3D image texture analysis of simulated and real-world vascular trees

doi:10.1016/j.cmpb.2011.06.004

Computer Methods and Programs in Biomedicine

Volume 107, Issue 2, August 2012, Pages 140-154

https://doi.org/10.1016/j.cmpb.2011.06.004 Get rights and content

Abstract

A method is proposed for quantitative description of blood-vessel trees, which can be used for tree classification and/or physical parameters indirect monitoring. The method is based on texture analysis of 3D images of the trees. Several types of trees were defined, with distinct tree parameters (number of terminal branches, blood viscosity, input and output flow). A number of trees were computer-simulated for each type. 3D image was computed for each tree and its texture features were calculated. Best discriminating features were found and applied to 1-NN nearest neighbor classifier. It was demonstrated that (i) tree images can be correctly classified for realistic signal-to-noise ratio, (ii) some texture features are monotonously related to tree parameters, (iii) 2D texture analysis is not sufficient to represent the trees in the discussed sense. Moreover, applicability of texture model to quantitative description of vascularity images was also supported by unsupervised exploratory analysis. Eventually, the experimental confirmation was done, with the use of confocal microscopy images of rat brain vasculature. Several classes of brain tissue were clearly distinguished based on 3D texture numerical parameters, including control and different kinds of tumours – treated with NG2 proteoglycan to promote angiogenesis-dependent growth of the abnormal tissue. The method, applied to magnetic resonance imaging e.g. real neovasculature or retinal images can be used to support noninvasive medical diagnosis of vascular system diseases.

Introduction

Extraction of quantitative information about blood-vessel trees from magnetic resonance images (MRIs), computed tomography (CT) and other imaging modalities can help in medical diagnosis of vascular system diseases. In fact, vessel segmentation algorithms are considered critical components of circulatory blood vessel analysis systems [1].

A vessel tree consists of very large diameter (e.g. 20–30 mm) arteries and veins that split into thinner and thinner vessels and, finally, capillaries whose diameter is in the range of 10 μm. On the other hand, spatial resolution of biomedical images is limited by the data acquisition hardware resources. As for example, in MRI the crucial determinants are strength of magnetic field B₀ and the power of coils and receiver noise [2], [3]. As a consequence, the number of image-slice pixels a whole-body scanner produces is at most 1024 × 1024, for a 7T magnet. Then, the smallest element of 3D image will average the tissue properties (expressed by spin density, relaxation times, etc.) in a cube (voxel) of, say, 0.5 mm a side. The voxel size will increase proportionally to the reduction of static magnetic field B₀. CT provides slightly better resolution with voxel sizes of e.g. 0.3125 mm × 0.3125 mm × 0.5 mm. In either case, thick vessels can be represented by regions with a substantial number of voxels, which allows relatively accurate evaluation of their geometry, and e.g. blood volume inside them, for diagnostic purposes.

If, however, the vessel diameter becomes comparable with the voxel side, its value can only be roughly estimated. In this diameter range, texture analysis [4] can be considered as a tool that provides the extra diagnostic information [5]. This information can be derived from the existing correlation between image texture parameters and blood vessel tree parameters. Furthermore, thinner branches and capillaries cannot be visualized individually with sub-millimeter voxels. The net effects of their performance can instead be quantified by measuring perfusion. Thus investigation of a whole blood-vessel tree with the use of fixed-resolution imaging techniques requires integration of three approaches of the modeling of the tree. One is geometric (e.g. tubular) model for large-diameter tree elements, second is the texture model for medium diameter range and third can be a lumped (e.g. compartmental) model for blood and nutrients exchange with tissue. This paper deals with the medium-vessel-diameter, i.e. the postulated texture analysis approach.

Texture is the property that reflects a presence of more or less regular patterns in the image [5, Chapter 1]. These patterns originate from spatial arrangement of structural elements of objects visualized in the image. Consider a volume sample from a densely populated tissue region filled with thin blood vessel branches. This region will produce images having large-magnitude components of high spatial frequencies. The texture of such images can be considered rough, or harsh. On the contrary, the spatial frequency spectrum of a region filled with thick veins will contain strong components at the lower range of the spectrum. The texture of their MRI will be perceived smooth – less “busy”. The image spectrum can be numerically described by means of wavelet analysis [6] where spatial frequency channels correspond to the scale factor of the transform. Thus, in this simple example, image spectrum carries the information about the diameter and density of blood vessels inside the region of interest. One can predict values of these two parameters by calculating texture features derived from MRI or CT scans measured for a region of interest. On the other hand, too much vessel formation supports a number of diseases, including cancer, inflammatory arthritis, blindness and obesity. Too little vessel formation is linked to stroke, damage to heart muscle after a heart attack and baldness (e.g. [7]). Thus one can expect that quantitative texture analysis has a potential for aiding the diagnosis of diseases that affect blood vessels.

The aim of this paper is to demonstrate that there exist relationships between the physical parameters of blood-vessel trees and numerical texture parameters computed with the use of vascular tree images. It is found that these relationships are stronger for three-dimensional (3D) than for two-dimensional (2D) texture. Computer-simulated blood vessel trees were used in the described study. The tree parameters investigated in this paper are number of output branches, input blood flow, terminal branches flow and blood viscosity. A simple simulator is used to generate images of the trees. Voxel intensity of the simulated image is proportional to the volume of this voxel part which is occupied by a vessel crossing it. The numerical simulation study is followed by experimental confirmation where the 3D confocal microscope images of rat brains are examined. Several classes of analyzed brain tissue were clearly distinguished based on 2D texture numerical parameters.

In Section 2, algorithms and techniques used for vascular tree modeling, imaging simulation and for texture analysis are characterized. Section 3 presents and discusses results of the numerically simulated experiments designed to reveal the links between vessel trees properties and texture parameters of their images.

Section snippets

Simulation of vascular tree growth

In the literature, two approaches to vascularity tree growth simulation are described – one proposed by Bezy-Wendling et al. [8], the other formulated by Karch et al. [9]. Both approaches rely on the same physical laws – mass preservation principle (1), Poiseuille law (2) and split law (3), the last describes relations between radii of the parent and children branches. $Q = Q_{l} + Q_{r},$ $Δ P = Q \frac{8 η L}{π R^{4}},$ $R_{p}^{γ} = R_{l}^{γ} + R_{r}^{γ},$ where Q is the blood flow; ΔP is the pressure drop in a vessel; η is the blood viscosity; L and R

Simulated data characteristics

Numerical parameters of 2D or 3D image texture can provide quantitative description of the underlying structure of visualized objects. The simulation and experimental results described below were aimed at establishing relationships between the image texture features and tree properties, to investigate (i) possibility of pre-classifying trees into normal and abnormal (e.g. with too high or too small viscosity or too many branches) on the basis of image texture descriptor values, with reference

Summary and conclusion

Based on numerical simulation, this paper shows that there exists a correlation between the texture parameters of MR-like and confocal microscope images of blood vessel trees and physical parameters of the trees. Two-dimensional texture analysis does not reveal these relationships, the 3D texture analysis is necessary. Simplified 3D image simulation with 28 degrees of intensity is sufficient to represent the relationships investigated, which was confirmed by studying the effect of image

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3D image texture analysis of simulated and real-world vascular trees

Abstract

Introduction

Section snippets

Simulation of vascular tree growth

Simulated data characteristics

Summary and conclusion

Computer Methods and Programs in Biomedicine

Journal of Magnetic Resonance

Computer Methods and Programs in Biomedicine

Intelligent Data Analysis

Microvascular Research

A review of vessel extraction techniques and algorithms

ACM Computing Surveys

Magnetic Resonance Imaging: Physical Principles and Sequence Design

Quantitative MRI of the Brain Measuring Changes Caused by Disease

Blood vessel segmentation from color retinal images using unsupervised texture classification

Voronoi polyhedra analysis of oprimized arterial tree models

Annals of Biomedical Engineering

Textbook of Medical Physiology

Quantifying 3-D vascular structures in MRA images using hybrid PDE and geometric deformable models

IEEE Transactions on Medical Imaging

MRI simulation-based evaluation of image-processing and classification methods

IEEE Transaction on Medical Imaging

Magnetic resonance imaging (MRI) simulation on a grid computing architecture

Vision by Man and Machine