X-ray phase sensitive imaging methods: basic physical principles and potential medical applications

All correspondence should be addressed to G.H.C. via ude.csiw@7nehcg, or mailing address: Guang-Hong Chen, Ph.D., Department of Medical Physics, University of Wisconsin-Madison, 1005 Wisconsin Institutes of Medical Research, 1111 Highland Avenue, Madison, WI 53705-2275, Tel: 608/263-0089, Fax: 608/265-9840

Abstract

Phase sensitive imaging theoretically allows for a drastic reduction in x-ray dose while simultaneously achieving comparable or better spatial and contrast resolution compared to traditional x-ray absorption based imaging. Several techniques exist to extract the phase information from an x-ray signal, including x-ray interferometry, diffraction enhanced imaging, in-line holography, coded aperture x-ray imaging, and grating-based interferometry. The physics of each method is reviewed, along with the potential clinical applications.

Introduction

X-rays have been widely used in medical imaging since their discovery in 1895. These relatively energetic photons interact with tissues that have different attenuating properties to generate contrast for visualization of the difference between tissues[1, 2]. Microscopically, the interaction between x-ray photons and tissue is described by different cross sections of physical processes such as photoelectric, Compton scattering, and others. In the diagnostic x-ray energy range (10keV–150keV), the photoelectric effect is predominant for contrast resolution, while the other physical processes only contribute to degrade image quality. The relative contrast between two tissue types drops quickly with increases in x-ray beam energy. However, when the x-ray beam energy is too low, the deposition of x-ray energy in tissues increases, and harmful radiobiological effects may occur. Thus, a delicate balance between the contrast needed for medical diagnosis and the potential detrimental effects of x-ray deposition must be achieved for x-ray-based medical imaging. Often, additional contrast is needed past the limitations of radiation dose constraints. To improve contrast resolution, external iodinated contrast agents are often administered either through an intravenous or intra-arterial injection. This has been proven to be extremely powerful in vascular imaging where a subtraction can be applied to remove the static anatomic background (also called “anatomic noise” in the literature) while the iodine-filled vasculature remains after the subtraction.

To improve contrast resolution such that the local difference between two neighboring local regions of tissues could be better differentiated in medical diagnosis, x-ray computed tomography (CT) was introduced in the 1970s. In this method, projection information is acquired from many different view angles and the local distribution of the x-ray attenuation coefficients is reconstructed. The introduction of CT methods significantly enhanced physicians’ capabilities in medical diagnosis. However, similarly to the conventional x-ray projection method, the requirement of lowering radiation dose favors higher energy beams, but at the cost of a decrease in contrast resolution.

In addition to the balance between contrast resolution and radiation dose, when high spatial resolution is needed for visualization of fine structures, the noise level of both x-ray projection and CT imaging increases dramatically. In order to maintain the required contrast-to-noise ratio (CNR) for visualization of differences between tissues, a high radiation dose is required to compensate for the increase in noise level.

Even if x-ray CT is used, the characterization of tissue type is still not completely quantitative. The ambiguity lies in the fact that different tissue compositions may generate exactly the same attenuation [3]. This is because the attenuation properties are determined by both electron density and the effective atomic number.

Since its conception, x-ray imaging has been successfully used in medical diagnosis, but the sole contrast mechanism, x-ray absorption, significantly limits wider and safer applications. An ongoing goal in the use of x-rays in medical applications is to have the lowest possible radiation dose, while maintaining the highest possible spatial and contrast resolution, in addition to having quantitative imaging capabilities.

The limitation of a single contrast mechanism in x-ray imaging has motivated investigators to explore the possibility of multiple contrast mechanisms. As a result of wave-particle duality, x-ray beams can also be viewed as waves. The only difference from the familiar wave examples is that the x-ray wavelength is very short, on the order of angstroms. Due to their wave nature, x-rays will not only be attenuated when they penetrate through matter, but will also experience distortions due to the interaction of the wave with the particles inside of the medium. As a result, a local phase shift will be generated in the x-ray wave after exiting the object. Physically, local phase shifts of x-ray waves are determined by the local electron density in the object. Namely, when x-rays propagate through matter, the internal structural information of the material is encoded into the corresponding wave front distortions. Thus, by detecting the wavefront distortion in x-ray waves, one may potentially obtain the structural information of an object. Several methods have been used to extract wave front distortion; these methods are collectively referred to as x-ray phase sensitive imaging methods.

In this article, we intend to provide a concise review of the methods used to extract phase shift, with an emphasis on potential application in medical fields. However, one should be aware that the same concepts and methods can be equally applied to non-destructive detection in industrial and other applications. When those applications are considered, the relative advantages and limitations of each method may be very different.

Basic physics of phase sensitive imaging

When a wave is considered, one is reminiscent of the macroscopic phenomena observed in visible light: reflection and refraction at the interface of two different media, as well as diffraction and interference. To describe these phenomena, a medium is often considered as homogeneous sub-regions with sharp boundaries, with each sub-region having its own macroscopic refractive index, n. By definition, vacuum should not affect the wave and thus has a refractive index of unity. For visible light, the refractive index is often larger than one. For example, the refractive index of visible light in glass ranges from about 1.5 to 1.8 [4]. This large refractive index makes the observation of reflection and refraction of visible light easy in normal laboratory conditions. In contrast, for x-rays, the refractive index is much closer to unity, with the difference from one often being only 10 −7 to 10 −5 . As a result, it is very difficult to directly observe x-ray refraction phenomenon. In general, the refractive index for x-rays is written as [5]:

where δ is the refractive index decrement, which is responsible for x-ray phase shift, and the imaginary part, β, is responsible for x-ray attenuation. The refractive index is a dimensionless quantity and its imaginary part, β, is related to the conventional linear attenuation coefficient, μ, as follows:

where λ is the wavelength of the x-ray. The decrement and the imaginary part of the x-ray refractive index are given as: