Multifractal Spectrum Analysis for Assessing Pulmonary Nodule Malignancy

Summary

This study introduces multifractal spectrum analysis for assessing pulmonary nodule malignancy. Using CT-DICOM data, the method calculates fractal dimensions across multiple voxel scales, revealing significant differences between early-stage and late-stage pulmonary nodules.

Abstract

Non-invasive assessment of pulmonary nodule malignancy remains a critical challenge in lung cancer diagnosis. Traditional methods often lack precision in differentiating benign from malignant nodules, particularly in the early stages. This study introduces an approach using multifractal spectrum analysis to quantitatively evaluate pulmonary nodule characteristics.

A fractal-based protocol was developed to process computed tomography (CT)-digital imaging and communications in medicine (DICOM) data, enabling three-dimensional (3D) visualization and analysis of pulmonary nodule's multifractal spectrum. The method involves 3D volume reconstruction, precise ROI delineation, and calculation of fractal dimensions across multiple scales. Multifractal spectra were computed for both early-stage and late-stage lung adenocarcinoma nodules, with comparative analysis performed using data tip tool quantification.

Analysis revealed that the fractal dimension of a pulmonary nodule's 3D digital matrix varies continuously with different voxel scales, forming a distinctive multifractal spectrum. Significant differences were observed between early-stage and late-stage nodules. Late-stage nodules demonstrated a wider scale range (longer X-axis) and higher extreme points in their multifractal spectra. These distinctions were quantitatively confirmed, indicating the method's potential for precise staging.

The multifractal spectrum analysis provides a highly significant and precise quantitative method for staging pulmonary nodules, effectively differentiating between benign and malignant cases. This non-invasive technique shows promise for improving early diagnosis and accurate staging of lung cancer, potentially enhancing clinical decision-making in pulmonary oncology.

Introduction

Lung cancer remains one of the leading causes of cancer-related deaths worldwide, with early detection and accurate diagnosis playing crucial roles in improving patient outcomes¹. Pulmonary nodules, often detected incidentally or through screening programs, present a significant diagnostic challenge for clinicians. The ability to differentiate between benign and malignant nodules, particularly in their early stages, is paramount for timely intervention and appropriate management².

Traditionally, the criterion standard for diagnosing pulmonary nodule malignancy has been histopathological examination through invasive procedures such as biopsy or surgical resection. While these methods provide definitive diagnoses, they carry inherent risks, including pneumothorax, bleeding, and infection³. Moreover, the invasive nature of these procedures can lead to patient discomfort and anxiety, as well as increased healthcare costs. Additionally, biopsy procedures themselves are subject to sampling accuracy issues, with the potential for obtaining non-representative tissue samples that may lead to misdiagnosis. Consequently, there is a pressing need for non-invasive diagnostic techniques that can accurately assess nodule malignancy without subjecting patients to unnecessary invasive procedures⁴.

Computed Tomography (CT) imaging has emerged as a powerful tool in the detection and characterization of pulmonary nodules⁵. However, the interpretation of CT images for nodule assessment remains challenging, with considerable inter-observer variability among radiologists. Current guidelines and expert consensus statements on CT-based nodule evaluation primarily rely on morphological features such as size, shape, and growth rate. While these criteria provide valuable information, they often lack the precision necessary for definitive diagnosis, particularly in cases of small or indeterminate nodules⁶.

In recent years, there has been growing interest in utilizing quantitative imaging features, often referred to as "radiomics," to enhance the diagnostic accuracy of CT-based nodule assessment⁷. Among these approaches, fractal analysis has shown promise in capturing the complex structural characteristics of pulmonary nodules⁸. Fractal dimension, a measure of an object's complexity across different scales, has been applied to various medical imaging problems, including the characterization of pulmonary nodules⁹.

However, existing fractal-based methods for nodule analysis typically employ a single-scale approach, calculating a single fractal dimension for each nodule¹⁰. While this approach has shown some utility in differentiating between benign and malignant nodules, it often results in significant overlap between the two categories, limiting its diagnostic precision. The inherent limitation of single-scale fractal analysis lies in its inability to capture the full spectrum of structural complexities that may exist within a nodule across different spatial scales¹¹.

To address these limitations, this study introduces a novel approach, multifractal spectrum analysis, for pulmonary nodule assessment. This method extends beyond traditional single-scale fractal analysis by computing fractal dimensions across multiple voxel scales, thereby generating a comprehensive spectrum that characterizes the nodule's structural complexity at various levels of detail¹². This approach is rooted in the understanding that biological structures, including tumors, often exhibit different fractal properties at different scales, a characteristic that single-scale methods fail to capture¹³.

The development of this multifractal spectrum analysis is motivated by the need for more precise, quantitative, and non-invasive methods for assessing pulmonary nodule malignancy. By leveraging advanced image processing techniques and mathematical models, this approach aims to extract a richer set of features from CT images, potentially revealing subtle differences between benign and malignant nodules that may not be apparent through conventional analysis or single-scale fractal methods¹⁴.

The significance of this research lies in its potential to enhance the accuracy of early-stage lung cancer diagnosis and staging. By providing a more nuanced and comprehensive characterization of nodule structure, the multifractal spectrum analysis may enable clinicians to make more informed decisions about patient management, potentially reducing the need for unnecessary invasive procedures in cases of benign nodules while ensuring timely intervention for malignant ones¹⁵.

In summary, this research introduces multifractal spectrum analysis for assessing pulmonary nodule malignancy, addressing the limitations of current diagnostic approaches and single-scale fractal methods. By providing a more comprehensive and precise quantitative assessment of nodule characteristics, this non-invasive technique aims to improve early diagnosis and accurate staging of lung cancer, ultimately enhancing clinical decision-making in pulmonary oncology and contributing to improved patient outcomes¹⁶.

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Protocol

This study was approved by the Ethics Committee of Dongzhimen Hospital, affiliated with the Beijing University of Chinese Medicine (2024DZMEC-165-02). The patient was recruited from the Fever Outpatient Clinic, Dongzhimen Hospital. The patients provided informed consent for their diagnosis through digital modeling and authorized the use of their data for scientific research purposes. The model reconstruction function is derived from a commercially available software tool (see Table of Materials).

1. Data preparation and visualization

1. Navigate to the folder containing the patient's CT scan DICOM data files.
2. Generate a 3D volume matrix from the DICOM files using the following MATLAB code:
   f=dir('*.dcm');
   for i=1:length(f)
   V(:,:,i)= dicomread(f(fidx(i)).name);
   end
3. Visualize the image sequence using MATLAB's sliceViewer function: (Figure 1)
   figure;
   H=sliceViewer(V);
   colormap(gray(1024));
   ​set(gcf, 'Toolbar', 'figure');
4. Interact with the 3D volume visualization.
   1. Use the scroll bar at the bottom of the graphical user interface (GUI) to browse through different slices in the CT sequence (Figure 1). Note the presence of a 22 mm malignant pulmonary nodule in the left lung at frame 325.
   2. Find the icons for zooming in, zooming out, and returning to the global view in the upper-right corner of the GUI in Figure 3. Use the Data Tip icon to mark the coordinates of the pixel selected. Use the Zoom function to observe the local features of the lesions and their relationships to surrounding tissues.
   3. The default color bar is the gray colormap, which means that blue to red represents values from low to high. Right-click the Color Bar in the pop-up menu to select the common gray colormap and reset the whole GUI.
   4. If the filter effect is not satisfied, use the left mouse button to drag up and down in the middle of the figure to adjust the window level. Drag left and right to adjust the window width, and the corresponding accurate filtering range will be displayed on the color bar.
      NOTE: These interactive controls enable flexible inspection of CT-DICOM data characteristics across both intensity space and sequence location.

2. Local 3D matrix visualization of pulmonary nodule lesions

NOTE: After locating the sequence position of the pulmonary nodule in the GUI shown in Figure 1, use the Data Tip tool to precisely delineate the nodule's position. This step is necessary before calculating the 3D matrix of the grayscale space for the lesion area.

1. Use the Data Tip tool to precisely identify the pixel coordinates of the pulmonary nodule.
   1. In the GUI shown in Figure 1, navigate to the slice containing the nodule (frame 325).
   2. Click the Data Tip icon in the upper-right corner of the GUI.
   3. Click on the edges of the nodule to mark its boundaries (Figure 2).
   4. Note the X and Y coordinates displayed in the data tip pop-up.
2. Extract the grayscale matrix of the pulmonary nodule.
   1. Based on the coordinates obtained, define the region of interest (ROI) in the MATLAB command window: M = V (304:335, 309:336, 325);
      NOTE: Adjust the coordinates (304:335, 309:336, 325) according to the specific nodule location in the image.
3. Visualize the local 3D matrix of the nodule:
   1. Enter the following MATLAB command to create a 3D surface plot: figure; surf(M);
   2. Observe the resulting 3D visualization of the nodule's grayscale intensities (Figure 3).
4. Interact with the 3D visualization GUI.
   NOTE: The X and Y axes represent the spatial dimensions of the nodule in pixels. The Z axis represents the grayscale intensity values.
   1. Find the tools for zooming in, zooming out, rotating, and returning to the default initial view (Restore View) in the upper-right corner of the GUI. Use these tools for precise examination of the 3D digitized pulmonary nodule.

3. Calculating the multifractal spectrum of pulmonary nodule

NOTE: The fractal dimension is not unique across different scales but rather forms a multifractal spectrum that varies with different computational scales.

1. Call the function Pix_size, fractal_dimension = PN_fractal_feature(M) with the previously obtained M matrix as input. This will yield the fractal dimensions (fractal_dimension) at different scales (Pix_size).
2. Visualize the Multifractal Spectrum (Figure 4) of the pulmonary nodule using the following code:
   figure;
   plot (Pix_size, fratal_dimention,'linewidth',2);
   xlabel('Fractal scale')
   ylabel('Fractal Dimension')
3. Using the same steps as in 1.1-3.2, calculate for another benign pulmonary nodule and plot it in the same coordinate system using a different color for comparison. This will produce Figure 5.
4. To more precisely compare the multifractal spectra of different benign and malignant pulmonary nodules, use the Data Tip tool to mark the coordinates of key extrema points in Figure 5.
   NOTE: The MATLAB code used for this protocol is available as Supplementary File 1.

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Results

Figure 1 uses a 3D-volume reconstruction of the patient's thoracic CT sequence, allowing for convenient viewing and localization of the subject's pulmonary nodules. The Data Tip tool can effectively outline the Region of Interest (ROI) of the nodule of interest (Figure 2). Figure 3 provides a digitized structure of the nodule's 3D intensity space.

This study found through practical experi...

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Discussion

The multifractal spectrum analysis presented in this study represents a significant advancement in the non-invasive assessment of pulmonary nodule malignancy. This method offers important advantages and addresses key limitations in existing approaches to pulmonary nodule diagnosis and staging¹⁷.

Critical steps in the protocol include precise 3D reconstruction of CT-DICOM data (Figure 1), accurate delineation of the region of interest (

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Materials

Name	Company	Catalog Number	Comments
MATLAB	MathWorks	2022B	Computing and visualization
Multifractal Spectrum software	Intelligent Entropy, Beijing Intelligent Entropy Science & Technology Co Ltd.	V1.0	Modeling for CT/MRI fusion