BP neural network-based analysis of the applicability of NMF in side-step cutting.

Background: Although the spatio-temporal structure of muscle activation in cutting have been studied extensively, including time-varying motor primitives and time-invariant motor modules under various conditions, the factorisation methods suitable for cutting are unclear, and the extent to which each factorisation method loses information about movement during dimensionality reduction is uncertain. Research question: To clarify the extent to which NMF, PCA and ICA retain information about movement when downscaling, and to explore the factorisation method suitable for cutting. Methods: The kinematic data during cutting was captured with a Vicon motion capture system, from which the kinematic features of the pelvic centre of mass were calculated. NMF, PCA and ICA were used to obtain muscle synergies based on sEMG of the cutting at different angles, respectively. A back propagation neural network was constructed using temporal component of synergy as input and the kinematics data of pelvic as output. Calculation of the Hurst index using fractal analysis based on the temporal component of muscle synergy. Results: The quality of sEMG reconstruction is significantly higher with ICA (P < 0.01) than with NMF and PCA for the cutting. The NMF reconstruction has a high degree of preservation of movement, whereas the ICA loses movement information about the most of the swing phase, and the PCA loses information related to the change of direction. Hurst index less than 0.5 for all three angles of cutting. Significance: NMF is suitable for extracting muscle synergies in all directions of cutting. Information related to movement may be lost when using PCA and ICA to extract the synergy of cutting. The high individual variability of muscle synergy in cutting may be responsible for the loss of movement information in muscle synergy.

Fractal Analysis in Clinical Neurosciences: An Overview.

Over the last years, fractals have entered into the realms of clinical neurosciences. The whole brain and its components (i.e., neurons and astrocytes) have been studied as fractal objects, and even more relevant, the fractal-based quantification of the geometrical complexity of histopathological and neuroradiological images as well as neurophysiopathological time series has suggested the existence of a gradient in the pattern representation of neurological diseases. Computational fractal-based parameters have been suggested as potential diagnostic and prognostic biomarkers in different brain diseases, including brain tumors, neurodegeneration, epilepsy, demyelinating diseases, cerebrovascular malformations, and psychiatric disorders as well. This chapter and the entire third section of this book are focused on practical applications of computational fractal-based analysis into the clinical neurosciences, namely, neurology and neuropsychiatry, neuroradiology and neurosurgery, neuropathology, neuro-oncology and neurorehabilitation, neuro-ophthalmology, and cognitive neurosciences, with special emphasis on the translation of the fractal dimension and other fractal parameters as clinical biomarkers useful from bench to bedside.

The Fractal Geometry of the Brain: AnOverview.

The first chapter of this book introduces some history, philosophy, and basic concepts of fractal geometry and discusses how the neurosciences can benefit from applying computational fractal-based analysis. Further, it compares fractal with Euclidean approaches to analyzing and quantifying the brain in its entire physiopathological spectrum and presents an overview of the first section of this book as well.

Point of Care Testing (POCT) in Psychopathology Using Fractal Analysis and Hilbert Huang Transform of Electroencephalogram (EEG).

Research has shown that relying only on self-reports for diagnosing psychiatric disorders does not yield accurate results at all times. The advances of technology as well as artificial intelligence and other machine learning algorithms have allowed the introduction of point of care testing (POCT) including EEG characterization and correlations with possible psychopathology. Nonlinear methods of EEG analysis have significant advantages over linear methods. Empirical mode decomposition (EMD) is a reliable nonlinear method of EEG pre-processing. In this chapter, we compare two existing EEG complexity measures - Higuchi fractal dimension (HFD) and sample entropy (SE), with our newly proposed method using Higuchi fractal dimension from the Hilbert Huang transform (HFD-HHT). We present an example using the three complexity measures on a 2-minute EEG recorded from a healthy 20-year-old male after signal pre-processing. Furthermore, we showed the usefulness of these complexity measures in the classification of major depressive disorder (MDD) with healthy controls. Our study is in line with previous research and has shown an increase in HFD and SE values in the full, alpha and beta frequency bands suggestive of an increase in EEG irregularity. Moreover, the HFD-HHT values decreased in those three bands for majority of electrodes which is suggestive of a decrease in irregularity in the frequency-time domain. We conclude that all three complexity measures can be vital features useful for EEG analysis which could be incorporated in POCT systems.

Box-Counting Fractal Analysis: A Primer for the Clinician.

This chapter lays out the elementary principles of fractal geometry underpinning much of the rest of this book. It assumes a minimal mathematical background, defines the key principles and terms in context, and outlines the basics of a fractal analysis method known as box counting and how it is used to perform fractal, lacunarity, and multifractal analyses. As a standalone reference, this chapter grounds the reader to be able to understand, evaluate, and apply essential methods to appreciate and heal the exquisitely detailed fractal geometry of the brain.

Morphology and Fractal-Based Classifications of Neurons and Microglia in Two and Three Dimensions.

Microglia and neurons live physically intertwined, intimately related structurally and functionally in a dynamic relationship in which microglia change continuously over a much shorter timescale than do neurons. Although microglia may unwind and depart from the neurons they attend under certain circumstances, in general, together both contribute to the fractal topology of the brain that defines its computational capabilities. Both neuronal and microglial morphologies are well-described using fractal analysis complementary to more traditional measures. For neurons, the fractal dimension has proved valuable for classifying dendritic branching and other neuronal features relevant to pathology and development. For microglia, fractal geometry has substantially contributed to classifying functional categories, where, in general, the more pathological the biological status, the lower the fractal dimension for individual cells, with some exceptions, including hyper-ramification. This chapter provides a review of the intimate relationships between neurons and microglia, by introducing 2D and 3D fractal analysis methodology and its applications in neuron-microglia function in health and disease.

Fractals, Pattern Recognition, Memetics, and AI: A Personal Journal in the Computational Neurosurgery.

In this chapter, the personal journey of the author in many countries, including Italy, Germany, Austria, the United Kingdom, Switzerland, the United States, Canada, and Australia, is summarized, aimed to merge different translational fields (such as neurosurgery and the clinical neurosciences in general, biomedical engineering, mathematics, computer science, and cognitive sciences) and lay the foundations of a new field defined computational neurosurgery, with fractals, pattern recognition, memetics, and artificial intelligence as the common key words of the journey.

Computational Fractal-Based Analysis of Brain Tumor Microvascular Networks.

Brain parenchyma microvasculature is set in disarray in the presence of tumors, and malignant brain tumors are among the most vascularized neoplasms in humans. As microvessels can be easily identified in histologic specimens, quantification of microvascularity can be used alone or in combination with other histological features to increase the understanding of the dynamic behavior, diagnosis, and prognosis of brain tumors. Different brain tumors, and even subtypes of the same tumor, show specific microvascular patterns, as a kind of "microvascular fingerprint," which is particular to each histotype. Reliable morphometric parameters are required for the qualitative and quantitative characterization of the neoplastic angioarchitecture, although the lack of standardization of a technique able to quantify the microvascular patterns in an objective way has limited the "morphometric approach" in neuro-oncology.In this chapter, we focus on the importance of computational-based morphometrics, for the objective description of tumoral microvascular fingerprinting. By also introducing the concept of "angio-space," which is the tumoral space occupied by the microvessels, we here present fractal analysis as the most reliable computational tool able to offer objective parameters for the description of the microvascular networks.The spectrum of different angioarchitectural configurations can be quantified by means of Euclidean and fractal-based parameters in a multiparametric analysis, aimed to offer surrogate biomarkers of cancer. Such parameters are here described from the methodological point of view (i.e., feature extraction) as well as from the clinical perspective (i.e., relation to underlying physiology), in order to offer new computational parameters to the clinicians with the final goal of improving diagnostic and prognostic power of patients affected by brain tumors.

Fractal Analysis in MATLAB: A Tutorial for Neuroscientists.

MATLAB is one of the software platforms most widely used for scientific computation. MATLAB includes a large set of functions, packages, and toolboxes that make it simple and fast to obtain complex mathematical and statistical computations for many applications. In this chapter, we review some tools available in MATLAB for performing fractal analyses on typical neuroscientific data in a practical way. We provide detailed examples of how to calculate the fractal dimension of 1D, 2D, and 3D data in MATLAB. Furthermore, we review other software packages for fractal analysis.

Fractal Geometry Meets Computational Intelligence: Future Perspectives.

Characterizations in terms of fractals are typically employed for systems with complex and multiscale descriptions. A prominent example of such systems is provided by the human brain, which can be idealized as a complex dynamical system made of many interacting subunits. The human brain can be modeled in terms of observable variables together with their spatio-temporal-functional relations. Computational intelligence is a research field bridging many nature-inspired computational methods, such as artificial neural networks, fuzzy systems, and evolutionary and swarm intelligence optimization techniques. Typical problems faced by means of computational intelligence methods include those of recognition, such as classification and prediction. Although historically conceived to operate in some vector space, such methods have been recently extended to the so-called nongeometric spaces, considering labeled graphs as the most general example of such patterns. Here, we suggest that fractal analysis and computational intelligence methods can be exploited together in neuroscience research. Fractal characterizations can be used to (i) assess scale-invariant properties and (ii) offer numeric, feature-based representations to complement the usually more complex pattern structures encountered in neurosciences. Computational intelligence methods could be used to exploit such fractal characterizations, considering also the possibility to perform data-driven analysis of nongeometric input spaces, therby overcoming the intrinsic limits related to Euclidean geometry.

Three-Dimensional Fractal Analysis of the Interstitial Cells of Cajal Networks of Gastrointestinal Tissue Specimens.

Introduction: Several functional gastrointestinal disorders (FGIDs) have been associated with the degradation or remodeling of the network of interstitial cells of Cajal (ICC). Introducing fractal analysis to the field of gastroenterology as a promising data analytics approach to extract key structural characteristics that may provide insightful features for machine learning applications in disease diagnostics. Fractal geometry has advantages over several physically based parameters (or classical metrics) for analysis of intricate and complex microstructures that could be applied to ICC networks. Methods: In this study, three fractal structural parameters: Fractal Dimension, Lacunarity, and Succolarity were employed to characterize scale-invariant complexity, heterogeneity, and anisotropy; respectively of three types of gastric ICC network structures from a flat-mount transgenic mouse stomach. Results: The Fractal Dimension of ICC in the longitudinal muscle layer was found to be significantly lower than ICC in the myenteric plexus and circumferential muscle in the proximal, and distal antrum, respectively (both p < 0.0001). Conversely, the Lacunarity parameters for ICC-LM and ICC-CM were found to be significantly higher than ICC-MP in the proximal and in the distal antrum, respectively (both p < 0.0001). The Succolarity measures of ICC-LM network in the aboral direction were found to be consistently higher in the proximal than in the distal antrum (p < 0.05). Conclusions: The fractal parameters presented here could go beyond the limitation of classical metrics to provide better understanding of the structural-functional relationship between ICC networks and the conduction of gastric bioelectrical slow waves.

One-step formation of three-dimensional interconnected T-shaped microstructures inside composites by orthogonal bidirectional self-assembly method.

The fillers inside a polymer matrix should typically be self-assembled in both the horizontal and vertical directions to obtain 3-dimentional (3D) percolation pathways, whereby the fields of application can be expanded and the properties of organic-inorganic composite films improved. Conventional dielectrophoresis techniques can typically only drive fillers to self-assemble in only one direction. We have devised a one-step dielectrophoresis-driven approach that effectively induces fillers self-assembly along two orthogonal axes, which results in the formation of 3D interconnected T-shaped iron microstructures (3D-T CIP) inside a polymer matrix. This approach to carbonyl iron powder (CIP) embedded in a polymer matrix results in a linear structure along the thickness direction and a network structure on the top surface of the film. The fillers in the polymer were controlled to achieve orthogonal bidirectional self-assembly using an external alternating current (AC) electric field and a non-contact technique that did not lead to electrical breakdown. The process of 3D-T CIP formation was observed in real time using in situ observation methods with optical microscopy, and the quantity and quality of self-assembly were characterized using statistical and fractal analysis. The process of fillers self-assembly along the direction perpendicular to the electric field was explained by finite element analogue simulations, and the results indicated that the insulating polyethylene terephthalate (PET) film between the electrode and the CIP/prepolymer suspension was the key to the formation of the 3D-T CIP. In contrast to the traditional two-step method of fabricating sandwich-structured film, the fabricated 3D-T CIP film with 3D electrically conductive pathways can be applied as magnetic field sensor.

A one-step electric field-induced self-assembly method was developed to efficiently control the self-assembly of fillers along two orthogonal axes to form three-dimensional interconnected T-shaped microstructure assembles of carbonyl iron powder inside a polymer matrix.

Comparison of periapical radiography, panoramic radiography, and CBCT in the evaluation of trabecular bone structure using fractal analysis.

OBJECTIVES: The aim of this study is to compare imaging techniques to evaluate trabecular bone structure using Fractal Analysis (FA). METHODS: Fifteen sheep hemimandibles were used for this study. Digital images were obtained using periapical radiography, panoramic radiography, and cone-beam computed tomography (CBCT). CBCT imaging was performed in standard (STD) and high-resolution (HR) modes. FA was conducted using ImageJ 1.3 software with the box-counting method on the images. The fractal dimension (FD) values were analyzed by the statistical software Jamovi 1.6.23. Statistical significance was accepted as p < 0.05. RESULTS: The highest mean FD value was the FD on digital periapical radiographs (PaFD) (1.28 ± 0.04), and the lowest mean FD value was the FD on standard resolution cone-beam computed tomography images (STD-CBCTFD) (1.12 ± 0.10). Although there was no statistically significant difference between the PaFD and the FD on digital panoramic radiographs (PanFD) (p = 0.485), the PaFD was found to be significantly higher than STD-CBCTFD (p < 0.001), and the FD on high-resolution cone-beam computed tomography images (HR-CBCTFD) (p = 0.007). The PanFD was found to be significantly higher than the STD-CBCTFD (p = 0.004). CONCLUSION: According to our results, in the evaluation of trabecular bone structure using FA, periapical radiographs and panoramic radiographs have similar image quality for assessment of the FD. On the other hand, CBCT results did not correlate with results from any of the other techniques in this study.

Prognostic value of left ventricular trabeculae fractal analysis in patients with dilated cardiomyopathy.

BACKGROUND: The prognostic value of left ventricular (LV) myocardial trabecular complexity on cardiovascular magnetic resonance (CMR) in dilated cardiomyopathy (DCM) remains unknown. This study aimed to evaluate the prognostic value of LV myocardial trabecular complexity using fractal analysis in patients with DCM. METHODS: Consecutive patients with DCM who underwent CMR between March 2017 and November 2021 at two hospitals were prospectively enrolled. The primary endpoints were defined as the combination of all-cause death and heart failure hospitalization. The events of cardiac death alone were defined as the secondary endpoints.LV trabeculae complexity was quantified by measuring the fractal dimension (FD) of the endocardial border based on fractal geometry on CMR. Cox proportional hazards regression and Kaplan-Meier survival analysis were used to examine the association between variables and outcomes. The incremental prognostic value of FD was assessed in nested models. RESULTS: A total of 403 patients with DCM (49.31 ± 14.68 years, 69% male) were recruited. After a median follow-up of 43 months (interquartile range, 28-55 months), 87 and 24 patients reached the primary and secondary endpoints, respectively. Age, heart rate, New York Heart Association functional class >II, N-terminal pro-B-type natriuretic peptide, LV ejection fraction, LV end-diastolic volume index, LV end-systolic volume index, LV mass index, presence of late gadolinium enhancement, global FD, LV mean apical FD, and LV maximal apical FD were univariably associated with the outcomes (all P < 0.05). After multivariate adjustment, LV maximal apical FD remained a significant independent predictor of outcome [hazard ratio = 1.179 (1.116, 1.246), P < 0.001]. The addition of LV maximal apical FD in the nested models added incremental prognostic value to other common clinical and imaging risk factors (all <0.001; C-statistic: 0.84-0.88, P < 0.001). CONCLUSION: LV maximal apical FD was an independent predictor of the adverse clinical outcomes in patients with DCM and provided incremental prognostic value over conventional clinical and imaging risk factors.

Comparative examination of trabecular bone structure in healthy and diabetic patients with periodontitis using fractal analysis.

OBJECTIVES: Fractal analysis is a numerical method that indicates the structural patterns and complexity of the trabecular bone on radiographs. The aim of this cross-sectional study was to evaluate the trabecular bone structure in systemically healthy patients and diabetes mellitus patients with periodontitis using fractal analysis. METHOD AND MATERIALS: The study included 125 mandibular first molars of nonsmoker patients. The subjects were divided into five subgroups: diabetes mellitus patients with mild-moderate periodontitis, diabetes mellitus patients with advanced periodontitis, systemically healthy individuals with mild-moderate periodontitis, systemically healthy individuals with advanced periodontitis, and systemically healthy individuals with gingivitis (control group). Clinical periodontal parameters (pocket depth, bleeding on probing, clinical attachment loss, and bone loss) were recorded. Two specific sites located in the mesial-distal regions (n = 250) of the mandibular first molars were identified using periapical radiographs captured with a parallel technique. Fractal analysis values were calculated using the box-counting method. One-way analysis of variance (ANOVA), and Pearson correlation analysis were used for statistical evaluation. RESULTS: The highest fractal analysis values were observed in systemically healthy with gingivitis patients (mesial fractal analysis: 1.86 ± 0.01; distal fractal analysis: 1.85 ± 0.01). Patients with periodontitis (mesial fractal analysis: 1.78 ± 0.02; distal fractal analysis: 1.79 ± 0.01) exhibited lower fractal analysis values compared to the control group. There was no significant difference in mesial and distal fractal analysis values between all periodontitis groups. No correlation was found between age, sex, clinical attachment loss, bone loss, and fractal analysis (P > .05). CONCLUSIONS: Although fractal analysis values were lower in the periodontitis groups compared to the control group, fractal analysis did not demonstrate any periodontitis-associated changes of bone trabeculation in diabetes at any stage of periodontitis. Furthermore, there was no significant association between fractal analysis values and age, sex, clinical attachment, and bone loss.

Improving morphological and functional properties of enteric neuronal networks in vitro using a novel upside-down culture approach.

The enteric nervous system (ENS) comprises millions of neurons and glia embedded in the wall of the gastrointestinal tract. It not only controls important functions of the gut but also interacts with the immune system, gut microbiota, and the gut-brain axis, thereby playing a key role in the health and disease of the whole organism. Any disturbance of this intricate system is mirrored in an alteration of electrical functionality, making electrophysiological methods important tools for investigating ENS-related disorders. Microelectrode arrays (MEAs) provide an appropriate noninvasive approach to recording signals from multiple neurons or whole networks simultaneously. However, studying isolated cells of the ENS can be challenging, considering the limited time that these cells can be kept vital in vitro. Therefore, we developed an alternative approach cultivating cells on glass samples with spacers (fabricated by photolithography methods). The spacers allow the cells to grow upside down in a spatially confined environment while enabling acute consecutive recordings of multiple ENS cultures on the same MEA. Upside-down culture also shows beneficial effects on the growth and behavior of enteric neural cultures. The number of dead cells was significantly decreased, and neural networks showed a higher resemblance to the myenteric plexus ex vivo while producing more stable signals than cultures grown in the conventional way. Overall, our results indicate that the upside-down approach not only allows to investigate the impact of neurological diseases in vitro but could also offer insights into the growth and development of the ENS under conditions much closer to the in vivo environment.NEW & NOTEWORTHY In this study, we devised a novel approach for culturing and electrophysiological recording of the enteric nervous system using custom-made glass substrates with spacers. This allows to turn cultures of isolated myenteric plexus upside down, enhancing the use of the microelectrode array technique by allowing recording of multiple cultures consecutively using only one chip. In addition, upside-down culture led to significant improvements in the culture conditions, resulting in a more in vivo-like growth.

3D Fractal Dimension Analysis: Prognostic Value of Right Ventricular Trabecular Complexity in Participants with Arrhythmogenic Cardiomyopathy.

BACKGROUND: Arrhythmogenic cardiomyopathy (ACM) is characterized by progressive myocardial fibro-fatty infiltration accompanied by trabecular disarray. Traditionally, two-dimensional (2D) instead of 3D fractal dimension (FD) analysis has been used to evaluate trabecular disarray. However, the prognostic value of trabecular disorder assessed by 3D FD measurement remains unclear. PURPOSE: To investigate the prognostic value of right ventricular trabecular complexity in ACM patients using 3D FD analysis based on cardiac MR cine images. STUDY TYPE: Retrospective. POPULATION: 85 ACM patients (mean age: 45 ± 17 years, 52 male). FIELD STRENGTH/SEQUENCE: 3.0T/cine imaging, T2-short tau inversion recovery (T2-STIR), and late gadolinium enhancement (LGE). ASSESSMENT: Using cine images, RV (right ventricular) volumetric and functional parameters were obtained. RV trabecular complexity was measured with 3D fractal analysis by box-counting method to calculate 3D-FD. Cox and logistic regression models were established to evaluate the prognostic value of 3D-FD for major adverse cardiac events (MACE). STATISTICAL TESTS: Cox regression and logistic regression to explore the prognostic value of 3D-FD. C-index, time-dependent receiver operating characteristic (ROC) curves and area under the ROC curve (AUC) to evaluate the incremental value of 3D-FD. Intraclass correlation coefficient for interobserver variability. P < 0.05 indicated statistical significance. RESULTS: 26 MACE were recorded during the 60 month follow-up (interquartile range: 48-67 months). RV 3D-FD significantly differed between ACM patients with MACE (2.67, interquartile range: 2.51 ~ 2.81) and without (2.52, interquartile range: 2.40 ~ 2.67) and was a significant independent risk factor for MACE (hazard ratio, 1.02; 95% confidence interval: 1.01, 1.04). In addition, prognostic model fitness was significantly improved after adding 3D-FD to RV global longitudinal strain, LV involvement, and 5-year risk score separately. DATA CONCLUSION: The myocardial trabecular complexity assessed through 3D FD analysis was found associated with MACE and provided incremental prognostic value beyond conventional ACM risk factors. EVIDENCE LEVEL: 4 TECHNICAL EFFICACY: Stage 1.

Multifractal Heart Rate Value Analysis: A Novel Approach for Diabetic Neuropathy Diagnosis.

Type 2 diabetes mellitus (T2DM) is characterized by several complications, such as retinopathy, renal failure, cardiovascular disease, and diabetic neuropathy. Among these, neuropathy is the most severe complication, due to the challenging nature of its early detection. The linear Hearth Rate Variability (HRV) analysis is the most common diagnosis technique for diabetic neuropathy, and it is characterized by the determination of the sympathetic-parasympathetic balance on the peripheral nerves through a linear analysis of the tachogram obtained using photoplethysmography. We aimed to perform a multifractal analysis to identify autonomic neuropathy, which was not yet manifest and not detectable with the linear HRV analysis. We enrolled 10 healthy controls, 10 T2DM-diagnosed patients with not-full-blown neuropathy, and 10 T2DM diagnosed patients with full-blown neuropathy. The tachograms for the HRV analysis were obtained using finger photoplethysmography and a linear and/or multifractal analysis was performed. Our preliminary results showed that the linear analysis could effectively differentiate between healthy patients and T2DM patients with full-blown neuropathy; nevertheless, no differences were revealed comparing the full-blown to not-full-blown neuropathic diabetic patients. Conversely, the multifractal HRV analysis was effective for discriminating between full-blown and not-full-blown neuropathic T2DM patients. The multifractal analysis can represent a powerful strategy to determine neuropathic onset, even without clinical diagnostic evidence.

Determination of growth and developmental stages in hand-wrist radiographs : Can fractal analysis in combination with artificial intelligence be used?

PURPOSE: The goal of this work was to assess the classification of maturation stage using artificial intelligence (AI) classifiers. METHODS: Hand-wrist radiographs (HWRs) from 1067 individuals aged between 7 and 18 years were included. Fifteen regions of interest were selected for fractal dimension (FD) analysis. Five predictive models with different inputs were created (model 1: only FD; model 2: FD and Chapman sesamoid stage; model 3: FD, age, and sex; model 4: FD, Chapman sesamoid stage, age, and sex; model 5: Chapman sesamoid stage, age, and sex). The target diagnoses were accelerating growth velocity, very high growth velocity, and decreasing growth velocity. Four AI algorithms were applied: multilayer perceptron (MLP), support vector machine (SVM), gradient boosting machine (GBM) and C 5.0 decision tree classifier. RESULTS: All AI algorithms except for C 5.0 yielded similar overall predictive accuracies for the five models. In order from lowest to highest, the predictive accuracies of the models were as follows: model 1 < model 3 < model 2 < model 5 < model 4. The highest overall F1 score, which was used instead of accuracy especially for models with unbalanced data, was obtained for models 1, 2, and 3 based on SVM, for model 4 based on MLP, and for model 5 based on C 5.0. Adding Chapman sesamoid stage, chronologic age, and sex as additional inputs to the FD values significantly increased the F1 score. CONCLUSION: Applying FD analysis to HWRs is not sufficient to predict maturation stage in growing patients but can be considered a growth rate prediction method if combined with the Chapman sesamoid stage, age, and sex.