A computational methodology for the staging of lung tumors considering geometric descriptors

Una metodología para la estadificación de tumores pulmonares considerandos descriptores geométricos

The diagnosis of lung diseases, specifically the presence of lung tumors, is usually carried out with the support of imaging techniques, among which the computed tomography currently used in the diagnosis, staging, prognosis and evaluation of therapeutic results in lung cancer stands out. This is due to the high spatial and / or contrast resolution typical of this technique¹.

When various researchers want to generate the morphology of these tumors, they face problems such as: poor delimitation of the borders associated with the anatomical lung structures, poison noise is characterized by being dependent on the intensity of each voxel in the image, as well as the voxel of higher intensity are at risk of being more affected by noise², ladder-type artifact, the possible causes of this artifact are due to inadequate collimation management and errors in reconstruction³ and non-homogeneity of levels of gray that define each object in the chest images⁴.

Lung cancer represents one of the leading causes of death in the world. 85% of cases of this type of cancer correspond to non-small cells and 15% to small cells. Hoyos et al.⁵, presents a synthesis of the classification of the most frequent epithelial lung tumors⁵.

In this classification, 6 major categories of pathologies are presented. However, in general, all of them can be classified as lung tumors. Additionally, the seventh edition of the system based on the descriptors Tumor-Nodules-Metastasis (TNM system), for staging lung cancer was established on a retrospective analysis of a large database (81,495 patients) collected by the International Association for the Study of Lung Cancer (IASLC) and analyzed by cancer research and biostatistics (CRAB), a non-profit organization which goal is to prevent and cure cancer⁶. In the TNM system, the descriptor or stage T refers to the characteristics of the primary tumor, N to regional lymph node involvement and M to intra and extra-thoracic metastases.

This retrospective analysis had its limitations, so the IASLC proposed in 1999 a new international prospective database for the study of the staging and prognostic factors of lung cancer that ended in 2010 and which has served to prepare the eighth edition of the TNM classification of lung cancer. In this new database from 16 countries 94,708 patients with lung cancer were initially registered and, after the exclusions made by the CRAB, only 77,156 patients were finally studied, of whom 70,967 had non-small cell lung cancer (NSCLC) and 6,189 had small cell lung cancer (CPCP)⁷.

In this article, a methodology to identify the stage of these tumors is presented. In this sense, first, anisotropic diffusion filter, based on curvature, and magnitude of the gradient filter were used in order to address the aforementioned problems. Secondly, the Hough transform and the level sets algorithm are used to segment lung tumors and, from them, geometric descriptors are obtained to establish the tumors staging.

Data Source

Table 1 shows the characteristics of the multislice computed tomography (MSCT) databases (DB), considered in this work, which are composed of chest images containing squamous cell lung tumors.

Additionally, we have the manual segmentations or ground truth, carried out by a clinical expert, which will serve as a reference to develop the tuning process of the parameters that operationally control all the techniques involved in the proposed strategy.

Computational strategy proposed

Using figure 1, a schematic diagram is presented. In this figure, it is synthesized the computational algorithms that make up the proposed methodology for staging lung tumors.

Curvature-based anisotropic diffusion filter.

This type of filter is iterative, it has a solid mathematical foundation and was developed by Álvarez et al⁸. In general, the curvature anisotropic diffusion filter incorporates, in a hybrid way, a parabolic nonlinear differential equation, level sets and elements of the diffusion models of Witkin, Koenderink¹⁰ and Perona-Malik¹¹.

Furthermore, anisotropic diffusion is characterized by performing effectively against the noise problem that exhibits medical images and, additionally, this filter has 3 parameters that control its operation. They are number of iterations (iter), time base (t) and diffusion threshold (k)¹².

Gradient Magnitude Filter

The gradient magnitude filter generates a smoothed version of the anisotropic diffusion image based on the calculation of the magnitude of the three-dimensional gradient of such image, using a given mathematical model based on finite differences^13,14.

Variational Algorithm

Algorithm Initialization

The generalized Hough transform (GHT) is an algorithm for detecting the centroid of objects, with an arbitrary shape, in an image considering the training and detection stages. In training, a prototype is extracted from a previously selected image.

Figure 2 it is used to present an example of a prototype in which certain geometric elements have been incorporated, which are identified below: a) (xc, yc): centroid of the prototype. b) (x, y): arbitrarily chosen contour point. c) r: radial distance between the centroid and the arbitrary point. d) α: angle that r forms with the horizontal line (line drawn in green). e) θ: angle formed by the horizontal with a line tangent to the arbitrary point (line drawn in blue). θ represents the direction of the gradient⁴.

On the other hand, in the detection stage, the parameters of Table-R are considered to automatically identify the centroid of the structure to be detected, in images other than the one used during training.

In this article, GHT is used to obtain the coordinates of the seed voxel required by the level sets (LS) to initiate tumor segmentation.

Level sets technique (LS)

LS are iterative methods that allow controlling the evolution of snake-like active contour models for the segmentation of objects present in an image, for example, the tumors present in the DB described¹⁵.

The aforementioned evolution is controlled by a differential equation that depends on 2 parameters: curvature (α) and smoothness (β).. From the seed voxel, an iso-sphere evolves iteratively considering α and β parameters until the iterations of the level set, reaches a value equal to 512, that is, the size of the horizontal image dimension (see table 1).

Additionally, in this work, the geometric descriptors of the segmented tumors coincide with their: perimeter (Pe), area (Ar) and diameter (Di). They allow precisely establishing the stage in which such tumors are classified, according to the criteria established¹⁶, which are presented using table 2.

Dice Coefficient

The Dice coefficient is a metric to evaluate the correspondence between the results of two procedures. In this paper, the Ds let us compare the manual and automatic segmentation of lung tumors. The expected values for the Dice score (Ds) are real numbers between 0 and 1. The main rule using Ds is: the performance of a particular procedure is better if its score is closer to 1¹⁷.

Qualitative results

Figure 3 presents axial views showing the effect of applying both the filters and the GHT and LS to the original images that make up the all DB described.

In this figure, we can appreciate a good edges definition which was an important step for faciliting the tumor segmentation process. In addition, figure 4 shows an excellent 3D representation about the 3 segmentated lung tumors.

Quantitative results

It is important to note that the parameters that control the performance of the entire strategy were adjusted by means of cross validation¹⁸, considering the comparison between ground truth and automatic segmentations which was assessed using the Dice coefficient (Ds) as a metric. In this sense, the optimal values reported in this section correspond to the maximum value obtained for the Ds, which was 0.9081.

Table 3 shows the results related to the tuning process about the parameters that, in this research, control the performance of the techniques that make up the methodology proposed.

Table 4 shows the values of the geometric descriptors and the stage established for segmented tumors.

According to the values obtained for the descriptors, showed in the previous table, the patients present tumors that go from the first to the third stage. This implies the adoption of different therapeutic, clinical or surgical protocols when planning, establishing or deciding on the most appropriate procedure to improve the health of patients suffering from the consequences of having these tumors lodged in their lungs.

An automatic methodology for the segmentation and staging of lung tumors has been presented. In it, the filter bank was used to minimize the problems associated with MSCT images.

Using the automatically generated segmentations, certain geometric descriptors were calculated, accurately and efficiently, which are useful to establish the stage in which each of the segmented tumors is.

The information derived from the aforementioned descriptors is of vital importance to define the clinical or surgical behavior to be followed, regarding the approach to detected tumors.