Emergence of fractal geometries in the evolution of a metabolic enzyme.

Fractals are patterns that are self-similar across multiple length-scales1. Macroscopic fractals are common in nature2-4; however, so far, molecular assembly into fractals is restricted to synthetic systems5-12. Here we report the discovery of a natural protein, citrate synthase from the cyanobacterium Synechococcus elongatus, which self-assembles into Sierpinski triangles. Using cryo-electron microscopy, we reveal how the fractal assembles from a hexameric building block. Although different stimuli modulate the formation of fractal complexes and these complexes can regulate the enzymatic activity of citrate synthase in vitro, the fractal may not serve a physiological function in vivo. We use ancestral sequence reconstruction to retrace how the citrate synthase fractal evolved from non-fractal precursors, and the results suggest it may have emerged as a harmless evolutionary accident. Our findings expand the space of possible protein complexes and demonstrate that intricate and regulatable assemblies can evolve in a single substitution.

The effect of reef morphology on coral recruitment at multiple spatial scales.

Coral reefs are in decline worldwide, making it increasingly important to promote coral recruitment in new or degraded habitat. Coral reef morphology-the structural form of reef substrate-affects many aspects of reef function, yet the effect of reef morphology on coral recruitment is not well understood. We used structure-from-motion photogrammetry and airborne remote sensing to measure reef morphology (rugosity, curvature, slope, and fractal dimension) across a broad continuum of spatial scales and evaluated the effect of morphology on coral recruitment in three broadcast-spawning genera. We also measured the effect of other environmental and biotic factors such as fish density, adult coral cover, hydrodynamic larval import, and depth on coral recruitment. All variables combined explained 72% of coral recruitment in the study region. Coarse reef rugosity and curvature mapped at ≥2 m spatial resolution-such as large colonies, knolls, and boulders-were positively correlated with coral recruitment, explaining 22% of variation in recruitment. Morphology mapped at finer scales (≤32 cm resolution) was not significant. Hydrodynamic larval import was also positively related to coral recruitment in Porites and Montipora spp., and grazer fish density was linked to significantly lower recruitment in all genera. In addition, grazer density, reef morphology, and hydrodynamic import had differential effects on coral genera, reflecting genus-specific life history traits, and model performance was lower in gonochoric species. Overall, coral reef morphology is a key indicator of recruitment potential that can be detected by remote sensing, allowing potential larval sinks to be identified and factored into restoration actions.

Genetic and functional insights into the fractal structure of the heart.

The inner surfaces of the human heart are covered by a complex network of muscular strands that is thought to be a remnant of embryonic development1,2. The function of these trabeculae in adults and their genetic architecture are unknown. Here we performed a genome-wide association study to investigate image-derived phenotypes of trabeculae using the fractal analysis of trabecular morphology in 18,096 participants of the UK Biobank. We identified 16 significant loci that contain genes associated with haemodynamic phenotypes and regulation of cytoskeletal arborization3,4. Using biomechanical simulations and observational data from human participants, we demonstrate that trabecular morphology is an important determinant of cardiac performance. Through genetic association studies with cardiac disease phenotypes and Mendelian randomization, we find a causal relationship between trabecular morphology and risk of cardiovascular disease. These findings suggest a previously unknown role for myocardial trabeculae in the function of the adult heart, identify conserved pathways that regulate structural complexity and reveal the influence of the myocardial trabeculae on susceptibility to cardiovascular disease.

Fractal feature selection model for enhancing high-dimensional biological problems.

The integration of biology, computer science, and statistics has given rise to the interdisciplinary field of bioinformatics, which aims to decode biological intricacies. It produces extensive and diverse features, presenting an enormous challenge in classifying bioinformatic problems. Therefore, an intelligent bioinformatics classification system must select the most relevant features to enhance machine learning performance. This paper proposes a feature selection model based on the fractal concept to improve the performance of intelligent systems in classifying high-dimensional biological problems. The proposed fractal feature selection (FFS) model divides features into blocks, measures the similarity between blocks using root mean square error (RMSE), and determines the importance of features based on low RMSE. The proposed FFS is tested and evaluated over ten high-dimensional bioinformatics datasets. The experiment results showed that the model significantly improved machine learning accuracy. The average accuracy rate was 79% with full features in machine learning algorithms, while FFS delivered promising results with an accuracy rate of 94%.

In Silico Design of Heterogeneous Microvascular Trees Using Generative Adversarial Networks and Constrained Constructive Optimization.

OBJECTIVE: Designing physiologically adequate microvascular trees is of crucial relevance for bioengineering functional tissues and organs. Yet, currently available methods are poorly suited to replicate the morphological and topological heterogeneity of real microvascular trees because the parameters used to control tree generation are too simplistic to mimic results of the complex angiogenetic and structural adaptation processes in vivo. METHODS: We propose a method to overcome this limitation by integrating a conditional deep convolutional generative adversarial network (cDCGAN) with a local fractal dimension-oriented constrained constructive optimization (LFDO-CCO) strategy. The cDCGAN learns the patterns of real microvascular bifurcations allowing for their artificial replication. The LFDO-CCO strategy connects the generated bifurcations hierarchically to form microvascular trees with a vessel density corresponding to that observed in healthy tissues. RESULTS: The generated artificial microvascular trees are consistent with real microvascular trees regarding characteristics such as fractal dimension, vascular density, and coefficient of variation of diameter, length, and tortuosity. CONCLUSIONS: These results support the adoption of the proposed strategy for the generation of artificial microvascular trees in tissue engineering as well as for computational modeling and simulations of microcirculatory physiology.

Local fractal dimension of collagen detects increased spatial complexity in fibrosis.

Increase of collagen content and reorganization characterizes fibrosis but quantifying the latter remains challenging. Spatially complex structures are often analyzed via the fractal dimension; however, established methods for calculating this quantity either provide a single dimension for an entire object or a spatially distributed dimension that only considers binary images. These neglect valuable information related to collagen density in images of fibrotic tissue. We sought to develop a fractal analysis that can be applied to 3-dimensional (3D) images of fibrotic tissue. A fractal dimension map for each image was calculated by determining a single fractal dimension for a small area surrounding each image pixel, using fiber thickness as the third dimension. We found that this local fractal dimension increased with age and with progression of fibrosis regardless of collagen content. Our new method of distributed 3D fractal analysis can thus distinguish between changes in collagen content and organization induced by fibrosis.

Neutron Scattering Analysis of Cryptococcus neoformans Polysaccharide Reveals Solution Rigidity and Repeating Fractal-like Structural Patterns.

Cryptococcus neoformans is a fungal pathogen that can cause life-threatening brain infections in immunocompromised individuals. Unlike other fungal pathogens, it possesses a protective polysaccharide capsule that is crucial for its virulence. During infections, Cryptococcus cells release copious amounts of extracellular polysaccharides (exo-PS) that interfere with host immune responses. Both exo-PS and capsular-PS play pivotal roles in Cryptococcus infections and serve as essential targets for disease diagnosis and vaccine development strategies. However, understanding their structure is complicated by their polydispersity, complexity, sensitivity to sample isolation and processing, and scarcity of methods capable of isolating and analyzing them while preserving their native structure. In this study, we employ small-angle neutron scattering (SANS) and ultra-small-angle neutron scattering (USANS) for the first time to investigate both fungal cell suspensions and extracellular polysaccharides in solution. Our data suggests that exo-PS in solution exhibits collapsed chain-like behavior and demonstrates mass fractal properties that indicate a relatively condensed pore structure in aqueous environments. This observation is also supported by scanning electron microscopy (SEM). The local structure of the polysaccharide is characterized as a rigid rod, with a length scale corresponding to 3-4 repeating units. This research not only unveils insights into exo-PS and capsular-PS structures but also demonstrates the potential of USANS for studying changes in cell dimensions and the promise of contrast variation in future neutron scattering studies.

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.

Prognostic value of right ventricular trabecular complexity in patients with arrhythmogenic cardiomyopathy.

OBJECTIVES: The present study aimed to investigate the incremental prognostic value of the right ventricular fractal dimension (FD), a novel marker of myocardial trabecular complexity by cardiac magnetic resonance (CMR) in patients with arrhythmogenic cardiomyopathy (ACM). METHODS: Consecutive patients with ACM undergoing CMR were followed up for major cardiac events, including sudden cardiac death, aborted cardiac arrest, and appropriate implantable cardioverter defibrillator intervention. Prognosis prediction was compared by Cox regression analysis. We established a multivariable model supplemented with RV FD and evaluated its discrimination by Harrell's C-statistic. We compared the category-free, continuous net reclassification improvement (cNRI) and integrated discrimination index (IDI) before and after the addition of FD. RESULTS: A total of 105 patients were prospectively included from three centers and followed up for a median of 60 (48, 66) months; experienced 36 major cardiac events were recorded. Trabecular FD displayed a strong unadjusted association with major cardiac events (p < 0.05). In the multivariable Cox regression analysis, RV maximal apical FD maintained an independent association with major cardiac events (hazard ratio, 1.31 (1.11-1.55), p < 0.002). The Hosmer-Lemeshow goodness of fit test displayed good fit (X2 = 0.68, p = 0.99). Diagnostic performance was significantly improved after the addition of RV maximal apical FD to the multivariable baseline model, and the continuous net reclassification improvement increased 21% (p = 0.001), and the integrated discrimination index improved 16% (p = 0.045). CONCLUSIONS: In patients with ACM, CMR-assessed myocardial trabecular complexity was independently correlated with adverse cardiovascular events and provided incremental prognostic value. CLINICAL RELEVANCE STATEMENT: The application of FD values for assessing RV myocardial trabeculae may become an accessible and promising parameter in monitoring and early diagnosis of risk factors for adverse cardiovascular events in patients with ACM. KEY POINTS: • Ventricular trabecular morphology, a novel quantitative marker by CMR, has been explored for the first time to determine the severity of ACM. • Patients with higher maximal apical fractal dimension of RV displayed significantly higher cumulative incidence of major cardiac events. • RV maximal apical FD was independently associated with major cardiac events and provided incremental prognostic value in patients with ACM.

Fractal characteristics of the trabecular pattern of the mandible in patients with renal transplantation.

OBJECTIVE: In this study, we examined the mandibular trabecular bone structures by performing fractal dimension (FD) analysis in patients who underwent renal transplantation (RTx). METHODS: Our study is an observational study with 69 RTx patients and 35 control group patients. The mean FD values of the patient and control groups were calculated and compared. In addition, biochemical parathyroid hormone (PTH), serum calcium, phosphorus, alkaline phosphatase (ALP), and vitamin-D parameters and FD values of both groups were analyzed. RESULTS: FD values were significantly lower in the patient group than in the healthy group (p < .05). In the RTx group compared to the control group, ALP (90.71 ± 34.25-66.54 ± 16.8, respectively) (p < .001) and PTH (75.76 ± 38.01-38.17 ± 12.39, respectively) (p < .001) values were higher. There was a positive correlation between the FD values and ALP (rspearman  = .305, p = .011) and a negative correlation between FD values and vitamin-D (rspearman  = .287, p = .017) of patients with RTx. CONCLUSION: FD values were found to be lower in patients who underwent RTx compared to the control group. It should be considered that FD analysis can be a method that can be used to evaluate trabecular bone structure in patients undergoing RTx.

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.

Multifractal fluctuations in zebrafish (Danio rerio) polarization time series.

In this work, we study the polarization time series obtained from experimental observation of a group of zebrafish (Danio rerio) confined in a circular tank. The complex dynamics of the individual trajectory evolution lead to the appearance of multiple characteristic scales. Employing the Multifractal Detrended Fluctuation Analysis (MF-DFA), we found distinct behaviors according to the parameters used. The polarization time series are multifractal at low fish densities and their average scales with ρ - 1 / 4 . On the other hand, they tend to be monofractal, and their average scales with ρ - 1 / 2 for high fish densities. These two regimes overlap at critical density ρ c , suggesting the existence of a phase transition separating them. We also observed that for low densities, the polarization velocity shows a non-Gaussian behavior with heavy tails associated with long-range correlation and becomes Gaussian for high densities, presenting an uncorrelated regime.

The fractal brain: scale-invariance in structure and dynamics.

The past 40 years have witnessed extensive research on fractal structure and scale-free dynamics in the brain. Although considerable progress has been made, a comprehensive picture has yet to emerge, and needs further linking to a mechanistic account of brain function. Here, we review these concepts, connecting observations across different levels of organization, from both a structural and functional perspective. We argue that, paradoxically, the level of cortical circuits is the least understood from a structural point of view and perhaps the best studied from a dynamical one. We further link observations about scale-freeness and fractality with evidence that the environment provides constraints that may explain the usefulness of fractal structure and scale-free dynamics in the brain. Moreover, we discuss evidence that behavior exhibits scale-free properties, likely emerging from similarly organized brain dynamics, enabling an organism to thrive in an environment that shares the same organizational principles. Finally, we review the sparse evidence for and try to speculate on the functional consequences of fractality and scale-freeness for brain computation. These properties may endow the brain with computational capabilities that transcend current models of neural computation and could hold the key to unraveling how the brain constructs percepts and generates behavior.

Using fractal dimension analysis to assess the effects of normal aging and sex on subregional cortex alterations across the lifespan from a Chinese dataset.

Fractal dimension (FD) is used to quantify brain structural complexity and is more sensitive to morphological variability than other cortical measures. However, the effects of normal aging and sex on FD are not fully understood. In this study, age- and sex-related differences in FD were investigated in a sample of 448 adults age of 19-80 years from a Chinese dataset. The FD was estimated with the surface-based morphometry (SBM) approach, sex differences were analyzed on a vertex level, and correlations between FD and age were examined. Generalized additive models (GAMs) were used to characterize the trajectories of age-related changes in 68 regions based on the Desikan-Killiany atlas. The SBM results showed sex differences in the entire sample and 3 subgroups defined by age. GAM results demonstrated that the FD values of 51 regions were significantly correlated with age. The trajectories of changes can be classified into 4 main patterns. Our results indicate that sex differences in FD are evident across developmental stages. Age-related trajectories in FD are not homogeneous across the cerebral cortex. Our results extend previous findings and provide a foundation for future investigation of the underlying mechanism.

Adsorption of Cd(II) ions on magnetic graphene oxide/cellulose modified with ß-cyclodextrin: Analytical interpretation via statistical physics modeling and fractal like kinetic approach.

In the present study, ß-cyclodextrin modified magnetic graphene oxide/cellulose (CN/IGO/Cel) was fabricated for removal of Cd(II) ions. The material was characterized through various analytical techniques like FTIR, XRD, TGA/DTA, SEM, TEM, and XPS. The point of zero charge of the material was obtained as 5.38. The controllable factors were optimized by Taguchi design and optimum values were: adsorbent dose-16 mg, equilibrium time-40 min, and initial concentration of Cd(II) ions-40 mg/L. The material shows high adsorption capacity (303.98 mg/g). The good fitting of Langmuir model to adsorption data (R2 = 0.9918-0.9936) revealed the monolayer coverage on adsorbent surface. Statistical physics model M 2 showed best fitting to adsorption data (R2 > 0.997), suggesting the binding of Cd(II) ions occurred on two different receptor sites (n). Stereographically n > 1 confirming vertical multi-molecular mechanisms of Cd(II) ions adsorption on CN/IGO/Cel surface. The adsorption energies (E1 = 23.71-28.95 kJ/mol; E2 = 22.69-29.38 kJ/mol) concluded the involvement of physical forces for Cd(II) ions adsorption. Kinetic data fitted well to fractal-like pseudo first-order model (R2 > 0.9952), concluding the adsorption of Cd(II) ions occurred on energetically heterogeneous surface. The kinetic analysis shows that both the film-diffusion and pore-diffusion were responsible for Cd(II) ions uptake. XPS analysis was utilized to explain the adsorption mechanism of Cd(II) ions onto CN/IGO/Cel.

Evaluation of Bone Mineral Changes in Panoramic Radiographs of Hypothyroid and Hyperthyroid Patients Using Fractal Dimension Analysis.

Objective Hyperthyroidism and hypothyroidism are endocrinopathies that cause a decrease in bone mineral density. The aim of this study is to investigate possible bone changes in the mandible caused by hyperthyroidism and hypothyroidism using fractal analysis (FA) on panoramic radiographs. Material and Methods Panoramic radiographs of a total of 180 patients, including 120 patient groups (60 hyperthyroid, 60 hypothyroid) and 60 healthy control groups, were used. Five regions of interests (ROI) were determined from panoramic radiographs and FA was performed. ROI1: geometric midpoint of mandibular notch and mandibular foramen, ROI2: geometric midpoint of mandibular angle, ROI3: anterior of mental foramen, ROI4: basal cortical area from distal mental foramen to distal root of first molar, ROI5: geometric center of mandibular foramen and mandibular ramus. Results While a significant difference was observed between the patient and control groups regarding ROI1 and ROI2 (p < 0.05); there was no significant difference between the groups in relation to ROI3, ROI4, and ROI5. All FA values were lower in the hyperthyroid group than in the hypothyroid group. Conclusion Fractal analysis proves to be an effective method for early detection of bone mass changes. In the present study, it was concluded that while the mandibular cortical bone was intact, trabecular rich regions were affected by osteoporosis caused by thyroid hormones. Necessary precautions should be taken against the risk of osteoporosis in patients with thyroid hormone disorders.

Fractal construction of constrained code words for DNA storage systems.

The use of complex biological molecules to solve computational problems is an emerging field at the interface between biology and computer science. There are two main categories in which biological molecules, especially DNA, are investigated as alternatives to silicon-based computer technologies. One is to use DNA as a storage medium, and the other is to use DNA for computing. Both strategies come with certain constraints. In the current study, we present a novel approach derived from chaos game representation for DNA to generate DNA code words that fulfill user-defined constraints, namely GC content, homopolymers, and undesired motifs, and thus, can be used to build codes for reliable DNA storage systems.

Emergent dual scaling of riverine biodiversity.

A prevailing paradigm suggests that species richness increases with area in a decelerating way. This ubiquitous power law scaling, the species-area relationship, has formed the foundation of many conservation strategies. In spatially complex ecosystems, however, the area may not be the sole dimension to scale biodiversity patterns because the scale-invariant complexity of fractal ecosystem structure may drive ecological dynamics in space. Here, we use theory and analysis of extensive fish community data from two distinct geographic regions to show that riverine biodiversity follows a robust scaling law along the two orthogonal dimensions of ecosystem size and complexity (i.e., the dual scaling law). In river networks, the recurrent merging of various tributaries forms fractal branching systems, where the prevalence of branching (ecosystem complexity) represents a macroscale control of the ecosystem's habitat heterogeneity. In the meantime, ecosystem size dictates metacommunity size and total habitat diversity, two factors regulating biodiversity in nature. Our theory predicted that, regardless of simulated species' traits, larger and more branched "complex" networks support greater species richness due to increased space and environmental heterogeneity. The relationships were linear on logarithmic axes, indicating power law scaling by ecosystem size and complexity. In support of this theoretical prediction, the power laws have consistently emerged in riverine fish communities across the study regions (Hokkaido Island in Japan and the midwestern United States) despite hosting different fauna with distinct evolutionary histories. The emergence of dual scaling law may be a pervasive property of branching networks with important implications for biodiversity conservation.

Hierarchical transitions and fractal wrinkling drive bacterial pellicle morphogenesis.

Bacterial cells can self-organize into structured communities at fluid-fluid interfaces. These soft, living materials composed of cells and extracellular matrix are called pellicles. Cells residing in pellicles garner group-level survival advantages such as increased antibiotic resistance. The dynamics of pellicle formation and, more generally, how complex morphologies arise from active biomaterials confined at interfaces are not well understood. Here, using Vibrio cholerae as our model organism, a custom-built adaptive stereo microscope, fluorescence imaging, mechanical theory, and simulations, we report a fractal wrinkling morphogenesis program that differs radically from the well-known coalescence of wrinkles into folds that occurs in passive thin films at fluid-fluid interfaces. Four stages occur: growth of founding colonies, onset of primary wrinkles, development of secondary curved ridge instabilities, and finally the emergence of a cascade of finer structures with fractal-like scaling in wavelength. The time evolution of pellicle formation depends on the initial heterogeneity of the film microstructure. Changing the starting bacterial seeding density produces three variations in the sequence of morphogenic stages, which we term the bypass, crystalline, and incomplete modes. Despite these global architectural transitions, individual microcolonies remain spatially segregated, and thus, the community maintains spatial and genetic heterogeneity. Our results suggest that the memory of the original microstructure is critical in setting the morphogenic dynamics of a pellicle as an active biomaterial.

Epidemic propagation risk study with effective fractal dimension.

In this article, the risk of epidemic transmission on complex networks is studied from the perspective of effective fractal dimension. First, we introduce the method of calculating the effective fractal dimension D B ${D}_B$ of the network by taking a scale-free network as an example. Second, we propose the construction method of administrative fractal network and calculate the D B ${D}_B$ . using the classical susceptible exposed infectious removed (SEIR) infectious disease model, we simulate the virus propagation process on the administrative fractal network. The results show that the larger the D B ${D}_B$ is, the higher the risk of virus transmission is. Later, we proposed five parameters P, M, B, F, and D, where P denotes population mobility, M denotes geographical distance, B denotes GDP, F denotes D B ${D}_B$ , and D denotes population density. The new epidemic growth index formula I = ( P + ( 1 - M ) + B ) ( F + D ) $I = {( {P + ( {1 - M} ) + B} )}^{( {F + D} )}$ was obtained by combining these five parameters, and the validity of I in epidemic transmission risk assessment was demonstrated by parameter sensitivity analysis and reliability analysis. Finally, we also confirmed the reliability of the SEIR dynamic transmission model in simulating early COVID-19 transmission trends and the ability of timely quarantine measures to effectively control the spread of the epidemic.