Experimental Study on the Flexural Performance of Steel-Polyvinyl Alcohol Hybrid Fiber-Reinforced Concrete.

This paper explores the impact of steel-PVA hybrid fibers (S-PVA HF) on the flexural performance of panel concrete via three-point bending tests. Crack development in the concrete is analyzed through Digital Image Correlation (DIC) and Scanning Electron Microscope (SEM) experiments, unveiling the underlying mechanisms. The evolution of cracks in concrete is quantitatively analyzed based on fractal theory, and a predictive model for flexural strength (PMFS) is established. The results show that the S-PVA HF exhibits a synergistic effect in enhancing and toughening the concrete at multi-scale. The crack area of steel-PVA hybrid fiber concrete (S-PVA HFRC) is linearly correlated with deflection (δ), and it further reduces the crack development rate and crack area compared to steel fiber-reinforced concrete (SFRC). The S-PVA HF improves the proportional ultimate strength (fL) and residual flexural strength (fR,j) of concrete, and the optimal flexural performance of concrete is achieved when the steel fiber dosage is 1.0% and the PVA fiber dosage is 0.2%. The established PMFS of hybrid fiber-reinforced concrete (HFRC) can effectively predict the flexural strength of concrete.

An Atomistic View on the Mechanism of Diatom Peptide-Guided Biomimetic Silica Formation.

Deciphering nature's remarkable way of encoding functions in its biominerals holds the potential to enable the rational development of nature-inspired materials with tailored properties. However, the complex processes that convert solution-state precursors into solid biomaterials remain largely unknown. In this study, an unconventional approach is presented to characterize these precursors for the diatom-derived peptides R5 and synthetic Silaffin-1A1 (synSil-1A1). These molecules can form defined supramolecular assemblies in solution, which act as templates for solid silica structures. Using a tailored structural biology toolbox, the structure-function relationships of these self-assemblies are unveiled. NMR-derived constraints are employed to enable a recently developed fractal-cluster formalism and then reveal the architecture of the peptide assemblies in atomistic detail. Finally, by monitoring the self-assembly activities during silica formation at simultaneous high temporal and residue resolution using real-time spectroscopy, the mechanism is elucidated underlying template-driven silica formation. Thus, it is demonstrated how to exercise morphology control over bioinorganic solids by manipulating the template architectures. It is found that the morphology of the templates is translated into the shape of bioinorganic particles via a mechanism that includes silica nucleation on the solution-state complexes' surfaces followed by complete surface coating and particle precipitation.

Novel Use of Fractal Analysis for Quantifying Polymethylmethacrylate Distribution Patterns in Osteoporotic and Malignant Vertebral Compression Fractures Following Vertebroplasty.

Purpose: Fractal analysis is a mathematical tool which allows the evaluation of complex microstructural features within materials that cannot be expressed in traditional geometric terms. The purpose of this study is to quantify the differences in polymethylmethacrylate intravertebral cement spatial distribution patterns following vertebroplasty using fractal analysis through the examination of osteoporotic and malignant compression fractures. Methods: Frontal and lateral post-vertebroplasty radiographs were evaluated from 29 patients with osteoporotic and malignant compression fractures who underwent vertebroplasty. The individually treated vertebra were divided into osteoporotic (n = 35) and malignant groups (n = 41). Images underwent segmentation, thresholding, and binarization prior to fractal analysis. Fractal dimension and lacunarity values were derived from the region of interest in treated vertebrae using the "box-counting" and "gliding-box" techniques respectively using ImageJ. The mean values of both parameters were compared between the 2 groups. Results: The mean fractal dimension was significantly higher in the malignant vertebral compression fracture group (1.53 ± 0.08) compared to the osteoporotic group (1.34 ± 0.17; P < .001). Similarly, mean lacunarity values were significantly higher in the malignant fracture group (0.50 ± 0.09) compared to the osteoporotic group (0.37 ± 0.10; P < .001). Conclusions: Fractal dimension and lacunarity values of cement spatial distribution patterns obtained from the post-vertebroplasty radiographs can differentiate between benign osteoporotic and malignant vertebral compression fractures. This novel technique may be useful for evaluating cement spatial distribution patterns in spine augmentation procedures, although further research is warranted in this area.

Development, Application and Utility of a Machine Learning Approach for Melanoma and Non-Melanoma Lesion Classification Using Counting Box Fractal Dimension.

The diagnosis and identification of melanoma are not always accurate, even for experienced dermatologists. Histopathology continues to be the gold standard, assessing specific parameters such as the Breslow index. However, it remains invasive and may lack effectiveness. Therefore, leveraging mathematical modeling and informatics has been a pursuit of diagnostic methods favoring early detection. Fractality, a mathematical parameter quantifying complexity and irregularity, has proven useful in melanoma diagnosis. Nonetheless, no studies have implemented this metric to feed artificial intelligence algorithms for the automatic classification of dermatological lesions, including melanoma. Hence, this study aimed to determine the combined utility of fractal dimension and unsupervised low-computational-requirements machine learning models in classifying melanoma and non-melanoma lesions. We analyzed 39,270 dermatological lesions obtained from the International Skin Imaging Collaboration. Box-counting fractal dimensions were calculated for these lesions. Fractal values were used to implement classification methods by unsupervised machine learning based on principal component analysis and iterated K-means (100 iterations). A clear separation was observed, using only fractal dimension values, between benign or malignant lesions (sensibility 72.4% and specificity 50.1%) and melanoma or non-melanoma lesions (sensibility 72.8% and specificity 50%) and subsequently, the classification quality based on the machine learning model was ≈80% for both benign and malignant or melanoma and non-melanoma lesions. However, the grouping of metastatic melanoma versus non-metastatic melanoma was less effective, probably due to the small sample size included in MM lesions. Nevertheless, we could suggest a decision algorithm based on fractal dimension for dermatological lesion discrimination. On the other hand, it was also determined that the fractal dimension is sufficient to generate unsupervised artificial intelligence models that allow for a more efficient classification of dermatological lesions.

EVALUATION OF MANDIBULAR TRABECULAR AND CORTICAL STRUCTURE BY FRACTAL ANALYSIS IN HYPERLIPIDEMIA AND HYPERTENSION PATIENTS.

INTRODUCTION: This study aimed to evaluate the mandibular trabecular and cortical changes in patients with hyperlipidemia (HL) and/or hypertension (HT) using fractal dimension (FD) analysis, mandibular cortical width (MCW), panoramic mandibular index (PMI) and mandibular cortical index (MCI). MATERIALS AND METHODS: Panoramic radiographs of 100 patients were evaluated. FD measurement of three region of interest (ROI) including the angulus, corpus and interdental bone area were made. MCW, PMI and MCI were also measured and noted. RESULTS: Angulus, corpus and interdental FD values were significantly lower in three disease groups than the control group. Angulus, corpus, and interdental FD values were significantly lower in the HL+HT group than in the HL group and HT group. MCW value was significantly lower in the HL group, HT group, and HL+HT group than the control group. The cortical index C1 was more common in the control group while C2 was more common in the HT, HL and HL+HT group. CONCLUSION: The fact that FD was significantly lower in the HL+HT group compared to the HL and HT groups indicates the positive effect of their association on bone loss and quality. FD measurements on images obtained using a direct digital panoramic system can be used for treatment planning and follow-up of patients with HL and/or HT.

Lineages of Fractal Genera Comprise the 88-Million-Year Steel Evolutionary Spine of the Ecosphere.

Fractal evolution is apparently effective in selectively preserving environmentally resilient traits for more than 80 million years in Streptotrichaceae (Bryophyta). An analysis simulated maximum destruction of ancestral traits in that large lineage. The constraints enforced were the preservation of newest ancestral traits, and all immediate descendant species obtained different new traits. Maximum character state changes in ancestral traits were 16 percent of all possible traits in any one sub-lineage, or 73 percent total of the entire lineage. Results showed, however, that only four ancestral traits were permanently eliminated in any one lineage or sub-lineage. A lineage maintains maximum biodiversity of temporally and regionally survival-effective traits at minimum expense to resilience across a geologic time of 88 million years for the group studied. Similar processes generating an extant punctuated equilibrium as bursts of about four descendants per genus and one genus per 1-2 epochs are possible in other living groups given similar emergent processes. The mechanism is considered complexity-related, the lineage being a self-organized emergent phenomenon strongly maintained in the ecosphere by natural selection on fractal genera.

The Pathologically Evolving Aggregation-State of Cells in Cancerous Tissues as Interpreted by Fractal and Multi-Fractal Dispersion Theory in Saturated Porous Formations.

A recent author's fractal fluid-dynamic dispersion theory in porous media has focused on the derivation of the associated nonergodic (or effective) macrodispersion coefficients by a 3-D stochastic Lagrangian approach. As shown by the present study, the Fickian (i.e., the asymptotic constant) component of a properly normalized version of these coefficients exhibits a clearly detectable minimum in correspondence with the same fractal dimension (d ≅ 1.7) that seems to characterize the diffusion-limited aggregation state of cells in advanced stages of cancerous lesion progression. That circumstance suggests that such a critical fractal dimension, which is also reminiscent of the colloidal state of solutions (and may therefore identify the microscale architecture of both living and non-living two-phase systems in state transition conditions) may actually represent a sort of universal nature imprint. Additionally, it suggests that the closed-form analytical solution that was provided for the effective macrodispersion coefficients in fractal porous media may be a reliable candidate as a physically-based descriptor of blood perfusion dynamics in healthy as well as cancerous tissues. In order to evaluate the biological meaningfulness of this specific fluid-dynamic parameter, a preliminary validation is performed by comparison with the results of imaging-based clinical surveys. Moreover, a multifractal extension of the theory is proposed and discussed in view of a perspective interpretative diagnostic utilization.

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.

Classifying breast cancer and fibroadenoma tissue biopsies from paraffined stain-free slides by fractal biomarkers in Fourier Ptychographic Microscopy.

Breast cancer is one of the most spread and monitored pathologies in high-income countries. After breast biopsy, histological tissue is stored in paraffin, sectioned and mounted. Conventional inspection of tissue slides under benchtop light microscopes involves paraffin removal and staining, typically with H&E. Then, expert pathologists are called to judge the stained slides. However, paraffin removal and staining are operator-dependent, time and resources consuming processes that can generate ambiguities due to non-uniform staining. Here we propose a novel method that can work directly on paraffined stain-free slides. We use Fourier Ptychography as a quantitative phase-contrast microscopy method, which allows accessing a very wide field of view (i.e., mm2) in one single image while guaranteeing high lateral resolution (i.e., 0.5 µm). This imaging method is multi-scale, since it enables looking at the big picture, i.e. the complex tissue structure and connections, with the possibility to zoom-in up to the single-cell level. To handle this informative image content, we introduce elements of fractal geometry as multi-scale analysis method. We show the effectiveness of fractal features in describing and classifying fibroadenoma and breast cancer tissue slides from ten patients with very high accuracy. We reach 94.0 ± 4.2% test accuracy in classifying single images. Above all, we show that combining the decisions of the single images, each patient's slide can be classified with no error. Besides, fractal geometry returns a guide map to help pathologist to judge the different tissue portions based on the likelihood these can be associated to a breast cancer or fibroadenoma biomarker. The proposed automatic method could significantly simplify the steps of tissue analysis and make it independent from the sample preparation, the skills of the lab operator and the pathologist.

Computational Fractal-Based Analysis of MR Susceptibility-Weighted Imaging (SWI) in Neuro-Oncology and Neurotraumatology.

Susceptibility-weighted imaging (SWI) is a magnetic resonance imaging (MRI) technique able to depict the magnetic susceptibility produced by different substances, such as deoxyhemoglobin, calcium, and iron. The main application of SWI in clinical neuroimaging is detecting microbleedings and venous vasculature. Quantitative analyses of SWI have been developed over the last few years, aimed to offer new parameters, which could be used as neuroimaging biomarkers. Each technique has shown pros and cons, but no gold standard exists yet. The fractal dimension (FD) has been investigated as a novel potential objective parameter for monitoring intratumoral space-filling properties of SWI patterns. We showed that SWI patterns found in different tumors or different glioma grades can be represented by a gradient in the fractal dimension, thereby enabling each tumor to be assigned a specific SWI fingerprint. Such results were especially relevant in the differentiation of low-grade versus high-grade gliomas, as well as from high-grade gliomas versus lymphomas.Therefore, FD has been suggested as a potential image biomarker to analyze intrinsic neoplastic architecture in order to improve the differential diagnosis within clinical neuroimaging, determine appropriate therapy, and improve outcome in patients.These promising preliminary findings could be extended into the field of neurotraumatology, by means of the application of computational fractal-based analysis for the qualitative and quantitative imaging of microbleedings in traumatic brain injury patients. In consideration of some evidences showing that SWI signals are correlated with trauma clinical severity, FD might offer some objective prognostic biomarkers.In conclusion, fractal-based morphometrics of SWI could be further investigated to be used in a complementary way with other techniques, in order to form a holistic understanding of the temporal evolution of brain tumors and follow-up response to treatment, with several further applications in other fields, such as neurotraumatology and cerebrovascular neurosurgery as well.

Fractal-Based Analysis of Arteriovenous Malformations (AVMs).

Arteriovenous malformations (AVMs) are cerebrovascular lesions consisting of a pathologic tangle of the vessels characterized by a core termed the nidus, which is the "nest" where the fistulous connections occur. AVMs can cause headache, stroke, and/or seizures. Their treatment can be challenging requiring surgery, endovascular embolization, and/or radiosurgery as well. AVMs' morphology varies greatly among patients, and there is still a lack of standardization of angioarchitectural parameters, which can be used as morphometric parameters as well as potential clinical biomarkers (e.g., related to prognosis).In search of new diagnostic and prognostic neuroimaging biomarkers of AVMs, computational fractal-based models have been proposed for describing and quantifying the angioarchitecture of the nidus. In fact, the fractal dimension (FD) can be used to quantify AVMs' branching pattern. Higher FD values are related to AVMs characterized by an increased number and tortuosity of the intranidal vessels or to an increasing angioarchitectural complexity as a whole. Moreover, FD has been investigated in relation to the outcome after Gamma Knife radiosurgery, and an inverse relationship between FD and AVM obliteration was found.Taken altogether, FD is able to quantify in a single and objective value what neuroradiologists describe in qualitative and/or semiquantitative way, thus confirming FD as a reliable morphometric neuroimaging biomarker of AVMs and as a potential surrogate imaging biomarker. Moreover, computational fractal-based techniques are under investigation for the automatic segmentation and extraction of the edges of the nidus in neuroimaging, which can be relevant for surgery and/or radiosurgery planning.

Fractal-Based Analysis of Histological Features of Brain Tumors.

The structural complexity of brain tumor tissue represents a major challenge for effective histopathological diagnosis. Tumor vasculature is known to be heterogeneous, and mixtures of patterns are usually present. Therefore, extracting key descriptive features for accurate quantification is not a straightforward task. Several steps are involved in the texture analysis process where tissue heterogeneity contributes to the variability of the results. One of the interesting aspects of the brain lies in its fractal nature. Many regions within the brain tissue yield similar statistical properties at different scales of magnification. Fractal-based analysis of the histological features of brain tumors can reveal the underlying complexity of tissue structure and angiostructure, also providing an indication of tissue abnormality development. It can further be used to quantify the chaotic signature of disease to distinguish between different temporal tumor stages and histopathological grades.Brain meningioma subtype classifications' improvement from histopathological images is the main focus of this chapter. Meningioma tissue texture exhibits a wide range of histological patterns whereby a single slide may show a combination of multiple patterns. Distinctive fractal patterns quantified in a multiresolution manner would be for better spatial relationship representation. Fractal features extracted from textural tissue patterns can be useful in characterizing meningioma tumors in terms of subtype classification, a challenging problem compared to histological grading, and furthermore can provide an objective measure for quantifying subtle features within subtypes that are hard to discriminate.

Percolation Images: Fractal Geometry Features for Brain Tumor Classification.

Brain tumor detection is crucial for clinical diagnosis and efficient therapy. In this work, we propose a hybrid approach for brain tumor classification based on both fractal geometry features and deep learning. In our proposed framework, we adopt the concept of fractal geometry to generate a "percolation" image with the aim of highlighting important spatial properties in brain images. Then both the original and the percolation images are provided as input to a convolutional neural network to detect the tumor. Extensive experiments, carried out on a well-known benchmark dataset, indicate that using percolation images can help the system perform better.

Multifractal Analysis of Brain Tumor Interface in Glioblastoma.

The dynamics of tumor growth is a very complex process, generally accompanied by numerous chromosomal aberrations that determine its genetic and dynamical heterogeneity. Consequently, the tumor interface exhibits a non-regular and heterogeneous behavior often described by a single fractal dimension. A more suitable approach is to consider the tumor interface as a multifractal object that can be described by a set of generalized fractal dimensions. In the present work, detrended fluctuation and multifractal analysis are used to characterize the complexity of glioblastoma.

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 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.

Fractal Dimension Analysis in Neurological Disorders: An Overview.

Fractal analysis has emerged as a powerful tool for characterizing irregular and complex patterns found in the nervous system. This characterization is typically applied by estimating the fractal dimension (FD), a scalar index that describes the topological complexity of the irregular components of the nervous system, both at the macroscopic and microscopic levels, that may be viewed as geometric fractals. Moreover, temporal properties of neurophysiological signals can also be interpreted as dynamic fractals. Given its sensitivity for detecting changes in brain morphology, FD has been explored as a clinically relevant marker of brain damage in several neuropsychiatric conditions as well as in normal and pathological cerebral aging. In this sense, evidence is accumulating for decreases in FD in Alzheimer's disease, frontotemporal dementia, Parkinson's disease, multiple sclerosis, and many other neurological disorders. In addition, it is becoming increasingly clear that fractal analysis in the field of clinical neurology opens the possibility of detecting structural alterations in the early stages of the disease, which highlights FD as a potential diagnostic and prognostic tool in clinical practice.

Bone Trabecular Pattern Analysis in Odontogenic Cysts Using Cone Beam Computed Tomography: A Clinical Retrospective Study.

Introduction The cysts of the maxillofacial region account for one of the most common pathologies of the head and neck region after the mucosal pathologies. Radiography provides an essential clue in early diagnosis and triaging, but it continues further as it is used to evaluate the post-treatment outcome. However, manual analysis is prone to errors. In this scenario, fractal analysis (FA) in radiographs uses mathematical methods to analyse the changes in grey scales in a given radiographic image. FA in odontogenic cysts is used to characterise their complexity, uncover hidden patterns, monitor treatment response, and potentially provide prognostic information. This paper aimed to assess the fractal characteristics of the radicular cyst (RC), dentigerous cyst (DC), and odontogenic keratocyst (OKC) using cone beam computed tomography (CBCT). The objective was to calculate fractal dimension (FD) values expressed in each of these cysts, which could prove to be a radiological adjunct in diagnosing the above cysts. Materials and methods As this is a retrospective study, the archives of CBCT images from June 2021 to December 2023 were obtained from patients diagnosed and confirmed with a histopathological diagnosis with RC, DC, and OKC. The FA was performed using Image J Software (Ver 1.51, National Institute of Health Bethesda, Fiji). The cortical and cancellous bones were segmented using thresholding techniques and converted to binary images. The mean FD of the three planes was then compared to establish the distinctive fractal characteristic for the specific odontogenic cysts. A one-way ANOVA was performed using the Statistical Product and Service Solutions (SPSS) (version 23.0; IBM SPSS Statistics for Windows, Armonk, NY) to determine the difference between FD values of RC, DC, and OKC with a significance level less than 0.05. Results The FD values of DC, RC, and OKC were 1.33 ± 0.17, 1.08 ± 0.16, and 1.65 ± 0.12, respectively. The results indicated that OKC had higher FD values than DC and RC, which means that OKC had lesser bone destruction compared to DC and RC. Inferential statistics showed that the one-way ANOVA was used to compare the means of the three groups of FD data. When calculated for the three groups, the F-statistic value was at 7.29, which yielded a P value of 0.03, making it statistically significant for a 95% confidence interval (p<0.05). Conclusion Our CBCT study on bone trabecular pattern analysis using FD and FA in odontogenic cysts reveals distinct alterations in bone parameters among different cyst types. The probability of higher FD values in OKC is because of lesser cortical bone destruction in OKC compared to the other cyst types. These findings have potential implications for diagnosing, treating, and prognosticating odontogenic cysts.

Low-Loading Mixed Matrix Materials: Fractal-Like Structure and Peculiarly Enhanced Gas Permeability.

Mixed matrix materials (MMMs) containing metal-organic framework (MOF) nanoparticles are attractive for membrane carbon capture. Particularly, adding <5 mass % MOFs in polymers dramatically increased gas permeability, far surpassing the Maxwell model's prediction. However, no sound mechanisms have been offered to explain this unusual low-loading phenomenon. Herein, we design an ideal series of MMMs containing polyethers (one of the leading polymers for CO2/N2 separation) and discrete metal-organic polyhedra (MOPs) with cage sizes of 2-5 nm. Adding 3 mass % MOP-3 in a polyether increases the CO2 permeability by 100% from 510 to 1000 Barrer at 35 °C because of the increased gas diffusivity. No discernible changes in typical physical properties governing gas transport properties are detected, such as glass transition temperature, fractional free volume, d-spacing, etc. We hypothesize that this behavior is attributed to fractal-like networks formed by highly porous MOPs, and for the first time, we validate this hypothesis using small-angle X-ray scattering analysis.

Fractal calculus in tumor growth simulations: The proof is in the pudding.

Mathematical modeling in oncology has a long history. Recently, mathematical models and their predictions have made inroads into prospective clinical trials with encouraging results. The goal of many such modeling efforts is to make predictions, either to clinician's choice therapy or into "optimal" therapy - often for individual patients. The mathematical oncology community rightfully puts great hope into predictive modeling and mechanistic digital twins - but with this great opportunity comes great responsibility. Mathematical models need to be rigorously calibrated and validated, and their predictive performance ascertained, before conclusions about predictions into the unknown can be drawn. The recent article "Modeling tumor growth using fractal calculus: Insights into tumor dynamics" (Golmankhaneh et al., 2023), applied fractal calculus to tumor growth data. In this short commentary, I raise concerns about the study design and interpretation. In its current form, this study is poised to put cancer patients at risk if interpreted as concluded by the authors.