF7, MCF10A, T98G, and U251MG human cells lines. Overall, MF2C3, which relies upon the concept of symmetry in the pixel local distributions, significantly outperformed our previous thresholding-based approach presented in [6].

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Examples of the analyzed cell types: (

**a**) MCF7; (

**b**) MCF10A; (

**c**) T98G; (

**d**) U251MG. It is possible to notice how the characteristics (e.g., size, shape, contrast, coloration) vary across the various cell lines. As described by [3], the images were taken after 2 weeks of cell incubation post-treatments.

**Figure 2.**The entropy feature extracted from the four-well image examples shown in Figure 1: (

**a**) MCF7; (

**b**) MCF10A; (

**c**) T98G; (

**d**) U251MG.

**Figure 3.**The SD feature extracted from the four-well image examples shown in Figure 1: (

**a**) MCF7; (

**b**) MCF10A; (

**c**) T98G; (

**d**) U251MG.

**Figure 4.**Parameter setting of the sliding window used for the local feature extraction (with size ω × ω pixels), in terms of the absolute error $|{\mathrm{SF}}_{\%\mathrm{Area}}-{\mathrm{SF}}_{\mathrm{Manual}}|$ by considering ω ∈ {3, 5, 7, 9}. The calibration set was composed of 20 randomly selected images (5 for each cell line). The dots and the error bars denote the mean and standard deviation for each setting, respectively.

**Figure 5.**Overall flow diagram of MF2C3, the proposed multi-feature spatial Fuzzy C-Means (sFCM) clustering approach for automatic clonogenic assay evaluation. The data block with thick-line borders represents the input multi-well plate image. The bold variable names denote vectors composed of single-well images, feature maps or cell colony clusters.

**Figure 6.**Graphical User Interface (GUI) of the proposed automatic approach for clonogenic evaluation.

**Figure 7.**Colony segmentation results obtained by using MF2C3, via sFCM clustering with C = 2 using the entropy and SD descriptors extracted from the input images in Figure 1: (

**a**) MCF7; (

**b**) MCF10A; (

**c**) T98G; (

**d**) U251MG. For each sub-image, a portion of the well is enlarged by over-imposing the corresponding segmentation result via a red contour.

**Figure 8.**Scatter plots of the automated MF2C3 Area Covered by Colony (ACC)-based Surviving Fraction (SF) evaluation (SF

_{%Area}) versus the mean manual colony counting measurements (SF

_{Manual}) from three distinct biologists, for: (

**a**) MCF7, (

**b**) MCF10A, (

**c**) T98G, and (

**d**) U251MG cell lines. Each diagram reports data related to the proposed detection approach exploiting multi-feature spatial FCM, using entropy and standard deviation as descriptive features of the colonies. The equality line through the origin is drawn as a dashed line and each diagram also displays the corresponding Pearson’s correlation coefficient.

**Figure 9.**Bland–Altman plots of the automated ACC-based SF evaluation (SF

_{%Area}) versus the manual colony counting measurements (SF

_{Manual}), for: (

**a**) MCF7, (

**b**) MCF10A, (

**c**) T98G, and (

**d**) U251MG cell lines. The results yielded by the proposed MF2C3 approach and the previous work [6] are displayed as red and blue circles, respectively. Solid horizontal and dashed lines denote the mean and ±1.96 standard deviation values, respectively.

Cell Line | Description | Number of Analyzed Wells |
---|---|---|

MCF7 ^{1} | human breast epithelial carcinoma estrogen receptor-positive | 79 |

MCF10A ^{1} | human non-tumorigenic breast epithelial | 40 |

T98G | human glioblastoma | 40 |

U251MG | human glioblastoma-astrocytoma | 40 |

^{1}Same datasets used in [6] in order to conduct a direct and fair comparison with the proposed method.

**Table 2.**Pearson’s correlation coefficient between the automatic ACC-based SF values (SF

_{%Area}) and the conventional colony counting measurements (SF

_{Manual}) on the analyzed MCF7, MCF10A, T98G, and U251MG cell lines. The results achieved by MF2C3 are compared against the approach proposed in [6]. The corresponding significance level (p value) and the statistical significance between the correlation coefficients was assessed by the Fisher’s z-transformation. Boldface values indicate statistical significance.

Cell Line | Number of Samples | Pearson’s Correlation Coefficient (p Value) [6] | Pearson’s Correlation Coefficient (p Value) [MF2C3] | Fisher’s z-Transformation (p Value) |
---|---|---|---|---|

MCF7 | 79 | 0.9791 (<0.0001) | 0.9931(<0.0001) | 5.87 × 10^{−4} |

MCF10A | 40 | 0.9682 (<0.0001) | 0.9873 (<0.0001) | 4.61 × 10^{−3} |

T98G | 40 | 0.9237 (<0.0001) | 0.9665 (<0.0001) | 6.94 × 10^{−3} |

U251MG | 40 | 0.8777 (<0.0001) | 0.9506 (<0.0001) | 4.23 × 10^{−3} |

Method | Approach Type | Human Intervention | Specific Hardware Needed | Plate Position Detection | Cells Type |
---|---|---|---|---|---|

Barber et al., 2001 [18] | Semi-automatic | processing method selection | Yes | fixed plate position | HT29, A172, U118, IN1265 |

Bernard et al., 2001 [19] | Supervised model | parameters tuning | Yes | fixed positioning mask | DC3F |

Dahle et al., 2004 [20] | Semi-automatic | thresholding interaction | No | fixed positioning mask | V79, HaCaT |

Siragusa et al., 2018 [21] | Semi-automatic | one parameter setting | Yes | fixed positioning mask | V79, HeLa |

Clarke et al., 2010 [22] | Semi-automatic | parameters selection | No | fixed position | Escherichia coli, Streptococcus pneumoniae |

Geissmann, 2013 [23] | Semi-automatic | interactive parameters initialization | No | automatic Petri dish detection | Staphylococcus aureus |

Chiang et al., 2015 [24] | Automatic | N.A. | Yes | fixed position | Escherichia coli K12 |

Khan et al., 2018 [25] | Automatic | N.A. | No | fixed positioning mask | Escherichia coli, Klebsiella pneumoniae, Pseudomonas aeruginosa, Staphylococcus aureus |

Boukouvalas et al., 2019 [26] | Automatic | N.A. | No | automatic ROIs detection | Streptococcus mutans, Candida albicans, Staphylococcus aureus |

Bewes et al., 2008 [30] | Automatic | N.A. | No | fixed flask position | MM576, NCI-H460, IMR-32 |

Guzmán et al., 2014 [36] | Semi-automatic | alignment and cropping of the image | No | fixed positioning mask | T98G |

Militello et al., 2017 [6] | Automatic | N.A. | No | automatic multi-well detection | MFC7, MCF10A |

MF2C3 | Automatic | N.A. | No | automatic multi-well detection | MCF7, MCF10A, T98G, U251MG |

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**MDPI and ACS Style**

Militello, C.; Rundo, L.; Minafra, L.; Cammarata, F.P.; Calvaruso, M.; Conti, V.; Russo, G.
MF2C3: Multi-Feature Fuzzy Clustering to Enhance Cell Colony Detection in Automated Clonogenic Assay Evaluation. *Symmetry* **2020**, *12*, 773.
https://doi.org/10.3390/sym12050773

**AMA Style**

Militello C, Rundo L, Minafra L, Cammarata FP, Calvaruso M, Conti V, Russo G.
MF2C3: Multi-Feature Fuzzy Clustering to Enhance Cell Colony Detection in Automated Clonogenic Assay Evaluation. *Symmetry*. 2020; 12(5):773.
https://doi.org/10.3390/sym12050773

**Chicago/Turabian Style**

Militello, Carmelo, Leonardo Rundo, Luigi Minafra, Francesco Paolo Cammarata, Marco Calvaruso, Vincenzo Conti, and Giorgio Russo.
2020. "MF2C3: Multi-Feature Fuzzy Clustering to Enhance Cell Colony Detection in Automated Clonogenic Assay Evaluation" *Symmetry* 12, no. 5: 773.
https://doi.org/10.3390/sym12050773