Original ContributionHeterogeneous Tissue Characterization Using Ultrasound: A Comparison of Fractal Analysis Backscatter Models on Liver Tumors
Introduction
Ultrasound tissue characterization can provide useful quantitative assessments for understanding the state of biological disease (Mamou and Oelze 2013). With advancement in medical image analysis, it is becoming a promising non-invasive technique for early detection of tumor response to treatment (Czarnota et al., 2013, Sadeghi-Naini et al., 2013a, Sadeghi-Naini et al., 2013b). It has the advantage of deriving parameters that can represent tissue properties in a fast, non-ionizing, easily operated and cost-effective way compared with other conventional follow-up imaging techniques. Soft tissue pathologies in the form of lesions tend to have scattering patterns distinct from those of normal tissue structure, and the associated acoustic properties could characterize the concentration of scatterers and microstructures; which is an indication of different tissue types. Biological tissue ultrasonic modeling followed by echo signal analysis can facilitate heterogeneity examination of tumor texture.
The interaction of an acoustic wave with different tissue regions can be modeled by the backscattered radiofrequency (RF) signal. Tissue properties based on the scatterer number density and spatial distribution can be derived subsequently for analysis. There are several approaches for which useful information can be extracted from the RF signal. One approach uses the local power spectral density to estimate the integrated backscatter and attenuation coefficient (Banihashemi et al., 2008, Nam et al., 2011, Rubert and Varghese, 2014, Sannachi et al., 2015) or to measure the mean central frequency and scatterer size (Bridal et al., 1997, Lavarello and Oelze, 2012, Nordberg and Hall, 2015, Saha and Kolios, 2011). Textural properties of the tissue spatial arrangement can also be estimated from the envelope-detected RF image (Bouhlel and Sevestre-Ghalila, 2009, Klein et al., 2011). As the first-order statistical properties of the backscattered RF signal rely on the number density and spatial distribution of scatterers (Pereyra and Batatia, 2012, Wagner et al., 1983), which may be coherent, random or a mixture of both, it would be difficult to account for all scatterer conditions using the former approaches. Therefore, others have investigated the probability density function of the backscattered echoes and proposed to account for the number, size, spacing and regularity of the scatterers in tissue. An overview of the various statistical distributions for modeling the envelope-detected RF signal can be found in Destrempes and Cloutier (2010). For the latter approach, the main objective is to provide a better characterization of the fundamental elements that form the coarse textural patterns, namely, speckles formed from the backscattered echoes. The speckle local arrangement represents the various scatterer concentrations and spatial distributions occurring in tissue, ranging from a fully developed to a partially developed to a coherent speckle pattern. In cases in which there are many randomly located scatterers per resolution cell (i.e., fully developed speckle), the envelope signal statistics would follow a square root of exponential distribution, known as the Rayleigh distribution (Wagner et al. 1983). The model can be further subdivided into pre-Rayleigh, Rayleigh and post-Rayleigh for characterizing heterogeneous, homogeneous and periodic textures, respectively (Cramblitt and Parker, 1999, Molthen et al., 1995, Shankar et al., 1996). Non-Rayleigh distributions can be observed when the scatterers become less condensed or have a structure with some regularity. That is, when the number of scatterers in a resolution cell is small (i.e., partially developed speckle), the K-distribution was found to be more effective in modeling the pre-Rayleigh statistics of the RF envelope (Shankar et al. 2000). The RF envelope statistics in this case would have a shape resembling a square root of the product of gamma and exponential distributions. Whereas if the scatterers become organized with some periodicity (i.e., coherent speckle), the Rician distribution, which is the generalization of the Rayleigh distribution, is more appropriate for characterizing the underlying regular structures in tissue (Sijbers et al. 1998).
Although the prior models account for specific aspects of scatterer localization, they are not general enough to model the various tissue texture conditions. This is true when a high degree of variability exists in the scattering cross-section associated with a low number of scatterers. In practice, it is very common to encounter non-Rayleigh conditions of ultrasound backscatter, such as mixtures of diffuse and coherent or periodically aligned scatterers in tissue microstructure. Therefore, a comprehensive approach is sought as in the generalized K-distribution (Jakeman and Tough 1987) and homodyne K-distribution (Dutt and Greenleaf, 1994, Mamou et al., 2011). A third parameter, which represents the envelope of the coherent signal, was added to the effective number of scatterers and energy of the random scatterers to account for post-Rayleigh conditions. However, a drawback lies in the analytical complexity of these model generalizations, rendering the process of parameter estimation computationally expensive. Other models that apply a generalization approach to the Rayleigh and Rice distributions to better fit the backscattered echo include the Weibull (Raju and Srinivasan 2002), Rician inverse Gaussian (Eltoft 2005) and generalized gamma (Tunis et al. 2005) models. On the other hand, the Nakagami distribution family can provide a simpler and general model for ultrasonic tissue characterization (Shankar 2000). In addition to the scatterer density and amplitude, the regularity of the scatterer spacing is taken into consideration, making it possible to account for hypo-echoic and hyper-echoic structures (Tsui et al. 2010). The model shape equivalent to a scaled square root of a gamma distribution can better represent the backscattered RF signal envelope and can be easily fine-tuned via the shape Nakagami parameter to represent low and high number of scatterer densities with minimal error (Tsui et al. 2014). The model was further generalized as a Nakagami-generalized inverse Gaussian distribution in Karmeshu and Agrawal (2006) by including an additional shape adjustment parameter to account for the tails of the density function. However, this generalization was not investigated with real tissue, where scatterers tend to have a high degree of variability in scattering cross sections.
All aforementioned statistical models of the backscattered echo envelope in the literature claim a better characterization of texture anisotropic properties. A large number of articles address the problem of soft tissue characterization and diagnosis from ultrasound images of various internal organs, such as in kidneys (Wu et al. 2013), liver (Ghoshal et al. 2012), breast (Tadayyon et al. 2014), gallbladder (Kumon et al. 2010), pancreas (Atiee et al. 2014), spleen (Roosens et al. 2013) and abdominal aorta (Tsui et al. 2008), all of which present practical examples of, but are not limited to, recent clinical work. However, to the best of our knowledge, the performance of the most well-known statistical models for characterizing ultrasonic liver tumor tissue has not been investigated. Local parametric fractal features extracted via maximum likelihood estimation for each statistical model will be used for liver tumor texture classifications. In the study described here, a fractal approach for evaluating the performance of the different statistical models was sought for automated detection of liver tumor response to chemotherapy treatment. The approach relates the fractal characteristics of the tissue scatterers to the underlying statistical properties derived from the RF envelope-detected signal. The fractal dimension, which represents the degree of self-similarity, and the derived lacunarity, which indicates the level of spaces within the texture, were related to the scatterer spatial distribution and number density, respectively. The fractal features are extracted via a multimodal statistical distribution, and results fed to a classifier for automated classification. The aim of the study was to demonstrate the efficacy of modeling the underlying tumor physiological changes from ultrasound parametric images of scatterer tissue properties. Tumor tissue scatterer characterization is a challenging task because of the chaotic behavior of disease. Therefore, we address the issue of best model selection and whether analytically complex models are really necessary for better characterizing complex tissue, such as liver tumors.
The article is organized as follows: The preference of working with RF envelope-detected signal rather than B-mode images is briefly explained under Ultrasound Data Representation, followed by Modeling the Backscattered RF Signal, which covers the different scatterer conditions and densities. Then, under Multiscale Feature Extraction, we discuss characterization of the fractal patterns of the tissue scatterers for automated classification. Major findings are listed and discussed in the Results and Discussion, and a summary is provided under Conclusions.
Section snippets
RF parametric image acquisition
The acquired ultrasound beams run through several signal and image pre-processing steps before they can be presented as a RF matrix and, subsequently, in a gray scale B-mode image (Fig. 1). The ultrasound operator may also choose to further optimize the visibility by increasing the gain of the reflected signals with increasing time from the transmitted pulse (i.e., time-gain compensation). Although the B-mode scans could be suitable for qualitative analysis in describing the tissue structure,
Modeling the Backscattered RF Signal
Ultrasound backscattering in tissue can be considered a random process. Many statistical models have been used to describe the probability density function of the envelope-detected RF signal. Evaluation has been carried out using five major statistical distributions that are widely used in the literature to describe the various aspects of tissue characteristics.
Parametric image generation
On the basis of a voxel-by-voxel approach, the statistical model parameters are estimated from the RF envelope data. Each estimated parameter in the generated parametric image corresponds to a voxel (short segment) of the RF signal. As we are dealing with a tumor volume, the RF envelope signal was presented as a matrix, and several matrices represent the tumor volume. Then the different statistical distribution models are fitted and their associated model parameters estimated by maximum
Results
The extracted fractal features from the texture of the various parametric images, which were derived from the RF envelope-detected signal of the different distribution models, are compared in Table 1, Table 2, Table 3, where values in boldface indicate the best achieved performance. A detailed classification performance of the 3-D clinical ultrasound liver tumor test set via a leave-one-out cross-validation approach is outlined in Table 1. The tissue characterization based on the Nakagami (Nkg)
Discussion
Heterogeneity in the tumor tissue scatterers could span different scattering conditions. Regions within the tumor tissue that respond to treatment might exhibit statistical properties different from those of the non-respondent counterpart. Thus, it is essential to evaluate the discriminative abilities of the statistical models while simultaneously taking into account all possible scatterer conditions and densities.
The sum of the individual backscattered signals from the various scattering
Conclusions
This article describes an evaluation of different statistical models that cover different aspects of tissue scatterer distributions and densities. The aim was to understand which model can give a better fit of the complex nature of liver tumors by providing discriminative features for supporting clinical diagnosis as part of health care delivery. Tumor heterogeneity was assessed via its tissue fractal properties derived from the RF envelope-detected signal and used as features for assessing
Acknowledgments
This work was support by the Engineering and Physical Sciences Research Council and Wellcome Trust [Grant number WT 088877/z/09/z]. The authors thank the anonymous reviewers for their constructive comments and suggestions to improve the quality of the article.
References (56)
A multiresolution clinical decision support system based on fractal model design for classification of histological brain tumours
Comput Med Imaging Graphics
(2015)- et al.
Quantification of ultrasonic texture intra-heterogeneity via volumetric stochastic modeling for tissue characterization
Med Image Anal
(2015) - et al.
Nakagami Markov random field as texture model for ultrasound RF envelope image
Computers Biol Med
(2009) - et al.
Parametric (integrated backscatter and attenuation) images constructed using backscattered radio frequency signals (25-56 MHz) from human aortae in vitro
Ultrasound Med Biol
(1997) - et al.
A critical review and uniformized representation of statistical distributions modeling the ultrasound echo envelope
Ultrasound Med Biol
(2010) - et al.
Ultrasound echo envelope analysis using a homodyned k-distribution signal model
Ultrasonic Imaging
(1994) - et al.
New response evaluation criteria in solid tumours: Revised RECIST guideline (Version 1.1)
Eur J Cancer
(2009) - et al.
Ex vivo study of quantitative ultrasound parameters in fatty rabbit livers
Ultrasound Med Biol
(2012) - et al.
Study of ultrasonic echo envelope based on Nakagami-inverse gaussian distribution
Ultrasound Med Biol
(2006) - et al.
In vivo characterization of pancreatic and lymph node tissue by using EUS spectrum analysis: A validation study
Gastrointest Endosc
(2010)