The Complexity and Fractal Geometry of Nuclear Medicine Images

Efficient calculation of fractal properties via the Higuchi method

Higuchi's method of determining fractal dimension is an important, well-used, research tool that, compared to many other methods, gives rapid, efficient, and robust estimations for the range of possible fractal dimensions. One major shortcoming in applying the method is the correct choice of tuning parameter (k _max); a poor choice can generate spurious results, and there is no agreed upon methodology to solve this issue. We analyze multiple instances of synthetic fractal signals to minimize an error metric. This allows us to offer a new and general method that allows determination, a priori, of the best value for the tuning parameter, for a particular length data set. We demonstrate its use on physical data, by calculating fractal dimensions for a shell model of the nonlinear dynamics of MHD turbulence, and severe acute respiratory syndrome coronavirus 2 isolate Wuhan-Hu-1 from the family Coronaviridae.

Structural complexity of the craniofacial trabecular bone in multiple myeloma assessed by fractal analysis

Purpose

This study aimed to evaluate the structural complexity of craniofacial trabecular bone in multiple myeloma by fractal analysis of panoramic and lateral skull radiography, and to compare the fractal dimension values of healthy patients (HPs), pre-treatment patients (PTPs), and patients during bisphosphonate treatment (DTPs).

Materials and Methods

Pairs of digital panoramic and lateral skull radiographs of 84 PTPs and 72 DTPs were selected. After application of exclusion criteria, 43 panoramic and 84 lateral skull radiographs of PTPs, 56 panoramic and 72 lateral skull radiographs of DTPs, and 99 panoramic radiographs of age- and sex-matched HPs were selected. The fractal dimension values from panoramic radiographs were compared among HPs, PTPs, and DTPs and between anatomical locations within patient groups using analysis of variance with the Tukey test. Fractal dimension values from lateral skull radiographs were compared between PTPs and DTPs using the Student t-test. Pearson correlation coefficients were used to assess the relationship between the mandible from panoramic radiographs and the skull from lateral skull radiographs. Intra-examiner agreement was assessed using intraclass correlation coefficients (α=0.05).

Results

The fractal dimension values were not significantly different among HPs, PTPs, and DTPs on panoramic radiographs or between PTPs and DTPs on lateral skull radiographs (P>0.05). The mandibular body presented the highest fractal dimension values (P≤0.05). The fractal dimension values of the mandible and skull in PTPs and DTPs were not correlated.

Conclusion

Fractal analysis was not sensitive for distinguishing craniofacial trabecular bone complexity in multiple myeloma patients using panoramic and lateral skull radiography.

Quantification of tumor heterogeneity: from data acquisition to metric generation

Tumors are unique and complex ecosystems, in which heterogeneous cell subpopulations with variable molecular profiles, aggressiveness, and proliferation potential coexist and interact. Understanding how heterogeneity influences tumor progression has important clinical implications for improving diagnosis, prognosis, and treatment response prediction. Several recent innovations in data acquisition methods and computational metrics have enabled the quantification of spatiotemporal heterogeneity across different scales of tumor organization. Here, we summarize the most promising efforts from a common experimental and computational perspective, discussing their advantages, shortcomings, and challenges. With personalized medicine entering a new era of unprecedented opportunities, our vision is that of future workflows integrating across modalities, scales, and dimensions to capture intricate aspects of the tumor ecosystem and to open new avenues for improved patient care.

Spherical coordinates transformation pre-processing in Deep Convolution Neural Networks for brain tumor segmentation in MRI

Magnetic Resonance Imaging (MRI) is used in everyday clinical practice to assess brain tumors. Deep Convolutional Neural Networks (DCNN) have recently shown very promising results in brain tumor segmentation tasks; however, DCNN models fail the task when applied to volumes that are different from the training dataset. One of the reasons is due to the lack of data standardization to adjust for different models and MR machines. In this work, a 3D spherical coordinates transform during the pre-processing phase has been hypothesized to improve DCNN models' accuracy and to allow more generalizable results even when the model is trained on small and heterogeneous datasets and translated into different domains. Indeed, the spherical coordinate system avoids several standardization issues since it works independently of resolution and imaging settings. The model trained on spherical transform pre-processed inputs resulted in superior performance over the Cartesian-input trained model on predicting gliomas' segmentation on Tumor Core and Enhancing Tumor classes, achieving a further improvement in accuracy by merging the two models together. The proposed model is not resolution-dependent, thus improving segmentation accuracy and theoretically solving some transfer learning problems related to the domain shifting, at least in terms of image resolution in the datasets.

Computational analysis of MRIs predicts osteosarcoma chemoresponsiveness

Aim: This study aimed to improve osteosarcoma chemoresponsiveness prediction by optimization of computational analysis of MRIs. Patients & methods: Our retrospective predictive model involved osteosarcoma patients with MRI scans performed before OsteoSa MAP neoadjuvant cytotoxic chemotherapy. Results: We found that several monofractal and multifractal algorithms were able to classify tumors according to their chemoresponsiveness. The predictive clues were defined as morphological complexity, homogeneity and fractality. The monofractal feature CV for Λ'(G) provided the best predictive association (area under the ROC curve = 0.88; p <0.001), followed by   Y-axis intersection of the regression line  for  box fractal dimension, r²  for  FD_M and tumor circularity. Conclusion: This is the first full-scale study to indicate that computational analysis of pretreatment MRIs could provide imaging biomarkers for the classification of osteosarcoma according to their chemoresponsiveness.

Effects of Continuous Positive Airway Pressure on Sleep EEG Characteristics in Patients with Primary Central Sleep Apnea Syndrome

This study aimed to investigate the effects of continuous positive airway pressure (CPAP) on the electroencephalographic (EEG) characteristics of patients with primary central sleep apnea syndrome (CSAS). Nine patients with primary CSAS were enrolled in this study. The raw sleep EEG data were analyzed based on two main factors: fractal dimension (FD) and zero-crossing rate of detrended FD. Additionally, conventional EEG spectral analysis in the delta, theta, alpha, and beta bands was conducted using a fast Fourier transform. The FD in patients with primary CSAS who underwent CPAP treatment was significantly decreased during nonrapid eye movement (NREM) sleep but increased during rapid eye movement (REM) sleep (p < 0.05). Regarding the EEG spectral analysis, the alpha power increased, while the delta/alpha ratio decreased during REM sleep in patients with CSAS (p < 0.05). In conclusion, CPAP treatment can reduce FD in NREM sleep and increase FD during REM sleep in patients with primary CSAS. FD may be used as a new biomarker of EEG stability and improvement in brain function after CPAP treatment for primary CSAS.

Additional value of volumetric and texture analysis on FDG PET assessment in paediatric Hodgkin lymphoma: an Italian multicentric study protocol

INTRODUCTION

Assessment of response to therapy in paediatric patients with Hodgkin lymphoma (HL) by 18F-fluorodeoxyglucose positron emission tomography/CT has become a powerful tool for the discrimination of responders from non-responders. The addition of volumetric and texture analyses can be regarded as a valuable help for disease prognostication and biological characterisation. Based on these premises, the Hodgkin Lymphoma Study Group of the Associazione Italiana Ematologia Oncologia Pediatrica (AIEOP) has designed a prospective evaluation of volumetric and texture analysis in the Italian cohort of patients enrolled in the EuroNet-PHL-C2.

METHODS AND ANALYSIS

The primary objective is to compare volumetric assessment in patiens with HL at baseline and during the course of therapy with standard visual and semiquantitative analyses. The secondary objective is to identify the impact of volumetric and texture analysis on bulky masses. The tertiary objective is to determine the additional value of multiparametric assessment in patients having a partial response on morphological imaging.The overall cohort of the study is expected to be round 400-500 patients, with approximately half presenting with bulky masses. All PET scans of the Italian cohort will be analysed for volumetric assessment, comprising metabolic tumour volume and total lesion glycolysis at baseline and during the course of therapy. A dedicated software will delineate semiautomatically contours using different threshold methods, and the impact of each segmentation techniques will be evaluated. Bulky will be defined on contiguous lymph node masses ≥200 mL on CT/MRI. All bulky masses will be outlined and analysed by the same software to provide textural features. Morphological assessment will be based on RECIL 2017 for response definition.

ETHICS AND DISSEMINATION

The current study has been ethically approved (AIFA/SC/P/27087 approved 09/03/2018; EudraCT 2012-004053-88, EM-04). The results of the different analyses performed during and after study completion the will be actively disseminated through peer-reviewed journals, conference presentations, social media, print media and internet.

Memory Effect in the Spatial Series Based on Diamond and Graphite Crystals

To study the relation between the structure of a compound and its properties is one of the fundamental trends in chemistry and materials science. A classic example is the well-known influence of the structures of diamond and graphite on their physicochemical properties, in particular, hardness. However, some other properties of these allotropic modifications of carbon, e.g., fractal properties, are poorly understood. In this work, the spatial series (interatomic distance histograms) calculated using the crystal structures of diamond and graphite are investigated. Hurst exponents H are estimated using detrended fluctuation analysis and power spectral density. The values of H are found to be 0.27–0.32 and 0.37–0.42 for diamond and graphite, respectively. The calculated data suggest that the spatial series have long memory with a negative correlation between the terms of the series; that is, they are antipersistent.

Prognostic Impact of Intratumoral Heterogeneity Based on Fractal Geometry Analysis in Operated NSCLC Patients

PURPOSE

To determine the heterogeneity of glucose uptake applying fractal analysis on positron emission tomography/computed tomography (PET/CT) with 2-deoxy-2-[¹⁸F]fluoro-D-glucose ([¹⁸F]FDG) images in patients with non-small cell lung carcinoma (NSCLC) before surgery, and to assess whether this heterogeneity was associated with disease-free survival (DFS).

PROCEDURES

[¹⁸F]FDG PET/CT scans of 113 patients' prior surgery were retrospectively revised. PET DICOM images were analyzed for fractal geometry using a ad hoc software to automatically determine the following indexes: (a) mean intensity value (MIV), (b) standard deviation (SD), (c) relative dispersion (RD), (d) three-dimensional (3D) histogram of the fractal dimension (3D HIST FR DIM), and (e) fractal dimension in 3D (3D-FD). All the fractal indexes were subsequently compared with metabolic parameters and disease-free survival (DFS).

RESULTS

We found a significant correlation between 3D-FD and SUVmax, SUVmean, MTV, and TLG. Additionally, positive correlations between MIV, SD, and all metabolic parameters were also detected. Patients with high 3D-FD tumor (≥ 1.62) showed significantly higher values of SUVmax, SUVmean, MTV, and TLG than those with lower 3D-FD. In univariate analysis, median 3D-FD and median TLG were significantly associated with DFS (p = 0.04 and p = 0.03, respectively). These findings were confirmed on log-rank test. On multivariate analysis, among age, stage disease, histotype, 3D-FD, and metabolic parameters, only 3D-FD was identified as independent prognostic factor for DFS (p = 0.032; HR 0.418, 95 % CI 0.189-0.926). 3D-FD was different between adenocarcinoma and squamous cell carcinoma (1.60 versus 1.88, p = 0.014), and 3D-FD value was found higher in advanced stage disease.

CONCLUSIONS

Metabolic heterogeneity determined applying fractal principles on PET images can be considered as a novel imaging biomarker for survival in patients with NSCLC.

Fractal Dimension Analysis of High-Resolution X-Ray Phase Contrast Micro-Tomography Images at Different Threshold Levels in a Mouse Spinal Cord

Fractal analysis is a powerful method for the morphological study of complex systems that is increasingly applied to biomedical images. Spatial resolution and image segmentation are crucial for the discrimination of tissue structures at the multiscale level. In this work, we have applied fractal analysis to high-resolution X-ray phase contrast micro-tomography (XrPCμT) images in both uninjured and injured tissue of a mouse spinal cord. We estimated the fractal dimension (FD) using the box-counting method on tomographic slices segmented at different threshold levels. We observed an increased FD in the ipsilateral injured hemicord compared with the contralateral uninjured tissue, which was almost independent of the chosen threshold. Moreover, we found that images exhibited the highest fractality close to the global histogram threshold level. Finally, we showed that the FD estimate largely depends on the image histogram regardless of tissue appearance. Our results demonstrate that the pre-processing of XrPCμT images is critical to fractal analysis and the estimation of FD.