How important is tumour shape? Quantification of the epithelial-connective tissue interface in oral lesions using local connected fractal dimension analysis

Surgical margins in head and neck squamous cell carcinoma: A narrative review

Head and neck squamous cell carcinoma (HNSCC), a prevalent and frequently recurring malignancy, often necessitates surgical intervention. The surgical margin (SM) plays a pivotal role in determining the postoperative treatment strategy and prognostic evaluation of HNSCC. Nonetheless, the process of clinical appraisal and assessment of the SMs remains a complex and indeterminate endeavor, thereby leading to potential difficulties for surgeons in defining the extent of resection. In this regard, we undertake a comprehensive review of the suggested surgical distance in varying circumstances, diverse methods of margin evaluation, and the delicate balance that must be maintained between tissue resection and preservation in head and neck surgical procedures. This review is intended to provide surgeons with pragmatic guidance in selecting the most suitable resection techniques, and in improving patients' quality of life by achieving optimal functional and aesthetic restoration.

Interfacial Organization and Forces Arising from Epithelial-Cancerous Monolayer Interactions

The interfacial interactions between epithelia and cancer cells have profound relevance for tumor development and metastasis. Through monolayer confrontation of MCF10A (nontumorigenic human breast epithelial cells) and MDA-MB-231 (human epithelial breast cancer cells) cells, we investigate the epithelial-cancerous interfacial interactions at the tissue level. We show that the monolayer interaction leads to competitive interfacial morphodynamics and drives an intricate spatial organization of MCF10A cells into multicellular finger-like structures, which further branch into multiple subfinger-like structures. These hierarchical interfacial structures penetrate the cancer monolayer and can spontaneously segregate or even envelop cancer cell clusters, consistent with our theoretical prediction. By tracking the substrate displacements via embedded fluorescent nanobeads and implementing nanomechanical modeling that combines atomic force microscopy and finite element simulations, we computed mechanical force patterns, including traction forces and monolayer stresses, caused by the monolayer interaction. It is found that the heterogeneous mechanical forces accumulated in the monolayers are able to squeeze cancer cells, leading to three-dimensional interfacial bulges or cell extrusion, initiating the p53 apoptosis signaling pathways of cancer cells. We reveal that intercellular E-cadherin and P-cadherin of epithelial cells differentially regulate the interfacial organization including migration speed, directionality, spatial correlation, F-actin alignment, and subcellular protrusions of MCF10A cells; whereas E-cadherin governs interfacial geometry that is relevant to force localization and cancer cell extrusion, P-cadherin maintains interfacial integrity that enables long-range force transmission. Our findings suggest that the collaborative molecular and mechanical behaviors are crucial for preventing epithelial tissues from undergoing tumor invasion.

Agent-based computational modeling of glioblastoma predicts that stromal density is central to oncolytic virus efficacy

Oncolytic viruses (OVs) are emerging cancer immunotherapy. Despite notable successes in the treatment of some tumors, OV therapy for central nervous system cancers has failed to show efficacy. We used an ex vivo tumor model developed from human glioblastoma tissue to evaluate the infiltration of herpes simplex OV rQNestin (oHSV-1) into glioblastoma tumors. We next leveraged our data to develop a computational, model of glioblastoma dynamics that accounts for cellular interactions within the tumor. Using our computational model, we found that low stromal density was highly predictive of oHSV-1 therapeutic success, suggesting that the efficacy of oHSV-1 in glioblastoma may be determined by stromal-to-tumor cell regional density. We validated these findings in heterogenous patient samples from brain metastatic adenocarcinoma. Our integrated modeling strategy can be applied to suggest mechanisms of therapeutic responses for central nervous system cancers and to facilitate the successful translation of OVs into the clinic.

Use of the Fractal Dimension to Differentiate Epithelium and Connective Tissue in Oral Leukoplakias

BACKGROUND

Oral leukoplakia (OL) is considered one of the most common potentially malignant oral disorders (OPMD), with a verified increased risk of developing oral cancer. The identification of the dysplasia grade (low-high) is the only consolidated factor used to evaluate this risk. The objective of this study was to verify the role of the fractal dimension (FD) in assessing this dysplasia.

METHODS

To begin, 29 OL and 10 normal oral mucosa (NOM) biopsies were retrieved for FD analysis of the epithelial (dime) and the connective (dimc) tissue.

RESULTS

In the OL group, the median value of dime is higher (1.67, IQR = 0.12) than for the NOM group (1.56, IQR = 0.08), with statistically significant differences (Wilcoxon test, p = 0.0031). There were no differences in relation to dimc. Significant differences were observed between the non-dysplasia vs. high-grade (p = 0.0156) and low-grade vs. high-grade (p = 0.0049) groups. No significant differences were identified in relation to dimc for the different degrees of dysplasia. For a cut-off point of 1.44 of dime, a specificity of 96.6% was obtained, a sensitivity of 100%, and an AUC = 0.819 (p = 0.003).

CONCLUSIONS

FD at the level of the epithelium may be used as a diagnostic tool in OL.

How Does a Tumor Get Its Shape? MicroRNAs Act as Morphogens at the Cancer Invasion Front

The generation and organization of the invasion front shape of neoplasms is an intriguing problem. The intimate mechanism is not yet understood, but the prevailing theory is that it represents an example of morphogenesis. Morphogenesis requires the presence of specific molecules, known as morphogens (activators and inhibitors), which can diffuse and elicit dose-dependent responses in their target cells. Due to their ability to modulate most of the coding transcriptome, their well-established role in embryogenesis, and their capacity to rapidly move between neighboring and distant cells, we propose microRNAs as inhibitors that could shape the cancer invasion front. In order to explain the genesis of the tumor border, we use Alan Turing’s reaction diffusion model, refined by Meinhardt and Gierer. This assumes the existence of an activator called a, and an inhibitor called h, which we hypothesize could be a freely moving microRNA. We used the fractal dimension as a measure of tumor border irregularity. We observed that the change in fractal dimension associates with variations in the diffusion coefficient of the activator (D_a) or the inhibitor (D_h). We determined that the fractal dimension remains constant (i.e., the irregularity of the tumor border does not change) across a D_h interval, which becomes narrower as D_a rises. We therefore conclude that a change in fractal dimension occurs when the balance between D_a and D_h is disrupted. Biologically, this could be explained by a faulty distribution of the inhibitor caused by an abnormal density of the intercellular connection network. From a translational perspective, if experimentally confirmed, our observations can be used for a better diagnosis of cancer aggressiveness.

EUS elastography (strain ratio) and fractal-based quantitative analysis for the diagnosis of solid pancreatic lesions

BACKGROUND AND AIMS

EUS elastography is useful in characterizing solid pancreatic lesions (SPLs), and fractal analysis-based technology has been used to evaluate geometric complexity in oncology. The aim of this study was to evaluate EUS elastography (strain ratio) and fractal analysis for the characterization of SPLs.

METHODS

Consecutive patients with SPLs were prospectively enrolled between December 2015 and February 2017. Elastographic evaluation included parenchymal strain ratio (pSR) and wall strain ratio (wSR) and was performed with a new compact US processor. Elastographic images were analyzed using a computer program to determine the 3-dimensional histogram fractal dimension. A composite cytology/histology/clinical reference standard was used to assess sensitivity, specificity, positive predictive value, negative predictive value, and area under the receiver operating curve.

RESULTS

Overall, 102 SPLs from 100 patients were studied. At final diagnosis, 69 (68%) were malignant and 33 benign. At elastography, both pSR and wSR appeared to be significantly higher in malignant as compared with benign SPLs (pSR, 24.5 vs 6.4 [P < .001]; wSR, 56.6 vs 15.3 [P < .001]). When the best cut-off levels of pSR and wSR at 9.10 and 16.2, respectively, were used, sensitivity, specificity, positive predictive value, negative predictive value, and area under the receiver operating curve were 88.4%, 78.8%, 89.7%, 76.9%, and 86.7% and 91.3%, 69.7%, 86.5%, 80%, and 85.7%, respectively. Fractal analysis showed a significant statistical difference (P = .0087) between the mean surface fractal dimension of malignant lesions (D = 2.66 ± .01) versus neuroendocrine tumor (D = 2.73 ± .03) and a statistical difference for all 3 channels red, green, and blue (P < .0001).

CONCLUSIONS

EUS elastography with pSR and fractal-based analysis are useful in characterizing SPLs. (Clinical trial registration number: NCT02855151.).

A model of the effects of cancer cell motility and cellular adhesion properties on tumour-immune dynamics

We present a three-dimensional model simulating the dynamics of an anti-cancer T-cell response against a small, avascular, early-stage tumour. Interactions at the tumour site are accounted for using an agent-based model (ABM), while immune cell dynamics in the lymph node are modelled as a system of delay differential equations (DDEs). We combine these separate approaches into a two-compartment hybrid ABM-DDE system to capture the T-cell response against the tumour. In the ABM at the tumour site, movement of tumour cells is modelled using effective physical forces with a specific focus on cell-to-cell adhesion properties and varying levels of tumour cell motility, thus taking into account the ability of cancer cells to spread and form clusters. We consider the effectiveness of the immune response over a range of parameters pertaining to tumour cell motility, cell-to-cell adhesion strength and growth rate. We also investigate the dependence of outcomes on the distribution of tumour cells. Low tumour cell motility is generally a good indicator for successful tumour eradication before relapse, while high motility leads, almost invariably, to relapse and tumour escape. In general, the effect of cell-to-cell adhesion on prognosis is dependent on the level of tumour cell motility, with an often unpredictable cross influence between adhesion and motility, which can lead to counterintuitive effects. In terms of overall tumour shape and structure, the spatial distribution of cancer cells in clusters of various sizes has shown to be strongly related to the likelihood of extinction.

On the morphological stability of multicellular tumour spheroids growing in porous media

Multicellular tumour spheroids (MCTSs) are extensively used as in vitro system models for investigating the avascular growth phase of solid tumours. In this work, we propose a continuous growth model of heterogeneous MCTSs within a porous material, taking into account a diffusing nutrient from the surrounding material directing both the proliferation rate and the mobility of tumour cells. At the time scale of interest, the MCTS behaves as an incompressible viscous fluid expanding inside a porous medium. The cell motion and proliferation rate are modelled using a non-convective chemotactic mass flux, driving the cell expansion in the direction of the external nutrients' source. At the early stages, the growth dynamics is derived by solving the quasi-stationary problem, obtaining an initial exponential growth followed by an almost linear regime, in accordance with experimental observations. We also perform a linear-stability analysis of the quasi-static solution in order to investigate the morphological stability of the radially symmetric growth pattern. We show that mechano-biological cues, as well as geometric effects related to the size of the MCTS subdomains with respect to the diffusion length of the nutrient, can drive a morphological transition to fingered structures, thus triggering the formation of complex shapes that might promote tumour invasiveness. The results also point out the formation of a retrograde flow in the MCTS close to the regions where protrusions form, that could describe the initial dynamics of metastasis detachment from the in vivo tumour mass. In conclusion, the results of the proposed model demonstrate that the integration of mathematical tools in biological research could be crucial for better understanding the tumour's ability to invade its host environment.

Angiographic Structural Differentiation between Native Arteriogenesis and Therapeutic Synangiosis in Intracranial Arterial Steno-Occlusive Disease

BACKGROUND AND PURPOSE

Encephaloduroarteriosynangiosis has been shown to generate collateral vessels from the extracranial-to-intracranial circulation in patients with Moyamoya disease and intracranial arterial steno-occlusive disease. The mechanisms involved are not well-understood. We hypothesized that angiogenesis is the leading mechanism forming collaterals after encephaloduroarteriosynangiosis because there are no pre-existing connections. Angiogenesis-generated collaterals should exhibit higher architectural complexity compared with innate collaterals.

MATERIALS AND METHODS

Pre- and postoperative digital subtraction angiograms were analyzed in patients enrolled in a prospective trial of encephaloduroarteriosynangiosis surgery. Branching angioscore, tortuosity index, and local connected fractal dimension were compared between innate and postoperative collaterals.

RESULTS

One hundred one angiograms (50 preoperative, 51 postoperative) were analyzed from 44 patients (22 with intracranial atherosclerosis and 22 with Moyamoya disease). There was a significantly higher median branching angioscore (13 versus 4, P < .001) and a lower median tortuosity index (1.08 versus 1.76, P < .001) in the encephaloduroarteriosynangiosis collaterals compared with innate collaterals. Higher mean local fractal dimension peaks (1.28 ± 0.1 versus 1.16 ± 0.11, P < .001) were observed in the encephaloduroarteriosynangiosis collaterals compared with innate collaterals for both intracranial atherosclerosis (P < .001) and Moyamoya disease (P < .001) groups. The observed increase in high connectivity was greater in the intracranial atherosclerosis group compared with patients with Moyamoya disease (P = .01).

CONCLUSIONS

The higher median branching angioscore and local connected fractal dimension, along with the lower median tortuosity index of encephaloduroarteriosynangiosis collaterals, are consistent with the greater complexity observed in the process of sprouting and splitting associated with angiogenesis.

Nuclear Fractal Dimensions as a Tool for Prognostication of Oral Squamous Cell Carcinoma

BACKGROUND

Carcinogenesis follows complex molecular alterations, which are triggered by subtle chromatin architectural changes that are imperceptible to the human eye. As the treatment decisions in Oral Squamous Cell Carcinoma (OSCC) are hindered by the imprecise clinical stage determination and inter-observer variability in histological grading, focus in recent years has shifted to discovering identifiers related to neoplastic cell morphology studied through computer-aided image analysis. One such approach is the assessment of fractal geometry, a technique first described by Mandelbrot, which aids in precise assessment of architecture of natural objects. Assessment and quantification of degree of complexity of these fractal objects (self-similarities in structural complexity at different magnifying scales) is described as fractal dimension (FD).

AIM

To evaluate the nuclear fractal dimension (NFD) in OSCC using computer-aided image analysis.

MATERIALS AND METHODS

Histological sections of 14 selected cases of Oral Squamous Cell Carcinoma (OSCC) and 6 samples of normal buccal mucosa (as control) were stained with Haematoxylin-Eosin and Feulgen stain for histopathological examination and evaluation of nuclear complexity respectively. Fifteen HPF at Invasive Tumour Front (ITF) and Tumour Proper (TP) of Feulgen-stained sections were selected and photographed in test and control samples. At ITF, TP and normal buccal mucosa 200 nuclei each were selected and analyzed using Image J software to quantify FD. The test and control groups were compared statistically using Independent sample t-test and One-way ANOVA.

RESULTS

Nuclear FD increased progressively towards worst tumour staging as compared to normal buccal mucosa.

CONCLUSION

Nuclear FD can be considered for quantification of nuclear architectural changes as a prognostic indicator in OSCC.

Fractal dimension and lacunarity of tumor microscopic images as prognostic indicators of clinical outcome in early breast cancer

AIM

Research in the field of breast cancer outcome prognosis has been focused on molecular biomarkers, while neglecting the discovery of novel tumor histology structural clues. We thus aimed to improve breast cancer prognosis by fractal analysis of tumor histomorphology.

PATIENTS & METHODS

This retrospective study included 92 breast cancer patients without systemic treatment.

RESULTS

Fractal dimension and lacunarity of the breast tumor microscopic histology possess prognostic value comparable to the major clinicopathological prognostic parameters.

CONCLUSION

Fractal analysis was performed for the first time on routinely produced archived pan-tissue stained primary breast tumor sections, indicating its potential for clinical use as a simple and cost-effective prognostic indicator of distant metastasis risk to complement the molecular approaches for cancer risk prognosis.

Wavelet-based 3D reconstruction of microcalcification clusters from two mammographic views: new evidence that fractal tumors are malignant and Euclidean tumors are benign

The 2D Wavelet-Transform Modulus Maxima (WTMM) method was used to detect microcalcifications (MC) in human breast tissue seen in mammograms and to characterize the fractal geometry of benign and malignant MC clusters. This was done in the context of a preliminary analysis of a small dataset, via a novel way to partition the wavelet-transform space-scale skeleton. For the first time, the estimated 3D fractal structure of a breast lesion was inferred by pairing the information from two separate 2D projected mammographic views of the same breast, i.e. the cranial-caudal (CC) and mediolateral-oblique (MLO) views. As a novelty, we define the “CC-MLO fractal dimension plot”, where a “fractal zone” and “Euclidean zones” (non-fractal) are defined. 118 images (59 cases, 25 malignant and 34 benign) obtained from a digital databank of mammograms with known radiologist diagnostics were analyzed to determine which cases would be plotted in the fractal zone and which cases would fall in the Euclidean zones. 92% of malignant breast lesions studied (23 out of 25 cases) were in the fractal zone while 88% of the benign lesions were in the Euclidean zones (30 out of 34 cases). Furthermore, a Bayesian statistical analysis shows that, with 95% credibility, the probability that fractal breast lesions are malignant is between 74% and 98%. Alternatively, with 95% credibility, the probability that Euclidean breast lesions are benign is between 76% and 96%. These results support the notion that the fractal structure of malignant tumors is more likely to be associated with an invasive behavior into the surrounding tissue compared to the less invasive, Euclidean structure of benign tumors. Finally, based on indirect 3D reconstructions from the 2D views, we conjecture that all breast tumors considered in this study, benign and malignant, fractal or Euclidean, restrict their growth to 2-dimensional manifolds within the breast tissue.

Fractal analysis in a systems biology approach to cancer

Cancer is a highly complex disease due to the disruption of tissue architecture. Thus, tissues, and not individual cells, are the proper level of observation for the study of carcinogenesis. This paradigm shift from a reductionist approach to a systems biology approach is long overdue. Indeed, cell phenotypes are emergent modes arising through collective non-linear interactions among different cellular and microenvironmental components, generally described by "phase space diagrams", where stable states (attractors) are embedded into a landscape model. Within this framework, cell states and cell transitions are generally conceived as mainly specified by gene-regulatory networks. However, the system's dynamics is not reducible to the integrated functioning of the genome-proteome network alone; the epithelia-stroma interacting system must be taken into consideration in order to give a more comprehensive picture. Given that cell shape represents the spatial geometric configuration acquired as a result of the integrated set of cellular and environmental cues, we posit that fractal-shape parameters represent "omics" descriptors of the epithelium-stroma system. Within this framework, function appears to follow form, and not the other way around.

A systems biology approach to cancer: fractals, attractors, and nonlinear dynamics

Cancer begins to be recognized as a highly complex disease, and advanced knowledge of the carcinogenic process claims to be acquired by means of supragenomic strategies. Experimental data evidence that tumor emerges from disruption of tissue architecture, and it is therefore consequential that the tissue level should be considered the proper level of observation for carcinogenic studies. This paradigm shift imposes to move from a reductionistic to a systems biology approach. Indeed, cell phenotypes are emergent modes arising through collective nonlinear interactions among different cellular and microenvironmental components, generally described by a phase space diagram, where stable states (attractors) are embedded into a landscape model. Within this framework cell states and cell transitions are generally conceived as mainly specified by the gene-regulatory network. However, the system's dynamics cannot be reduced to only the integrated functioning of the genome-proteome network, and the cell-stroma interacting system must be taken into consideration in order to give a more reliable picture. As cell form represents the spatial geometric configuration shaped by an integrated set of cellular and environmental cues participating in biological functions control, it is conceivable that fractal-shape parameters could be considered as "omics" descriptors of the cell-stroma system. Within this framework it seems that function follows form, and not the other way around.

An off-lattice hybrid discrete-continuum model of tumor growth and invasion

We have developed an off-lattice hybrid discrete-continuum (OLHDC) model of tumor growth and invasion. The continuum part of the OLHDC model describes microenvironmental components such as matrix-degrading enzymes, nutrients or oxygen, and extracellular matrix (ECM) concentrations, whereas the discrete portion represents individual cell behavior such as cell cycle, cell-cell, and cell-ECM interactions and cell motility by the often-used persistent random walk, which can be depicted by the Langevin equation. Using this framework of the OLHDC model, we develop a phenomenologically realistic and bio/physically relevant model that encompasses the experimentally observed superdiffusive behavior (at short times) of mammalian cells. When systemic simulations based on the OLHDC model are performed, tumor growth and its morphology are found to be strongly affected by cell-cell adhesion and haptotaxis. There is a combination of the strength of cell-cell adhesion and haptotaxis in which fingerlike shapes, characteristic of invasive tumor, are observed.

A systems biology approach to invasive behavior: comparing cancer metastasis and suburban sprawl development

Background

Despite constant progress, cancer remains the second leading cause of death in the United States. The ability of tumors to metastasize is central to this dilemma, as many studies demonstrate successful treatment correlating to diagnosis prior to cancer spread. Hence a better understanding of cancer invasiveness and metastasis could provide critical insight.

Presentation of the hypothesis

We hypothesize that a systems biology-based comparison of cancer invasiveness and suburban sprawl will reveal similarities that are instructive.

Testing the hypothesis

We compare the structure and behavior of invasive cancer to suburban sprawl development. While these two systems differ vastly in dimension, they appear to adhere to scale-invariant laws consistent with invasive behavior in general. We demonstrate that cancer and sprawl have striking similarities in their natural history, initiating factors, patterns of invasion, vessel distribution and even methods of causing death.

Implications of the hypothesis

We propose that metastatic cancer and suburban sprawl provide striking analogs in invasive behavior, to the extent that conclusions from one system could be predictive of behavior in the other. We suggest ways in which this model could be used to advance our understanding of cancer biology and treatment.

Vascular fractal dimension and total vascular area in the study of oral cancer

BACKGROUND

Microvessel quantification has been studied extensively as a factor reflecting angiogenesis in various malignant tumors. The aim of our study was to evaluate the vascular fractal dimension and the immunohistochemically positive total vascular area in oral cavity carcinomas in order to assess their potential value as factors reflecting angiogenesis.

METHODS

Histologic sections from 48 carcinomas and 17 nonmalignant mucosa specimens were evaluated by image analysis using fractal analysis software. Total vascular area was also quantified.

RESULTS

Carcinomas presented higher mean values of vascular fractal dimension and total vascular area compared to normal mucosa. The difference for the vascular fractal dimension was statistically significant.

CONCLUSIONS

This study provides evidence that vascular fractal dimension could be used as a reliable factor reflecting angiogenesis in oral squamous cell carcinoma and that there are several statistically significant correlations among total vascular area, vascular fractal dimension, nuclear size, and clinicopathologic factors.

Fractal dimension as a quantitator of the microvasculature of normal and adenomatous pituitary tissue

It is well known that angiogenesis is a complex process that accompanies neoplastic growth, but pituitary tumours are less vascularized than normal pituitary glands. Several analytical methods aimed at quantifying the vascular system in two-dimensional histological sections have been proposed, with very discordant results. In this study we investigated the non-Euclidean geometrical complexity of the two-dimensional microvasculature of normal pituitary glands and pituitary adenomas by quantifying the surface fractal dimension that measures its space-filling property. We found a statistical significant difference between the mean vascular surface fractal dimension estimated in normal versus adenomatous tissues (P = 0.01), normal versus secreting adenomatous tissues (P = 0.0003), and normal versus non-secreting adenomatous tissues (P = 0.047), whereas the difference between the secreting and non-secreting adenomatous tissues was not statistically significant. This study provides the first demonstration that fractal dimension is an objective and valid quantitator of the two-dimensional geometrical complexity of the pituitary gland microvascular network in physiological and pathological states. Further studies are needed to compare the vascular surface fractal dimension estimates in different subtypes of pituitary tumours and correlate them with clinical parameters in order to evaluate whether the distribution pattern of vascular growth is related to a particular state of the pituitary gland.

Nuclear fractal dimension as a prognostic factor in oral squamous cell carcinoma

Strong theoretical reasons exist for using fractal geometry in measurements of natural objects, including most objects studied in pathology. Indeed, fractal dimension provides a more precise and theoretically more appropriate approximation of their structure properties and especially their shape complexity. The aim of our study was to evaluate the nuclear fractal dimension (FD) in tissue specimens from patients with oral cavity carcinomas in order to assess its potential value as prognostic factor. Relationships between FD and other factors including clinicopathologic characteristics were also investigated. Histological sections from 48 oral squamous cell carcinomas as well as from 17 non-malignant mucosa specimens were stained with Hematoxylin-Eosin for pathological examination and with Feulgen for nuclear complexity evaluation. The sections were evaluated by image analysis using fractal analysis software to quantify nuclear FD by the box-counting method. Carcinomas presented higher mean values of FD compared to normal mucosa. Well differentiated neoplasms had lower FD values than poorly differentiated ones. FD was significantly correlated with the nuclear size. Patients with FD lower than the median value of the sample had statistically significant higher survival rates. Within the sample of patients studied, FD was proved to be an independent prognostic factor of survival in oral cancer patients. In addition this study provides evidence that there are several statistically significant correlations between FD and other morphometric characteristics or clinicopathologic factors in oral squamous cell carcinomas.

Computer simulation of the influence of cellular adhesion on the morphology of the interface between tissues of proliferating and quiescent cells

We investigate the influence of cellular adhesion on the morphology of the interface between a tissue of proliferating and quiescent cells using the cellular Potts model. We show that a decrease in surface tension changes the morphology of the interface and that only for negative surface tensions cell detachment from the proliferative tissue occurs suggesting that this might be a necessary condition for metastatization in malignant neoplasies.

Quantification of the global and local complexity of the epithelial-connective tissue interface of normal, dysplastic, and neoplastic oral mucosae using digital imaging

This study aimed at quantifying the complexity of the epithelial-connective tissue interface (ECTI) in human normal mucosa, premalignant, and malignant lesions using fractal geometry. Two approaches were used to describe the complexity of 377 oral mucosa ECTI profiles. The box counting method was used to estimate their global fractal dimension, while local fractal dimensions were estimated using the mass radius relation at various local scales. The ECTI complexity significantly increased from normal through premalignant to malignant profiles in both global and local (over 283 microm) scales. Normal mucosa samples from different sites of the oral cavity also had different degrees of global complexity. Fractal geometry is a useful morphological marker of tissue complexity changes taking place during epithelial malignancy and premalignancy, and we propose it as a quantitative marker of epithelial complexity.

Analysis of nerve fibers and their distribution in histologic sections of the human brain

The field of quantitative analysis and subsequent mapping of the cerebral cortex has developed rapidly. New powerful tools have been applied to investigate large regions of complex folded gyrencephalic cortices in order to detect structural transition regions that might partition different cortical fields of disjunct neuronal functions. We have developed a new mapping approach based on axoarchitectonics, a method of cortical visualization that previously has been used only indirectly with regard to myeloarchitectonics. Myeloarchitectonic visualization has the disadvantage of producing strong agglomerative effects of closely neighbored nerve fibers. Therefore, single and neurofunctional-relevant parameters such as axonal branchings, axon areas, and axon numbers have not been determinable with satisfying precision. As a result, different staining techniques had to be explored in order to achieve a suitable histologic staining for axon visualization. The best results were obtained after modifying the Naoumenko-Feigin staining for axons. From these contrast-rich stained histologic sections, videomicroscopic digital image tiles were generated and analyzed using a new fiber analysis framework. Finally, the analysis of histologic images provided topologic ordered parameters of axons that were transferred into parameter maps. The axon parameter maps were analyzed further via a recently developed traverse generating algorithm that calculated test lines oriented perpendicular to the cortical surface and white matter border. The gray value coded parameters of the parameter maps were then transferred into profile arrays. These profile arrays were statistically analyzed by a reliable excess mass approach we recently developed. We found that specific axonal parameters are preferentially distributed throughout granular and agranular types of cortex. Furthermore, our new procedure detected transition regions originally defined by changes of cytoarchitectonic layering. Statistically significant inhomogeneities of the distribution of certain axon quantities were shown to indicate a subparcellation of areas 4 and 6. The quantification techniques established here for the analysis of spatial axon distributions within larger regions of the cerebral cortex are suitable to detect inhomogeneities of laminar axon patterns. Hence, these techniques can be recommended for systematic and observer-supported cortical area mapping and parcellation studies.

Architectural analysis of oral cancer, dysplastic, and normal epithelia

BACKGROUND

We present a novel, automated, and quantitative approach to evaluate local epithelial tissue architecture based on mathematical graph theory.

METHODS

Four hundred forty-one images of three diagnostic classes of oral epithelium (normal, dysplastic, and neoplastic) were analysed. The epithelial compartment was partitioned into exclusive areas associated with each nucleus to approach the theoretical cell extents. The spatial arrangement of cells in neighbourhoods of two sizes was characterised by constructing graph networks based on the cell centroids and recording 29 statistical properties. We analysed 104,627 and 67,590 neighbourhoods of diameters 37.5 and 75 microm, respectively.

RESULTS

The discrimination power of the architectural descriptors was evaluated by using discriminant analysis. The best neighbourhood discrimination rate was 75% for normal versus carcinoma. For the pooled data, discrimination into three classes based on largest number of neighbourhoods associated with each class was 100% correct. Case-wise, discrimination rates were 67%, 100%, and 80% correct for normal, premalignant, and malignant. When considering two classes, discrimination rates was 89% (normal) and 100% (malignant) correct, with 71% of premalignant cases assigned to the malignant class.

CONCLUSIONS

The results indicate that unbiased and reproducible quantification of tissue architectural features is possible and may provide valuable morphological information for diagnostic purposes.

Characterization of ovarian nuclei with the parameter of power ratio

The nucleoli and chromatin clumps of ovarian cells contain important features in discriminating malignant cells from normal ones. In geometric properties, the ovarian nucleoli and chromatin clumps appear as irregularly shaped dark spots in the nuclear images from specimens immunohistochemically stained with antibody to Mib-1. Malignant cells often have more active and larger nucleoli and chromatin clumps. However, estimating the size of the nucleoli or chromatin clumps is a difficult task since it is not easy to recognize and accurately separate the regions of nucleoli and chromatin clumps from the rest of the nuclei that are highly irregular and variant in contents and intensities. In this paper, we develop a method to derive a parameter called power ratio that is proportionally related to the size of nucleoli and chromatin clumps based on an ideal nuclear model without the region segmentation of nucleoli or chromatin clumps. Results of characterization of the parameter and comparison between malignant and normal cells are provided.

Short-term rhythmic proliferation of human breast cancer cell lines: surface effects and fractal growth patterns

Kinetic studies of cell proliferation rates shed light on the growth dynamics of cancer. Most such studies are based on measurements of cell numbers that were evaluated in time intervals of about 12 h. Studies of the initial tumour growth with short measuring intervals are rare. This study was therefore designed with 1 h measuring intervals over a 24 h period. Human breast cancer cell lines (ZR-75-1, SK-BR-3, MCF-7) and a benign cell line (HBL-100) were used to study the hourly thymidine uptake as a measure of cells in synthesis. In parallel experiments, the same cell lines were also exposed to tumour necrosis factor alpha (TNF-alpha) to explore the effect of an apoptosis-inducing substance on initial tumour growth kinetics. In time-evolution plots, there was an oscillation of the labelling index of thymidine uptake for all investigated cell lines, with and without TNF-alpha. Based on the results obtained, a mathematical model was developed mimicking the real experiment. To describe the system dynamically a cellular automaton model was studied. The growth kinetics revealed by the simulation were in accordance with our experimental data. Two- and three-dimensional growth simulations of this computer model yielded objects morphologically similar to real images of human breast cancer. Almost identical fractal dimensions of the virtual and real tumours further supported this visual similarity. The cellular automata models could, therefore, be seen as a bridge towards realistic in vivo scenarios. From a clinical point of view, the results obtained may be applicable not only to primary tumours, but even to tumour cell microfoci and small metastases, which are a major concern in early metastasizing tumours such as breast cancer.

Increased fractal complexity of the epithelial-connective tissue interface in the tongue of 4NQO-treated rats

The effect of the carcinogen 4-nitroquinoline 1-oxide (0.001% in drinking water) on the irregularity of the epithelial connective tissue interface (ECTI) of the ventral surface of the tongue was quantified in Dark Agouti and Wistar Furth rats. Histological tongue sections stained with the Azan-Mallory method were digitised (111 images, resolution 1 pixel = 3.1 microns), and the limit between epithelium and stroma of the ventral surface was extracted and analysed using a fractal geometry technique (local connected dimension). The results showed that although none of the images included carcinomas on the ventral surface of the tongue (all cases had other oral carcinomas), the epithelial profiles of the treated cases showed a statistically significant increase in irregularity when compared to controls. Canonical discriminant analysis of the parameters describing the irregularity of the ECTI classified 81.1% of the images in the original groups (treated or control). Fractal analysis is capable of detecting subtle architectural changes in the oral epithelium of the rat occurring after exposure to the carcinogen, even when full malignant transformation has not yet taken place. Fractal analysis, which may prove useful for monitoring the progression of carcinogenesis in this animal model, is a morphometrical parameter in the diagnosis of oral epithelial dysplasia.

Fractal analysis: an objective method for identifying atypical nuclei in dysplastic lesions of the cervix uteri

OBJECTIVES

Fractal geometry is a tool used to characterize irregularly shaped and complex figures. It can be used not only to generate biological structures (e.g., the human renal artery tree), but also to derive parameters such as the fractal dimension in order to quantify the shapes of structures. As such, it allows user-independent evaluation and does not rely on the experience level of the examiner.

METHODS

We applied a box-counting algorithm to determine the fractal dimension of atypical nuclei in dysplastic cervical epithelium. An automatic algorithm was used to determine the fractal dimension of nuclei in order to prevent errors from manual segmentation. Four groups of patients (CIN 1-3 and control) with 10 subjects each were examined. In total, the fractal dimensions of 1200 nuclei were calculated.

RESULTS

We found that the fractal dimensions of the nuclei increased as the degree of dysplasia increased. There were significant differences between control and atypical nuclei found by an analysis of variance. Atypical nuclei associated with CIN 1, CIN 2, and CIN 3 also differed significantly among these groups.

CONCLUSION

We conclude that the fractal dimension is a valuable tool for detecting irregularities in atypical nuclei of the cervix uteri and thus allows objective nuclear grading.

Chaodynamic loss of complexity and self-similarity in cancer

'Omnis cellula a cellula': each cell descends from another cell--and most complex organ structures are built up of multiple cells at least. Even the underlying mechanisms of physiological as well as pathological processes reflect complexity in a pronounced manner. Loss of complexity, however, has been detected in aging and apparently also in the case of a number of diseases. This paper describes the loss of complexity in both carcinogenesis and the related growth pattern of cancer. After disruption of the cell's stability as a result of mutations, a decrease in the ability of the cell to induce a self-organized response is associated with the loss of control parameters at the cellular and molecular level. Complexity, understood as a principle of order, is altered in certain malignant tumors, as is indicated by a loss of the golden mean and by the disappearance of self-similarity. The lack of self-similarity could, therefore, be an ideal practical marker of malignancy in medical image analysis.

Fractal characterization of chromatin appearance for diagnosis in breast cytology

This study explores the use of fractal analysis in the numerical description of chromatin appearance in breast cytology. Images of nuclei from fine-needle aspiration biopsies of the breast are characterized in terms of their Minkowski and spectral fractal dimensions, for 19 patients with benign epithelial cell lesions and 22 with invasive ductal carcinomas. Chromatin appearance in breast epithelial cell nuclear images is demonstrated to be fractal, suggesting that the three-dimensional chromatin structure in these cells also has fractal properties. A statistically significant difference between the mean spectral dimensions of the benign and malignant cases is demonstrated. The two fractal dimensions are very weakly correlated. A statistically significant difference between the benign and malignant cases in lacunarity, a fractal property characterizing the size of holes or gaps in a texture, is found over a wide range of scales. These differences are particularly pronounced at the smallest and largest scales, corresponding respectively to fine-scale texture, indicating whether chromatin is clumped or fine, and to large-scale structures like nucleoli. Logistic regression and artificial neural network classification models are developed to classify unknown cases on the basis of fractal measures of chromatin texture. Using leave-one-out cross-validation, the best logistic regression classifier correctly diagnoses 95.1 per cent of the cases. The best neural network model can correctly classify all of the cases, but it is unclear whether this is due to overtraining. Fractal dimensions and lacunarity are useful tools for the quantitative characterization of chromatin appearance, and can potentially be incorporated into image analysis devices to assure the quality and reproducibility of diagnosis by breast fine-needle aspiration biopsy.

Fractals in pathology

Many natural objects, including most objects studied in pathology, have complex structural characteristics and the complexity of their structures, for example the degree of branching of vessels or the irregularity of a tumour boundary, remains at a constant level over a wide range of magnifications. These structures also have patterns that repeat themselves at different magnifications, a property known as scaling self-similarity. This has important implications for measurement of parameters such as length and area, since Euclidean measurements of these may be invalid. The fractal system of geometry overcomes the limitations of the Euclidean geometry for such objects and measurement of the fractal dimension gives an index of their space-filling properties. The fractal dimension may be measured using image analysis systems and the box-counting, divider (perimeter-stepping) and pixel dilation methods have all been described in the published literature. Fractal analysis has found applications in the detection of coding of coding regions in DNA and measurement of the space-filling properties of tumours, blood vessels and neurones. Fractal concepts have also been usefully incorporated into models of biological processes, including epithelial cell growth, blood vessel growth, periodontal disease and viral infections.