Fractal dimensions of breast lesions on cytology smears

An image analysis approach to characterize micronuclei differences in different subtypes of breast cancer

BACKGROUND

Micronuclei (MN) have been used as screening, diagnostic and prognostic markers in multiple cancer types, including breast cancer (BC). However, the question that the MN present in all subtypes of BC are similar or different remains unanswered. We thus hypothesized that MN present in different subtypes of BC may differ in their contents which may be visible as differences in their morphologic and morphometric features. This study was thus carried out with the aim to identify the differences between MN morphometry, complexity, and texture in different subtypes of BC, such as estrogen and progesterone receptor-positive (ER+/PR+; MCF-7, T-47D), human epidermal growth factor receptor-positive (Her2 +;SKBR3) and triple-negative BC (TNBC; MDA-MB-231, MDA-MB-468) cell lines (CLs) by ImageJ software.

METHODS

For analysis of MN dimensions, MN irregularity, and texture, we used morphometry and two mathematical computer-assisted algorithms, i.e., fractal dimension (FD) and grey level co-occurrence matrix (GLCM) of ImageJ software.

RESULTS

MN area and perimeter values showed differences in the size of MN in different subtypes of BC, with the largest MN in TNBC CLs. GLCM parameters (entropy, angular second moment, inverse difference moment, contrast, and correlation) showed highly heterogenous texture in case of TNBC MN as compared to the others. FD analysis also revealed more complexity and irregularity in MN found in TNBC cells.

CONCLUSION

The study for the first time showed morphometric, architectural and texture related differences amongst MN present in different subtypes of BC. The above may reflect differences in their composition and contents. Further, these differences may point towards the distinct mechanisms involved in the formation of MN in different subtypes of BC that need to be explored further.

The Fractal and GLCM Textural Parameters of Chromatin May Be Potential Biomarkers of Papillary Thyroid Carcinoma in Hashimoto's Thyroiditis Specimens

Occasionally, Hashimoto's thyroiditis (HT) and papillary thyroid carcinoma (PTC) share similar nuclear features. The current study aims to quantify the differences between the investigated specimens of HT-associated PTC versus the HT alone, to reduce the subjective experience of an observer, by the use of fractal parameters as well as gray-level co-occurrence matrix (GLCM) textural parameters. We have analyzed 250 segmented nuclei per group (nn = 25 per patient and np = 10 patients per group) using the ImageJ software (NIH, Bethesda, MD, USA) as well as an in-house written code for the GLCM analysis. The mean values of parameters were calculated for each patient. The results demonstrated that the malignant cells from the HT-associated PTC specimens showed lower chromatin fractal dimension (p = 0.0321) and higher lacunarity (p = 0.0038) compared with the corresponding cells from the HT specimens. Also, there was a statistically significant difference between the investigated specimens, in the contrast, correlation, angular second moment, and homogeneity, of the GLCM corresponding to the visual texture of follicular cell chromatin. The differences in chromatin fractal and GLCM parameters could be integrated with other diagnostic methods for the improved evaluation of distinctive features of the HT-associated PTC versus the HT in cytology and surgical pathology specimens.

Fuzzy controller design for breast cancer treatment based on fractal dimension using breast thermograms

In this study, three non-linear indices consist of compression, one-dimensional (1D) and two-dimensional (2D) fractal dimensions are used for the determination of the malignancy or benignity of cancer tumours in breast thermograms. On the other hand, by developing the high-precision infrared cameras as well as new methods of image processing, biomedical thermography images have found a prominent position among the others. Furthermore, cancerous tissue can be affected by the laser. In this study, in order to treat the cancerous lesion identified by breast thermograms, the laser parameters are designed. The basis of controller designing is the obtained non-linear indices. If the indices are moved from the chaotic behaviour to normal condition, the treating tissue is going from cancerous to a healthy condition and the treatment process is completed. Radiation frequency and the energy density of laser are designed as two key elements in the cancer treatment. In this study, the type I and type II fuzzy controllers are employed for the control strategies. Using the proposed closed-loop control, the non-linear indices of the cancerous lesion will be reduced during the treatment process. The simulation results on two datasets of breast thermograms indicate the superiority of type II fuzzy controller.

The Goodness-of-fit of the Fractal Dimension as a Diagnostic Factor in Breast Cancer

A large number of studies have found that the fractal dimension increases with the progression towards pathological or more pathological states, but there are also studies that have demonstrated the opposite relationship. In this study, we calculate the nuclear box-counting fractal dimension of 109 malignant, 113 benign, and 80 normal isolated breast cells in order to investigate its possible diagnostic importance. We computed the fractal dimension and its goodness-of-fit (i.e., the r-squared value that describes how well the regression line fits the set of the measurements) for two different sets of box size lengths. The statistical analysis did not confirm an important diagnostic potential of the nuclear fractal dimension of isolated breast cells. However, the goodness-of-fit did display a diagnostic potential. The r-squared value may be able to serve as a complementary diagnostic parameter.

ARTIFICIAL INTELLIGENT SYSTEMS APPLICATION IN CERVICAL CANCER PATHOLOGICAL CELL IMAGE CLASSIFICATION SYSTEMS — A REVIEW

Cervical cancer cell images play an important part in diagnosing the cancer among the females worldwide. Existing noises, overlapping cells, mucus, blood and air artifacts in cervical cancer cell images makes their classification a hard task. It makes it difficult for both pathologists and intelligent systems to segment and classify them into normal, pre-cancerous and cancerous cells. However, true cell segmentation is needed for pathologists to make for accurate diagnosis. In this paper, a review of algorithms used for cervical cancer cell image classification is presented. This includes pre-processing steps (noise reduction and cell segmentation/without segmentation), feature extraction, and intelligent diagnosis systems and their evaluations. Finally, future research trends on cervical cell classification to achieve complete accuracy are described.

Multi-field-of-view framework for distinguishing tumor grade in ER+ breast cancer from entire histopathology slides

Modified Bloom-Richardson (mBR) grading is known to have prognostic value in breast cancer (BCa), yet its use in clinical practice has been limited by intra- and interobserver variability. The development of a computerized system to distinguish mBR grade from entire estrogen receptor-positive (ER+) BCa histopathology slides will help clinicians identify grading discrepancies and improve overall confidence in the diagnostic result. In this paper, we isolate salient image features characterizing tumor morphology and texture to differentiate entire hematoxylin and eosin (H and E) stained histopathology slides based on mBR grade. The features are used in conjunction with a novel multi-field-of-view (multi-FOV) classifier--a whole-slide classifier that extracts features from a multitude of FOVs of varying sizes--to identify important image features at different FOV sizes. Image features utilized include those related to the spatial arrangement of cancer nuclei (i.e., nuclear architecture) and the textural patterns within nuclei (i.e., nuclear texture). Using slides from 126 ER+ patients (46 low, 60 intermediate, and 20 high mBR grade), our grading system was able to distinguish low versus high, low versus intermediate, and intermediate versus high grade patients with area under curve values of 0.93, 0.72, and 0.74, respectively. Our results suggest that the multi-FOV classifier is able to 1) successfully discriminate low, medium, and high mBR grade and 2) identify specific image features at different FOV sizes that are important for distinguishing mBR grade in H and E stained ER+ BCa histology slides.

Morphometic analysis of TCGA glioblastoma multiforme

Background

Our goals are to develop a computational histopathology pipeline for characterizing tumor types that are being generated by The Cancer Genome Atlas (TCGA) for genomic association. TCGA is a national collaborative program where different tumor types are being collected, and each tumor is being characterized using a variety of genome-wide platforms. Here, we have developed a tumor-centric analytical pipeline to process tissue sections stained with hematoxylin and eosin (H&E) for visualization and cell-by-cell quantitative analysis. Thus far, analysis is limited to Glioblastoma Multiforme (GBM) and kidney renal clear cell carcinoma tissue sections. The final results are being distributed for subtyping and linking the histology sections to the genomic data.

Results

A computational pipeline has been designed to continuously update a local image database, with limited clinical information, from an NIH repository. Each image is partitioned into blocks, where each cell in the block is characterized through a multidimensional representation (e.g., nuclear size, cellularity). A subset of morphometric indices, representing potential underlying biological processes, can then be selected for subtyping and genomic association. Simultaneously, these subtypes can also be predictive of the outcome as a result of clinical treatments. Using the cellularity index and nuclear size, the computational pipeline has revealed five subtypes, and one subtype, corresponding to the extreme high cellularity, has shown to be a predictor of survival as a result of a more aggressive therapeutic regime. Further association of this subtype with the corresponding gene expression data has identified enrichment of (i) the immune response and AP-1 signaling pathways, and (ii) IFNG, TGFB1, PKC, Cytokine, and MAPK14 hubs.

Conclusion

While subtyping is often performed with genome-wide molecular data, we have shown that it can also be applied to categorizing histology sections. Accordingly, we have identified a subtype that is a predictor of the outcome as a result of a therapeutic regime. Computed representation has become publicly available through our Web site.

Application of fractal analysis to mammography

We report on a morphological study of 192 breast masses as seen in mammograms, with the aim of discrimination between benign masses and malignant tumors. From the contour of each mass, we computed the fractal dimension (FD) and a few shape factors, including compactness, fractional concavity, and spiculation index. We calculated FD using four different methods: the ruler and box-counting methods applied to each 2-dimensional (2D) contour and its 1-dimensional signature. The ANOVA test indicated statistically significant differences in the values of the various shape features between benign masses and malignant tumors. Analysis using receiver operating characteristics indicated the area under the curve, A(z), of up to 0.92 with the individual shape features. The combination of compactness, FD with the 2D ruler method, and the spiculation index resulted in the highest A(z) value of 0.93.

Fractal dimension of chromatin texture of squamous intraepithelial lesions of cervix

The aim of this study was to explore the role of fractal dimension (FD) of chromatin texture in routinely stained Papanicolaou's smears and to distinguish the different grades of cervical intraepithelial lesions and normal cervical cells. We selected 14 each cases of normal, low grade cervical intra epithelial lesions (LSIL), and high-grade cervical intra epithelial lesions (HSIL) of Papanicolaou's stained cervical smears. Fractal dimension of the pseudo three-dimensional grey image of the nuclear chromatin was measured in 140 nuclei of each group. Mean FD of the normal cases, LSIL cases, and HSIL cases were 2.4225 ± 0.06410, 2.5159 ± 0.03291, and 2.5905 ± 0.06840, respectively. ANOVA test showed significant differences of mean FD in all these three groups (P < 0.000). Fractal dimension of the chromatin texture is easy to perform and can be done in routinely stained Papanicolaou's smear. It is reproducible and gives valuable information about the chromatin texture of the nucleus. In future, this promising variable can be incorporated along with other image morphometric features for accurate classification of dysplastic cells in cervical smear.

Nuclear planimetry on the samples from cytologically overlapping proliferative breast lesions

Differentiation of low-grade breast carcinomas from fibroadenomas with atypia on fine-needle aspiration cytology material may sometimes be problematic. In some cytological samples of these lesions, both the nuclei of cells and patterns of cell clusters display substantial overlapping morphological characteristics. Nuclear morphometry on cytological material is suggested as an ancillary method for the differential diagnosis in many lesions, including breast tumors. Twenty-five cytological samples obtained from patients with breast lesions, which were histopathologically confirmed as grade I ductal carcinomas (n=10), tubular carcinomas (n=5), and fibroadenomas with atypia (n=10), were utilized in this study. Eight geometric features of about 2002 nuclei from these tumors were measured. Discriminant analysis was performed on this data set in order to test the correct classification based on the eight measured variables. Statistical analyses were carried out with two fundamentally different approaches: in the first one, the entire data from all measured nuclei were used for classification. In the second one, a subset of data representing the 10% most deviated values of variables was extracted from the entire dataset to simulate the "selective examination" performed during classical morphologic evaluation. When the entire data was used in discriminant analysis, the overall performance in the correct classification rate was found to be approximately 50%, which was considered an unacceptable value in routine diagnostic practice. In the subset of data constructed with our systematic and reproducible "selection bias", the overall performance of correct classification rate of the same discriminant model improved substantially to 97%. Morphologic examination is actually based on selection. The use of data obtained from all of the cells in morphometry, as previously used in nearly all of the statistical methods, may cause a masking effect in diagnostically important features. Morphometric studies may seem to be useless when this effect is not taken into account. However, with a systematic and reproducible selection of the values with a proper "bias", morphometry may provide some discriminatory information in overlapping lesions.

Fractal analysis of contours of breast masses in mammograms

Fractal analysis has been shown to be useful in image processing for characterizing shape and gray-scale complexity. Breast masses present shape and gray-scale characteristics that vary between benign masses and malignant tumors in mammograms. Limited studies have been conducted on the application of fractal analysis specifically for classifying breast masses based on shape. The fractal dimension of the contour of a mass may be computed either directly from the 2-dimensional (2D) contour or from a 1-dimensional (1D) signature derived from the contour. We present a study of four methods to compute the fractal dimension of the contours of breast masses, including the ruler method and the box counting method applied to 1D and 2D representations of the contours. The methods were applied to a data set of 111 contours of breast masses. Receiver operating characteristics (ROC) analysis was performed to assess and compare the performance of fractal dimension and four previously developed shape factors in the classification of breast masses as benign or malignant. Fractal dimension was observed to complement the other shape factors, in particular fractional concavity, in the representation of the complexity of the contours. The combination of fractal dimension with fractional concavity yielded the highest area (A ( z )) under the ROC curve of 0.93; the two measures, on their own, resulted in A ( z ) values of 0.89 and 0.88, respectively.

Conceptual and Practical Implications of Breast Tissue Geometry: Toward a More Effective, Less Toxic Therapy

Mathematics provides greater understanding of the complex process of tumorigenesis. Based on the Gompertzian phenomenon and the Norton-Simon hypothesis, enhanced cell kill can be obtained through a greater chemotherapy dose rate. Results from the 1995 Bonadonna et al. study and the CALGB/Intergroup C9741 study demonstrated that patients in the dose-dense arms had significantly longer disease-free survival and overall survival. Because of the demonstrated applicability of Gompertzian kinetics, attention has been turned to the etiology of the Gompertzian curve. Breast tumor dimensions, as with all tissue dimensions in biology, can be calculated by fractals. A less cell-dense tissue usually has a lower fractal dimension than a tissue with more cells (i.e., a higher cell density is usually due to a higher fractal dimension). Density is the number of cells divided by the tissue volume. When allowed to grow, the density of a tissue with a lower fractal dimension drops quickly. However, a tumor, since it has a higher fractal mass dimension, maintains a high density as it grows bigger, resulting in a more rapid growth rate and a larger final size. Fractal dimensions of infiltrating ductal adenocarcinomas of the breast are high (i.e., 2.98), which results in a very dense tissue compared with normal breast tissue (with a fractal dimension of about 2.25). As expected, the higher fractal dimension results in a high rate of growth. The reason for this high fractal dimension is that breast cancer can be considered as a conglomerate of many small Gompertzian tumors, each of which has a high cell density and hence ratio of mitosis to apoptosis. In mathematical terms, each component of the conglomerate can be considered a small metastasis in itself. Thus, the primary tumor is composed of multiple self-metastases that form around a seed from the tumor to itself. Conventional thinking is that cancers metastasize because they are large, but in fact it may be that they are large because they are self-metastatic. Many genes are associated with the biology of metastasis; these include: A) obligatory cancer genes (most of which regulate mitosis and mitotic rate); B) genes relating to self-metastasis and growth of tumors at local sites, conferring the ability to invade and grow with high cell density; and C) genes that relate to the ability of the cancer to metastasize to distant areas. Additionally, fibroblasts may send out abnormal growth signals causing abnormal breast tissue growth. Consequently, we are not only dealing with abnormal cancer cells, but also with the tissue that surrounds them, or the microenvironment, that is, the "Smith-Bissell" model. These new insights may lead us to change the thrust of our attack from genes involved in mitosis to those involved in metastasis, including metastasis to self, and to use and further improve dose-dense regimens.

Image analysis of irregularity of cluster shape in cytological diagnosis of breast tumors: Cluster analysis with 2D-fractal dimension

To establish diagnostic criteria using comparison of cell cluster shapes, between benign and malignant tumors, breast tumors demonstrating weak cellular atypia in low grade invasive ductal carcinoma (IDC) were compared. Fine-needle aspiration (FNA) specimens of breast tumors were obtained from 37 patients. Among these, 16 were histologically diagnosed as IDC low-grade and the other 21 as benign fibroadenoma (FA). For evaluation, we examined 740 clusters from these 37 FNA specimens. Nine image morphometric parameters were studied, including the cluster area, circumference, maximal length, maximal breadth, ratio of length to breadth, cluster roundness, cluster size, and the edge and distribution image fractal dimensions for cluster analysis. We evaluated the irregularity in cell cluster shape using fractal dimension analysis, and determined the correlation to cluster size. The irregularity in the IDC cluster shape was higher than that in the FA cluster shape. However, six cases (28.5%) of 21 FA clusters showed high fractal dimensions similar to those for IDC. The clusters were classified by cluster analysis into three types: IDC clusters, FA with irregular cluster shape, and FA with no irregular clusters. The average cell cluster area of the FA with irregular shape was found to be about three times larger than that of IDC clusters. When the differential diagnosis between IDC and FA is difficult, it is important to focus on irregularities in the shape and on overall size of the cell clusters. For accurate diagnosis, the cell cluster shape is as important as the individual cellular atypia.