Lung cancer-a fractal viewpoint

Recent Insights into the Roles of PEST-Containing Nuclear Protein

PEST-containing nuclear protein (PCNP), a short-lived small nuclear protein with 178 amino acids, is a nuclear protein containing two PEST sequences. PCNP is highly expressed in several malignant tumors such as cervical cancer, rectal cancer, and lung cancer. It is also associated with cell cycle regulation and the phosphoinositide 3-kinase/protein kinase B/mammalian target of rapamycin (PI3K/AKT/mTOR) and Wnt signaling pathways during tumor growth. The present article discuss how PCNP regulates the PI3K/AKT/mTOR and Wnt signaling pathways and related proteins, and the ubiquitination of PCNP regulates tumor cell cycle as well as the progress of the application of PCNP in the pathophysiology and treatment of colon cancer, human ovarian cancer, thyroid cancer, lung adenocarcinoma and oral squamous cell carcinoma. The main relevant articles were retrieved from PubMed, with keywords such as PEST-containing nuclear protein (PCNP), cancer (tumor), and signaling pathways as inclusion/exclusion criteria. Relevant references has been included and cited in the manuscript.

Study of association between corneal shape parameters and axial length elongation during orthokeratology using image-pro plus software

BACKGROUND

The aim was to validate the correlation between corneal shape parameters and axial length growth (ALG) during orthokeratology using Image-Pro Plus (IPP) 6.0 software.

METHODS

This retrospective study used medical records of myopic children aged 8-13 years (n = 104) undergoing orthokeratology. Their corneal topography and axial length were measured at baseline and subsequent follow-ups after lens wear. Corneal shape parameters, including the treatment zone (TZ) area, TZ diameter, TZ fractal dimension, TZ radius ratio, eccentric distance, pupil area, and pupillary peripheral steepened zone(PSZ) area, were measured using IPP software. The impact of corneal shape parameters at 3 months post-orthokeratology visit on 1.5-year ALG was evaluated using multivariate linear regression analysis.

RESULTS

ALG exhibited significant associations with age, TZ area, TZ diameter, TZ fractal dimension, and eccentric distance on univariate linear regression analysis. Multivariate regression analysis identified age, TZ area, and eccentric distance as significantly correlated with ALG (all P < 0.01), with eccentric distance showing the strongest correlation (β = -0.370). The regressive equation was y = 1.870 - 0.235a + 0.276b - 0.370c, where y represents ALG, a represents age, b represents TZ area, and c represents eccentric distance; R2 = 0.27). No significant relationships were observed between the TZ radius ratio, pupillary PSZ area, and ALG.

CONCLUSIONS

IPP software proves effective in capturing precise corneal shape parameters after orthokeratology. Eccentric distance, rather than age or the TZ area, significantly influences ALG retardation.

Use of fractals in determining the malignancy degree of lung nodules

Introduction

A Computer-Assisted Detection (CAD) System for classification into malignant-benign classes using CT images is proposed.

Methods

Two methods that use the fractal dimension (FD) as a measure of the lung nodule contour irregularities (Box counting and Power spectrum) were implemented. The LIDC-IDRI database was used for this study. Of these, 100 slices belonging to 100 patients were analyzed with both methods.

Results

The performance between both methods was similar with an accuracy higher than 90%. Little overlap was obtained between FD ranges for the different malignancy grades with both methods, being slightly better in Power spectrum. Box counting had one more false positive than Power spectrum.

Discussion

Both methods are able to establish a boundary between the high and low malignancy degree. To further validate these results and enhance the performance of the CAD system, additional studies will be necessary.

Non-invasive differential diagnosis of teratomas from other intracranial germ cell tumours using MRI-based fractal and radiomic analyses

OBJECTIVES

The histologic subtype of intracranial germ cell tumours (IGCTs) is an important factor in deciding the treatment strategy, especially for teratomas. In this study, we aimed to non-invasively diagnose teratomas based on fractal and radiomic features.

MATERIALS AND METHODS

This retrospective study included 330 IGCT patients, including a discovery set (n = 296) and an independent validation set (n = 34). Fractal and radiomic features were extracted from T1-weighted, T2-weighted, and post-contrast T1-weighted images. Five classifiers, including logistic regression, random forests, support vector machines, K-nearest neighbours, and XGBoost, were compared for our task. Based on the optimal classifier, we compared the performance of clinical, fractal, and radiomic models and the model combining these features in predicting teratomas.

RESULTS

Among the diagnostic models, the fractal and radiomic models performed better than the clinical model. The final model that combined all the features showed the best performance, with an area under the curve, precision, sensitivity, and specificity of 0.946 [95% confidence interval (CI): 0.882-0.994], 95.65% (95% CI: 88.64-100%), 88.00% (95% CI: 77.78-96.36%), and 91.67% (95% CI: 78.26-100%), respectively, in the test set of the discovery set, and 0.944 (95% CI: 0.855-1.000), 85.71% (95% CI: 68.18-100%), 94.74% (95% CI: 83.33-100%), and 80.00% (95% CI: 58.33-100%), respectively, in the independent validation set. SHapley Additive exPlanations indicated that two fractal features, two radiomic features, and age were the top five features highly associated with the presence of teratomas.

CONCLUSION

The predictive model including image and clinical features could help guide treatment strategies for IGCTs.

CLINICAL RELEVANCE STATEMENT

Our machine learning model including image and clinical features can non-invasively predict teratoma components, which could help guide treatment strategies for intracranial germ cell tumours (IGCT).

KEY POINTS

• Fractals and radiomics can quantitatively evaluate imaging characteristics of intracranial germ cell tumours. • Model combing imaging and clinical features had the best predictive performance. • The diagnostic model could guide treatment strategies for intracranial germ cell tumours.

3D topographies promote macrophage M2d-Subset differentiation

In vitro cellular models denote a crucial part of drug discovery programs as they aid in identifying successful drug candidates based on their initial efficacy and potency. While tremendous headway has been achieved in improving 2D and 3D culture techniques, there is still a need for physiologically relevant systems that can mimic or alter cellular responses without the addition of external biochemical stimuli. A way forward to alter cellular responses is using physical cues, like 3D topographical inorganic substrates, to differentiate macrophage-like cells. Herein, protein secretion and gene expression markers for various macrophage subsets cultivated on a 3D topographical substrate are investigated. The results show that macrophages differentiate into anti-inflammatory M2-type macrophages, secreting increased IL-10 levels compared to the controls. Remarkably, these macrophage cells are differentiated into the M2d subset, making up the main component of tumour-associated macrophages (TAMs), as measured by upregulated Il-10 and Vegf mRNA. M2d subset differentiation is attributed to the topographical substrates with 3D fractal-like geometries arrayed over the surface, else primarily achieved by tumour-associated factors in vivo. From a broad perspective, this work paves the way for implementing 3D topographical inorganic surfaces for drug discovery programs, harnessing the advantages of in vitro assays without external stimulation and allowing the rapid characterisation of therapeutic modalities in physiologically relevant environments.

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.

Development of an invasion score based on metastasis-related pathway activity profiles for identifying invasive molecular subtypes of lung adenocarcinoma

The invasive capacity of lung adenocarcinoma (LUAD) is an important factor influencing patients' metastatic status and survival outcomes. However, there is still a lack of suitable biomarkers to evaluate tumor invasiveness. LUAD molecular subtypes were identified by unsupervised consistent clustering of LUAD. The differences in prognosis, tumor microenvironment (TME), and mutation were assessed among different subtypes. After that, the invasion-related gene score (IRGS) was constructed by genetic differential analysis, WGCNA analysis, and LASSO analysis, then we evaluated the relationship between IRGS and invasive characteristics, TME, and prognosis. The predictive ability of the IRGS was verified by in vitro experiments. Next, the "oncoPredict" R package and CMap were used to assess the potential value of IRGS in drug therapy. The results showed that LUAD was clustered into two molecular subtypes. And the C1 subtype exhibited a worse prognosis, higher stemness enrichment activity, less immune infiltration, and higher mutation frequency. Subsequently, IRGS developed based on molecular subtypes demonstrated a strong association with malignant characteristics such as invasive features, higher stemness scores, less immune infiltration, and worse survival. In vitro experiments showed that the higher IRGS LUAD cell had a stronger invasive capacity than the lower IRGS LUAD cell. Predictive analysis based on the "oncoPredict" R package showed that the high IRGS group was more sensitive to docetaxel, erlotinib, paclitaxel, and gefitinib. Among them, in vitro experiments verified the greater killing effect of paclitaxel on high IRGS cell lines. In addition, CMap showed that purvalanol-a, angiogenesis-inhibitor, and masitinib have potential therapeutic effects in the high IRGS group. In summary we identified and analyzed the molecular subtypes associated with the invasiveness of LUAD and developed IRGS that can efficiently predict the prognosis and invasive ability of the tumor. IRGS may be able to facilitate the precision treatment of LUAD to some extent.

Fractal Analysis in Neurodegenerative Diseases

Neurodegenerative diseases are defined by progressive nervous system dysfunction and death of neurons. The abnormal conformation and assembly of proteins is suggested to be the most probable cause for many of these neurodegenerative disorders, leading to the accumulation of abnormally aggregated proteins, for example, amyloid β (Aβ) (Alzheimer's disease and vascular dementia), tau protein (Alzheimer's disease and frontotemporal lobar degeneration), α-synuclein (Parkinson's disease and Lewy body dementia), polyglutamine expansion diseases (Huntington disease), or prion proteins (Creutzfeldt-Jakob disease). An aberrant gain-of-function mechanism toward excessive intraparenchymal accumulation thus represents a common pathogenic denominator in all these proteinopathies. Moreover, depending upon the predominant brain area involvement, these different neurodegenerative diseases lead to either movement disorders or dementia syndromes, although the underlying mechanism(s) can sometimes be very similar, and on other occasions, clinically similar syndromes can have quite distinct pathologies. Non-Euclidean image analysis approaches such as fractal dimension (FD) analysis have been applied extensively in quantifying highly variable morphopathological patterns, as well as many other connected biological processes; however, their application to understand and link abnormal proteinaceous depositions to other clinical and pathological features composing these syndromes is yet to be clarified. Thus, this short review aims to present the most important applications of FD in investigating the clinical-pathological spectrum of neurodegenerative diseases.

Network efficiency of spatial systems with fractal morphology: a geometric graphs approach

The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal morphology. Under a geometric graphs approach, we quantify the effectiveness of the exchange of information in the system from center to perimeter and over the entire network structure. We mainly consider two paradigmatic models of disordered fractal formation, the Ballistic Aggregation and Diffusion-Limited Aggregation models, and complementary, the Viscek and Hexaflake fractals, and Kagome and Hexagonal lattices. First, we show that complex tree morphologies provide important advantages over regular configurations, such as an invariant structural cost for different fractal dimensions. Furthermore, although these systems are known to be scale-free in space, they have bounded degree distributions for different values of an euclidean connectivity parameter and, therefore, do not represent ordinary scale-free networks. Finally, compared to regular structures, fractal trees are fragile and overall inefficient as expected, however, we show that this efficiency can become similar to that of a robust hexagonal lattice, at a similar cost, by just considering a very short euclidean connectivity beyond first neighbors.

Multifractality in Surface Potential for Cancer Diagnosis

Recent advances in high-resolution biomedical imaging have improved cancer diagnosis, focusing on morphological, electrical, and biochemical properties of cells and tissues, scaling from cell clusters down to the molecular level. Multiscale imaging revealed high complexity that requires advanced data processing methods of multifractal analysis. We performed label-free multiscale imaging of surface potential variations in human ovarian cancer cells using Kelvin probe force microscopy (KPFM). An improvement in the differentiation between nonmalignant and cancerous cells by multifractal analysis using adaptive versus median threshold for image binarization was demonstrated. The results reveal the multifractality of cancer cells as a new biomarker for cancer diagnosis.

Histologic Analysis of Idiopathic Pulmonary Fibrosis by Morphometric and Fractal Analysis

Idiopathic pulmonary fibrosis (IPF) is a chronic, progressive fibrotic lung disorder, ultimately leading to respiratory failure and death. Despite great research advances in understanding the mechanisms underlying the disease, its diagnosis, and its treatment, IPF still remains idiopathic without known biological or histological markers able to predict disease progression or response to treatment. The histologic hallmark of IPF is usual interstitial pneumonia (UIP), with its intricate architectural distortion and temporal inhomogeneity. We hypothesize that normal lung alveolar architecture can be compared to fractals, such as the Pythagoras tree with its fractal dimension (D_f), and every pathological insult, distorting the normal lung structure, could result in D_f variations. In this study, we aimed to assess the UIP histologic fractal dimension in relationship to other morphometric parameters in newly diagnosed IPF patients and its possible role in the prognostic stratification of the disease. Clinical data and lung tissue specimens were obtained from twelve patients with IPF, twelve patients with non-specific interstitial pneumonia (NSIP), and age-matched "healthy" control lung tissue from patients undergoing lung surgery for other causes. Histology and histomorphometry were performed to evaluate D_f and lacunarity measures, using the box counting method on the FracLac ImageJ plugin. The results showed that D_f was significantly higher in IPF patients compared to controls and fibrotic NSIP patients, indicating greater architectural distortion in IPF. Additionally, high D_f values were associated with higher fibroblastic foci density and worse prognostic outcomes in IPF, suggesting that D_f may serve as a potential novel prognostic marker for IPF. The scalability of D_f measurements was demonstrated through repeated measurements on smaller portions from the same surgical biopsies, which were selected to mimic a cryobiopsy. Our study provides further evidence to support the use of fractal morphometry as a tool for quantifying and determining lung tissue remodeling in IPF, and we demonstrated a significant correlation between histological and radiological D_f in UIP pattern, as well as a significant association between D_f and FF density. Furthermore, our study demonstrates the scalability and self-similarity of D_f measurements across different biopsy types, including surgical and smaller specimens.

Nanoscale Prognosis of Colorectal Cancer Metastasis from AFM Image Processing of Histological Sections

Early ascertainment of metastatic tumour phases is crucial to improve cancer survival, formulate an accurate prognostic report of disease advancement, and, most importantly, quantify the metastatic progression and malignancy state of primary cancer cells with a universal numerical indexing system. This work proposes an early improvement to metastatic cancer detection with 97.7 nm spatial resolution by indexing the metastatic cancer phases from the analysis of atomic force microscopy images of human colorectal cancer histological sections. The procedure applies variograms of residuals of Gaussian filtering and theta statistics of colorectal cancer tissue image settings. This methodology elucidates the early metastatic progression at the nanoscale level by setting metastatic indexes and critical thresholds based on relatively large histological sections and categorising the malignancy state of a few suspicious cells not identified with optical image analysis. In addition, we sought to detect early tiny morphological differentiations indicating potential cell transition from epithelial cell phenotypes of low metastatic potential to those of high metastatic potential. This metastatic differentiation, which is also identified in higher moments of variograms, sets different hierarchical levels for metastatic progression dynamics.

Fractal analysis of healthy and diseased vasculature in pediatric Moyamoya disease

BACKGROUND AND PURPOSE

Fractal dimension is an objective metric for the notion of structural complexity. We sought to investigate differences in structural complexity between healthy and affected territories of cerebral vasculature in moyamoya, as well as associated scalp vasculature and native transdural collaterals in patients with moyamoya by comparing their respective fractal dimensions.

METHODS

Our cohort consisted of 15 transdural collaterals from 12 patients with unilateral anterior circulation moyamoya. Frames of distal arterial vasculature from internal and external carotid angiograms were selected then automatically segmented and also manually annotated by a cerebrovascular surgeon. In the affected hemisphere, the region with transdural collateral supply was compared to the contralateral region. The resulting skeletonized angiograms were analyzed for their fractal dimensions.

RESULTS

We found the average fractal dimension (Df) of the moyamoya-side ICA was 1.82 with slightly different means for the anteroposterial (AP) and lateral views (mean  =  1.82; mean  =  1.81). The overall mean for healthy cerebral vasculature was also found to be 1.82 (AP: mean  =  1.83; lateral: mean  =  1.81). Mean Df of native transdural collaterals was found to be 1.82 (AP: mean  =  1.83; lateral: mean  =  1.81). The mean Df difference between autosegmented and manually segmented images was 0.013.

CONCLUSION

In accordance with the clinical understanding of moyamoya disease, the distal arterial structural complexity is not affected in moyamoya, and is maintained by transdural collaterals formed by vasculogenesis. Autosegmentation of cerebral vasculature is also shown to be accurate when compared to manual segmentation.

Neuron arbor geometry is sensitive to the limited-range fractal properties of their dendrites

Fractal geometry is a well-known model for capturing the multi-scaled complexity of many natural objects. By analyzing three-dimensional images of pyramidal neurons in the rat hippocampus CA1 region, we examine how the individual dendrites within the neuron arbor relate to the fractal properties of the arbor as a whole. We find that the dendrites reveal unexpectedly mild fractal characteristics quantified by a low fractal dimension. This is confirmed by comparing two fractal methods-a traditional "coastline" method and a novel method that examines the dendrites' tortuosity across multiple scales. This comparison also allows the dendrites' fractal geometry to be related to more traditional measures of their complexity. In contrast, the arbor's fractal characteristics are quantified by a much higher fractal dimension. Employing distorted neuron models that modify the dendritic patterns, deviations from natural dendrite behavior are found to induce large systematic changes in the arbor's structure and its connectivity within a neural network. We discuss how this sensitivity to dendrite fractality impacts neuron functionality in terms of balancing neuron connectivity with its operating costs. We also consider implications for applications focusing on deviations from natural behavior, including pathological conditions and investigations of neuron interactions with artificial surfaces in human implants.

Comparison of fractal and grid electrodes for studying the effects of spatial confinement on dissociated retinal neuronal and glial behavior

Understanding the impact of the geometry and material composition of electrodes on the survival and behavior of retinal cells is of importance for both fundamental cell studies and neuromodulation applications. We investigate how dissociated retinal cells from C57BL/6J mice interact with electrodes made of vertically-aligned carbon nanotubes grown on silicon dioxide substrates. We compare electrodes with different degrees of spatial confinement, specifically fractal and grid electrodes featuring connected and disconnected gaps between the electrodes, respectively. For both electrodes, we find that neuron processes predominantly accumulate on the electrode rather than the gap surfaces and that this behavior is strongest for the grid electrodes. However, the 'closed' character of the grid electrode gaps inhibits glia from covering the gap surfaces. This lack of glial coverage for the grids is expected to have long-term detrimental effects on neuronal survival and electrical activity. In contrast, the interconnected gaps within the fractal electrodes promote glial coverage. We describe the differing cell responses to the two electrodes and hypothesize that there is an optimal geometry that maximizes the positive response of both neurons and glia when interacting with electrodes.

Three-dimensional fractal dimension and lacunarity features may noninvasively predict TERT promoter mutation status in grade 2 meningiomas

PURPOSE

The 2021 World Health Organization classification includes telomerase reverse transcriptase promoter (TERTp) mutation status as a factor for differentiating meningioma grades. Therefore, preoperative prediction of TERTp mutation may assist in clinical decision making. However, no previous study has applied fractal analysis for TERTp mutation status prediction in meningiomas. The purpose of this study was to assess the utility of three-dimensional (3D) fractal analysis for predicting the TERTp mutation status in grade 2 meningiomas.

METHODS

Forty-eight patients with surgically confirmed grade 2 meningiomas (41 TERTp-wildtype and 7 TERTp-mutant) were included. 3D fractal dimension (FD) and lacunarity values were extracted from the fractal analysis. A predictive model combining clinical, conventional, and fractal parameters was built using logistic regression analysis. Receiver operating characteristic curve analysis was used to assess the ability of the model to predict TERTp mutation status.

RESULTS

Patients with TERTp-mutant grade 2 meningiomas were older (P = 0.029) and had higher 3D FD (P = 0.026) and lacunarity (P = 0.004) values than patients with TERTp-wildtype grade 2 meningiomas. On multivariable logistic analysis, higher 3D FD values (odds ratio = 32.50, P = 0.039) and higher 3D lacunarity values (odds ratio = 20.54, P = 0.014) were significant predictors of TERTp mutation status. The area under the curve, accuracy, sensitivity, and specificity of the multivariable model were 0.84 (95% confidence interval 0.71-0.93), 83.3%, 71.4%, and 85.4%, respectively.

CONCLUSION

3D FD and lacunarity may be useful imaging biomarkers for predicting TERTp mutation status in grade 2 meningiomas.

Identification and validation of a ferroptosis-related gene to predict survival outcomes and the immune microenvironment in lung adenocarcinoma

Background

Lung adenocarcinoma (LUAD) is a leading cause of cancer-related death worldwide. Ferroptosis, a form of cell death characterized by iron-dependent lipid peroxidation. However, the involvement of ferroptosis in the regulation of immune cell infiltration and its immunotherapeutic efficacy in LUAD remain unclear.

Methods

The Cancer Genome Atlas (TCGA) LUAD cohort was used to assess the survival prognosis of FRGs and construct a seven-gene risk signature. Correlation tests, difference tests, and a cluster analysis were performed to explore the role of FRGs in the immune microenvironment and their immunotherapeutic efficacy in LUAD. The effects of FRGs on LUAD cells were assessed by Western blot, iron assay, and lipid peroxidation assay.

Results

The seven-gene risk signatures of patients with LUAD were established and validated. FRG clustering based on 70 differentially expressed FRGs was associated with the immune microenvironment and indicated potential immune subtypes of LUAD. The seven-gene risk signature was an independent prognostic factor for LUAD and was used to divide the LUAD cohort into a high-risk and a low-risk group. Immunocyte infiltration levels, immune checkpoints, and immunotherapy response rates were significantly different between the two groups. Patients with high risk scores had lower overall levels of immunocyte infiltration but higher immunotherapy response rates. The key gene ribonucleotide reductase subunit M2 (RRM2) was associated with LUAD prognosis, which may be related to its ability to regulate the infiltration levels of activated mast cells and activated CD4 memory T cells. In addition, RRM2 was involved in ferroptosis, and its expression was up regulated in lung cancer tissues and the LUAD cell lines. Silencing RRM2 can inhibit the proliferation and induce ferroptosis of H1975 cells suggesting that silencing RRM2 could promote ferroptosis in H1975 cells.

Conclusion

Our results revealed RRM2 as a promising biomarker and therapeutic target associated with tumor immune infiltration in patients with LUAD.

Universal Markers Unveil Metastatic Cancerous Cross-Sections at Nanoscale

Simple Summary

We propose the use of two universal morphometric indices whose synergetic potency leads to the classification of a cancerous tissue of a few nanometers in size as metastatic or non-metastatic. The method is label-free, operates on conventional histological cross-sections, recording surface height–height roughness by AFM, and detects nanoscale changes associated with the progress of carcinogenesis which are the output of combined statistical approaches, namely multifractal analysis and the generalized moments method. The benefit of this approach is at least two-fold. On the one hand, its application in the context of early diagnosis can increase the life expectancy of patients, and on the other hand, differentiation between metastatic and non-metastatic tissues at the singular cell level can lead to new methodologies to treat cancer biology and therapies.

Abstract

The characterization of cancer histological sections as metastatic, M, or not-metastatic, NM, at the cellular size level is important for early diagnosis and treatment. We present timely warning markers of metastasis, not identified by existing protocols and used methods. Digitized atomic force microscopy images of human histological cross-sections of M and NM colorectal cancer cells were analyzed by multifractal detrended fluctuation analysis and the generalized moments method analysis. Findings emphasize the multifractal character of all samples and accentuate room for the differentiation of M from NM cross-sections. Two universal markers emphatically achieve this goal performing very well: (a) the ratio of the singularity parameters (left/right), which are defined relative to weak/strong fluctuations in the multifractal spectrum, is always greater than 0.8 for NM tissues; and (b) the index of multifractality, used to classify universal multifractals, points to log-normal distribution for NM and to log-Cauchy for M tissues. An immediate large-scale screening of cancerous sections is doable based on these findings.

A Review of Mathematical and Computational Methods in Cancer Dynamics

Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires the integration of information dynamics across multidimensional spatiotemporal scales, including genetic, transcriptional, metabolic, proteomic, epigenetic, and multi-cellular networks. However, the time-series analysis of these complex networks remains vastly absent in cancer research. With longitudinal screening and time-series analysis of cellular dynamics, universally observed causal patterns pertaining to dynamical systems, may self-organize in the signaling or gene expression state-space of cancer triggering processes. A class of these patterns, strange attractors, may be mathematical biomarkers of cancer progression. The emergence of intracellular chaos and chaotic cell population dynamics remains a new paradigm in systems medicine. As such, chaotic and complex dynamics are discussed as mathematical hallmarks of cancer cell fate dynamics herein. Given the assumption that time-resolved single-cell datasets are made available, a survey of interdisciplinary tools and algorithms from complexity theory, are hereby reviewed to investigate critical phenomena and chaotic dynamics in cancer ecosystems. To conclude, the perspective cultivates an intuition for computational systems oncology in terms of nonlinear dynamics, information theory, inverse problems, and complexity. We highlight the limitations we see in the area of statistical machine learning but the opportunity at combining it with the symbolic computational power offered by the mathematical tools explored.

Identification of metastasis-related long non-coding RNAs in lung cancer through a novel tumor mesenchymal score

Long non-coding RNAs (lncRNAs) have been proven to play critical roles in epithelial-mesenchymal transition (EMT) and metastasis of lung cancer. However, the biological functions and related mechanisms of lncRNAs are unclear. In addition, the EMT-based prognosis prediction in lung cancer still lacks investigation. Here, we established the methodology of identifying critical metastasis-related lncRNAs using comprehensive datasets of cancer transcriptome, genome and epigenome, and also provided tools for prognosis prediction in lung cancer. Initially, important mesenchymal marker genes were identified to compose the tumor mesenchymal score, which predicted patient prognosis in lung cancer, especially lung adenocarcinoma (LUAD). The score was also correlated with several crucial biological and physiological processes, such as tumor immune and hypoxia. Based on the score, lung cancer patients was classified into epithelial and mesenchymal subtypes, and lncRNAs which exhibited expressional dysregulation, promotor methylation alteration and copy number variation between the two subtypes in LUAD were identified and underwent further prognostic analyses. Finally, we identified 14 lncRNAs as EMT-related and significant biomarkers in prognosis prediction of LUAD. As validation, lncRNA RBPMS-AS1 was proven to be co-expressed with epithelial biomarkers, suppressive for A549 cell migration, invasion and EMT, and also significantly associated with better outcomes of LUAD patients, suggesting the potential of RBPMS-AS1 to serve as a lncRNA epithelial biomarker in metastasis of LUAD. Based on the identified lncRNAs, an EMT-linked lncRNA prognostic signature was further established. Taken together, our study provides robust predictive tools, potential lncRNA targets and feasible screening strategies for future study of lung cancer metastasis.

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.

Association Between Retinal Microvascular Metrics Using Optical Coherence Tomography Angiography and Carotid Artery Stenosis in a Chinese Cohort

Objectives: The main aim was to investigate the association between retinal microvascular metrics using optical coherence tomography angiography (OCTA) and carotid artery stenosis (CAS) in an aging Chinese cohort.

Methods: In this cross-sectional and observational study, 138 eyes of 138 participants were examined. Indices of the microcirculation measured by OCTA included mean vessel density (VD), skeleton density (SD), vessel diameter index (VDI), fractal dimension (FD) and foveal avascular zone (FAZ) of the superficial retinal layer (SRL) and deep retinal layer (DRL), and peripapillary vessel caliber. The correlation of these indices with the carotid atherosclerotic lesions including carotid intima media thickness (CIMT) and common carotid artery (CCA) plaque was assessed.

Results: A total of 72 of 138 eyes demonstrated an increased (≥1 mm) CIMT, and 32 of the eyes presented common carotid plaques. Macular VD, SD, and FD were decreased with the increasing CCA caliber diameter (p &lt; 0.05, respectively). Superficial and deep macular FDs were negatively associated with CIMT as well as the existence of CCA plaques (p &lt; 0.05, respectively).

Conclusion: Changes in retinal microvasculature accessed by OCTA may be used as one of the non-invasive early indicators to monitor asymptomatic CAS.

An Online Pattern Recognition-Oriented Workshop to Promote Interest among Undergraduate Students in How Mathematical Principles Could Be Applied within Veterinary Science

Knowing the importance of mathematics and its relationship with veterinary medicine plays an important role for students. To promote interest in this relationship, we developed the workshop “Math in Nature” that utilizes the surrounding environment for stimulating pattern-recognition and observational skills. It consisted of four sections: A talk by a professional researcher, a question-and-answer section, a mathematical pattern identification session, and a discussion of the ideas proposed by students. The effectiveness of the program to raise interest in mathematics was evaluated using a questionnaire applied before and after the workshop. Following the course, a higher number of students agreed with the fact that biological phenomena can be explained and predicted by applying mathematics, and that it is possible to identify mathematical patterns in living beings. However, the students’ perspectives regarding the importance of mathematics in their careers, as well as their interest in deepening their mathematical knowledge, did not change. Arguably, “Math in Nature” could have exerted a positive effect on the students’ interest in mathematics. We thus recommend the application of similar workshops to improve interests and skills in relevant subjects among undergraduate students.

Monte Carlo simulations in anomalous radiative transfer: tutorial

Anomalous radiative transfer (ART) theory represents a generalization of classical radiative transfer theory. The present tutorial aims to show how Monte Carlo (MC) codes describing the transport of photons in anomalous media can be implemented. We show that the heart of the method involves suitably describing, in a "non-classical" manner, photon steps starting from fixed light sources or from boundaries separating regions of the medium with different optical properties. To give a better sense of the importance of these particular photon step lengths, we also show numerically that the described approach is essential in preserving the invariance property for light propagation. An interesting byproduct of the MC method for ART is that it allows us to simplify the structure of "classical" MC codes, utilized, for example, in biomedical optics.

Spatial structure impacts adaptive therapy by shaping intra-tumoral competition

Background

Adaptive therapy aims to tackle cancer drug resistance by leveraging resource competition between drug-sensitive and resistant cells. Here, we present a theoretical study of intra-tumoral competition during adaptive therapy, to investigate under which circumstances it will be superior to aggressive treatment.

Methods

We develop and analyse a simple, 2-D, on-lattice, agent-based tumour model in which cells are classified as fully drug-sensitive or resistant. Subsequently, we compare this model to its corresponding non-spatial ordinary differential equation model, and fit it to longitudinal prostate-specific antigen data from 65 prostate cancer patients undergoing intermittent androgen deprivation therapy following biochemical recurrence.

Results

Leveraging the individual-based nature of our model, we explicitly demonstrate competitive suppression of resistance during adaptive therapy, and examine how different factors, such as the initial resistance fraction or resistance costs, alter competition. This not only corroborates our theoretical understanding of adaptive therapy, but also reveals that competition of resistant cells with each other may play a more important role in adaptive therapy in solid tumours than was previously thought. To conclude, we present two case studies, which demonstrate the implications of our work for: (i) mathematical modelling of adaptive therapy, and (ii) the intra-tumoral dynamics in prostate cancer patients during intermittent androgen deprivation treatment, a precursor of adaptive therapy.

Conclusion

Our work shows that the tumour’s spatial architecture is an important factor in adaptive therapy and provides insights into how adaptive therapy leverages both inter- and intra-specific competition to control resistance.

Cancer therapy traditionally focuses on maximising tumour cell kill with the aim of achieving a cure, but such aggressive treatment can open up space for drug-resistant cells to grow. In contrast, adaptive therapy aims to leverage competition between drug-sensitive and resistant cells by adjusting treatment to maintain the tumour at a tolerable size, whilst preserving drug-sensitive cells. This approach is being tested in trials but is not yet widely used as deeper understanding of cell-cell competition is required. Here, we used a mathematical model to investigate how strongly, and with whom, resistant cells compete during continuous and adaptive therapy, and applied our insights to hormone therapy in prostate cancer where adaptive therapy has recently been successfully trialed. Our results provide new insights into how adaptive therapy works and show that, by shaping cell competition, the tumour’s spatial architecture is important in determining therapy response.

Strobl et al. develop an agent-based spatial model of drug resistance in tumour cells under adaptive therapy. Using this model, they investigate how the tumour’s spatial architecture impacts intratumoural competitive dynamics of drug-sensitive vs. -resistant clones in response to therapy.

Shape matters: morphological metrics of glioblastoma imaging abnormalities as biomarkers of prognosis

Lacunarity, a quantitative morphological measure of how shapes fill space, and fractal dimension, a morphological measure of the complexity of pixel arrangement, have shown relationships with outcome across a variety of cancers. However, the application of these metrics to glioblastoma (GBM), a very aggressive primary brain tumor, has not been fully explored. In this project, we computed lacunarity and fractal dimension values for GBM-induced abnormalities on clinically standard magnetic resonance imaging (MRI). In our patient cohort (n = 402), we connect these morphological metrics calculated on pretreatment MRI with the survival of patients with GBM. We calculated lacunarity and fractal dimension on necrotic regions (n = 390), all abnormalities present on T1Gd MRI (n = 402), and abnormalities present on T2/FLAIR MRI (n = 257). We also explored the relationship between these metrics and age at diagnosis, as well as abnormality volume. We found statistically significant relationships to outcome for all three imaging regions that we tested, with the shape of T2/FLAIR abnormalities that are typically associated with edema showing the strongest relationship with overall survival. This link between morphological and survival metrics could be driven by underlying biological phenomena, tumor location or microenvironmental factors that should be further explored.

Morphological, fractal, and textural features for the blood cell classification: the case of acute myeloid leukemia

Microscopic examination of stained peripheral blood smears is, nowadays, an indispensable tool in the evaluation of patients with hematological and non-hematological diseases. While a rapid automated quantification of the regular blood cells is available, recognition and counting of immature white blood cells (WBC) still relies mostly on the microscopic examination of blood smears by an experienced observer. Recently, there are efforts to improve the prediction by various machine learning approaches. An open dataset collection including the recently digitalized single-cell images for 200 patients, from peripheral blood smears at 100 × magnification, was used. We studied different morphological, fractal, and textural descriptors for WBC classification, with an aim to indicate the most reliable parameters for the recognition of certain cell types. Structural properties of both the mature and non-mature leukocytes obtained from (i) acute myeloid leukemia patients, or (ii) non-malignant controls, were studied in depth, with a sample size of about 25 WBC per group. We quantified structural and textural differences and, based on the statistical ranges of parameters for different WBC types, selected eight features for classification: Cell area, Nucleus-to-cell ratio, Nucleus solidity, Fractal dimension, Correlation, Contrast, Homogeneity, and Energy. Classification Precision of up to 100% (80% on average) was achieved.

Lung cancer dynamics using fractional order impedance modeling on a mimicked lung tumor setup

Introduction

As pulmonary dysfunctions are prospective factors for developing cancer, efforts are needed to solve the limitations regarding applications in lung cancer. Fractional order respiratory impedance models can be indicative of lung cancer dynamics and tissue heterogeneity.

Objective

The purpose of this study is to investigate how the existence of a tumorous tissue in the lung modifies the parameters of the proposed models. The first use of a prototype forced oscillations technique (FOT) device in a mimicked lung tumor setup is investigated by comparing and interpreting the experimental findings.

Methods

The fractional order model parameters are determined for the mechanical properties of the healthy and tumorous lung. Two protocols have been performed for a mimicked lung tumor setup in a laboratory environment. A low frequency evaluation of respiratory impedance model and nonlinearity index were assessed using the forced oscillations technique.

Results

The viscoelastic properties of the lung tissue change, results being mirrored in the respiratory impedance assessment via FOT. The results demonstrate significant differences among the mimicked healthy and tumor measurements, (p-values < 0.05) for impedance values and also for heterogeneity index. However, there was no significant difference in lung function before and after immersing the mimicked lung in water or saline solution, denoting no structural changes.

Conclusion

Simulation tests comparing the changes in impedance support the research hypothesis. The impedance frequency response is effective in non-invasive identification of respiratory tissue abnormalities in tumorous lung, analyzed with appropriate fractional models.

Morphological characterization of Etv2 vascular explants using fractal analysis and atomic force microscopy

The rapid engraftment of vascular networks is critical for functional incorporation of tissue explants. However, existing methods for inducing angiogenesis utilize approaches that yield vasculature with poor temporal stability or inadequate mechanical integrity, which reduce their robustness in vivo. The transcription factor Ets variant 2 (Etv2) specifies embryonic hematopoietic and vascular endothelial cell (EC) development, and is transiently reactivated during postnatal vascular regeneration and tumor angiogenesis. This study investigates the role for Etv2 upregulation in forming stable vascular beds both in vitro and in vivo. Control and Etv2⁺ prototypical fetal-derived human umbilical vein ECs (HUVECs) and adult ECs were angiogenically grown into vascular beds. These vessel beds were characterized using fractal dimension and lacunarity, to quantify their branching complexity and space-filling homogeneity, respectively. Atomic force microscopy (AFM) was used to explore whether greater complexity and homogeneity lead to more mechanically stable vessels. Additionally, markers of EC integrity were used to probe for mechanistic clues. Etv2⁺ HUVECs exhibit greater branching, vessel density, and structural homogeneity, and decreased stiffness in vitro and in vivo, indicating a greater propensity for stable vessel formation. When co-cultured with colon tumor organoid tissue, Etv2⁺ HUVECs had decreased fractal dimension and lacunarity compared to Etv2⁺ HUVECs cultured alone, indicating that vessel density and homogeneity of vessel spacing increased due to the presence of Etv2. This study sets forth the novel concept that fractal dimension, lacunarity, and AFM are as informative as conventional angiogenic measurements, including vessel branching and density, to assess vascular perfusion and stability.

Are radiomics features universally applicable to different organs?

BACKGROUND

Many studies have successfully identified radiomics features reflecting macroscale tumor features and tumor microenvironment for various organs. There is an increased interest in applying these radiomics features found in a given organ to other organs. Here, we explored whether common radiomics features could be identified over target organs in vastly different environments.

METHODS

Four datasets of three organs were analyzed. One radiomics model was constructed from the training set (lungs, n = 401), and was further evaluated in three independent test sets spanning three organs (lungs, n = 59; kidneys, n = 48; and brains, n = 43). Intensity histograms derived from the whole organ were compared to establish organ-level differences. We constructed a radiomics score based on selected features using training lung data over the tumor region. A total of 143 features were computed for each tumor. We adopted a feature selection approach that favored stable features, which can also capture survival. The radiomics score was applied to three independent test data from lung, kidney, and brain tumors, and whether the score could be used to separate high- and low-risk groups, was evaluated.

RESULTS

Each organ showed a distinct pattern in the histogram and the derived parameters (mean and median) at the organ-level. The radiomics score trained from the lung data of the tumor region included seven features, and the score was only effective in stratifying survival for other lung data, not in other organs such as the kidney and brain. Eliminating the lung-specific feature (2.5 percentile) from the radiomics score led to similar results. There were no common features between training and test sets, but a common category of features (texture category) was identified.

CONCLUSION

Although the possibility of a generally applicable model cannot be excluded, we suggest that radiomics score models for survival were mostly specific for a given organ; applying them to other organs would require careful consideration of organ-specific properties.

Tumor Margin Contains Prognostic Information: Radiomic Margin Characteristics Analysis in Lung Adenocarcinoma Patients

Simple Summary

The tumor microenvironment is a dynamic area, with continuous interaction between tumor cells and their surrounding environment. We aimed to investigate the relationship between tumor radiomic margin characteristics and prognosis in patients with lung cancer. When compared to the model with clinical variables only (C-index = 0.738), the model incorporating clinical variables and radiomic margin characteristics (C-index = 0.753) demonstrated a higher C-index for predicting overall survival. In the model integrating both clinical variables and radiomic margin characteristics, convexity, Laplace of Gaussian (LoG) kurtosis 3, and roundness factor were independent predictive factors of overall survival. Our study showed that radiomic margin characteristics helped predict overall survival in patients with lung adenocarcinomas, thus implying that the tumor margin contains prognostic information.

Abstract

We aimed to investigate the relationship between tumor radiomic margin characteristics and prognosis in patients with lung cancer. We enrolled 334 patients who underwent complete resection for lung adenocarcinoma. A quantitative computed tomography analysis was performed, and 76 radiomic margin characteristics were extracted. The radiomic margin characteristics were correlated with overall survival. The selected clinical variables and radiomic margin characteristics were used to calculate a prognostic model with subsequent internal and external validation. Nearly all of the radiomic margin characteristics showed excellent reproducibility. The least absolute shrinkage and selection operator (LASSO) method was used to select eight radiomic margin characteristics. When compared to the model with clinical variables only (C-index = 0.738), the model incorporating clinical variables and radiomic margin characteristics (C-index = 0.753) demonstrated a higher C-index for predicting overall survival. In the model integrating both clinical variables and radiomic margin characteristics, convexity, a Laplace of Gaussian (LoG) kurtosis of 3, and the roundness factor were each independently predictive of overall survival. In addition, radiomic margin characteristics were also correlated with the micropapillary subtype, and the sphericity value was able to predict the presence of the micropapillary subtype. In conclusion, our study showed that radiomic margin characteristics helped predict overall survival in patients with lung adenocarcinomas, thus implying that the tumor margin contains prognostic information.

Human-interpretable image features derived from densely mapped cancer pathology slides predict diverse molecular phenotypes

Computational methods have made substantial progress in improving the accuracy and throughput of pathology workflows for diagnostic, prognostic, and genomic prediction. Still, lack of interpretability remains a significant barrier to clinical integration. We present an approach for predicting clinically-relevant molecular phenotypes from whole-slide histopathology images using human-interpretable image features (HIFs). Our method leverages >1.6 million annotations from board-certified pathologists across >5700 samples to train deep learning models for cell and tissue classification that can exhaustively map whole-slide images at two and four micron-resolution. Cell- and tissue-type model outputs are combined into 607 HIFs that quantify specific and biologically-relevant characteristics across five cancer types. We demonstrate that these HIFs correlate with well-known markers of the tumor microenvironment and can predict diverse molecular signatures (AUROC 0.601-0.864), including expression of four immune checkpoint proteins and homologous recombination deficiency, with performance comparable to 'black-box' methods. Our HIF-based approach provides a comprehensive, quantitative, and interpretable window into the composition and spatial architecture of the tumor microenvironment.

How neurons exploit fractal geometry to optimize their network connectivity

We investigate the degree to which neurons are fractal, the origin of this fractality, and its impact on functionality. By analyzing three-dimensional images of rat neurons, we show the way their dendrites fork and weave through space is unexpectedly important for generating fractal-like behavior well-described by an ‘effective’ fractal dimension D. This discovery motivated us to create distorted neuron models by modifying the dendritic patterns, so generating neurons across wide ranges of D extending beyond their natural values. By charting the D-dependent variations in inter-neuron connectivity along with the associated costs, we propose that their D values reflect a network cooperation that optimizes these constraints. We discuss the implications for healthy and pathological neurons, and for connecting neurons to medical implants. Our automated approach also facilitates insights relating form and function, applicable to individual neurons and their networks, providing a crucial tool for addressing massive data collection projects (e.g. connectomes).

Mechanism underlying dynamic scaling properties observed in the contour of spreading epithelial monolayer

We found evidence of dynamic scaling in the spreading of Madin-Darby canine kidney (MDCK) cell monolayer, which can be characterized by the Hurst exponent α=0.86 and the growth exponent β=0.73, and theoretically and experimentally clarified the mechanism that governs the contour shape dynamics. Dynamic scaling refers to the roughness of the surface scales, both spatially and temporally. During the spreading of the monolayer, it is known that so-called leader cells generate the driving force and lead the other cells. Our time-lapse observations of cell behavior showed that these leader cells appeared at the early stage of the spreading and formed the monolayer protrusion. Informed by these observations, we developed a simple mathematical model that included differences in cell motility, cell-cell adhesion, and random cell movement. The model reproduced the quantitative characteristics obtained from the experiment, such as the spreading speed, the distribution of the increment, and the dynamic scaling law. Analysis of the model equation shows that the model can reproduce different scaling laws from (α=0.5,β=0.25) to (α=0.9,β=0.75), where the exponents α and β are determined by two dimensionless quantities determined by the microscopic cell behavior. From the analytical result, parameter estimation from the experimental results was achieved. The monolayer on the collagen-coated dishes showed a different scaling law, α=0.74,β=0.68, suggesting that cell motility increased ninefold. This result was consistent with the assay of the single-cell motility. Our study demonstrated that the dynamics of the contour of the monolayer were explained by the simple model, and we propose a mechanism that exhibits the dynamic scaling property.

Fractal structures arising from interfacial instabilities in bio-oil atomization

The intriguing multi-scale fractal patterns ubiquitously observed in nature similarly emerge as fascinating structures in two-phase fluid flows of bio-oil breakup and atomization processes. High-resolution microscopy of the two-phase flows under 15 flow conditions (cases of different flow rates of the liquid and co-flowing air streams as well as different degrees of liquid preheating) reveal that the geometrical complexities evolve under the competing/combined action of the instability mechanisms such as Kelvin-Helmholtz, Rayleigh-Taylor and Rayleigh-Plateau leading into the transition from break-up to atomization. A thorough analysis of the higher order moments of statistics evaluated based on the probability density functions from 15,000 fractal dimension samples suggest that a single-value analysis is not sufficient to describe the complex reshaping mechanisms in two-phase flows. Consistently positive skewness of the statistics reveal the role of abrupt two-phase mechanisms such as liquid column rupture, ligament disintegration, liquid sheet bursting and droplet distortions in a hierarchical geometrical entanglement. Further, large kurtosis values at increased flow inertia are found associated with turbulence-induced intermittent geometrical reshaping. Interestingly, the proposed power-law correlation reveals that the global droplet size obtained from laser-diffraction measurements declines as the two-phase geometrical complexity increases.

Computed Tomography Radiomics for Residual Positron Emission Tomography-Computed Tomography Uptake in Lymph Nodes after Treatment

Simple Summary

In this study we explored the predictive ability of radiomics in non-small cell lung cancer patients, and reported the complementary role of radiomics in predicting the treatment response of the lymph nodes. Radiomics analysis is a cutting-edge technology for the noninvasive assessment of tumor biology, which converts medical images into mineable high-dimensional data. Our method is cost-effective with no need for additional studies, and moreover, we used an easily reproducible study method that can be applicable in further studies using radiomics in oncology.

Abstract

Although a substantial decrease in 2-[fluorine-18]fluoro-2-deoxy-d-glucose (FDG) uptake on positron emission tomography-computed tomography (PET-CT) indicates a promising metabolic response to treatment, predicting the pathologic status of lymph nodes (LN) remains challenging. We investigated the potential of a CT radiomics approach to predict the pathologic complete response of LNs showing residual uptake after neoadjuvant concurrent chemoradiotherapy (NeoCCRT) in patients with non-small cell lung cancer (NSCLC). Two hundred and thirty-seven patients who underwent NeoCCRT for stage IIIa NSCLC were included. Two hundred fifty-two CT radiomics features were extracted from LNs showing remaining positive FDG uptake upon restaging PET-CT. A multivariable logistic regression analysis of radiomics features and clinicopathologic characteristics was used to develop a prediction model. Of the 237 patients, 135 patients (185 nodes) met our inclusion criteria. Eighty-seven LNs were proven to be malignant (47.0%, 87/185). Upon multivariable analysis, metastatic LNs were significantly prevalent in females and patients with adenocarcinoma (odds ratio (OR) = 2.02, 95% confidence interval (CI) = 0.88–4.62 and OR = 0.39, 95% CI = 0.19–0.77 each). Metastatic LNs also had a larger maximal 3D diameter and higher cluster tendency (OR = 9.92, 95% CI = 3.15–31.17 and OR = 2.36, 95% CI = 1.22–4.55 each). The predictive model for metastasis showed a discrimination performance with an area under the receiver operating characteristic curve of 0.728 (95% CI = 0.654–0.801, p value < 0.001). The radiomics approach allows for the noninvasive detection of metastases in LNs with residual FDG uptake after the treatment of NSCLC patients.

Cancer: A turbulence problem

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Application of nonlinear dynamics to cancer ecosystems.

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Chemical turbulence and strange attractor models in tumor growth, invasion and pattern formation are investigated.

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Computational algorithms for detecting such structures are proposed.

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Complex systems applications to cancer dynamics.

Cancers are complex, adaptive ecosystems. They remain the leading cause of disease-related death among children in North America. As we approach computational oncology and Deep Learning Healthcare, our mathematical models of cancer dynamics must be revised. Recent findings support the perspective that cancer-microenvironment interactions may consist of chaotic gene expressions and turbulent protein flows during pattern formation. As such, cancer pattern formation, protein-folding and metastatic invasion are discussed herein as processes driven by chemical turbulence within the framework of complex systems theory. To conclude, cancer stem cells are presented as strange attractors of the Waddington landscape.

Fractal Dimension Analysis of Widefield Choroidal Vasculature as Predictor of Stage of Macular Degeneration

Purpose

To evaluate the fractal dimension (D_f) of the choroidal vasculature using widefield indocyanine green (ICG) angiography and correlate it with the stage of age-related macular degeneration (AMD).

Methods

Widefield ICG angiography performed on 38 eyes was retrospectively analyzed using the FracLac application within the National Institutes of Health ImageJ software to determine regional fractal dimensions in the macular field and widefield. These values were then associated with a diagnosis of no AMD, non-exudative AMD (subdivided into early/intermediate stage vs. advanced stage), or exudative AMD (subdivided into with or without geographic atrophy). The mean values were compared using Wilcoxon's test.

Results

Early/intermediate non-exudative AMD and exudative AMD without geographic atrophy were found to have statistically significantly lower D_f values compared to an absence of AMD when examining the macular field. Exudative AMD with geographic atrophy was found to have a statistically significant lower choroidal fractal dimension compared to no AMD when studied in the widefield.

Conclusions

Advanced stages of macular degeneration were found to have significantly decreased the fractal dimensions of choroidal vasculature on widefield ICG compared to early/intermediate stages, possibly implying a generalized reduction in complexity and/or vessel caliber of the choroid with advancing stage of AMD. This finding agrees with previous understanding of the development of choriocapillaris atrophy in advanced macular degeneration.

Translational Relevance

These findings suggest that using automated fractal analysis techniques can aid in differentiating stages of macular degeneration and, with further study, may be used to predict advancement of macular degeneration.

Computational image analysis reveals the structural complexity of Toxoplasma gondii tissue cysts

Toxoplasma gondii is an obligate intracellular parasite infecting up to one third of the human population. The central event in the pathogenesis of toxoplasmosis is the conversion of tachyzoites into encysted bradyzoites. A novel approach to analyze the structure of in vivo-derived tissue cysts may be the increasingly used computational image analysis. The objective of this study was to quantify the geometrical complexity of T. gondii cysts by morphological, particle, and fractal analysis, as well as to determine if it is impacted by parasite strain, cyst age, and host type. A total of 31 images of T. gondii brain cysts of four type-2 strains (Me49, and local isolates BGD1, BGD14, and BGD26) was analyzed using ImageJ software. The parameters of interest included diameter, circularity, packing density (PD), fractal dimension (FD), and lacunarity. Although cyst diameter varied widely, its negative correlation with PD was observed. Circularity was remarkably close to 1, indicating a perfectly round shape of the cysts. PD and FD did not vary among cysts of different strains, age, and derived from mice of different genetic background. Conversely, lacunarity, which is a measure of heterogeneity, was significantly lower for BGD1 strain vs. all other strains, and higher for Me49 vs. BGD14 and BGD26, but did not differ among Me49 cysts of different age, or those derived from genetically different mice. The results indicate a highly uniform structure and occupancy of the different T. gondii tissue cysts. This study furthers the use of image analysis in describing the structural complexity of T. gondii cyst morphology, and presents the first application of fractal analysis for this purpose. The presented results show that use of a freely available software is a cost-effective approach to advance automated image scoring for T. gondii cysts.

Prediction of tumor doubling time of lung adenocarcinoma using radiomic margin characteristics

Background

Because shape or irregularity along the tumor perimeter can result from interactions between the tumor and the surrounding parenchyma, there could be a difference in tumor growth rate according to tumor margin or shape. However, no attempt has been made to evaluate the correlation between margin or shape features and tumor growth.

Methods

We evaluated 52 lung adenocarcinoma (ADC) patients who had at least two computed tomographic (CT) examinations before curative resection. Volume‐based doubling times (DTs) were calculated based on CT scans, and patients were divided into two groups according to the growth pattern (GP) of their ADCs (gradually growing tumors [GP I] vs. growing tumors with a temporary decrease in DT [GP II]). CT radiomic features reflecting margin characteristics were extracted, and radiomic features reflective of tumor DT were selected.

Results

Among the 52 patients, 41 (78.8%) were assigned to GP I and 11 (21.2%) to GP II. Of the 94 radiomic features extracted, eccentricity, surface‐to‐volume ratio, LoG uniformity (σ = 3.5), and LoG skewness (σ = 0.5) were ultimately selected for tumor DT prediction. Selected radiomic features in GP I were surface‐to‐volume ratio, contrast, LoG uniformity (σ = 3.5), and LoG skewness (σ = 0.5), similar to those for total subjects, whereas the radiomic features in GP II were solidity, energy, and busyness.

Conclusions

This study demonstrated the potential of margin‐related radiomic features to predict tumor DT in lung ADCs.

Key points

Significant findings of the study

We found a relationship between margin‐related radiomic features and tumor doubling time.

What this study adds

Margin‐related radiomic features can potentially be used as noninvasive biomarkers to predict tumor doubling time in lung adenocarcinoma and inform treatment strategies.

Fractal analysis of concurrently prepared latex rubber casts of the bronchial and vascular systems of the human lung

Fractal geometry (FG) is a branch of mathematics that instructively characterizes structural complexity. Branched structures are ubiquitous in both the physical and the biological realms. Fractility has therefore been termed nature's design. The fractal properties of the bronchial (airway) system, the pulmonary artery and the pulmonary vein of the human lung generates large respiratory surface area that is crammed in the lung. Also, it permits the inhaled air to intimately approximate the pulmonary capillary blood across a very thin blood-gas barrier through which gas exchange to occur by diffusion. Here, the bronchial (airway) and vascular systems were simultaneously cast with latex rubber. After corrosion, the bronchial and vascular system casts were physically separated and cleared to expose the branches. The morphogenetic (Weibel's) ordering method was used to categorize the branches on which the diameters and the lengths, as well as the angles of bifurcation, were measured. The fractal dimensions (DF) were determined by plotting the total branch measurements against the mean branch diameters on double logarithmic coordinates (axes). The diameter-determined DF values were 2.714 for the bronchial system, 2.882 for the pulmonary artery and 2.334 for the pulmonary vein while the respective values from lengths were 3.098, 3.916 and 4.041. The diameters yielded DF values that were consistent with the properties of fractal structures (i.e. self-similarity and space-filling). The data obtained here compellingly suggest that the design of the bronchial system, the pulmonary artery and the pulmonary vein of the human lung functionally comply with the Hess-Murray law or 'the principle of minimum work'.

Small-Angle Scattering and Multifractal Analysis of DNA Sequences

The arrangement of A, C, G and T nucleotides in large DNA sequences of many prokaryotic and eukaryotic cells exhibit long-range correlations with fractal properties. Chaos game representation (CGR) of such DNA sequences, followed by a multifractal analysis, is a useful way to analyze the corresponding scaling properties. This approach provides a powerful visualization method to characterize their spatial inhomogeneity, and allows discrimination between mono- and multifractal distributions. However, in some cases, two different arbitrary point distributions, may generate indistinguishable multifractal spectra. By using a new model based on multiplicative deterministic cascades, here it is shown that small-angle scattering (SAS) formalism can be used to address such issue, and to extract additional structural information. It is shown that the box-counting dimension given by multifractal spectra can be recovered from the scattering exponent of SAS intensity in the fractal region. This approach is illustrated for point distributions of CGR data corresponding to Escherichia coli, Phospholamban and Mouse mitochondrial DNA, and it is shown that for the latter two cases, SAS allows extraction of the fractal iteration number and the scaling factor corresponding to "ACGT" square, or to recover the number of bases. The results are compared with a model based on multiplicative deterministic cascades, and respectively with one which takes into account the existence of forbidden sequences in DNA. This allows a classification of the DNA sequences in terms of random and deterministic fractals structures emerging in CGR.

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.

Kinetic modeling and parametric imaging with dynamic PET for oncological applications: general considerations, current clinical applications, and future perspectives

Dynamic PET (dPET) studies have been used until now primarily within research purposes. Although it is generally accepted that the information provided by dPET is superior to that of conventional static PET acquisitions acquired usually 60 min post injection of the radiotracer, the duration of dynamic protocols, the limited axial field of view (FOV) of current generation clinical PET systems covering a relatively small axial extent of the human body for a dynamic measurement, and the complexity of data evaluation have hampered its implementation into clinical routine. However, the development of new-generation PET/CT scanners with an extended FOV as well as of more sophisticated evaluation software packages that offer better segmentation algorithms, automatic retrieval of the arterial input function, and automatic calculation of parametric imaging, in combination with dedicated shorter dynamic protocols, will facilitate the wider use of dPET. This is expected to aid in oncological diagnostics and therapy assessment. The aim of this review is to present some general considerations about dPET analysis in oncology by means of kinetic modeling, based on compartmental and noncompartmental approaches, and parametric imaging. Moreover, the current clinical applications and future perspectives of the modality are outlined.

The Complexity and Fractal Geometry of Nuclear Medicine Images

Irregularity in shape and behavior is the main feature of every anatomical system, including human organs, tissues, cells, and sub-cellular entities. It has been shown that this property cannot be quantified by means of the classical Euclidean geometry, which is only able to describe regular geometrical objects. In contrast, fractal geometry has been widely applied in several scientific fields. This rapid growth has also produced substantial insights in the biomedical imaging. Consequently, particular attention has been given to the identification of pathognomonic patterns of "shape" in anatomical entities and their changes from natural to pathological states. Despite the advantages of fractal mathematics and several studies demonstrating its applicability to oncological research, many researchers and clinicians remain unaware of its potential. Therefore, this review aims to summarize the complexity and fractal geometry of nuclear medicine images.

Analysis of gene expression profiles of lung cancer subtypes with machine learning algorithms

Lung cancer is one of the most common cancer types worldwide and causes more than one million deaths annually. Lung adenocarcinoma (AC) and lung squamous cell cancer (SCC) are two major lung cancer subtypes and have different characteristics in several aspects. Identifying their differentially expressed genes and different gene expression patterns can deepen our understanding of these two subtypes at the transcriptomic level. In this work, we used several machine learning algorithms to investigate the gene expression profiles of lung AC and lung SCC samples retrieved from Gene Expression Omnibus. First, the profiles were analyzed by using a powerful feature selection method, namely, Monte Carlo feature selection. A feature list, ranking all features according to their importance, and some informative features were obtained. Then, the feature list was used in the incremental feature selection method to extract optimal features, which can allow the support vector machine (SVM) to yield the best performance for classifying lung AC and lung SCC samples. Some top genes (CSTA, TP63, SERPINB13, CLCA2, BICD2, PERP, FAT2, BNC1, ATP11B, FAM83B, KRT5, PARD6G, PKP1) were extensively analyzed to prove that they can be differentially expressed genes between lung AC and lung SCC. Meanwhile, a rule learning procedure was applied on informative features to construct the classification rules. These rules provide a clear procedure of classification and show some different gene expression patterns between lung AC and lung SCC.

Complex Network Characterization Using Graph Theory and Fractal Geometry: The Case Study of Lung Cancer DNA Sequences

This paper discusses an approach developed for exploiting the local elementary movements of evolution to study complex networks in terms of shared common embedding and, consequently, shared fractal properties. This approach can be useful for the analysis of lung cancer DNA sequences and their properties by using the concepts of graph theory and fractal geometry. The proposed method advances a renewed consideration of network complexity both on local and global scales. Several researchers have illustrated the advantages of fractal mathematics, as well as its applicability to lung cancer research. Nevertheless, many researchers and clinicians continue to be unaware of its potential. Therefore, this paper aims to examine the underlying assumptions of fractals and analyze the fractal dimension and related measurements for possible application to complex networks and, especially, to the lung cancer network. The strict relationship between the lung cancer network properties and the fractal dimension is proved. Results show that the fractal dimension decreases in the lung cancer network while the topological properties of the network increase in the lung cancer network. Finally, statistical and topological significance between the complexity of the network and lung cancer network is shown.